{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Daniel, Owen, Chloe, Ava, Joseph, Alexander, Riley, and Noah. In a statement by Daniel: \"Joseph is a knave and Owen is a knave\". Owen was heard saying, \"Ava is a knight and Daniel is a knight\". Chloe commented, \"Riley is not a knave\". Ava stated, \"Noah is a knight if and only if Joseph is a knight\". \"If Ava is a knight then Alexander is a knight\" - Joseph. Alexander commented, \"Ava is a knight if and only if Daniel is a knave\". Riley remarked, \"Ava is not a knave\". Noah expressed that Owen is a knight or Daniel is a knave. So who is a knight and who is a knave?", "names": ["Daniel", "Owen", "Chloe", "Ava", "Joseph", "Alexander", "Riley", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true, true, true], "solution_text": "Daniel is a knave, Owen is a knave, Chloe is a knight, Ava is a knight, Joseph is a knight, Alexander is a knight, Riley is a knight, and Noah is a knight.", "solution_text_format": "(1) Daniel is a knave\n(2) Owen is a knave\n(3) Chloe is a knight\n(4) Ava is a knight\n(5) Joseph is a knight\n(6) Alexander is a knight\n(7) Riley is a knight\n(8) Noah is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that Joseph is a knave and Owen is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Daniel that Joseph is a knave and Owen is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that If Ava is a knight then Alexander is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Noah is a knight if and only if Joseph is a knight.", "Noah cannot be a knight, because this would contradict the claim of Ava that Noah is a knight if and only if Joseph is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Owen is a knight or Daniel is a knave.", "Owen cannot be a knight, because this would contradict the claim of Daniel that Joseph is a knave and Owen is a knave.", "Owen cannot be a knave, because this would contradict the false claim of their own that Ava is a knight and Daniel is a knight.", "We have exhausted all possibilities for Owen and Noah, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the false claim of Joseph that If Ava is a knight then Alexander is a knight.", "We have exhausted all possibilities for Ava and Joseph, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Joseph is a knave and Owen is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that If Ava is a knight then Alexander is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Noah is a knight if and only if Joseph is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Owen is a knight or Daniel is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Ava is a knight and Daniel is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Ava is a knight and Daniel is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Ava is a knight if and only if Daniel is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Riley is not a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Ava is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('lying', 1)), ('and', ('telling-truth', 3), ('telling-truth', 0)), ('not', ('lying', 6)), ('<=>', ('telling-truth', 7), ('telling-truth', 4)), ('->', ('telling-truth', 3), ('telling-truth', 5)), ('<=>', ('telling-truth', 3), ('lying', 0)), ('not', ('lying', 3)), ('or', ('telling-truth', 1), ('lying', 0)))", "index": 100}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Matthew, Emily, Alexander, Sophia, Victoria, Abigail, Isabella, and Mason. Matthew asserted: \"Sophia is a knight and Isabella is a knave\". Emily expressed that Mason is a knight or Abigail is a knight. Alexander noted, \"If Mason is a knave then Isabella is a knave\". According to Sophia, \"If Abigail is a knight then Mason is a knight\". Victoria told you that Victoria is a knight or Sophia is a knave. According to Abigail, \"Alexander is not a knight\". In Isabella's words: \"Abigail is a knave or Mason is a knave\". Mason expressed that Victoria is a knight and Victoria is a knave. So who is a knight and who is a knave?", "names": ["Matthew", "Emily", "Alexander", "Sophia", "Victoria", "Abigail", "Isabella", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true, true, false], "solution_text": "Matthew is a knave, Emily is a knight, Alexander is a knave, Sophia is a knave, Victoria is a knight, Abigail is a knight, Isabella is a knight, and Mason is a knave.", "solution_text_format": "(1) Matthew is a knave\n(2) Emily is a knight\n(3) Alexander is a knave\n(4) Sophia is a knave\n(5) Victoria is a knight\n(6) Abigail is a knight\n(7) Isabella is a knight\n(8) Mason is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that Sophia is a knight and Isabella is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that If Abigail is a knight then Mason is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of Abigail that Alexander is not a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that If Mason is a knave then Isabella is a knave.", "Mason cannot be a knight, because this would contradict the false claim of Alexander that If Mason is a knave then Isabella is a knave.", "Mason cannot be a knave, because this would contradict the claim of Sophia that If Abigail is a knight then Mason is a knight.", "We have exhausted all possibilities for Mason and Alexander, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Alexander is not a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that If Mason is a knave then Isabella is a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Victoria is a knight and Victoria is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Victoria is a knight and Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Victoria is a knight or Sophia is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Matthew that Sophia is a knight and Isabella is a knave.", "Isabella cannot be a knave, because this would contradict the false claim of their own that Abigail is a knave or Mason is a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Victoria is a knight or Sophia is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Matthew that Sophia is a knight and Isabella is a knave.", "Isabella cannot be a knave, because this would contradict the false claim of their own that Abigail is a knave or Mason is a knave.", "We have exhausted all possibilities for Isabella, Victoria, and Mason, so let us go back and reconsider Alexander.", "Alexander cannot be a knave, because this would contradict the false claim of Abigail that Alexander is not a knight.", "We have exhausted all possibilities for Alexander and Abigail, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the claim of Matthew that Sophia is a knight and Isabella is a knave.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Sophia is a knight and Isabella is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that If Abigail is a knight then Mason is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of Abigail that Alexander is not a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that If Mason is a knave then Isabella is a knave.", "Mason cannot be a knight, because this would contradict the false claim of Alexander that If Mason is a knave then Isabella is a knave.", "Mason cannot be a knave, because this would contradict the claim of Sophia that If Abigail is a knight then Mason is a knight.", "We have exhausted all possibilities for Mason and Alexander, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Alexander is not a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that If Mason is a knave then Isabella is a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Victoria is a knight and Victoria is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Victoria is a knight and Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Victoria is a knight or Sophia is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Alexander that If Mason is a knave then Isabella is a knave.", "Isabella cannot be a knave, because this would contradict the false claim of Matthew that Sophia is a knight and Isabella is a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Victoria is a knight or Sophia is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Alexander that If Mason is a knave then Isabella is a knave.", "Isabella cannot be a knave, because this would contradict the false claim of Matthew that Sophia is a knight and Isabella is a knave.", "We have exhausted all possibilities for Isabella, Victoria, and Mason, so let us go back and reconsider Alexander.", "Alexander cannot be a knave, because this would contradict the false claim of Abigail that Alexander is not a knight.", "We have exhausted all possibilities for Alexander and Abigail, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that If Abigail is a knight then Mason is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of Abigail that Alexander is not a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that If Mason is a knave then Isabella is a knave.", "Mason cannot be a knight, because this would contradict the false claim of Alexander that If Mason is a knave then Isabella is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Victoria is a knight and Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Victoria is a knight or Sophia is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Abigail is a knave or Mason is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Mason is a knight or Abigail is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('lying', 6)), ('or', ('telling-truth', 7), ('telling-truth', 5)), ('->', ('lying', 7), ('lying', 6)), ('->', ('telling-truth', 5), ('telling-truth', 7)), ('or', ('telling-truth', 4), ('lying', 3)), ('not', ('telling-truth', 2)), ('or', ('lying', 5), ('lying', 7)), ('and', ('telling-truth', 4), ('lying', 4)))", "index": 101}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Luke, Aria, Amelia, Scarlett, Benjamin, Sofia, David, and Michael. \"Sofia is a knight and Benjamin is a knight,\" Luke claimed. Aria was heard saying, \"Michael is a knight\". Amelia remarked, \"Michael is not a knave\". \"Benjamin is a knave,\" Scarlett claimed. Benjamin remarked, \"Michael is a knave and Amelia is a knave\". Sofia noted, \"Amelia is a knave\". David commented, \"Scarlett is a knave or Luke is a knight\". \"Scarlett is a knave if and only if David is a knight,\" Michael claimed. So who is a knight and who is a knave?", "names": ["Luke", "Aria", "Amelia", "Scarlett", "Benjamin", "Sofia", "David", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false, false, true], "solution_text": "Luke is a knave, Aria is a knight, Amelia is a knight, Scarlett is a knight, Benjamin is a knave, Sofia is a knave, David is a knave, and Michael is a knight.", "solution_text_format": "(1) Luke is a knave\n(2) Aria is a knight\n(3) Amelia is a knight\n(4) Scarlett is a knight\n(5) Benjamin is a knave\n(6) Sofia is a knave\n(7) David is a knave\n(8) Michael is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Sofia is a knight and Benjamin is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Sofia that Amelia is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Michael is not a knave.", "Michael cannot be a knight, because this would contradict the false claim of Amelia that Michael is not a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Scarlett is a knave if and only if David is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Scarlett that Benjamin is a knave.", "Benjamin cannot be a knave, because this would contradict the claim of Luke that Sofia is a knight and Benjamin is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Benjamin is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Michael is a knave and Amelia is a knave.", "David cannot be a knight, because this would contradict the false claim of Michael that Scarlett is a knave if and only if David is a knight.", "David cannot be a knave, because this would contradict the false claim of their own that Scarlett is a knave or Luke is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the claim of Luke that Sofia is a knight and Benjamin is a knight.", "We have exhausted all possibilities for Benjamin, Scarlett, Michael, and Amelia, so let us go back and reconsider Sofia.", "Sofia cannot be a knave, because this would contradict the claim of Luke that Sofia is a knight and Benjamin is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Sofia is a knight and Benjamin is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Sofia that Amelia is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Michael is not a knave.", "Michael cannot be a knight, because this would contradict the false claim of Amelia that Michael is not a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Scarlett is a knave if and only if David is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Luke that Sofia is a knight and Benjamin is a knight.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that Michael is a knave and Amelia is a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Luke that Sofia is a knight and Benjamin is a knight.", "Benjamin cannot be a knave, because this would contradict the false claim of Scarlett that Benjamin is a knave.", "We have exhausted all possibilities for Benjamin, Scarlett, Michael, and Amelia, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Amelia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Michael is not a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Scarlett is a knave if and only if David is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Scarlett that Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Michael is a knave and Amelia is a knave.", "David cannot be a knight, because this would contradict the claim of their own that Scarlett is a knave or Luke is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Scarlett is a knave or Luke is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Michael is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('telling-truth', 4)), ('telling-truth', 7), ('not', ('lying', 7)), ('lying', 4), ('and', ('lying', 7), ('lying', 2)), ('lying', 2), ('or', ('lying', 3), ('telling-truth', 0)), ('<=>', ('lying', 3), ('telling-truth', 6)))", "index": 102}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Samuel, Luke, Isabella, Jacob, Elizabeth, Zoey, Alexander, and Jack. Samuel remarked, \"Elizabeth is not a knave\". According to Luke, \"Elizabeth is not a knave\". Isabella was heard saying, \"Jack is a knave or Elizabeth is a knave\". \"Luke is a knight\" - Jacob. Elizabeth noted, \"Isabella is not a knave\". According to Zoey, \"If Elizabeth is a knight then Alexander is a knight\". Alexander said that Isabella is a knight. Jack expressed that Samuel is a knave or Luke is a knave. So who is a knight and who is a knave?", "names": ["Samuel", "Luke", "Isabella", "Jacob", "Elizabeth", "Zoey", "Alexander", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true, true, false], "solution_text": "Samuel is a knight, Luke is a knight, Isabella is a knight, Jacob is a knight, Elizabeth is a knight, Zoey is a knight, Alexander is a knight, and Jack is a knave.", "solution_text_format": "(1) Samuel is a knight\n(2) Luke is a knight\n(3) Isabella is a knight\n(4) Jacob is a knight\n(5) Elizabeth is a knight\n(6) Zoey is a knight\n(7) Alexander is a knight\n(8) Jack is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that Elizabeth is not a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Isabella is not a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Jack is a knave or Elizabeth is a knave.", "Jack cannot be a knight, because this would contradict the claim of Isabella that Jack is a knave or Elizabeth is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Samuel is a knave or Luke is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Elizabeth is not a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Luke is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that If Elizabeth is a knight then Alexander is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Isabella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('not', ('lying', 4)), ('or', ('lying', 7), ('lying', 4)), ('telling-truth', 1), ('not', ('lying', 2)), ('->', ('telling-truth', 4), ('telling-truth', 6)), ('telling-truth', 2), ('or', ('lying', 0), ('lying', 1)))", "index": 103}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Alexander, Harper, Evelyn, Jackson, James, Jack, Amelia, and Lucas. \"Jack is a knight\" - Alexander. Harper was heard saying, \"Lucas is a knight or Evelyn is a knave\". Evelyn said, \"James is a knave.\" Jackson remarked, \"Jack is a knight and Amelia is a knave\". \"Lucas is not a knight,\" James claimed. Jack commented, \"Harper is a knave\". As Amelia put it, \"Alexander is a knave and Jack is a knight\". Lucas stated, \"Alexander is a knave if and only if Harper is a knight\". So who is a knight and who is a knave?", "names": ["Alexander", "Harper", "Evelyn", "Jackson", "James", "Jack", "Amelia", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false, false, true], "solution_text": "Alexander is a knave, Harper is a knight, Evelyn is a knight, Jackson is a knave, James is a knave, Jack is a knave, Amelia is a knave, and Lucas is a knight.", "solution_text_format": "(1) Alexander is a knave\n(2) Harper is a knight\n(3) Evelyn is a knight\n(4) Jackson is a knave\n(5) James is a knave\n(6) Jack is a knave\n(7) Amelia is a knave\n(8) Lucas is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Harper is a knave.", "Harper cannot be a knight, because this would contradict the claim of Jack that Harper is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Lucas is a knight or Evelyn is a knave.", "Lucas cannot be a knight, because this would contradict the false claim of Harper that Lucas is a knight or Evelyn is a knave.", "Lucas cannot be a knave, because this would contradict the false claim of their own that Alexander is a knave if and only if Harper is a knight.", "We have exhausted all possibilities for Lucas and Harper, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the claim of Alexander that Jack is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Jack is a knight.", "Jack cannot be a knight, because this would contradict the false claim of Alexander that Jack is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Harper is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Lucas is a knight or Evelyn is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Alexander is a knave if and only if Harper is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that James is a knave.", "James cannot be a knight, because this would contradict the claim of Evelyn that James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Lucas is not a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Jack is a knight and Amelia is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Jack is a knight and Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Alexander is a knave and Jack is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Alexander is a knave and Jack is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 5), ('or', ('telling-truth', 7), ('lying', 2)), ('lying', 4), ('and', ('telling-truth', 5), ('lying', 6)), ('not', ('telling-truth', 7)), ('lying', 1), ('and', ('lying', 0), ('telling-truth', 5)), ('<=>', ('lying', 0), ('telling-truth', 1)))", "index": 104}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Liam, Elizabeth, Aurora, Owen, Luke, Benjamin, Samuel, and Grace. Liam said, \"Benjamin is a knight or Samuel is a knight.\" Elizabeth commented, \"Grace is a knight or Owen is a knight\". \"Benjamin is a knight or Luke is a knave,\" Aurora declared. Owen expressed that Samuel is a knight if and only if Luke is a knight. As Luke put it, \"If Liam is a knave then Grace is a knight\". Benjamin asserted: \"If Elizabeth is a knave then Owen is a knight\". In a statement by Samuel: \"Elizabeth is a knight\". Grace stated, \"Elizabeth is a knight and Liam is a knave\". So who is a knight and who is a knave?", "names": ["Liam", "Elizabeth", "Aurora", "Owen", "Luke", "Benjamin", "Samuel", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true, true, false], "solution_text": "Liam is a knight, Elizabeth is a knight, Aurora is a knight, Owen is a knight, Luke is a knight, Benjamin is a knight, Samuel is a knight, and Grace is a knave.", "solution_text_format": "(1) Liam is a knight\n(2) Elizabeth is a knight\n(3) Aurora is a knight\n(4) Owen is a knight\n(5) Luke is a knight\n(6) Benjamin is a knight\n(7) Samuel is a knight\n(8) Grace is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Benjamin is a knight or Samuel is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Owen is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Grace is a knight or Owen is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight and Liam is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Elizabeth is a knight and Liam is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Samuel is a knight if and only if Luke is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that If Liam is a knave then Grace is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Benjamin is a knight or Luke is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('telling-truth', 6)), ('or', ('telling-truth', 7), ('telling-truth', 3)), ('or', ('telling-truth', 5), ('lying', 4)), ('<=>', ('telling-truth', 6), ('telling-truth', 4)), ('->', ('lying', 0), ('telling-truth', 7)), ('->', ('lying', 1), ('telling-truth', 3)), ('telling-truth', 1), ('and', ('telling-truth', 1), ('lying', 0)))", "index": 105}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emily, Benjamin, Abigail, Penelope, Samuel, Sophia, Liam, and Noah. \"Samuel is a knight and Penelope is a knight,\" Emily mentioned. Benjamin said that Liam is a knight. As Abigail put it, \"Abigail is a knight if and only if Benjamin is a knave\". \"Emily is not a knave,\" Penelope claimed. Samuel said that Emily is a knave and Penelope is a knave. \"Liam is not a knave,\" Sophia mentioned. Liam told you that Samuel is a knave if and only if Abigail is a knight. Noah commented, \"Sophia is a knave if and only if Samuel is a knight\". So who is a knight and who is a knave?", "names": ["Emily", "Benjamin", "Abigail", "Penelope", "Samuel", "Sophia", "Liam", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, false, false, true], "solution_text": "Emily is a knave, Benjamin is a knave, Abigail is a knight, Penelope is a knave, Samuel is a knight, Sophia is a knave, Liam is a knave, and Noah is a knight.", "solution_text_format": "(1) Emily is a knave\n(2) Benjamin is a knave\n(3) Abigail is a knight\n(4) Penelope is a knave\n(5) Samuel is a knight\n(6) Sophia is a knave\n(7) Liam is a knave\n(8) Noah is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Samuel is a knight and Penelope is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Emily is a knave and Penelope is a knave.", "Samuel cannot be a knave, because this would contradict the claim of Emily that Samuel is a knight and Penelope is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Samuel is a knight and Penelope is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Emily is a knave and Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the false claim of Emily that Samuel is a knight and Penelope is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Emily is not a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Liam is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Abigail is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Abigail is a knight if and only if Benjamin is a knave.", "Abigail cannot be a knave, because this would contradict the false claim of their own that Abigail is a knight if and only if Benjamin is a knave.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the claim of Benjamin that Liam is a knight.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Liam is a knight.", "Liam cannot be a knight, because this would contradict the false claim of Benjamin that Liam is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Samuel is a knave if and only if Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Abigail is a knight if and only if Benjamin is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that Liam is not a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Liam is not a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Sophia is a knave if and only if Samuel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 4), ('telling-truth', 3)), ('telling-truth', 6), ('<=>', ('telling-truth', 2), ('lying', 1)), ('not', ('lying', 0)), ('and', ('lying', 0), ('lying', 3)), ('not', ('lying', 6)), ('<=>', ('lying', 4), ('telling-truth', 2)), ('<=>', ('lying', 5), ('telling-truth', 4)))", "index": 106}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sebastian, David, Victoria, Ethan, Ava, Penelope, Lucas, and Alexander. \"Penelope is a knight if and only if Ava is a knight,\" Sebastian mentioned. In David's words: \"Lucas is a knight and Ava is a knave\". Victoria was heard saying, \"Ava is a knave and David is a knave\". \"David is a knave and Lucas is a knave,\" Ethan claimed. Ava noted, \"Alexander is a knave and Ethan is a knight\". In Penelope's words: \"Victoria is not a knave\". In Lucas's words: \"Alexander is a knave and Victoria is a knight\". Alexander stated, \"Ethan is a knight if and only if David is a knight\". So who is a knight and who is a knave?", "names": ["Sebastian", "David", "Victoria", "Ethan", "Ava", "Penelope", "Lucas", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, false, false, false], "solution_text": "Sebastian is a knave, David is a knave, Victoria is a knave, Ethan is a knight, Ava is a knight, Penelope is a knave, Lucas is a knave, and Alexander is a knave.", "solution_text_format": "(1) Sebastian is a knave\n(2) David is a knave\n(3) Victoria is a knave\n(4) Ethan is a knight\n(5) Ava is a knight\n(6) Penelope is a knave\n(7) Lucas is a knave\n(8) Alexander is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that Penelope is a knight if and only if Ava is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Victoria is not a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Ava is a knave and David is a knave.", "Ava cannot be a knight, because this would contradict the claim of Victoria that Ava is a knave and David is a knave.", "Ava cannot be a knave, because this would contradict the claim of Sebastian that Penelope is a knight if and only if Ava is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Victoria.", "Victoria cannot be a knave, because this would contradict the claim of Penelope that Victoria is not a knave.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Victoria is not a knave.", "Victoria cannot be a knight, because this would contradict the false claim of Penelope that Victoria is not a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Ava is a knave and David is a knave.", "Ava cannot be a knight, because this would contradict the claim of Sebastian that Penelope is a knight if and only if Ava is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Alexander is a knave and Ethan is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Ethan is a knight if and only if David is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that David is a knave and Lucas is a knave.", "David cannot be a knight, because this would contradict the claim of Ethan that David is a knave and Lucas is a knave.", "David cannot be a knave, because this would contradict the false claim of Victoria that Ava is a knave and David is a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that David is a knave and Lucas is a knave.", "David cannot be a knight, because this would contradict the claim of Alexander that Ethan is a knight if and only if David is a knight.", "David cannot be a knave, because this would contradict the false claim of Victoria that Ava is a knave and David is a knave.", "We have exhausted all possibilities for David and Ethan, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Ethan is a knight if and only if David is a knight.", "Ethan cannot be a knight, because this would contradict the false claim of Ava that Alexander is a knave and Ethan is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that David is a knave and Lucas is a knave.", "Assume David is a knight. No contradiction is found in their claim that Lucas is a knight and Ava is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Alexander is a knave and Victoria is a knight.", "Lucas cannot be a knave, because this would contradict the claim of David that Lucas is a knight and Ava is a knave.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the false claim of Victoria that Ava is a knave and David is a knave.", "We have exhausted all possibilities for David, Ethan, Alexander, Ava, Victoria, and Penelope, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Penelope is a knight if and only if Ava is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Victoria is not a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Ava is a knave and David is a knave.", "Ava cannot be a knight, because this would contradict the false claim of Sebastian that Penelope is a knight if and only if Ava is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Alexander is a knave and Ethan is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Ethan is a knight if and only if David is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that David is a knave and Lucas is a knave.", "David cannot be a knight, because this would contradict the claim of Victoria that Ava is a knave and David is a knave.", "David cannot be a knave, because this would contradict the claim of Alexander that Ethan is a knight if and only if David is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that David is a knave and Lucas is a knave.", "David cannot be a knight, because this would contradict the claim of Victoria that Ava is a knave and David is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Lucas is a knight and Ava is a knave.", "Lucas cannot be a knight, because this would contradict the false claim of David that Lucas is a knight and Ava is a knave.", "Lucas cannot be a knave, because this would contradict the false claim of Ethan that David is a knave and Lucas is a knave.", "We have exhausted all possibilities for Lucas, David, and Ethan, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Ethan is a knight if and only if David is a knight.", "Ethan cannot be a knight, because this would contradict the false claim of Ava that Alexander is a knave and Ethan is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that David is a knave and Lucas is a knave.", "David cannot be a knight, because this would contradict the claim of Victoria that Ava is a knave and David is a knave.", "David cannot be a knave, because this would contradict the false claim of Alexander that Ethan is a knight if and only if David is a knight.", "We have exhausted all possibilities for David, Ethan, Alexander, and Ava, so let us go back and reconsider Victoria.", "Victoria cannot be a knave, because this would contradict the claim of Penelope that Victoria is not a knave.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Victoria is not a knave.", "Victoria cannot be a knight, because this would contradict the false claim of Penelope that Victoria is not a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Ava is a knave and David is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Alexander is a knave and Ethan is a knight.", "Alexander cannot be a knight, because this would contradict the claim of Ava that Alexander is a knave and Ethan is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Ethan is a knight if and only if David is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that David is a knave and Lucas is a knave.", "David cannot be a knight, because this would contradict the claim of their own that Lucas is a knight and Ava is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Lucas is a knight and Ava is a knave.", "Lucas cannot be a knight, because this would contradict the claim of Ethan that David is a knave and Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Alexander is a knave and Victoria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 5), ('telling-truth', 4)), ('and', ('telling-truth', 6), ('lying', 4)), ('and', ('lying', 4), ('lying', 1)), ('and', ('lying', 1), ('lying', 6)), ('and', ('lying', 7), ('telling-truth', 3)), ('not', ('lying', 2)), ('and', ('lying', 7), ('telling-truth', 2)), ('<=>', ('telling-truth', 3), ('telling-truth', 1)))", "index": 107}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Henry, Logan, James, Lily, Zoey, Scarlett, Victoria, and Mason. Henry commented, \"Henry is a knight and Scarlett is a knave\". As Logan put it, \"James is a knight or Zoey is a knave\". James told you that Henry is a knight and Zoey is a knight. Lily told you that Scarlett is a knave. \"Lily is a knave and Lily is a knight\" - Zoey. Scarlett stated, \"Henry is a knave or Victoria is a knave\". According to Victoria, \"Zoey is not a knave\". \"Lily is a knave or Scarlett is a knave,\" Mason claimed. So who is a knight and who is a knave?", "names": ["Henry", "Logan", "James", "Lily", "Zoey", "Scarlett", "Victoria", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, true, false, true], "solution_text": "Henry is a knave, Logan is a knight, James is a knave, Lily is a knave, Zoey is a knave, Scarlett is a knight, Victoria is a knave, and Mason is a knight.", "solution_text_format": "(1) Henry is a knave\n(2) Logan is a knight\n(3) James is a knave\n(4) Lily is a knave\n(5) Zoey is a knave\n(6) Scarlett is a knight\n(7) Victoria is a knave\n(8) Mason is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that Henry is a knight and Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Henry that Henry is a knight and Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Henry is a knave or Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Zoey is not a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that Lily is a knave and Lily is a knight.", "Zoey cannot be a knave, because this would contradict the claim of Victoria that Zoey is not a knave.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Victoria.", "Victoria cannot be a knave, because this would contradict the false claim of Scarlett that Henry is a knave or Victoria is a knave.", "We have exhausted all possibilities for Victoria and Scarlett, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Henry is a knight and Scarlett is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Henry is a knave or Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Zoey is not a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that Lily is a knave and Lily is a knight.", "Zoey cannot be a knave, because this would contradict the claim of Victoria that Zoey is not a knave.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Zoey is not a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that Lily is a knave and Lily is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Lily is a knave and Lily is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Scarlett is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Scarlett is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that James is a knight or Zoey is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Henry is a knight and Zoey is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Henry is a knight and Zoey is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Lily is a knave or Scarlett is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 0), ('lying', 5)), ('or', ('telling-truth', 2), ('lying', 4)), ('and', ('telling-truth', 0), ('telling-truth', 4)), ('lying', 5), ('and', ('lying', 3), ('telling-truth', 3)), ('or', ('lying', 0), ('lying', 6)), ('not', ('lying', 4)), ('or', ('lying', 3), ('lying', 5)))", "index": 108}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sebastian, Logan, Mia, Ethan, Riley, Harper, Matthew, and Aiden. In a statement by Sebastian: \"Aiden is a knight or Harper is a knave\". Logan was heard saying, \"Ethan is a knight or Aiden is a knight\". Mia was heard saying, \"Matthew is a knave and Harper is a knight\". Ethan commented, \"Logan is a knight\". Riley remarked, \"If Harper is a knight then Logan is a knight\". Harper commented, \"Ethan is not a knave\". Matthew noted, \"Sebastian is a knight and Mia is a knave\". \"Logan is a knave\" - Aiden. So who is a knight and who is a knave?", "names": ["Sebastian", "Logan", "Mia", "Ethan", "Riley", "Harper", "Matthew", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true, false, false], "solution_text": "Sebastian is a knave, Logan is a knight, Mia is a knight, Ethan is a knight, Riley is a knight, Harper is a knight, Matthew is a knave, and Aiden is a knave.", "solution_text_format": "(1) Sebastian is a knave\n(2) Logan is a knight\n(3) Mia is a knight\n(4) Ethan is a knight\n(5) Riley is a knight\n(6) Harper is a knight\n(7) Matthew is a knave\n(8) Aiden is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that Aiden is a knight or Harper is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of Aiden that Logan is a knave.", "Logan cannot be a knave, because this would contradict the false claim of their own that Ethan is a knight or Aiden is a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Logan is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Ethan is a knight or Aiden is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Logan is a knight.", "Harper cannot be a knight, because this would contradict the claim of Sebastian that Aiden is a knight or Harper is a knave.", "Harper cannot be a knave, because this would contradict the false claim of their own that Ethan is not a knave.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the claim of Logan that Ethan is a knight or Aiden is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the false claim of Aiden that Logan is a knave.", "We have exhausted all possibilities for Logan and Aiden, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Aiden is a knight or Harper is a knave.", "Aiden cannot be a knight, because this would contradict the false claim of Sebastian that Aiden is a knight or Harper is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Logan is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Ethan is a knight or Aiden is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Logan is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Ethan is not a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Matthew is a knave and Harper is a knight.", "Matthew cannot be a knight, because this would contradict the claim of Mia that Matthew is a knave and Harper is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Sebastian is a knight and Mia is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that If Harper is a knight then Logan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 7), ('lying', 5)), ('or', ('telling-truth', 3), ('telling-truth', 7)), ('and', ('lying', 6), ('telling-truth', 5)), ('telling-truth', 1), ('->', ('telling-truth', 5), ('telling-truth', 1)), ('not', ('lying', 3)), ('and', ('telling-truth', 0), ('lying', 2)), ('lying', 1))", "index": 109}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Matthew, Emily, Aurora, Jacob, Amelia, Liam, James, and Alexander. \"Emily is not a knight\" - Matthew. As Emily put it, \"If Matthew is a knight then Alexander is a knight\". \"Emily is not a knave,\" Aurora claimed. \"Alexander is a knave and James is a knave\" - Jacob. Amelia said that Emily is a knight or Aurora is a knight. \"Emily is a knave and Alexander is a knight,\" Liam claimed. \"Liam is a knight if and only if Aurora is a knave,\" James claimed. Alexander asserted: \"If Alexander is a knight then Jacob is a knave\". So who is a knight and who is a knave?", "names": ["Matthew", "Emily", "Aurora", "Jacob", "Amelia", "Liam", "James", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, false, true, true], "solution_text": "Matthew is a knave, Emily is a knight, Aurora is a knight, Jacob is a knave, Amelia is a knight, Liam is a knave, James is a knight, and Alexander is a knight.", "solution_text_format": "(1) Matthew is a knave\n(2) Emily is a knight\n(3) Aurora is a knight\n(4) Jacob is a knave\n(5) Amelia is a knight\n(6) Liam is a knave\n(7) James is a knight\n(8) Alexander is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that Emily is not a knight.", "Emily cannot be a knight, because this would contradict the claim of Matthew that Emily is not a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that If Matthew is a knight then Alexander is a knight.", "Alexander cannot be a knight, because this would contradict the false claim of Emily that If Matthew is a knight then Alexander is a knight.", "Alexander cannot be a knave, because this would contradict the false claim of their own that If Alexander is a knight then Jacob is a knave.", "We have exhausted all possibilities for Alexander and Emily, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Emily is not a knight.", "Assume Emily is a knight. No contradiction is found in their claim that If Matthew is a knight then Alexander is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that If Alexander is a knight then Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of their own that Alexander is a knave and James is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Alexander is a knave and James is a knave.", "Assume James is a knight. No contradiction is found in their claim that Liam is a knight if and only if Aurora is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Emily is a knave and Alexander is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Emily is a knave and Alexander is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Emily is not a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Emily is a knight or Aurora is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 1)), ('->', ('telling-truth', 0), ('telling-truth', 7)), ('not', ('lying', 1)), ('and', ('lying', 7), ('lying', 6)), ('or', ('telling-truth', 1), ('telling-truth', 2)), ('and', ('lying', 1), ('telling-truth', 7)), ('<=>', ('telling-truth', 5), ('lying', 2)), ('->', ('telling-truth', 7), ('lying', 3)))", "index": 110}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Avery, Jacob, Emily, Owen, Chloe, Sebastian, Logan, and Jack. In Avery's words: \"Jacob is not a knave\". Jacob told you that Jack is a knight and Sebastian is a knave. \"Jack is a knave and Jack is a knight,\" Emily declared. Owen was heard saying, \"Emily is a knave\". In a statement by Chloe: \"Sebastian is a knave or Logan is a knight\". Sebastian expressed that Avery is a knave and Emily is a knight. Logan remarked, \"Chloe is a knave or Jack is a knight\". \"Chloe is a knight or Sebastian is a knight,\" Jack claimed. So who is a knight and who is a knave?", "names": ["Avery", "Jacob", "Emily", "Owen", "Chloe", "Sebastian", "Logan", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false, true, true], "solution_text": "Avery is a knight, Jacob is a knight, Emily is a knave, Owen is a knight, Chloe is a knight, Sebastian is a knave, Logan is a knight, and Jack is a knight.", "solution_text_format": "(1) Avery is a knight\n(2) Jacob is a knight\n(3) Emily is a knave\n(4) Owen is a knight\n(5) Chloe is a knight\n(6) Sebastian is a knave\n(7) Logan is a knight\n(8) Jack is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Jacob is not a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Jack is a knight and Sebastian is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Chloe is a knight or Sebastian is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Sebastian is a knave or Logan is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of Jacob that Jack is a knight and Sebastian is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Avery is a knave and Emily is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Jack is a knave and Jack is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Jack is a knave and Jack is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Chloe is a knave or Jack is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Emily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('and', ('telling-truth', 7), ('lying', 5)), ('and', ('lying', 7), ('telling-truth', 7)), ('lying', 2), ('or', ('lying', 5), ('telling-truth', 6)), ('and', ('lying', 0), ('telling-truth', 2)), ('or', ('lying', 4), ('telling-truth', 7)), ('or', ('telling-truth', 4), ('telling-truth', 5)))", "index": 111}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mason, Emily, Luke, James, Riley, Amelia, Alexander, and Daniel. Mason said, \"Emily is a knave and Daniel is a knight.\" According to Emily, \"Mason is a knight\". Luke asserted: \"If Amelia is a knave then Alexander is a knight\". James expressed that Mason is a knave or Luke is a knight. Riley stated, \"Mason is a knight or Alexander is a knight\". In a statement by Amelia: \"Emily is a knave if and only if Amelia is a knight\". Alexander stated, \"Amelia is a knave if and only if Luke is a knight\". Daniel remarked, \"Mason is a knave if and only if Alexander is a knave\". So who is a knight and who is a knave?", "names": ["Mason", "Emily", "Luke", "James", "Riley", "Amelia", "Alexander", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false, true, false], "solution_text": "Mason is a knave, Emily is a knave, Luke is a knight, James is a knight, Riley is a knight, Amelia is a knave, Alexander is a knight, and Daniel is a knave.", "solution_text_format": "(1) Mason is a knave\n(2) Emily is a knave\n(3) Luke is a knight\n(4) James is a knight\n(5) Riley is a knight\n(6) Amelia is a knave\n(7) Alexander is a knight\n(8) Daniel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Emily is a knave and Daniel is a knight.", "Emily cannot be a knight, because this would contradict the claim of Mason that Emily is a knave and Daniel is a knight.", "Emily cannot be a knave, because this would contradict the false claim of their own that Mason is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Emily is a knave and Daniel is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Mason is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Mason is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of Mason that Emily is a knave and Daniel is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Mason is a knave if and only if Alexander is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Amelia is a knave if and only if Luke is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Emily is a knave if and only if Amelia is a knight.", "Luke cannot be a knight, because this would contradict the claim of Alexander that Amelia is a knave if and only if Luke is a knight.", "Luke cannot be a knave, because this would contradict the false claim of their own that If Amelia is a knave then Alexander is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Emily is a knave if and only if Amelia is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that If Amelia is a knave then Alexander is a knight.", "Assume James is a knight. No contradiction is found in their claim that Mason is a knave or Luke is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Mason is a knight or Alexander is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 1), ('telling-truth', 7)), ('telling-truth', 0), ('->', ('lying', 5), ('telling-truth', 6)), ('or', ('lying', 0), ('telling-truth', 2)), ('or', ('telling-truth', 0), ('telling-truth', 6)), ('<=>', ('lying', 1), ('telling-truth', 5)), ('<=>', ('lying', 5), ('telling-truth', 2)), ('<=>', ('lying', 0), ('lying', 6)))", "index": 112}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Evelyn, Zoey, Logan, Scarlett, Noah, Luke, Mia, and Jacob. \"Jacob is a knave\" - Evelyn. \"Luke is a knight and Evelyn is a knight,\" Zoey mentioned. \"Zoey is not a knave,\" Logan declared. Scarlett remarked, \"Luke is a knave and Zoey is a knight\". Noah was heard saying, \"Scarlett is a knave\". Luke expressed that Logan is a knight or Luke is a knight. \"Zoey is a knave or Mia is a knight,\" Mia declared. Jacob was heard saying, \"Luke is a knight and Logan is a knight\". So who is a knight and who is a knave?", "names": ["Evelyn", "Zoey", "Logan", "Scarlett", "Noah", "Luke", "Mia", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, false, true, false], "solution_text": "Evelyn is a knight, Zoey is a knave, Logan is a knave, Scarlett is a knave, Noah is a knight, Luke is a knave, Mia is a knight, and Jacob is a knave.", "solution_text_format": "(1) Evelyn is a knight\n(2) Zoey is a knave\n(3) Logan is a knave\n(4) Scarlett is a knave\n(5) Noah is a knight\n(6) Luke is a knave\n(7) Mia is a knight\n(8) Jacob is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Evelyn that Jacob is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Luke is a knight and Logan is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Logan is a knight or Luke is a knight.", "Logan cannot be a knight, because this would contradict the false claim of Jacob that Luke is a knight and Logan is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Zoey is not a knave.", "Zoey cannot be a knight, because this would contradict the false claim of Logan that Zoey is not a knave.", "Zoey cannot be a knave, because this would contradict the false claim of their own that Luke is a knight and Evelyn is a knight.", "We have exhausted all possibilities for Zoey and Logan, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Logan is a knight or Luke is a knight.", "Logan cannot be a knight, because this would contradict the false claim of Luke that Logan is a knight or Luke is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Zoey is not a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that Luke is a knight and Evelyn is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Luke is a knight and Evelyn is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Luke is a knave and Zoey is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Luke is a knave and Zoey is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Scarlett is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Zoey is a knave or Mia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 7), ('and', ('telling-truth', 5), ('telling-truth', 0)), ('not', ('lying', 1)), ('and', ('lying', 5), ('telling-truth', 1)), ('lying', 3), ('or', ('telling-truth', 2), ('telling-truth', 5)), ('or', ('lying', 1), ('telling-truth', 6)), ('and', ('telling-truth', 5), ('telling-truth', 2)))", "index": 113}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Logan, Isabella, Emily, Victoria, Joseph, Jacob, Henry, and Grace. Logan noted, \"Isabella is a knight or Jacob is a knave\". Isabella noted, \"Henry is a knave or Jacob is a knave\". \"Emily is a knight and Grace is a knight\" - Emily. Victoria was heard saying, \"Logan is a knight and Grace is a knave\". Joseph stated, \"Isabella is a knave or Henry is a knight\". As Jacob put it, \"Logan is not a knight\". Henry commented, \"Isabella is a knight\". Grace noted, \"Emily is not a knight\". So who is a knight and who is a knave?", "names": ["Logan", "Isabella", "Emily", "Victoria", "Joseph", "Jacob", "Henry", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, false, true, true], "solution_text": "Logan is a knight, Isabella is a knight, Emily is a knave, Victoria is a knave, Joseph is a knight, Jacob is a knave, Henry is a knight, and Grace is a knight.", "solution_text_format": "(1) Logan is a knight\n(2) Isabella is a knight\n(3) Emily is a knave\n(4) Victoria is a knave\n(5) Joseph is a knight\n(6) Jacob is a knave\n(7) Henry is a knight\n(8) Grace is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that Isabella is a knight or Jacob is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Henry is a knave or Jacob is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Isabella is a knight.", "Jacob cannot be a knight, because this would contradict the claim of Isabella that Henry is a knave or Jacob is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Logan is not a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Emily is a knight and Grace is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Emily is not a knight.", "Grace cannot be a knave, because this would contradict the claim of Emily that Emily is a knight and Grace is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Emily is a knight and Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Emily is not a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Logan is a knight and Grace is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Logan is a knight and Grace is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Isabella is a knave or Henry is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('lying', 5)), ('or', ('lying', 6), ('lying', 5)), ('and', ('telling-truth', 2), ('telling-truth', 7)), ('and', ('telling-truth', 0), ('lying', 7)), ('or', ('lying', 1), ('telling-truth', 6)), ('not', ('telling-truth', 0)), ('telling-truth', 1), ('not', ('telling-truth', 2)))", "index": 114}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jackson, David, Harper, Chloe, James, Logan, Lily, and Zoey. Jackson noted, \"Zoey is a knight\". As David put it, \"James is a knight and David is a knight\". As Harper put it, \"Lily is a knave\". Chloe stated, \"David is a knight if and only if James is a knight\". James remarked, \"If James is a knight then Chloe is a knave\". Logan remarked, \"David is a knave or David is a knight\". Lily commented, \"David is not a knave\". Zoey said that Logan is a knight and James is a knight. So who is a knight and who is a knave?", "names": ["Jackson", "David", "Harper", "Chloe", "James", "Logan", "Lily", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true, false, true], "solution_text": "Jackson is a knight, David is a knave, Harper is a knight, Chloe is a knave, James is a knight, Logan is a knight, Lily is a knave, and Zoey is a knight.", "solution_text_format": "(1) Jackson is a knight\n(2) David is a knave\n(3) Harper is a knight\n(4) Chloe is a knave\n(5) James is a knight\n(6) Logan is a knight\n(7) Lily is a knave\n(8) Zoey is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Logan is a knight and James is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that David is a knave or David is a knight.", "Assume David is a knight. No contradiction is found in their claim that James is a knight and David is a knight.", "Assume James is a knight. No contradiction is found in their claim that If James is a knight then Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of James that If James is a knight then Chloe is a knave.", "Chloe cannot be a knave, because this would contradict the false claim of their own that David is a knight if and only if James is a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider James.", "James cannot be a knave, because this would contradict the claim of David that James is a knight and David is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that James is a knight and David is a knight.", "Assume James is a knight. No contradiction is found in their claim that If James is a knight then Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that David is a knight if and only if James is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that David is a knight if and only if James is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of Harper that Lily is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that David is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 7), ('and', ('telling-truth', 4), ('telling-truth', 1)), ('lying', 6), ('<=>', ('telling-truth', 1), ('telling-truth', 4)), ('->', ('telling-truth', 4), ('lying', 3)), ('or', ('lying', 1), ('telling-truth', 1)), ('not', ('lying', 1)), ('and', ('telling-truth', 5), ('telling-truth', 4)))", "index": 115}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sophia, Liam, Charlotte, Zoey, Victoria, Emily, Jack, and Riley. Sophia said that Victoria is a knave or Victoria is a knight. Liam stated, \"If Victoria is a knight then Sophia is a knight\". Charlotte told you that Riley is a knave or Jack is a knight. \"Liam is a knight and Jack is a knave\" - Zoey. Victoria stated, \"Zoey is not a knave\". Emily commented, \"Riley is a knave and Jack is a knight\". Jack told you that Sophia is not a knight. In Riley's words: \"Emily is not a knave\". So who is a knight and who is a knave?", "names": ["Sophia", "Liam", "Charlotte", "Zoey", "Victoria", "Emily", "Jack", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false, false, false], "solution_text": "Sophia is a knight, Liam is a knight, Charlotte is a knight, Zoey is a knight, Victoria is a knight, Emily is a knave, Jack is a knave, and Riley is a knave.", "solution_text_format": "(1) Sophia is a knight\n(2) Liam is a knight\n(3) Charlotte is a knight\n(4) Zoey is a knight\n(5) Victoria is a knight\n(6) Emily is a knave\n(7) Jack is a knave\n(8) Riley is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Victoria is a knave or Victoria is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Zoey is not a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Liam is a knight and Jack is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that If Victoria is a knight then Sophia is a knight.", "Jack cannot be a knight, because this would contradict the claim of Zoey that Liam is a knight and Jack is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Sophia is not a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Riley is a knave or Jack is a knight.", "Riley cannot be a knight, because this would contradict the claim of Charlotte that Riley is a knave or Jack is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Emily is not a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Riley is a knave and Jack is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Riley is a knave and Jack is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 4), ('telling-truth', 4)), ('->', ('telling-truth', 4), ('telling-truth', 0)), ('or', ('lying', 7), ('telling-truth', 6)), ('and', ('telling-truth', 1), ('lying', 6)), ('not', ('lying', 3)), ('and', ('lying', 7), ('telling-truth', 6)), ('not', ('telling-truth', 0)), ('not', ('lying', 5)))", "index": 116}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Michael, Avery, Noah, Jack, Henry, Amelia, Charlotte, and Penelope. \"Charlotte is a knave\" - Michael. Avery told you that If Penelope is a knave then Noah is a knight. Noah expressed that Amelia is not a knave. \"If Noah is a knave then Henry is a knight,\" Jack mentioned. \"Michael is a knave and Henry is a knight\" - Henry. Amelia expressed that If Penelope is a knave then Avery is a knight. Charlotte noted, \"Jack is a knave if and only if Avery is a knave\". As Penelope put it, \"Avery is a knave if and only if Penelope is a knight\". So who is a knight and who is a knave?", "names": ["Michael", "Avery", "Noah", "Jack", "Henry", "Amelia", "Charlotte", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, false, true, false], "solution_text": "Michael is a knave, Avery is a knave, Noah is a knave, Jack is a knave, Henry is a knave, Amelia is a knave, Charlotte is a knight, and Penelope is a knave.", "solution_text_format": "(1) Michael is a knave\n(2) Avery is a knave\n(3) Noah is a knave\n(4) Jack is a knave\n(5) Henry is a knave\n(6) Amelia is a knave\n(7) Charlotte is a knight\n(8) Penelope is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Michael that Charlotte is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Jack is a knave if and only if Avery is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that If Noah is a knave then Henry is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Amelia is not a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that If Penelope is a knave then Avery is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Avery is a knave if and only if Penelope is a knight.", "Avery cannot be a knight, because this would contradict the false claim of Charlotte that Jack is a knave if and only if Avery is a knave.", "Avery cannot be a knave, because this would contradict the false claim of their own that If Penelope is a knave then Noah is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Avery is a knave if and only if Penelope is a knight.", "Avery cannot be a knight, because this would contradict the false claim of Charlotte that Jack is a knave if and only if Avery is a knave.", "Avery cannot be a knave, because this would contradict the false claim of their own that If Penelope is a knave then Noah is a knight.", "We have exhausted all possibilities for Avery and Penelope, so let us go back and reconsider Amelia.", "Amelia cannot be a knave, because this would contradict the claim of Noah that Amelia is not a knave.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Amelia is not a knave.", "Amelia cannot be a knight, because this would contradict the false claim of Noah that Amelia is not a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that If Penelope is a knave then Avery is a knight.", "Penelope cannot be a knight, because this would contradict the false claim of Amelia that If Penelope is a knave then Avery is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Avery is a knave if and only if Penelope is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that If Penelope is a knave then Noah is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that If Penelope is a knave then Noah is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Henry is a knight.", "Henry cannot be a knave, because this would contradict the claim of Jack that If Noah is a knave then Henry is a knight.", "We have exhausted all possibilities for Henry, Avery, Penelope, Amelia, and Noah, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that If Noah is a knave then Henry is a knight.", "Noah cannot be a knight, because this would contradict the false claim of Jack that If Noah is a knave then Henry is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Amelia is not a knave.", "Amelia cannot be a knight, because this would contradict the false claim of Noah that Amelia is not a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that If Penelope is a knave then Avery is a knight.", "Penelope cannot be a knight, because this would contradict the false claim of Amelia that If Penelope is a knave then Avery is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Avery is a knave if and only if Penelope is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that If Penelope is a knave then Noah is a knight.", "Avery cannot be a knave, because this would contradict the false claim of Charlotte that Jack is a knave if and only if Avery is a knave.", "We have exhausted all possibilities for Avery, Penelope, Amelia, Noah, Jack, and Charlotte, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Charlotte is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Jack is a knave if and only if Avery is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that If Noah is a knave then Henry is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Amelia is not a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that If Penelope is a knave then Avery is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Avery is a knave if and only if Penelope is a knight.", "Avery cannot be a knight, because this would contradict the claim of Penelope that Avery is a knave if and only if Penelope is a knight.", "Avery cannot be a knave, because this would contradict the false claim of their own that If Penelope is a knave then Noah is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Avery is a knave if and only if Penelope is a knight.", "Avery cannot be a knight, because this would contradict the false claim of Penelope that Avery is a knave if and only if Penelope is a knight.", "Avery cannot be a knave, because this would contradict the false claim of their own that If Penelope is a knave then Noah is a knight.", "We have exhausted all possibilities for Avery and Penelope, so let us go back and reconsider Amelia.", "Amelia cannot be a knave, because this would contradict the claim of Noah that Amelia is not a knave.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Amelia is not a knave.", "Amelia cannot be a knight, because this would contradict the false claim of Noah that Amelia is not a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that If Penelope is a knave then Avery is a knight.", "Penelope cannot be a knight, because this would contradict the false claim of Amelia that If Penelope is a knave then Avery is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Avery is a knave if and only if Penelope is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that If Penelope is a knave then Noah is a knight.", "Avery cannot be a knave, because this would contradict the claim of Charlotte that Jack is a knave if and only if Avery is a knave.", "We have exhausted all possibilities for Avery, Penelope, Amelia, and Noah, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that If Noah is a knave then Henry is a knight.", "Noah cannot be a knight, because this would contradict the false claim of Jack that If Noah is a knave then Henry is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Amelia is not a knave.", "Amelia cannot be a knight, because this would contradict the false claim of Noah that Amelia is not a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that If Penelope is a knave then Avery is a knight.", "Penelope cannot be a knight, because this would contradict the false claim of Amelia that If Penelope is a knave then Avery is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Avery is a knave if and only if Penelope is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that If Penelope is a knave then Noah is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that If Penelope is a knave then Noah is a knight.", "Henry cannot be a knight, because this would contradict the false claim of Jack that If Noah is a knave then Henry is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Michael is a knave and Henry is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 6), ('->', ('lying', 7), ('telling-truth', 2)), ('not', ('lying', 5)), ('->', ('lying', 2), ('telling-truth', 4)), ('and', ('lying', 0), ('telling-truth', 4)), ('->', ('lying', 7), ('telling-truth', 1)), ('<=>', ('lying', 3), ('lying', 1)), ('<=>', ('lying', 1), ('telling-truth', 7)))", "index": 117}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Avery, Aurora, Sophia, Michael, Charlotte, Penelope, Zoey, and Victoria. Avery stated, \"Sophia is a knave and Avery is a knight\". Aurora said, \"Michael is a knight.\" Sophia expressed that Charlotte is a knight or Avery is a knave. \"Michael is a knight and Penelope is a knave,\" Michael declared. Charlotte stated, \"Penelope is a knave or Michael is a knight\". Penelope was heard saying, \"Michael is a knight\". In Zoey's words: \"If Zoey is a knight then Michael is a knave\". Victoria said, \"Charlotte is not a knight.\" So who is a knight and who is a knave?", "names": ["Avery", "Aurora", "Sophia", "Michael", "Charlotte", "Penelope", "Zoey", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, false, true, false], "solution_text": "Avery is a knave, Aurora is a knave, Sophia is a knight, Michael is a knave, Charlotte is a knight, Penelope is a knave, Zoey is a knight, and Victoria is a knave.", "solution_text_format": "(1) Avery is a knave\n(2) Aurora is a knave\n(3) Sophia is a knight\n(4) Michael is a knave\n(5) Charlotte is a knight\n(6) Penelope is a knave\n(7) Zoey is a knight\n(8) Victoria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Sophia is a knave and Avery is a knight.", "Sophia cannot be a knight, because this would contradict the claim of Avery that Sophia is a knave and Avery is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Charlotte is a knight or Avery is a knave.", "Charlotte cannot be a knight, because this would contradict the false claim of Sophia that Charlotte is a knight or Avery is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Penelope is a knave or Michael is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Michael is a knight.", "Michael cannot be a knight, because this would contradict the claim of their own that Michael is a knight and Penelope is a knave.", "Michael cannot be a knave, because this would contradict the claim of Penelope that Michael is a knight.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the false claim of Charlotte that Penelope is a knave or Michael is a knight.", "We have exhausted all possibilities for Penelope, Charlotte, and Sophia, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Sophia is a knave and Avery is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Charlotte is a knight or Avery is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Penelope is a knave or Michael is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Michael is a knight.", "Michael cannot be a knight, because this would contradict the claim of their own that Michael is a knight and Penelope is a knave.", "Michael cannot be a knave, because this would contradict the claim of Charlotte that Penelope is a knave or Michael is a knight.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Michael is a knight.", "Michael cannot be a knight, because this would contradict the false claim of Penelope that Michael is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Michael is a knight and Penelope is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Michael is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Michael is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that If Zoey is a knight then Michael is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that Charlotte is not a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Charlotte is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('telling-truth', 0)), ('telling-truth', 3), ('or', ('telling-truth', 4), ('lying', 0)), ('and', ('telling-truth', 3), ('lying', 5)), ('or', ('lying', 5), ('telling-truth', 3)), ('telling-truth', 3), ('->', ('telling-truth', 6), ('lying', 3)), ('not', ('telling-truth', 4)))", "index": 118}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mia, Ethan, Alexander, Noah, Jackson, Ava, Abigail, and Aiden. Mia expressed that If Ethan is a knave then Mia is a knight. Ethan commented, \"Mia is a knave\". Alexander said that Ethan is a knight. Noah expressed that Mia is a knight. Jackson stated, \"Noah is a knave\". Ava said that Alexander is a knight and Ethan is a knave. \"Noah is a knave and Abigail is a knight\" - Abigail. \"Ethan is a knight or Ava is a knave\" - Aiden. So who is a knight and who is a knave?", "names": ["Mia", "Ethan", "Alexander", "Noah", "Jackson", "Ava", "Abigail", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, false, false, true], "solution_text": "Mia is a knight, Ethan is a knave, Alexander is a knave, Noah is a knight, Jackson is a knave, Ava is a knave, Abigail is a knave, and Aiden is a knight.", "solution_text_format": "(1) Mia is a knight\n(2) Ethan is a knave\n(3) Alexander is a knave\n(4) Noah is a knight\n(5) Jackson is a knave\n(6) Ava is a knave\n(7) Abigail is a knave\n(8) Aiden is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that If Ethan is a knave then Mia is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Mia is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Mia is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that Ethan is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Ethan is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Mia is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Noah is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Noah is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Alexander is a knight and Ethan is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Alexander is a knight and Ethan is a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Noah is a knave and Abigail is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Noah is a knave and Abigail is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Ethan is a knight or Ava is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 1), ('telling-truth', 0)), ('lying', 0), ('telling-truth', 1), ('telling-truth', 0), ('lying', 3), ('and', ('telling-truth', 2), ('lying', 1)), ('and', ('lying', 3), ('telling-truth', 6)), ('or', ('telling-truth', 1), ('lying', 5)))", "index": 119}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Joseph, Luke, Harper, Sophia, Michael, Penelope, Henry, and Chloe. Joseph remarked, \"Chloe is a knave or Luke is a knave\". Luke stated, \"Penelope is not a knight\". Harper noted, \"Michael is not a knight\". Sophia was heard saying, \"If Luke is a knave then Henry is a knave\". Michael expressed that Joseph is a knave. \"Luke is a knave\" - Penelope. Henry expressed that Penelope is a knave if and only if Luke is a knight. \"Joseph is a knight and Henry is a knight\" - Chloe. So who is a knight and who is a knave?", "names": ["Joseph", "Luke", "Harper", "Sophia", "Michael", "Penelope", "Henry", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true, true, true], "solution_text": "Joseph is a knight, Luke is a knave, Harper is a knight, Sophia is a knave, Michael is a knave, Penelope is a knight, Henry is a knight, and Chloe is a knight.", "solution_text_format": "(1) Joseph is a knight\n(2) Luke is a knave\n(3) Harper is a knight\n(4) Sophia is a knave\n(5) Michael is a knave\n(6) Penelope is a knight\n(7) Henry is a knight\n(8) Chloe is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that Chloe is a knave or Luke is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Joseph is a knight and Henry is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Penelope is a knave if and only if Luke is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Luke is a knave.", "Luke cannot be a knight, because this would contradict the claim of Joseph that Chloe is a knave or Luke is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Penelope is not a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Michael is not a knight.", "Michael cannot be a knight, because this would contradict the claim of Harper that Michael is not a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Joseph is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that If Luke is a knave then Henry is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that If Luke is a knave then Henry is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 7), ('lying', 1)), ('not', ('telling-truth', 5)), ('not', ('telling-truth', 4)), ('->', ('lying', 1), ('lying', 6)), ('lying', 0), ('lying', 1), ('<=>', ('lying', 5), ('telling-truth', 1)), ('and', ('telling-truth', 0), ('telling-truth', 6)))", "index": 120}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Samuel, Amelia, Elizabeth, Abigail, Joseph, Mia, Evelyn, and William. Samuel asserted: \"Joseph is a knave and Mia is a knight\". In a statement by Amelia: \"Joseph is a knight and Samuel is a knight\". Elizabeth commented, \"Amelia is a knave if and only if Joseph is a knight\". \"Elizabeth is a knave if and only if Elizabeth is a knight,\" Abigail mentioned. Joseph commented, \"If Mia is a knight then Amelia is a knave\". According to Mia, \"Abigail is a knave\". Evelyn commented, \"Elizabeth is a knave\". William expressed that William is a knight and Joseph is a knave. So who is a knight and who is a knave?", "names": ["Samuel", "Amelia", "Elizabeth", "Abigail", "Joseph", "Mia", "Evelyn", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true, false, false], "solution_text": "Samuel is a knave, Amelia is a knave, Elizabeth is a knight, Abigail is a knave, Joseph is a knight, Mia is a knight, Evelyn is a knave, and William is a knave.", "solution_text_format": "(1) Samuel is a knave\n(2) Amelia is a knave\n(3) Elizabeth is a knight\n(4) Abigail is a knave\n(5) Joseph is a knight\n(6) Mia is a knight\n(7) Evelyn is a knave\n(8) William is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that Joseph is a knave and Mia is a knight.", "Joseph cannot be a knight, because this would contradict the claim of Samuel that Joseph is a knave and Mia is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that If Mia is a knight then Amelia is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave if and only if Elizabeth is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Elizabeth is a knave if and only if Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Amelia is a knave if and only if Joseph is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Joseph is a knight and Samuel is a knight.", "Amelia cannot be a knave, because this would contradict the claim of Elizabeth that Amelia is a knave if and only if Joseph is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Amelia is a knave if and only if Joseph is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Joseph is a knight and Samuel is a knight.", "Amelia cannot be a knave, because this would contradict the false claim of Joseph that If Mia is a knight then Amelia is a knave.", "We have exhausted all possibilities for Amelia, Elizabeth, and Abigail, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the claim of Samuel that Joseph is a knave and Mia is a knight.", "We have exhausted all possibilities for Mia and Joseph, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Joseph is a knave and Mia is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Mia is a knight then Amelia is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave if and only if Elizabeth is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Elizabeth is a knave if and only if Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Amelia is a knave if and only if Joseph is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Joseph is a knight and Samuel is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Joseph is a knight and Samuel is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Elizabeth is a knave.", "William cannot be a knight, because this would contradict the claim of their own that William is a knight and Joseph is a knave.", "Assume William is a knave. No contradiction is found in their false claim that William is a knight and Joseph is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('telling-truth', 5)), ('and', ('telling-truth', 4), ('telling-truth', 0)), ('<=>', ('lying', 1), ('telling-truth', 4)), ('<=>', ('lying', 2), ('telling-truth', 2)), ('->', ('telling-truth', 5), ('lying', 1)), ('lying', 3), ('lying', 2), ('and', ('telling-truth', 7), ('lying', 4)))", "index": 121}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Benjamin, Ethan, Alexander, Mia, Luke, Elizabeth, Olivia, and Harper. \"Olivia is a knave or Elizabeth is a knight,\" Benjamin mentioned. \"Alexander is a knight or Mia is a knight,\" Ethan declared. \"If Olivia is a knave then Harper is a knight,\" Alexander mentioned. Mia stated, \"Ethan is a knight if and only if Ethan is a knave\". \"Olivia is a knight if and only if Harper is a knight,\" Luke claimed. As Elizabeth put it, \"Luke is a knight\". In a statement by Olivia: \"If Ethan is a knave then Alexander is a knave\". In a statement by Harper: \"Olivia is a knight\". So who is a knight and who is a knave?", "names": ["Benjamin", "Ethan", "Alexander", "Mia", "Luke", "Elizabeth", "Olivia", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true, true, true], "solution_text": "Benjamin is a knight, Ethan is a knight, Alexander is a knight, Mia is a knave, Luke is a knight, Elizabeth is a knight, Olivia is a knight, and Harper is a knight.", "solution_text_format": "(1) Benjamin is a knight\n(2) Ethan is a knight\n(3) Alexander is a knight\n(4) Mia is a knave\n(5) Luke is a knight\n(6) Elizabeth is a knight\n(7) Olivia is a knight\n(8) Harper is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Olivia is a knave or Elizabeth is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that If Ethan is a knave then Alexander is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Alexander is a knight or Mia is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that If Olivia is a knave then Harper is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Olivia is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that Ethan is a knight if and only if Ethan is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Ethan is a knight if and only if Ethan is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Luke is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Harper is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 6), ('telling-truth', 5)), ('or', ('telling-truth', 2), ('telling-truth', 3)), ('->', ('lying', 6), ('telling-truth', 7)), ('<=>', ('telling-truth', 1), ('lying', 1)), ('<=>', ('telling-truth', 6), ('telling-truth', 7)), ('telling-truth', 4), ('->', ('lying', 1), ('lying', 2)), ('telling-truth', 6))", "index": 122}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: William, Zoey, Ethan, James, Michael, Henry, Penelope, and Oliver. \"Michael is a knight,\" William declared. Zoey remarked, \"Ethan is a knight or Oliver is a knave\". According to Ethan, \"Michael is a knave and Ethan is a knight\". In James's words: \"Zoey is a knave or Ethan is a knight\". As Michael put it, \"William is a knight or Oliver is a knight\". As Henry put it, \"Ethan is not a knave\". According to Penelope, \"James is a knight if and only if Oliver is a knave\". \"Zoey is a knight or James is a knight\" - Oliver. So who is a knight and who is a knave?", "names": ["William", "Zoey", "Ethan", "James", "Michael", "Henry", "Penelope", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false, false, true], "solution_text": "William is a knight, Zoey is a knave, Ethan is a knave, James is a knight, Michael is a knight, Henry is a knave, Penelope is a knave, and Oliver is a knight.", "solution_text_format": "(1) William is a knight\n(2) Zoey is a knave\n(3) Ethan is a knave\n(4) James is a knight\n(5) Michael is a knight\n(6) Henry is a knave\n(7) Penelope is a knave\n(8) Oliver is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Michael is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that William is a knight or Oliver is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Zoey is a knight or James is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Ethan is a knight or Oliver is a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Ethan is a knight.", "Ethan cannot be a knave, because this would contradict the claim of Zoey that Ethan is a knight or Oliver is a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Ethan is a knight or Oliver is a knave.", "Ethan cannot be a knight, because this would contradict the false claim of Zoey that Ethan is a knight or Oliver is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Michael is a knave and Ethan is a knight.", "Assume James is a knight. No contradiction is found in their claim that Zoey is a knave or Ethan is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Ethan is not a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Ethan is not a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that James is a knight if and only if Oliver is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that James is a knight if and only if Oliver is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('or', ('telling-truth', 2), ('lying', 7)), ('and', ('lying', 4), ('telling-truth', 2)), ('or', ('lying', 1), ('telling-truth', 2)), ('or', ('telling-truth', 0), ('telling-truth', 7)), ('not', ('lying', 2)), ('<=>', ('telling-truth', 3), ('lying', 7)), ('or', ('telling-truth', 1), ('telling-truth', 3)))", "index": 123}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Noah, Chloe, Zoey, Luke, Mia, Sebastian, James, and Harper. \"Mia is a knight,\" Noah declared. In a statement by Chloe: \"Zoey is not a knight\". Zoey stated, \"James is not a knight\". According to Luke, \"Mia is a knight and Noah is a knave\". Mia said that James is not a knave. Sebastian asserted: \"Noah is a knight if and only if Harper is a knight\". \"Chloe is a knave if and only if Noah is a knave\" - James. Harper told you that Luke is not a knave. So who is a knight and who is a knave?", "names": ["Noah", "Chloe", "Zoey", "Luke", "Mia", "Sebastian", "James", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, false, true, false], "solution_text": "Noah is a knight, Chloe is a knight, Zoey is a knave, Luke is a knave, Mia is a knight, Sebastian is a knave, James is a knight, and Harper is a knave.", "solution_text_format": "(1) Noah is a knight\n(2) Chloe is a knight\n(3) Zoey is a knave\n(4) Luke is a knave\n(5) Mia is a knight\n(6) Sebastian is a knave\n(7) James is a knight\n(8) Harper is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Noah is a knight. No contradiction is found in their claim that Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that James is not a knave.", "Assume James is a knight. No contradiction is found in their claim that Chloe is a knave if and only if Noah is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Zoey is not a knight.", "Zoey cannot be a knight, because this would contradict the claim of Chloe that Zoey is not a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that James is not a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Mia is a knight and Noah is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Mia is a knight and Noah is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Noah is a knight if and only if Harper is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that Luke is not a knave.", "Harper cannot be a knave, because this would contradict the claim of Sebastian that Noah is a knight if and only if Harper is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Noah is a knight if and only if Harper is a knight.", "Harper cannot be a knight, because this would contradict the false claim of Sebastian that Noah is a knight if and only if Harper is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Luke is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('not', ('telling-truth', 2)), ('not', ('telling-truth', 6)), ('and', ('telling-truth', 4), ('lying', 0)), ('not', ('lying', 6)), ('<=>', ('telling-truth', 0), ('telling-truth', 7)), ('<=>', ('lying', 1), ('lying', 0)), ('not', ('lying', 3)))", "index": 124}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Matthew, Mia, William, Sofia, Samuel, Emily, Avery, and Isabella. In Matthew's words: \"Isabella is not a knight\". As Mia put it, \"Mia is a knight or William is a knight\". \"Avery is a knave or Avery is a knight,\" William mentioned. Sofia was heard saying, \"Mia is not a knave\". Samuel commented, \"William is a knight or Sofia is a knight\". Emily told you that Isabella is not a knave. Avery was heard saying, \"If Mia is a knave then Samuel is a knight\". According to Isabella, \"Mia is a knight if and only if Avery is a knave\". So who is a knight and who is a knave?", "names": ["Matthew", "Mia", "William", "Sofia", "Samuel", "Emily", "Avery", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false, true, false], "solution_text": "Matthew is a knight, Mia is a knight, William is a knight, Sofia is a knight, Samuel is a knight, Emily is a knave, Avery is a knight, and Isabella is a knave.", "solution_text_format": "(1) Matthew is a knight\n(2) Mia is a knight\n(3) William is a knight\n(4) Sofia is a knight\n(5) Samuel is a knight\n(6) Emily is a knave\n(7) Avery is a knight\n(8) Isabella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that Isabella is not a knight.", "Isabella cannot be a knight, because this would contradict the claim of Matthew that Isabella is not a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Mia is a knight if and only if Avery is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Mia is a knight or William is a knight.", "Assume William is a knight. No contradiction is found in their claim that Avery is a knave or Avery is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that If Mia is a knave then Samuel is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that William is a knight or Sofia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Mia is not a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Isabella is not a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Isabella is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 7)), ('or', ('telling-truth', 1), ('telling-truth', 2)), ('or', ('lying', 6), ('telling-truth', 6)), ('not', ('lying', 1)), ('or', ('telling-truth', 2), ('telling-truth', 3)), ('not', ('lying', 7)), ('->', ('lying', 1), ('telling-truth', 4)), ('<=>', ('telling-truth', 1), ('lying', 6)))", "index": 125}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aria, Ava, Amelia, Sebastian, James, Liam, Benjamin, and Mason. Aria was heard saying, \"Ava is a knight or Benjamin is a knave\". Ava said, \"Benjamin is a knave or James is a knight.\" Amelia said, \"Liam is a knight and Benjamin is a knight.\" Sebastian said, \"Mason is a knave and Aria is a knight.\" According to James, \"If Aria is a knight then Liam is a knight\". Liam asserted: \"Sebastian is a knave or Benjamin is a knight\". Benjamin said that Sebastian is a knave or Aria is a knight. \"Aria is a knave and Aria is a knight,\" Mason declared. So who is a knight and who is a knave?", "names": ["Aria", "Ava", "Amelia", "Sebastian", "James", "Liam", "Benjamin", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true, true, false], "solution_text": "Aria is a knight, Ava is a knight, Amelia is a knight, Sebastian is a knight, James is a knight, Liam is a knight, Benjamin is a knight, and Mason is a knave.", "solution_text_format": "(1) Aria is a knight\n(2) Ava is a knight\n(3) Amelia is a knight\n(4) Sebastian is a knight\n(5) James is a knight\n(6) Liam is a knight\n(7) Benjamin is a knight\n(8) Mason is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that Ava is a knight or Benjamin is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Benjamin is a knave or James is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Sebastian is a knave or Aria is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Mason is a knave and Aria is a knight.", "Mason cannot be a knight, because this would contradict the claim of Sebastian that Mason is a knave and Aria is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Aria is a knave and Aria is a knight.", "Assume James is a knight. No contradiction is found in their claim that If Aria is a knight then Liam is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Sebastian is a knave or Benjamin is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Liam is a knight and Benjamin is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('lying', 6)), ('or', ('lying', 6), ('telling-truth', 4)), ('and', ('telling-truth', 5), ('telling-truth', 6)), ('and', ('lying', 7), ('telling-truth', 0)), ('->', ('telling-truth', 0), ('telling-truth', 5)), ('or', ('lying', 3), ('telling-truth', 6)), ('or', ('lying', 3), ('telling-truth', 0)), ('and', ('lying', 0), ('telling-truth', 0)))", "index": 126}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Avery, Emily, Samuel, Abigail, Michael, Noah, Henry, and Charlotte. Avery asserted: \"Noah is a knave if and only if Samuel is a knight\". In a statement by Emily: \"Henry is a knave\". Samuel commented, \"Abigail is not a knight\". Abigail expressed that Charlotte is a knave if and only if Noah is a knight. Michael said, \"Noah is not a knight.\" \"Henry is a knave or Samuel is a knight,\" Noah mentioned. Henry said that Michael is a knight if and only if Abigail is a knave. \"If Michael is a knight then Henry is a knight,\" Charlotte claimed. So who is a knight and who is a knave?", "names": ["Avery", "Emily", "Samuel", "Abigail", "Michael", "Noah", "Henry", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true, false, true], "solution_text": "Avery is a knave, Emily is a knight, Samuel is a knight, Abigail is a knave, Michael is a knave, Noah is a knight, Henry is a knave, and Charlotte is a knight.", "solution_text_format": "(1) Avery is a knave\n(2) Emily is a knight\n(3) Samuel is a knight\n(4) Abigail is a knave\n(5) Michael is a knave\n(6) Noah is a knight\n(7) Henry is a knave\n(8) Charlotte is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Noah is a knave if and only if Samuel is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Henry is a knave or Samuel is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Michael is a knight if and only if Abigail is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Noah is not a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Noah is not a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Charlotte is a knave if and only if Noah is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Abigail that Charlotte is a knave if and only if Noah is a knight.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that If Michael is a knight then Henry is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the claim of Henry that Michael is a knight if and only if Abigail is a knave.", "We have exhausted all possibilities for Abigail and Michael, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Michael is a knight if and only if Abigail is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Noah is not a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Noah is not a knight.", "Abigail cannot be a knight, because this would contradict the false claim of Henry that Michael is a knight if and only if Abigail is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Charlotte is a knave if and only if Noah is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Michael is a knight then Henry is a knight.", "Samuel cannot be a knight, because this would contradict the claim of Avery that Noah is a knave if and only if Samuel is a knight.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Abigail is not a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the false claim of Abigail that Charlotte is a knave if and only if Noah is a knight.", "We have exhausted all possibilities for Charlotte, Abigail, Michael, and Henry, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Henry is a knave or Samuel is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Michael is a knight if and only if Abigail is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Noah is not a knight.", "Abigail cannot be a knight, because this would contradict the claim of Henry that Michael is a knight if and only if Abigail is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Charlotte is a knave if and only if Noah is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of Abigail that Charlotte is a knave if and only if Noah is a knight.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that If Michael is a knight then Henry is a knight.", "We have exhausted all possibilities for Charlotte and Abigail, so let us go back and reconsider Michael.", "Michael cannot be a knave, because this would contradict the false claim of their own that Noah is not a knight.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the false claim of Noah that Henry is a knave or Samuel is a knight.", "We have exhausted all possibilities for Henry and Noah, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Noah is a knave if and only if Samuel is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Henry is a knave or Samuel is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Michael is a knight if and only if Abigail is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Noah is not a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Noah is not a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Charlotte is a knave if and only if Noah is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Abigail that Charlotte is a knave if and only if Noah is a knight.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that If Michael is a knight then Henry is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the claim of Henry that Michael is a knight if and only if Abigail is a knave.", "We have exhausted all possibilities for Abigail and Michael, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Michael is a knight if and only if Abigail is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Noah is not a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Noah is not a knight.", "Abigail cannot be a knight, because this would contradict the false claim of Henry that Michael is a knight if and only if Abigail is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Charlotte is a knave if and only if Noah is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Michael is a knight then Henry is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Abigail is not a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Henry is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 5), ('telling-truth', 2)), ('lying', 6), ('not', ('telling-truth', 3)), ('<=>', ('lying', 7), ('telling-truth', 5)), ('not', ('telling-truth', 5)), ('or', ('lying', 6), ('telling-truth', 2)), ('<=>', ('telling-truth', 4), ('lying', 3)), ('->', ('telling-truth', 4), ('telling-truth', 6)))", "index": 127}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Logan, Lucas, Elizabeth, Noah, Ava, Harper, Charlotte, and Jackson. Logan noted, \"Jackson is a knave if and only if Elizabeth is a knave\". Lucas asserted: \"Jackson is not a knight\". In a statement by Elizabeth: \"Ava is not a knight\". As Noah put it, \"Charlotte is a knave\". As Ava put it, \"If Elizabeth is a knave then Noah is a knave\". Harper noted, \"Jackson is a knave\". Charlotte asserted: \"Jackson is a knave or Elizabeth is a knight\". As Jackson put it, \"Jackson is a knight if and only if Logan is a knight\". So who is a knight and who is a knave?", "names": ["Logan", "Lucas", "Elizabeth", "Noah", "Ava", "Harper", "Charlotte", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true, true, false], "solution_text": "Logan is a knight, Lucas is a knight, Elizabeth is a knave, Noah is a knave, Ava is a knight, Harper is a knight, Charlotte is a knight, and Jackson is a knave.", "solution_text_format": "(1) Logan is a knight\n(2) Lucas is a knight\n(3) Elizabeth is a knave\n(4) Noah is a knave\n(5) Ava is a knight\n(6) Harper is a knight\n(7) Charlotte is a knight\n(8) Jackson is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that Jackson is a knave if and only if Elizabeth is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Logan is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Ava is not a knight.", "Ava cannot be a knight, because this would contradict the claim of Elizabeth that Ava is not a knight.", "Ava cannot be a knave, because this would contradict the false claim of their own that If Elizabeth is a knave then Noah is a knave.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Elizabeth.", "Elizabeth cannot be a knave, because this would contradict the claim of Logan that Jackson is a knave if and only if Elizabeth is a knave.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Jackson is a knight if and only if Logan is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Logan that Jackson is a knave if and only if Elizabeth is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Ava is not a knight.", "Assume Ava is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of Ava that If Elizabeth is a knave then Noah is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Charlotte is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Jackson is a knave or Elizabeth is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Jackson is not a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Jackson is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 7), ('lying', 2)), ('not', ('telling-truth', 7)), ('not', ('telling-truth', 4)), ('lying', 6), ('->', ('lying', 2), ('lying', 3)), ('lying', 7), ('or', ('lying', 7), ('telling-truth', 2)), ('<=>', ('telling-truth', 7), ('telling-truth', 0)))", "index": 128}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Liam, Sophia, Noah, Alexander, Michael, Grace, Mason, and Ella. In a statement by Liam: \"Sophia is not a knight\". Sophia remarked, \"Alexander is a knave\". Noah commented, \"Mason is not a knight\". Alexander stated, \"Mason is a knight if and only if Alexander is a knight\". Michael asserted: \"Noah is a knave or Mason is a knave\". Grace told you that Liam is a knight if and only if Michael is a knave. \"Sophia is a knave,\" Mason declared. In Ella's words: \"If Alexander is a knight then Mason is a knave\". So who is a knight and who is a knave?", "names": ["Liam", "Sophia", "Noah", "Alexander", "Michael", "Grace", "Mason", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false, true, false], "solution_text": "Liam is a knight, Sophia is a knave, Noah is a knave, Alexander is a knight, Michael is a knight, Grace is a knave, Mason is a knight, and Ella is a knave.", "solution_text_format": "(1) Liam is a knight\n(2) Sophia is a knave\n(3) Noah is a knave\n(4) Alexander is a knight\n(5) Michael is a knight\n(6) Grace is a knave\n(7) Mason is a knight\n(8) Ella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Sophia is not a knight.", "Sophia cannot be a knight, because this would contradict the claim of Liam that Sophia is not a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Alexander is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Mason is a knight if and only if Alexander is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Sophia is a knave.", "Noah cannot be a knight, because this would contradict the claim of their own that Mason is not a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Mason is not a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Noah is a knave or Mason is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Liam is a knight if and only if Michael is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Liam is a knight if and only if Michael is a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that If Alexander is a knight then Mason is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that If Alexander is a knight then Mason is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 1)), ('lying', 3), ('not', ('telling-truth', 6)), ('<=>', ('telling-truth', 6), ('telling-truth', 3)), ('or', ('lying', 2), ('lying', 6)), ('<=>', ('telling-truth', 0), ('lying', 4)), ('lying', 1), ('->', ('telling-truth', 3), ('lying', 6)))", "index": 129}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Harper, Michael, Matthew, Avery, Jack, Henry, Owen, and Liam. \"Michael is not a knight,\" Harper claimed. Michael said that Matthew is a knave or Liam is a knight. Matthew noted, \"Jack is a knight or Henry is a knave\". Avery asserted: \"If Owen is a knave then Henry is a knave\". \"Jack is a knight if and only if Harper is a knight\" - Jack. In a statement by Henry: \"Harper is a knight or Jack is a knight\". In Owen's words: \"Henry is not a knight\". Liam said, \"Avery is a knight and Avery is a knave.\" So who is a knight and who is a knave?", "names": ["Harper", "Michael", "Matthew", "Avery", "Jack", "Henry", "Owen", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true, false, false], "solution_text": "Harper is a knight, Michael is a knave, Matthew is a knight, Avery is a knave, Jack is a knight, Henry is a knight, Owen is a knave, and Liam is a knave.", "solution_text_format": "(1) Harper is a knight\n(2) Michael is a knave\n(3) Matthew is a knight\n(4) Avery is a knave\n(5) Jack is a knight\n(6) Henry is a knight\n(7) Owen is a knave\n(8) Liam is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that Michael is not a knight.", "Michael cannot be a knight, because this would contradict the claim of Harper that Michael is not a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Matthew is a knave or Liam is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Jack is a knight or Henry is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Jack is a knight if and only if Harper is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Harper is a knight or Jack is a knight.", "Liam cannot be a knight, because this would contradict the false claim of Michael that Matthew is a knave or Liam is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Avery is a knight and Avery is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that If Owen is a knave then Henry is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Henry is not a knight.", "Owen cannot be a knave, because this would contradict the claim of Avery that If Owen is a knave then Henry is a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that If Owen is a knave then Henry is a knave.", "Owen cannot be a knight, because this would contradict the false claim of Avery that If Owen is a knave then Henry is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Henry is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 1)), ('or', ('lying', 2), ('telling-truth', 7)), ('or', ('telling-truth', 4), ('lying', 5)), ('->', ('lying', 6), ('lying', 5)), ('<=>', ('telling-truth', 4), ('telling-truth', 0)), ('or', ('telling-truth', 0), ('telling-truth', 4)), ('not', ('telling-truth', 5)), ('and', ('telling-truth', 3), ('lying', 3)))", "index": 130}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Olivia, Riley, William, Henry, Isabella, Charlotte, Evelyn, and Elizabeth. Olivia said that Isabella is a knave. Riley asserted: \"Isabella is a knight or Olivia is a knave\". William remarked, \"If Henry is a knave then Evelyn is a knave\". In Henry's words: \"Riley is a knave if and only if Henry is a knight\". In Isabella's words: \"If Henry is a knight then Henry is a knave\". According to Charlotte, \"If Riley is a knight then Charlotte is a knight\". In a statement by Evelyn: \"Charlotte is not a knave\". According to Elizabeth, \"Olivia is a knight and Olivia is a knave\". So who is a knight and who is a knave?", "names": ["Olivia", "Riley", "William", "Henry", "Isabella", "Charlotte", "Evelyn", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true, true, false], "solution_text": "Olivia is a knight, Riley is a knave, William is a knight, Henry is a knight, Isabella is a knave, Charlotte is a knight, Evelyn is a knight, and Elizabeth is a knave.", "solution_text_format": "(1) Olivia is a knight\n(2) Riley is a knave\n(3) William is a knight\n(4) Henry is a knight\n(5) Isabella is a knave\n(6) Charlotte is a knight\n(7) Evelyn is a knight\n(8) Elizabeth is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Isabella is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Olivia that Isabella is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that If Henry is a knight then Henry is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Riley is a knave if and only if Henry is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Isabella is a knight or Olivia is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Isabella is a knight or Olivia is a knave.", "Assume William is a knight. No contradiction is found in their claim that If Henry is a knave then Evelyn is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Charlotte is not a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Riley is a knight then Charlotte is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Olivia is a knight and Olivia is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Olivia is a knight and Olivia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('or', ('telling-truth', 4), ('lying', 0)), ('->', ('lying', 3), ('lying', 6)), ('<=>', ('lying', 1), ('telling-truth', 3)), ('->', ('telling-truth', 3), ('lying', 3)), ('->', ('telling-truth', 1), ('telling-truth', 5)), ('not', ('lying', 5)), ('and', ('telling-truth', 0), ('lying', 0)))", "index": 131}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sophia, William, Owen, Henry, Abigail, Penelope, Grace, and Chloe. Sophia stated, \"Henry is a knave\". William remarked, \"Owen is not a knight\". Owen was heard saying, \"Chloe is a knight and Abigail is a knight\". Henry said, \"Grace is not a knight.\" According to Abigail, \"Chloe is a knight or Penelope is a knight\". \"Owen is not a knight,\" Penelope mentioned. According to Grace, \"Sophia is a knight or Penelope is a knight\". In Chloe's words: \"If Owen is a knight then Henry is a knave\". So who is a knight and who is a knave?", "names": ["Sophia", "William", "Owen", "Henry", "Abigail", "Penelope", "Grace", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, false, true, true], "solution_text": "Sophia is a knight, William is a knave, Owen is a knight, Henry is a knave, Abigail is a knight, Penelope is a knave, Grace is a knight, and Chloe is a knight.", "solution_text_format": "(1) Sophia is a knight\n(2) William is a knave\n(3) Owen is a knight\n(4) Henry is a knave\n(5) Abigail is a knight\n(6) Penelope is a knave\n(7) Grace is a knight\n(8) Chloe is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of Sophia that Henry is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Grace is not a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Sophia is a knight or Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Owen is not a knight.", "Owen cannot be a knight, because this would contradict the claim of Penelope that Owen is not a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Chloe is a knight and Abigail is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that If Owen is a knight then Henry is a knave.", "Abigail cannot be a knight, because this would contradict the false claim of Owen that Chloe is a knight and Abigail is a knight.", "Abigail cannot be a knave, because this would contradict the false claim of their own that Chloe is a knight or Penelope is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the false claim of their own that If Owen is a knight then Henry is a knave.", "We have exhausted all possibilities for Chloe and Owen, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Owen is not a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Chloe is a knight and Abigail is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that If Owen is a knight then Henry is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Chloe is a knight or Penelope is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Owen is not a knight.", "Assume William is a knave. No contradiction is found in their false claim that Owen is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('not', ('telling-truth', 2)), ('and', ('telling-truth', 7), ('telling-truth', 4)), ('not', ('telling-truth', 6)), ('or', ('telling-truth', 7), ('telling-truth', 5)), ('not', ('telling-truth', 2)), ('or', ('telling-truth', 0), ('telling-truth', 5)), ('->', ('telling-truth', 2), ('lying', 3)))", "index": 132}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: James, Joseph, David, Ella, Aria, Benjamin, Matthew, and Penelope. James stated, \"Benjamin is a knave if and only if Matthew is a knave\". \"Aria is a knave if and only if Benjamin is a knave,\" Joseph declared. David told you that If David is a knight then Penelope is a knight. Ella said that If James is a knight then Aria is a knight. \"If Ella is a knight then David is a knight,\" Aria claimed. Benjamin remarked, \"Joseph is a knight or Penelope is a knave\". Matthew told you that Ella is a knight and Ella is a knave. Penelope said, \"David is a knave or James is a knight.\" So who is a knight and who is a knave?", "names": ["James", "Joseph", "David", "Ella", "Aria", "Benjamin", "Matthew", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false, false, true], "solution_text": "James is a knight, Joseph is a knave, David is a knight, Ella is a knight, Aria is a knight, Benjamin is a knave, Matthew is a knave, and Penelope is a knight.", "solution_text_format": "(1) James is a knight\n(2) Joseph is a knave\n(3) David is a knight\n(4) Ella is a knight\n(5) Aria is a knight\n(6) Benjamin is a knave\n(7) Matthew is a knave\n(8) Penelope is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Benjamin is a knave if and only if Matthew is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Joseph is a knight or Penelope is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Aria is a knave if and only if Benjamin is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that If Ella is a knight then David is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that If James is a knight then Aria is a knight.", "Assume David is a knight. No contradiction is found in their claim that If David is a knight then Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that David is a knave or James is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Ella is a knight and Ella is a knave.", "Matthew cannot be a knave, because this would contradict the claim of James that Benjamin is a knave if and only if Matthew is a knave.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the claim of David that If David is a knight then Penelope is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the false claim of their own that If David is a knight then Penelope is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the false claim of their own that If James is a knight then Aria is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Aria.", "Aria cannot be a knave, because this would contradict the claim of Joseph that Aria is a knave if and only if Benjamin is a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Aria is a knave if and only if Benjamin is a knave.", "Aria cannot be a knight, because this would contradict the false claim of Joseph that Aria is a knave if and only if Benjamin is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that If Ella is a knight then David is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that If James is a knight then Aria is a knight.", "Ella cannot be a knave, because this would contradict the false claim of Aria that If Ella is a knight then David is a knight.", "We have exhausted all possibilities for Ella, Aria, and Joseph, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Joseph is a knight or Penelope is a knave.", "Joseph cannot be a knight, because this would contradict the false claim of Benjamin that Joseph is a knight or Penelope is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Aria is a knave if and only if Benjamin is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that If Ella is a knight then David is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that If James is a knight then Aria is a knight.", "Assume David is a knight. No contradiction is found in their claim that If David is a knight then Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that David is a knave or James is a knight.", "Matthew cannot be a knight, because this would contradict the claim of James that Benjamin is a knave if and only if Matthew is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Ella is a knight and Ella is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 5), ('lying', 6)), ('<=>', ('lying', 4), ('lying', 5)), ('->', ('telling-truth', 2), ('telling-truth', 7)), ('->', ('telling-truth', 0), ('telling-truth', 4)), ('->', ('telling-truth', 3), ('telling-truth', 2)), ('or', ('telling-truth', 1), ('lying', 7)), ('and', ('telling-truth', 3), ('lying', 3)), ('or', ('lying', 2), ('telling-truth', 0)))", "index": 133}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jack, Emily, Evelyn, Ella, Scarlett, Jackson, William, and Avery. \"Evelyn is not a knight,\" Jack mentioned. Emily stated, \"William is a knight if and only if Jackson is a knight\". Evelyn noted, \"If Scarlett is a knave then Ella is a knight\". According to Ella, \"Avery is a knave\". In a statement by Scarlett: \"William is not a knave\". Jackson said, \"Evelyn is a knave and Scarlett is a knave.\" William noted, \"Emily is a knave or Scarlett is a knight\". Avery told you that Jack is a knave. So who is a knight and who is a knave?", "names": ["Jack", "Emily", "Evelyn", "Ella", "Scarlett", "Jackson", "William", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, false, true, true], "solution_text": "Jack is a knave, Emily is a knave, Evelyn is a knight, Ella is a knave, Scarlett is a knight, Jackson is a knave, William is a knight, and Avery is a knight.", "solution_text_format": "(1) Jack is a knave\n(2) Emily is a knave\n(3) Evelyn is a knight\n(4) Ella is a knave\n(5) Scarlett is a knight\n(6) Jackson is a knave\n(7) William is a knight\n(8) Avery is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Evelyn is not a knight.", "Evelyn cannot be a knight, because this would contradict the claim of Jack that Evelyn is not a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that If Scarlett is a knave then Ella is a knight.", "Scarlett cannot be a knight, because this would contradict the false claim of Evelyn that If Scarlett is a knave then Ella is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that William is not a knave.", "William cannot be a knight, because this would contradict the false claim of Scarlett that William is not a knave.", "Assume William is a knave. No contradiction is found in their false claim that Emily is a knave or Scarlett is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that William is a knight if and only if Jackson is a knight.", "Jackson cannot be a knight, because this would contradict the claim of Emily that William is a knight if and only if Jackson is a knight.", "Jackson cannot be a knave, because this would contradict the false claim of their own that Evelyn is a knave and Scarlett is a knave.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the false claim of William that Emily is a knave or Scarlett is a knight.", "We have exhausted all possibilities for Emily, William, Scarlett, and Evelyn, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Evelyn is not a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Scarlett is a knave then Ella is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that William is not a knave.", "Assume William is a knight. No contradiction is found in their claim that Emily is a knave or Scarlett is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that William is a knight if and only if Jackson is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave and Scarlett is a knave.", "Jackson cannot be a knave, because this would contradict the claim of Emily that William is a knight if and only if Jackson is a knight.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that William is a knight if and only if Jackson is a knight.", "Jackson cannot be a knight, because this would contradict the false claim of Emily that William is a knight if and only if Jackson is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Evelyn is a knave and Scarlett is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Avery is a knave.", "Avery cannot be a knight, because this would contradict the claim of Ella that Avery is a knave.", "Avery cannot be a knave, because this would contradict the false claim of their own that Jack is a knave.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Avery is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Jack is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('<=>', ('telling-truth', 6), ('telling-truth', 5)), ('->', ('lying', 4), ('telling-truth', 3)), ('lying', 7), ('not', ('lying', 6)), ('and', ('lying', 2), ('lying', 4)), ('or', ('lying', 1), ('telling-truth', 4)), ('lying', 0))", "index": 134}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mason, Matthew, Chloe, Aurora, Liam, Michael, Victoria, and Daniel. Mason expressed that Aurora is a knave if and only if Aurora is a knight. \"If Chloe is a knave then Chloe is a knight,\" Matthew claimed. \"If Michael is a knight then Matthew is a knight,\" Chloe mentioned. \"Michael is not a knight,\" Aurora mentioned. Liam expressed that Victoria is a knight or Michael is a knight. Michael was heard saying, \"Chloe is a knave and Victoria is a knave\". Victoria said, \"Matthew is a knave if and only if Michael is a knight.\" Daniel asserted: \"If Michael is a knave then Chloe is a knight\". So who is a knight and who is a knave?", "names": ["Mason", "Matthew", "Chloe", "Aurora", "Liam", "Michael", "Victoria", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false, true, true], "solution_text": "Mason is a knave, Matthew is a knight, Chloe is a knight, Aurora is a knight, Liam is a knight, Michael is a knave, Victoria is a knight, and Daniel is a knight.", "solution_text_format": "(1) Mason is a knave\n(2) Matthew is a knight\n(3) Chloe is a knight\n(4) Aurora is a knight\n(5) Liam is a knight\n(6) Michael is a knave\n(7) Victoria is a knight\n(8) Daniel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Mason cannot be a knight, because this would contradict the claim of their own that Aurora is a knave if and only if Aurora is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Aurora is a knave if and only if Aurora is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Michael is not a knight.", "Michael cannot be a knight, because this would contradict the claim of Aurora that Michael is not a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Chloe is a knave and Victoria is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that If Michael is a knight then Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that If Chloe is a knave then Chloe is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Matthew is a knave if and only if Michael is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Victoria is a knight or Michael is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that If Michael is a knave then Chloe is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('telling-truth', 3)), ('->', ('lying', 2), ('telling-truth', 2)), ('->', ('telling-truth', 5), ('telling-truth', 1)), ('not', ('telling-truth', 5)), ('or', ('telling-truth', 6), ('telling-truth', 5)), ('and', ('lying', 2), ('lying', 6)), ('<=>', ('lying', 1), ('telling-truth', 5)), ('->', ('lying', 5), ('telling-truth', 2)))", "index": 135}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Grace, Liam, Abigail, Mason, Jacob, Henry, Avery, and Isabella. In Grace's words: \"Mason is a knight and Isabella is a knight\". \"If Avery is a knight then Henry is a knight\" - Liam. According to Abigail, \"Abigail is a knight or Avery is a knight\". Mason expressed that Liam is not a knave. Jacob said, \"Liam is a knave or Isabella is a knave.\" Henry commented, \"Mason is a knight and Abigail is a knave\". Avery noted, \"Henry is a knight if and only if Isabella is a knave\". As Isabella put it, \"Jacob is a knight if and only if Jacob is a knave\". So who is a knight and who is a knave?", "names": ["Grace", "Liam", "Abigail", "Mason", "Jacob", "Henry", "Avery", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false, false, false], "solution_text": "Grace is a knave, Liam is a knight, Abigail is a knight, Mason is a knight, Jacob is a knight, Henry is a knave, Avery is a knave, and Isabella is a knave.", "solution_text_format": "(1) Grace is a knave\n(2) Liam is a knight\n(3) Abigail is a knight\n(4) Mason is a knight\n(5) Jacob is a knight\n(6) Henry is a knave\n(7) Avery is a knave\n(8) Isabella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Mason is a knight and Isabella is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Liam is not a knave.", "Assume Liam is a knight. No contradiction is found in their claim that If Avery is a knight then Henry is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Henry is a knight if and only if Isabella is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Mason is a knight and Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Henry that Mason is a knight and Abigail is a knave.", "Abigail cannot be a knave, because this would contradict the false claim of their own that Abigail is a knight or Avery is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the claim of Liam that If Avery is a knight then Henry is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Henry is a knight if and only if Isabella is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Mason is a knight and Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Henry that Mason is a knight and Abigail is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Abigail is a knight or Avery is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Jacob is a knight if and only if Jacob is a knave.", "Isabella cannot be a knave, because this would contradict the claim of Grace that Mason is a knight and Isabella is a knight.", "We have exhausted all possibilities for Isabella and Abigail, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Mason is a knight and Abigail is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Abigail is a knight or Avery is a knight.", "Isabella cannot be a knight, because this would contradict the false claim of Avery that Henry is a knight if and only if Isabella is a knave.", "Isabella cannot be a knave, because this would contradict the claim of Grace that Mason is a knight and Isabella is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the false claim of Henry that Mason is a knight and Abigail is a knave.", "We have exhausted all possibilities for Abigail, Henry, and Avery, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the claim of Mason that Liam is not a knave.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Mason.", "Mason cannot be a knave, because this would contradict the claim of Grace that Mason is a knight and Isabella is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Mason is a knight and Isabella is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Liam is not a knave.", "Assume Liam is a knight. No contradiction is found in their claim that If Avery is a knight then Henry is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Henry is a knight if and only if Isabella is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Mason is a knight and Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Henry that Mason is a knight and Abigail is a knave.", "Abigail cannot be a knave, because this would contradict the false claim of their own that Abigail is a knight or Avery is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the claim of Liam that If Avery is a knight then Henry is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Henry is a knight if and only if Isabella is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Mason is a knight and Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Henry that Mason is a knight and Abigail is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Abigail is a knight or Avery is a knight.", "Isabella cannot be a knight, because this would contradict the false claim of Grace that Mason is a knight and Isabella is a knight.", "Isabella cannot be a knave, because this would contradict the false claim of Avery that Henry is a knight if and only if Isabella is a knave.", "We have exhausted all possibilities for Isabella and Abigail, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Mason is a knight and Abigail is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Abigail is a knight or Avery is a knight.", "Isabella cannot be a knight, because this would contradict the false claim of Grace that Mason is a knight and Isabella is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Jacob is a knight if and only if Jacob is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Liam is a knave or Isabella is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('telling-truth', 7)), ('->', ('telling-truth', 6), ('telling-truth', 5)), ('or', ('telling-truth', 2), ('telling-truth', 6)), ('not', ('lying', 1)), ('or', ('lying', 1), ('lying', 7)), ('and', ('telling-truth', 3), ('lying', 2)), ('<=>', ('telling-truth', 5), ('lying', 7)), ('<=>', ('telling-truth', 4), ('lying', 4)))", "index": 136}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Samuel, Amelia, Alexander, Ava, James, Aiden, Michael, and Olivia. \"James is a knave if and only if Alexander is a knight,\" Samuel mentioned. Amelia asserted: \"Alexander is a knave and Aiden is a knight\". In Alexander's words: \"Michael is a knave if and only if Samuel is a knave\". Ava told you that If Aiden is a knight then Amelia is a knight. \"Alexander is not a knight\" - James. Aiden noted, \"Olivia is a knave if and only if Ava is a knight\". Michael commented, \"Ava is a knight and Olivia is a knave\". Olivia expressed that Alexander is a knave or James is a knave. So who is a knight and who is a knave?", "names": ["Samuel", "Amelia", "Alexander", "Ava", "James", "Aiden", "Michael", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false, false, true], "solution_text": "Samuel is a knight, Amelia is a knave, Alexander is a knave, Ava is a knight, James is a knight, Aiden is a knave, Michael is a knave, and Olivia is a knight.", "solution_text_format": "(1) Samuel is a knight\n(2) Amelia is a knave\n(3) Alexander is a knave\n(4) Ava is a knight\n(5) James is a knight\n(6) Aiden is a knave\n(7) Michael is a knave\n(8) Olivia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that James is a knave if and only if Alexander is a knight.", "Assume James is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of Samuel that James is a knave if and only if Alexander is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Michael is a knave if and only if Samuel is a knave.", "Michael cannot be a knight, because this would contradict the false claim of Alexander that Michael is a knave if and only if Samuel is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Ava is a knight and Olivia is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that If Aiden is a knight then Amelia is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Olivia is a knave if and only if Ava is a knight.", "Olivia cannot be a knight, because this would contradict the claim of Aiden that Olivia is a knave if and only if Ava is a knight.", "Olivia cannot be a knave, because this would contradict the false claim of Michael that Ava is a knight and Olivia is a knave.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Olivia is a knave if and only if Ava is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Alexander is a knave or James is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Alexander is a knave and Aiden is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Alexander is a knave and Aiden is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 4), ('telling-truth', 2)), ('and', ('lying', 2), ('telling-truth', 5)), ('<=>', ('lying', 6), ('lying', 0)), ('->', ('telling-truth', 5), ('telling-truth', 1)), ('not', ('telling-truth', 2)), ('<=>', ('lying', 7), ('telling-truth', 3)), ('and', ('telling-truth', 3), ('lying', 7)), ('or', ('lying', 2), ('lying', 4)))", "index": 137}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Scarlett, Chloe, Elizabeth, Aurora, Amelia, Sophia, Isabella, and Aria. Scarlett commented, \"Aria is a knave and Aurora is a knave\". Chloe asserted: \"Amelia is not a knight\". Elizabeth was heard saying, \"Isabella is a knave and Sophia is a knave\". Aurora noted, \"Chloe is a knight and Aria is a knight\". \"Aurora is a knave,\" Amelia claimed. Sophia told you that Aurora is not a knight. Isabella commented, \"Amelia is a knave and Elizabeth is a knight\". Aria remarked, \"Sophia is not a knight\". So who is a knight and who is a knave?", "names": ["Scarlett", "Chloe", "Elizabeth", "Aurora", "Amelia", "Sophia", "Isabella", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true, false, false], "solution_text": "Scarlett is a knight, Chloe is a knave, Elizabeth is a knave, Aurora is a knave, Amelia is a knight, Sophia is a knight, Isabella is a knave, and Aria is a knave.", "solution_text_format": "(1) Scarlett is a knight\n(2) Chloe is a knave\n(3) Elizabeth is a knave\n(4) Aurora is a knave\n(5) Amelia is a knight\n(6) Sophia is a knight\n(7) Isabella is a knave\n(8) Aria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Aria is a knave and Aurora is a knave.", "Aria cannot be a knight, because this would contradict the claim of Scarlett that Aria is a knave and Aurora is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Sophia is not a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Aurora is not a knight.", "Aurora cannot be a knight, because this would contradict the claim of Scarlett that Aria is a knave and Aurora is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Chloe is a knight and Aria is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Amelia is not a knight.", "Amelia cannot be a knight, because this would contradict the claim of Chloe that Amelia is not a knight.", "Amelia cannot be a knave, because this would contradict the false claim of their own that Aurora is a knave.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Amelia is not a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Aurora is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Isabella is a knave and Sophia is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Isabella is a knave and Sophia is a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that Amelia is a knave and Elizabeth is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Amelia is a knave and Elizabeth is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 7), ('lying', 3)), ('not', ('telling-truth', 4)), ('and', ('lying', 6), ('lying', 5)), ('and', ('telling-truth', 1), ('telling-truth', 7)), ('lying', 3), ('not', ('telling-truth', 3)), ('and', ('lying', 4), ('telling-truth', 2)), ('not', ('telling-truth', 5)))", "index": 138}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mia, Luke, Victoria, Harper, Sophia, Zoey, Lily, and Avery. \"Victoria is a knave or Avery is a knave\" - Mia. Luke stated, \"Harper is a knight or Mia is a knight\". Victoria remarked, \"Lily is a knight\". Harper told you that Zoey is not a knave. Sophia said that Zoey is a knave and Victoria is a knight. \"Lily is not a knave\" - Zoey. In a statement by Lily: \"If Sophia is a knight then Victoria is a knight\". As Avery put it, \"Zoey is a knave\". So who is a knight and who is a knave?", "names": ["Mia", "Luke", "Victoria", "Harper", "Sophia", "Zoey", "Lily", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true, true, false], "solution_text": "Mia is a knight, Luke is a knight, Victoria is a knight, Harper is a knight, Sophia is a knave, Zoey is a knight, Lily is a knight, and Avery is a knave.", "solution_text_format": "(1) Mia is a knight\n(2) Luke is a knight\n(3) Victoria is a knight\n(4) Harper is a knight\n(5) Sophia is a knave\n(6) Zoey is a knight\n(7) Lily is a knight\n(8) Avery is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Victoria is a knave or Avery is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Lily is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that If Sophia is a knight then Victoria is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Zoey is a knave and Victoria is a knight.", "Zoey cannot be a knight, because this would contradict the claim of Sophia that Zoey is a knave and Victoria is a knight.", "Zoey cannot be a knave, because this would contradict the false claim of their own that Lily is not a knave.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Zoey is a knave and Victoria is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Lily is not a knave.", "Avery cannot be a knight, because this would contradict the claim of Mia that Victoria is a knave or Avery is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Zoey is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Harper is a knight or Mia is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Zoey is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('lying', 7)), ('or', ('telling-truth', 3), ('telling-truth', 0)), ('telling-truth', 6), ('not', ('lying', 5)), ('and', ('lying', 5), ('telling-truth', 2)), ('not', ('lying', 6)), ('->', ('telling-truth', 4), ('telling-truth', 2)), ('lying', 5))", "index": 139}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: William, Evelyn, Sebastian, Alexander, Matthew, Isabella, Zoey, and Jack. William noted, \"Matthew is a knight if and only if Sebastian is a knave\". \"Jack is a knave or Zoey is a knave\" - Evelyn. \"Matthew is a knave,\" Sebastian mentioned. Alexander commented, \"Evelyn is not a knave\". Matthew noted, \"William is a knave or Alexander is a knave\". Isabella noted, \"Alexander is a knight or William is a knight\". Zoey expressed that William is a knight or Evelyn is a knave. \"Sebastian is a knight and Evelyn is a knave,\" Jack mentioned. So who is a knight and who is a knave?", "names": ["William", "Evelyn", "Sebastian", "Alexander", "Matthew", "Isabella", "Zoey", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true, true, false], "solution_text": "William is a knight, Evelyn is a knight, Sebastian is a knight, Alexander is a knight, Matthew is a knave, Isabella is a knight, Zoey is a knight, and Jack is a knave.", "solution_text_format": "(1) William is a knight\n(2) Evelyn is a knight\n(3) Sebastian is a knight\n(4) Alexander is a knight\n(5) Matthew is a knave\n(6) Isabella is a knight\n(7) Zoey is a knight\n(8) Jack is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Matthew is a knight if and only if Sebastian is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that William is a knave or Alexander is a knave.", "Alexander cannot be a knight, because this would contradict the claim of Matthew that William is a knave or Alexander is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Evelyn is not a knave.", "Evelyn cannot be a knight, because this would contradict the false claim of Alexander that Evelyn is not a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Jack is a knave or Zoey is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Sebastian is a knight and Evelyn is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of William that Matthew is a knight if and only if Sebastian is a knave.", "Sebastian cannot be a knave, because this would contradict the claim of Jack that Sebastian is a knight and Evelyn is a knave.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the false claim of Evelyn that Jack is a knave or Zoey is a knave.", "We have exhausted all possibilities for Jack, Evelyn, and Alexander, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that William is a knave or Alexander is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Evelyn is not a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Jack is a knave or Zoey is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight and Evelyn is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Sebastian is a knight and Evelyn is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Matthew is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that William is a knight or Evelyn is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Alexander is a knight or William is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 4), ('lying', 2)), ('or', ('lying', 7), ('lying', 6)), ('lying', 4), ('not', ('lying', 1)), ('or', ('lying', 0), ('lying', 3)), ('or', ('telling-truth', 3), ('telling-truth', 0)), ('or', ('telling-truth', 0), ('lying', 1)), ('and', ('telling-truth', 2), ('lying', 1)))", "index": 140}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aria, Logan, Noah, Liam, Sofia, Emily, Joseph, and Sophia. In Aria's words: \"Emily is a knight and Joseph is a knight\". As Logan put it, \"Aria is a knight or Joseph is a knight\". As Noah put it, \"Sofia is a knave or Sofia is a knight\". Liam told you that Noah is a knight. \"Liam is a knave,\" Sofia mentioned. \"Noah is not a knave\" - Emily. As Joseph put it, \"Emily is a knave and Logan is a knight\". Sophia told you that If Logan is a knave then Logan is a knight. So who is a knight and who is a knave?", "names": ["Aria", "Logan", "Noah", "Liam", "Sofia", "Emily", "Joseph", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, true, false, false], "solution_text": "Aria is a knave, Logan is a knave, Noah is a knight, Liam is a knight, Sofia is a knave, Emily is a knight, Joseph is a knave, and Sophia is a knave.", "solution_text_format": "(1) Aria is a knave\n(2) Logan is a knave\n(3) Noah is a knight\n(4) Liam is a knight\n(5) Sofia is a knave\n(6) Emily is a knight\n(7) Joseph is a knave\n(8) Sophia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that Emily is a knight and Joseph is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Noah is not a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Sofia is a knave or Sofia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of Sofia that Liam is a knave.", "Liam cannot be a knave, because this would contradict the false claim of their own that Noah is a knight.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Liam is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Noah is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Emily is a knave and Logan is a knight.", "Joseph cannot be a knave, because this would contradict the claim of Aria that Emily is a knight and Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the false claim of their own that Noah is a knight.", "We have exhausted all possibilities for Liam and Sofia, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the false claim of their own that Sofia is a knave or Sofia is a knight.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the claim of Aria that Emily is a knight and Joseph is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Emily is a knight and Joseph is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Noah is not a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Sofia is a knave or Sofia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of Sofia that Liam is a knave.", "Liam cannot be a knave, because this would contradict the false claim of their own that Noah is a knight.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Liam is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Noah is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of Aria that Emily is a knight and Joseph is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Emily is a knave and Logan is a knight.", "Logan cannot be a knight, because this would contradict the claim of their own that Aria is a knight or Joseph is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Aria is a knight or Joseph is a knight.", "Sophia cannot be a knight, because this would contradict the claim of their own that If Logan is a knave then Logan is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that If Logan is a knave then Logan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('telling-truth', 6)), ('or', ('telling-truth', 0), ('telling-truth', 6)), ('or', ('lying', 4), ('telling-truth', 4)), ('telling-truth', 2), ('lying', 3), ('not', ('lying', 2)), ('and', ('lying', 5), ('telling-truth', 1)), ('->', ('lying', 1), ('telling-truth', 1)))", "index": 141}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Evelyn, Chloe, Joseph, Harper, Aiden, Aria, Riley, and Mia. \"Aria is a knave or Mia is a knight\" - Evelyn. Chloe expressed that Riley is not a knave. \"Harper is not a knave,\" Joseph claimed. Harper commented, \"If Riley is a knight then Mia is a knave\". In a statement by Aiden: \"Harper is a knight or Mia is a knight\". \"If Riley is a knight then Harper is a knave,\" Aria mentioned. Riley noted, \"Chloe is a knight and Joseph is a knave\". Mia said, \"Aria is not a knight.\" So who is a knight and who is a knave?", "names": ["Evelyn", "Chloe", "Joseph", "Harper", "Aiden", "Aria", "Riley", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true, false, false], "solution_text": "Evelyn is a knave, Chloe is a knave, Joseph is a knight, Harper is a knight, Aiden is a knight, Aria is a knight, Riley is a knave, and Mia is a knave.", "solution_text_format": "(1) Evelyn is a knave\n(2) Chloe is a knave\n(3) Joseph is a knight\n(4) Harper is a knight\n(5) Aiden is a knight\n(6) Aria is a knight\n(7) Riley is a knave\n(8) Mia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Aria is a knave or Mia is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that If Riley is a knight then Harper is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Chloe is a knight and Joseph is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Riley is not a knave.", "Joseph cannot be a knight, because this would contradict the claim of Riley that Chloe is a knight and Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Harper is not a knave.", "Harper cannot be a knight, because this would contradict the false claim of Joseph that Harper is not a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that If Riley is a knight then Mia is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Aria is not a knight.", "Mia cannot be a knave, because this would contradict the claim of Evelyn that Aria is a knave or Mia is a knight.", "We have exhausted all possibilities for Mia, Harper, and Joseph, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the false claim of their own that Riley is not a knave.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Chloe is a knight and Joseph is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Riley is not a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Riley is not a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Harper is not a knave.", "Assume Harper is a knight. No contradiction is found in their claim that If Riley is a knight then Mia is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Aria is not a knight.", "Mia cannot be a knave, because this would contradict the claim of Evelyn that Aria is a knave or Mia is a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the claim of Joseph that Harper is not a knave.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Harper is not a knave.", "Harper cannot be a knight, because this would contradict the false claim of Joseph that Harper is not a knave.", "Harper cannot be a knave, because this would contradict the false claim of their own that If Riley is a knight then Mia is a knave.", "We have exhausted all possibilities for Harper, Joseph, Chloe, and Riley, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that If Riley is a knight then Harper is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Chloe is a knight and Joseph is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Riley is not a knave.", "Joseph cannot be a knight, because this would contradict the claim of Riley that Chloe is a knight and Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Harper is not a knave.", "Harper cannot be a knight, because this would contradict the false claim of Joseph that Harper is not a knave.", "Harper cannot be a knave, because this would contradict the false claim of Aria that If Riley is a knight then Harper is a knave.", "We have exhausted all possibilities for Harper and Joseph, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the false claim of their own that Riley is not a knave.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Riley.", "Riley cannot be a knave, because this would contradict the false claim of Aria that If Riley is a knight then Harper is a knave.", "We have exhausted all possibilities for Riley and Aria, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Aria is a knave or Mia is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that If Riley is a knight then Harper is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Chloe is a knight and Joseph is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Riley is not a knave.", "Joseph cannot be a knight, because this would contradict the claim of Riley that Chloe is a knight and Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Harper is not a knave.", "Harper cannot be a knight, because this would contradict the false claim of Joseph that Harper is not a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that If Riley is a knight then Mia is a knave.", "Mia cannot be a knight, because this would contradict the false claim of Evelyn that Aria is a knave or Mia is a knight.", "Mia cannot be a knave, because this would contradict the false claim of Harper that If Riley is a knight then Mia is a knave.", "We have exhausted all possibilities for Mia, Harper, and Joseph, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the false claim of their own that Riley is not a knave.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Chloe is a knight and Joseph is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Riley is not a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Riley is not a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Harper is not a knave.", "Assume Harper is a knight. No contradiction is found in their claim that If Riley is a knight then Mia is a knave.", "Mia cannot be a knight, because this would contradict the false claim of Evelyn that Aria is a knave or Mia is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Aria is not a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Harper is a knight or Mia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 5), ('telling-truth', 7)), ('not', ('lying', 6)), ('not', ('lying', 3)), ('->', ('telling-truth', 6), ('lying', 7)), ('or', ('telling-truth', 3), ('telling-truth', 7)), ('->', ('telling-truth', 6), ('lying', 3)), ('and', ('telling-truth', 1), ('lying', 2)), ('not', ('telling-truth', 5)))", "index": 142}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sophia, Henry, Liam, Aiden, Abigail, Jackson, Mia, and Jacob. \"Sophia is a knight and Jacob is a knight\" - Sophia. Henry said that If Jacob is a knight then Liam is a knave. Liam stated, \"Abigail is a knave and Mia is a knight\". Aiden asserted: \"Henry is a knight if and only if Jackson is a knave\". Abigail told you that If Sophia is a knight then Mia is a knight. In Jackson's words: \"Sophia is a knave or Aiden is a knight\". Mia was heard saying, \"Liam is a knight and Abigail is a knave\". Jacob was heard saying, \"Aiden is not a knave\". So who is a knight and who is a knave?", "names": ["Sophia", "Henry", "Liam", "Aiden", "Abigail", "Jackson", "Mia", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true, false, false], "solution_text": "Sophia is a knave, Henry is a knight, Liam is a knave, Aiden is a knave, Abigail is a knight, Jackson is a knight, Mia is a knave, and Jacob is a knave.", "solution_text_format": "(1) Sophia is a knave\n(2) Henry is a knight\n(3) Liam is a knave\n(4) Aiden is a knave\n(5) Abigail is a knight\n(6) Jackson is a knight\n(7) Mia is a knave\n(8) Jacob is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Sophia is a knight and Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Aiden is not a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Henry is a knight if and only if Jackson is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Jacob is a knight then Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of Henry that If Jacob is a knight then Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Abigail is a knave and Mia is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If Sophia is a knight then Mia is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that Liam is a knight and Abigail is a knave.", "Mia cannot be a knave, because this would contradict the claim of Abigail that If Sophia is a knight then Mia is a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that If Sophia is a knight then Mia is a knight.", "Mia cannot be a knight, because this would contradict the false claim of Liam that Abigail is a knave and Mia is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Liam is a knight and Abigail is a knave.", "Jackson cannot be a knight, because this would contradict the claim of Aiden that Henry is a knight if and only if Jackson is a knave.", "Jackson cannot be a knave, because this would contradict the false claim of their own that Sophia is a knave or Aiden is a knight.", "We have exhausted all possibilities for Jackson, Mia, Abigail, and Liam, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that If Jacob is a knight then Liam is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Abigail is a knave and Mia is a knight.", "Abigail cannot be a knight, because this would contradict the claim of Liam that Abigail is a knave and Mia is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that If Sophia is a knight then Mia is a knight.", "Mia cannot be a knight, because this would contradict the false claim of Abigail that If Sophia is a knight then Mia is a knight.", "Mia cannot be a knave, because this would contradict the claim of Liam that Abigail is a knave and Mia is a knight.", "We have exhausted all possibilities for Mia and Abigail, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the false claim of Henry that If Jacob is a knight then Liam is a knave.", "We have exhausted all possibilities for Liam and Henry, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the claim of Jacob that Aiden is not a knave.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the claim of Sophia that Sophia is a knight and Jacob is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Sophia is a knight and Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Aiden is not a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Henry is a knight if and only if Jackson is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Jacob is a knight then Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of Henry that If Jacob is a knight then Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Abigail is a knave and Mia is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If Sophia is a knight then Mia is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that Liam is a knight and Abigail is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Liam is a knight and Abigail is a knave.", "Jackson cannot be a knight, because this would contradict the claim of Aiden that Henry is a knight if and only if Jackson is a knave.", "Jackson cannot be a knave, because this would contradict the false claim of their own that Sophia is a knave or Aiden is a knight.", "We have exhausted all possibilities for Jackson and Mia, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the false claim of their own that If Sophia is a knight then Mia is a knight.", "We have exhausted all possibilities for Abigail and Liam, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that If Jacob is a knight then Liam is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Abigail is a knave and Mia is a knight.", "Abigail cannot be a knight, because this would contradict the claim of Liam that Abigail is a knave and Mia is a knight.", "Abigail cannot be a knave, because this would contradict the false claim of their own that If Sophia is a knight then Mia is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the false claim of Henry that If Jacob is a knight then Liam is a knave.", "We have exhausted all possibilities for Liam and Henry, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the claim of Jacob that Aiden is not a knave.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Aiden is not a knave.", "Aiden cannot be a knight, because this would contradict the false claim of Jacob that Aiden is not a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Henry is a knight if and only if Jackson is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Jacob is a knight then Liam is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Abigail is a knave and Mia is a knight.", "Abigail cannot be a knight, because this would contradict the claim of Liam that Abigail is a knave and Mia is a knight.", "Abigail cannot be a knave, because this would contradict the false claim of their own that If Sophia is a knight then Mia is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Abigail is a knave and Mia is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If Sophia is a knight then Mia is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that Liam is a knight and Abigail is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Liam is a knight and Abigail is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Sophia is a knave or Aiden is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 0), ('telling-truth', 7)), ('->', ('telling-truth', 7), ('lying', 2)), ('and', ('lying', 4), ('telling-truth', 6)), ('<=>', ('telling-truth', 1), ('lying', 5)), ('->', ('telling-truth', 0), ('telling-truth', 6)), ('or', ('lying', 0), ('telling-truth', 3)), ('and', ('telling-truth', 2), ('lying', 4)), ('not', ('lying', 3)))", "index": 143}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Olivia, Harper, Aiden, Ella, Michael, Amelia, Benjamin, and Oliver. Olivia stated, \"Oliver is a knight\". Harper asserted: \"Michael is not a knight\". In Aiden's words: \"Amelia is a knight and Olivia is a knave\". In Ella's words: \"Harper is a knight or Olivia is a knight\". In a statement by Michael: \"Aiden is a knave if and only if Oliver is a knight\". In Amelia's words: \"Ella is not a knight\". Benjamin expressed that Ella is a knave and Olivia is a knight. \"Oliver is a knight if and only if Aiden is a knight,\" Oliver claimed. So who is a knight and who is a knave?", "names": ["Olivia", "Harper", "Aiden", "Ella", "Michael", "Amelia", "Benjamin", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true, false, false], "solution_text": "Olivia is a knave, Harper is a knave, Aiden is a knight, Ella is a knave, Michael is a knight, Amelia is a knight, Benjamin is a knave, and Oliver is a knave.", "solution_text_format": "(1) Olivia is a knave\n(2) Harper is a knave\n(3) Aiden is a knight\n(4) Ella is a knave\n(5) Michael is a knight\n(6) Amelia is a knight\n(7) Benjamin is a knave\n(8) Oliver is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Oliver is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Oliver is a knight if and only if Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Amelia is a knight and Olivia is a knave.", "Aiden cannot be a knave, because this would contradict the claim of Oliver that Oliver is a knight if and only if Aiden is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the claim of Olivia that Oliver is a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Oliver is a knight.", "Oliver cannot be a knight, because this would contradict the false claim of Olivia that Oliver is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Oliver is a knight if and only if Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Amelia is a knight and Olivia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Ella is not a knight.", "Ella cannot be a knight, because this would contradict the claim of Amelia that Ella is not a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Harper is a knight or Olivia is a knight.", "Harper cannot be a knight, because this would contradict the false claim of Ella that Harper is a knight or Olivia is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Michael is not a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Aiden is a knave if and only if Oliver is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Ella is a knave and Olivia is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Ella is a knave and Olivia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 7), ('not', ('telling-truth', 4)), ('and', ('telling-truth', 5), ('lying', 0)), ('or', ('telling-truth', 1), ('telling-truth', 0)), ('<=>', ('lying', 2), ('telling-truth', 7)), ('not', ('telling-truth', 3)), ('and', ('lying', 3), ('telling-truth', 0)), ('<=>', ('telling-truth', 7), ('telling-truth', 2)))", "index": 144}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Alexander, Luke, Henry, Abigail, Elizabeth, Michael, Isabella, and Grace. Alexander said, \"Grace is a knight or Isabella is a knave.\" In a statement by Luke: \"Henry is a knight\". Henry asserted: \"If Grace is a knight then Abigail is a knight\". Abigail commented, \"Elizabeth is a knave and Henry is a knave\". Elizabeth told you that Isabella is a knight. Michael expressed that Luke is a knight if and only if Grace is a knave. Isabella commented, \"Michael is a knight or Isabella is a knight\". Grace said, \"Michael is a knight or Abigail is a knave.\" So who is a knight and who is a knave?", "names": ["Alexander", "Luke", "Henry", "Abigail", "Elizabeth", "Michael", "Isabella", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true, true, true], "solution_text": "Alexander is a knight, Luke is a knave, Henry is a knave, Abigail is a knave, Elizabeth is a knight, Michael is a knight, Isabella is a knight, and Grace is a knight.", "solution_text_format": "(1) Alexander is a knight\n(2) Luke is a knave\n(3) Henry is a knave\n(4) Abigail is a knave\n(5) Elizabeth is a knight\n(6) Michael is a knight\n(7) Isabella is a knight\n(8) Grace is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that Grace is a knight or Isabella is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Michael is a knight or Abigail is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Luke is a knight if and only if Grace is a knave.", "Luke cannot be a knight, because this would contradict the claim of Michael that Luke is a knight if and only if Grace is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Henry is a knight.", "Henry cannot be a knight, because this would contradict the false claim of Luke that Henry is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that If Grace is a knight then Abigail is a knight.", "Abigail cannot be a knight, because this would contradict the false claim of Henry that If Grace is a knight then Abigail is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Elizabeth is a knave and Henry is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Isabella is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Michael is a knight or Isabella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 7), ('lying', 6)), ('telling-truth', 2), ('->', ('telling-truth', 7), ('telling-truth', 3)), ('and', ('lying', 4), ('lying', 2)), ('telling-truth', 6), ('<=>', ('telling-truth', 1), ('lying', 7)), ('or', ('telling-truth', 5), ('telling-truth', 6)), ('or', ('telling-truth', 5), ('lying', 3)))", "index": 145}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Grace, Zoey, Charlotte, Riley, Evelyn, Michael, Joseph, and James. Grace said that If James is a knight then Charlotte is a knave. As Zoey put it, \"Joseph is a knight or James is a knave\". Charlotte was heard saying, \"Zoey is a knight\". As Riley put it, \"Zoey is a knight or Michael is a knave\". Evelyn expressed that James is not a knave. In a statement by Michael: \"Riley is a knave if and only if Charlotte is a knight\". Joseph told you that Michael is a knave and James is a knight. James was heard saying, \"Zoey is a knight\". So who is a knight and who is a knave?", "names": ["Grace", "Zoey", "Charlotte", "Riley", "Evelyn", "Michael", "Joseph", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false, true, true], "solution_text": "Grace is a knave, Zoey is a knight, Charlotte is a knight, Riley is a knight, Evelyn is a knight, Michael is a knave, Joseph is a knight, and James is a knight.", "solution_text_format": "(1) Grace is a knave\n(2) Zoey is a knight\n(3) Charlotte is a knight\n(4) Riley is a knight\n(5) Evelyn is a knight\n(6) Michael is a knave\n(7) Joseph is a knight\n(8) James is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that If James is a knight then Charlotte is a knave.", "Assume James is a knight. No contradiction is found in their claim that Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Joseph is a knight or James is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Michael is a knave and James is a knight.", "Michael cannot be a knight, because this would contradict the claim of Joseph that Michael is a knave and James is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Riley is a knave if and only if Charlotte is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Zoey is a knight or Michael is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Grace that If James is a knight then Charlotte is a knave.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that Zoey is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Riley.", "Riley cannot be a knave, because this would contradict the false claim of their own that Zoey is a knight or Michael is a knave.", "We have exhausted all possibilities for Riley and Michael, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of Zoey that Joseph is a knight or James is a knave.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Zoey.", "Zoey cannot be a knave, because this would contradict the claim of James that Zoey is a knight.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Zoey is a knight.", "Zoey cannot be a knight, because this would contradict the false claim of James that Zoey is a knight.", "Zoey cannot be a knave, because this would contradict the false claim of their own that Joseph is a knight or James is a knave.", "We have exhausted all possibilities for Zoey and James, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that If James is a knight then Charlotte is a knave.", "Assume James is a knight. No contradiction is found in their claim that Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Joseph is a knight or James is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Michael is a knave and James is a knight.", "Michael cannot be a knight, because this would contradict the claim of Joseph that Michael is a knave and James is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Riley is a knave if and only if Charlotte is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Zoey is a knight or Michael is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Zoey is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that James is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 7), ('lying', 2)), ('or', ('telling-truth', 6), ('lying', 7)), ('telling-truth', 1), ('or', ('telling-truth', 1), ('lying', 5)), ('not', ('lying', 7)), ('<=>', ('lying', 3), ('telling-truth', 2)), ('and', ('lying', 5), ('telling-truth', 7)), ('telling-truth', 1))", "index": 146}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Riley, Evelyn, Avery, Isabella, Aiden, Ethan, Grace, and Charlotte. In a statement by Riley: \"Grace is not a knave\". As Evelyn put it, \"Isabella is not a knight\". Avery told you that Evelyn is not a knight. \"If Charlotte is a knight then Ethan is a knave,\" Isabella declared. Aiden asserted: \"Avery is a knave if and only if Charlotte is a knave\". Ethan commented, \"If Riley is a knave then Grace is a knight\". Grace remarked, \"Ethan is a knight and Evelyn is a knight\". Charlotte stated, \"If Ethan is a knight then Ethan is a knave\". So who is a knight and who is a knave?", "names": ["Riley", "Evelyn", "Avery", "Isabella", "Aiden", "Ethan", "Grace", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false, false, true], "solution_text": "Riley is a knave, Evelyn is a knave, Avery is a knight, Isabella is a knight, Aiden is a knight, Ethan is a knave, Grace is a knave, and Charlotte is a knight.", "solution_text_format": "(1) Riley is a knave\n(2) Evelyn is a knave\n(3) Avery is a knight\n(4) Isabella is a knight\n(5) Aiden is a knight\n(6) Ethan is a knave\n(7) Grace is a knave\n(8) Charlotte is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Grace is not a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Ethan is a knight and Evelyn is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If Riley is a knave then Grace is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Isabella is not a knight.", "Isabella cannot be a knight, because this would contradict the claim of Evelyn that Isabella is not a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that If Charlotte is a knight then Ethan is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that If Ethan is a knight then Ethan is a knave.", "Charlotte cannot be a knave, because this would contradict the false claim of Isabella that If Charlotte is a knight then Ethan is a knave.", "We have exhausted all possibilities for Charlotte and Isabella, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the claim of Grace that Ethan is a knight and Evelyn is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the false claim of their own that If Riley is a knave then Grace is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Grace.", "Grace cannot be a knave, because this would contradict the claim of Riley that Grace is not a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Grace is not a knave.", "Grace cannot be a knight, because this would contradict the false claim of Riley that Grace is not a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Ethan is a knight and Evelyn is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that If Riley is a knave then Grace is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that If Riley is a knave then Grace is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Isabella is not a knight.", "Isabella cannot be a knight, because this would contradict the claim of Evelyn that Isabella is not a knight.", "Isabella cannot be a knave, because this would contradict the false claim of their own that If Charlotte is a knight then Ethan is a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Isabella is not a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that If Charlotte is a knight then Ethan is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Ethan is a knight then Ethan is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Evelyn is not a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Avery is a knave if and only if Charlotte is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 6)), ('not', ('telling-truth', 3)), ('not', ('telling-truth', 1)), ('->', ('telling-truth', 7), ('lying', 5)), ('<=>', ('lying', 2), ('lying', 7)), ('->', ('lying', 0), ('telling-truth', 6)), ('and', ('telling-truth', 5), ('telling-truth', 1)), ('->', ('telling-truth', 5), ('lying', 5)))", "index": 147}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Liam, William, Penelope, Luke, Sofia, David, Joseph, and Lily. Liam commented, \"Luke is not a knight\". In a statement by William: \"Liam is a knight if and only if David is a knave\". Penelope said that Sofia is a knave if and only if Joseph is a knave. \"Penelope is a knight and David is a knight,\" Luke claimed. Sofia was heard saying, \"If Penelope is a knight then Lily is a knave\". David said, \"If Liam is a knave then David is a knight.\" Joseph said that Sofia is not a knight. \"If William is a knave then Joseph is a knave\" - Lily. So who is a knight and who is a knave?", "names": ["Liam", "William", "Penelope", "Luke", "Sofia", "David", "Joseph", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true, false, true], "solution_text": "Liam is a knight, William is a knave, Penelope is a knave, Luke is a knave, Sofia is a knight, David is a knight, Joseph is a knave, and Lily is a knight.", "solution_text_format": "(1) Liam is a knight\n(2) William is a knave\n(3) Penelope is a knave\n(4) Luke is a knave\n(5) Sofia is a knight\n(6) David is a knight\n(7) Joseph is a knave\n(8) Lily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Luke is not a knight.", "Luke cannot be a knight, because this would contradict the claim of Liam that Luke is not a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Penelope is a knight and David is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Sofia is a knave if and only if Joseph is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that If Penelope is a knight then Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of Sofia that If Penelope is a knight then Lily is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that If William is a knave then Joseph is a knave.", "William cannot be a knight, because this would contradict the false claim of Lily that If William is a knave then Joseph is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Liam is a knight if and only if David is a knave.", "David cannot be a knight, because this would contradict the false claim of Luke that Penelope is a knight and David is a knight.", "David cannot be a knave, because this would contradict the false claim of William that Liam is a knight if and only if David is a knave.", "We have exhausted all possibilities for David, William, and Lily, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that If Penelope is a knight then Lily is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that If William is a knave then Joseph is a knave.", "Assume William is a knight. No contradiction is found in their claim that Liam is a knight if and only if David is a knave.", "David cannot be a knight, because this would contradict the claim of William that Liam is a knight if and only if David is a knave.", "David cannot be a knave, because this would contradict the false claim of their own that If Liam is a knave then David is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Liam is a knight if and only if David is a knave.", "David cannot be a knight, because this would contradict the false claim of Luke that Penelope is a knight and David is a knight.", "David cannot be a knave, because this would contradict the false claim of William that Liam is a knight if and only if David is a knave.", "We have exhausted all possibilities for David and William, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the false claim of Sofia that If Penelope is a knight then Lily is a knave.", "We have exhausted all possibilities for Lily and Sofia, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Sofia is a knave if and only if Joseph is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that If Penelope is a knight then Lily is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that If William is a knave then Joseph is a knave.", "Assume William is a knight. No contradiction is found in their claim that Liam is a knight if and only if David is a knave.", "David cannot be a knight, because this would contradict the claim of William that Liam is a knight if and only if David is a knave.", "David cannot be a knave, because this would contradict the false claim of their own that If Liam is a knave then David is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Liam is a knight if and only if David is a knave.", "Assume David is a knight. No contradiction is found in their claim that If Liam is a knave then David is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of Penelope that Sofia is a knave if and only if Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Sofia is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 3)), ('<=>', ('telling-truth', 0), ('lying', 5)), ('<=>', ('lying', 4), ('lying', 6)), ('and', ('telling-truth', 2), ('telling-truth', 5)), ('->', ('telling-truth', 2), ('lying', 7)), ('->', ('lying', 0), ('telling-truth', 5)), ('not', ('telling-truth', 4)), ('->', ('lying', 1), ('lying', 6)))", "index": 148}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Scarlett, William, Alexander, Jack, James, Jackson, Ella, and Olivia. Scarlett commented, \"Jack is a knight or Ella is a knave\". According to William, \"William is a knight and Ella is a knight\". Alexander was heard saying, \"Jackson is a knave and James is a knave\". In Jack's words: \"If Ella is a knight then Jackson is a knave\". James commented, \"Jack is not a knave\". Jackson expressed that William is not a knave. Ella told you that Jack is not a knave. In a statement by Olivia: \"James is a knave and William is a knave\". So who is a knight and who is a knave?", "names": ["Scarlett", "William", "Alexander", "Jack", "James", "Jackson", "Ella", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false, true, false], "solution_text": "Scarlett is a knight, William is a knave, Alexander is a knave, Jack is a knight, James is a knight, Jackson is a knave, Ella is a knight, and Olivia is a knave.", "solution_text_format": "(1) Scarlett is a knight\n(2) William is a knave\n(3) Alexander is a knave\n(4) Jack is a knight\n(5) James is a knight\n(6) Jackson is a knave\n(7) Ella is a knight\n(8) Olivia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Jack is a knight or Ella is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that If Ella is a knight then Jackson is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Jack is not a knave.", "Jackson cannot be a knight, because this would contradict the claim of Jack that If Ella is a knight then Jackson is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that William is not a knave.", "William cannot be a knight, because this would contradict the false claim of Jackson that William is not a knave.", "Assume William is a knave. No contradiction is found in their false claim that William is a knight and Ella is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Jackson is a knave and James is a knave.", "James cannot be a knight, because this would contradict the claim of Alexander that Jackson is a knave and James is a knave.", "James cannot be a knave, because this would contradict the false claim of their own that Jack is not a knave.", "We have exhausted all possibilities for James, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Jackson is a knave and James is a knave.", "Assume James is a knight. No contradiction is found in their claim that Jack is not a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that James is a knave and William is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that James is a knave and William is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('lying', 6)), ('and', ('telling-truth', 1), ('telling-truth', 6)), ('and', ('lying', 5), ('lying', 4)), ('->', ('telling-truth', 6), ('lying', 5)), ('not', ('lying', 3)), ('not', ('lying', 1)), ('not', ('lying', 3)), ('and', ('lying', 4), ('lying', 1)))", "index": 149}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Grace, Riley, Luke, Matthew, Penelope, Mia, Charlotte, and Lucas. Grace was heard saying, \"Charlotte is a knight if and only if Charlotte is a knave\". Riley stated, \"Penelope is a knave and Lucas is a knave\". Luke was heard saying, \"Riley is a knave if and only if Lucas is a knight\". \"Charlotte is not a knight,\" Matthew declared. \"If Luke is a knave then Mia is a knave,\" Penelope claimed. \"Riley is a knight if and only if Matthew is a knave,\" Mia claimed. Charlotte stated, \"Lucas is not a knight\". \"Charlotte is a knave and Charlotte is a knight,\" Lucas claimed. So who is a knight and who is a knave?", "names": ["Grace", "Riley", "Luke", "Matthew", "Penelope", "Mia", "Charlotte", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, false, true, false], "solution_text": "Grace is a knave, Riley is a knave, Luke is a knave, Matthew is a knave, Penelope is a knight, Mia is a knave, Charlotte is a knight, and Lucas is a knave.", "solution_text_format": "(1) Grace is a knave\n(2) Riley is a knave\n(3) Luke is a knave\n(4) Matthew is a knave\n(5) Penelope is a knight\n(6) Mia is a knave\n(7) Charlotte is a knight\n(8) Lucas is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Grace cannot be a knight, because this would contradict the claim of their own that Charlotte is a knight if and only if Charlotte is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Charlotte is a knight if and only if Charlotte is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Lucas is not a knight.", "Lucas cannot be a knight, because this would contradict the claim of Charlotte that Lucas is not a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Charlotte is a knave and Charlotte is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Penelope is a knave and Lucas is a knave.", "Penelope cannot be a knight, because this would contradict the claim of Riley that Penelope is a knave and Lucas is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that If Luke is a knave then Mia is a knave.", "Luke cannot be a knight, because this would contradict the false claim of Penelope that If Luke is a knave then Mia is a knave.", "Luke cannot be a knave, because this would contradict the false claim of their own that Riley is a knave if and only if Lucas is a knight.", "We have exhausted all possibilities for Luke and Penelope, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Penelope is a knave and Lucas is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that If Luke is a knave then Mia is a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that Riley is a knave if and only if Lucas is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Riley is a knave if and only if Lucas is a knight.", "Mia cannot be a knight, because this would contradict the claim of Penelope that If Luke is a knave then Mia is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Matthew is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Charlotte is not a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Charlotte is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 6), ('lying', 6)), ('and', ('lying', 4), ('lying', 7)), ('<=>', ('lying', 1), ('telling-truth', 7)), ('not', ('telling-truth', 6)), ('->', ('lying', 2), ('lying', 5)), ('<=>', ('telling-truth', 1), ('lying', 3)), ('not', ('telling-truth', 7)), ('and', ('lying', 6), ('telling-truth', 6)))", "index": 150}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Noah, Riley, Joseph, Emma, Michael, Jackson, Lucas, and Harper. As Noah put it, \"Michael is a knight\". Riley was heard saying, \"Harper is a knight if and only if Michael is a knight\". In Joseph's words: \"Emma is a knave or Emma is a knight\". Emma commented, \"If Jackson is a knight then Jackson is a knave\". \"Riley is a knight or Lucas is a knave\" - Michael. \"Lucas is a knave or Harper is a knave,\" Jackson claimed. In a statement by Lucas: \"Joseph is not a knight\". Harper remarked, \"Joseph is a knave\". So who is a knight and who is a knave?", "names": ["Noah", "Riley", "Joseph", "Emma", "Michael", "Jackson", "Lucas", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true, false, false], "solution_text": "Noah is a knight, Riley is a knave, Joseph is a knight, Emma is a knave, Michael is a knight, Jackson is a knight, Lucas is a knave, and Harper is a knave.", "solution_text_format": "(1) Noah is a knight\n(2) Riley is a knave\n(3) Joseph is a knight\n(4) Emma is a knave\n(5) Michael is a knight\n(6) Jackson is a knight\n(7) Lucas is a knave\n(8) Harper is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Noah is a knight. No contradiction is found in their claim that Michael is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Riley is a knight or Lucas is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Harper is a knight if and only if Michael is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Harper that Joseph is a knave.", "Joseph cannot be a knave, because this would contradict the false claim of their own that Emma is a knave or Emma is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the claim of Riley that Harper is a knight if and only if Michael is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Harper is a knight if and only if Michael is a knight.", "Harper cannot be a knight, because this would contradict the false claim of Riley that Harper is a knight if and only if Michael is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Joseph is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Emma is a knave or Emma is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If Jackson is a knight then Jackson is a knave.", "Jackson cannot be a knight, because this would contradict the claim of Emma that If Jackson is a knight then Jackson is a knave.", "Jackson cannot be a knave, because this would contradict the false claim of their own that Lucas is a knave or Harper is a knave.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that If Jackson is a knight then Jackson is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Lucas is a knave or Harper is a knave.", "Lucas cannot be a knight, because this would contradict the claim of Michael that Riley is a knight or Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Joseph is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('<=>', ('telling-truth', 7), ('telling-truth', 4)), ('or', ('lying', 3), ('telling-truth', 3)), ('->', ('telling-truth', 5), ('lying', 5)), ('or', ('telling-truth', 1), ('lying', 6)), ('or', ('lying', 6), ('lying', 7)), ('not', ('telling-truth', 2)), ('lying', 2))", "index": 151}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Michael, Jacob, Joseph, Abigail, Alexander, Ava, Sofia, and Avery. As Michael put it, \"Sofia is not a knight\". As Jacob put it, \"Abigail is a knight or Michael is a knave\". \"Michael is a knave and Avery is a knave,\" Joseph declared. Abigail remarked, \"Avery is a knave\". Alexander noted, \"Sofia is a knight or Joseph is a knight\". \"If Alexander is a knight then Avery is a knight\" - Ava. Sofia commented, \"Alexander is a knave if and only if Jacob is a knight\". In a statement by Avery: \"Alexander is a knave or Sofia is a knight\". So who is a knight and who is a knave?", "names": ["Michael", "Jacob", "Joseph", "Abigail", "Alexander", "Ava", "Sofia", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, true, false, true], "solution_text": "Michael is a knight, Jacob is a knave, Joseph is a knave, Abigail is a knave, Alexander is a knave, Ava is a knight, Sofia is a knave, and Avery is a knight.", "solution_text_format": "(1) Michael is a knight\n(2) Jacob is a knave\n(3) Joseph is a knave\n(4) Abigail is a knave\n(5) Alexander is a knave\n(6) Ava is a knight\n(7) Sofia is a knave\n(8) Avery is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Sofia is not a knight.", "Sofia cannot be a knight, because this would contradict the claim of Michael that Sofia is not a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Alexander is a knave if and only if Jacob is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Sofia is a knight or Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Avery is a knave.", "Joseph cannot be a knave, because this would contradict the claim of Alexander that Sofia is a knight or Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Sofia is a knight or Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Avery is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Michael is a knave and Avery is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Alexander is a knave or Sofia is a knight.", "Jacob cannot be a knight, because this would contradict the false claim of Sofia that Alexander is a knave if and only if Jacob is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Abigail is a knight or Michael is a knave.", "Abigail cannot be a knight, because this would contradict the false claim of Jacob that Abigail is a knight or Michael is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Avery is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that If Alexander is a knight then Avery is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 6)), ('or', ('telling-truth', 3), ('lying', 0)), ('and', ('lying', 0), ('lying', 7)), ('lying', 7), ('or', ('telling-truth', 6), ('telling-truth', 2)), ('->', ('telling-truth', 4), ('telling-truth', 7)), ('<=>', ('lying', 4), ('telling-truth', 1)), ('or', ('lying', 4), ('telling-truth', 6)))", "index": 152}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: William, Emma, Sebastian, Zoey, Logan, Samuel, Penelope, and Ethan. In William's words: \"Samuel is a knight and Sebastian is a knave\". Emma said, \"Logan is not a knave.\" \"Samuel is a knight if and only if Zoey is a knave,\" Sebastian declared. \"Emma is a knave and William is a knave,\" Zoey declared. Logan was heard saying, \"Sebastian is a knave\". As Samuel put it, \"Logan is a knave if and only if Ethan is a knight\". As Penelope put it, \"William is a knight or Emma is a knave\". Ethan told you that Penelope is a knight and Emma is a knight. So who is a knight and who is a knave?", "names": ["William", "Emma", "Sebastian", "Zoey", "Logan", "Samuel", "Penelope", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false, true, false], "solution_text": "William is a knave, Emma is a knave, Sebastian is a knight, Zoey is a knight, Logan is a knave, Samuel is a knave, Penelope is a knight, and Ethan is a knave.", "solution_text_format": "(1) William is a knave\n(2) Emma is a knave\n(3) Sebastian is a knight\n(4) Zoey is a knight\n(5) Logan is a knave\n(6) Samuel is a knave\n(7) Penelope is a knight\n(8) Ethan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Samuel is a knight and Sebastian is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Logan is a knave if and only if Ethan is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of William that Samuel is a knight and Sebastian is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Samuel is a knight if and only if Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that Emma is a knave and William is a knave.", "Zoey cannot be a knave, because this would contradict the false claim of Sebastian that Samuel is a knight if and only if Zoey is a knave.", "We have exhausted all possibilities for Zoey and Sebastian, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of William that Samuel is a knight and Sebastian is a knave.", "Sebastian cannot be a knave, because this would contradict the false claim of Logan that Sebastian is a knave.", "We have exhausted all possibilities for Sebastian and Logan, so let us go back and reconsider Samuel.", "Samuel cannot be a knave, because this would contradict the claim of William that Samuel is a knight and Sebastian is a knave.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Samuel is a knight and Sebastian is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Logan is a knave if and only if Ethan is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Logan that Sebastian is a knave.", "Sebastian cannot be a knave, because this would contradict the false claim of William that Samuel is a knight and Sebastian is a knave.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Sebastian is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Samuel is a knight if and only if Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Sebastian that Samuel is a knight if and only if Zoey is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Emma is a knave and William is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Logan is not a knave.", "Emma cannot be a knave, because this would contradict the false claim of Zoey that Emma is a knave and William is a knave.", "We have exhausted all possibilities for Emma and Zoey, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the false claim of William that Samuel is a knight and Sebastian is a knave.", "We have exhausted all possibilities for Sebastian and Logan, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Logan is a knave if and only if Ethan is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Logan that Sebastian is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Samuel is a knight if and only if Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the false claim of Sebastian that Samuel is a knight if and only if Zoey is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Emma is a knave and William is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Logan is not a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Penelope is a knight and Emma is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that William is a knight or Emma is a knave.", "Penelope cannot be a knave, because this would contradict the claim of Ethan that Penelope is a knight and Emma is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the false claim of Samuel that Logan is a knave if and only if Ethan is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Emma.", "Emma cannot be a knave, because this would contradict the false claim of their own that Logan is not a knave.", "We have exhausted all possibilities for Emma, Zoey, and Sebastian, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Sebastian is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Samuel is a knight if and only if Zoey is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Emma is a knave and William is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Logan is not a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Logan is not a knave.", "Ethan cannot be a knight, because this would contradict the false claim of Samuel that Logan is a knave if and only if Ethan is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Penelope is a knight and Emma is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that William is a knight or Emma is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('lying', 2)), ('not', ('lying', 4)), ('<=>', ('telling-truth', 5), ('lying', 3)), ('and', ('lying', 1), ('lying', 0)), ('lying', 2), ('<=>', ('lying', 4), ('telling-truth', 7)), ('or', ('telling-truth', 0), ('lying', 1)), ('and', ('telling-truth', 6), ('telling-truth', 1)))", "index": 153}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Zoey, Avery, Alexander, Sebastian, Noah, Logan, Emma, and Samuel. Zoey remarked, \"Noah is a knave and Sebastian is a knave\". \"Zoey is a knave or Samuel is a knave,\" Avery claimed. \"Zoey is a knight if and only if Sebastian is a knave,\" Alexander mentioned. Sebastian said that If Avery is a knave then Samuel is a knight. Noah remarked, \"Zoey is not a knave\". \"Alexander is a knave or Avery is a knight,\" Logan declared. Emma was heard saying, \"If Avery is a knave then Samuel is a knave\". Samuel remarked, \"Emma is a knave\". So who is a knight and who is a knave?", "names": ["Zoey", "Avery", "Alexander", "Sebastian", "Noah", "Logan", "Emma", "Samuel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true, true, false], "solution_text": "Zoey is a knave, Avery is a knight, Alexander is a knight, Sebastian is a knight, Noah is a knave, Logan is a knight, Emma is a knight, and Samuel is a knave.", "solution_text_format": "(1) Zoey is a knave\n(2) Avery is a knight\n(3) Alexander is a knight\n(4) Sebastian is a knight\n(5) Noah is a knave\n(6) Logan is a knight\n(7) Emma is a knight\n(8) Samuel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Zoey is a knight. No contradiction is found in their claim that Noah is a knave and Sebastian is a knave.", "Noah cannot be a knight, because this would contradict the claim of Zoey that Noah is a knave and Sebastian is a knave.", "Noah cannot be a knave, because this would contradict the false claim of their own that Zoey is not a knave.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Noah is a knave and Sebastian is a knave.", "Noah cannot be a knight, because this would contradict the claim of their own that Zoey is not a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Zoey is not a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Avery is a knave then Samuel is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Zoey is a knave or Samuel is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of Samuel that Emma is a knave.", "Emma cannot be a knave, because this would contradict the false claim of their own that If Avery is a knave then Samuel is a knave.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Emma is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that If Avery is a knave then Samuel is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Zoey is a knight if and only if Sebastian is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Alexander is a knave or Avery is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('lying', 3)), ('or', ('lying', 0), ('lying', 7)), ('<=>', ('telling-truth', 0), ('lying', 3)), ('->', ('lying', 1), ('telling-truth', 7)), ('not', ('lying', 0)), ('or', ('lying', 2), ('telling-truth', 1)), ('->', ('lying', 1), ('lying', 7)), ('lying', 6))", "index": 154}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Grace, Zoey, Elizabeth, Victoria, Joseph, Sebastian, Noah, and Mia. Grace noted, \"Elizabeth is a knave and Noah is a knave\". Zoey expressed that If Mia is a knight then Victoria is a knight. Elizabeth was heard saying, \"Victoria is a knave\". Victoria was heard saying, \"Joseph is a knight and Grace is a knight\". Joseph asserted: \"Grace is a knight and Elizabeth is a knight\". \"Noah is a knight,\" Sebastian declared. Noah remarked, \"Zoey is a knight or Elizabeth is a knight\". Mia asserted: \"Victoria is not a knight\". So who is a knight and who is a knave?", "names": ["Grace", "Zoey", "Elizabeth", "Victoria", "Joseph", "Sebastian", "Noah", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, true, true, true], "solution_text": "Grace is a knave, Zoey is a knave, Elizabeth is a knight, Victoria is a knave, Joseph is a knave, Sebastian is a knight, Noah is a knight, and Mia is a knight.", "solution_text_format": "(1) Grace is a knave\n(2) Zoey is a knave\n(3) Elizabeth is a knight\n(4) Victoria is a knave\n(5) Joseph is a knave\n(6) Sebastian is a knight\n(7) Noah is a knight\n(8) Mia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Elizabeth is a knave and Noah is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of Grace that Elizabeth is a knave and Noah is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Joseph is a knight and Grace is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Grace is a knight and Elizabeth is a knight.", "Joseph cannot be a knave, because this would contradict the claim of Victoria that Joseph is a knight and Grace is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Victoria.", "Victoria cannot be a knave, because this would contradict the false claim of Elizabeth that Victoria is a knave.", "We have exhausted all possibilities for Victoria and Elizabeth, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Elizabeth is a knave and Noah is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Victoria is a knave.", "Victoria cannot be a knight, because this would contradict the claim of Elizabeth that Victoria is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Joseph is a knight and Grace is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Grace is a knight and Elizabeth is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Grace is a knight and Elizabeth is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Zoey is a knight or Elizabeth is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that If Mia is a knight then Victoria is a knight.", "Mia cannot be a knight, because this would contradict the claim of Zoey that If Mia is a knight then Victoria is a knight.", "Mia cannot be a knave, because this would contradict the false claim of their own that Victoria is not a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that If Mia is a knight then Victoria is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Victoria is not a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Noah is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('lying', 6)), ('->', ('telling-truth', 7), ('telling-truth', 3)), ('lying', 3), ('and', ('telling-truth', 4), ('telling-truth', 0)), ('and', ('telling-truth', 0), ('telling-truth', 2)), ('telling-truth', 6), ('or', ('telling-truth', 1), ('telling-truth', 2)), ('not', ('telling-truth', 3)))", "index": 155}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ella, Luke, Chloe, Aiden, Harper, Emma, Mason, and Aurora. As Ella put it, \"Aiden is a knave and Mason is a knight\". Luke was heard saying, \"Harper is not a knight\". Chloe stated, \"Mason is not a knight\". \"Emma is a knight if and only if Mason is a knave,\" Aiden declared. In a statement by Harper: \"Chloe is not a knight\". Emma was heard saying, \"Luke is a knave\". Mason said, \"Chloe is a knave or Ella is a knave.\" In Aurora's words: \"Mason is a knight\". So who is a knight and who is a knave?", "names": ["Ella", "Luke", "Chloe", "Aiden", "Harper", "Emma", "Mason", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true, true, true], "solution_text": "Ella is a knight, Luke is a knave, Chloe is a knave, Aiden is a knave, Harper is a knight, Emma is a knight, Mason is a knight, and Aurora is a knight.", "solution_text_format": "(1) Ella is a knight\n(2) Luke is a knave\n(3) Chloe is a knave\n(4) Aiden is a knave\n(5) Harper is a knight\n(6) Emma is a knight\n(7) Mason is a knight\n(8) Aurora is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Aiden is a knave and Mason is a knight.", "Aiden cannot be a knight, because this would contradict the claim of Ella that Aiden is a knave and Mason is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Emma is a knight if and only if Mason is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Luke is a knave.", "Luke cannot be a knight, because this would contradict the claim of Emma that Luke is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Harper is not a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Chloe is not a knight.", "Chloe cannot be a knight, because this would contradict the claim of Harper that Chloe is not a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Mason is not a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Chloe is a knave or Ella is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Mason is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('telling-truth', 6)), ('not', ('telling-truth', 4)), ('not', ('telling-truth', 6)), ('<=>', ('telling-truth', 5), ('lying', 6)), ('not', ('telling-truth', 2)), ('lying', 1), ('or', ('lying', 2), ('lying', 0)), ('telling-truth', 6))", "index": 156}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lily, Evelyn, Sofia, Aiden, Oliver, Mason, Jack, and Henry. \"Aiden is a knight and Henry is a knave,\" Lily mentioned. Evelyn asserted: \"If Evelyn is a knight then Sofia is a knight\". Sofia expressed that Lily is a knave or Lily is a knight. Aiden asserted: \"Oliver is a knight or Aiden is a knight\". Oliver commented, \"If Evelyn is a knight then Oliver is a knight\". \"Sofia is a knight,\" Mason mentioned. According to Jack, \"Oliver is a knight if and only if Evelyn is a knight\". Henry stated, \"Lily is a knight\". So who is a knight and who is a knave?", "names": ["Lily", "Evelyn", "Sofia", "Aiden", "Oliver", "Mason", "Jack", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true, false, false], "solution_text": "Lily is a knave, Evelyn is a knight, Sofia is a knight, Aiden is a knave, Oliver is a knave, Mason is a knight, Jack is a knave, and Henry is a knave.", "solution_text_format": "(1) Lily is a knave\n(2) Evelyn is a knight\n(3) Sofia is a knight\n(4) Aiden is a knave\n(5) Oliver is a knave\n(6) Mason is a knight\n(7) Jack is a knave\n(8) Henry is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that Aiden is a knight and Henry is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Oliver is a knight or Aiden is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that If Evelyn is a knight then Oliver is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Evelyn is a knight then Sofia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Lily is a knave or Lily is a knight.", "Henry cannot be a knight, because this would contradict the claim of Lily that Aiden is a knight and Henry is a knave.", "Henry cannot be a knave, because this would contradict the false claim of their own that Lily is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Sofia.", "Sofia cannot be a knave, because this would contradict the claim of Evelyn that If Evelyn is a knight then Sofia is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that If Evelyn is a knight then Sofia is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that If Evelyn is a knight then Oliver is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Evelyn is a knight then Sofia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Lily is a knave or Lily is a knight.", "Henry cannot be a knight, because this would contradict the claim of Lily that Aiden is a knight and Henry is a knave.", "Henry cannot be a knave, because this would contradict the false claim of their own that Lily is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Sofia.", "Sofia cannot be a knave, because this would contradict the claim of Evelyn that If Evelyn is a knight then Sofia is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that If Evelyn is a knight then Sofia is a knight.", "We have exhausted all possibilities for Evelyn and Oliver, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the claim of Lily that Aiden is a knight and Henry is a knave.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Aiden is a knight and Henry is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Oliver is a knight or Aiden is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that If Evelyn is a knight then Oliver is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Evelyn is a knight then Sofia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Lily is a knave or Lily is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Lily is a knight.", "Henry cannot be a knave, because this would contradict the false claim of Lily that Aiden is a knight and Henry is a knave.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Sofia.", "Sofia cannot be a knave, because this would contradict the claim of Evelyn that If Evelyn is a knight then Sofia is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that If Evelyn is a knight then Sofia is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that If Evelyn is a knight then Oliver is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Evelyn is a knight then Sofia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Lily is a knave or Lily is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Lily is a knight.", "Henry cannot be a knave, because this would contradict the false claim of Lily that Aiden is a knight and Henry is a knave.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Sofia.", "Sofia cannot be a knave, because this would contradict the claim of Evelyn that If Evelyn is a knight then Sofia is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that If Evelyn is a knight then Sofia is a knight.", "We have exhausted all possibilities for Evelyn and Oliver, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Oliver is a knight or Aiden is a knight.", "Oliver cannot be a knight, because this would contradict the false claim of Aiden that Oliver is a knight or Aiden is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that If Evelyn is a knight then Oliver is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Evelyn is a knight then Sofia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Lily is a knave or Lily is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Lily is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Lily is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Sofia is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Oliver is a knight if and only if Evelyn is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Oliver is a knight if and only if Evelyn is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('lying', 7)), ('->', ('telling-truth', 1), ('telling-truth', 2)), ('or', ('lying', 0), ('telling-truth', 0)), ('or', ('telling-truth', 4), ('telling-truth', 3)), ('->', ('telling-truth', 1), ('telling-truth', 4)), ('telling-truth', 2), ('<=>', ('telling-truth', 4), ('telling-truth', 1)), ('telling-truth', 0))", "index": 157}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jackson, Sophia, Lily, Riley, Ethan, Abigail, Henry, and James. Jackson told you that If Riley is a knight then James is a knave. Sophia asserted: \"Riley is a knight and Abigail is a knight\". \"Henry is a knave or Jackson is a knight,\" Lily claimed. Riley was heard saying, \"Henry is not a knight\". In a statement by Ethan: \"Jackson is a knight or Lily is a knave\". \"If Ethan is a knight then Sophia is a knave,\" Abigail mentioned. Henry expressed that Riley is a knight or Ethan is a knight. James commented, \"If Abigail is a knave then Jackson is a knave\". So who is a knight and who is a knave?", "names": ["Jackson", "Sophia", "Lily", "Riley", "Ethan", "Abigail", "Henry", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true, true, true], "solution_text": "Jackson is a knight, Sophia is a knave, Lily is a knight, Riley is a knave, Ethan is a knight, Abigail is a knight, Henry is a knight, and James is a knight.", "solution_text_format": "(1) Jackson is a knight\n(2) Sophia is a knave\n(3) Lily is a knight\n(4) Riley is a knave\n(5) Ethan is a knight\n(6) Abigail is a knight\n(7) Henry is a knight\n(8) James is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that If Riley is a knight then James is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Henry is not a knight.", "Henry cannot be a knight, because this would contradict the claim of Riley that Henry is not a knight.", "Henry cannot be a knave, because this would contradict the false claim of their own that Riley is a knight or Ethan is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Henry is not a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Riley is a knight or Ethan is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Jackson is a knight or Lily is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Henry is a knave or Jackson is a knight.", "Assume James is a knight. No contradiction is found in their claim that If Abigail is a knave then Jackson is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that If Ethan is a knight then Sophia is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that Riley is a knight and Abigail is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Riley is a knight and Abigail is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('lying', 7)), ('and', ('telling-truth', 3), ('telling-truth', 5)), ('or', ('lying', 6), ('telling-truth', 0)), ('not', ('telling-truth', 6)), ('or', ('telling-truth', 0), ('lying', 2)), ('->', ('telling-truth', 4), ('lying', 1)), ('or', ('telling-truth', 3), ('telling-truth', 4)), ('->', ('lying', 5), ('lying', 0)))", "index": 158}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Grace, Riley, Samuel, Alexander, Noah, Owen, Olivia, and James. Grace said, \"Olivia is a knight and Owen is a knave.\" \"If Noah is a knight then Samuel is a knight,\" Riley declared. Samuel was heard saying, \"If James is a knave then Riley is a knight\". \"Samuel is a knave if and only if Alexander is a knight\" - Alexander. Noah noted, \"If Noah is a knight then Alexander is a knight\". \"If James is a knave then Riley is a knight,\" Owen claimed. Olivia was heard saying, \"If Alexander is a knave then James is a knave\". \"James is a knight or Alexander is a knave,\" James declared. So who is a knight and who is a knave?", "names": ["Grace", "Riley", "Samuel", "Alexander", "Noah", "Owen", "Olivia", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false, true, false], "solution_text": "Grace is a knight, Riley is a knave, Samuel is a knave, Alexander is a knight, Noah is a knight, Owen is a knave, Olivia is a knight, and James is a knave.", "solution_text_format": "(1) Grace is a knight\n(2) Riley is a knave\n(3) Samuel is a knave\n(4) Alexander is a knight\n(5) Noah is a knight\n(6) Owen is a knave\n(7) Olivia is a knight\n(8) James is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Olivia is a knight and Owen is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that If Alexander is a knave then James is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Alexander is a knight.", "Samuel cannot be a knight, because this would contradict the claim of Alexander that Samuel is a knave if and only if Alexander is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that If James is a knave then Riley is a knight.", "James cannot be a knight, because this would contradict the false claim of Samuel that If James is a knave then Riley is a knight.", "Assume James is a knave. No contradiction is found in their false claim that James is a knight or Alexander is a knave.", "Riley cannot be a knight, because this would contradict the false claim of Samuel that If James is a knave then Riley is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that If Noah is a knight then Samuel is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that If Noah is a knight then Alexander is a knight.", "Owen cannot be a knight, because this would contradict the claim of Grace that Olivia is a knight and Owen is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that If James is a knave then Riley is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 6), ('lying', 5)), ('->', ('telling-truth', 4), ('telling-truth', 2)), ('->', ('lying', 7), ('telling-truth', 1)), ('<=>', ('lying', 2), ('telling-truth', 3)), ('->', ('telling-truth', 4), ('telling-truth', 3)), ('->', ('lying', 7), ('telling-truth', 1)), ('->', ('lying', 3), ('lying', 7)), ('or', ('telling-truth', 7), ('lying', 3)))", "index": 159}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Olivia, Matthew, Ella, Owen, Emma, Jacob, Mia, and David. Olivia told you that Mia is a knight if and only if Ella is a knight. In Matthew's words: \"Jacob is a knave and Mia is a knight\". \"Ella is a knight if and only if Emma is a knight,\" Ella declared. \"Ella is a knight\" - Owen. \"Matthew is not a knave,\" Emma mentioned. Jacob told you that Olivia is a knight. Mia expressed that If Olivia is a knight then Jacob is a knight. David said that Owen is a knave if and only if Emma is a knight. So who is a knight and who is a knave?", "names": ["Olivia", "Matthew", "Ella", "Owen", "Emma", "Jacob", "Mia", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, false, true, true], "solution_text": "Olivia is a knave, Matthew is a knight, Ella is a knave, Owen is a knave, Emma is a knight, Jacob is a knave, Mia is a knight, and David is a knight.", "solution_text_format": "(1) Olivia is a knave\n(2) Matthew is a knight\n(3) Ella is a knave\n(4) Owen is a knave\n(5) Emma is a knight\n(6) Jacob is a knave\n(7) Mia is a knight\n(8) David is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Mia is a knight if and only if Ella is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that If Olivia is a knight then Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Olivia is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Ella is a knight if and only if Emma is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Matthew is not a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Jacob is a knave and Mia is a knight.", "Matthew cannot be a knave, because this would contradict the claim of Emma that Matthew is not a knave.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Emma.", "Emma cannot be a knave, because this would contradict the claim of Ella that Ella is a knight if and only if Emma is a knight.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the claim of Olivia that Mia is a knight if and only if Ella is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the false claim of their own that Olivia is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that If Olivia is a knight then Jacob is a knight.", "Jacob cannot be a knight, because this would contradict the false claim of Mia that If Olivia is a knight then Jacob is a knight.", "Jacob cannot be a knave, because this would contradict the false claim of their own that Olivia is a knight.", "We have exhausted all possibilities for Jacob and Mia, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Mia is a knight if and only if Ella is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that If Olivia is a knight then Jacob is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Olivia is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Olivia is a knight.", "Ella cannot be a knight, because this would contradict the false claim of Olivia that Mia is a knight if and only if Ella is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Ella is a knight if and only if Emma is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Matthew is not a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Jacob is a knave and Mia is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Ella is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Ella is a knight.", "Assume David is a knight. No contradiction is found in their claim that Owen is a knave if and only if Emma is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 6), ('telling-truth', 2)), ('and', ('lying', 5), ('telling-truth', 6)), ('<=>', ('telling-truth', 2), ('telling-truth', 4)), ('telling-truth', 2), ('not', ('lying', 1)), ('telling-truth', 0), ('->', ('telling-truth', 0), ('telling-truth', 5)), ('<=>', ('lying', 3), ('telling-truth', 4)))", "index": 160}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sofia, Ava, Lily, Penelope, Amelia, Sebastian, Ethan, and Luke. \"Amelia is a knave and Penelope is a knave,\" Sofia claimed. Ava noted, \"Sofia is a knight or Lily is a knave\". Lily told you that Sofia is a knight. \"Amelia is a knave or Sofia is a knight,\" Penelope mentioned. \"If Luke is a knave then Sofia is a knave,\" Amelia declared. Sebastian noted, \"Lily is a knight\". \"Sebastian is not a knave,\" Ethan mentioned. In a statement by Luke: \"Lily is not a knight\". So who is a knight and who is a knave?", "names": ["Sofia", "Ava", "Lily", "Penelope", "Amelia", "Sebastian", "Ethan", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, false, false, true], "solution_text": "Sofia is a knave, Ava is a knight, Lily is a knave, Penelope is a knave, Amelia is a knight, Sebastian is a knave, Ethan is a knave, and Luke is a knight.", "solution_text_format": "(1) Sofia is a knave\n(2) Ava is a knight\n(3) Lily is a knave\n(4) Penelope is a knave\n(5) Amelia is a knight\n(6) Sebastian is a knave\n(7) Ethan is a knave\n(8) Luke is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Amelia is a knave and Penelope is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Sofia that Amelia is a knave and Penelope is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that If Luke is a knave then Sofia is a knave.", "Luke cannot be a knight, because this would contradict the false claim of Amelia that If Luke is a knave then Sofia is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Lily is not a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Sofia is a knight.", "Penelope cannot be a knight, because this would contradict the claim of Sofia that Amelia is a knave and Penelope is a knave.", "Penelope cannot be a knave, because this would contradict the false claim of their own that Amelia is a knave or Sofia is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the false claim of their own that Sofia is a knight.", "We have exhausted all possibilities for Lily, Luke, and Amelia, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Amelia is a knave and Penelope is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that If Luke is a knave then Sofia is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Lily is not a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Sofia is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Sofia is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Amelia is a knave or Sofia is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Amelia is a knave or Sofia is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Sofia is a knight or Lily is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Lily is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Lily is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Sebastian is not a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Sebastian is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('lying', 3)), ('or', ('telling-truth', 0), ('lying', 2)), ('telling-truth', 0), ('or', ('lying', 4), ('telling-truth', 0)), ('->', ('lying', 7), ('lying', 0)), ('telling-truth', 2), ('not', ('lying', 5)), ('not', ('telling-truth', 2)))", "index": 161}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Michael, Emma, Sophia, Aria, Henry, Chloe, Grace, and Joseph. \"If Chloe is a knave then Chloe is a knight\" - Michael. \"If Joseph is a knave then Aria is a knave,\" Emma claimed. Sophia expressed that Emma is a knave if and only if Grace is a knave. Aria said that Aria is a knight or Joseph is a knight. In a statement by Henry: \"Michael is not a knight\". Chloe said, \"If Chloe is a knight then Aria is a knight.\" As Grace put it, \"If Henry is a knave then Aria is a knight\". Joseph said, \"If Henry is a knave then Chloe is a knight.\" So who is a knight and who is a knave?", "names": ["Michael", "Emma", "Sophia", "Aria", "Henry", "Chloe", "Grace", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true, true, true], "solution_text": "Michael is a knight, Emma is a knight, Sophia is a knight, Aria is a knight, Henry is a knave, Chloe is a knight, Grace is a knight, and Joseph is a knight.", "solution_text_format": "(1) Michael is a knight\n(2) Emma is a knight\n(3) Sophia is a knight\n(4) Aria is a knight\n(5) Henry is a knave\n(6) Chloe is a knight\n(7) Grace is a knight\n(8) Joseph is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that If Chloe is a knave then Chloe is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that If Chloe is a knight then Aria is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Aria is a knight or Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Henry is a knave then Chloe is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Michael is not a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Michael is not a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If Joseph is a knave then Aria is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Emma is a knave if and only if Grace is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that If Henry is a knave then Aria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('telling-truth', 5)), ('->', ('lying', 7), ('lying', 3)), ('<=>', ('lying', 1), ('lying', 6)), ('or', ('telling-truth', 3), ('telling-truth', 7)), ('not', ('telling-truth', 0)), ('->', ('telling-truth', 5), ('telling-truth', 3)), ('->', ('lying', 4), ('telling-truth', 3)), ('->', ('lying', 4), ('telling-truth', 5)))", "index": 162}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aria, Daniel, Victoria, Aurora, Emma, Logan, Sofia, and Zoey. \"Victoria is a knave,\" Aria declared. In a statement by Daniel: \"Zoey is a knave\". Victoria told you that If Aria is a knight then Logan is a knight. \"Zoey is a knave and Daniel is a knave\" - Aurora. In a statement by Emma: \"Aria is a knight if and only if Logan is a knight\". \"Victoria is a knight if and only if Zoey is a knight,\" Logan claimed. Sofia was heard saying, \"Aurora is a knave or Daniel is a knave\". Zoey commented, \"Aurora is a knight if and only if Aria is a knight\". So who is a knight and who is a knave?", "names": ["Aria", "Daniel", "Victoria", "Aurora", "Emma", "Logan", "Sofia", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, true, true, true], "solution_text": "Aria is a knave, Daniel is a knave, Victoria is a knight, Aurora is a knave, Emma is a knave, Logan is a knight, Sofia is a knight, and Zoey is a knight.", "solution_text_format": "(1) Aria is a knave\n(2) Daniel is a knave\n(3) Victoria is a knight\n(4) Aurora is a knave\n(5) Emma is a knave\n(6) Logan is a knight\n(7) Sofia is a knight\n(8) Zoey is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that Victoria is a knave.", "Victoria cannot be a knight, because this would contradict the claim of Aria that Victoria is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that If Aria is a knight then Logan is a knight.", "Logan cannot be a knight, because this would contradict the false claim of Victoria that If Aria is a knight then Logan is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Victoria is a knight if and only if Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Aurora is a knight if and only if Aria is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Zoey is a knave and Daniel is a knave.", "Aurora cannot be a knave, because this would contradict the claim of Zoey that Aurora is a knight if and only if Aria is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Zoey.", "Zoey cannot be a knave, because this would contradict the false claim of Logan that Victoria is a knight if and only if Zoey is a knight.", "We have exhausted all possibilities for Zoey, Logan, and Victoria, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that If Aria is a knight then Logan is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Aurora is a knight if and only if Aria is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Zoey is a knave and Daniel is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Zoey is a knave and Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of their own that Zoey is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Zoey is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Aria is a knight if and only if Logan is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Aria is a knight if and only if Logan is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Aurora is a knave or Daniel is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('lying', 7), ('->', ('telling-truth', 0), ('telling-truth', 5)), ('and', ('lying', 7), ('lying', 1)), ('<=>', ('telling-truth', 0), ('telling-truth', 5)), ('<=>', ('telling-truth', 2), ('telling-truth', 7)), ('or', ('lying', 3), ('lying', 1)), ('<=>', ('telling-truth', 3), ('telling-truth', 0)))", "index": 163}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Noah, Lucas, Chloe, Olivia, Sophia, Michael, James, and Riley. In Noah's words: \"Olivia is a knave and James is a knave\". \"James is a knave or Michael is a knave,\" Lucas mentioned. As Chloe put it, \"Noah is not a knight\". \"If Michael is a knight then Noah is a knave\" - Olivia. Sophia was heard saying, \"Lucas is a knight if and only if Olivia is a knave\". \"If Chloe is a knight then Michael is a knight,\" Michael mentioned. James said, \"Michael is a knave or Lucas is a knight.\" Riley commented, \"Sophia is a knight or Lucas is a knight\". So who is a knight and who is a knave?", "names": ["Noah", "Lucas", "Chloe", "Olivia", "Sophia", "Michael", "James", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false, true, true], "solution_text": "Noah is a knave, Lucas is a knight, Chloe is a knight, Olivia is a knight, Sophia is a knave, Michael is a knave, James is a knight, and Riley is a knight.", "solution_text_format": "(1) Noah is a knave\n(2) Lucas is a knight\n(3) Chloe is a knight\n(4) Olivia is a knight\n(5) Sophia is a knave\n(6) Michael is a knave\n(7) James is a knight\n(8) Riley is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Noah is a knight. No contradiction is found in their claim that Olivia is a knave and James is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Noah that Olivia is a knave and James is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that If Michael is a knight then Noah is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that If Chloe is a knight then Michael is a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Noah is not a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Noah is not a knight.", "James cannot be a knight, because this would contradict the claim of Noah that Olivia is a knave and James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Michael is a knave or Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of James that Michael is a knave or Lucas is a knight.", "Lucas cannot be a knave, because this would contradict the false claim of their own that James is a knave or Michael is a knave.", "We have exhausted all possibilities for Lucas, James, and Chloe, so let us go back and reconsider Michael.", "Michael cannot be a knave, because this would contradict the false claim of Olivia that If Michael is a knight then Noah is a knave.", "We have exhausted all possibilities for Michael and Olivia, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Olivia is a knave and James is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that If Michael is a knight then Noah is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that If Chloe is a knight then Michael is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Noah is not a knight.", "Assume James is a knight. No contradiction is found in their claim that Michael is a knave or Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that James is a knave or Michael is a knave.", "Lucas cannot be a knave, because this would contradict the claim of James that Michael is a knave or Lucas is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Michael is a knave or Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of James that Michael is a knave or Lucas is a knight.", "Lucas cannot be a knave, because this would contradict the false claim of their own that James is a knave or Michael is a knave.", "We have exhausted all possibilities for Lucas and James, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the false claim of their own that Noah is not a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that If Chloe is a knight then Michael is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Noah is not a knight.", "Assume James is a knight. No contradiction is found in their claim that Michael is a knave or Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that James is a knave or Michael is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that Lucas is a knight if and only if Olivia is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Lucas is a knight if and only if Olivia is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Sophia is a knight or Lucas is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('lying', 6)), ('or', ('lying', 6), ('lying', 5)), ('not', ('telling-truth', 0)), ('->', ('telling-truth', 5), ('lying', 0)), ('<=>', ('telling-truth', 1), ('lying', 3)), ('->', ('telling-truth', 2), ('telling-truth', 5)), ('or', ('lying', 5), ('telling-truth', 1)), ('or', ('telling-truth', 4), ('telling-truth', 1)))", "index": 164}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emma, Jacob, Olivia, Sebastian, James, Scarlett, Owen, and Mia. Emma remarked, \"Scarlett is a knight if and only if James is a knave\". Jacob expressed that Owen is a knight. Olivia commented, \"If Owen is a knave then Mia is a knight\". Sebastian commented, \"James is a knight\". In James's words: \"Mia is a knight and Mia is a knave\". \"Mia is a knave and Scarlett is a knight,\" Scarlett claimed. In a statement by Owen: \"If Mia is a knave then Sebastian is a knave\". Mia asserted: \"Jacob is a knight and Sebastian is a knave\". So who is a knight and who is a knave?", "names": ["Emma", "Jacob", "Olivia", "Sebastian", "James", "Scarlett", "Owen", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false, true, true], "solution_text": "Emma is a knave, Jacob is a knight, Olivia is a knight, Sebastian is a knave, James is a knave, Scarlett is a knave, Owen is a knight, and Mia is a knight.", "solution_text_format": "(1) Emma is a knave\n(2) Jacob is a knight\n(3) Olivia is a knight\n(4) Sebastian is a knave\n(5) James is a knave\n(6) Scarlett is a knave\n(7) Owen is a knight\n(8) Mia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Scarlett is a knight if and only if James is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Mia is a knave and Scarlett is a knight.", "Mia cannot be a knight, because this would contradict the claim of Scarlett that Mia is a knave and Scarlett is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Jacob is a knight and Sebastian is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Owen is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that If Mia is a knave then Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Owen that If Mia is a knave then Sebastian is a knave.", "Sebastian cannot be a knave, because this would contradict the false claim of Mia that Jacob is a knight and Sebastian is a knave.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the claim of Jacob that Owen is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Owen is a knight.", "Owen cannot be a knight, because this would contradict the false claim of Jacob that Owen is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that If Mia is a knave then Sebastian is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that James is a knight.", "James cannot be a knight, because this would contradict the claim of Emma that Scarlett is a knight if and only if James is a knave.", "James cannot be a knave, because this would contradict the claim of Sebastian that James is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the false claim of Owen that If Mia is a knave then Sebastian is a knave.", "We have exhausted all possibilities for Sebastian, Owen, Jacob, and Mia, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Mia is a knave and Scarlett is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Jacob is a knight and Sebastian is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Owen is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that If Mia is a knave then Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Mia that Jacob is a knight and Sebastian is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that James is a knight.", "James cannot be a knight, because this would contradict the false claim of Sebastian that James is a knight.", "James cannot be a knave, because this would contradict the claim of Emma that Scarlett is a knight if and only if James is a knave.", "We have exhausted all possibilities for James and Sebastian, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the claim of Jacob that Owen is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the claim of Mia that Jacob is a knight and Sebastian is a knave.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Jacob is a knight and Sebastian is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Owen is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that If Mia is a knave then Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Owen that If Mia is a knave then Sebastian is a knave.", "Sebastian cannot be a knave, because this would contradict the false claim of Mia that Jacob is a knight and Sebastian is a knave.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the claim of Jacob that Owen is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Owen is a knight.", "Owen cannot be a knight, because this would contradict the false claim of Jacob that Owen is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that If Mia is a knave then Sebastian is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that James is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Mia is a knight and Mia is a knave.", "James cannot be a knave, because this would contradict the claim of Emma that Scarlett is a knight if and only if James is a knave.", "We have exhausted all possibilities for James, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the false claim of Owen that If Mia is a knave then Sebastian is a knave.", "We have exhausted all possibilities for Sebastian, Owen, Jacob, Mia, and Scarlett, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Scarlett is a knight if and only if James is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Mia is a knave and Scarlett is a knight.", "Mia cannot be a knight, because this would contradict the claim of Scarlett that Mia is a knave and Scarlett is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Jacob is a knight and Sebastian is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Owen is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that If Mia is a knave then Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Owen that If Mia is a knave then Sebastian is a knave.", "Sebastian cannot be a knave, because this would contradict the false claim of Mia that Jacob is a knight and Sebastian is a knave.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the claim of Jacob that Owen is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Owen is a knight.", "Owen cannot be a knight, because this would contradict the false claim of Jacob that Owen is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that If Mia is a knave then Sebastian is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that James is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Mia is a knight and Mia is a knave.", "James cannot be a knave, because this would contradict the false claim of Emma that Scarlett is a knight if and only if James is a knave.", "We have exhausted all possibilities for James, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the false claim of Owen that If Mia is a knave then Sebastian is a knave.", "We have exhausted all possibilities for Sebastian, Owen, Jacob, and Mia, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Mia is a knave and Scarlett is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Jacob is a knight and Sebastian is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Owen is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that If Mia is a knave then Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Mia that Jacob is a knight and Sebastian is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that James is a knight.", "James cannot be a knight, because this would contradict the false claim of Emma that Scarlett is a knight if and only if James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Mia is a knight and Mia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that If Owen is a knave then Mia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 5), ('lying', 4)), ('telling-truth', 6), ('->', ('lying', 6), ('telling-truth', 7)), ('telling-truth', 4), ('and', ('telling-truth', 7), ('lying', 7)), ('and', ('lying', 7), ('telling-truth', 5)), ('->', ('lying', 7), ('lying', 3)), ('and', ('telling-truth', 1), ('lying', 3)))", "index": 165}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Penelope, Ethan, Ava, Isabella, Aurora, Samuel, Harper, and Emma. Penelope stated, \"Penelope is a knight\". Ethan said, \"If Ava is a knave then Ethan is a knight.\" \"Harper is a knight or Emma is a knight\" - Ava. Isabella noted, \"If Aurora is a knight then Penelope is a knight\". Aurora remarked, \"Harper is a knave or Isabella is a knight\". Samuel noted, \"Isabella is a knight or Emma is a knave\". \"Aurora is a knight or Penelope is a knave,\" Harper claimed. In Emma's words: \"Ethan is a knave and Harper is a knave\". So who is a knight and who is a knave?", "names": ["Penelope", "Ethan", "Ava", "Isabella", "Aurora", "Samuel", "Harper", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true, true, false], "solution_text": "Penelope is a knight, Ethan is a knight, Ava is a knight, Isabella is a knight, Aurora is a knight, Samuel is a knight, Harper is a knight, and Emma is a knave.", "solution_text_format": "(1) Penelope is a knight\n(2) Ethan is a knight\n(3) Ava is a knight\n(4) Isabella is a knight\n(5) Aurora is a knight\n(6) Samuel is a knight\n(7) Harper is a knight\n(8) Emma is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that Penelope is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If Ava is a knave then Ethan is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Harper is a knight or Emma is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Aurora is a knight or Penelope is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Harper is a knave or Isabella is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that If Aurora is a knight then Penelope is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Ethan is a knave and Harper is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Ethan is a knave and Harper is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Isabella is a knight or Emma is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 0), ('->', ('lying', 2), ('telling-truth', 1)), ('or', ('telling-truth', 6), ('telling-truth', 7)), ('->', ('telling-truth', 4), ('telling-truth', 0)), ('or', ('lying', 6), ('telling-truth', 3)), ('or', ('telling-truth', 3), ('lying', 7)), ('or', ('telling-truth', 4), ('lying', 0)), ('and', ('lying', 1), ('lying', 6)))", "index": 166}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Grace, Aiden, Chloe, Matthew, Jack, Lucas, Amelia, and Mia. In a statement by Grace: \"If Lucas is a knave then Amelia is a knave\". Aiden noted, \"Lucas is a knave if and only if Aiden is a knight\". In a statement by Chloe: \"Jack is a knight\". According to Matthew, \"Chloe is a knave and Aiden is a knight\". Jack remarked, \"If Lucas is a knave then Amelia is a knight\". Lucas noted, \"Matthew is not a knave\". \"If Aiden is a knave then Grace is a knight,\" Amelia mentioned. Mia was heard saying, \"Amelia is not a knave\". So who is a knight and who is a knave?", "names": ["Grace", "Aiden", "Chloe", "Matthew", "Jack", "Lucas", "Amelia", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, false, true, true], "solution_text": "Grace is a knave, Aiden is a knight, Chloe is a knight, Matthew is a knave, Jack is a knight, Lucas is a knave, Amelia is a knight, and Mia is a knight.", "solution_text_format": "(1) Grace is a knave\n(2) Aiden is a knight\n(3) Chloe is a knight\n(4) Matthew is a knave\n(5) Jack is a knight\n(6) Lucas is a knave\n(7) Amelia is a knight\n(8) Mia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that If Lucas is a knave then Amelia is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Matthew is not a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Chloe is a knave and Aiden is a knight.", "Chloe cannot be a knight, because this would contradict the claim of Matthew that Chloe is a knave and Aiden is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Jack is a knight.", "Jack cannot be a knight, because this would contradict the false claim of Chloe that Jack is a knight.", "Jack cannot be a knave, because this would contradict the false claim of their own that If Lucas is a knave then Amelia is a knight.", "We have exhausted all possibilities for Jack and Chloe, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the claim of Lucas that Matthew is not a knave.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Matthew is not a knave.", "Matthew cannot be a knight, because this would contradict the false claim of Lucas that Matthew is not a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Chloe is a knave and Aiden is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that If Lucas is a knave then Amelia is a knight.", "Amelia cannot be a knight, because this would contradict the claim of Grace that If Lucas is a knave then Amelia is a knave.", "Amelia cannot be a knave, because this would contradict the claim of Jack that If Lucas is a knave then Amelia is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the claim of Chloe that Jack is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Jack is a knight.", "Jack cannot be a knight, because this would contradict the false claim of Chloe that Jack is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that If Lucas is a knave then Amelia is a knight.", "Amelia cannot be a knight, because this would contradict the claim of Grace that If Lucas is a knave then Amelia is a knave.", "Amelia cannot be a knave, because this would contradict the false claim of their own that If Aiden is a knave then Grace is a knight.", "We have exhausted all possibilities for Amelia, Jack, Chloe, Matthew, and Lucas, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that If Lucas is a knave then Amelia is a knave.", "Lucas cannot be a knight, because this would contradict the false claim of Grace that If Lucas is a knave then Amelia is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Matthew is not a knave.", "Matthew cannot be a knight, because this would contradict the false claim of Lucas that Matthew is not a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Chloe is a knave and Aiden is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that If Lucas is a knave then Amelia is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that If Aiden is a knave then Grace is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Lucas is a knave if and only if Aiden is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Amelia is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('lying', 6)), ('<=>', ('lying', 5), ('telling-truth', 1)), ('telling-truth', 4), ('and', ('lying', 2), ('telling-truth', 1)), ('->', ('lying', 5), ('telling-truth', 6)), ('not', ('lying', 3)), ('->', ('lying', 1), ('telling-truth', 0)), ('not', ('lying', 6)))", "index": 167}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Abigail, Charlotte, William, Evelyn, Victoria, Sofia, Isabella, and Aurora. According to Abigail, \"If Isabella is a knight then Abigail is a knight\". Charlotte commented, \"William is a knave and Isabella is a knave\". William said that Abigail is a knave. Evelyn remarked, \"If William is a knight then Sofia is a knight\". Victoria said that Abigail is not a knight. Sofia said, \"Isabella is a knave and William is a knight.\" Isabella remarked, \"Sofia is a knight and Abigail is a knave\". Aurora said, \"Evelyn is a knight or Isabella is a knight.\" So who is a knight and who is a knave?", "names": ["Abigail", "Charlotte", "William", "Evelyn", "Victoria", "Sofia", "Isabella", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false, false, true], "solution_text": "Abigail is a knight, Charlotte is a knight, William is a knave, Evelyn is a knight, Victoria is a knave, Sofia is a knave, Isabella is a knave, and Aurora is a knight.", "solution_text_format": "(1) Abigail is a knight\n(2) Charlotte is a knight\n(3) William is a knave\n(4) Evelyn is a knight\n(5) Victoria is a knave\n(6) Sofia is a knave\n(7) Isabella is a knave\n(8) Aurora is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that If Isabella is a knight then Abigail is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Sofia is a knight and Abigail is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Sofia is a knight and Abigail is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Isabella is a knave and William is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Abigail is a knave.", "William cannot be a knave, because this would contradict the claim of Sofia that Isabella is a knave and William is a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Isabella is a knave and William is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Abigail is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Abigail is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that William is a knave and Isabella is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that If William is a knight then Sofia is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Abigail is not a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Abigail is not a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Evelyn is a knight or Isabella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 6), ('telling-truth', 0)), ('and', ('lying', 2), ('lying', 6)), ('lying', 0), ('->', ('telling-truth', 2), ('telling-truth', 5)), ('not', ('telling-truth', 0)), ('and', ('lying', 6), ('telling-truth', 2)), ('and', ('telling-truth', 5), ('lying', 0)), ('or', ('telling-truth', 3), ('telling-truth', 6)))", "index": 168}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Henry, Elizabeth, Samuel, Emily, Sophia, Benjamin, Mason, and James. Henry told you that Mason is a knight and Sophia is a knave. Elizabeth said, \"Henry is not a knave.\" Samuel noted, \"Sophia is a knight\". In Emily's words: \"James is a knight or Elizabeth is a knave\". In a statement by Sophia: \"Elizabeth is a knave and Benjamin is a knave\". Benjamin said that Henry is a knight. Mason stated, \"Sophia is a knave if and only if Elizabeth is a knave\". James remarked, \"Mason is a knave\". So who is a knight and who is a knave?", "names": ["Henry", "Elizabeth", "Samuel", "Emily", "Sophia", "Benjamin", "Mason", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false, false, true], "solution_text": "Henry is a knave, Elizabeth is a knave, Samuel is a knight, Emily is a knight, Sophia is a knight, Benjamin is a knave, Mason is a knave, and James is a knight.", "solution_text_format": "(1) Henry is a knave\n(2) Elizabeth is a knave\n(3) Samuel is a knight\n(4) Emily is a knight\n(5) Sophia is a knight\n(6) Benjamin is a knave\n(7) Mason is a knave\n(8) James is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that Mason is a knight and Sophia is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Sophia is a knave if and only if Elizabeth is a knave.", "Sophia cannot be a knight, because this would contradict the claim of Henry that Mason is a knight and Sophia is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Elizabeth is a knave and Benjamin is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of Mason that Sophia is a knave if and only if Elizabeth is a knave.", "Elizabeth cannot be a knave, because this would contradict the false claim of their own that Henry is not a knave.", "We have exhausted all possibilities for Elizabeth and Sophia, so let us go back and reconsider Mason.", "Mason cannot be a knave, because this would contradict the claim of Henry that Mason is a knight and Sophia is a knave.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Mason is a knight and Sophia is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Sophia is a knave if and only if Elizabeth is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Elizabeth is a knave and Benjamin is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Henry is not a knave.", "Elizabeth cannot be a knave, because this would contradict the claim of Mason that Sophia is a knave if and only if Elizabeth is a knave.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the false claim of Henry that Mason is a knight and Sophia is a knave.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Sophia is a knave if and only if Elizabeth is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Elizabeth is a knave and Benjamin is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Henry is not a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Henry is not a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Sophia that Elizabeth is a knave and Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Henry is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Sophia is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that James is a knight or Elizabeth is a knave.", "Assume James is a knight. No contradiction is found in their claim that Mason is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 6), ('lying', 4)), ('not', ('lying', 0)), ('telling-truth', 4), ('or', ('telling-truth', 7), ('lying', 1)), ('and', ('lying', 1), ('lying', 5)), ('telling-truth', 0), ('<=>', ('lying', 4), ('lying', 1)), ('lying', 6))", "index": 169}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Grace, Sophia, Ava, David, Isabella, Henry, William, and Elizabeth. According to Grace, \"Ava is a knight if and only if Henry is a knight\". Sophia told you that If Ava is a knight then Ava is a knave. \"David is a knave and Grace is a knight,\" Ava claimed. David asserted: \"Sophia is not a knight\". \"If Sophia is a knight then Grace is a knave,\" Isabella declared. Henry said that If Sophia is a knave then Ava is a knight. As William put it, \"Elizabeth is a knave and Isabella is a knave\". Elizabeth said, \"Henry is a knight or Elizabeth is a knight.\" So who is a knight and who is a knave?", "names": ["Grace", "Sophia", "Ava", "David", "Isabella", "Henry", "William", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true, false, true], "solution_text": "Grace is a knave, Sophia is a knight, Ava is a knave, David is a knave, Isabella is a knight, Henry is a knight, William is a knave, and Elizabeth is a knight.", "solution_text_format": "(1) Grace is a knave\n(2) Sophia is a knight\n(3) Ava is a knave\n(4) David is a knave\n(5) Isabella is a knight\n(6) Henry is a knight\n(7) William is a knave\n(8) Elizabeth is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Ava is a knight if and only if Henry is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that David is a knave and Grace is a knight.", "David cannot be a knight, because this would contradict the claim of Ava that David is a knave and Grace is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Sophia is not a knight.", "Sophia cannot be a knight, because this would contradict the claim of their own that If Ava is a knight then Ava is a knave.", "Sophia cannot be a knave, because this would contradict the false claim of David that Sophia is not a knight.", "We have exhausted all possibilities for Sophia and David, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that David is a knave and Grace is a knight.", "Assume David is a knight. No contradiction is found in their claim that Sophia is not a knight.", "Sophia cannot be a knight, because this would contradict the claim of David that Sophia is not a knight.", "Sophia cannot be a knave, because this would contradict the false claim of their own that If Ava is a knight then Ava is a knave.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the false claim of Ava that David is a knave and Grace is a knight.", "We have exhausted all possibilities for David and Ava, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Ava is a knight if and only if Henry is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that David is a knave and Grace is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that David is a knave and Grace is a knight.", "Assume David is a knight. No contradiction is found in their claim that Sophia is not a knight.", "Sophia cannot be a knight, because this would contradict the claim of David that Sophia is not a knight.", "Sophia cannot be a knave, because this would contradict the false claim of their own that If Ava is a knight then Ava is a knave.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Sophia is not a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that If Ava is a knight then Ava is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Sophia is a knave then Ava is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that If Sophia is a knight then Grace is a knave.", "William cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave and Isabella is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Elizabeth is a knave and Isabella is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Henry is a knight or Elizabeth is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('telling-truth', 5)), ('->', ('telling-truth', 2), ('lying', 2)), ('and', ('lying', 3), ('telling-truth', 0)), ('not', ('telling-truth', 1)), ('->', ('telling-truth', 1), ('lying', 0)), ('->', ('lying', 1), ('telling-truth', 2)), ('and', ('lying', 7), ('lying', 4)), ('or', ('telling-truth', 5), ('telling-truth', 7)))", "index": 170}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: James, Elizabeth, Penelope, Lucas, Mason, Oliver, Zoey, and Emma. According to James, \"Oliver is a knave\". Elizabeth expressed that Penelope is a knave or Mason is a knave. \"Emma is not a knave,\" Penelope mentioned. In a statement by Lucas: \"Elizabeth is a knave or Mason is a knave\". Mason asserted: \"If Elizabeth is a knave then Elizabeth is a knight\". \"Penelope is not a knight,\" Oliver declared. As Zoey put it, \"Mason is a knave\". Emma said, \"Penelope is a knave and Lucas is a knight.\" So who is a knight and who is a knave?", "names": ["James", "Elizabeth", "Penelope", "Lucas", "Mason", "Oliver", "Zoey", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true, false, false], "solution_text": "James is a knave, Elizabeth is a knight, Penelope is a knave, Lucas is a knave, Mason is a knight, Oliver is a knight, Zoey is a knave, and Emma is a knave.", "solution_text_format": "(1) James is a knave\n(2) Elizabeth is a knight\n(3) Penelope is a knave\n(4) Lucas is a knave\n(5) Mason is a knight\n(6) Oliver is a knight\n(7) Zoey is a knave\n(8) Emma is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Oliver is a knave.", "Oliver cannot be a knight, because this would contradict the claim of James that Oliver is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Penelope is not a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Emma is not a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Penelope is a knave and Lucas is a knight.", "Emma cannot be a knave, because this would contradict the claim of Penelope that Emma is not a knave.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the false claim of Oliver that Penelope is not a knight.", "We have exhausted all possibilities for Penelope and Oliver, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Oliver is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Penelope cannot be a knight, because this would contradict the claim of Oliver that Penelope is not a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Emma is not a knave.", "Emma cannot be a knight, because this would contradict the false claim of Penelope that Emma is not a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Penelope is a knave and Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of Emma that Penelope is a knave and Lucas is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Elizabeth is a knave or Mason is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Penelope is a knave or Mason is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Elizabeth is a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that Mason is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Mason is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 5), ('or', ('lying', 2), ('lying', 4)), ('not', ('lying', 7)), ('or', ('lying', 1), ('lying', 4)), ('->', ('lying', 1), ('telling-truth', 1)), ('not', ('telling-truth', 2)), ('lying', 4), ('and', ('lying', 2), ('telling-truth', 3)))", "index": 171}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Samuel, William, Avery, Victoria, Mason, Noah, Oliver, and Olivia. In a statement by Samuel: \"Olivia is not a knave\". William noted, \"If Oliver is a knight then Mason is a knight\". \"Olivia is a knave or Oliver is a knave,\" Avery mentioned. \"Oliver is not a knave,\" Victoria claimed. \"Noah is a knight and Olivia is a knight,\" Mason claimed. \"Mason is a knight,\" Noah claimed. Oliver remarked, \"Olivia is a knave\". Olivia commented, \"Victoria is a knight and Victoria is a knave\". So who is a knight and who is a knave?", "names": ["Samuel", "William", "Avery", "Victoria", "Mason", "Noah", "Oliver", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false, true, false], "solution_text": "Samuel is a knave, William is a knave, Avery is a knight, Victoria is a knight, Mason is a knave, Noah is a knave, Oliver is a knight, and Olivia is a knave.", "solution_text_format": "(1) Samuel is a knave\n(2) William is a knave\n(3) Avery is a knight\n(4) Victoria is a knight\n(5) Mason is a knave\n(6) Noah is a knave\n(7) Oliver is a knight\n(8) Olivia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that Olivia is not a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that Victoria is a knight and Victoria is a knave.", "Olivia cannot be a knave, because this would contradict the claim of Samuel that Olivia is not a knave.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Olivia is not a knave.", "Olivia cannot be a knight, because this would contradict the false claim of Samuel that Olivia is not a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Victoria is a knight and Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Oliver is not a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Olivia is a knave.", "Assume William is a knight. No contradiction is found in their claim that If Oliver is a knight then Mason is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Noah is a knight and Olivia is a knight.", "Mason cannot be a knave, because this would contradict the claim of William that If Oliver is a knight then Mason is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that If Oliver is a knight then Mason is a knight.", "Mason cannot be a knight, because this would contradict the false claim of William that If Oliver is a knight then Mason is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Noah is a knight and Olivia is a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that Mason is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Mason is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Olivia is a knave or Oliver is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 7)), ('->', ('telling-truth', 6), ('telling-truth', 4)), ('or', ('lying', 7), ('lying', 6)), ('not', ('lying', 6)), ('and', ('telling-truth', 5), ('telling-truth', 7)), ('telling-truth', 4), ('lying', 7), ('and', ('telling-truth', 3), ('lying', 3)))", "index": 172}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Oliver, Luke, Henry, Lily, Jackson, Noah, Joseph, and Sofia. \"Jackson is a knight or Luke is a knave,\" Oliver claimed. Luke asserted: \"Jackson is a knight or Joseph is a knight\". Henry was heard saying, \"Oliver is not a knave\". In Lily's words: \"Noah is a knight if and only if Sofia is a knight\". Jackson commented, \"Lily is not a knight\". Noah was heard saying, \"If Oliver is a knight then Joseph is a knight\". Joseph stated, \"Sofia is a knight if and only if Noah is a knave\". Sofia noted, \"Lily is a knave if and only if Oliver is a knight\". So who is a knight and who is a knave?", "names": ["Oliver", "Luke", "Henry", "Lily", "Jackson", "Noah", "Joseph", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, false, false, false], "solution_text": "Oliver is a knight, Luke is a knave, Henry is a knight, Lily is a knight, Jackson is a knave, Noah is a knave, Joseph is a knave, and Sofia is a knave.", "solution_text_format": "(1) Oliver is a knight\n(2) Luke is a knave\n(3) Henry is a knight\n(4) Lily is a knight\n(5) Jackson is a knave\n(6) Noah is a knave\n(7) Joseph is a knave\n(8) Sofia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Jackson is a knight or Luke is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Lily is not a knight.", "Lily cannot be a knight, because this would contradict the claim of Jackson that Lily is not a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Noah is a knight if and only if Sofia is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that If Oliver is a knight then Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Sofia is a knight if and only if Noah is a knave.", "Sofia cannot be a knight, because this would contradict the false claim of Lily that Noah is a knight if and only if Sofia is a knight.", "Sofia cannot be a knave, because this would contradict the false claim of their own that Lily is a knave if and only if Oliver is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of Noah that If Oliver is a knight then Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that If Oliver is a knight then Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of Noah that If Oliver is a knight then Joseph is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Sofia is a knight if and only if Noah is a knave.", "Sofia cannot be a knight, because this would contradict the false claim of Joseph that Sofia is a knight if and only if Noah is a knave.", "Sofia cannot be a knave, because this would contradict the false claim of Lily that Noah is a knight if and only if Sofia is a knight.", "We have exhausted all possibilities for Sofia, Joseph, Noah, and Lily, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Lily is not a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Noah is a knight if and only if Sofia is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that If Oliver is a knight then Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Sofia is a knight if and only if Noah is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Joseph that Sofia is a knight if and only if Noah is a knave.", "Sofia cannot be a knave, because this would contradict the claim of Lily that Noah is a knight if and only if Sofia is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of Noah that If Oliver is a knight then Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that If Oliver is a knight then Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of Noah that If Oliver is a knight then Joseph is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Sofia is a knight if and only if Noah is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Lily that Noah is a knight if and only if Sofia is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Lily is a knave if and only if Oliver is a knight.", "Luke cannot be a knight, because this would contradict the claim of Oliver that Jackson is a knight or Luke is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Jackson is a knight or Joseph is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Oliver is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('lying', 1)), ('or', ('telling-truth', 4), ('telling-truth', 6)), ('not', ('lying', 0)), ('<=>', ('telling-truth', 5), ('telling-truth', 7)), ('not', ('telling-truth', 3)), ('->', ('telling-truth', 0), ('telling-truth', 6)), ('<=>', ('telling-truth', 7), ('lying', 5)), ('<=>', ('lying', 3), ('telling-truth', 0)))", "index": 173}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Benjamin, Alexander, Harper, Evelyn, Emma, Ella, Ava, and Riley. Benjamin said, \"Emma is a knave if and only if Harper is a knave.\" Alexander said, \"Ava is a knave or Emma is a knight.\" According to Harper, \"Ava is a knave and Ava is a knight\". \"If Ava is a knave then Ella is a knave,\" Evelyn declared. Emma stated, \"Alexander is a knight if and only if Benjamin is a knave\". Ella was heard saying, \"If Riley is a knight then Ella is a knight\". In Ava's words: \"Benjamin is not a knave\". In Riley's words: \"Harper is a knight\". So who is a knight and who is a knave?", "names": ["Benjamin", "Alexander", "Harper", "Evelyn", "Emma", "Ella", "Ava", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true, false, false], "solution_text": "Benjamin is a knave, Alexander is a knight, Harper is a knave, Evelyn is a knave, Emma is a knight, Ella is a knight, Ava is a knave, and Riley is a knave.", "solution_text_format": "(1) Benjamin is a knave\n(2) Alexander is a knight\n(3) Harper is a knave\n(4) Evelyn is a knave\n(5) Emma is a knight\n(6) Ella is a knight\n(7) Ava is a knave\n(8) Riley is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Emma is a knave if and only if Harper is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Alexander is a knight if and only if Benjamin is a knave.", "Alexander cannot be a knight, because this would contradict the claim of Emma that Alexander is a knight if and only if Benjamin is a knave.", "Alexander cannot be a knave, because this would contradict the false claim of their own that Ava is a knave or Emma is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Alexander is a knight if and only if Benjamin is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Ava is a knave or Emma is a knight.", "Ava cannot be a knight, because this would contradict the claim of Alexander that Ava is a knave or Emma is a knight.", "Ava cannot be a knave, because this would contradict the false claim of their own that Benjamin is not a knave.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Alexander.", "Alexander cannot be a knave, because this would contradict the false claim of Emma that Alexander is a knight if and only if Benjamin is a knave.", "We have exhausted all possibilities for Alexander and Emma, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Emma is a knave if and only if Harper is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Alexander is a knight if and only if Benjamin is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Ava is a knave or Emma is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Benjamin is not a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Benjamin is not a knave.", "Harper cannot be a knight, because this would contradict the false claim of Benjamin that Emma is a knave if and only if Harper is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Ava is a knave and Ava is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Ava is a knave then Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of Evelyn that If Ava is a knave then Ella is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that If Riley is a knight then Ella is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Harper is a knight.", "Riley cannot be a knave, because this would contradict the false claim of Ella that If Riley is a knight then Ella is a knight.", "We have exhausted all possibilities for Riley and Ella, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that If Ava is a knave then Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that If Riley is a knight then Ella is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Harper is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Harper is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 4), ('lying', 2)), ('or', ('lying', 6), ('telling-truth', 4)), ('and', ('lying', 6), ('telling-truth', 6)), ('->', ('lying', 6), ('lying', 5)), ('<=>', ('telling-truth', 1), ('lying', 0)), ('->', ('telling-truth', 7), ('telling-truth', 5)), ('not', ('lying', 0)), ('telling-truth', 2))", "index": 174}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Abigail, Mason, Riley, Victoria, Ethan, Jacob, Charlotte, and Lucas. Abigail was heard saying, \"Victoria is a knave\". Mason was heard saying, \"Lucas is a knight if and only if Charlotte is a knight\". Riley was heard saying, \"Victoria is a knave or Victoria is a knight\". \"Mason is a knave\" - Victoria. Ethan noted, \"Abigail is a knight and Abigail is a knave\". Jacob commented, \"Ethan is a knave\". Charlotte noted, \"If Ethan is a knight then Lucas is a knight\". Lucas stated, \"If Mason is a knight then Jacob is a knight\". So who is a knight and who is a knave?", "names": ["Abigail", "Mason", "Riley", "Victoria", "Ethan", "Jacob", "Charlotte", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true, true, true], "solution_text": "Abigail is a knight, Mason is a knight, Riley is a knight, Victoria is a knave, Ethan is a knave, Jacob is a knight, Charlotte is a knight, and Lucas is a knight.", "solution_text_format": "(1) Abigail is a knight\n(2) Mason is a knight\n(3) Riley is a knight\n(4) Victoria is a knave\n(5) Ethan is a knave\n(6) Jacob is a knight\n(7) Charlotte is a knight\n(8) Lucas is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Victoria is a knave.", "Victoria cannot be a knight, because this would contradict the claim of Abigail that Victoria is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Mason is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Lucas is a knight if and only if Charlotte is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that If Mason is a knight then Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Ethan is a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Abigail is a knight and Abigail is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Abigail is a knight and Abigail is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Ethan is a knight then Lucas is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Victoria is a knave or Victoria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('<=>', ('telling-truth', 7), ('telling-truth', 6)), ('or', ('lying', 3), ('telling-truth', 3)), ('lying', 1), ('and', ('telling-truth', 0), ('lying', 0)), ('lying', 4), ('->', ('telling-truth', 4), ('telling-truth', 7)), ('->', ('telling-truth', 1), ('telling-truth', 5)))", "index": 175}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Amelia, William, Mason, Lucas, James, Victoria, Daniel, and Riley. Amelia expressed that Victoria is a knight if and only if Lucas is a knight. William told you that If Daniel is a knave then James is a knave. Mason was heard saying, \"If Amelia is a knight then Lucas is a knight\". In a statement by Lucas: \"James is a knight or Daniel is a knight\". According to James, \"Mason is a knave or Victoria is a knave\". Victoria said, \"Riley is not a knight.\" As Daniel put it, \"William is a knight\". \"Amelia is a knave if and only if William is a knave,\" Riley mentioned. So who is a knight and who is a knave?", "names": ["Amelia", "William", "Mason", "Lucas", "James", "Victoria", "Daniel", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false, false, true], "solution_text": "Amelia is a knave, William is a knave, Mason is a knight, Lucas is a knight, James is a knight, Victoria is a knave, Daniel is a knave, and Riley is a knight.", "solution_text_format": "(1) Amelia is a knave\n(2) William is a knave\n(3) Mason is a knight\n(4) Lucas is a knight\n(5) James is a knight\n(6) Victoria is a knave\n(7) Daniel is a knave\n(8) Riley is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Amelia is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Lucas is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Riley is not a knight.", "Riley cannot be a knight, because this would contradict the claim of Victoria that Riley is not a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Amelia is a knave if and only if William is a knave.", "William cannot be a knight, because this would contradict the false claim of Riley that Amelia is a knave if and only if William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that If Daniel is a knave then James is a knave.", "Daniel cannot be a knight, because this would contradict the false claim of William that If Daniel is a knave then James is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that William is a knight.", "Assume James is a knight. No contradiction is found in their claim that Mason is a knave or Victoria is a knave.", "Mason cannot be a knight, because this would contradict the claim of James that Mason is a knave or Victoria is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that If Amelia is a knight then Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of Mason that If Amelia is a knight then Lucas is a knight.", "Lucas cannot be a knave, because this would contradict the claim of Amelia that Victoria is a knight if and only if Lucas is a knight.", "We have exhausted all possibilities for Lucas and Mason, so let us go back and reconsider James.", "James cannot be a knave, because this would contradict the false claim of William that If Daniel is a knave then James is a knave.", "We have exhausted all possibilities for James, Daniel, William, and Riley, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Riley is not a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Amelia is a knave if and only if William is a knave.", "Assume William is a knight. No contradiction is found in their claim that If Daniel is a knave then James is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that William is a knight.", "Assume James is a knight. No contradiction is found in their claim that Mason is a knave or Victoria is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Amelia is a knight then Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the claim of Amelia that Victoria is a knight if and only if Lucas is a knight.", "Lucas cannot be a knave, because this would contradict the claim of Mason that If Amelia is a knight then Lucas is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that If Amelia is a knight then Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the claim of Amelia that Victoria is a knight if and only if Lucas is a knight.", "Lucas cannot be a knave, because this would contradict the false claim of their own that James is a knight or Daniel is a knight.", "We have exhausted all possibilities for Lucas and Mason, so let us go back and reconsider James.", "James cannot be a knave, because this would contradict the false claim of their own that Mason is a knave or Victoria is a knave.", "We have exhausted all possibilities for James, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the false claim of their own that William is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the claim of Riley that Amelia is a knave if and only if William is a knave.", "We have exhausted all possibilities for William, so let us go back and reconsider Riley.", "Riley cannot be a knave, because this would contradict the false claim of Victoria that Riley is not a knight.", "We have exhausted all possibilities for Riley and Victoria, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Victoria is a knight if and only if Lucas is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Riley is not a knight.", "Riley cannot be a knight, because this would contradict the claim of Victoria that Riley is not a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Amelia is a knave if and only if William is a knave.", "Assume William is a knight. No contradiction is found in their claim that If Daniel is a knave then James is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that William is a knight.", "Assume James is a knight. No contradiction is found in their claim that Mason is a knave or Victoria is a knave.", "Mason cannot be a knight, because this would contradict the claim of James that Mason is a knave or Victoria is a knave.", "Mason cannot be a knave, because this would contradict the false claim of their own that If Amelia is a knight then Lucas is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Mason is a knave or Victoria is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Amelia is a knight then Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of Amelia that Victoria is a knight if and only if Lucas is a knight.", "Lucas cannot be a knave, because this would contradict the false claim of their own that James is a knight or Daniel is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Mason.", "Mason cannot be a knave, because this would contradict the false claim of their own that If Amelia is a knight then Lucas is a knight.", "We have exhausted all possibilities for Mason and James, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the false claim of their own that William is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the false claim of Riley that Amelia is a knave if and only if William is a knave.", "We have exhausted all possibilities for William and Riley, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Riley is not a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Amelia is a knave if and only if William is a knave.", "William cannot be a knight, because this would contradict the claim of Riley that Amelia is a knave if and only if William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that If Daniel is a knave then James is a knave.", "Daniel cannot be a knight, because this would contradict the false claim of William that If Daniel is a knave then James is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that William is a knight.", "Assume James is a knight. No contradiction is found in their claim that Mason is a knave or Victoria is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Amelia is a knight then Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that James is a knight or Daniel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 5), ('telling-truth', 3)), ('->', ('lying', 6), ('lying', 4)), ('->', ('telling-truth', 0), ('telling-truth', 3)), ('or', ('telling-truth', 4), ('telling-truth', 6)), ('or', ('lying', 2), ('lying', 5)), ('not', ('telling-truth', 7)), ('telling-truth', 1), ('<=>', ('lying', 0), ('lying', 1)))", "index": 176}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emma, Lily, Avery, Aurora, Evelyn, Noah, Abigail, and Grace. Emma stated, \"Noah is a knave\". According to Lily, \"If Abigail is a knight then Noah is a knave\". Avery told you that If Grace is a knave then Avery is a knight. Aurora said that Grace is a knight and Evelyn is a knight. Evelyn said, \"Lily is a knave or Aurora is a knave.\" Noah commented, \"Evelyn is a knight and Evelyn is a knave\". In Abigail's words: \"Avery is a knight if and only if Lily is a knave\". Grace remarked, \"Evelyn is a knave if and only if Avery is a knave\". So who is a knight and who is a knave?", "names": ["Emma", "Lily", "Avery", "Aurora", "Evelyn", "Noah", "Abigail", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, false, true, false], "solution_text": "Emma is a knight, Lily is a knight, Avery is a knave, Aurora is a knave, Evelyn is a knight, Noah is a knave, Abigail is a knight, and Grace is a knave.", "solution_text_format": "(1) Emma is a knight\n(2) Lily is a knight\n(3) Avery is a knave\n(4) Aurora is a knave\n(5) Evelyn is a knight\n(6) Noah is a knave\n(7) Abigail is a knight\n(8) Grace is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of Emma that Noah is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Evelyn is a knight and Evelyn is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Lily is a knave or Aurora is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that If Abigail is a knight then Noah is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Avery is a knight if and only if Lily is a knave.", "Avery cannot be a knight, because this would contradict the claim of Abigail that Avery is a knight if and only if Lily is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that If Grace is a knave then Avery is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Avery that If Grace is a knave then Avery is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Evelyn is a knave if and only if Avery is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Grace is a knight and Evelyn is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Grace is a knight and Evelyn is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 5), ('->', ('telling-truth', 6), ('lying', 5)), ('->', ('lying', 7), ('telling-truth', 2)), ('and', ('telling-truth', 7), ('telling-truth', 4)), ('or', ('lying', 1), ('lying', 3)), ('and', ('telling-truth', 4), ('lying', 4)), ('<=>', ('telling-truth', 2), ('lying', 1)), ('<=>', ('lying', 4), ('lying', 2)))", "index": 177}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jack, James, Daniel, Luke, Aiden, William, David, and Olivia. \"Luke is a knight,\" Jack declared. James was heard saying, \"William is a knight and Olivia is a knight\". Daniel commented, \"William is a knight or William is a knave\". \"James is a knave or Daniel is a knight,\" Luke declared. Aiden said, \"Daniel is a knight or James is a knight.\" William expressed that If James is a knight then Aiden is a knave. David noted, \"If William is a knave then Jack is a knave\". Olivia stated, \"William is a knave and David is a knight\". So who is a knight and who is a knave?", "names": ["Jack", "James", "Daniel", "Luke", "Aiden", "William", "David", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true, true, false], "solution_text": "Jack is a knight, James is a knave, Daniel is a knight, Luke is a knight, Aiden is a knight, William is a knight, David is a knight, and Olivia is a knave.", "solution_text_format": "(1) Jack is a knight\n(2) James is a knave\n(3) Daniel is a knight\n(4) Luke is a knight\n(5) Aiden is a knight\n(6) William is a knight\n(7) David is a knight\n(8) Olivia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Luke is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that James is a knave or Daniel is a knight.", "Assume James is a knight. No contradiction is found in their claim that William is a knight and Olivia is a knight.", "Assume William is a knight. No contradiction is found in their claim that If James is a knight then Aiden is a knave.", "Aiden cannot be a knight, because this would contradict the claim of William that If James is a knight then Aiden is a knave.", "Aiden cannot be a knave, because this would contradict the false claim of their own that Daniel is a knight or James is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the claim of James that William is a knight and Olivia is a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that William is a knight and Olivia is a knight.", "Assume William is a knight. No contradiction is found in their claim that If James is a knight then Aiden is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Daniel is a knight or James is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that William is a knight or William is a knave.", "Olivia cannot be a knight, because this would contradict the false claim of James that William is a knight and Olivia is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that William is a knave and David is a knight.", "Assume David is a knight. No contradiction is found in their claim that If William is a knave then Jack is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 3), ('and', ('telling-truth', 5), ('telling-truth', 7)), ('or', ('telling-truth', 5), ('lying', 5)), ('or', ('lying', 1), ('telling-truth', 2)), ('or', ('telling-truth', 2), ('telling-truth', 1)), ('->', ('telling-truth', 1), ('lying', 4)), ('->', ('lying', 5), ('lying', 0)), ('and', ('lying', 5), ('telling-truth', 6)))", "index": 178}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Owen, Amelia, Emily, Jack, Michael, Joseph, Sebastian, and Ella. In a statement by Owen: \"Ella is a knight or Joseph is a knight\". \"Sebastian is a knave or Amelia is a knight,\" Amelia mentioned. \"Owen is a knave,\" Emily mentioned. According to Jack, \"Michael is a knight and Joseph is a knave\". Michael expressed that Michael is a knight if and only if Jack is a knight. Joseph told you that Sebastian is a knave if and only if Jack is a knave. As Sebastian put it, \"Sebastian is a knight or Ella is a knave\". Ella remarked, \"Owen is not a knave\". So who is a knight and who is a knave?", "names": ["Owen", "Amelia", "Emily", "Jack", "Michael", "Joseph", "Sebastian", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false, false, true], "solution_text": "Owen is a knight, Amelia is a knight, Emily is a knave, Jack is a knight, Michael is a knight, Joseph is a knave, Sebastian is a knave, and Ella is a knight.", "solution_text_format": "(1) Owen is a knight\n(2) Amelia is a knight\n(3) Emily is a knave\n(4) Jack is a knight\n(5) Michael is a knight\n(6) Joseph is a knave\n(7) Sebastian is a knave\n(8) Ella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Ella is a knight or Joseph is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Owen is not a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Sebastian is a knave if and only if Jack is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Sebastian is a knight or Ella is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Michael is a knight and Joseph is a knave.", "Jack cannot be a knave, because this would contradict the claim of Joseph that Sebastian is a knave if and only if Jack is a knave.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Sebastian is a knight or Ella is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Michael is a knight and Joseph is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Michael is a knight and Joseph is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Michael is a knight if and only if Jack is a knight.", "Michael cannot be a knave, because this would contradict the false claim of their own that Michael is a knight if and only if Jack is a knight.", "We have exhausted all possibilities for Michael, Jack, and Sebastian, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Sebastian is a knave if and only if Jack is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Sebastian is a knight or Ella is a knave.", "Jack cannot be a knight, because this would contradict the false claim of Joseph that Sebastian is a knave if and only if Jack is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Michael is a knight and Joseph is a knave.", "Michael cannot be a knight, because this would contradict the false claim of Jack that Michael is a knight and Joseph is a knave.", "Michael cannot be a knave, because this would contradict the false claim of their own that Michael is a knight if and only if Jack is a knight.", "We have exhausted all possibilities for Michael and Jack, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Sebastian is a knight or Ella is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Michael is a knight and Joseph is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Michael is a knight if and only if Jack is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Sebastian is a knave or Amelia is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Owen is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Owen is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 7), ('telling-truth', 5)), ('or', ('lying', 6), ('telling-truth', 1)), ('lying', 0), ('and', ('telling-truth', 4), ('lying', 5)), ('<=>', ('telling-truth', 4), ('telling-truth', 3)), ('<=>', ('lying', 6), ('lying', 3)), ('or', ('telling-truth', 6), ('lying', 7)), ('not', ('lying', 0)))", "index": 179}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aiden, Riley, Charlotte, William, Michael, Zoey, Isabella, and Samuel. Aiden said, \"Aiden is a knight or Michael is a knight.\" Riley was heard saying, \"If Samuel is a knight then Aiden is a knave\". According to Charlotte, \"Samuel is a knave or Aiden is a knave\". William remarked, \"Riley is not a knave\". \"Samuel is a knave if and only if Isabella is a knave,\" Michael mentioned. Zoey said that William is a knave if and only if Riley is a knave. Isabella asserted: \"William is a knight\". Samuel remarked, \"Aiden is a knave\". So who is a knight and who is a knave?", "names": ["Aiden", "Riley", "Charlotte", "William", "Michael", "Zoey", "Isabella", "Samuel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true, true, false], "solution_text": "Aiden is a knight, Riley is a knight, Charlotte is a knight, William is a knight, Michael is a knave, Zoey is a knight, Isabella is a knight, and Samuel is a knave.", "solution_text_format": "(1) Aiden is a knight\n(2) Riley is a knight\n(3) Charlotte is a knight\n(4) William is a knight\n(5) Michael is a knave\n(6) Zoey is a knight\n(7) Isabella is a knight\n(8) Samuel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Aiden is a knight or Michael is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Isabella is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that Aiden is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Aiden is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Michael that Samuel is a knave if and only if Isabella is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that William is a knight.", "William cannot be a knight, because this would contradict the false claim of Isabella that William is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Riley is not a knave.", "Riley cannot be a knight, because this would contradict the false claim of William that Riley is not a knave.", "Riley cannot be a knave, because this would contradict the false claim of their own that If Samuel is a knight then Aiden is a knave.", "We have exhausted all possibilities for Riley, William, Isabella, and Samuel, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Samuel is a knave if and only if Isabella is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that Aiden is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Aiden is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that William is a knight.", "Assume William is a knight. No contradiction is found in their claim that Riley is not a knave.", "Assume Riley is a knight. No contradiction is found in their claim that If Samuel is a knight then Aiden is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Samuel is a knave or Aiden is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that William is a knave if and only if Riley is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 0), ('telling-truth', 4)), ('->', ('telling-truth', 7), ('lying', 0)), ('or', ('lying', 7), ('lying', 0)), ('not', ('lying', 1)), ('<=>', ('lying', 7), ('lying', 6)), ('<=>', ('lying', 3), ('lying', 1)), ('telling-truth', 3), ('lying', 0))", "index": 180}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: James, Aurora, Michael, Scarlett, Amelia, Benjamin, Henry, and Charlotte. In James's words: \"Charlotte is a knave if and only if Amelia is a knight\". In Aurora's words: \"Michael is a knight or Benjamin is a knave\". \"James is a knight if and only if Scarlett is a knight,\" Michael declared. Scarlett told you that Aurora is not a knave. In Amelia's words: \"Aurora is a knight if and only if Scarlett is a knight\". According to Benjamin, \"Michael is a knight and Aurora is a knave\". Henry was heard saying, \"Amelia is not a knight\". Charlotte remarked, \"If Michael is a knave then Amelia is a knight\". So who is a knight and who is a knave?", "names": ["James", "Aurora", "Michael", "Scarlett", "Amelia", "Benjamin", "Henry", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false, false, true], "solution_text": "James is a knave, Aurora is a knight, Michael is a knave, Scarlett is a knight, Amelia is a knight, Benjamin is a knave, Henry is a knave, and Charlotte is a knight.", "solution_text_format": "(1) James is a knave\n(2) Aurora is a knight\n(3) Michael is a knave\n(4) Scarlett is a knight\n(5) Amelia is a knight\n(6) Benjamin is a knave\n(7) Henry is a knave\n(8) Charlotte is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Charlotte is a knave if and only if Amelia is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Michael is a knave then Amelia is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that James is a knight if and only if Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Aurora is not a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Michael is a knight or Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Michael is a knight and Aurora is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Michael is a knight and Aurora is a knave.", "Amelia cannot be a knight, because this would contradict the claim of James that Charlotte is a knave if and only if Amelia is a knight.", "Amelia cannot be a knave, because this would contradict the false claim of their own that Aurora is a knight if and only if Scarlett is a knight.", "We have exhausted all possibilities for Amelia and Benjamin, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the false claim of their own that Michael is a knight or Benjamin is a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the claim of Michael that James is a knight if and only if Scarlett is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that James is a knight if and only if Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the false claim of Michael that James is a knight if and only if Scarlett is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Aurora is not a knave.", "Aurora cannot be a knight, because this would contradict the false claim of Scarlett that Aurora is not a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Michael is a knight or Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Michael is a knight and Aurora is a knave.", "Benjamin cannot be a knave, because this would contradict the false claim of Aurora that Michael is a knight or Benjamin is a knave.", "We have exhausted all possibilities for Benjamin, Aurora, Scarlett, and Michael, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that If Michael is a knave then Amelia is a knight.", "Michael cannot be a knight, because this would contradict the false claim of Charlotte that If Michael is a knave then Amelia is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that James is a knight if and only if Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the false claim of Michael that James is a knight if and only if Scarlett is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Aurora is not a knave.", "Aurora cannot be a knight, because this would contradict the false claim of Scarlett that Aurora is not a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Michael is a knight or Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Michael is a knight and Aurora is a knave.", "Benjamin cannot be a knave, because this would contradict the false claim of Aurora that Michael is a knight or Benjamin is a knave.", "We have exhausted all possibilities for Benjamin, Aurora, Scarlett, Michael, and Charlotte, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Charlotte is a knave if and only if Amelia is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Michael is a knave then Amelia is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that James is a knight if and only if Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of Michael that James is a knight if and only if Scarlett is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Aurora is not a knave.", "Aurora cannot be a knight, because this would contradict the false claim of Scarlett that Aurora is not a knave.", "Aurora cannot be a knave, because this would contradict the false claim of their own that Michael is a knight or Benjamin is a knave.", "We have exhausted all possibilities for Aurora and Scarlett, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that James is a knight if and only if Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Aurora is not a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Michael is a knight or Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Aurora that Michael is a knight or Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Michael is a knight and Aurora is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Aurora is a knight if and only if Scarlett is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Amelia is not a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Amelia is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 7), ('telling-truth', 4)), ('or', ('telling-truth', 2), ('lying', 5)), ('<=>', ('telling-truth', 0), ('telling-truth', 3)), ('not', ('lying', 1)), ('<=>', ('telling-truth', 1), ('telling-truth', 3)), ('and', ('telling-truth', 2), ('lying', 1)), ('not', ('telling-truth', 4)), ('->', ('lying', 2), ('telling-truth', 4)))", "index": 181}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Benjamin, Liam, Alexander, Ava, Jacob, Matthew, Mason, and Emma. According to Benjamin, \"Ava is a knight if and only if Benjamin is a knight\". \"If Emma is a knight then Benjamin is a knave,\" Liam claimed. \"If Benjamin is a knave then Liam is a knave,\" Alexander claimed. In Ava's words: \"Alexander is a knight and Liam is a knave\". \"Emma is a knave and Mason is a knave\" - Jacob. Matthew expressed that Emma is not a knave. Mason stated, \"If Benjamin is a knave then Liam is a knave\". Emma stated, \"Ava is a knight if and only if Jacob is a knave\". So who is a knight and who is a knave?", "names": ["Benjamin", "Liam", "Alexander", "Ava", "Jacob", "Matthew", "Mason", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true, true, true], "solution_text": "Benjamin is a knight, Liam is a knave, Alexander is a knight, Ava is a knight, Jacob is a knave, Matthew is a knight, Mason is a knight, and Emma is a knight.", "solution_text_format": "(1) Benjamin is a knight\n(2) Liam is a knave\n(3) Alexander is a knight\n(4) Ava is a knight\n(5) Jacob is a knave\n(6) Matthew is a knight\n(7) Mason is a knight\n(8) Emma is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Ava is a knight if and only if Benjamin is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Alexander is a knight and Liam is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that If Benjamin is a knave then Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of Ava that Alexander is a knight and Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that If Emma is a knight then Benjamin is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Ava is a knight if and only if Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of their own that Emma is a knave and Mason is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Emma is a knave and Mason is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Benjamin is a knave then Liam is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Emma is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 3), ('telling-truth', 0)), ('->', ('telling-truth', 7), ('lying', 0)), ('->', ('lying', 0), ('lying', 1)), ('and', ('telling-truth', 2), ('lying', 1)), ('and', ('lying', 7), ('lying', 6)), ('not', ('lying', 7)), ('->', ('lying', 0), ('lying', 1)), ('<=>', ('telling-truth', 3), ('lying', 4)))", "index": 182}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: David, Abigail, Lucas, Zoey, Ethan, William, Harper, and Isabella. \"Abigail is a knight and William is a knight\" - David. Abigail told you that Harper is not a knave. Lucas noted, \"If William is a knight then Zoey is a knight\". According to Zoey, \"David is a knave if and only if William is a knight\". \"Lucas is not a knave,\" Ethan claimed. As William put it, \"Harper is a knave and Abigail is a knave\". Harper asserted: \"Ethan is a knave\". \"Harper is not a knight,\" Isabella mentioned. So who is a knight and who is a knave?", "names": ["David", "Abigail", "Lucas", "Zoey", "Ethan", "William", "Harper", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true, false, true], "solution_text": "David is a knave, Abigail is a knave, Lucas is a knight, Zoey is a knight, Ethan is a knight, William is a knight, Harper is a knave, and Isabella is a knight.", "solution_text_format": "(1) David is a knave\n(2) Abigail is a knave\n(3) Lucas is a knight\n(4) Zoey is a knight\n(5) Ethan is a knight\n(6) William is a knight\n(7) Harper is a knave\n(8) Isabella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Abigail is a knight and William is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Harper is not a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Ethan is a knave.", "Ethan cannot be a knight, because this would contradict the claim of Harper that Ethan is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Lucas is not a knave.", "Lucas cannot be a knight, because this would contradict the false claim of Ethan that Lucas is not a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that If William is a knight then Zoey is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Harper is a knave and Abigail is a knave.", "William cannot be a knave, because this would contradict the claim of David that Abigail is a knight and William is a knight.", "We have exhausted all possibilities for William, Lucas, and Ethan, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the claim of Abigail that Harper is not a knave.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the claim of David that Abigail is a knight and William is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Abigail is a knight and William is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Harper is not a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Ethan is a knave.", "Ethan cannot be a knight, because this would contradict the claim of Harper that Ethan is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Lucas is not a knave.", "Lucas cannot be a knight, because this would contradict the false claim of Ethan that Lucas is not a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that If William is a knight then Zoey is a knight.", "William cannot be a knight, because this would contradict the false claim of David that Abigail is a knight and William is a knight.", "William cannot be a knave, because this would contradict the false claim of Lucas that If William is a knight then Zoey is a knight.", "We have exhausted all possibilities for William, Lucas, and Ethan, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the claim of Abigail that Harper is not a knave.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Harper is not a knave.", "Harper cannot be a knight, because this would contradict the false claim of Abigail that Harper is not a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Ethan is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Lucas is not a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that If William is a knight then Zoey is a knight.", "Assume William is a knight. No contradiction is found in their claim that Harper is a knave and Abigail is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that David is a knave if and only if William is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Harper is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('telling-truth', 5)), ('not', ('lying', 6)), ('->', ('telling-truth', 5), ('telling-truth', 3)), ('<=>', ('lying', 0), ('telling-truth', 5)), ('not', ('lying', 2)), ('and', ('lying', 6), ('lying', 1)), ('lying', 4), ('not', ('telling-truth', 6)))", "index": 183}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Zoey, Oliver, Alexander, Sofia, Jack, Emma, Luke, and Emily. Zoey was heard saying, \"Sofia is a knight\". In Oliver's words: \"Emma is not a knight\". Alexander commented, \"Sofia is a knave or Sofia is a knight\". Sofia remarked, \"Jack is not a knight\". Jack said that Oliver is a knight. Emma noted, \"Luke is not a knight\". As Luke put it, \"Sofia is a knight if and only if Zoey is a knave\". \"Sofia is a knave if and only if Jack is a knight\" - Emily. So who is a knight and who is a knave?", "names": ["Zoey", "Oliver", "Alexander", "Sofia", "Jack", "Emma", "Luke", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true, false, true], "solution_text": "Zoey is a knight, Oliver is a knave, Alexander is a knight, Sofia is a knight, Jack is a knave, Emma is a knight, Luke is a knave, and Emily is a knight.", "solution_text_format": "(1) Zoey is a knight\n(2) Oliver is a knave\n(3) Alexander is a knight\n(4) Sofia is a knight\n(5) Jack is a knave\n(6) Emma is a knight\n(7) Luke is a knave\n(8) Emily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Zoey is a knight. No contradiction is found in their claim that Sofia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Jack is not a knight.", "Jack cannot be a knight, because this would contradict the claim of Sofia that Jack is not a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Oliver is a knight.", "Oliver cannot be a knight, because this would contradict the false claim of Jack that Oliver is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Emma is not a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Luke is not a knight.", "Luke cannot be a knight, because this would contradict the claim of Emma that Luke is not a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Sofia is a knight if and only if Zoey is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Sofia is a knave or Sofia is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Sofia is a knave if and only if Jack is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 3), ('not', ('telling-truth', 5)), ('or', ('lying', 3), ('telling-truth', 3)), ('not', ('telling-truth', 4)), ('telling-truth', 1), ('not', ('telling-truth', 6)), ('<=>', ('telling-truth', 3), ('lying', 0)), ('<=>', ('lying', 3), ('telling-truth', 4)))", "index": 184}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Luke, Owen, Jackson, Evelyn, Henry, Sofia, Noah, and Joseph. \"Jackson is a knight if and only if Owen is a knight\" - Luke. \"Jackson is a knave if and only if Sofia is a knave,\" Owen claimed. Jackson expressed that Joseph is a knave. As Evelyn put it, \"Owen is not a knight\". In a statement by Henry: \"Owen is not a knight\". In Sofia's words: \"Owen is a knight and Owen is a knave\". Noah was heard saying, \"Luke is a knave or Joseph is a knave\". Joseph said, \"Noah is a knave if and only if Sofia is a knight.\" So who is a knight and who is a knave?", "names": ["Luke", "Owen", "Jackson", "Evelyn", "Henry", "Sofia", "Noah", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, false, true, true], "solution_text": "Luke is a knave, Owen is a knight, Jackson is a knave, Evelyn is a knave, Henry is a knave, Sofia is a knave, Noah is a knight, and Joseph is a knight.", "solution_text_format": "(1) Luke is a knave\n(2) Owen is a knight\n(3) Jackson is a knave\n(4) Evelyn is a knave\n(5) Henry is a knave\n(6) Sofia is a knave\n(7) Noah is a knight\n(8) Joseph is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Owen is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Jackson that Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Noah is a knave if and only if Sofia is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Luke is a knave or Joseph is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Owen is a knight and Owen is a knave.", "Sofia cannot be a knave, because this would contradict the false claim of Joseph that Noah is a knave if and only if Sofia is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the false claim of their own that Luke is a knave or Joseph is a knave.", "We have exhausted all possibilities for Noah and Joseph, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Joseph is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Noah is a knave if and only if Sofia is a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that Luke is a knave or Joseph is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Luke is a knave or Joseph is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Owen is a knight and Owen is a knave.", "Sofia cannot be a knave, because this would contradict the claim of Joseph that Noah is a knave if and only if Sofia is a knight.", "We have exhausted all possibilities for Sofia and Noah, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the false claim of Jackson that Joseph is a knave.", "We have exhausted all possibilities for Joseph and Jackson, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Jackson is a knight if and only if Owen is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Jackson that Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Noah is a knave if and only if Sofia is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Luke is a knave or Joseph is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Owen is a knight and Owen is a knave.", "Sofia cannot be a knave, because this would contradict the false claim of Joseph that Noah is a knave if and only if Sofia is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the false claim of their own that Luke is a knave or Joseph is a knave.", "We have exhausted all possibilities for Noah and Joseph, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Joseph is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Noah is a knave if and only if Sofia is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Luke is a knave or Joseph is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Owen is a knight and Owen is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Owen is a knight and Owen is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Jackson is a knave if and only if Sofia is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Owen is not a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Owen is not a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Owen is not a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Owen is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('telling-truth', 1)), ('<=>', ('lying', 2), ('lying', 5)), ('lying', 7), ('not', ('telling-truth', 1)), ('not', ('telling-truth', 1)), ('and', ('telling-truth', 1), ('lying', 1)), ('or', ('lying', 0), ('lying', 7)), ('<=>', ('lying', 6), ('telling-truth', 5)))", "index": 185}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aiden, Amelia, Joseph, Emily, Ava, Benjamin, Olivia, and Aurora. According to Aiden, \"Olivia is a knight and Benjamin is a knight\". According to Amelia, \"Ava is not a knight\". Joseph told you that Joseph is a knight or Olivia is a knight. Emily remarked, \"Olivia is not a knight\". \"Benjamin is a knave if and only if Aurora is a knight,\" Ava declared. \"If Emily is a knave then Aiden is a knight,\" Benjamin declared. \"Benjamin is a knight,\" Olivia mentioned. \"Emily is a knave,\" Aurora mentioned. So who is a knight and who is a knave?", "names": ["Aiden", "Amelia", "Joseph", "Emily", "Ava", "Benjamin", "Olivia", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true, true, true], "solution_text": "Aiden is a knight, Amelia is a knight, Joseph is a knight, Emily is a knave, Ava is a knave, Benjamin is a knight, Olivia is a knight, and Aurora is a knight.", "solution_text_format": "(1) Aiden is a knight\n(2) Amelia is a knight\n(3) Joseph is a knight\n(4) Emily is a knave\n(5) Ava is a knave\n(6) Benjamin is a knight\n(7) Olivia is a knight\n(8) Aurora is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Olivia is a knight and Benjamin is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Benjamin is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Emily is a knave then Aiden is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Olivia is not a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Olivia is not a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Ava is not a knight.", "Ava cannot be a knight, because this would contradict the claim of Amelia that Ava is not a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Benjamin is a knave if and only if Aurora is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Emily is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Joseph is a knight or Olivia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 6), ('telling-truth', 5)), ('not', ('telling-truth', 4)), ('or', ('telling-truth', 2), ('telling-truth', 6)), ('not', ('telling-truth', 6)), ('<=>', ('lying', 5), ('telling-truth', 7)), ('->', ('lying', 3), ('telling-truth', 0)), ('telling-truth', 5), ('lying', 3))", "index": 186}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mia, Chloe, Joseph, Elizabeth, Sebastian, Aurora, Alexander, and Sophia. \"Elizabeth is a knave or Sebastian is a knight,\" Mia mentioned. \"Sophia is a knave if and only if Alexander is a knight\" - Chloe. In a statement by Joseph: \"If Chloe is a knave then Chloe is a knight\". In Elizabeth's words: \"If Alexander is a knave then Chloe is a knight\". In a statement by Sebastian: \"Elizabeth is a knight\". Aurora noted, \"Alexander is not a knight\". According to Alexander, \"Chloe is a knave or Mia is a knave\". Sophia said, \"Chloe is not a knight.\" So who is a knight and who is a knave?", "names": ["Mia", "Chloe", "Joseph", "Elizabeth", "Sebastian", "Aurora", "Alexander", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false, true, true], "solution_text": "Mia is a knight, Chloe is a knave, Joseph is a knave, Elizabeth is a knight, Sebastian is a knight, Aurora is a knave, Alexander is a knight, and Sophia is a knight.", "solution_text_format": "(1) Mia is a knight\n(2) Chloe is a knave\n(3) Joseph is a knave\n(4) Elizabeth is a knight\n(5) Sebastian is a knight\n(6) Aurora is a knave\n(7) Alexander is a knight\n(8) Sophia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Elizabeth is a knave or Sebastian is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Alexander is a knave then Chloe is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Chloe is a knave or Mia is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Alexander that Chloe is a knave or Mia is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Sophia is a knave if and only if Alexander is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Chloe is not a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that If Chloe is a knave then Chloe is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that If Chloe is a knave then Chloe is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Alexander is not a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Alexander is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('telling-truth', 4)), ('<=>', ('lying', 7), ('telling-truth', 6)), ('->', ('lying', 1), ('telling-truth', 1)), ('->', ('lying', 6), ('telling-truth', 1)), ('telling-truth', 3), ('not', ('telling-truth', 6)), ('or', ('lying', 1), ('lying', 0)), ('not', ('telling-truth', 1)))", "index": 187}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: David, Chloe, Evelyn, Benjamin, Jackson, Matthew, James, and Ethan. David asserted: \"Ethan is a knave\". Chloe expressed that Ethan is a knight if and only if James is a knight. In a statement by Evelyn: \"Evelyn is a knight or Benjamin is a knight\". Benjamin noted, \"If James is a knight then Chloe is a knave\". \"David is a knave and Chloe is a knave,\" Jackson claimed. As Matthew put it, \"Benjamin is a knave if and only if David is a knave\". According to James, \"Evelyn is a knave if and only if David is a knave\". Ethan noted, \"David is a knave if and only if Benjamin is a knave\". So who is a knight and who is a knave?", "names": ["David", "Chloe", "Evelyn", "Benjamin", "Jackson", "Matthew", "James", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, true, true, true], "solution_text": "David is a knave, Chloe is a knight, Evelyn is a knave, Benjamin is a knave, Jackson is a knave, Matthew is a knight, James is a knight, and Ethan is a knight.", "solution_text_format": "(1) David is a knave\n(2) Chloe is a knight\n(3) Evelyn is a knave\n(4) Benjamin is a knave\n(5) Jackson is a knave\n(6) Matthew is a knight\n(7) James is a knight\n(8) Ethan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Ethan is a knave.", "Ethan cannot be a knight, because this would contradict the claim of David that Ethan is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that David is a knave if and only if Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Ethan that David is a knave if and only if Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that If James is a knight then Chloe is a knave.", "Assume James is a knight. No contradiction is found in their claim that Evelyn is a knave if and only if David is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Evelyn is a knight or Benjamin is a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Ethan is a knight if and only if James is a knight.", "Chloe cannot be a knave, because this would contradict the false claim of Benjamin that If James is a knight then Chloe is a knave.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the claim of James that Evelyn is a knave if and only if David is a knave.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider James.", "James cannot be a knave, because this would contradict the false claim of Benjamin that If James is a knight then Chloe is a knave.", "We have exhausted all possibilities for James, Benjamin, and Ethan, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Ethan is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that David is a knave if and only if Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Ethan that David is a knave if and only if Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that If James is a knight then Chloe is a knave.", "Assume James is a knight. No contradiction is found in their claim that Evelyn is a knave if and only if David is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of James that Evelyn is a knave if and only if David is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Evelyn is a knight or Benjamin is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Ethan is a knight if and only if James is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that David is a knave and Chloe is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that David is a knave and Chloe is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Benjamin is a knave if and only if David is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 7), ('<=>', ('telling-truth', 7), ('telling-truth', 6)), ('or', ('telling-truth', 2), ('telling-truth', 3)), ('->', ('telling-truth', 6), ('lying', 1)), ('and', ('lying', 0), ('lying', 1)), ('<=>', ('lying', 3), ('lying', 0)), ('<=>', ('lying', 2), ('lying', 0)), ('<=>', ('lying', 0), ('lying', 3)))", "index": 188}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Riley, Elizabeth, Matthew, Ava, Charlotte, Alexander, Emily, and Abigail. Riley commented, \"Alexander is a knight\". Elizabeth noted, \"Charlotte is a knight or Matthew is a knave\". Matthew expressed that Charlotte is a knave and Matthew is a knight. In Ava's words: \"Ava is a knight or Emily is a knight\". Charlotte told you that Alexander is a knight or Matthew is a knight. Alexander asserted: \"Matthew is a knave\". According to Emily, \"Ava is a knave or Elizabeth is a knight\". In Abigail's words: \"Charlotte is a knave\". So who is a knight and who is a knave?", "names": ["Riley", "Elizabeth", "Matthew", "Ava", "Charlotte", "Alexander", "Emily", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true, true, false], "solution_text": "Riley is a knight, Elizabeth is a knight, Matthew is a knave, Ava is a knight, Charlotte is a knight, Alexander is a knight, Emily is a knight, and Abigail is a knave.", "solution_text_format": "(1) Riley is a knight\n(2) Elizabeth is a knight\n(3) Matthew is a knave\n(4) Ava is a knight\n(5) Charlotte is a knight\n(6) Alexander is a knight\n(7) Emily is a knight\n(8) Abigail is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Alexander is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Matthew is a knave.", "Matthew cannot be a knight, because this would contradict the claim of Alexander that Matthew is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Charlotte is a knave and Matthew is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Alexander is a knight or Matthew is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Charlotte is a knight or Matthew is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Ava is a knight or Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Ava is a knave or Elizabeth is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Charlotte is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Charlotte is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 5), ('or', ('telling-truth', 4), ('lying', 2)), ('and', ('lying', 4), ('telling-truth', 2)), ('or', ('telling-truth', 3), ('telling-truth', 6)), ('or', ('telling-truth', 5), ('telling-truth', 2)), ('lying', 2), ('or', ('lying', 3), ('telling-truth', 1)), ('lying', 4))", "index": 189}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Grace, Avery, Benjamin, Isabella, Michael, Olivia, Aiden, and Owen. Grace commented, \"Olivia is a knave and Benjamin is a knave\". Avery asserted: \"If Olivia is a knave then Benjamin is a knave\". Benjamin stated, \"If Isabella is a knave then Isabella is a knight\". \"Benjamin is a knave if and only if Grace is a knight\" - Isabella. Michael asserted: \"Benjamin is a knight if and only if Avery is a knave\". Olivia said that Aiden is a knave and Michael is a knight. \"If Benjamin is a knight then Isabella is a knight\" - Aiden. Owen commented, \"Michael is a knight if and only if Avery is a knave\". So who is a knight and who is a knave?", "names": ["Grace", "Avery", "Benjamin", "Isabella", "Michael", "Olivia", "Aiden", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false, true, true], "solution_text": "Grace is a knave, Avery is a knave, Benjamin is a knight, Isabella is a knight, Michael is a knight, Olivia is a knave, Aiden is a knight, and Owen is a knight.", "solution_text_format": "(1) Grace is a knave\n(2) Avery is a knave\n(3) Benjamin is a knight\n(4) Isabella is a knight\n(5) Michael is a knight\n(6) Olivia is a knave\n(7) Aiden is a knight\n(8) Owen is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Olivia is a knave and Benjamin is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Grace that Olivia is a knave and Benjamin is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Aiden is a knave and Michael is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that If Benjamin is a knight then Isabella is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of Grace that Olivia is a knave and Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that If Isabella is a knave then Isabella is a knight.", "Isabella cannot be a knight, because this would contradict the false claim of Benjamin that If Isabella is a knave then Isabella is a knight.", "Isabella cannot be a knave, because this would contradict the false claim of their own that Benjamin is a knave if and only if Grace is a knight.", "We have exhausted all possibilities for Isabella and Benjamin, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that If Benjamin is a knight then Isabella is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of Grace that Olivia is a knave and Benjamin is a knave.", "Benjamin cannot be a knave, because this would contradict the false claim of Aiden that If Benjamin is a knight then Isabella is a knight.", "We have exhausted all possibilities for Benjamin, Aiden, and Olivia, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Olivia is a knave and Benjamin is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Aiden is a knave and Michael is a knight.", "Aiden cannot be a knight, because this would contradict the claim of Olivia that Aiden is a knave and Michael is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that If Benjamin is a knight then Isabella is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Isabella is a knave then Isabella is a knight.", "Isabella cannot be a knight, because this would contradict the false claim of Aiden that If Benjamin is a knight then Isabella is a knight.", "Isabella cannot be a knave, because this would contradict the claim of Benjamin that If Isabella is a knave then Isabella is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the false claim of Aiden that If Benjamin is a knight then Isabella is a knight.", "We have exhausted all possibilities for Benjamin and Aiden, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Aiden is a knave and Michael is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that If Benjamin is a knight then Isabella is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Isabella is a knave then Isabella is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Benjamin is a knave if and only if Grace is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Benjamin is a knight if and only if Avery is a knave.", "Avery cannot be a knight, because this would contradict the claim of their own that If Olivia is a knave then Benjamin is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that If Olivia is a knave then Benjamin is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Michael is a knight if and only if Avery is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 5), ('lying', 2)), ('->', ('lying', 5), ('lying', 2)), ('->', ('lying', 3), ('telling-truth', 3)), ('<=>', ('lying', 2), ('telling-truth', 0)), ('<=>', ('telling-truth', 2), ('lying', 1)), ('and', ('lying', 6), ('telling-truth', 4)), ('->', ('telling-truth', 2), ('telling-truth', 3)), ('<=>', ('telling-truth', 4), ('lying', 1)))", "index": 190}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Riley, Sophia, Benjamin, Amelia, Daniel, Isabella, Michael, and Chloe. In Riley's words: \"Isabella is not a knave\". \"Chloe is a knight and Daniel is a knight\" - Sophia. According to Benjamin, \"Isabella is a knave\". Amelia noted, \"Daniel is not a knave\". According to Daniel, \"Chloe is a knave if and only if Michael is a knave\". In a statement by Isabella: \"Benjamin is a knight or Daniel is a knave\". \"Chloe is not a knight\" - Michael. In Chloe's words: \"Benjamin is not a knight\". So who is a knight and who is a knave?", "names": ["Riley", "Sophia", "Benjamin", "Amelia", "Daniel", "Isabella", "Michael", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, true, false, true], "solution_text": "Riley is a knight, Sophia is a knave, Benjamin is a knave, Amelia is a knave, Daniel is a knave, Isabella is a knight, Michael is a knave, and Chloe is a knight.", "solution_text_format": "(1) Riley is a knight\n(2) Sophia is a knave\n(3) Benjamin is a knave\n(4) Amelia is a knave\n(5) Daniel is a knave\n(6) Isabella is a knight\n(7) Michael is a knave\n(8) Chloe is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Isabella is not a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Benjamin is a knight or Daniel is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Isabella is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Isabella is a knave.", "Daniel cannot be a knight, because this would contradict the claim of Isabella that Benjamin is a knight or Daniel is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Chloe is a knave if and only if Michael is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Benjamin is not a knight.", "Michael cannot be a knight, because this would contradict the false claim of Daniel that Chloe is a knave if and only if Michael is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Chloe is not a knight.", "Sophia cannot be a knight, because this would contradict the claim of their own that Chloe is a knight and Daniel is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Chloe is a knight and Daniel is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Daniel is not a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Daniel is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 5)), ('and', ('telling-truth', 7), ('telling-truth', 4)), ('lying', 5), ('not', ('lying', 4)), ('<=>', ('lying', 7), ('lying', 6)), ('or', ('telling-truth', 2), ('lying', 4)), ('not', ('telling-truth', 7)), ('not', ('telling-truth', 2)))", "index": 191}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Abigail, Ella, Charlotte, Sebastian, Scarlett, Ava, Riley, and Oliver. Abigail was heard saying, \"Ava is not a knave\". As Ella put it, \"Ava is a knight if and only if Abigail is a knave\". \"If Ella is a knight then Abigail is a knave\" - Charlotte. \"Riley is a knave and Riley is a knight\" - Sebastian. \"Charlotte is a knight if and only if Oliver is a knave,\" Scarlett claimed. According to Ava, \"Scarlett is not a knight\". Riley remarked, \"If Ella is a knight then Scarlett is a knight\". Oliver remarked, \"Ella is not a knight\". So who is a knight and who is a knave?", "names": ["Abigail", "Ella", "Charlotte", "Sebastian", "Scarlett", "Ava", "Riley", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true, true, true], "solution_text": "Abigail is a knight, Ella is a knave, Charlotte is a knight, Sebastian is a knave, Scarlett is a knave, Ava is a knight, Riley is a knight, and Oliver is a knight.", "solution_text_format": "(1) Abigail is a knight\n(2) Ella is a knave\n(3) Charlotte is a knight\n(4) Sebastian is a knave\n(5) Scarlett is a knave\n(6) Ava is a knight\n(7) Riley is a knight\n(8) Oliver is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Ava is not a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Scarlett is not a knight.", "Scarlett cannot be a knight, because this would contradict the claim of Ava that Scarlett is not a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Charlotte is a knight if and only if Oliver is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Ella is a knight then Abigail is a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Ava is a knight if and only if Abigail is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Ava is a knight if and only if Abigail is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Ella is not a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Riley is a knave and Riley is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Riley is a knave and Riley is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that If Ella is a knight then Scarlett is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 5)), ('<=>', ('telling-truth', 5), ('lying', 0)), ('->', ('telling-truth', 1), ('lying', 0)), ('and', ('lying', 6), ('telling-truth', 6)), ('<=>', ('telling-truth', 2), ('lying', 7)), ('not', ('telling-truth', 4)), ('->', ('telling-truth', 1), ('telling-truth', 4)), ('not', ('telling-truth', 1)))", "index": 192}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sebastian, Evelyn, Jacob, Aurora, Amelia, Harper, Mia, and Grace. Sebastian remarked, \"Mia is a knight if and only if Grace is a knight\". Evelyn said that Jacob is a knight or Grace is a knight. Jacob noted, \"Harper is a knave if and only if Sebastian is a knight\". Aurora noted, \"Evelyn is a knave\". Amelia commented, \"If Sebastian is a knave then Mia is a knight\". Harper stated, \"Amelia is a knight or Sebastian is a knave\". \"If Harper is a knight then Sebastian is a knave,\" Mia mentioned. In Grace's words: \"If Evelyn is a knave then Evelyn is a knight\". So who is a knight and who is a knave?", "names": ["Sebastian", "Evelyn", "Jacob", "Aurora", "Amelia", "Harper", "Mia", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true, false, false], "solution_text": "Sebastian is a knight, Evelyn is a knave, Jacob is a knave, Aurora is a knight, Amelia is a knight, Harper is a knight, Mia is a knave, and Grace is a knave.", "solution_text_format": "(1) Sebastian is a knight\n(2) Evelyn is a knave\n(3) Jacob is a knave\n(4) Aurora is a knight\n(5) Amelia is a knight\n(6) Harper is a knight\n(7) Mia is a knave\n(8) Grace is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that Mia is a knight if and only if Grace is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that If Harper is a knight then Sebastian is a knave.", "Harper cannot be a knight, because this would contradict the claim of Mia that If Harper is a knight then Sebastian is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Amelia is a knight or Sebastian is a knave.", "Amelia cannot be a knight, because this would contradict the false claim of Harper that Amelia is a knight or Sebastian is a knave.", "Amelia cannot be a knave, because this would contradict the false claim of their own that If Sebastian is a knave then Mia is a knight.", "We have exhausted all possibilities for Amelia and Harper, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that If Harper is a knight then Sebastian is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Amelia is a knight or Sebastian is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that If Sebastian is a knave then Mia is a knight.", "Grace cannot be a knight, because this would contradict the claim of Sebastian that Mia is a knight if and only if Grace is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that If Evelyn is a knave then Evelyn is a knight.", "Evelyn cannot be a knight, because this would contradict the false claim of Grace that If Evelyn is a knave then Evelyn is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Jacob is a knight or Grace is a knight.", "Jacob cannot be a knight, because this would contradict the false claim of Evelyn that Jacob is a knight or Grace is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Harper is a knave if and only if Sebastian is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Evelyn is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 6), ('telling-truth', 7)), ('or', ('telling-truth', 2), ('telling-truth', 7)), ('<=>', ('lying', 5), ('telling-truth', 0)), ('lying', 1), ('->', ('lying', 0), ('telling-truth', 6)), ('or', ('telling-truth', 4), ('lying', 0)), ('->', ('telling-truth', 5), ('lying', 0)), ('->', ('lying', 1), ('telling-truth', 1)))", "index": 193}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Abigail, Ava, Jacob, Penelope, Ethan, Samuel, Luke, and Alexander. Abigail asserted: \"If Ethan is a knight then Ethan is a knave\". Ava expressed that Alexander is a knave and Abigail is a knight. \"Ethan is a knave if and only if Jacob is a knight,\" Jacob claimed. \"Ethan is not a knave\" - Penelope. Ethan told you that Ava is a knight. \"Alexander is a knight\" - Samuel. As Luke put it, \"Jacob is a knight if and only if Samuel is a knave\". Alexander asserted: \"Luke is a knight and Penelope is a knave\". So who is a knight and who is a knave?", "names": ["Abigail", "Ava", "Jacob", "Penelope", "Ethan", "Samuel", "Luke", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, true, true, true], "solution_text": "Abigail is a knight, Ava is a knave, Jacob is a knave, Penelope is a knave, Ethan is a knave, Samuel is a knight, Luke is a knight, and Alexander is a knight.", "solution_text_format": "(1) Abigail is a knight\n(2) Ava is a knave\n(3) Jacob is a knave\n(4) Penelope is a knave\n(5) Ethan is a knave\n(6) Samuel is a knight\n(7) Luke is a knight\n(8) Alexander is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that If Ethan is a knight then Ethan is a knave.", "Ethan cannot be a knight, because this would contradict the claim of Abigail that If Ethan is a knight then Ethan is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Ava is a knight.", "Ava cannot be a knight, because this would contradict the false claim of Ethan that Ava is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Alexander is a knave and Abigail is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Luke is a knight and Penelope is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Jacob is a knight if and only if Samuel is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Ethan is a knave if and only if Jacob is a knight.", "Samuel cannot be a knight, because this would contradict the claim of Luke that Jacob is a knight if and only if Samuel is a knave.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Alexander is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Ethan is a knave if and only if Jacob is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Alexander is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Ethan is not a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Ethan is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 4), ('lying', 4)), ('and', ('lying', 7), ('telling-truth', 0)), ('<=>', ('lying', 4), ('telling-truth', 2)), ('not', ('lying', 4)), ('telling-truth', 1), ('telling-truth', 7), ('<=>', ('telling-truth', 2), ('lying', 5)), ('and', ('telling-truth', 6), ('lying', 3)))", "index": 194}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Elizabeth, Jack, Emily, Avery, James, Zoey, Liam, and Charlotte. In a statement by Elizabeth: \"Avery is a knave\". In a statement by Jack: \"Elizabeth is a knave and Emily is a knight\". Emily stated, \"Charlotte is a knight or Liam is a knight\". According to Avery, \"If Elizabeth is a knave then Emily is a knight\". James remarked, \"Liam is a knave\". \"If Liam is a knave then Charlotte is a knight,\" Zoey declared. According to Liam, \"Elizabeth is a knave or Charlotte is a knave\". Charlotte said that If Jack is a knave then James is a knight. So who is a knight and who is a knave?", "names": ["Elizabeth", "Jack", "Emily", "Avery", "James", "Zoey", "Liam", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true, true, true], "solution_text": "Elizabeth is a knave, Jack is a knight, Emily is a knight, Avery is a knight, James is a knave, Zoey is a knight, Liam is a knight, and Charlotte is a knight.", "solution_text_format": "(1) Elizabeth is a knave\n(2) Jack is a knight\n(3) Emily is a knight\n(4) Avery is a knight\n(5) James is a knave\n(6) Zoey is a knight\n(7) Liam is a knight\n(8) Charlotte is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Avery is a knave.", "Avery cannot be a knight, because this would contradict the claim of Elizabeth that Avery is a knave.", "Avery cannot be a knave, because this would contradict the false claim of their own that If Elizabeth is a knave then Emily is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Avery is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Charlotte is a knight or Liam is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Jack is a knave then James is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Elizabeth is a knave and Emily is a knight.", "Assume James is a knight. No contradiction is found in their claim that Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of James that Liam is a knave.", "Liam cannot be a knave, because this would contradict the false claim of their own that Elizabeth is a knave or Charlotte is a knave.", "We have exhausted all possibilities for Liam, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Liam is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Elizabeth is a knave or Charlotte is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that If Liam is a knave then Charlotte is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('and', ('lying', 0), ('telling-truth', 2)), ('or', ('telling-truth', 7), ('telling-truth', 6)), ('->', ('lying', 0), ('telling-truth', 2)), ('lying', 6), ('->', ('lying', 6), ('telling-truth', 7)), ('or', ('lying', 0), ('lying', 7)), ('->', ('lying', 1), ('telling-truth', 4)))", "index": 195}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jackson, Mason, Lucas, Henry, James, Michael, William, and Emma. Jackson commented, \"Michael is a knave or Henry is a knight\". According to Mason, \"James is a knave if and only if William is a knave\". \"Emma is a knight and Michael is a knight,\" Lucas claimed. \"If Michael is a knave then William is a knight\" - Henry. James expressed that Jackson is a knight or Henry is a knave. According to Michael, \"Mason is a knave and James is a knave\". In a statement by William: \"Michael is a knave or Mason is a knave\". Emma commented, \"James is a knave and Michael is a knight\". So who is a knight and who is a knave?", "names": ["Jackson", "Mason", "Lucas", "Henry", "James", "Michael", "William", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false, true, false], "solution_text": "Jackson is a knight, Mason is a knight, Lucas is a knave, Henry is a knight, James is a knight, Michael is a knave, William is a knight, and Emma is a knave.", "solution_text_format": "(1) Jackson is a knight\n(2) Mason is a knight\n(3) Lucas is a knave\n(4) Henry is a knight\n(5) James is a knight\n(6) Michael is a knave\n(7) William is a knight\n(8) Emma is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Michael is a knave or Henry is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Mason is a knave and James is a knave.", "Mason cannot be a knight, because this would contradict the claim of Michael that Mason is a knave and James is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that James is a knave if and only if William is a knave.", "James cannot be a knight, because this would contradict the claim of Michael that Mason is a knave and James is a knave.", "James cannot be a knave, because this would contradict the false claim of their own that Jackson is a knight or Henry is a knave.", "We have exhausted all possibilities for James and Mason, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Mason is a knave and James is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that James is a knave if and only if William is a knave.", "Assume James is a knight. No contradiction is found in their claim that Jackson is a knight or Henry is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Michael is a knave then William is a knight.", "Assume William is a knight. No contradiction is found in their claim that Michael is a knave or Mason is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Emma is a knight and Michael is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Emma is a knight and Michael is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that James is a knave and Michael is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that James is a knave and Michael is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 5), ('telling-truth', 3)), ('<=>', ('lying', 4), ('lying', 6)), ('and', ('telling-truth', 7), ('telling-truth', 5)), ('->', ('lying', 5), ('telling-truth', 6)), ('or', ('telling-truth', 0), ('lying', 3)), ('and', ('lying', 1), ('lying', 4)), ('or', ('lying', 5), ('lying', 1)), ('and', ('lying', 4), ('telling-truth', 5)))", "index": 196}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aria, Owen, Aiden, Oliver, Chloe, Olivia, Jacob, and Ethan. As Aria put it, \"Chloe is not a knight\". Owen asserted: \"If Chloe is a knave then Jacob is a knave\". Aiden stated, \"Ethan is a knight or Owen is a knight\". Oliver stated, \"If Olivia is a knave then Ethan is a knight\". \"Ethan is a knight if and only if Owen is a knave,\" Chloe mentioned. \"Aiden is not a knave,\" Olivia claimed. Jacob told you that Ethan is not a knight. According to Ethan, \"Owen is not a knight\". So who is a knight and who is a knave?", "names": ["Aria", "Owen", "Aiden", "Oliver", "Chloe", "Olivia", "Jacob", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true, true, false], "solution_text": "Aria is a knave, Owen is a knight, Aiden is a knight, Oliver is a knight, Chloe is a knight, Olivia is a knight, Jacob is a knight, and Ethan is a knave.", "solution_text_format": "(1) Aria is a knave\n(2) Owen is a knight\n(3) Aiden is a knight\n(4) Oliver is a knight\n(5) Chloe is a knight\n(6) Olivia is a knight\n(7) Jacob is a knight\n(8) Ethan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that Chloe is not a knight.", "Chloe cannot be a knight, because this would contradict the claim of Aria that Chloe is not a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Ethan is a knight if and only if Owen is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Owen is not a knight.", "Owen cannot be a knight, because this would contradict the claim of Ethan that Owen is not a knight.", "Owen cannot be a knave, because this would contradict the false claim of Chloe that Ethan is a knight if and only if Owen is a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Owen is not a knight.", "Owen cannot be a knight, because this would contradict the false claim of Chloe that Ethan is a knight if and only if Owen is a knave.", "Owen cannot be a knave, because this would contradict the false claim of Ethan that Owen is not a knight.", "We have exhausted all possibilities for Owen, Ethan, and Chloe, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Chloe is not a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Ethan is a knight if and only if Owen is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Owen is not a knight.", "Owen cannot be a knight, because this would contradict the claim of Chloe that Ethan is a knight if and only if Owen is a knave.", "Owen cannot be a knave, because this would contradict the false claim of their own that If Chloe is a knave then Jacob is a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Owen is not a knight.", "Assume Owen is a knight. No contradiction is found in their claim that If Chloe is a knave then Jacob is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Ethan is not a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Ethan is a knight or Owen is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that If Olivia is a knave then Ethan is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Aiden is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 4)), ('->', ('lying', 4), ('lying', 6)), ('or', ('telling-truth', 7), ('telling-truth', 1)), ('->', ('lying', 5), ('telling-truth', 7)), ('<=>', ('telling-truth', 7), ('lying', 1)), ('not', ('lying', 2)), ('not', ('telling-truth', 7)), ('not', ('telling-truth', 1)))", "index": 197}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jackson, Emma, Logan, Aria, Grace, Liam, Penelope, and Matthew. Jackson said, \"If Matthew is a knight then Liam is a knave.\" Emma stated, \"If Matthew is a knave then Liam is a knave\". \"Matthew is a knave and Jackson is a knave,\" Logan mentioned. According to Aria, \"Emma is a knave and Liam is a knight\". In Grace's words: \"Jackson is a knave and Liam is a knight\". Liam noted, \"Matthew is a knave and Penelope is a knight\". \"Emma is a knight if and only if Matthew is a knave,\" Penelope claimed. As Matthew put it, \"If Aria is a knight then Grace is a knave\". So who is a knight and who is a knave?", "names": ["Jackson", "Emma", "Logan", "Aria", "Grace", "Liam", "Penelope", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, false, false, true], "solution_text": "Jackson is a knight, Emma is a knight, Logan is a knave, Aria is a knave, Grace is a knave, Liam is a knave, Penelope is a knave, and Matthew is a knight.", "solution_text_format": "(1) Jackson is a knight\n(2) Emma is a knight\n(3) Logan is a knave\n(4) Aria is a knave\n(5) Grace is a knave\n(6) Liam is a knave\n(7) Penelope is a knave\n(8) Matthew is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that If Matthew is a knight then Liam is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that If Aria is a knight then Grace is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Emma is a knave and Liam is a knight.", "Emma cannot be a knight, because this would contradict the claim of Aria that Emma is a knave and Liam is a knight.", "Emma cannot be a knave, because this would contradict the false claim of their own that If Matthew is a knave then Liam is a knave.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Emma is a knave and Liam is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If Matthew is a knave then Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of Jackson that If Matthew is a knight then Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Matthew is a knave and Penelope is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Emma is a knight if and only if Matthew is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Emma is a knight if and only if Matthew is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Jackson is a knave and Liam is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Jackson is a knave and Liam is a knight.", "Logan cannot be a knight, because this would contradict the claim of their own that Matthew is a knave and Jackson is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Matthew is a knave and Jackson is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 7), ('lying', 5)), ('->', ('lying', 7), ('lying', 5)), ('and', ('lying', 7), ('lying', 0)), ('and', ('lying', 1), ('telling-truth', 5)), ('and', ('lying', 0), ('telling-truth', 5)), ('and', ('lying', 7), ('telling-truth', 6)), ('<=>', ('telling-truth', 1), ('lying', 7)), ('->', ('telling-truth', 3), ('lying', 4)))", "index": 198}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Joseph, Olivia, Amelia, Grace, Emily, Michael, Noah, and Luke. Joseph stated, \"Emily is a knave or Amelia is a knight\". Olivia remarked, \"Noah is a knave if and only if Olivia is a knight\". Amelia remarked, \"Olivia is a knave and Luke is a knave\". Grace expressed that Joseph is a knave and Noah is a knave. As Emily put it, \"Olivia is not a knave\". Michael told you that Joseph is a knight and Joseph is a knave. Noah stated, \"Joseph is a knight\". Luke stated, \"Amelia is a knave and Michael is a knave\". So who is a knight and who is a knave?", "names": ["Joseph", "Olivia", "Amelia", "Grace", "Emily", "Michael", "Noah", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false, false, true], "solution_text": "Joseph is a knave, Olivia is a knight, Amelia is a knave, Grace is a knight, Emily is a knight, Michael is a knave, Noah is a knave, and Luke is a knight.", "solution_text_format": "(1) Joseph is a knave\n(2) Olivia is a knight\n(3) Amelia is a knave\n(4) Grace is a knight\n(5) Emily is a knight\n(6) Michael is a knave\n(7) Noah is a knave\n(8) Luke is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that Emily is a knave or Amelia is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Olivia is not a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Noah is a knave if and only if Olivia is a knight.", "Noah cannot be a knight, because this would contradict the claim of Olivia that Noah is a knave if and only if Olivia is a knight.", "Noah cannot be a knave, because this would contradict the false claim of their own that Joseph is a knight.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the claim of Emily that Olivia is not a knave.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Olivia is not a knave.", "Olivia cannot be a knight, because this would contradict the false claim of Emily that Olivia is not a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Noah is a knave if and only if Olivia is a knight.", "Noah cannot be a knight, because this would contradict the false claim of Olivia that Noah is a knave if and only if Olivia is a knight.", "Noah cannot be a knave, because this would contradict the false claim of their own that Joseph is a knight.", "We have exhausted all possibilities for Noah, Olivia, and Emily, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Emily is a knave or Amelia is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Olivia is not a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Noah is a knave if and only if Olivia is a knight.", "Noah cannot be a knight, because this would contradict the claim of Olivia that Noah is a knave if and only if Olivia is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Joseph is a knight.", "Amelia cannot be a knight, because this would contradict the false claim of Joseph that Emily is a knave or Amelia is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Olivia is a knave and Luke is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Amelia is a knave and Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Joseph is a knight and Joseph is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Joseph is a knight and Joseph is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Joseph is a knave and Noah is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 4), ('telling-truth', 2)), ('<=>', ('lying', 6), ('telling-truth', 1)), ('and', ('lying', 1), ('lying', 7)), ('and', ('lying', 0), ('lying', 6)), ('not', ('lying', 1)), ('and', ('telling-truth', 0), ('lying', 0)), ('telling-truth', 0), ('and', ('lying', 2), ('lying', 5)))", "index": 199}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Benjamin, Olivia, James, Aurora, Michael, Jackson, Mason, and Isabella. According to Benjamin, \"Isabella is a knight if and only if Jackson is a knight\". In a statement by Olivia: \"If Benjamin is a knight then Olivia is a knight\". In James's words: \"Benjamin is not a knave\". Aurora remarked, \"Mason is not a knight\". Michael remarked, \"Olivia is a knave\". In a statement by Jackson: \"If Isabella is a knight then Aurora is a knight\". Mason stated, \"If Benjamin is a knight then Benjamin is a knave\". Isabella asserted: \"Benjamin is not a knight\". So who is a knight and who is a knave?", "names": ["Benjamin", "Olivia", "James", "Aurora", "Michael", "Jackson", "Mason", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, false, true, true], "solution_text": "Benjamin is a knave, Olivia is a knight, James is a knave, Aurora is a knave, Michael is a knave, Jackson is a knave, Mason is a knight, and Isabella is a knight.", "solution_text_format": "(1) Benjamin is a knave\n(2) Olivia is a knight\n(3) James is a knave\n(4) Aurora is a knave\n(5) Michael is a knave\n(6) Jackson is a knave\n(7) Mason is a knight\n(8) Isabella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Jackson is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Benjamin is not a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Benjamin is not a knight.", "Jackson cannot be a knight, because this would contradict the claim of Benjamin that Isabella is a knight if and only if Jackson is a knight.", "Jackson cannot be a knave, because this would contradict the false claim of their own that If Isabella is a knight then Aurora is a knight.", "We have exhausted all possibilities for Jackson and Isabella, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Isabella is a knight if and only if Jackson is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Benjamin is not a knight.", "Jackson cannot be a knight, because this would contradict the false claim of Benjamin that Isabella is a knight if and only if Jackson is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that If Isabella is a knight then Aurora is a knight.", "Aurora cannot be a knight, because this would contradict the false claim of Jackson that If Isabella is a knight then Aurora is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Mason is not a knight.", "Assume Mason is a knight. No contradiction is found in their claim that If Benjamin is a knight then Benjamin is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that If Benjamin is a knight then Olivia is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Benjamin is not a knave.", "Assume James is a knave. No contradiction is found in their false claim that Benjamin is not a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Olivia is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Olivia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 7), ('telling-truth', 5)), ('->', ('telling-truth', 0), ('telling-truth', 1)), ('not', ('lying', 0)), ('not', ('telling-truth', 6)), ('lying', 1), ('->', ('telling-truth', 7), ('telling-truth', 3)), ('->', ('telling-truth', 0), ('lying', 0)), ('not', ('telling-truth', 0)))", "index": 200}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ava, Logan, Jack, Lily, Michael, Penelope, Sophia, and Jackson. Ava was heard saying, \"Lily is a knight\". Logan was heard saying, \"Jack is not a knave\". In a statement by Jack: \"Ava is not a knight\". Lily said that Penelope is a knave. In Michael's words: \"If Jack is a knight then Logan is a knave\". As Penelope put it, \"Logan is a knight or Ava is a knight\". Sophia was heard saying, \"If Logan is a knight then Ava is a knave\". Jackson remarked, \"Sophia is a knight and Ava is a knight\". So who is a knight and who is a knave?", "names": ["Ava", "Logan", "Jack", "Lily", "Michael", "Penelope", "Sophia", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true, true, false], "solution_text": "Ava is a knave, Logan is a knight, Jack is a knight, Lily is a knave, Michael is a knave, Penelope is a knight, Sophia is a knight, and Jackson is a knave.", "solution_text_format": "(1) Ava is a knave\n(2) Logan is a knight\n(3) Jack is a knight\n(4) Lily is a knave\n(5) Michael is a knave\n(6) Penelope is a knight\n(7) Sophia is a knight\n(8) Jackson is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Lily is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the claim of Lily that Penelope is a knave.", "Penelope cannot be a knave, because this would contradict the false claim of their own that Logan is a knight or Ava is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the claim of Ava that Lily is a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Lily is a knight.", "Lily cannot be a knight, because this would contradict the false claim of Ava that Lily is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Penelope is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Logan is a knight or Ava is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Jack is not a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Ava is not a knight.", "Michael cannot be a knight, because this would contradict the claim of their own that If Jack is a knight then Logan is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that If Jack is a knight then Logan is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that If Logan is a knight then Ava is a knave.", "Jackson cannot be a knight, because this would contradict the claim of their own that Sophia is a knight and Ava is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Sophia is a knight and Ava is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 3), ('not', ('lying', 2)), ('not', ('telling-truth', 0)), ('lying', 5), ('->', ('telling-truth', 2), ('lying', 1)), ('or', ('telling-truth', 1), ('telling-truth', 0)), ('->', ('telling-truth', 1), ('lying', 0)), ('and', ('telling-truth', 6), ('telling-truth', 0)))", "index": 201}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sebastian, Olivia, Harper, Samuel, Alexander, Sofia, Liam, and William. Sebastian said that Sofia is a knight or Sofia is a knave. \"Liam is not a knave,\" Olivia declared. \"Alexander is a knave or William is a knight,\" Harper declared. \"Sebastian is a knight,\" Samuel claimed. In Alexander's words: \"Sebastian is a knight\". Sofia remarked, \"Liam is a knave or Liam is a knight\". \"Olivia is a knave and Harper is a knight,\" Liam claimed. William expressed that Harper is not a knave. So who is a knight and who is a knave?", "names": ["Sebastian", "Olivia", "Harper", "Samuel", "Alexander", "Sofia", "Liam", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true, false, false], "solution_text": "Sebastian is a knight, Olivia is a knave, Harper is a knave, Samuel is a knight, Alexander is a knight, Sofia is a knight, Liam is a knave, and William is a knave.", "solution_text_format": "(1) Sebastian is a knight\n(2) Olivia is a knave\n(3) Harper is a knave\n(4) Samuel is a knight\n(5) Alexander is a knight\n(6) Sofia is a knight\n(7) Liam is a knave\n(8) William is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that Sofia is a knight or Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Liam is a knave or Liam is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Olivia is a knave and Harper is a knight.", "Olivia cannot be a knight, because this would contradict the claim of Liam that Olivia is a knave and Harper is a knight.", "Olivia cannot be a knave, because this would contradict the false claim of their own that Liam is not a knave.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Olivia is a knave and Harper is a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that Liam is not a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Liam is not a knave.", "Harper cannot be a knight, because this would contradict the false claim of Liam that Olivia is a knave and Harper is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Alexander is a knave or William is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Sebastian is a knight.", "William cannot be a knight, because this would contradict the false claim of Harper that Alexander is a knave or William is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Harper is not a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Sebastian is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('lying', 5)), ('not', ('lying', 6)), ('or', ('lying', 4), ('telling-truth', 7)), ('telling-truth', 0), ('telling-truth', 0), ('or', ('lying', 6), ('telling-truth', 6)), ('and', ('lying', 1), ('telling-truth', 2)), ('not', ('lying', 2)))", "index": 202}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Luke, Ava, Sofia, Emma, Aria, Matthew, Charlotte, and Mason. \"Matthew is a knight,\" Luke claimed. Ava stated, \"Mason is a knave or Aria is a knave\". As Sofia put it, \"Charlotte is not a knave\". Emma was heard saying, \"If Mason is a knave then Sofia is a knight\". As Aria put it, \"Matthew is a knight if and only if Luke is a knight\". Matthew expressed that Sofia is a knave. Charlotte asserted: \"Emma is a knight\". Mason said, \"Matthew is a knight and Aria is a knight.\" So who is a knight and who is a knave?", "names": ["Luke", "Ava", "Sofia", "Emma", "Aria", "Matthew", "Charlotte", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false, true, false], "solution_text": "Luke is a knave, Ava is a knight, Sofia is a knight, Emma is a knight, Aria is a knight, Matthew is a knave, Charlotte is a knight, and Mason is a knave.", "solution_text_format": "(1) Luke is a knave\n(2) Ava is a knight\n(3) Sofia is a knight\n(4) Emma is a knight\n(5) Aria is a knight\n(6) Matthew is a knave\n(7) Charlotte is a knight\n(8) Mason is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Matthew that Sofia is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Charlotte is not a knave.", "Charlotte cannot be a knight, because this would contradict the false claim of Sofia that Charlotte is not a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Emma is a knight.", "Emma cannot be a knight, because this would contradict the false claim of Charlotte that Emma is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that If Mason is a knave then Sofia is a knight.", "Mason cannot be a knight, because this would contradict the false claim of Emma that If Mason is a knave then Sofia is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Matthew is a knight and Aria is a knight.", "Aria cannot be a knight, because this would contradict the false claim of Mason that Matthew is a knight and Aria is a knight.", "Aria cannot be a knave, because this would contradict the false claim of their own that Matthew is a knight if and only if Luke is a knight.", "We have exhausted all possibilities for Aria, Mason, Emma, Charlotte, and Sofia, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the claim of Luke that Matthew is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the false claim of Luke that Matthew is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Charlotte is not a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Emma is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If Mason is a knave then Sofia is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Matthew is a knight and Aria is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Matthew is a knight and Aria is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Matthew is a knight if and only if Luke is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Mason is a knave or Aria is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 5), ('or', ('lying', 7), ('lying', 4)), ('not', ('lying', 6)), ('->', ('lying', 7), ('telling-truth', 2)), ('<=>', ('telling-truth', 5), ('telling-truth', 0)), ('lying', 2), ('telling-truth', 3), ('and', ('telling-truth', 5), ('telling-truth', 4)))", "index": 203}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Logan, Aria, Mia, Isabella, Jack, Victoria, Evelyn, and Noah. \"Evelyn is a knight and Logan is a knight,\" Logan declared. Aria asserted: \"If Noah is a knave then Jack is a knight\". \"Aria is a knave,\" Mia claimed. \"Mia is a knave if and only if Aria is a knave,\" Isabella claimed. In Jack's words: \"If Aria is a knave then Logan is a knight\". \"Aria is a knight,\" Victoria mentioned. Evelyn commented, \"If Isabella is a knave then Logan is a knave\". Noah asserted: \"If Jack is a knight then Aria is a knight\". So who is a knight and who is a knave?", "names": ["Logan", "Aria", "Mia", "Isabella", "Jack", "Victoria", "Evelyn", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true, true, true], "solution_text": "Logan is a knave, Aria is a knight, Mia is a knave, Isabella is a knave, Jack is a knight, Victoria is a knight, Evelyn is a knight, and Noah is a knight.", "solution_text_format": "(1) Logan is a knave\n(2) Aria is a knight\n(3) Mia is a knave\n(4) Isabella is a knave\n(5) Jack is a knight\n(6) Victoria is a knight\n(7) Evelyn is a knight\n(8) Noah is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that Evelyn is a knight and Logan is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Isabella is a knave then Logan is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Mia is a knave if and only if Aria is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of Mia that Aria is a knave.", "Aria cannot be a knave, because this would contradict the claim of Isabella that Mia is a knave if and only if Aria is a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of Isabella that Mia is a knave if and only if Aria is a knave.", "Aria cannot be a knave, because this would contradict the false claim of Mia that Aria is a knave.", "We have exhausted all possibilities for Aria and Mia, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the claim of Evelyn that If Isabella is a knave then Logan is a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the claim of Logan that Evelyn is a knight and Logan is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Evelyn is a knight and Logan is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Isabella is a knave then Logan is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Mia is a knave if and only if Aria is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of Mia that Aria is a knave.", "Aria cannot be a knave, because this would contradict the claim of Isabella that Mia is a knave if and only if Aria is a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of Isabella that Mia is a knave if and only if Aria is a knave.", "Aria cannot be a knave, because this would contradict the false claim of Mia that Aria is a knave.", "We have exhausted all possibilities for Aria and Mia, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Mia is a knave if and only if Aria is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of Mia that Aria is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that If Noah is a knave then Jack is a knight.", "Noah cannot be a knight, because this would contradict the false claim of Aria that If Noah is a knave then Jack is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that If Jack is a knight then Aria is a knight.", "Jack cannot be a knight, because this would contradict the false claim of Aria that If Noah is a knave then Jack is a knight.", "Jack cannot be a knave, because this would contradict the false claim of Noah that If Jack is a knight then Aria is a knight.", "We have exhausted all possibilities for Jack, Noah, and Aria, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Aria is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that If Noah is a knave then Jack is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that If Jack is a knight then Aria is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that If Aria is a knave then Logan is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Aria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 6), ('telling-truth', 0)), ('->', ('lying', 7), ('telling-truth', 4)), ('lying', 1), ('<=>', ('lying', 2), ('lying', 1)), ('->', ('lying', 1), ('telling-truth', 0)), ('telling-truth', 1), ('->', ('lying', 3), ('lying', 0)), ('->', ('telling-truth', 4), ('telling-truth', 1)))", "index": 204}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Logan, Aiden, Joseph, Daniel, Abigail, Isabella, Lucas, and Aria. Logan remarked, \"Daniel is not a knave\". Aiden noted, \"Abigail is a knave if and only if Logan is a knave\". \"Logan is a knight and Isabella is a knave,\" Joseph declared. \"If Aria is a knight then Logan is a knave,\" Daniel declared. Abigail was heard saying, \"Logan is a knave and Lucas is a knave\". \"Daniel is a knight\" - Isabella. As Lucas put it, \"Joseph is a knight\". \"Aiden is a knave and Joseph is a knight,\" Aria mentioned. So who is a knight and who is a knave?", "names": ["Logan", "Aiden", "Joseph", "Daniel", "Abigail", "Isabella", "Lucas", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, true, false, false], "solution_text": "Logan is a knight, Aiden is a knave, Joseph is a knave, Daniel is a knight, Abigail is a knave, Isabella is a knight, Lucas is a knave, and Aria is a knave.", "solution_text_format": "(1) Logan is a knight\n(2) Aiden is a knave\n(3) Joseph is a knave\n(4) Daniel is a knight\n(5) Abigail is a knave\n(6) Isabella is a knight\n(7) Lucas is a knave\n(8) Aria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that Daniel is not a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that If Aria is a knight then Logan is a knave.", "Aria cannot be a knight, because this would contradict the claim of Daniel that If Aria is a knight then Logan is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Aiden is a knave and Joseph is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Abigail is a knave if and only if Logan is a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Logan is a knave and Lucas is a knave.", "Abigail cannot be a knave, because this would contradict the claim of Aiden that Abigail is a knave if and only if Logan is a knave.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Abigail is a knave if and only if Logan is a knave.", "Abigail cannot be a knight, because this would contradict the false claim of Aiden that Abigail is a knave if and only if Logan is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Logan is a knave and Lucas is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of Aria that Aiden is a knave and Joseph is a knight.", "Joseph cannot be a knave, because this would contradict the claim of Lucas that Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of Lucas that Joseph is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Logan is a knight and Isabella is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Daniel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 3)), ('<=>', ('lying', 4), ('lying', 0)), ('and', ('telling-truth', 0), ('lying', 5)), ('->', ('telling-truth', 7), ('lying', 0)), ('and', ('lying', 0), ('lying', 6)), ('telling-truth', 3), ('telling-truth', 2), ('and', ('lying', 1), ('telling-truth', 2)))", "index": 205}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Isabella, Jack, Jackson, Owen, Noah, Ethan, Amelia, and David. In a statement by Isabella: \"Jackson is a knight or Jackson is a knave\". As Jack put it, \"Noah is a knight\". Jackson noted, \"Owen is a knight or Isabella is a knight\". In Owen's words: \"If Owen is a knight then Amelia is a knave\". Noah told you that If Amelia is a knight then Owen is a knave. In a statement by Ethan: \"Amelia is a knave and Noah is a knight\". According to Amelia, \"David is a knight and Ethan is a knight\". David expressed that If Amelia is a knave then Isabella is a knave. So who is a knight and who is a knave?", "names": ["Isabella", "Jack", "Jackson", "Owen", "Noah", "Ethan", "Amelia", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true, false, false], "solution_text": "Isabella is a knight, Jack is a knight, Jackson is a knight, Owen is a knight, Noah is a knight, Ethan is a knight, Amelia is a knave, and David is a knave.", "solution_text_format": "(1) Isabella is a knight\n(2) Jack is a knight\n(3) Jackson is a knight\n(4) Owen is a knight\n(5) Noah is a knight\n(6) Ethan is a knight\n(7) Amelia is a knave\n(8) David is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Jackson is a knight or Jackson is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Owen is a knight or Isabella is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that If Owen is a knight then Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Owen that If Owen is a knight then Amelia is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that David is a knight and Ethan is a knight.", "David cannot be a knight, because this would contradict the claim of their own that If Amelia is a knave then Isabella is a knave.", "Assume David is a knave. No contradiction is found in their false claim that If Amelia is a knave then Isabella is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Amelia is a knave and Noah is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that If Amelia is a knight then Owen is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Noah is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('lying', 2)), ('telling-truth', 4), ('or', ('telling-truth', 3), ('telling-truth', 0)), ('->', ('telling-truth', 3), ('lying', 6)), ('->', ('telling-truth', 6), ('lying', 3)), ('and', ('lying', 6), ('telling-truth', 4)), ('and', ('telling-truth', 7), ('telling-truth', 5)), ('->', ('lying', 6), ('lying', 0)))", "index": 206}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: James, Benjamin, Noah, Elizabeth, Avery, Aiden, Penelope, and Jackson. James expressed that Noah is a knave. Benjamin expressed that James is a knight. Noah remarked, \"Jackson is a knave and Avery is a knight\". Elizabeth expressed that Penelope is a knight. Avery noted, \"Avery is a knight or James is a knight\". Aiden was heard saying, \"Benjamin is a knave or Noah is a knave\". According to Penelope, \"Aiden is not a knight\". In a statement by Jackson: \"Noah is a knight or Noah is a knave\". So who is a knight and who is a knave?", "names": ["James", "Benjamin", "Noah", "Elizabeth", "Avery", "Aiden", "Penelope", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true, false, true], "solution_text": "James is a knight, Benjamin is a knight, Noah is a knave, Elizabeth is a knave, Avery is a knight, Aiden is a knight, Penelope is a knave, and Jackson is a knight.", "solution_text_format": "(1) James is a knight\n(2) Benjamin is a knight\n(3) Noah is a knave\n(4) Elizabeth is a knave\n(5) Avery is a knight\n(6) Aiden is a knight\n(7) Penelope is a knave\n(8) Jackson is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of James that Noah is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Jackson is a knave and Avery is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Noah is a knight or Noah is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Avery is a knight or James is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that James is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Aiden is not a knight.", "Aiden cannot be a knight, because this would contradict the claim of Penelope that Aiden is not a knight.", "Aiden cannot be a knave, because this would contradict the false claim of their own that Benjamin is a knave or Noah is a knave.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the claim of Elizabeth that Penelope is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Penelope is a knight.", "Penelope cannot be a knight, because this would contradict the false claim of Elizabeth that Penelope is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Aiden is not a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Benjamin is a knave or Noah is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('telling-truth', 0), ('and', ('lying', 7), ('telling-truth', 4)), ('telling-truth', 6), ('or', ('telling-truth', 4), ('telling-truth', 0)), ('or', ('lying', 1), ('lying', 2)), ('not', ('telling-truth', 5)), ('or', ('telling-truth', 2), ('lying', 2)))", "index": 207}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Victoria, Jackson, Mason, Avery, Daniel, Emma, Isabella, and Amelia. Victoria stated, \"Emma is a knight\". As Jackson put it, \"Daniel is a knave or Isabella is a knight\". Mason expressed that If Amelia is a knave then Daniel is a knight. Avery said that If Isabella is a knight then Jackson is a knave. Daniel was heard saying, \"Isabella is a knave\". Emma told you that If Mason is a knight then Isabella is a knave. According to Isabella, \"If Emma is a knave then Avery is a knight\". Amelia said, \"Avery is a knight or Daniel is a knight.\" So who is a knight and who is a knave?", "names": ["Victoria", "Jackson", "Mason", "Avery", "Daniel", "Emma", "Isabella", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, true, true, false], "solution_text": "Victoria is a knight, Jackson is a knight, Mason is a knave, Avery is a knave, Daniel is a knave, Emma is a knight, Isabella is a knight, and Amelia is a knave.", "solution_text_format": "(1) Victoria is a knight\n(2) Jackson is a knight\n(3) Mason is a knave\n(4) Avery is a knave\n(5) Daniel is a knave\n(6) Emma is a knight\n(7) Isabella is a knight\n(8) Amelia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that Emma is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If Mason is a knight then Isabella is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Amelia is a knave then Daniel is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Avery is a knight or Daniel is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that If Isabella is a knight then Jackson is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Emma that If Mason is a knight then Isabella is a knave.", "Isabella cannot be a knave, because this would contradict the false claim of their own that If Emma is a knave then Avery is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that If Isabella is a knight then Jackson is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Emma that If Mason is a knight then Isabella is a knave.", "Isabella cannot be a knave, because this would contradict the false claim of Avery that If Isabella is a knight then Jackson is a knave.", "We have exhausted all possibilities for Isabella and Avery, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Avery is a knight or Daniel is a knight.", "Avery cannot be a knight, because this would contradict the false claim of Amelia that Avery is a knight or Daniel is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that If Isabella is a knight then Jackson is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Emma that If Mason is a knight then Isabella is a knave.", "Isabella cannot be a knave, because this would contradict the false claim of Avery that If Isabella is a knight then Jackson is a knave.", "We have exhausted all possibilities for Isabella, Avery, and Amelia, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that If Amelia is a knave then Daniel is a knight.", "Amelia cannot be a knight, because this would contradict the false claim of Mason that If Amelia is a knave then Daniel is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Avery is a knight or Daniel is a knight.", "Avery cannot be a knight, because this would contradict the false claim of Amelia that Avery is a knight or Daniel is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that If Isabella is a knight then Jackson is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that If Emma is a knave then Avery is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Daniel is a knave or Isabella is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of Mason that If Amelia is a knave then Daniel is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Isabella is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 5), ('or', ('lying', 4), ('telling-truth', 6)), ('->', ('lying', 7), ('telling-truth', 4)), ('->', ('telling-truth', 6), ('lying', 1)), ('lying', 6), ('->', ('telling-truth', 2), ('lying', 6)), ('->', ('lying', 5), ('telling-truth', 3)), ('or', ('telling-truth', 3), ('telling-truth', 4)))", "index": 208}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Isabella, Chloe, Victoria, Benjamin, Michael, Alexander, Emily, and Sophia. Isabella stated, \"Michael is a knight if and only if Michael is a knave\". Chloe stated, \"Benjamin is a knave or Michael is a knight\". Victoria said that If Benjamin is a knight then Michael is a knight. Benjamin said, \"Victoria is not a knight.\" \"If Isabella is a knight then Alexander is a knight\" - Michael. \"If Sophia is a knight then Isabella is a knight\" - Alexander. Emily asserted: \"Isabella is a knight if and only if Victoria is a knight\". Sophia remarked, \"Victoria is a knight if and only if Isabella is a knave\". So who is a knight and who is a knave?", "names": ["Isabella", "Chloe", "Victoria", "Benjamin", "Michael", "Alexander", "Emily", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, false, false, true], "solution_text": "Isabella is a knave, Chloe is a knight, Victoria is a knight, Benjamin is a knave, Michael is a knight, Alexander is a knave, Emily is a knave, and Sophia is a knight.", "solution_text_format": "(1) Isabella is a knave\n(2) Chloe is a knight\n(3) Victoria is a knight\n(4) Benjamin is a knave\n(5) Michael is a knight\n(6) Alexander is a knave\n(7) Emily is a knave\n(8) Sophia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Isabella cannot be a knight, because this would contradict the claim of their own that Michael is a knight if and only if Michael is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Michael is a knight if and only if Michael is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that If Isabella is a knight then Alexander is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that If Sophia is a knight then Isabella is a knight.", "Sophia cannot be a knight, because this would contradict the claim of Alexander that If Sophia is a knight then Isabella is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Victoria is a knight if and only if Isabella is a knave.", "Victoria cannot be a knight, because this would contradict the false claim of Sophia that Victoria is a knight if and only if Isabella is a knave.", "Victoria cannot be a knave, because this would contradict the false claim of their own that If Benjamin is a knight then Michael is a knight.", "We have exhausted all possibilities for Victoria and Sophia, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that If Sophia is a knight then Isabella is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Isabella is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that If Benjamin is a knight then Michael is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Victoria is not a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Victoria is not a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Benjamin is a knave or Michael is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Isabella is a knight if and only if Victoria is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Isabella is a knight if and only if Victoria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 4), ('lying', 4)), ('or', ('lying', 3), ('telling-truth', 4)), ('->', ('telling-truth', 3), ('telling-truth', 4)), ('not', ('telling-truth', 2)), ('->', ('telling-truth', 0), ('telling-truth', 5)), ('->', ('telling-truth', 7), ('telling-truth', 0)), ('<=>', ('telling-truth', 0), ('telling-truth', 2)), ('<=>', ('telling-truth', 2), ('lying', 0)))", "index": 209}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mason, Olivia, David, Grace, Ella, Isabella, Sofia, and Aiden. Mason asserted: \"David is not a knave\". In Olivia's words: \"Ella is not a knight\". According to David, \"David is a knight\". As Grace put it, \"Isabella is a knight and Aiden is a knave\". In a statement by Ella: \"Isabella is a knight and Sofia is a knave\". Isabella told you that If Olivia is a knight then Sofia is a knave. Sofia stated, \"If Mason is a knight then Ella is a knight\". According to Aiden, \"Mason is a knave if and only if Grace is a knave\". So who is a knight and who is a knave?", "names": ["Mason", "Olivia", "David", "Grace", "Ella", "Isabella", "Sofia", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, false, true, true], "solution_text": "Mason is a knave, Olivia is a knight, David is a knave, Grace is a knave, Ella is a knave, Isabella is a knave, Sofia is a knight, and Aiden is a knight.", "solution_text_format": "(1) Mason is a knave\n(2) Olivia is a knight\n(3) David is a knave\n(4) Grace is a knave\n(5) Ella is a knave\n(6) Isabella is a knave\n(7) Sofia is a knight\n(8) Aiden is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that David is not a knave.", "Assume David is a knight. No contradiction is found in their claim that David is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Ella is not a knight.", "Ella cannot be a knight, because this would contradict the claim of Olivia that Ella is not a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Isabella is a knight and Sofia is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that If Olivia is a knight then Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Isabella that If Olivia is a knight then Sofia is a knave.", "Sofia cannot be a knave, because this would contradict the false claim of Ella that Isabella is a knight and Sofia is a knave.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that If Olivia is a knight then Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that If Mason is a knight then Ella is a knight.", "Sofia cannot be a knave, because this would contradict the false claim of Isabella that If Olivia is a knight then Sofia is a knave.", "We have exhausted all possibilities for Sofia, Isabella, and Ella, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Ella is not a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Isabella is a knight and Sofia is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that If Olivia is a knight then Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Ella that Isabella is a knight and Sofia is a knave.", "Sofia cannot be a knave, because this would contradict the false claim of their own that If Mason is a knight then Ella is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the claim of Ella that Isabella is a knight and Sofia is a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the false claim of Olivia that Ella is not a knight.", "We have exhausted all possibilities for Ella and Olivia, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the claim of Mason that David is not a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that David is not a knave.", "David cannot be a knight, because this would contradict the false claim of Mason that David is not a knave.", "Assume David is a knave. No contradiction is found in their false claim that David is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Ella is not a knight.", "Ella cannot be a knight, because this would contradict the claim of Olivia that Ella is not a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Isabella is a knight and Sofia is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that If Olivia is a knight then Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Isabella that If Olivia is a knight then Sofia is a knave.", "Sofia cannot be a knave, because this would contradict the false claim of Ella that Isabella is a knight and Sofia is a knave.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that If Olivia is a knight then Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that If Mason is a knight then Ella is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Isabella is a knight and Aiden is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Isabella is a knight and Aiden is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Mason is a knave if and only if Grace is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('not', ('telling-truth', 4)), ('telling-truth', 2), ('and', ('telling-truth', 5), ('lying', 7)), ('and', ('telling-truth', 5), ('lying', 6)), ('->', ('telling-truth', 1), ('lying', 6)), ('->', ('telling-truth', 0), ('telling-truth', 4)), ('<=>', ('lying', 0), ('lying', 3)))", "index": 210}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mason, Alexander, Aurora, Owen, Abigail, Sophia, Emma, and Evelyn. \"Mason is a knight,\" Mason declared. Alexander asserted: \"Owen is a knight or Mason is a knight\". In a statement by Aurora: \"Alexander is a knight if and only if Emma is a knave\". In a statement by Owen: \"Mason is a knave and Evelyn is a knight\". \"Mason is a knight or Evelyn is a knight,\" Abigail claimed. Sophia was heard saying, \"If Aurora is a knight then Mason is a knave\". In Emma's words: \"Owen is a knave or Aurora is a knight\". Evelyn asserted: \"If Sophia is a knave then Alexander is a knave\". So who is a knight and who is a knave?", "names": ["Mason", "Alexander", "Aurora", "Owen", "Abigail", "Sophia", "Emma", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true, true, true], "solution_text": "Mason is a knight, Alexander is a knight, Aurora is a knave, Owen is a knave, Abigail is a knight, Sophia is a knight, Emma is a knight, and Evelyn is a knight.", "solution_text_format": "(1) Mason is a knight\n(2) Alexander is a knight\n(3) Aurora is a knave\n(4) Owen is a knave\n(5) Abigail is a knight\n(6) Sophia is a knight\n(7) Emma is a knight\n(8) Evelyn is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Mason is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Owen is a knight or Mason is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Mason is a knave and Evelyn is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Mason is a knave and Evelyn is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Sophia is a knave then Alexander is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that If Aurora is a knight then Mason is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Sophia that If Aurora is a knight then Mason is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Alexander is a knight if and only if Emma is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Owen is a knave or Aurora is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Mason is a knight or Evelyn is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 0), ('or', ('telling-truth', 3), ('telling-truth', 0)), ('<=>', ('telling-truth', 1), ('lying', 6)), ('and', ('lying', 0), ('telling-truth', 7)), ('or', ('telling-truth', 0), ('telling-truth', 7)), ('->', ('telling-truth', 2), ('lying', 0)), ('or', ('lying', 3), ('telling-truth', 2)), ('->', ('lying', 5), ('lying', 1)))", "index": 211}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Luke, Liam, Scarlett, Sebastian, Jack, Sophia, Ella, and Joseph. \"Ella is a knave,\" Luke claimed. Liam asserted: \"Sebastian is a knight or Ella is a knight\". Scarlett said that Joseph is a knave if and only if Ella is a knight. Sebastian stated, \"Jack is a knave\". Jack asserted: \"Joseph is a knight or Scarlett is a knave\". \"Jack is a knight,\" Sophia claimed. \"Liam is a knight and Scarlett is a knight,\" Ella claimed. Joseph was heard saying, \"Jack is not a knight\". So who is a knight and who is a knave?", "names": ["Luke", "Liam", "Scarlett", "Sebastian", "Jack", "Sophia", "Ella", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true, false, false], "solution_text": "Luke is a knight, Liam is a knave, Scarlett is a knave, Sebastian is a knave, Jack is a knight, Sophia is a knight, Ella is a knave, and Joseph is a knave.", "solution_text_format": "(1) Luke is a knight\n(2) Liam is a knave\n(3) Scarlett is a knave\n(4) Sebastian is a knave\n(5) Jack is a knight\n(6) Sophia is a knight\n(7) Ella is a knave\n(8) Joseph is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of Luke that Ella is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Liam is a knight and Scarlett is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Sebastian is a knight or Ella is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of Sebastian that Jack is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Joseph is a knight or Scarlett is a knave.", "Joseph cannot be a knight, because this would contradict the false claim of Jack that Joseph is a knight or Scarlett is a knave.", "Joseph cannot be a knave, because this would contradict the false claim of their own that Jack is not a knight.", "We have exhausted all possibilities for Joseph and Jack, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the claim of Liam that Sebastian is a knight or Ella is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Sebastian is a knight or Ella is a knight.", "Sebastian cannot be a knight, because this would contradict the false claim of Liam that Sebastian is a knight or Ella is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Jack is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Joseph is a knight or Scarlett is a knave.", "Joseph cannot be a knight, because this would contradict the claim of their own that Jack is not a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Jack is not a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Joseph is a knave if and only if Ella is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Joseph is a knave if and only if Ella is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Jack is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 6), ('or', ('telling-truth', 3), ('telling-truth', 6)), ('<=>', ('lying', 7), ('telling-truth', 6)), ('lying', 4), ('or', ('telling-truth', 7), ('lying', 2)), ('telling-truth', 4), ('and', ('telling-truth', 1), ('telling-truth', 2)), ('not', ('telling-truth', 4)))", "index": 212}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Olivia, Daniel, Samuel, Jackson, Mason, Zoey, Charlotte, and James. Olivia asserted: \"If Charlotte is a knave then Samuel is a knight\". Daniel remarked, \"Jackson is a knave\". Samuel asserted: \"Zoey is a knave or Mason is a knave\". According to Jackson, \"Olivia is a knave\". Mason said, \"James is a knight if and only if Mason is a knight.\" Zoey told you that Mason is not a knave. Charlotte asserted: \"Samuel is a knight or Olivia is a knight\". James stated, \"Jackson is a knave and Samuel is a knight\". So who is a knight and who is a knave?", "names": ["Olivia", "Daniel", "Samuel", "Jackson", "Mason", "Zoey", "Charlotte", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false, true, true], "solution_text": "Olivia is a knight, Daniel is a knight, Samuel is a knight, Jackson is a knave, Mason is a knave, Zoey is a knave, Charlotte is a knight, and James is a knight.", "solution_text_format": "(1) Olivia is a knight\n(2) Daniel is a knight\n(3) Samuel is a knight\n(4) Jackson is a knave\n(5) Mason is a knave\n(6) Zoey is a knave\n(7) Charlotte is a knight\n(8) James is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that If Charlotte is a knave then Samuel is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Samuel is a knight or Olivia is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Zoey is a knave or Mason is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Mason is not a knave.", "Mason cannot be a knight, because this would contradict the claim of Samuel that Zoey is a knave or Mason is a knave.", "Mason cannot be a knave, because this would contradict the claim of Zoey that Mason is not a knave.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Mason is not a knave.", "Mason cannot be a knight, because this would contradict the false claim of Zoey that Mason is not a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that James is a knight if and only if Mason is a knight.", "Assume James is a knight. No contradiction is found in their claim that Jackson is a knave and Samuel is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Olivia is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Olivia is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Jackson is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 6), ('telling-truth', 2)), ('lying', 3), ('or', ('lying', 5), ('lying', 4)), ('lying', 0), ('<=>', ('telling-truth', 7), ('telling-truth', 4)), ('not', ('lying', 4)), ('or', ('telling-truth', 2), ('telling-truth', 0)), ('and', ('lying', 3), ('telling-truth', 2)))", "index": 213}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Riley, Logan, Benjamin, Penelope, Harper, Aria, Henry, and Olivia. Riley told you that Penelope is a knave. Logan stated, \"If Harper is a knave then Benjamin is a knave\". \"Olivia is a knave\" - Benjamin. Penelope told you that If Harper is a knight then Henry is a knave. Harper remarked, \"If Benjamin is a knight then Penelope is a knave\". In Aria's words: \"Harper is a knight if and only if Benjamin is a knave\". In Henry's words: \"Aria is a knave if and only if Riley is a knave\". In Olivia's words: \"Henry is not a knight\". So who is a knight and who is a knave?", "names": ["Riley", "Logan", "Benjamin", "Penelope", "Harper", "Aria", "Henry", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true, false, true], "solution_text": "Riley is a knave, Logan is a knight, Benjamin is a knave, Penelope is a knight, Harper is a knight, Aria is a knight, Henry is a knave, and Olivia is a knight.", "solution_text_format": "(1) Riley is a knave\n(2) Logan is a knight\n(3) Benjamin is a knave\n(4) Penelope is a knight\n(5) Harper is a knight\n(6) Aria is a knight\n(7) Henry is a knave\n(8) Olivia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the claim of Riley that Penelope is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that If Harper is a knight then Henry is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that If Benjamin is a knight then Penelope is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Benjamin that Olivia is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Henry is not a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Aria is a knave if and only if Riley is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Harper is a knight if and only if Benjamin is a knave.", "Aria cannot be a knave, because this would contradict the claim of Henry that Aria is a knave if and only if Riley is a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the false claim of Penelope that If Harper is a knight then Henry is a knave.", "We have exhausted all possibilities for Henry and Olivia, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Henry is not a knight.", "Henry cannot be a knight, because this would contradict the claim of Olivia that Henry is not a knight.", "Henry cannot be a knave, because this would contradict the false claim of Penelope that If Harper is a knight then Henry is a knave.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the false claim of Benjamin that Olivia is a knave.", "We have exhausted all possibilities for Olivia and Benjamin, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the false claim of Penelope that If Harper is a knight then Henry is a knave.", "We have exhausted all possibilities for Harper and Penelope, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Penelope is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that If Harper is a knight then Henry is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that If Benjamin is a knight then Penelope is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Harper that If Benjamin is a knight then Penelope is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Henry is not a knight.", "Henry cannot be a knight, because this would contradict the claim of Penelope that If Harper is a knight then Henry is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Aria is a knave if and only if Riley is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Harper is a knight if and only if Benjamin is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that If Harper is a knave then Benjamin is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('->', ('lying', 4), ('lying', 2)), ('lying', 7), ('->', ('telling-truth', 4), ('lying', 6)), ('->', ('telling-truth', 2), ('lying', 3)), ('<=>', ('telling-truth', 4), ('lying', 2)), ('<=>', ('lying', 5), ('lying', 0)), ('not', ('telling-truth', 6)))", "index": 214}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Riley, William, Benjamin, Isabella, Zoey, Lily, Mason, and Ethan. \"If Lily is a knave then Zoey is a knave\" - Riley. William said that Benjamin is not a knave. Benjamin expressed that If Zoey is a knight then William is a knight. Isabella remarked, \"William is not a knave\". Zoey remarked, \"Benjamin is a knight or William is a knight\". Lily expressed that Mason is a knight or Riley is a knight. \"Zoey is a knave or Riley is a knave,\" Mason mentioned. Ethan remarked, \"Mason is a knight and Zoey is a knave\". So who is a knight and who is a knave?", "names": ["Riley", "William", "Benjamin", "Isabella", "Zoey", "Lily", "Mason", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true, false, false], "solution_text": "Riley is a knight, William is a knight, Benjamin is a knight, Isabella is a knight, Zoey is a knight, Lily is a knight, Mason is a knave, and Ethan is a knave.", "solution_text_format": "(1) Riley is a knight\n(2) William is a knight\n(3) Benjamin is a knight\n(4) Isabella is a knight\n(5) Zoey is a knight\n(6) Lily is a knight\n(7) Mason is a knave\n(8) Ethan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that If Lily is a knave then Zoey is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Mason is a knight or Riley is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Zoey is a knave or Riley is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Mason that Zoey is a knave or Riley is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Benjamin is a knight or William is a knight.", "Benjamin cannot be a knight, because this would contradict the false claim of Zoey that Benjamin is a knight or William is a knight.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that If Zoey is a knight then William is a knight.", "We have exhausted all possibilities for Benjamin and Zoey, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Zoey is a knave or Riley is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Benjamin is a knight or William is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Zoey is a knight then William is a knight.", "Assume William is a knight. No contradiction is found in their claim that Benjamin is not a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that William is not a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Mason is a knight and Zoey is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Mason is a knight and Zoey is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('lying', 4)), ('not', ('lying', 2)), ('->', ('telling-truth', 4), ('telling-truth', 1)), ('not', ('lying', 1)), ('or', ('telling-truth', 2), ('telling-truth', 1)), ('or', ('telling-truth', 6), ('telling-truth', 0)), ('or', ('lying', 4), ('lying', 0)), ('and', ('telling-truth', 6), ('lying', 4)))", "index": 215}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Liam, Michael, Isabella, Charlotte, Aurora, Harper, Matthew, and Mason. Liam commented, \"Isabella is a knight\". Michael said, \"Isabella is a knight.\" Isabella told you that Michael is a knave if and only if Michael is a knight. Charlotte said, \"Mason is not a knave.\" Aurora remarked, \"Harper is a knave if and only if Michael is a knave\". In Harper's words: \"Mason is a knave if and only if Matthew is a knight\". Matthew remarked, \"Charlotte is a knave and Michael is a knave\". Mason expressed that Michael is a knight if and only if Aurora is a knight. So who is a knight and who is a knave?", "names": ["Liam", "Michael", "Isabella", "Charlotte", "Aurora", "Harper", "Matthew", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, true, false, true], "solution_text": "Liam is a knave, Michael is a knave, Isabella is a knave, Charlotte is a knight, Aurora is a knave, Harper is a knight, Matthew is a knave, and Mason is a knight.", "solution_text_format": "(1) Liam is a knave\n(2) Michael is a knave\n(3) Isabella is a knave\n(4) Charlotte is a knight\n(5) Aurora is a knave\n(6) Harper is a knight\n(7) Matthew is a knave\n(8) Mason is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Isabella is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Michael is a knave if and only if Michael is a knight.", "Isabella cannot be a knave, because this would contradict the claim of Liam that Isabella is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Isabella is a knight.", "Isabella cannot be a knight, because this would contradict the false claim of Liam that Isabella is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Michael is a knave if and only if Michael is a knight.", "Michael cannot be a knight, because this would contradict the claim of their own that Isabella is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Isabella is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Mason is not a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Michael is a knight if and only if Aurora is a knight.", "Aurora cannot be a knight, because this would contradict the claim of Mason that Michael is a knight if and only if Aurora is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Harper is a knave if and only if Michael is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Mason is a knave if and only if Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the claim of Harper that Mason is a knave if and only if Matthew is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Charlotte is a knave and Michael is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('telling-truth', 2), ('<=>', ('lying', 1), ('telling-truth', 1)), ('not', ('lying', 7)), ('<=>', ('lying', 5), ('lying', 1)), ('<=>', ('lying', 7), ('telling-truth', 6)), ('and', ('lying', 3), ('lying', 1)), ('<=>', ('telling-truth', 1), ('telling-truth', 4)))", "index": 216}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Zoey, Emma, Sofia, Aurora, Henry, Noah, Jack, and Abigail. Zoey expressed that Aurora is a knight and Sofia is a knave. Emma was heard saying, \"Zoey is not a knave\". Sofia stated, \"If Zoey is a knight then Sofia is a knight\". Aurora asserted: \"Abigail is a knight\". In Henry's words: \"If Abigail is a knight then Zoey is a knave\". Noah asserted: \"If Aurora is a knave then Sofia is a knight\". According to Jack, \"Emma is not a knave\". According to Abigail, \"Noah is not a knight\". So who is a knight and who is a knave?", "names": ["Zoey", "Emma", "Sofia", "Aurora", "Henry", "Noah", "Jack", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true, false, false], "solution_text": "Zoey is a knave, Emma is a knave, Sofia is a knight, Aurora is a knave, Henry is a knight, Noah is a knight, Jack is a knave, and Abigail is a knave.", "solution_text_format": "(1) Zoey is a knave\n(2) Emma is a knave\n(3) Sofia is a knight\n(4) Aurora is a knave\n(5) Henry is a knight\n(6) Noah is a knight\n(7) Jack is a knave\n(8) Abigail is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Zoey is a knight. No contradiction is found in their claim that Aurora is a knight and Sofia is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Noah is not a knight.", "Noah cannot be a knight, because this would contradict the claim of Abigail that Noah is not a knight.", "Noah cannot be a knave, because this would contradict the false claim of their own that If Aurora is a knave then Sofia is a knight.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the claim of Aurora that Abigail is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the claim of Zoey that Aurora is a knight and Sofia is a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Aurora is a knight and Sofia is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Noah is not a knight.", "Noah cannot be a knight, because this would contradict the claim of Abigail that Noah is not a knight.", "Noah cannot be a knave, because this would contradict the false claim of their own that If Aurora is a knave then Sofia is a knight.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the claim of Aurora that Abigail is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Abigail is a knight.", "Abigail cannot be a knight, because this would contradict the false claim of Aurora that Abigail is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Noah is not a knight.", "Assume Noah is a knight. No contradiction is found in their claim that If Aurora is a knave then Sofia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that If Zoey is a knight then Sofia is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Zoey is not a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Zoey is not a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Abigail is a knight then Zoey is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Emma is not a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Emma is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('lying', 2)), ('not', ('lying', 0)), ('->', ('telling-truth', 0), ('telling-truth', 2)), ('telling-truth', 7), ('->', ('telling-truth', 7), ('lying', 0)), ('->', ('lying', 3), ('telling-truth', 2)), ('not', ('lying', 1)), ('not', ('telling-truth', 5)))", "index": 217}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Owen, Samuel, Oliver, James, Isabella, Amelia, Victoria, and Aria. Owen commented, \"Isabella is not a knave\". Samuel expressed that If Isabella is a knave then Victoria is a knight. Oliver told you that Aria is a knave. James said that Isabella is a knight if and only if Aria is a knight. In Isabella's words: \"Victoria is a knight or Amelia is a knave\". \"Victoria is a knave or Samuel is a knave\" - Amelia. As Victoria put it, \"Amelia is a knave if and only if Amelia is a knight\". Aria said that James is a knight if and only if Aria is a knight. So who is a knight and who is a knave?", "names": ["Owen", "Samuel", "Oliver", "James", "Isabella", "Amelia", "Victoria", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, true, false, false], "solution_text": "Owen is a knave, Samuel is a knave, Oliver is a knight, James is a knight, Isabella is a knave, Amelia is a knight, Victoria is a knave, and Aria is a knave.", "solution_text_format": "(1) Owen is a knave\n(2) Samuel is a knave\n(3) Oliver is a knight\n(4) James is a knight\n(5) Isabella is a knave\n(6) Amelia is a knight\n(7) Victoria is a knave\n(8) Aria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Isabella is not a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Victoria is a knight or Amelia is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that Amelia is a knave if and only if Amelia is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Amelia is a knave if and only if Amelia is a knight.", "Amelia cannot be a knight, because this would contradict the claim of Isabella that Victoria is a knight or Amelia is a knave.", "Amelia cannot be a knave, because this would contradict the false claim of their own that Victoria is a knave or Samuel is a knave.", "We have exhausted all possibilities for Amelia and Victoria, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the claim of Owen that Isabella is not a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Isabella is not a knave.", "Isabella cannot be a knight, because this would contradict the false claim of Owen that Isabella is not a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Victoria is a knight or Amelia is a knave.", "Victoria cannot be a knight, because this would contradict the false claim of Isabella that Victoria is a knight or Amelia is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Amelia is a knave if and only if Amelia is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Victoria is a knave or Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that If Isabella is a knave then Victoria is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that If Isabella is a knave then Victoria is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of Oliver that Aria is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that James is a knight if and only if Aria is a knight.", "Assume James is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Aria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('->', ('lying', 4), ('telling-truth', 6)), ('lying', 7), ('<=>', ('telling-truth', 4), ('telling-truth', 7)), ('or', ('telling-truth', 6), ('lying', 5)), ('or', ('lying', 6), ('lying', 1)), ('<=>', ('lying', 5), ('telling-truth', 5)), ('<=>', ('telling-truth', 3), ('telling-truth', 7)))", "index": 218}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Avery, Sofia, Riley, Aiden, Oliver, Emily, Victoria, and Michael. Avery expressed that If Victoria is a knight then Sofia is a knave. Sofia said that Aiden is a knight if and only if Oliver is a knave. In a statement by Riley: \"Emily is not a knave\". Aiden noted, \"Michael is a knave or Riley is a knight\". Oliver stated, \"Avery is a knight or Riley is a knave\". Emily said, \"Victoria is a knight or Riley is a knight.\" Victoria was heard saying, \"Oliver is a knight or Avery is a knight\". Michael said that Avery is a knight. So who is a knight and who is a knave?", "names": ["Avery", "Sofia", "Riley", "Aiden", "Oliver", "Emily", "Victoria", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true, true, true], "solution_text": "Avery is a knight, Sofia is a knave, Riley is a knight, Aiden is a knight, Oliver is a knight, Emily is a knight, Victoria is a knight, and Michael is a knight.", "solution_text_format": "(1) Avery is a knight\n(2) Sofia is a knave\n(3) Riley is a knight\n(4) Aiden is a knight\n(5) Oliver is a knight\n(6) Emily is a knight\n(7) Victoria is a knight\n(8) Michael is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that If Victoria is a knight then Sofia is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Oliver is a knight or Avery is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Avery is a knight or Riley is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Emily is not a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Victoria is a knight or Riley is a knight.", "Sofia cannot be a knight, because this would contradict the claim of Avery that If Victoria is a knight then Sofia is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Aiden is a knight if and only if Oliver is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Michael is a knave or Riley is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Avery is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 6), ('lying', 1)), ('<=>', ('telling-truth', 3), ('lying', 4)), ('not', ('lying', 5)), ('or', ('lying', 7), ('telling-truth', 2)), ('or', ('telling-truth', 0), ('lying', 2)), ('or', ('telling-truth', 6), ('telling-truth', 2)), ('or', ('telling-truth', 4), ('telling-truth', 0)), ('telling-truth', 0))", "index": 219}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Benjamin, Grace, Ethan, Elizabeth, Aurora, Henry, Scarlett, and Lily. \"If Ethan is a knave then Ethan is a knight\" - Benjamin. Grace expressed that Henry is a knave if and only if Lily is a knave. \"Elizabeth is not a knave,\" Ethan mentioned. Elizabeth asserted: \"Benjamin is a knight or Scarlett is a knave\". \"Benjamin is a knave\" - Aurora. According to Henry, \"Elizabeth is a knight\". In Scarlett's words: \"Ethan is a knight\". \"Henry is not a knave,\" Lily declared. So who is a knight and who is a knave?", "names": ["Benjamin", "Grace", "Ethan", "Elizabeth", "Aurora", "Henry", "Scarlett", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true, true, true], "solution_text": "Benjamin is a knight, Grace is a knight, Ethan is a knight, Elizabeth is a knight, Aurora is a knave, Henry is a knight, Scarlett is a knight, and Lily is a knight.", "solution_text_format": "(1) Benjamin is a knight\n(2) Grace is a knight\n(3) Ethan is a knight\n(4) Elizabeth is a knight\n(5) Aurora is a knave\n(6) Henry is a knight\n(7) Scarlett is a knight\n(8) Lily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that If Ethan is a knave then Ethan is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Elizabeth is not a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Benjamin is a knight or Scarlett is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Ethan is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Henry is a knave if and only if Lily is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Henry is not a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Benjamin is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 2), ('telling-truth', 2)), ('<=>', ('lying', 5), ('lying', 7)), ('not', ('lying', 3)), ('or', ('telling-truth', 0), ('lying', 6)), ('lying', 0), ('telling-truth', 3), ('telling-truth', 2), ('not', ('lying', 5)))", "index": 220}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Penelope, Liam, Amelia, Abigail, Olivia, Emily, Mia, and Logan. Penelope said, \"Olivia is not a knave.\" Liam asserted: \"Olivia is a knave\". \"Abigail is a knight and Liam is a knight,\" Amelia mentioned. According to Abigail, \"Liam is a knave\". Olivia commented, \"Logan is not a knave\". \"Amelia is a knight and Mia is a knight,\" Emily declared. Mia commented, \"If Abigail is a knave then Liam is a knave\". Logan told you that Amelia is not a knight. So who is a knight and who is a knave?", "names": ["Penelope", "Liam", "Amelia", "Abigail", "Olivia", "Emily", "Mia", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false, true, true], "solution_text": "Penelope is a knight, Liam is a knave, Amelia is a knave, Abigail is a knight, Olivia is a knight, Emily is a knave, Mia is a knight, and Logan is a knight.", "solution_text_format": "(1) Penelope is a knight\n(2) Liam is a knave\n(3) Amelia is a knave\n(4) Abigail is a knight\n(5) Olivia is a knight\n(6) Emily is a knave\n(7) Mia is a knight\n(8) Logan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that Olivia is not a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Logan is not a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Amelia is not a knight.", "Amelia cannot be a knight, because this would contradict the claim of Logan that Amelia is not a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Abigail is a knight and Liam is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Olivia is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Olivia is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Amelia is a knight and Mia is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Amelia is a knight and Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that If Abigail is a knave then Liam is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('lying', 4), ('and', ('telling-truth', 3), ('telling-truth', 1)), ('lying', 1), ('not', ('lying', 7)), ('and', ('telling-truth', 2), ('telling-truth', 6)), ('->', ('lying', 3), ('lying', 1)), ('not', ('telling-truth', 2)))", "index": 221}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: James, Mason, Noah, Jackson, Jack, Ella, Lily, and Aurora. \"If Lily is a knight then Jackson is a knight,\" James declared. \"James is a knight\" - Mason. Noah told you that Ella is not a knave. As Jackson put it, \"If Lily is a knight then Jack is a knave\". \"If Noah is a knave then Aurora is a knave\" - Jack. Ella remarked, \"Mason is a knave\". \"Ella is not a knave\" - Lily. Aurora noted, \"If Aurora is a knight then Jackson is a knave\". So who is a knight and who is a knave?", "names": ["James", "Mason", "Noah", "Jackson", "Jack", "Ella", "Lily", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true, true, true], "solution_text": "James is a knave, Mason is a knave, Noah is a knight, Jackson is a knave, Jack is a knight, Ella is a knight, Lily is a knight, and Aurora is a knight.", "solution_text_format": "(1) James is a knave\n(2) Mason is a knave\n(3) Noah is a knight\n(4) Jackson is a knave\n(5) Jack is a knight\n(6) Ella is a knight\n(7) Lily is a knight\n(8) Aurora is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that If Lily is a knight then Jackson is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Ella is not a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of Ella that Mason is a knave.", "Mason cannot be a knave, because this would contradict the false claim of their own that James is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the claim of Lily that Ella is not a knave.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Ella is not a knave.", "Ella cannot be a knight, because this would contradict the false claim of Lily that Ella is not a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Mason is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that James is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that If Lily is a knight then Jack is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that If Noah is a knave then Aurora is a knave.", "Noah cannot be a knight, because this would contradict the claim of their own that Ella is not a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Ella is not a knave.", "Aurora cannot be a knight, because this would contradict the claim of Jack that If Noah is a knave then Aurora is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of their own that If Aurora is a knight then Jackson is a knave.", "We have exhausted all possibilities for Aurora and Noah, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that If Noah is a knave then Aurora is a knave.", "Noah cannot be a knight, because this would contradict the claim of their own that Ella is not a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Ella is not a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that If Aurora is a knight then Jackson is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of Jack that If Noah is a knave then Aurora is a knave.", "We have exhausted all possibilities for Aurora, Noah, and Jack, so let us go back and reconsider Jackson.", "Jackson cannot be a knave, because this would contradict the false claim of their own that If Lily is a knight then Jack is a knave.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Mason.", "Mason cannot be a knave, because this would contradict the false claim of their own that James is a knight.", "We have exhausted all possibilities for Mason, Ella, and Lily, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that If Lily is a knight then Jackson is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Ella is not a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that James is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that James is a knight.", "Jackson cannot be a knight, because this would contradict the false claim of James that If Lily is a knight then Jackson is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that If Lily is a knight then Jack is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that If Noah is a knave then Aurora is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Ella is not a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that If Aurora is a knight then Jackson is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 6), ('telling-truth', 3)), ('telling-truth', 0), ('not', ('lying', 5)), ('->', ('telling-truth', 6), ('lying', 4)), ('->', ('lying', 2), ('lying', 7)), ('lying', 1), ('not', ('lying', 5)), ('->', ('telling-truth', 7), ('lying', 3)))", "index": 222}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: James, William, Lucas, David, Benjamin, Elizabeth, Daniel, and Liam. In a statement by James: \"Daniel is a knight if and only if Daniel is a knave\". William expressed that Daniel is a knight if and only if Benjamin is a knight. Lucas stated, \"Lucas is a knight and Elizabeth is a knave\". David asserted: \"James is not a knave\". Benjamin said, \"James is a knave.\" Elizabeth noted, \"If David is a knave then James is a knave\". Daniel told you that If Lucas is a knight then William is a knave. Liam asserted: \"David is a knight or Elizabeth is a knave\". So who is a knight and who is a knave?", "names": ["James", "William", "Lucas", "David", "Benjamin", "Elizabeth", "Daniel", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true, true, false], "solution_text": "James is a knave, William is a knight, Lucas is a knave, David is a knave, Benjamin is a knight, Elizabeth is a knight, Daniel is a knight, and Liam is a knave.", "solution_text_format": "(1) James is a knave\n(2) William is a knight\n(3) Lucas is a knave\n(4) David is a knave\n(5) Benjamin is a knight\n(6) Elizabeth is a knight\n(7) Daniel is a knight\n(8) Liam is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["James cannot be a knight, because this would contradict the claim of their own that Daniel is a knight if and only if Daniel is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Daniel is a knight if and only if Daniel is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that If Lucas is a knight then William is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Lucas is a knight and Elizabeth is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of Lucas that Lucas is a knight and Elizabeth is a knave.", "Elizabeth cannot be a knave, because this would contradict the false claim of their own that If David is a knave then James is a knave.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Lucas is a knight and Elizabeth is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If David is a knave then James is a knave.", "David cannot be a knight, because this would contradict the claim of their own that James is not a knave.", "Assume David is a knave. No contradiction is found in their false claim that James is not a knave.", "Assume William is a knight. No contradiction is found in their claim that Daniel is a knight if and only if Benjamin is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that James is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that David is a knight or Elizabeth is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that David is a knight or Elizabeth is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 6), ('lying', 6)), ('<=>', ('telling-truth', 6), ('telling-truth', 4)), ('and', ('telling-truth', 2), ('lying', 5)), ('not', ('lying', 0)), ('lying', 0), ('->', ('lying', 3), ('lying', 0)), ('->', ('telling-truth', 2), ('lying', 1)), ('or', ('telling-truth', 3), ('lying', 5)))", "index": 223}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jackson, Joseph, Matthew, Noah, Aurora, Charlotte, David, and Jacob. Jackson said that David is not a knight. In Joseph's words: \"If Noah is a knight then David is a knight\". In Matthew's words: \"Noah is a knave if and only if Noah is a knight\". Noah stated, \"If Charlotte is a knight then Jackson is a knight\". Aurora said that Jackson is not a knight. Charlotte stated, \"Jacob is a knave and David is a knight\". In David's words: \"Noah is a knave or Matthew is a knight\". Jacob noted, \"Charlotte is a knight and David is a knight\". So who is a knight and who is a knave?", "names": ["Jackson", "Joseph", "Matthew", "Noah", "Aurora", "Charlotte", "David", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, false, false, false], "solution_text": "Jackson is a knight, Joseph is a knave, Matthew is a knave, Noah is a knight, Aurora is a knave, Charlotte is a knave, David is a knave, and Jacob is a knave.", "solution_text_format": "(1) Jackson is a knight\n(2) Joseph is a knave\n(3) Matthew is a knave\n(4) Noah is a knight\n(5) Aurora is a knave\n(6) Charlotte is a knave\n(7) David is a knave\n(8) Jacob is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that David is not a knight.", "David cannot be a knight, because this would contradict the claim of Jackson that David is not a knight.", "Assume David is a knave. No contradiction is found in their false claim that Noah is a knave or Matthew is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that If Charlotte is a knight then Jackson is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Jacob is a knave and David is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Jacob is a knave and David is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Charlotte is a knight and David is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Charlotte is a knight and David is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Noah is a knave if and only if Noah is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Noah is a knave if and only if Noah is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that If Noah is a knight then David is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that If Noah is a knight then David is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Jackson is not a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Jackson is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 6)), ('->', ('telling-truth', 3), ('telling-truth', 6)), ('<=>', ('lying', 3), ('telling-truth', 3)), ('->', ('telling-truth', 5), ('telling-truth', 0)), ('not', ('telling-truth', 0)), ('and', ('lying', 7), ('telling-truth', 6)), ('or', ('lying', 3), ('telling-truth', 2)), ('and', ('telling-truth', 5), ('telling-truth', 6)))", "index": 224}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emily, Charlotte, Emma, Noah, Joseph, Lucas, Scarlett, and Jack. Emily said that Scarlett is a knight or Jack is a knight. Charlotte said, \"Emma is a knight.\" Emma said that If Emma is a knight then Noah is a knave. \"Charlotte is a knight if and only if Lucas is a knave,\" Noah declared. Joseph said, \"Emily is a knight or Jack is a knave.\" In Lucas's words: \"Emily is a knight\". \"Lucas is a knight or Lucas is a knave,\" Scarlett claimed. In a statement by Jack: \"Noah is not a knight\". So who is a knight and who is a knave?", "names": ["Emily", "Charlotte", "Emma", "Noah", "Joseph", "Lucas", "Scarlett", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true, true, true], "solution_text": "Emily is a knight, Charlotte is a knight, Emma is a knight, Noah is a knave, Joseph is a knight, Lucas is a knight, Scarlett is a knight, and Jack is a knight.", "solution_text_format": "(1) Emily is a knight\n(2) Charlotte is a knight\n(3) Emma is a knight\n(4) Noah is a knave\n(5) Joseph is a knight\n(6) Lucas is a knight\n(7) Scarlett is a knight\n(8) Jack is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Scarlett is a knight or Jack is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Lucas is a knight or Lucas is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Emily is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Noah is not a knight.", "Noah cannot be a knight, because this would contradict the claim of Jack that Noah is not a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Charlotte is a knight if and only if Lucas is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Emma is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If Emma is a knight then Noah is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Emily is a knight or Jack is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 6), ('telling-truth', 7)), ('telling-truth', 2), ('->', ('telling-truth', 2), ('lying', 3)), ('<=>', ('telling-truth', 1), ('lying', 5)), ('or', ('telling-truth', 0), ('lying', 7)), ('telling-truth', 0), ('or', ('telling-truth', 5), ('lying', 5)), ('not', ('telling-truth', 3)))", "index": 225}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jack, Charlotte, Oliver, Luke, Michael, Logan, Aiden, and Alexander. As Jack put it, \"Alexander is not a knight\". Charlotte stated, \"Oliver is a knight\". Oliver noted, \"Aiden is a knave and Logan is a knave\". In Luke's words: \"Michael is not a knight\". Michael remarked, \"Logan is a knave or Charlotte is a knave\". In a statement by Logan: \"Aiden is not a knave\". Aiden asserted: \"Logan is a knight if and only if Charlotte is a knave\". Alexander remarked, \"Oliver is not a knight\". So who is a knight and who is a knave?", "names": ["Jack", "Charlotte", "Oliver", "Luke", "Michael", "Logan", "Aiden", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, true, true, true], "solution_text": "Jack is a knave, Charlotte is a knave, Oliver is a knave, Luke is a knave, Michael is a knight, Logan is a knight, Aiden is a knight, and Alexander is a knight.", "solution_text_format": "(1) Jack is a knave\n(2) Charlotte is a knave\n(3) Oliver is a knave\n(4) Luke is a knave\n(5) Michael is a knight\n(6) Logan is a knight\n(7) Aiden is a knight\n(8) Alexander is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of Jack that Alexander is not a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Oliver is not a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Aiden is a knave and Logan is a knave.", "Aiden cannot be a knight, because this would contradict the claim of Oliver that Aiden is a knave and Logan is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Logan is a knight if and only if Charlotte is a knave.", "Logan cannot be a knight, because this would contradict the claim of Oliver that Aiden is a knave and Logan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Aiden is not a knave.", "Charlotte cannot be a knight, because this would contradict the false claim of Aiden that Logan is a knight if and only if Charlotte is a knave.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that Oliver is a knight.", "We have exhausted all possibilities for Charlotte, Logan, and Aiden, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the false claim of Alexander that Oliver is not a knight.", "We have exhausted all possibilities for Oliver and Alexander, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Alexander is not a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Oliver is not a knight.", "Oliver cannot be a knight, because this would contradict the claim of Alexander that Oliver is not a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Aiden is a knave and Logan is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Logan is a knight if and only if Charlotte is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Aiden is not a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Oliver is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Oliver is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Michael is not a knight.", "Michael cannot be a knight, because this would contradict the claim of Luke that Michael is not a knight.", "Michael cannot be a knave, because this would contradict the false claim of their own that Logan is a knave or Charlotte is a knave.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Michael is not a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Logan is a knave or Charlotte is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 7)), ('telling-truth', 2), ('and', ('lying', 6), ('lying', 5)), ('not', ('telling-truth', 4)), ('or', ('lying', 5), ('lying', 1)), ('not', ('lying', 6)), ('<=>', ('telling-truth', 5), ('lying', 1)), ('not', ('telling-truth', 2)))", "index": 226}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ethan, Aria, James, Jacob, Lucas, Luke, Scarlett, and Isabella. According to Ethan, \"Lucas is a knave\". \"Isabella is a knave and Luke is a knight\" - Aria. James expressed that Isabella is a knight. According to Jacob, \"If Aria is a knight then James is a knight\". Lucas stated, \"Isabella is a knave\". \"Ethan is a knight or Scarlett is a knave\" - Luke. Scarlett asserted: \"Aria is a knight\". \"Jacob is a knight or Luke is a knight,\" Isabella claimed. So who is a knight and who is a knave?", "names": ["Ethan", "Aria", "James", "Jacob", "Lucas", "Luke", "Scarlett", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true, false, true], "solution_text": "Ethan is a knight, Aria is a knave, James is a knight, Jacob is a knight, Lucas is a knave, Luke is a knight, Scarlett is a knave, and Isabella is a knight.", "solution_text_format": "(1) Ethan is a knight\n(2) Aria is a knave\n(3) James is a knight\n(4) Jacob is a knight\n(5) Lucas is a knave\n(6) Luke is a knight\n(7) Scarlett is a knave\n(8) Isabella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the claim of Ethan that Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Isabella is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Jacob is a knight or Luke is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that If Aria is a knight then James is a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that Isabella is a knave and Luke is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Isabella is a knave and Luke is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Ethan is a knight or Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Aria is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Aria is a knight.", "Assume James is a knight. No contradiction is found in their claim that Isabella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('and', ('lying', 7), ('telling-truth', 5)), ('telling-truth', 7), ('->', ('telling-truth', 1), ('telling-truth', 2)), ('lying', 7), ('or', ('telling-truth', 0), ('lying', 6)), ('telling-truth', 1), ('or', ('telling-truth', 3), ('telling-truth', 5)))", "index": 227}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: James, Aiden, Ethan, Charlotte, Aria, Matthew, Elizabeth, and Henry. James stated, \"Elizabeth is not a knight\". Aiden stated, \"Matthew is a knave or Matthew is a knight\". In a statement by Ethan: \"If Elizabeth is a knight then Matthew is a knight\". Charlotte commented, \"If Aiden is a knave then Matthew is a knave\". Aria said that James is a knight. Matthew said that James is a knight or Henry is a knave. \"Matthew is a knave and Ethan is a knight\" - Elizabeth. \"If Aria is a knave then James is a knave,\" Henry declared. So who is a knight and who is a knave?", "names": ["James", "Aiden", "Ethan", "Charlotte", "Aria", "Matthew", "Elizabeth", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true, false, true], "solution_text": "James is a knight, Aiden is a knight, Ethan is a knight, Charlotte is a knight, Aria is a knight, Matthew is a knight, Elizabeth is a knave, and Henry is a knight.", "solution_text_format": "(1) James is a knight\n(2) Aiden is a knight\n(3) Ethan is a knight\n(4) Charlotte is a knight\n(5) Aria is a knight\n(6) Matthew is a knight\n(7) Elizabeth is a knave\n(8) Henry is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Elizabeth is not a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of James that Elizabeth is not a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Matthew is a knave and Ethan is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that James is a knight or Henry is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Aria is a knave then James is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that James is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If Elizabeth is a knight then Matthew is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Matthew is a knave or Matthew is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Aiden is a knave then Matthew is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 6)), ('or', ('lying', 5), ('telling-truth', 5)), ('->', ('telling-truth', 6), ('telling-truth', 5)), ('->', ('lying', 1), ('lying', 5)), ('telling-truth', 0), ('or', ('telling-truth', 0), ('lying', 7)), ('and', ('lying', 5), ('telling-truth', 2)), ('->', ('lying', 4), ('lying', 0)))", "index": 228}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Matthew, Riley, Noah, Aria, Victoria, Lily, James, and Isabella. \"Riley is not a knave,\" Matthew declared. \"If Riley is a knight then Lily is a knave,\" Riley declared. \"If Aria is a knave then Riley is a knight,\" Noah declared. Aria expressed that If Matthew is a knight then Riley is a knave. According to Victoria, \"Matthew is a knave or Isabella is a knight\". \"Noah is not a knight,\" Lily mentioned. \"Noah is not a knave,\" James declared. \"Aria is a knave and Riley is a knave,\" Isabella mentioned. So who is a knight and who is a knave?", "names": ["Matthew", "Riley", "Noah", "Aria", "Victoria", "Lily", "James", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false, true, false], "solution_text": "Matthew is a knight, Riley is a knight, Noah is a knight, Aria is a knave, Victoria is a knave, Lily is a knave, James is a knight, and Isabella is a knave.", "solution_text_format": "(1) Matthew is a knight\n(2) Riley is a knight\n(3) Noah is a knight\n(4) Aria is a knave\n(5) Victoria is a knave\n(6) Lily is a knave\n(7) James is a knight\n(8) Isabella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that Riley is not a knave.", "Assume Riley is a knight. No contradiction is found in their claim that If Riley is a knight then Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of Riley that If Riley is a knight then Lily is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Noah is not a knight.", "Assume Noah is a knight. No contradiction is found in their claim that If Aria is a knave then Riley is a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that If Matthew is a knight then Riley is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that If Matthew is a knight then Riley is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Matthew is a knave or Isabella is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Aria is a knave and Riley is a knave.", "Isabella cannot be a knave, because this would contradict the claim of Victoria that Matthew is a knave or Isabella is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Matthew is a knave or Isabella is a knight.", "Isabella cannot be a knight, because this would contradict the false claim of Victoria that Matthew is a knave or Isabella is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Aria is a knave and Riley is a knave.", "Assume James is a knight. No contradiction is found in their claim that Noah is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('->', ('telling-truth', 1), ('lying', 5)), ('->', ('lying', 3), ('telling-truth', 1)), ('->', ('telling-truth', 0), ('lying', 1)), ('or', ('lying', 0), ('telling-truth', 7)), ('not', ('telling-truth', 2)), ('not', ('lying', 2)), ('and', ('lying', 3), ('lying', 1)))", "index": 229}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Elizabeth, Lily, Amelia, Mason, Charlotte, Henry, Emma, and Jackson. Elizabeth asserted: \"Henry is a knave\". \"Charlotte is a knave or Elizabeth is a knave,\" Lily mentioned. Amelia asserted: \"Mason is a knight or Charlotte is a knave\". Mason noted, \"If Henry is a knave then Amelia is a knight\". Charlotte told you that Emma is not a knight. Henry stated, \"Elizabeth is a knight or Emma is a knight\". Emma said, \"Lily is a knave or Amelia is a knight.\" \"Mason is not a knave\" - Jackson. So who is a knight and who is a knave?", "names": ["Elizabeth", "Lily", "Amelia", "Mason", "Charlotte", "Henry", "Emma", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true, true, true], "solution_text": "Elizabeth is a knave, Lily is a knight, Amelia is a knight, Mason is a knight, Charlotte is a knave, Henry is a knight, Emma is a knight, and Jackson is a knight.", "solution_text_format": "(1) Elizabeth is a knave\n(2) Lily is a knight\n(3) Amelia is a knight\n(4) Mason is a knight\n(5) Charlotte is a knave\n(6) Henry is a knight\n(7) Emma is a knight\n(8) Jackson is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of Elizabeth that Henry is a knave.", "Henry cannot be a knave, because this would contradict the false claim of their own that Elizabeth is a knight or Emma is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Henry is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Elizabeth is a knight or Emma is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Lily is a knave or Amelia is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Charlotte is a knave or Elizabeth is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Emma is not a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Emma is not a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Mason is a knight or Charlotte is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Henry is a knave then Amelia is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Mason is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 5), ('or', ('lying', 4), ('lying', 0)), ('or', ('telling-truth', 3), ('lying', 4)), ('->', ('lying', 5), ('telling-truth', 2)), ('not', ('telling-truth', 6)), ('or', ('telling-truth', 0), ('telling-truth', 6)), ('or', ('lying', 1), ('telling-truth', 2)), ('not', ('lying', 3)))", "index": 230}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mia, Elizabeth, Benjamin, Zoey, Luke, Chloe, Lucas, and Harper. \"If Elizabeth is a knave then Zoey is a knight\" - Mia. \"If Zoey is a knight then Harper is a knight,\" Elizabeth claimed. In a statement by Benjamin: \"If Elizabeth is a knave then Chloe is a knight\". In a statement by Zoey: \"Harper is a knight or Zoey is a knight\". Luke stated, \"Elizabeth is a knight\". \"If Mia is a knight then Zoey is a knight,\" Chloe claimed. As Lucas put it, \"Chloe is a knight or Zoey is a knave\". \"Mia is a knight,\" Harper mentioned. So who is a knight and who is a knave?", "names": ["Mia", "Elizabeth", "Benjamin", "Zoey", "Luke", "Chloe", "Lucas", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true, true, true], "solution_text": "Mia is a knight, Elizabeth is a knight, Benjamin is a knight, Zoey is a knight, Luke is a knight, Chloe is a knight, Lucas is a knight, and Harper is a knight.", "solution_text_format": "(1) Mia is a knight\n(2) Elizabeth is a knight\n(3) Benjamin is a knight\n(4) Zoey is a knight\n(5) Luke is a knight\n(6) Chloe is a knight\n(7) Lucas is a knight\n(8) Harper is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Zoey is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Zoey is a knight then Harper is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Harper is a knight or Zoey is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Mia is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Chloe is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that If Mia is a knight then Zoey is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Chloe is a knight or Zoey is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 1), ('telling-truth', 3)), ('->', ('telling-truth', 3), ('telling-truth', 7)), ('->', ('lying', 1), ('telling-truth', 5)), ('or', ('telling-truth', 7), ('telling-truth', 3)), ('telling-truth', 1), ('->', ('telling-truth', 0), ('telling-truth', 3)), ('or', ('telling-truth', 5), ('lying', 3)), ('telling-truth', 0))", "index": 231}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mason, Jack, Michael, Lily, Charlotte, Sebastian, Noah, and Joseph. As Mason put it, \"Michael is a knave if and only if Sebastian is a knave\". In Jack's words: \"Noah is a knave and Mason is a knight\". In a statement by Michael: \"Lily is a knave if and only if Lily is a knight\". Lily stated, \"Mason is not a knave\". Charlotte remarked, \"Jack is a knight or Lily is a knight\". Sebastian expressed that Noah is a knave if and only if Michael is a knight. Noah remarked, \"Charlotte is a knight if and only if Mason is a knight\". Joseph said that Mason is a knave or Charlotte is a knight. So who is a knight and who is a knave?", "names": ["Mason", "Jack", "Michael", "Lily", "Charlotte", "Sebastian", "Noah", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, true, true, true], "solution_text": "Mason is a knave, Jack is a knave, Michael is a knave, Lily is a knave, Charlotte is a knave, Sebastian is a knight, Noah is a knight, and Joseph is a knight.", "solution_text_format": "(1) Mason is a knave\n(2) Jack is a knave\n(3) Michael is a knave\n(4) Lily is a knave\n(5) Charlotte is a knave\n(6) Sebastian is a knight\n(7) Noah is a knight\n(8) Joseph is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Michael is a knave if and only if Sebastian is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Lily is a knave if and only if Lily is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Lily is a knave if and only if Lily is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Mason is not a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Mason that Michael is a knave if and only if Sebastian is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Noah is a knave if and only if Michael is a knight.", "Noah cannot be a knight, because this would contradict the false claim of Sebastian that Noah is a knave if and only if Michael is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Charlotte is a knight if and only if Mason is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of Noah that Charlotte is a knight if and only if Mason is a knight.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that Jack is a knight or Lily is a knight.", "We have exhausted all possibilities for Charlotte, Noah, and Sebastian, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the false claim of their own that Mason is not a knave.", "We have exhausted all possibilities for Lily and Michael, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Michael is a knave if and only if Sebastian is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Lily is a knave if and only if Lily is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Lily is a knave if and only if Lily is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Mason is not a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Mason is not a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Noah is a knave if and only if Michael is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Charlotte is a knight if and only if Mason is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Noah that Charlotte is a knight if and only if Mason is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Jack is a knight or Lily is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Noah is a knave and Mason is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Noah is a knave and Mason is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Mason is a knave or Charlotte is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('lying', 5)), ('and', ('lying', 6), ('telling-truth', 0)), ('<=>', ('lying', 3), ('telling-truth', 3)), ('not', ('lying', 0)), ('or', ('telling-truth', 1), ('telling-truth', 3)), ('<=>', ('lying', 6), ('telling-truth', 2)), ('<=>', ('telling-truth', 4), ('telling-truth', 0)), ('or', ('lying', 0), ('telling-truth', 4)))", "index": 232}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sofia, Emma, James, Amelia, Oliver, Aria, Scarlett, and Ella. Sofia said, \"If Ella is a knight then Emma is a knight.\" Emma said, \"Sofia is a knave if and only if James is a knight.\" James asserted: \"Aria is not a knight\". As Amelia put it, \"Scarlett is a knight if and only if Oliver is a knight\". Oliver told you that Scarlett is a knave if and only if Emma is a knave. Aria told you that Sofia is a knight. In a statement by Scarlett: \"Aria is a knight and James is a knight\". \"If Emma is a knave then Scarlett is a knight,\" Ella claimed. So who is a knight and who is a knave?", "names": ["Sofia", "Emma", "James", "Amelia", "Oliver", "Aria", "Scarlett", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true, false, true], "solution_text": "Sofia is a knight, Emma is a knight, James is a knave, Amelia is a knight, Oliver is a knave, Aria is a knight, Scarlett is a knave, and Ella is a knight.", "solution_text_format": "(1) Sofia is a knight\n(2) Emma is a knight\n(3) James is a knave\n(4) Amelia is a knight\n(5) Oliver is a knave\n(6) Aria is a knight\n(7) Scarlett is a knave\n(8) Ella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that If Ella is a knight then Emma is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that If Emma is a knave then Scarlett is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Sofia is a knave if and only if James is a knight.", "James cannot be a knight, because this would contradict the claim of Emma that Sofia is a knave if and only if James is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Aria is not a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Sofia is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Aria is a knight and James is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Aria is a knight and James is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Scarlett is a knight if and only if Oliver is a knight.", "Oliver cannot be a knight, because this would contradict the claim of Amelia that Scarlett is a knight if and only if Oliver is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Scarlett is a knave if and only if Emma is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 7), ('telling-truth', 1)), ('<=>', ('lying', 0), ('telling-truth', 2)), ('not', ('telling-truth', 5)), ('<=>', ('telling-truth', 6), ('telling-truth', 4)), ('<=>', ('lying', 6), ('lying', 1)), ('telling-truth', 0), ('and', ('telling-truth', 5), ('telling-truth', 2)), ('->', ('lying', 1), ('telling-truth', 6)))", "index": 233}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Abigail, Luke, Avery, Emily, Lucas, Alexander, Oliver, and Sebastian. In a statement by Abigail: \"If Avery is a knight then Lucas is a knave\". Luke expressed that Sebastian is a knave or Abigail is a knight. \"If Alexander is a knave then Luke is a knave\" - Avery. In a statement by Emily: \"Lucas is a knave and Luke is a knight\". Lucas said, \"Avery is a knight and Alexander is a knave.\" Alexander told you that Luke is a knight or Sebastian is a knight. \"Lucas is a knight and Emily is a knight\" - Oliver. In Sebastian's words: \"Alexander is a knight and Luke is a knave\". So who is a knight and who is a knave?", "names": ["Abigail", "Luke", "Avery", "Emily", "Lucas", "Alexander", "Oliver", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true, false, false], "solution_text": "Abigail is a knight, Luke is a knight, Avery is a knight, Emily is a knight, Lucas is a knave, Alexander is a knight, Oliver is a knave, and Sebastian is a knave.", "solution_text_format": "(1) Abigail is a knight\n(2) Luke is a knight\n(3) Avery is a knight\n(4) Emily is a knight\n(5) Lucas is a knave\n(6) Alexander is a knight\n(7) Oliver is a knave\n(8) Sebastian is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that If Avery is a knight then Lucas is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that If Alexander is a knave then Luke is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Luke is a knight or Sebastian is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Sebastian is a knave or Abigail is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Alexander is a knight and Luke is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Alexander is a knight and Luke is a knave.", "Lucas cannot be a knight, because this would contradict the claim of Abigail that If Avery is a knight then Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Avery is a knight and Alexander is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Lucas is a knave and Luke is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Lucas is a knight and Emily is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Lucas is a knight and Emily is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('lying', 4)), ('or', ('lying', 7), ('telling-truth', 0)), ('->', ('lying', 5), ('lying', 1)), ('and', ('lying', 4), ('telling-truth', 1)), ('and', ('telling-truth', 2), ('lying', 5)), ('or', ('telling-truth', 1), ('telling-truth', 7)), ('and', ('telling-truth', 4), ('telling-truth', 3)), ('and', ('telling-truth', 5), ('lying', 1)))", "index": 234}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ava, Noah, William, Sophia, Ethan, Luke, Penelope, and Grace. \"Noah is not a knave,\" Ava declared. Noah said, \"Penelope is not a knave.\" In a statement by William: \"Sophia is a knight if and only if Penelope is a knave\". Sophia told you that Luke is not a knave. \"Sophia is a knave if and only if Sophia is a knight,\" Ethan claimed. In Luke's words: \"Ava is a knight or Penelope is a knight\". Penelope noted, \"William is a knight and Sophia is a knight\". Grace told you that Penelope is a knight. So who is a knight and who is a knave?", "names": ["Ava", "Noah", "William", "Sophia", "Ethan", "Luke", "Penelope", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, false, false, false], "solution_text": "Ava is a knave, Noah is a knave, William is a knave, Sophia is a knave, Ethan is a knave, Luke is a knave, Penelope is a knave, and Grace is a knave.", "solution_text_format": "(1) Ava is a knave\n(2) Noah is a knave\n(3) William is a knave\n(4) Sophia is a knave\n(5) Ethan is a knave\n(6) Luke is a knave\n(7) Penelope is a knave\n(8) Grace is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Noah is not a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Penelope is not a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that William is a knight and Sophia is a knight.", "Assume William is a knight. No contradiction is found in their claim that Sophia is a knight if and only if Penelope is a knave.", "Sophia cannot be a knight, because this would contradict the claim of William that Sophia is a knight if and only if Penelope is a knave.", "Sophia cannot be a knave, because this would contradict the claim of Penelope that William is a knight and Sophia is a knight.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the claim of Penelope that William is a knight and Sophia is a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the claim of Noah that Penelope is not a knave.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the claim of Ava that Noah is not a knave.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Noah is not a knave.", "Noah cannot be a knight, because this would contradict the false claim of Ava that Noah is not a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Penelope is not a knave.", "Penelope cannot be a knight, because this would contradict the false claim of Noah that Penelope is not a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that William is a knight and Sophia is a knight.", "Assume William is a knight. No contradiction is found in their claim that Sophia is a knight if and only if Penelope is a knave.", "Sophia cannot be a knight, because this would contradict the false claim of Penelope that William is a knight and Sophia is a knight.", "Sophia cannot be a knave, because this would contradict the claim of William that Sophia is a knight if and only if Penelope is a knave.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Sophia is a knight if and only if Penelope is a knave.", "Sophia cannot be a knight, because this would contradict the false claim of William that Sophia is a knight if and only if Penelope is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Luke is not a knave.", "Luke cannot be a knight, because this would contradict the false claim of Sophia that Luke is not a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Ava is a knight or Penelope is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Sophia is a knave if and only if Sophia is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Sophia is a knave if and only if Sophia is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Penelope is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Penelope is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('not', ('lying', 6)), ('<=>', ('telling-truth', 3), ('lying', 6)), ('not', ('lying', 5)), ('<=>', ('lying', 3), ('telling-truth', 3)), ('or', ('telling-truth', 0), ('telling-truth', 6)), ('and', ('telling-truth', 2), ('telling-truth', 3)), ('telling-truth', 6))", "index": 235}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Matthew, Ava, Zoey, Olivia, Charlotte, Liam, Ella, and James. \"Liam is a knave,\" Matthew claimed. Ava expressed that Olivia is a knave if and only if Liam is a knave. Zoey said that If Matthew is a knight then Liam is a knave. In a statement by Olivia: \"James is a knight if and only if James is a knave\". Charlotte stated, \"Ava is a knight and Ella is a knight\". Liam expressed that Charlotte is a knave and Olivia is a knight. As Ella put it, \"James is a knight and James is a knave\". James stated, \"Ella is not a knight\". So who is a knight and who is a knave?", "names": ["Matthew", "Ava", "Zoey", "Olivia", "Charlotte", "Liam", "Ella", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false, false, true], "solution_text": "Matthew is a knight, Ava is a knight, Zoey is a knight, Olivia is a knave, Charlotte is a knave, Liam is a knave, Ella is a knave, and James is a knight.", "solution_text_format": "(1) Matthew is a knight\n(2) Ava is a knight\n(3) Zoey is a knight\n(4) Olivia is a knave\n(5) Charlotte is a knave\n(6) Liam is a knave\n(7) Ella is a knave\n(8) James is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of Matthew that Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Charlotte is a knave and Olivia is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Ava is a knight and Ella is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Olivia is a knave if and only if Liam is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Ava that Olivia is a knave if and only if Liam is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that James is a knight if and only if James is a knave.", "Assume James is a knight. No contradiction is found in their claim that Ella is not a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that James is a knight and James is a knave.", "Ella cannot be a knave, because this would contradict the claim of Charlotte that Ava is a knight and Ella is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Ella is not a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that James is a knight and James is a knave.", "Ella cannot be a knave, because this would contradict the claim of Charlotte that Ava is a knight and Ella is a knight.", "We have exhausted all possibilities for Ella, James, and Olivia, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the claim of Charlotte that Ava is a knight and Ella is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Ava is a knight and Ella is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Olivia is a knave if and only if Liam is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Ava that Olivia is a knave if and only if Liam is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that James is a knight if and only if James is a knave.", "Assume James is a knight. No contradiction is found in their claim that Ella is not a knight.", "Ella cannot be a knight, because this would contradict the false claim of Charlotte that Ava is a knight and Ella is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that James is a knight and James is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that If Matthew is a knight then Liam is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 5), ('<=>', ('lying', 3), ('lying', 5)), ('->', ('telling-truth', 0), ('lying', 5)), ('<=>', ('telling-truth', 7), ('lying', 7)), ('and', ('telling-truth', 1), ('telling-truth', 6)), ('and', ('lying', 4), ('telling-truth', 3)), ('and', ('telling-truth', 7), ('lying', 7)), ('not', ('telling-truth', 6)))", "index": 236}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aria, David, Jack, Olivia, Lily, Ella, Sophia, and Penelope. \"Sophia is a knave if and only if Lily is a knight,\" Aria mentioned. David noted, \"If Lily is a knight then Lily is a knave\". \"Penelope is a knight or Penelope is a knave,\" Jack claimed. According to Olivia, \"Lily is a knight\". Lily stated, \"Aria is a knight\". As Ella put it, \"Aria is not a knave\". Sophia expressed that David is a knight or Jack is a knave. Penelope told you that Ella is a knave and Aria is a knight. So who is a knight and who is a knave?", "names": ["Aria", "David", "Jack", "Olivia", "Lily", "Ella", "Sophia", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true, false, false], "solution_text": "Aria is a knight, David is a knave, Jack is a knight, Olivia is a knight, Lily is a knight, Ella is a knight, Sophia is a knave, and Penelope is a knave.", "solution_text_format": "(1) Aria is a knight\n(2) David is a knave\n(3) Jack is a knight\n(4) Olivia is a knight\n(5) Lily is a knight\n(6) Ella is a knight\n(7) Sophia is a knave\n(8) Penelope is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that Sophia is a knave if and only if Lily is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that David is a knight or Jack is a knave.", "Assume David is a knight. No contradiction is found in their claim that If Lily is a knight then Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of Aria that Sophia is a knave if and only if Lily is a knight.", "Lily cannot be a knave, because this would contradict the false claim of their own that Aria is a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that If Lily is a knight then Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of Aria that Sophia is a knave if and only if Lily is a knight.", "Lily cannot be a knave, because this would contradict the false claim of David that If Lily is a knight then Lily is a knave.", "We have exhausted all possibilities for Lily and David, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that David is a knight or Jack is a knave.", "David cannot be a knight, because this would contradict the false claim of Sophia that David is a knight or Jack is a knave.", "Assume David is a knave. No contradiction is found in their false claim that If Lily is a knight then Lily is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Aria is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Penelope is a knight or Penelope is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Ella is a knave and Aria is a knight.", "Ella cannot be a knight, because this would contradict the claim of Penelope that Ella is a knave and Aria is a knight.", "Ella cannot be a knave, because this would contradict the false claim of their own that Aria is not a knave.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Ella is a knave and Aria is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Aria is not a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Lily is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 6), ('telling-truth', 4)), ('->', ('telling-truth', 4), ('lying', 4)), ('or', ('telling-truth', 7), ('lying', 7)), ('telling-truth', 4), ('telling-truth', 0), ('not', ('lying', 0)), ('or', ('telling-truth', 1), ('lying', 2)), ('and', ('lying', 5), ('telling-truth', 0)))", "index": 237}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sophia, Benjamin, Matthew, Jack, Emma, Aria, Logan, and Evelyn. In a statement by Sophia: \"If Jack is a knight then Logan is a knight\". Benjamin expressed that Aria is a knave or Emma is a knight. \"Emma is a knave if and only if Sophia is a knight\" - Matthew. Jack told you that Emma is a knight. Emma noted, \"Logan is a knave or Aria is a knight\". In Aria's words: \"Benjamin is a knave\". \"Matthew is not a knave,\" Logan mentioned. \"Matthew is a knave or Matthew is a knight,\" Evelyn mentioned. So who is a knight and who is a knave?", "names": ["Sophia", "Benjamin", "Matthew", "Jack", "Emma", "Aria", "Logan", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false, true, true], "solution_text": "Sophia is a knight, Benjamin is a knight, Matthew is a knight, Jack is a knave, Emma is a knave, Aria is a knave, Logan is a knight, and Evelyn is a knight.", "solution_text_format": "(1) Sophia is a knight\n(2) Benjamin is a knight\n(3) Matthew is a knight\n(4) Jack is a knave\n(5) Emma is a knave\n(6) Aria is a knave\n(7) Logan is a knight\n(8) Evelyn is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that If Jack is a knight then Logan is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Emma is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Logan is a knave or Aria is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Matthew is not a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Emma is a knave if and only if Sophia is a knight.", "Matthew cannot be a knave, because this would contradict the claim of Logan that Matthew is not a knave.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the claim of Sophia that If Jack is a knight then Logan is a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Emma.", "Emma cannot be a knave, because this would contradict the claim of Jack that Emma is a knight.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Emma is a knight.", "Emma cannot be a knight, because this would contradict the false claim of Jack that Emma is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Logan is a knave or Aria is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Matthew is not a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Emma is a knave if and only if Sophia is a knight.", "Aria cannot be a knight, because this would contradict the false claim of Emma that Logan is a knave or Aria is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Benjamin is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Aria is a knave or Emma is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Matthew is a knave or Matthew is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('telling-truth', 6)), ('or', ('lying', 5), ('telling-truth', 4)), ('<=>', ('lying', 4), ('telling-truth', 0)), ('telling-truth', 4), ('or', ('lying', 6), ('telling-truth', 5)), ('lying', 1), ('not', ('lying', 2)), ('or', ('lying', 2), ('telling-truth', 2)))", "index": 238}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Benjamin, Alexander, Chloe, Emily, Riley, Ethan, Matthew, and Daniel. \"If Ethan is a knight then Matthew is a knave,\" Benjamin mentioned. In Alexander's words: \"Emily is a knave if and only if Daniel is a knight\". Chloe asserted: \"Benjamin is a knight\". Emily expressed that If Riley is a knave then Alexander is a knave. Riley said, \"Alexander is a knave or Ethan is a knave.\" Ethan said that Alexander is not a knight. Matthew was heard saying, \"Daniel is a knight if and only if Matthew is a knight\". Daniel expressed that Matthew is a knave. So who is a knight and who is a knave?", "names": ["Benjamin", "Alexander", "Chloe", "Emily", "Riley", "Ethan", "Matthew", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true, false, true], "solution_text": "Benjamin is a knight, Alexander is a knave, Chloe is a knight, Emily is a knight, Riley is a knight, Ethan is a knight, Matthew is a knave, and Daniel is a knight.", "solution_text_format": "(1) Benjamin is a knight\n(2) Alexander is a knave\n(3) Chloe is a knight\n(4) Emily is a knight\n(5) Riley is a knight\n(6) Ethan is a knight\n(7) Matthew is a knave\n(8) Daniel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that If Ethan is a knight then Matthew is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of Ethan that Alexander is not a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Emily is a knave if and only if Daniel is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that If Riley is a knave then Alexander is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Alexander is a knave or Ethan is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Matthew is a knave.", "Matthew cannot be a knight, because this would contradict the claim of Benjamin that If Ethan is a knight then Matthew is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Daniel is a knight if and only if Matthew is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Benjamin is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 5), ('lying', 6)), ('<=>', ('lying', 3), ('telling-truth', 7)), ('telling-truth', 0), ('->', ('lying', 4), ('lying', 1)), ('or', ('lying', 1), ('lying', 5)), ('not', ('telling-truth', 1)), ('<=>', ('telling-truth', 7), ('telling-truth', 6)), ('lying', 6))", "index": 239}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: William, Aria, Amelia, Olivia, Charlotte, Victoria, Ava, and Riley. William stated, \"Aria is a knave or Olivia is a knave\". Aria said that Charlotte is a knight. \"Olivia is a knight\" - Amelia. Olivia said, \"William is a knight and Charlotte is a knave.\" Charlotte said that Amelia is a knight if and only if Olivia is a knave. \"Olivia is a knave and Victoria is a knight,\" Victoria declared. \"Olivia is a knave and Aria is a knave,\" Ava declared. Riley commented, \"William is a knight and Amelia is a knave\". So who is a knight and who is a knave?", "names": ["William", "Aria", "Amelia", "Olivia", "Charlotte", "Victoria", "Ava", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, false, false, false], "solution_text": "William is a knight, Aria is a knave, Amelia is a knight, Olivia is a knight, Charlotte is a knave, Victoria is a knave, Ava is a knave, and Riley is a knave.", "solution_text_format": "(1) William is a knight\n(2) Aria is a knave\n(3) Amelia is a knight\n(4) Olivia is a knight\n(5) Charlotte is a knave\n(6) Victoria is a knave\n(7) Ava is a knave\n(8) Riley is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Aria is a knave or Olivia is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Amelia is a knight if and only if Olivia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Olivia is a knight.", "Olivia cannot be a knight, because this would contradict the claim of William that Aria is a knave or Olivia is a knave.", "Olivia cannot be a knave, because this would contradict the claim of Amelia that Olivia is a knight.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Olivia is a knight.", "Olivia cannot be a knight, because this would contradict the claim of William that Aria is a knave or Olivia is a knave.", "Olivia cannot be a knave, because this would contradict the claim of Charlotte that Amelia is a knight if and only if Olivia is a knave.", "We have exhausted all possibilities for Olivia and Amelia, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the claim of Aria that Charlotte is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of Aria that Charlotte is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Amelia is a knight if and only if Olivia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Olivia is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that William is a knight and Charlotte is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that Olivia is a knave and Victoria is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Olivia is a knave and Victoria is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Olivia is a knave and Aria is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Olivia is a knave and Aria is a knave.", "Riley cannot be a knight, because this would contradict the claim of their own that William is a knight and Amelia is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that William is a knight and Amelia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('lying', 3)), ('telling-truth', 4), ('telling-truth', 3), ('and', ('telling-truth', 0), ('lying', 4)), ('<=>', ('telling-truth', 2), ('lying', 3)), ('and', ('lying', 3), ('telling-truth', 5)), ('and', ('lying', 3), ('lying', 1)), ('and', ('telling-truth', 0), ('lying', 2)))", "index": 240}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: William, Aria, Daniel, Harper, Grace, Lucas, Emily, and James. \"If Aria is a knight then Lucas is a knave,\" William declared. \"Lucas is a knave or Grace is a knight,\" Aria declared. Daniel stated, \"Harper is a knight if and only if Lucas is a knave\". \"Grace is a knave or Grace is a knight,\" Harper mentioned. Grace said, \"Aria is a knight or Lucas is a knight.\" Lucas commented, \"If Daniel is a knight then Grace is a knight\". Emily told you that William is a knave if and only if Grace is a knave. James asserted: \"Aria is a knight and Daniel is a knave\". So who is a knight and who is a knave?", "names": ["William", "Aria", "Daniel", "Harper", "Grace", "Lucas", "Emily", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true, false, true], "solution_text": "William is a knave, Aria is a knight, Daniel is a knave, Harper is a knight, Grace is a knight, Lucas is a knight, Emily is a knave, and James is a knight.", "solution_text_format": "(1) William is a knave\n(2) Aria is a knight\n(3) Daniel is a knave\n(4) Harper is a knight\n(5) Grace is a knight\n(6) Lucas is a knight\n(7) Emily is a knave\n(8) James is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that If Aria is a knight then Lucas is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Lucas is a knave or Grace is a knight.", "Lucas cannot be a knight, because this would contradict the claim of William that If Aria is a knight then Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that If Daniel is a knight then Grace is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Harper is a knight if and only if Lucas is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Grace is a knave or Grace is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Lucas that If Daniel is a knight then Grace is a knight.", "Grace cannot be a knave, because this would contradict the false claim of their own that Aria is a knight or Lucas is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the claim of Daniel that Harper is a knight if and only if Lucas is a knave.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the false claim of Lucas that If Daniel is a knight then Grace is a knight.", "We have exhausted all possibilities for Daniel and Lucas, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Lucas is a knave or Grace is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that If Daniel is a knight then Grace is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Harper is a knight if and only if Lucas is a knave.", "Harper cannot be a knight, because this would contradict the claim of Daniel that Harper is a knight if and only if Lucas is a knave.", "Harper cannot be a knave, because this would contradict the false claim of their own that Grace is a knave or Grace is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Harper is a knight if and only if Lucas is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Grace is a knave or Grace is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Aria that Lucas is a knave or Grace is a knight.", "Grace cannot be a knave, because this would contradict the false claim of their own that Aria is a knight or Lucas is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the false claim of Daniel that Harper is a knight if and only if Lucas is a knave.", "We have exhausted all possibilities for Harper and Daniel, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the false claim of Aria that Lucas is a knave or Grace is a knight.", "We have exhausted all possibilities for Lucas and Aria, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that If Aria is a knight then Lucas is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Lucas is a knave or Grace is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that If Daniel is a knight then Grace is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Harper is a knight if and only if Lucas is a knave.", "Harper cannot be a knight, because this would contradict the claim of Daniel that Harper is a knight if and only if Lucas is a knave.", "Harper cannot be a knave, because this would contradict the false claim of their own that Grace is a knave or Grace is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Harper is a knight if and only if Lucas is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Grace is a knave or Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Aria is a knight or Lucas is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that William is a knave if and only if Grace is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that William is a knave if and only if Grace is a knave.", "Assume James is a knight. No contradiction is found in their claim that Aria is a knight and Daniel is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 1), ('lying', 5)), ('or', ('lying', 5), ('telling-truth', 4)), ('<=>', ('telling-truth', 3), ('lying', 5)), ('or', ('lying', 4), ('telling-truth', 4)), ('or', ('telling-truth', 1), ('telling-truth', 5)), ('->', ('telling-truth', 2), ('telling-truth', 4)), ('<=>', ('lying', 0), ('lying', 4)), ('and', ('telling-truth', 1), ('lying', 2)))", "index": 241}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Zoey, Jacob, Jack, Riley, Michael, Luke, Liam, and Penelope. Zoey said, \"Penelope is a knave or Riley is a knight.\" According to Jacob, \"Penelope is a knave and Liam is a knight\". Jack told you that Jacob is not a knave. Riley expressed that Michael is a knight. Michael stated, \"Penelope is a knave and Liam is a knight\". According to Luke, \"Riley is a knight if and only if Liam is a knight\". In a statement by Liam: \"Zoey is not a knight\". According to Penelope, \"Jacob is a knight and Penelope is a knight\". So who is a knight and who is a knave?", "names": ["Zoey", "Jacob", "Jack", "Riley", "Michael", "Luke", "Liam", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, true, false, false], "solution_text": "Zoey is a knight, Jacob is a knave, Jack is a knave, Riley is a knave, Michael is a knave, Luke is a knight, Liam is a knave, and Penelope is a knave.", "solution_text_format": "(1) Zoey is a knight\n(2) Jacob is a knave\n(3) Jack is a knave\n(4) Riley is a knave\n(5) Michael is a knave\n(6) Luke is a knight\n(7) Liam is a knave\n(8) Penelope is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Zoey is a knight. No contradiction is found in their claim that Penelope is a knave or Riley is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Jacob is a knight and Penelope is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Penelope is a knave and Liam is a knight.", "Jacob cannot be a knave, because this would contradict the claim of Penelope that Jacob is a knight and Penelope is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Jacob is a knight and Penelope is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Penelope is a knave and Liam is a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that Zoey is not a knight.", "Liam cannot be a knave, because this would contradict the claim of Jacob that Penelope is a knave and Liam is a knight.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Penelope is a knave and Liam is a knight.", "Liam cannot be a knight, because this would contradict the false claim of Jacob that Penelope is a knave and Liam is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Zoey is not a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Michael is a knight.", "Michael cannot be a knight, because this would contradict the claim of their own that Penelope is a knave and Liam is a knight.", "Michael cannot be a knave, because this would contradict the claim of Riley that Michael is a knight.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Michael is a knight.", "Michael cannot be a knight, because this would contradict the false claim of Riley that Michael is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Penelope is a knave and Liam is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Jacob is not a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Jacob is not a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Riley is a knight if and only if Liam is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 7), ('telling-truth', 3)), ('and', ('lying', 7), ('telling-truth', 6)), ('not', ('lying', 1)), ('telling-truth', 4), ('and', ('lying', 7), ('telling-truth', 6)), ('<=>', ('telling-truth', 3), ('telling-truth', 6)), ('not', ('telling-truth', 0)), ('and', ('telling-truth', 1), ('telling-truth', 7)))", "index": 242}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Henry, Jacob, Mia, Logan, Benjamin, Emily, Aurora, and Sophia. \"Mia is a knight or Sophia is a knave,\" Henry declared. \"Mia is a knight or Aurora is a knave,\" Jacob mentioned. Mia remarked, \"If Henry is a knave then Logan is a knight\". In a statement by Logan: \"If Henry is a knave then Henry is a knight\". Benjamin noted, \"If Benjamin is a knight then Sophia is a knave\". \"Aurora is a knave,\" Emily declared. \"Benjamin is a knave and Henry is a knave,\" Aurora mentioned. Sophia remarked, \"Emily is a knave if and only if Benjamin is a knight\". So who is a knight and who is a knave?", "names": ["Henry", "Jacob", "Mia", "Logan", "Benjamin", "Emily", "Aurora", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true, false, false], "solution_text": "Henry is a knight, Jacob is a knight, Mia is a knight, Logan is a knight, Benjamin is a knight, Emily is a knight, Aurora is a knave, and Sophia is a knave.", "solution_text_format": "(1) Henry is a knight\n(2) Jacob is a knight\n(3) Mia is a knight\n(4) Logan is a knight\n(5) Benjamin is a knight\n(6) Emily is a knight\n(7) Aurora is a knave\n(8) Sophia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that Mia is a knight or Sophia is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that If Henry is a knave then Logan is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that If Henry is a knave then Henry is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Emily is a knave if and only if Benjamin is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Aurora is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Emily that Aurora is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Benjamin is a knave and Henry is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that If Benjamin is a knight then Sophia is a knave.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that If Benjamin is a knight then Sophia is a knave.", "We have exhausted all possibilities for Benjamin and Aurora, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Aurora is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave and Henry is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of Emily that Aurora is a knave.", "We have exhausted all possibilities for Aurora and Emily, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Emily is a knave if and only if Benjamin is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Aurora is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Emily that Aurora is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Benjamin is a knave and Henry is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Benjamin is a knight then Sophia is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Mia is a knight or Aurora is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('lying', 7)), ('or', ('telling-truth', 2), ('lying', 6)), ('->', ('lying', 0), ('telling-truth', 3)), ('->', ('lying', 0), ('telling-truth', 0)), ('->', ('telling-truth', 4), ('lying', 7)), ('lying', 6), ('and', ('lying', 4), ('lying', 0)), ('<=>', ('lying', 5), ('telling-truth', 4)))", "index": 243}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jacob, Elizabeth, Joseph, Harper, Sebastian, Alexander, Penelope, and Lucas. \"Sebastian is a knight or Alexander is a knight,\" Jacob declared. According to Elizabeth, \"Harper is a knight if and only if Penelope is a knave\". Joseph said that Jacob is a knave and Jacob is a knight. \"Joseph is a knight,\" Harper claimed. According to Sebastian, \"Elizabeth is a knave if and only if Sebastian is a knight\". In Alexander's words: \"Harper is a knight or Jacob is a knave\". In a statement by Penelope: \"Sebastian is not a knight\". Lucas remarked, \"Alexander is not a knave\". So who is a knight and who is a knave?", "names": ["Jacob", "Elizabeth", "Joseph", "Harper", "Sebastian", "Alexander", "Penelope", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, false, false, false], "solution_text": "Jacob is a knight, Elizabeth is a knave, Joseph is a knave, Harper is a knave, Sebastian is a knight, Alexander is a knave, Penelope is a knave, and Lucas is a knave.", "solution_text_format": "(1) Jacob is a knight\n(2) Elizabeth is a knave\n(3) Joseph is a knave\n(4) Harper is a knave\n(5) Sebastian is a knight\n(6) Alexander is a knave\n(7) Penelope is a knave\n(8) Lucas is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that Sebastian is a knight or Alexander is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Elizabeth is a knave if and only if Sebastian is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Sebastian that Elizabeth is a knave if and only if Sebastian is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Harper is a knight if and only if Penelope is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Jacob is a knave and Jacob is a knight.", "Joseph cannot be a knave, because this would contradict the claim of Harper that Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Jacob is a knave and Jacob is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Jacob is a knave and Jacob is a knight.", "Penelope cannot be a knight, because this would contradict the false claim of Elizabeth that Harper is a knight if and only if Penelope is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Sebastian is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that Harper is a knight or Jacob is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Harper is a knight or Jacob is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Alexander is not a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Alexander is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('telling-truth', 5)), ('<=>', ('telling-truth', 3), ('lying', 6)), ('and', ('lying', 0), ('telling-truth', 0)), ('telling-truth', 2), ('<=>', ('lying', 1), ('telling-truth', 4)), ('or', ('telling-truth', 3), ('lying', 0)), ('not', ('telling-truth', 4)), ('not', ('lying', 5)))", "index": 244}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sofia, William, Benjamin, Jack, Jacob, Charlotte, Samuel, and Isabella. Sofia asserted: \"William is a knave if and only if Jacob is a knight\". William remarked, \"Samuel is a knave if and only if Jack is a knight\". \"William is a knave,\" Benjamin mentioned. In Jack's words: \"Charlotte is not a knave\". Jacob said, \"Benjamin is a knight or Charlotte is a knight.\" Charlotte was heard saying, \"If William is a knave then Jack is a knight\". \"Sofia is a knight and Charlotte is a knave\" - Samuel. \"Benjamin is a knight if and only if Benjamin is a knave,\" Isabella mentioned. So who is a knight and who is a knave?", "names": ["Sofia", "William", "Benjamin", "Jack", "Jacob", "Charlotte", "Samuel", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true, false, false], "solution_text": "Sofia is a knave, William is a knight, Benjamin is a knave, Jack is a knight, Jacob is a knight, Charlotte is a knight, Samuel is a knave, and Isabella is a knave.", "solution_text_format": "(1) Sofia is a knave\n(2) William is a knight\n(3) Benjamin is a knave\n(4) Jack is a knight\n(5) Jacob is a knight\n(6) Charlotte is a knight\n(7) Samuel is a knave\n(8) Isabella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that William is a knave if and only if Jacob is a knight.", "Assume William is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Jack is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Sofia is a knight and Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Samuel that Sofia is a knight and Charlotte is a knave.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that If William is a knave then Jack is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Sofia is a knight and Charlotte is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that If William is a knave then Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Charlotte is not a knave.", "Jacob cannot be a knight, because this would contradict the claim of Sofia that William is a knave if and only if Jacob is a knight.", "Jacob cannot be a knave, because this would contradict the false claim of their own that Benjamin is a knight or Charlotte is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the claim of William that Samuel is a knave if and only if Jack is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that If William is a knave then Jack is a knight.", "We have exhausted all possibilities for Charlotte and Samuel, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Samuel is a knave if and only if Jack is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Sofia is a knight and Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Samuel that Sofia is a knight and Charlotte is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that If William is a knave then Jack is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Charlotte is not a knave.", "Jack cannot be a knave, because this would contradict the false claim of William that Samuel is a knave if and only if Jack is a knight.", "We have exhausted all possibilities for Jack and Charlotte, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Sofia is a knight and Charlotte is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that If William is a knave then Jack is a knight.", "Jack cannot be a knight, because this would contradict the false claim of William that Samuel is a knave if and only if Jack is a knight.", "Jack cannot be a knave, because this would contradict the false claim of their own that Charlotte is not a knave.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the false claim of Samuel that Sofia is a knight and Charlotte is a knave.", "We have exhausted all possibilities for Charlotte, Samuel, and William, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that William is a knave if and only if Jacob is a knight.", "Assume William is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Jack is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Sofia is a knight and Charlotte is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Sofia is a knight and Charlotte is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that If William is a knave then Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Charlotte is not a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Benjamin is a knight or Charlotte is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that William is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that William is a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight if and only if Benjamin is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Benjamin is a knight if and only if Benjamin is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('telling-truth', 4)), ('<=>', ('lying', 6), ('telling-truth', 3)), ('lying', 1), ('not', ('lying', 5)), ('or', ('telling-truth', 2), ('telling-truth', 5)), ('->', ('lying', 1), ('telling-truth', 3)), ('and', ('telling-truth', 0), ('lying', 5)), ('<=>', ('telling-truth', 2), ('lying', 2)))", "index": 245}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Benjamin, Riley, William, Jacob, Matthew, David, Luke, and Harper. Benjamin told you that Jacob is not a knave. Riley asserted: \"Riley is a knight or Jacob is a knight\". William was heard saying, \"Benjamin is a knight if and only if David is a knight\". In Jacob's words: \"If Harper is a knave then Benjamin is a knight\". As Matthew put it, \"Luke is a knight if and only if Riley is a knave\". \"Matthew is a knave and Benjamin is a knave,\" David mentioned. Luke asserted: \"Jacob is a knave\". \"Matthew is a knight or Matthew is a knave\" - Harper. So who is a knight and who is a knave?", "names": ["Benjamin", "Riley", "William", "Jacob", "Matthew", "David", "Luke", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false, false, true], "solution_text": "Benjamin is a knight, Riley is a knight, William is a knave, Jacob is a knight, Matthew is a knight, David is a knave, Luke is a knave, and Harper is a knight.", "solution_text_format": "(1) Benjamin is a knight\n(2) Riley is a knight\n(3) William is a knave\n(4) Jacob is a knight\n(5) Matthew is a knight\n(6) David is a knave\n(7) Luke is a knave\n(8) Harper is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Jacob is not a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that If Harper is a knave then Benjamin is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Matthew is a knight or Matthew is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Luke is a knight if and only if Riley is a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that Jacob is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Jacob is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Riley is a knight or Jacob is a knight.", "Assume William is a knight. No contradiction is found in their claim that Benjamin is a knight if and only if David is a knight.", "David cannot be a knight, because this would contradict the claim of their own that Matthew is a knave and Benjamin is a knave.", "David cannot be a knave, because this would contradict the claim of William that Benjamin is a knight if and only if David is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Benjamin is a knight if and only if David is a knight.", "David cannot be a knight, because this would contradict the false claim of William that Benjamin is a knight if and only if David is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Matthew is a knave and Benjamin is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 3)), ('or', ('telling-truth', 1), ('telling-truth', 3)), ('<=>', ('telling-truth', 0), ('telling-truth', 5)), ('->', ('lying', 7), ('telling-truth', 0)), ('<=>', ('telling-truth', 6), ('lying', 1)), ('and', ('lying', 4), ('lying', 0)), ('lying', 3), ('or', ('telling-truth', 4), ('lying', 4)))", "index": 246}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ethan, Victoria, Jack, Owen, Zoey, Scarlett, Jacob, and Logan. As Ethan put it, \"Zoey is a knight and Scarlett is a knight\". Victoria expressed that Zoey is a knight and Logan is a knight. Jack expressed that Zoey is a knight. \"Scarlett is a knight or Jacob is a knight,\" Owen claimed. Zoey expressed that If Jack is a knight then Logan is a knave. \"Ethan is a knave if and only if Jacob is a knight,\" Scarlett mentioned. Jacob said, \"Scarlett is not a knight.\" \"Ethan is a knave,\" Logan declared. So who is a knight and who is a knave?", "names": ["Ethan", "Victoria", "Jack", "Owen", "Zoey", "Scarlett", "Jacob", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true, false, false], "solution_text": "Ethan is a knight, Victoria is a knave, Jack is a knight, Owen is a knight, Zoey is a knight, Scarlett is a knight, Jacob is a knave, and Logan is a knave.", "solution_text_format": "(1) Ethan is a knight\n(2) Victoria is a knave\n(3) Jack is a knight\n(4) Owen is a knight\n(5) Zoey is a knight\n(6) Scarlett is a knight\n(7) Jacob is a knave\n(8) Logan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Zoey is a knight and Scarlett is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that If Jack is a knight then Logan is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Zoey is a knight.", "Logan cannot be a knight, because this would contradict the claim of Zoey that If Jack is a knight then Logan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Ethan is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Ethan is a knave if and only if Jacob is a knight.", "Jacob cannot be a knight, because this would contradict the claim of Scarlett that Ethan is a knave if and only if Jacob is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Scarlett is not a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Zoey is a knight and Logan is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Zoey is a knight and Logan is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Scarlett is a knight or Jacob is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 4), ('telling-truth', 5)), ('and', ('telling-truth', 4), ('telling-truth', 7)), ('telling-truth', 4), ('or', ('telling-truth', 5), ('telling-truth', 6)), ('->', ('telling-truth', 2), ('lying', 7)), ('<=>', ('lying', 0), ('telling-truth', 6)), ('not', ('telling-truth', 5)), ('lying', 0))", "index": 247}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ethan, Chloe, Emma, Luke, Aria, Penelope, Joseph, and Lucas. Ethan stated, \"Chloe is a knave\". Chloe was heard saying, \"Penelope is not a knave\". According to Emma, \"Lucas is a knight or Penelope is a knave\". \"Aria is a knight and Penelope is a knight,\" Luke mentioned. In Aria's words: \"Chloe is a knight or Penelope is a knave\". \"Lucas is a knave,\" Penelope claimed. Joseph expressed that Emma is a knave if and only if Joseph is a knight. Lucas asserted: \"Joseph is a knight\". So who is a knight and who is a knave?", "names": ["Ethan", "Chloe", "Emma", "Luke", "Aria", "Penelope", "Joseph", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true, false, false], "solution_text": "Ethan is a knave, Chloe is a knight, Emma is a knave, Luke is a knight, Aria is a knight, Penelope is a knight, Joseph is a knave, and Lucas is a knave.", "solution_text_format": "(1) Ethan is a knave\n(2) Chloe is a knight\n(3) Emma is a knave\n(4) Luke is a knight\n(5) Aria is a knight\n(6) Penelope is a knight\n(7) Joseph is a knave\n(8) Lucas is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Ethan that Chloe is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Penelope is not a knave.", "Penelope cannot be a knight, because this would contradict the false claim of Chloe that Penelope is not a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Lucas is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Emma is a knave if and only if Joseph is a knight.", "Emma cannot be a knight, because this would contradict the claim of Joseph that Emma is a knave if and only if Joseph is a knight.", "Emma cannot be a knave, because this would contradict the false claim of their own that Lucas is a knight or Penelope is a knave.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of Lucas that Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the false claim of Penelope that Lucas is a knave.", "We have exhausted all possibilities for Lucas, Penelope, and Chloe, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Chloe is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Penelope is not a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the claim of Penelope that Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of Lucas that Joseph is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Emma is a knave if and only if Joseph is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Lucas is a knight or Penelope is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Lucas is a knight or Penelope is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Aria is a knight and Penelope is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Chloe is a knight or Penelope is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 1), ('not', ('lying', 5)), ('or', ('telling-truth', 7), ('lying', 5)), ('and', ('telling-truth', 4), ('telling-truth', 5)), ('or', ('telling-truth', 1), ('lying', 5)), ('lying', 7), ('<=>', ('lying', 2), ('telling-truth', 6)), ('telling-truth', 6))", "index": 248}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Oliver, Mason, Henry, Isabella, Charlotte, Alexander, Lily, and Jackson. In a statement by Oliver: \"Alexander is not a knave\". Mason told you that Henry is a knight. Henry said, \"Charlotte is a knave or Lily is a knave.\" According to Isabella, \"Alexander is a knave\". Charlotte said that Henry is a knave if and only if Lily is a knave. According to Alexander, \"Lily is a knave\". In a statement by Lily: \"Isabella is a knight or Alexander is a knave\". Jackson commented, \"Charlotte is a knight\". So who is a knight and who is a knave?", "names": ["Oliver", "Mason", "Henry", "Isabella", "Charlotte", "Alexander", "Lily", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true, false, false], "solution_text": "Oliver is a knight, Mason is a knight, Henry is a knight, Isabella is a knave, Charlotte is a knave, Alexander is a knight, Lily is a knave, and Jackson is a knave.", "solution_text_format": "(1) Oliver is a knight\n(2) Mason is a knight\n(3) Henry is a knight\n(4) Isabella is a knave\n(5) Charlotte is a knave\n(6) Alexander is a knight\n(7) Lily is a knave\n(8) Jackson is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Alexander is not a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of Alexander that Lily is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Isabella is a knight or Alexander is a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that Alexander is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Alexander is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Henry is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Charlotte is a knave or Lily is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Henry is a knave if and only if Lily is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Henry is a knave if and only if Lily is a knave.", "Jackson cannot be a knight, because this would contradict the claim of their own that Charlotte is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Charlotte is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 5)), ('telling-truth', 2), ('or', ('lying', 4), ('lying', 6)), ('lying', 5), ('<=>', ('lying', 2), ('lying', 6)), ('lying', 6), ('or', ('telling-truth', 3), ('lying', 5)), ('telling-truth', 4))", "index": 249}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: David, Ava, Daniel, Samuel, Noah, Emily, Sofia, and Elizabeth. David remarked, \"Sofia is a knave or Sofia is a knight\". \"Daniel is a knave if and only if Samuel is a knight,\" Ava mentioned. Daniel said that Samuel is a knave or Ava is a knave. Samuel noted, \"David is a knave\". Noah told you that If David is a knight then Emily is a knave. Emily stated, \"Sofia is not a knave\". \"Samuel is a knave if and only if Daniel is a knave,\" Sofia mentioned. Elizabeth was heard saying, \"Samuel is a knave and Ava is a knight\". So who is a knight and who is a knave?", "names": ["David", "Ava", "Daniel", "Samuel", "Noah", "Emily", "Sofia", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false, false, true], "solution_text": "David is a knight, Ava is a knight, Daniel is a knight, Samuel is a knave, Noah is a knight, Emily is a knave, Sofia is a knave, and Elizabeth is a knight.", "solution_text_format": "(1) David is a knight\n(2) Ava is a knight\n(3) Daniel is a knight\n(4) Samuel is a knave\n(5) Noah is a knight\n(6) Emily is a knave\n(7) Sofia is a knave\n(8) Elizabeth is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Sofia is a knave or Sofia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Daniel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that David is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that David is a knave.", "Daniel cannot be a knight, because this would contradict the claim of Sofia that Samuel is a knave if and only if Daniel is a knave.", "Daniel cannot be a knave, because this would contradict the false claim of their own that Samuel is a knave or Ava is a knave.", "We have exhausted all possibilities for Daniel and Samuel, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Samuel is a knave if and only if Daniel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that David is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that David is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Samuel is a knave or Ava is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Daniel is a knave if and only if Samuel is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that If David is a knight then Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of Noah that If David is a knight then Emily is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Sofia is not a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Samuel is a knave and Ava is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 6), ('telling-truth', 6)), ('<=>', ('lying', 2), ('telling-truth', 3)), ('or', ('lying', 3), ('lying', 1)), ('lying', 0), ('->', ('telling-truth', 0), ('lying', 5)), ('not', ('lying', 6)), ('<=>', ('lying', 3), ('lying', 2)), ('and', ('lying', 3), ('telling-truth', 1)))", "index": 250}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jackson, Jack, Sebastian, Ava, Joseph, Penelope, Ella, and Elizabeth. As Jackson put it, \"Elizabeth is a knight or Ella is a knight\". \"Jackson is a knave or Jack is a knight,\" Jack claimed. Sebastian was heard saying, \"Penelope is not a knave\". \"Sebastian is not a knave,\" Ava claimed. Joseph told you that If Ava is a knave then Elizabeth is a knave. According to Penelope, \"If Jackson is a knight then Ella is a knave\". Ella expressed that Ava is a knave if and only if Jackson is a knave. \"Jack is a knight and Joseph is a knave,\" Elizabeth claimed. So who is a knight and who is a knave?", "names": ["Jackson", "Jack", "Sebastian", "Ava", "Joseph", "Penelope", "Ella", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true, false, false], "solution_text": "Jackson is a knave, Jack is a knight, Sebastian is a knight, Ava is a knight, Joseph is a knight, Penelope is a knight, Ella is a knave, and Elizabeth is a knave.", "solution_text_format": "(1) Jackson is a knave\n(2) Jack is a knight\n(3) Sebastian is a knight\n(4) Ava is a knight\n(5) Joseph is a knight\n(6) Penelope is a knight\n(7) Ella is a knave\n(8) Elizabeth is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Elizabeth is a knight or Ella is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Jack is a knight and Joseph is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Jackson is a knave or Jack is a knight.", "Joseph cannot be a knight, because this would contradict the claim of Elizabeth that Jack is a knight and Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that If Ava is a knave then Elizabeth is a knave.", "Ava cannot be a knight, because this would contradict the false claim of Joseph that If Ava is a knave then Elizabeth is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Sebastian is not a knave.", "Sebastian cannot be a knight, because this would contradict the false claim of Ava that Sebastian is not a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Penelope is not a knave.", "Penelope cannot be a knight, because this would contradict the false claim of Sebastian that Penelope is not a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that If Jackson is a knight then Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Ava is a knave if and only if Jackson is a knave.", "Ella cannot be a knave, because this would contradict the false claim of Penelope that If Jackson is a knight then Ella is a knave.", "We have exhausted all possibilities for Ella, Penelope, Sebastian, Ava, and Joseph, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the claim of Elizabeth that Jack is a knight and Joseph is a knave.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Jack is a knight and Joseph is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Jackson is a knave or Jack is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Ava is a knave then Elizabeth is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Sebastian is not a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Penelope is not a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that If Jackson is a knight then Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of Penelope that If Jackson is a knight then Ella is a knave.", "Ella cannot be a knave, because this would contradict the claim of Jackson that Elizabeth is a knight or Ella is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the claim of Sebastian that Penelope is not a knave.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the claim of Ava that Sebastian is not a knave.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Sebastian is not a knave.", "Sebastian cannot be a knight, because this would contradict the false claim of Ava that Sebastian is not a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Penelope is not a knave.", "Penelope cannot be a knight, because this would contradict the false claim of Sebastian that Penelope is not a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that If Jackson is a knight then Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Ava is a knave if and only if Jackson is a knave.", "Ella cannot be a knave, because this would contradict the claim of Jackson that Elizabeth is a knight or Ella is a knight.", "We have exhausted all possibilities for Ella, Penelope, Sebastian, and Ava, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the false claim of their own that If Ava is a knave then Elizabeth is a knave.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Jackson is a knave or Jack is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Ava is a knave then Elizabeth is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Sebastian is not a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Penelope is not a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that If Jackson is a knight then Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of Penelope that If Jackson is a knight then Ella is a knave.", "Ella cannot be a knave, because this would contradict the claim of Jackson that Elizabeth is a knight or Ella is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the claim of Sebastian that Penelope is not a knave.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the claim of Ava that Sebastian is not a knave.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Sebastian is not a knave.", "Sebastian cannot be a knight, because this would contradict the false claim of Ava that Sebastian is not a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Penelope is not a knave.", "Penelope cannot be a knight, because this would contradict the false claim of Sebastian that Penelope is not a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that If Jackson is a knight then Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Ava is a knave if and only if Jackson is a knave.", "Ella cannot be a knave, because this would contradict the claim of Jackson that Elizabeth is a knight or Ella is a knight.", "We have exhausted all possibilities for Ella, Penelope, Sebastian, and Ava, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the false claim of their own that If Ava is a knave then Elizabeth is a knave.", "We have exhausted all possibilities for Joseph, Jack, and Elizabeth, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Elizabeth is a knight or Ella is a knight.", "Elizabeth cannot be a knight, because this would contradict the false claim of Jackson that Elizabeth is a knight or Ella is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Jack is a knight and Joseph is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Jackson is a knave or Jack is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Ava is a knave then Elizabeth is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Sebastian is not a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Penelope is not a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that If Jackson is a knight then Ella is a knave.", "Ella cannot be a knight, because this would contradict the false claim of Jackson that Elizabeth is a knight or Ella is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Ava is a knave if and only if Jackson is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 7), ('telling-truth', 6)), ('or', ('lying', 0), ('telling-truth', 1)), ('not', ('lying', 5)), ('not', ('lying', 2)), ('->', ('lying', 3), ('lying', 7)), ('->', ('telling-truth', 0), ('lying', 6)), ('<=>', ('lying', 3), ('lying', 0)), ('and', ('telling-truth', 1), ('lying', 4)))", "index": 251}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mason, William, Penelope, Mia, Benjamin, Emma, Oliver, and Ethan. Mason commented, \"Ethan is a knave and Penelope is a knave\". William told you that Benjamin is a knave and William is a knight. Penelope told you that If Oliver is a knave then Emma is a knight. Mia expressed that Emma is a knave. Benjamin said that If Oliver is a knight then Penelope is a knight. \"If William is a knight then Mason is a knight,\" Emma declared. Oliver said, \"Ethan is not a knight.\" \"Penelope is a knight if and only if Mason is a knight,\" Ethan declared. So who is a knight and who is a knave?", "names": ["Mason", "William", "Penelope", "Mia", "Benjamin", "Emma", "Oliver", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true, true, false], "solution_text": "Mason is a knave, William is a knave, Penelope is a knight, Mia is a knave, Benjamin is a knight, Emma is a knight, Oliver is a knight, and Ethan is a knave.", "solution_text_format": "(1) Mason is a knave\n(2) William is a knave\n(3) Penelope is a knight\n(4) Mia is a knave\n(5) Benjamin is a knight\n(6) Emma is a knight\n(7) Oliver is a knight\n(8) Ethan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Ethan is a knave and Penelope is a knave.", "Ethan cannot be a knight, because this would contradict the claim of Mason that Ethan is a knave and Penelope is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Penelope is a knight if and only if Mason is a knight.", "Penelope cannot be a knight, because this would contradict the claim of Mason that Ethan is a knave and Penelope is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that If Oliver is a knave then Emma is a knight.", "Oliver cannot be a knight, because this would contradict the false claim of Penelope that If Oliver is a knave then Emma is a knight.", "Oliver cannot be a knave, because this would contradict the false claim of their own that Ethan is not a knight.", "We have exhausted all possibilities for Oliver, Penelope, and Ethan, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Ethan is a knave and Penelope is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Penelope is a knight if and only if Mason is a knight.", "Penelope cannot be a knight, because this would contradict the claim of Ethan that Penelope is a knight if and only if Mason is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that If Oliver is a knave then Emma is a knight.", "Oliver cannot be a knight, because this would contradict the false claim of Penelope that If Oliver is a knave then Emma is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Ethan is not a knight.", "Emma cannot be a knight, because this would contradict the false claim of Penelope that If Oliver is a knave then Emma is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that If William is a knight then Mason is a knight.", "Assume William is a knight. No contradiction is found in their claim that Benjamin is a knave and William is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of William that Benjamin is a knave and William is a knight.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that If Oliver is a knight then Penelope is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the false claim of Emma that If William is a knight then Mason is a knight.", "We have exhausted all possibilities for William, Emma, Oliver, and Penelope, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Penelope is a knight if and only if Mason is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that If Oliver is a knave then Emma is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Ethan is not a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If William is a knight then Mason is a knight.", "William cannot be a knight, because this would contradict the claim of Emma that If William is a knight then Mason is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Benjamin is a knave and William is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Oliver is a knight then Penelope is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that Emma is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Emma is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 7), ('lying', 2)), ('and', ('lying', 4), ('telling-truth', 1)), ('->', ('lying', 6), ('telling-truth', 5)), ('lying', 5), ('->', ('telling-truth', 6), ('telling-truth', 2)), ('->', ('telling-truth', 1), ('telling-truth', 0)), ('not', ('telling-truth', 7)), ('<=>', ('telling-truth', 2), ('telling-truth', 0)))", "index": 252}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sofia, Charlotte, Elizabeth, Oliver, Olivia, Riley, Aurora, and Grace. As Sofia put it, \"Riley is a knight if and only if Oliver is a knave\". According to Charlotte, \"Oliver is a knight and Elizabeth is a knight\". \"Olivia is a knight if and only if Aurora is a knave,\" Elizabeth declared. \"Charlotte is a knight\" - Oliver. Olivia asserted: \"Oliver is a knave\". Riley asserted: \"If Grace is a knave then Olivia is a knight\". In Aurora's words: \"Charlotte is not a knight\". Grace expressed that Charlotte is a knave or Aurora is a knave. So who is a knight and who is a knave?", "names": ["Sofia", "Charlotte", "Elizabeth", "Oliver", "Olivia", "Riley", "Aurora", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true, true, true], "solution_text": "Sofia is a knight, Charlotte is a knave, Elizabeth is a knave, Oliver is a knave, Olivia is a knight, Riley is a knight, Aurora is a knight, and Grace is a knight.", "solution_text_format": "(1) Sofia is a knight\n(2) Charlotte is a knave\n(3) Elizabeth is a knave\n(4) Oliver is a knave\n(5) Olivia is a knight\n(6) Riley is a knight\n(7) Aurora is a knight\n(8) Grace is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Riley is a knight if and only if Oliver is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that If Grace is a knave then Olivia is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Charlotte is a knave or Aurora is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Oliver is a knight and Elizabeth is a knight.", "Oliver cannot be a knight, because this would contradict the claim of Sofia that Riley is a knight if and only if Oliver is a knave.", "Oliver cannot be a knave, because this would contradict the claim of Charlotte that Oliver is a knight and Elizabeth is a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Oliver is a knight and Elizabeth is a knight.", "Oliver cannot be a knight, because this would contradict the claim of Sofia that Riley is a knight if and only if Oliver is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Charlotte is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Aurora is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Oliver is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Elizabeth that Olivia is a knight if and only if Aurora is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of their own that Charlotte is not a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the false claim of their own that Oliver is a knave.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Olivia is a knight if and only if Aurora is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Oliver is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Charlotte is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 5), ('lying', 3)), ('and', ('telling-truth', 3), ('telling-truth', 2)), ('<=>', ('telling-truth', 4), ('lying', 6)), ('telling-truth', 1), ('lying', 3), ('->', ('lying', 7), ('telling-truth', 4)), ('not', ('telling-truth', 1)), ('or', ('lying', 1), ('lying', 6)))", "index": 253}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lily, Jackson, James, Aurora, Emily, Charlotte, Samuel, and William. Lily stated, \"If William is a knave then Aurora is a knave\". Jackson was heard saying, \"Charlotte is a knight\". James said, \"Emily is not a knight.\" \"If Lily is a knave then Charlotte is a knight,\" Aurora claimed. \"If Emily is a knight then Aurora is a knight,\" Emily declared. As Charlotte put it, \"Aurora is a knight if and only if Lily is a knave\". Samuel was heard saying, \"If Charlotte is a knight then Jackson is a knave\". \"Lily is a knight and Emily is a knave,\" William claimed. So who is a knight and who is a knave?", "names": ["Lily", "Jackson", "James", "Aurora", "Emily", "Charlotte", "Samuel", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true, false, false], "solution_text": "Lily is a knave, Jackson is a knight, James is a knave, Aurora is a knight, Emily is a knight, Charlotte is a knight, Samuel is a knave, and William is a knave.", "solution_text_format": "(1) Lily is a knave\n(2) Jackson is a knight\n(3) James is a knave\n(4) Aurora is a knight\n(5) Emily is a knight\n(6) Charlotte is a knight\n(7) Samuel is a knave\n(8) William is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that If William is a knave then Aurora is a knave.", "Assume William is a knight. No contradiction is found in their claim that Lily is a knight and Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of William that Lily is a knight and Emily is a knave.", "Emily cannot be a knave, because this would contradict the false claim of their own that If Emily is a knight then Aurora is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Lily is a knight and Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that If Emily is a knight then Aurora is a knight.", "Aurora cannot be a knight, because this would contradict the claim of Lily that If William is a knave then Aurora is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of their own that If Lily is a knave then Charlotte is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the false claim of their own that If Emily is a knight then Aurora is a knight.", "We have exhausted all possibilities for Emily and William, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that If William is a knave then Aurora is a knave.", "William cannot be a knight, because this would contradict the false claim of Lily that If William is a knave then Aurora is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Lily is a knight and Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that If Emily is a knight then Aurora is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that If Lily is a knave then Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Aurora is a knight if and only if Lily is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Charlotte is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Emily is not a knight.", "Assume James is a knave. No contradiction is found in their false claim that Emily is not a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that If Charlotte is a knight then Jackson is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that If Charlotte is a knight then Jackson is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 7), ('lying', 3)), ('telling-truth', 5), ('not', ('telling-truth', 4)), ('->', ('lying', 0), ('telling-truth', 5)), ('->', ('telling-truth', 4), ('telling-truth', 3)), ('<=>', ('telling-truth', 3), ('lying', 0)), ('->', ('telling-truth', 5), ('lying', 1)), ('and', ('telling-truth', 0), ('lying', 4)))", "index": 254}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Charlotte, Sophia, Emily, Sebastian, James, Victoria, Samuel, and Avery. Charlotte expressed that If Emily is a knight then Sebastian is a knight. Sophia noted, \"Samuel is not a knight\". Emily expressed that Victoria is a knight. \"If Samuel is a knight then Charlotte is a knave,\" Sebastian declared. \"If James is a knight then Samuel is a knave,\" James mentioned. Victoria said that Samuel is not a knave. Samuel said, \"Charlotte is a knave and Sophia is a knight.\" Avery said, \"Victoria is a knave or Sebastian is a knave.\" So who is a knight and who is a knave?", "names": ["Charlotte", "Sophia", "Emily", "Sebastian", "James", "Victoria", "Samuel", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false, false, true], "solution_text": "Charlotte is a knight, Sophia is a knight, Emily is a knave, Sebastian is a knight, James is a knight, Victoria is a knave, Samuel is a knave, and Avery is a knight.", "solution_text_format": "(1) Charlotte is a knight\n(2) Sophia is a knight\n(3) Emily is a knave\n(4) Sebastian is a knight\n(5) James is a knight\n(6) Victoria is a knave\n(7) Samuel is a knave\n(8) Avery is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that If Emily is a knight then Sebastian is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Victoria is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Samuel is not a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that Charlotte is a knave and Sophia is a knight.", "Samuel cannot be a knave, because this would contradict the claim of Victoria that Samuel is not a knave.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Victoria.", "Victoria cannot be a knave, because this would contradict the claim of Emily that Victoria is a knight.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Victoria is a knight.", "Victoria cannot be a knight, because this would contradict the false claim of Emily that Victoria is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Samuel is not a knave.", "Samuel cannot be a knight, because this would contradict the false claim of Victoria that Samuel is not a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Charlotte is a knave and Sophia is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Samuel is not a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Samuel is a knight then Charlotte is a knave.", "Assume James is a knight. No contradiction is found in their claim that If James is a knight then Samuel is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Victoria is a knave or Sebastian is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('telling-truth', 3)), ('not', ('telling-truth', 6)), ('telling-truth', 5), ('->', ('telling-truth', 6), ('lying', 0)), ('->', ('telling-truth', 4), ('lying', 6)), ('not', ('lying', 6)), ('and', ('lying', 0), ('telling-truth', 1)), ('or', ('lying', 5), ('lying', 3)))", "index": 255}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ella, Sofia, David, Lily, William, Scarlett, Benjamin, and Abigail. Ella noted, \"William is not a knave\". \"Scarlett is a knight or Sofia is a knight\" - Sofia. David remarked, \"If Abigail is a knight then Abigail is a knave\". \"If William is a knave then Ella is a knave,\" Lily declared. In a statement by William: \"Benjamin is a knight and Ella is a knight\". Scarlett was heard saying, \"If Scarlett is a knight then David is a knave\". \"Ella is a knight and Scarlett is a knave\" - Benjamin. \"David is not a knight,\" Abigail declared. So who is a knight and who is a knave?", "names": ["Ella", "Sofia", "David", "Lily", "William", "Scarlett", "Benjamin", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, true, false, true], "solution_text": "Ella is a knave, Sofia is a knight, David is a knave, Lily is a knight, William is a knave, Scarlett is a knight, Benjamin is a knave, and Abigail is a knight.", "solution_text_format": "(1) Ella is a knave\n(2) Sofia is a knight\n(3) David is a knave\n(4) Lily is a knight\n(5) William is a knave\n(6) Scarlett is a knight\n(7) Benjamin is a knave\n(8) Abigail is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that William is not a knave.", "Assume William is a knight. No contradiction is found in their claim that Benjamin is a knight and Ella is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Ella is a knight and Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Benjamin that Ella is a knight and Scarlett is a knave.", "Scarlett cannot be a knave, because this would contradict the false claim of their own that If Scarlett is a knight then David is a knave.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the claim of William that Benjamin is a knight and Ella is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the claim of Ella that William is not a knave.", "We have exhausted all possibilities for William, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that William is not a knave.", "William cannot be a knight, because this would contradict the false claim of Ella that William is not a knave.", "Assume William is a knave. No contradiction is found in their false claim that Benjamin is a knight and Ella is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Ella is a knight and Scarlett is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Ella is a knight and Scarlett is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Scarlett is a knight then David is a knave.", "David cannot be a knight, because this would contradict the claim of Scarlett that If Scarlett is a knight then David is a knave.", "Assume David is a knave. No contradiction is found in their false claim that If Abigail is a knight then Abigail is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that David is not a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Scarlett is a knight or Sofia is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that If William is a knave then Ella is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('or', ('telling-truth', 5), ('telling-truth', 1)), ('->', ('telling-truth', 7), ('lying', 7)), ('->', ('lying', 4), ('lying', 0)), ('and', ('telling-truth', 6), ('telling-truth', 0)), ('->', ('telling-truth', 5), ('lying', 2)), ('and', ('telling-truth', 0), ('lying', 5)), ('not', ('telling-truth', 2)))", "index": 256}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lucas, Avery, Jacob, Liam, Michael, Owen, Sebastian, and Victoria. Lucas stated, \"Owen is a knave if and only if Owen is a knight\". According to Avery, \"Michael is a knave\". Jacob stated, \"If Liam is a knave then Liam is a knight\". According to Liam, \"Liam is a knight or Avery is a knave\". As Michael put it, \"Jacob is not a knight\". Owen noted, \"Sebastian is a knave and Lucas is a knight\". Sebastian remarked, \"Avery is a knight or Lucas is a knave\". Victoria told you that Liam is a knave or Avery is a knave. So who is a knight and who is a knave?", "names": ["Lucas", "Avery", "Jacob", "Liam", "Michael", "Owen", "Sebastian", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false, true, false], "solution_text": "Lucas is a knave, Avery is a knight, Jacob is a knight, Liam is a knight, Michael is a knave, Owen is a knave, Sebastian is a knight, and Victoria is a knave.", "solution_text_format": "(1) Lucas is a knave\n(2) Avery is a knight\n(3) Jacob is a knight\n(4) Liam is a knight\n(5) Michael is a knave\n(6) Owen is a knave\n(7) Sebastian is a knight\n(8) Victoria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Lucas cannot be a knight, because this would contradict the claim of their own that Owen is a knave if and only if Owen is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Owen is a knave if and only if Owen is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave and Lucas is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Sebastian is a knave and Lucas is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Avery is a knight or Lucas is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of Avery that Michael is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Jacob is not a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that If Liam is a knave then Liam is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Liam is a knight or Avery is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that Liam is a knave or Avery is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Liam is a knave or Avery is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 5), ('telling-truth', 5)), ('lying', 4), ('->', ('lying', 3), ('telling-truth', 3)), ('or', ('telling-truth', 3), ('lying', 1)), ('not', ('telling-truth', 2)), ('and', ('lying', 6), ('telling-truth', 0)), ('or', ('telling-truth', 1), ('lying', 0)), ('or', ('lying', 3), ('lying', 1)))", "index": 257}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emily, Aiden, James, Zoey, Ava, Riley, Aurora, and Elizabeth. As Emily put it, \"James is a knave if and only if Aurora is a knight\". Aiden remarked, \"Elizabeth is a knight and Aiden is a knight\". \"Elizabeth is a knight and Riley is a knave,\" James declared. Zoey told you that Emily is a knight and Aurora is a knight. Ava commented, \"James is not a knight\". According to Riley, \"Aiden is not a knight\". Aurora expressed that Emily is a knave and Elizabeth is a knight. Elizabeth told you that Emily is a knave or Aurora is a knight. So who is a knight and who is a knave?", "names": ["Emily", "Aiden", "James", "Zoey", "Ava", "Riley", "Aurora", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false, true, true], "solution_text": "Emily is a knave, Aiden is a knight, James is a knight, Zoey is a knave, Ava is a knave, Riley is a knave, Aurora is a knight, and Elizabeth is a knight.", "solution_text_format": "(1) Emily is a knave\n(2) Aiden is a knight\n(3) James is a knight\n(4) Zoey is a knave\n(5) Ava is a knave\n(6) Riley is a knave\n(7) Aurora is a knight\n(8) Elizabeth is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that James is a knave if and only if Aurora is a knight.", "Assume James is a knight. No contradiction is found in their claim that Elizabeth is a knight and Riley is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Emily is a knave or Aurora is a knight.", "Aurora cannot be a knight, because this would contradict the claim of Emily that James is a knave if and only if Aurora is a knight.", "Aurora cannot be a knave, because this would contradict the claim of Elizabeth that Emily is a knave or Aurora is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Elizabeth.", "Elizabeth cannot be a knave, because this would contradict the claim of James that Elizabeth is a knight and Riley is a knave.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Elizabeth is a knight and Riley is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Emily is a knave or Aurora is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Emily is a knave and Elizabeth is a knight.", "Aurora cannot be a knave, because this would contradict the claim of Emily that James is a knave if and only if Aurora is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Emily is a knave or Aurora is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Emily is a knave and Elizabeth is a knight.", "Aurora cannot be a knave, because this would contradict the claim of Emily that James is a knave if and only if Aurora is a knight.", "We have exhausted all possibilities for Aurora, Elizabeth, and James, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that James is a knave if and only if Aurora is a knight.", "Assume James is a knight. No contradiction is found in their claim that Elizabeth is a knight and Riley is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Emily is a knave or Aurora is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Emily is a knave and Elizabeth is a knight.", "Riley cannot be a knight, because this would contradict the claim of James that Elizabeth is a knight and Riley is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Aiden is not a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Elizabeth is a knight and Aiden is a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that Emily is a knight and Aurora is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Emily is a knight and Aurora is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that James is not a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that James is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('telling-truth', 6)), ('and', ('telling-truth', 7), ('telling-truth', 1)), ('and', ('telling-truth', 7), ('lying', 5)), ('and', ('telling-truth', 0), ('telling-truth', 6)), ('not', ('telling-truth', 2)), ('not', ('telling-truth', 1)), ('and', ('lying', 0), ('telling-truth', 7)), ('or', ('lying', 0), ('telling-truth', 6)))", "index": 258}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Daniel, Jack, Luke, Matthew, Scarlett, Mason, Mia, and Aurora. Daniel was heard saying, \"Mia is a knight or Matthew is a knight\". Jack asserted: \"If Aurora is a knave then Matthew is a knight\". Luke told you that Mia is a knave or Scarlett is a knave. Matthew said that Mason is a knave if and only if Luke is a knight. \"If Luke is a knight then Daniel is a knight,\" Scarlett mentioned. Mason told you that Mia is a knight if and only if Luke is a knave. Mia asserted: \"Luke is a knave or Daniel is a knave\". According to Aurora, \"Mason is a knave if and only if Mia is a knave\". So who is a knight and who is a knave?", "names": ["Daniel", "Jack", "Luke", "Matthew", "Scarlett", "Mason", "Mia", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true, true, true], "solution_text": "Daniel is a knight, Jack is a knight, Luke is a knave, Matthew is a knight, Scarlett is a knight, Mason is a knight, Mia is a knight, and Aurora is a knight.", "solution_text_format": "(1) Daniel is a knight\n(2) Jack is a knight\n(3) Luke is a knave\n(4) Matthew is a knight\n(5) Scarlett is a knight\n(6) Mason is a knight\n(7) Mia is a knight\n(8) Aurora is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that Mia is a knight or Matthew is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Luke is a knave or Daniel is a knave.", "Luke cannot be a knight, because this would contradict the claim of Mia that Luke is a knave or Daniel is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Mia is a knave or Scarlett is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Luke is a knight then Daniel is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Mason is a knave if and only if Luke is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Mia is a knight if and only if Luke is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that If Aurora is a knave then Matthew is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Mason is a knave if and only if Mia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 6), ('telling-truth', 3)), ('->', ('lying', 7), ('telling-truth', 3)), ('or', ('lying', 6), ('lying', 4)), ('<=>', ('lying', 5), ('telling-truth', 2)), ('->', ('telling-truth', 2), ('telling-truth', 0)), ('<=>', ('telling-truth', 6), ('lying', 2)), ('or', ('lying', 2), ('lying', 0)), ('<=>', ('lying', 5), ('lying', 6)))", "index": 259}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Michael, Ella, Jackson, Noah, Penelope, Oliver, Isabella, and David. As Michael put it, \"If Noah is a knave then David is a knight\". \"If Jackson is a knave then Noah is a knave\" - Ella. \"Oliver is a knight if and only if Penelope is a knight\" - Jackson. \"Oliver is a knight if and only if Isabella is a knight\" - Noah. Penelope said, \"Oliver is a knight.\" Oliver told you that If Ella is a knave then David is a knight. Isabella expressed that Oliver is a knave or Penelope is a knave. David noted, \"Isabella is a knight and Penelope is a knight\". So who is a knight and who is a knave?", "names": ["Michael", "Ella", "Jackson", "Noah", "Penelope", "Oliver", "Isabella", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true, false, false], "solution_text": "Michael is a knave, Ella is a knight, Jackson is a knight, Noah is a knave, Penelope is a knight, Oliver is a knight, Isabella is a knave, and David is a knave.", "solution_text_format": "(1) Michael is a knave\n(2) Ella is a knight\n(3) Jackson is a knight\n(4) Noah is a knave\n(5) Penelope is a knight\n(6) Oliver is a knight\n(7) Isabella is a knave\n(8) David is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that If Noah is a knave then David is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Oliver is a knight if and only if Isabella is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that If Ella is a knave then David is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that If Jackson is a knave then Noah is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Oliver is a knight if and only if Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Oliver is a knight.", "Assume David is a knight. No contradiction is found in their claim that Isabella is a knight and Penelope is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Oliver is a knave or Penelope is a knave.", "Isabella cannot be a knave, because this would contradict the claim of Noah that Oliver is a knight if and only if Isabella is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Isabella is a knight and Penelope is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Oliver is a knave or Penelope is a knave.", "Isabella cannot be a knave, because this would contradict the claim of Noah that Oliver is a knight if and only if Isabella is a knight.", "We have exhausted all possibilities for Isabella and David, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the claim of Jackson that Oliver is a knight if and only if Penelope is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Jackson.", "Jackson cannot be a knave, because this would contradict the claim of Ella that If Jackson is a knave then Noah is a knave.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that If Jackson is a knave then Noah is a knave.", "Jackson cannot be a knight, because this would contradict the false claim of Ella that If Jackson is a knave then Noah is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Oliver is a knight if and only if Penelope is a knight.", "Penelope cannot be a knight, because this would contradict the false claim of Jackson that Oliver is a knight if and only if Penelope is a knight.", "Penelope cannot be a knave, because this would contradict the false claim of their own that Oliver is a knight.", "We have exhausted all possibilities for Penelope, Jackson, and Ella, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that If Ella is a knave then David is a knight.", "Ella cannot be a knight, because this would contradict the false claim of Oliver that If Ella is a knave then David is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that If Jackson is a knave then Noah is a knave.", "Jackson cannot be a knight, because this would contradict the false claim of Ella that If Jackson is a knave then Noah is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Oliver is a knight if and only if Penelope is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Oliver is a knight.", "Penelope cannot be a knave, because this would contradict the false claim of Jackson that Oliver is a knight if and only if Penelope is a knight.", "We have exhausted all possibilities for Penelope, Jackson, Ella, and Oliver, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Oliver is a knight if and only if Isabella is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that If Ella is a knave then David is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that If Jackson is a knave then Noah is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Oliver is a knight if and only if Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Oliver is a knight.", "Assume David is a knight. No contradiction is found in their claim that Isabella is a knight and Penelope is a knight.", "Isabella cannot be a knight, because this would contradict the false claim of Noah that Oliver is a knight if and only if Isabella is a knight.", "Isabella cannot be a knave, because this would contradict the claim of David that Isabella is a knight and Penelope is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the claim of Michael that If Noah is a knave then David is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the claim of Jackson that Oliver is a knight if and only if Penelope is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Oliver is a knight if and only if Penelope is a knight.", "Penelope cannot be a knight, because this would contradict the false claim of Jackson that Oliver is a knight if and only if Penelope is a knight.", "Penelope cannot be a knave, because this would contradict the false claim of their own that Oliver is a knight.", "We have exhausted all possibilities for Penelope and Jackson, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the false claim of their own that If Jackson is a knave then Noah is a knave.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that If Ella is a knave then David is a knight.", "Ella cannot be a knight, because this would contradict the false claim of Oliver that If Ella is a knave then David is a knight.", "Ella cannot be a knave, because this would contradict the false claim of their own that If Jackson is a knave then Noah is a knave.", "We have exhausted all possibilities for Ella, Oliver, and Noah, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that If Noah is a knave then David is a knight.", "Noah cannot be a knight, because this would contradict the false claim of Michael that If Noah is a knave then David is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Oliver is a knight if and only if Isabella is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that If Ella is a knave then David is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that If Jackson is a knave then Noah is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Oliver is a knight if and only if Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Oliver is a knight.", "David cannot be a knight, because this would contradict the false claim of Michael that If Noah is a knave then David is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Isabella is a knight and Penelope is a knight.", "Isabella cannot be a knight, because this would contradict the false claim of Noah that Oliver is a knight if and only if Isabella is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Oliver is a knave or Penelope is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('telling-truth', 7)), ('->', ('lying', 2), ('lying', 3)), ('<=>', ('telling-truth', 5), ('telling-truth', 4)), ('<=>', ('telling-truth', 5), ('telling-truth', 6)), ('telling-truth', 5), ('->', ('lying', 1), ('telling-truth', 7)), ('or', ('lying', 5), ('lying', 4)), ('and', ('telling-truth', 6), ('telling-truth', 4)))", "index": 260}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Avery, Evelyn, Emma, Oliver, Matthew, Jackson, Grace, and James. In Avery's words: \"Evelyn is a knight if and only if Avery is a knight\". As Evelyn put it, \"Avery is a knight if and only if Matthew is a knave\". \"Evelyn is a knave or Grace is a knight,\" Emma claimed. \"If Avery is a knight then Evelyn is a knight,\" Oliver claimed. Matthew said that Evelyn is a knave and Jackson is a knave. According to Jackson, \"Evelyn is a knave or Avery is a knight\". In Grace's words: \"Evelyn is a knight and Matthew is a knave\". \"If Matthew is a knave then Jackson is a knave,\" James declared. So who is a knight and who is a knave?", "names": ["Avery", "Evelyn", "Emma", "Oliver", "Matthew", "Jackson", "Grace", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true, true, false], "solution_text": "Avery is a knight, Evelyn is a knight, Emma is a knight, Oliver is a knight, Matthew is a knave, Jackson is a knight, Grace is a knight, and James is a knave.", "solution_text_format": "(1) Avery is a knight\n(2) Evelyn is a knight\n(3) Emma is a knight\n(4) Oliver is a knight\n(5) Matthew is a knave\n(6) Jackson is a knight\n(7) Grace is a knight\n(8) James is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Evelyn is a knight if and only if Avery is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Avery is a knight if and only if Matthew is a knave.", "Matthew cannot be a knight, because this would contradict the claim of Evelyn that Avery is a knight if and only if Matthew is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Evelyn is a knave and Jackson is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Evelyn is a knave or Avery is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Evelyn is a knave or Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Evelyn is a knight and Matthew is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that If Avery is a knight then Evelyn is a knight.", "James cannot be a knight, because this would contradict the claim of their own that If Matthew is a knave then Jackson is a knave.", "Assume James is a knave. No contradiction is found in their false claim that If Matthew is a knave then Jackson is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('<=>', ('telling-truth', 0), ('lying', 4)), ('or', ('lying', 1), ('telling-truth', 6)), ('->', ('telling-truth', 0), ('telling-truth', 1)), ('and', ('lying', 1), ('lying', 5)), ('or', ('lying', 1), ('telling-truth', 0)), ('and', ('telling-truth', 1), ('lying', 4)), ('->', ('lying', 4), ('lying', 5)))", "index": 261}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sofia, Owen, Henry, Grace, Emily, Harper, Logan, and Lily. \"Harper is a knave and Harper is a knight\" - Sofia. In Owen's words: \"Grace is a knave and Harper is a knight\". According to Henry, \"Logan is a knight or Owen is a knight\". \"Logan is a knight and Henry is a knight,\" Grace declared. Emily said that Owen is a knight and Owen is a knave. Harper remarked, \"Henry is not a knight\". Logan commented, \"Henry is a knight if and only if Emily is a knave\". Lily was heard saying, \"Grace is a knight if and only if Sofia is a knight\". So who is a knight and who is a knave?", "names": ["Sofia", "Owen", "Henry", "Grace", "Emily", "Harper", "Logan", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false, true, false], "solution_text": "Sofia is a knave, Owen is a knave, Henry is a knight, Grace is a knight, Emily is a knave, Harper is a knave, Logan is a knight, and Lily is a knave.", "solution_text_format": "(1) Sofia is a knave\n(2) Owen is a knave\n(3) Henry is a knight\n(4) Grace is a knight\n(5) Emily is a knave\n(6) Harper is a knave\n(7) Logan is a knight\n(8) Lily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Sofia cannot be a knight, because this would contradict the claim of their own that Harper is a knave and Harper is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Harper is a knave and Harper is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Henry is not a knight.", "Henry cannot be a knight, because this would contradict the claim of Harper that Henry is not a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Logan is a knight or Owen is a knight.", "Logan cannot be a knight, because this would contradict the false claim of Henry that Logan is a knight or Owen is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Henry is a knight if and only if Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Owen is a knight and Owen is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Owen is a knight and Owen is a knave.", "Owen cannot be a knight, because this would contradict the false claim of Henry that Logan is a knight or Owen is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Grace is a knave and Harper is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Logan is a knight and Henry is a knight.", "Grace cannot be a knave, because this would contradict the false claim of Owen that Grace is a knave and Harper is a knight.", "We have exhausted all possibilities for Grace, Owen, Emily, Logan, and Henry, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Henry is not a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Logan is a knight or Owen is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Henry is a knight if and only if Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Owen is a knight and Owen is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Owen is a knight and Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Grace is a knave and Harper is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Grace is a knave and Harper is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Logan is a knight and Henry is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Grace is a knight if and only if Sofia is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Grace is a knight if and only if Sofia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 5), ('telling-truth', 5)), ('and', ('lying', 3), ('telling-truth', 5)), ('or', ('telling-truth', 6), ('telling-truth', 1)), ('and', ('telling-truth', 6), ('telling-truth', 2)), ('and', ('telling-truth', 1), ('lying', 1)), ('not', ('telling-truth', 2)), ('<=>', ('telling-truth', 2), ('lying', 4)), ('<=>', ('telling-truth', 3), ('telling-truth', 0)))", "index": 262}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Benjamin, Harper, Abigail, Jack, Elizabeth, Sophia, Owen, and William. Benjamin expressed that Jack is a knight and Jack is a knave. \"Owen is a knave if and only if Abigail is a knave,\" Harper mentioned. In a statement by Abigail: \"If Jack is a knave then William is a knight\". Jack asserted: \"Abigail is a knight if and only if Abigail is a knave\". Elizabeth noted, \"Benjamin is not a knight\". In a statement by Sophia: \"Jack is a knave and Owen is a knight\". Owen said that Benjamin is a knave and Elizabeth is a knave. William expressed that Abigail is a knave or Elizabeth is a knight. So who is a knight and who is a knave?", "names": ["Benjamin", "Harper", "Abigail", "Jack", "Elizabeth", "Sophia", "Owen", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, false, false, true], "solution_text": "Benjamin is a knave, Harper is a knave, Abigail is a knight, Jack is a knave, Elizabeth is a knight, Sophia is a knave, Owen is a knave, and William is a knight.", "solution_text_format": "(1) Benjamin is a knave\n(2) Harper is a knave\n(3) Abigail is a knight\n(4) Jack is a knave\n(5) Elizabeth is a knight\n(6) Sophia is a knave\n(7) Owen is a knave\n(8) William is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Benjamin cannot be a knight, because this would contradict the claim of their own that Jack is a knight and Jack is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Jack is a knight and Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Abigail is a knight if and only if Abigail is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Abigail is a knight if and only if Abigail is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that If Jack is a knave then William is a knight.", "Assume William is a knight. No contradiction is found in their claim that Abigail is a knave or Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Benjamin is not a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Owen is a knave if and only if Abigail is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave and Elizabeth is a knave.", "Owen cannot be a knave, because this would contradict the claim of Harper that Owen is a knave if and only if Abigail is a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Owen is a knave if and only if Abigail is a knave.", "Owen cannot be a knight, because this would contradict the false claim of Harper that Owen is a knave if and only if Abigail is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Benjamin is a knave and Elizabeth is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that Jack is a knave and Owen is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Jack is a knave and Owen is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('lying', 3)), ('<=>', ('lying', 6), ('lying', 2)), ('->', ('lying', 3), ('telling-truth', 7)), ('<=>', ('telling-truth', 2), ('lying', 2)), ('not', ('telling-truth', 0)), ('and', ('lying', 3), ('telling-truth', 6)), ('and', ('lying', 0), ('lying', 4)), ('or', ('lying', 2), ('telling-truth', 4)))", "index": 263}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Isabella, Owen, Michael, Liam, Mason, Henry, Olivia, and Aiden. In Isabella's words: \"Liam is a knave or Mason is a knave\". \"Mason is a knave\" - Owen. \"Henry is a knave if and only if Isabella is a knight,\" Michael claimed. Liam told you that Aiden is a knave or Owen is a knight. Mason noted, \"Henry is a knave\". Henry remarked, \"Michael is a knave and Isabella is a knave\". Olivia remarked, \"Mason is a knave and Michael is a knight\". As Aiden put it, \"If Olivia is a knave then Isabella is a knight\". So who is a knight and who is a knave?", "names": ["Isabella", "Owen", "Michael", "Liam", "Mason", "Henry", "Olivia", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, false, false, true], "solution_text": "Isabella is a knight, Owen is a knave, Michael is a knight, Liam is a knave, Mason is a knight, Henry is a knave, Olivia is a knave, and Aiden is a knight.", "solution_text_format": "(1) Isabella is a knight\n(2) Owen is a knave\n(3) Michael is a knight\n(4) Liam is a knave\n(5) Mason is a knight\n(6) Henry is a knave\n(7) Olivia is a knave\n(8) Aiden is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Liam is a knave or Mason is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Aiden is a knave or Owen is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that If Olivia is a knave then Isabella is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Mason is a knave and Michael is a knight.", "Mason cannot be a knight, because this would contradict the claim of Isabella that Liam is a knave or Mason is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Isabella is a knave.", "Henry cannot be a knave, because this would contradict the false claim of Mason that Henry is a knave.", "We have exhausted all possibilities for Henry and Mason, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Mason is a knave and Michael is a knight.", "Mason cannot be a knight, because this would contradict the claim of Isabella that Liam is a knave or Mason is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Isabella is a knave.", "Henry cannot be a knave, because this would contradict the false claim of Mason that Henry is a knave.", "We have exhausted all possibilities for Henry, Mason, and Olivia, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the false claim of their own that If Olivia is a knave then Isabella is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Aiden is a knave or Owen is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that If Olivia is a knave then Isabella is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Mason is a knave and Michael is a knight.", "Mason cannot be a knight, because this would contradict the claim of Olivia that Mason is a knave and Michael is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Isabella is a knave.", "Henry cannot be a knave, because this would contradict the false claim of Mason that Henry is a knave.", "We have exhausted all possibilities for Henry and Mason, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Mason is a knave and Michael is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of Mason that Henry is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Michael is a knave and Isabella is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Henry is a knave if and only if Isabella is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Mason is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Mason is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('lying', 4)), ('lying', 4), ('<=>', ('lying', 5), ('telling-truth', 0)), ('or', ('lying', 7), ('telling-truth', 1)), ('lying', 5), ('and', ('lying', 2), ('lying', 0)), ('and', ('lying', 4), ('telling-truth', 2)), ('->', ('lying', 6), ('telling-truth', 0)))", "index": 264}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mason, David, Owen, Amelia, Harper, James, Michael, and Sebastian. Mason commented, \"Owen is a knave\". \"Harper is a knight and Mason is a knight,\" David declared. According to Owen, \"David is a knave or Sebastian is a knight\". As Amelia put it, \"Owen is a knight\". Harper remarked, \"James is a knave if and only if James is a knight\". James told you that Michael is a knight or David is a knave. Michael said that Amelia is a knight or Mason is a knight. Sebastian stated, \"Mason is a knight\". So who is a knight and who is a knave?", "names": ["Mason", "David", "Owen", "Amelia", "Harper", "James", "Michael", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, true, true, false], "solution_text": "Mason is a knave, David is a knave, Owen is a knight, Amelia is a knight, Harper is a knave, James is a knight, Michael is a knight, and Sebastian is a knave.", "solution_text_format": "(1) Mason is a knave\n(2) David is a knave\n(3) Owen is a knight\n(4) Amelia is a knight\n(5) Harper is a knave\n(6) James is a knight\n(7) Michael is a knight\n(8) Sebastian is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of Mason that Owen is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that David is a knave or Sebastian is a knight.", "Assume David is a knight. No contradiction is found in their claim that Harper is a knight and Mason is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that James is a knave if and only if James is a knight.", "Harper cannot be a knave, because this would contradict the claim of David that Harper is a knight and Mason is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the false claim of Owen that David is a knave or Sebastian is a knight.", "We have exhausted all possibilities for David and Owen, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Owen is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that David is a knave or Sebastian is a knight.", "David cannot be a knight, because this would contradict the claim of their own that Harper is a knight and Mason is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Harper is a knight and Mason is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that James is a knave if and only if James is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that James is a knave if and only if James is a knight.", "Assume James is a knight. No contradiction is found in their claim that Michael is a knight or David is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Amelia is a knight or Mason is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Owen is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Mason is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Mason is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('and', ('telling-truth', 4), ('telling-truth', 0)), ('or', ('lying', 1), ('telling-truth', 7)), ('telling-truth', 2), ('<=>', ('lying', 5), ('telling-truth', 5)), ('or', ('telling-truth', 6), ('lying', 1)), ('or', ('telling-truth', 3), ('telling-truth', 0)), ('telling-truth', 0))", "index": 265}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mia, Emily, Owen, Ella, Aurora, Ava, Olivia, and David. According to Mia, \"Owen is a knave and Ava is a knight\". As Emily put it, \"Ava is a knave if and only if David is a knave\". Owen asserted: \"Emily is a knight if and only if Olivia is a knave\". Ella commented, \"Olivia is a knight if and only if Ava is a knight\". Aurora commented, \"Emily is a knave\". Ava told you that If Ella is a knight then Aurora is a knight. Olivia expressed that If Owen is a knave then Mia is a knight. David remarked, \"Aurora is a knave or Emily is a knight\". So who is a knight and who is a knave?", "names": ["Mia", "Emily", "Owen", "Ella", "Aurora", "Ava", "Olivia", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true, true, false], "solution_text": "Mia is a knave, Emily is a knave, Owen is a knight, Ella is a knight, Aurora is a knight, Ava is a knight, Olivia is a knight, and David is a knave.", "solution_text_format": "(1) Mia is a knave\n(2) Emily is a knave\n(3) Owen is a knight\n(4) Ella is a knight\n(5) Aurora is a knight\n(6) Ava is a knight\n(7) Olivia is a knight\n(8) David is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Owen is a knave and Ava is a knight.", "Owen cannot be a knight, because this would contradict the claim of Mia that Owen is a knave and Ava is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Emily is a knight if and only if Olivia is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Ava is a knave if and only if David is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that If Ella is a knight then Aurora is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Ava is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that If Owen is a knave then Mia is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Emily is a knave.", "Aurora cannot be a knave, because this would contradict the claim of Ava that If Ella is a knight then Aurora is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the false claim of Owen that Emily is a knight if and only if Olivia is a knave.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Olivia is a knight if and only if Ava is a knight.", "Olivia cannot be a knight, because this would contradict the false claim of Ella that Olivia is a knight if and only if Ava is a knight.", "Olivia cannot be a knave, because this would contradict the false claim of Owen that Emily is a knight if and only if Olivia is a knave.", "We have exhausted all possibilities for Olivia and Ella, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the claim of Mia that Owen is a knave and Ava is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Ava is a knave if and only if David is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that If Ella is a knight then Aurora is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Ava is a knight.", "Olivia cannot be a knight, because this would contradict the false claim of Owen that Emily is a knight if and only if Olivia is a knave.", "Olivia cannot be a knave, because this would contradict the claim of Ella that Olivia is a knight if and only if Ava is a knight.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Olivia is a knight if and only if Ava is a knight.", "Olivia cannot be a knight, because this would contradict the false claim of Owen that Emily is a knight if and only if Olivia is a knave.", "Olivia cannot be a knave, because this would contradict the false claim of their own that If Owen is a knave then Mia is a knight.", "We have exhausted all possibilities for Olivia and Ella, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the claim of Mia that Owen is a knave and Ava is a knight.", "We have exhausted all possibilities for Ava, Emily, and Owen, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Owen is a knave and Ava is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Emily is a knight if and only if Olivia is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Ava is a knave if and only if David is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that If Ella is a knight then Aurora is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Ava is a knight.", "Olivia cannot be a knight, because this would contradict the claim of Owen that Emily is a knight if and only if Olivia is a knave.", "Olivia cannot be a knave, because this would contradict the claim of Ella that Olivia is a knight if and only if Ava is a knight.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Olivia is a knight if and only if Ava is a knight.", "Olivia cannot be a knight, because this would contradict the claim of Owen that Emily is a knight if and only if Olivia is a knave.", "Olivia cannot be a knave, because this would contradict the false claim of their own that If Owen is a knave then Mia is a knight.", "We have exhausted all possibilities for Olivia and Ella, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that If Ella is a knight then Aurora is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Ava is a knight.", "Olivia cannot be a knight, because this would contradict the claim of Owen that Emily is a knight if and only if Olivia is a knave.", "Olivia cannot be a knave, because this would contradict the false claim of their own that If Owen is a knave then Mia is a knight.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the false claim of Ava that If Ella is a knight then Aurora is a knight.", "We have exhausted all possibilities for Ella and Ava, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Ava is a knave if and only if David is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that If Ella is a knight then Aurora is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Ava is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that If Owen is a knave then Mia is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Emily is a knave.", "David cannot be a knight, because this would contradict the false claim of Emily that Ava is a knave if and only if David is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Aurora is a knave or Emily is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('telling-truth', 5)), ('<=>', ('lying', 5), ('lying', 7)), ('<=>', ('telling-truth', 1), ('lying', 6)), ('<=>', ('telling-truth', 6), ('telling-truth', 5)), ('lying', 1), ('->', ('telling-truth', 3), ('telling-truth', 4)), ('->', ('lying', 2), ('telling-truth', 0)), ('or', ('lying', 4), ('telling-truth', 1)))", "index": 266}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Evelyn, Aurora, Alexander, David, Oliver, Joseph, Mason, and Aria. Evelyn commented, \"Aurora is a knave or Alexander is a knight\". \"Oliver is a knight if and only if Evelyn is a knight,\" Aurora mentioned. Alexander expressed that Joseph is a knight and Aria is a knight. David noted, \"Aurora is not a knave\". Oliver noted, \"David is not a knight\". Joseph said, \"David is a knave and Mason is a knight.\" Mason asserted: \"If Aria is a knave then Joseph is a knave\". \"Aurora is a knight if and only if David is a knight,\" Aria declared. So who is a knight and who is a knave?", "names": ["Evelyn", "Aurora", "Alexander", "David", "Oliver", "Joseph", "Mason", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, false, true, true], "solution_text": "Evelyn is a knave, Aurora is a knight, Alexander is a knave, David is a knight, Oliver is a knave, Joseph is a knave, Mason is a knight, and Aria is a knight.", "solution_text_format": "(1) Evelyn is a knave\n(2) Aurora is a knight\n(3) Alexander is a knave\n(4) David is a knight\n(5) Oliver is a knave\n(6) Joseph is a knave\n(7) Mason is a knight\n(8) Aria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Aurora is a knave or Alexander is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Oliver is a knight if and only if Evelyn is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that David is not a knight.", "David cannot be a knight, because this would contradict the claim of Oliver that David is not a knight.", "David cannot be a knave, because this would contradict the false claim of their own that Aurora is not a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the claim of Aurora that Oliver is a knight if and only if Evelyn is a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Oliver is a knight if and only if Evelyn is a knight.", "Oliver cannot be a knight, because this would contradict the false claim of Aurora that Oliver is a knight if and only if Evelyn is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that David is not a knight.", "David cannot be a knight, because this would contradict the claim of their own that Aurora is not a knave.", "David cannot be a knave, because this would contradict the false claim of Oliver that David is not a knight.", "We have exhausted all possibilities for David, Oliver, and Aurora, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Aurora is a knave or Alexander is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Oliver is a knight if and only if Evelyn is a knight.", "Oliver cannot be a knight, because this would contradict the claim of Aurora that Oliver is a knight if and only if Evelyn is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that David is not a knight.", "Assume David is a knight. No contradiction is found in their claim that Aurora is not a knave.", "Alexander cannot be a knight, because this would contradict the false claim of Evelyn that Aurora is a knave or Alexander is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Joseph is a knight and Aria is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that David is a knave and Mason is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that David is a knave and Mason is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that If Aria is a knave then Joseph is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Aurora is a knight if and only if David is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('telling-truth', 2)), ('<=>', ('telling-truth', 4), ('telling-truth', 0)), ('and', ('telling-truth', 5), ('telling-truth', 7)), ('not', ('lying', 1)), ('not', ('telling-truth', 3)), ('and', ('lying', 3), ('telling-truth', 6)), ('->', ('lying', 7), ('lying', 5)), ('<=>', ('telling-truth', 1), ('telling-truth', 3)))", "index": 267}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sofia, Aria, Jackson, Ethan, James, Jacob, Logan, and Noah. Sofia commented, \"Logan is a knave and Jacob is a knave\". \"Jacob is not a knight\" - Aria. Jackson said that Sofia is a knight if and only if Noah is a knave. Ethan told you that James is not a knave. James remarked, \"If Jackson is a knight then Jacob is a knight\". Jacob remarked, \"James is a knave or Jackson is a knight\". \"Ethan is not a knave,\" Logan mentioned. Noah remarked, \"Logan is a knave\". So who is a knight and who is a knave?", "names": ["Sofia", "Aria", "Jackson", "Ethan", "James", "Jacob", "Logan", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false, true, false], "solution_text": "Sofia is a knave, Aria is a knight, Jackson is a knave, Ethan is a knight, James is a knight, Jacob is a knave, Logan is a knight, and Noah is a knave.", "solution_text_format": "(1) Sofia is a knave\n(2) Aria is a knight\n(3) Jackson is a knave\n(4) Ethan is a knight\n(5) James is a knight\n(6) Jacob is a knave\n(7) Logan is a knight\n(8) Noah is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Logan is a knave and Jacob is a knave.", "Logan cannot be a knight, because this would contradict the claim of Sofia that Logan is a knave and Jacob is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Ethan is not a knave.", "Ethan cannot be a knight, because this would contradict the false claim of Logan that Ethan is not a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that James is not a knave.", "James cannot be a knight, because this would contradict the false claim of Ethan that James is not a knave.", "Assume James is a knave. No contradiction is found in their false claim that If Jackson is a knight then Jacob is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Sofia is a knight if and only if Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of Jackson that Sofia is a knight if and only if Noah is a knave.", "Noah cannot be a knave, because this would contradict the false claim of their own that Logan is a knave.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Jackson.", "Jackson cannot be a knave, because this would contradict the false claim of James that If Jackson is a knight then Jacob is a knight.", "We have exhausted all possibilities for Jackson, James, Ethan, and Logan, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Logan is a knave and Jacob is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Ethan is not a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that James is not a knave.", "Assume James is a knight. No contradiction is found in their claim that If Jackson is a knight then Jacob is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Sofia is a knight if and only if Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of their own that Logan is a knave.", "Noah cannot be a knave, because this would contradict the claim of Jackson that Sofia is a knight if and only if Noah is a knave.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Sofia is a knight if and only if Noah is a knave.", "Noah cannot be a knight, because this would contradict the false claim of Jackson that Sofia is a knight if and only if Noah is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Logan is a knave.", "Jacob cannot be a knight, because this would contradict the claim of their own that James is a knave or Jackson is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that James is a knave or Jackson is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Jacob is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 6), ('lying', 5)), ('not', ('telling-truth', 5)), ('<=>', ('telling-truth', 0), ('lying', 7)), ('not', ('lying', 4)), ('->', ('telling-truth', 2), ('telling-truth', 5)), ('or', ('lying', 4), ('telling-truth', 2)), ('not', ('lying', 3)), ('lying', 6))", "index": 268}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Matthew, William, Ella, James, Michael, Ava, Samuel, and Grace. \"If Michael is a knave then Ava is a knave,\" Matthew declared. William stated, \"Michael is not a knight\". Ella remarked, \"Grace is a knight if and only if Ella is a knight\". James remarked, \"Grace is a knave or Ella is a knight\". Michael was heard saying, \"If Ava is a knight then Grace is a knave\". Ava commented, \"If Michael is a knight then Grace is a knight\". Samuel expressed that Grace is a knight and Ava is a knight. As Grace put it, \"Ella is a knight if and only if William is a knave\". So who is a knight and who is a knave?", "names": ["Matthew", "William", "Ella", "James", "Michael", "Ava", "Samuel", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, true, true, true], "solution_text": "Matthew is a knave, William is a knight, Ella is a knave, James is a knave, Michael is a knave, Ava is a knight, Samuel is a knight, and Grace is a knight.", "solution_text_format": "(1) Matthew is a knave\n(2) William is a knight\n(3) Ella is a knave\n(4) James is a knave\n(5) Michael is a knave\n(6) Ava is a knight\n(7) Samuel is a knight\n(8) Grace is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that If Michael is a knave then Ava is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that If Ava is a knight then Grace is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that If Michael is a knight then Grace is a knight.", "Grace cannot be a knight, because this would contradict the claim of Michael that If Ava is a knight then Grace is a knave.", "Grace cannot be a knave, because this would contradict the claim of Ava that If Michael is a knight then Grace is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that If Michael is a knight then Grace is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Ava that If Michael is a knight then Grace is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Ella is a knight if and only if William is a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Grace is a knight if and only if Ella is a knight.", "Ella cannot be a knave, because this would contradict the false claim of their own that Grace is a knight if and only if Ella is a knight.", "We have exhausted all possibilities for Ella, Grace, and Ava, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that If Ava is a knight then Grace is a knave.", "Ava cannot be a knight, because this would contradict the claim of Matthew that If Michael is a knave then Ava is a knave.", "Ava cannot be a knave, because this would contradict the false claim of Michael that If Ava is a knight then Grace is a knave.", "We have exhausted all possibilities for Ava and Michael, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that If Michael is a knave then Ava is a knave.", "Michael cannot be a knight, because this would contradict the false claim of Matthew that If Michael is a knave then Ava is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that If Ava is a knight then Grace is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that If Michael is a knight then Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Ella is a knight if and only if William is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Grace is a knight if and only if Ella is a knight.", "William cannot be a knight, because this would contradict the claim of Grace that Ella is a knight if and only if William is a knave.", "William cannot be a knave, because this would contradict the false claim of their own that Michael is not a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Grace is a knight if and only if Ella is a knight.", "Assume William is a knight. No contradiction is found in their claim that Michael is not a knight.", "James cannot be a knight, because this would contradict the claim of their own that Grace is a knave or Ella is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Grace is a knave or Ella is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Grace is a knight and Ava is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 4), ('lying', 5)), ('not', ('telling-truth', 4)), ('<=>', ('telling-truth', 7), ('telling-truth', 2)), ('or', ('lying', 7), ('telling-truth', 2)), ('->', ('telling-truth', 5), ('lying', 7)), ('->', ('telling-truth', 4), ('telling-truth', 7)), ('and', ('telling-truth', 7), ('telling-truth', 5)), ('<=>', ('telling-truth', 2), ('lying', 1)))", "index": 269}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jack, Alexander, David, Sofia, Penelope, Ella, Zoey, and Daniel. Jack told you that David is a knave if and only if Penelope is a knave. In Alexander's words: \"If David is a knave then Jack is a knave\". David remarked, \"Daniel is a knave or Penelope is a knight\". Sofia said that Jack is not a knight. Penelope said, \"Alexander is not a knight.\" Ella expressed that Ella is a knight and Penelope is a knight. Zoey said, \"If Sofia is a knight then Ella is a knight.\" Daniel was heard saying, \"Daniel is a knight\". So who is a knight and who is a knave?", "names": ["Jack", "Alexander", "David", "Sofia", "Penelope", "Ella", "Zoey", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false, false, false], "solution_text": "Jack is a knave, Alexander is a knight, David is a knight, Sofia is a knight, Penelope is a knave, Ella is a knave, Zoey is a knave, and Daniel is a knave.", "solution_text_format": "(1) Jack is a knave\n(2) Alexander is a knight\n(3) David is a knight\n(4) Sofia is a knight\n(5) Penelope is a knave\n(6) Ella is a knave\n(7) Zoey is a knave\n(8) Daniel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that David is a knave if and only if Penelope is a knave.", "Assume David is a knight. No contradiction is found in their claim that Daniel is a knave or Penelope is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Daniel is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of Penelope that Alexander is not a knight.", "Alexander cannot be a knave, because this would contradict the false claim of their own that If David is a knave then Jack is a knave.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the claim of Jack that David is a knave if and only if Penelope is a knave.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Daniel is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of Penelope that Alexander is not a knight.", "Alexander cannot be a knave, because this would contradict the false claim of their own that If David is a knave then Jack is a knave.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the claim of Jack that David is a knave if and only if Penelope is a knave.", "We have exhausted all possibilities for Penelope and Daniel, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Daniel is a knave or Penelope is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Daniel is a knight.", "Penelope cannot be a knight, because this would contradict the claim of Jack that David is a knave if and only if Penelope is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that If David is a knave then Jack is a knave.", "Alexander cannot be a knave, because this would contradict the false claim of Penelope that Alexander is not a knight.", "We have exhausted all possibilities for Alexander and Penelope, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the false claim of David that Daniel is a knave or Penelope is a knight.", "We have exhausted all possibilities for Daniel and David, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that David is a knave if and only if Penelope is a knave.", "Assume David is a knight. No contradiction is found in their claim that Daniel is a knave or Penelope is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Daniel is a knight.", "Penelope cannot be a knight, because this would contradict the false claim of Jack that David is a knave if and only if Penelope is a knave.", "Penelope cannot be a knave, because this would contradict the claim of David that Daniel is a knave or Penelope is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Daniel is a knight.", "Penelope cannot be a knight, because this would contradict the false claim of Jack that David is a knave if and only if Penelope is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Alexander is not a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that If David is a knave then Jack is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Jack is not a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Ella is a knight and Penelope is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Ella is a knight and Penelope is a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that If Sofia is a knight then Ella is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that If Sofia is a knight then Ella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('lying', 4)), ('->', ('lying', 2), ('lying', 0)), ('or', ('lying', 7), ('telling-truth', 4)), ('not', ('telling-truth', 0)), ('not', ('telling-truth', 1)), ('and', ('telling-truth', 5), ('telling-truth', 4)), ('->', ('telling-truth', 3), ('telling-truth', 5)), ('telling-truth', 7))", "index": 270}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Logan, Owen, Amelia, Aria, Victoria, James, Joseph, and Jacob. Logan asserted: \"If Aria is a knave then Amelia is a knave\". Owen remarked, \"Logan is a knight\". \"Owen is a knave or Joseph is a knave,\" Amelia mentioned. In a statement by Aria: \"Owen is a knight\". Victoria said that If Amelia is a knave then Victoria is a knight. James said, \"Aria is a knight and Amelia is a knave.\" Joseph asserted: \"James is a knave if and only if Aria is a knight\". Jacob remarked, \"Victoria is not a knight\". So who is a knight and who is a knave?", "names": ["Logan", "Owen", "Amelia", "Aria", "Victoria", "James", "Joseph", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, false, false, false], "solution_text": "Logan is a knave, Owen is a knave, Amelia is a knight, Aria is a knave, Victoria is a knight, James is a knave, Joseph is a knave, and Jacob is a knave.", "solution_text_format": "(1) Logan is a knave\n(2) Owen is a knave\n(3) Amelia is a knight\n(4) Aria is a knave\n(5) Victoria is a knight\n(6) James is a knave\n(7) Joseph is a knave\n(8) Jacob is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that If Aria is a knave then Amelia is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Owen is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Logan is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Owen is a knave or Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Amelia that Owen is a knave or Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that James is a knave if and only if Aria is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Aria is a knight and Amelia is a knave.", "James cannot be a knave, because this would contradict the false claim of Joseph that James is a knave if and only if Aria is a knight.", "We have exhausted all possibilities for James and Joseph, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Owen is a knave or Joseph is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that James is a knave if and only if Aria is a knight.", "James cannot be a knight, because this would contradict the claim of Joseph that James is a knave if and only if Aria is a knight.", "James cannot be a knave, because this would contradict the false claim of their own that Aria is a knight and Amelia is a knave.", "We have exhausted all possibilities for James, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the false claim of Amelia that Owen is a knave or Joseph is a knave.", "We have exhausted all possibilities for Joseph and Amelia, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the false claim of their own that Logan is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Owen is a knight.", "Owen cannot be a knight, because this would contradict the false claim of Aria that Owen is a knight.", "Owen cannot be a knave, because this would contradict the false claim of their own that Logan is a knight.", "We have exhausted all possibilities for Owen and Aria, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that If Aria is a knave then Amelia is a knave.", "Aria cannot be a knight, because this would contradict the false claim of Logan that If Aria is a knave then Amelia is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Owen is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Logan is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Logan is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Owen is a knave or Joseph is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that James is a knave if and only if Aria is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Aria is a knight and Amelia is a knave.", "James cannot be a knave, because this would contradict the claim of Joseph that James is a knave if and only if Aria is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that James is a knave if and only if Aria is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Aria is a knight and Amelia is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Aria is a knight and Amelia is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that If Amelia is a knave then Victoria is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Victoria is not a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Victoria is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('lying', 2)), ('telling-truth', 0), ('or', ('lying', 1), ('lying', 6)), ('telling-truth', 1), ('->', ('lying', 2), ('telling-truth', 4)), ('and', ('telling-truth', 3), ('lying', 2)), ('<=>', ('lying', 5), ('telling-truth', 3)), ('not', ('telling-truth', 4)))", "index": 271}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Charlotte, Alexander, Noah, Joseph, Amelia, Jackson, Avery, and Benjamin. Charlotte said that Joseph is a knave if and only if Charlotte is a knight. In a statement by Alexander: \"Jackson is not a knight\". In a statement by Noah: \"Charlotte is not a knave\". As Joseph put it, \"Alexander is a knight\". Amelia said that Avery is a knight and Noah is a knight. Jackson was heard saying, \"If Alexander is a knave then Charlotte is a knight\". \"Benjamin is a knave and Jackson is a knave,\" Avery declared. In Benjamin's words: \"Alexander is a knight and Noah is a knave\". So who is a knight and who is a knave?", "names": ["Charlotte", "Alexander", "Noah", "Joseph", "Amelia", "Jackson", "Avery", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true, false, false], "solution_text": "Charlotte is a knight, Alexander is a knave, Noah is a knight, Joseph is a knave, Amelia is a knave, Jackson is a knight, Avery is a knave, and Benjamin is a knave.", "solution_text_format": "(1) Charlotte is a knight\n(2) Alexander is a knave\n(3) Noah is a knight\n(4) Joseph is a knave\n(5) Amelia is a knave\n(6) Jackson is a knight\n(7) Avery is a knave\n(8) Benjamin is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that Joseph is a knave if and only if Charlotte is a knight.", "Joseph cannot be a knight, because this would contradict the claim of Charlotte that Joseph is a knave if and only if Charlotte is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Alexander is a knight.", "Alexander cannot be a knight, because this would contradict the false claim of Joseph that Alexander is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Jackson is not a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that If Alexander is a knave then Charlotte is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Charlotte is not a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Avery is a knight and Noah is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave and Jackson is a knave.", "Avery cannot be a knave, because this would contradict the claim of Amelia that Avery is a knight and Noah is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Avery is a knight and Noah is a knight.", "Avery cannot be a knight, because this would contradict the false claim of Amelia that Avery is a knight and Noah is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Benjamin is a knave and Jackson is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Alexander is a knight and Noah is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Alexander is a knight and Noah is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('telling-truth', 0)), ('not', ('telling-truth', 5)), ('not', ('lying', 0)), ('telling-truth', 1), ('and', ('telling-truth', 6), ('telling-truth', 2)), ('->', ('lying', 1), ('telling-truth', 0)), ('and', ('lying', 7), ('lying', 5)), ('and', ('telling-truth', 1), ('lying', 2)))", "index": 272}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Noah, Jacob, Sofia, Scarlett, Owen, Henry, Aiden, and Grace. In a statement by Noah: \"Henry is a knave\". Jacob expressed that Owen is not a knight. \"Sofia is a knight if and only if Aiden is a knight,\" Sofia declared. Scarlett stated, \"Grace is a knave if and only if Henry is a knave\". \"Grace is a knight or Noah is a knave\" - Owen. As Henry put it, \"If Owen is a knave then Sofia is a knight\". \"Sofia is not a knave,\" Aiden mentioned. \"Jacob is a knave or Jacob is a knight,\" Grace declared. So who is a knight and who is a knave?", "names": ["Noah", "Jacob", "Sofia", "Scarlett", "Owen", "Henry", "Aiden", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true, true, true], "solution_text": "Noah is a knave, Jacob is a knave, Sofia is a knight, Scarlett is a knight, Owen is a knight, Henry is a knight, Aiden is a knight, and Grace is a knight.", "solution_text_format": "(1) Noah is a knave\n(2) Jacob is a knave\n(3) Sofia is a knight\n(4) Scarlett is a knight\n(5) Owen is a knight\n(6) Henry is a knight\n(7) Aiden is a knight\n(8) Grace is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Noah is a knight. No contradiction is found in their claim that Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of Noah that Henry is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that If Owen is a knave then Sofia is a knight.", "Owen cannot be a knight, because this would contradict the false claim of Henry that If Owen is a knave then Sofia is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Grace is a knight or Noah is a knave.", "Grace cannot be a knight, because this would contradict the false claim of Owen that Grace is a knight or Noah is a knave.", "Grace cannot be a knave, because this would contradict the false claim of their own that Jacob is a knave or Jacob is a knight.", "We have exhausted all possibilities for Grace, Owen, and Henry, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Henry is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Owen is a knave then Sofia is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Grace is a knight or Noah is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Jacob is a knave or Jacob is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Owen is not a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Owen is not a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Sofia is a knight if and only if Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Sofia is not a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Grace is a knave if and only if Henry is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 5), ('not', ('telling-truth', 4)), ('<=>', ('telling-truth', 2), ('telling-truth', 6)), ('<=>', ('lying', 7), ('lying', 5)), ('or', ('telling-truth', 7), ('lying', 0)), ('->', ('lying', 4), ('telling-truth', 2)), ('not', ('lying', 2)), ('or', ('lying', 1), ('telling-truth', 1)))", "index": 273}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Avery, Ella, Lucas, Isabella, Emma, Emily, Luke, and Olivia. Avery stated, \"Isabella is a knight and Luke is a knave\". Ella commented, \"Avery is a knight or Isabella is a knave\". As Lucas put it, \"Ella is a knave and Isabella is a knave\". Isabella noted, \"Isabella is a knight and Emily is a knave\". According to Emma, \"Olivia is a knave\". \"If Avery is a knight then Isabella is a knight,\" Emily declared. Luke was heard saying, \"Isabella is a knave\". As Olivia put it, \"If Avery is a knight then Lucas is a knight\". So who is a knight and who is a knave?", "names": ["Avery", "Ella", "Lucas", "Isabella", "Emma", "Emily", "Luke", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, true, true, true], "solution_text": "Avery is a knave, Ella is a knight, Lucas is a knave, Isabella is a knave, Emma is a knave, Emily is a knight, Luke is a knight, and Olivia is a knight.", "solution_text_format": "(1) Avery is a knave\n(2) Ella is a knight\n(3) Lucas is a knave\n(4) Isabella is a knave\n(5) Emma is a knave\n(6) Emily is a knight\n(7) Luke is a knight\n(8) Olivia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Isabella is a knight and Luke is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Isabella is a knight and Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of Isabella that Isabella is a knight and Emily is a knave.", "Emily cannot be a knave, because this would contradict the false claim of their own that If Avery is a knight then Isabella is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the claim of Avery that Isabella is a knight and Luke is a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Isabella is a knight and Luke is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Isabella is a knight and Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of Isabella that Isabella is a knight and Emily is a knave.", "Emily cannot be a knave, because this would contradict the false claim of their own that If Avery is a knight then Isabella is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Isabella is a knight and Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that If Avery is a knight then Isabella is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Isabella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Avery is a knight or Isabella is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Ella is a knave and Isabella is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Ella is a knave and Isabella is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Emma that Olivia is a knave.", "Olivia cannot be a knave, because this would contradict the false claim of their own that If Avery is a knight then Lucas is a knight.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that If Avery is a knight then Lucas is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('lying', 6)), ('or', ('telling-truth', 0), ('lying', 3)), ('and', ('lying', 1), ('lying', 3)), ('and', ('telling-truth', 3), ('lying', 5)), ('lying', 7), ('->', ('telling-truth', 0), ('telling-truth', 3)), ('lying', 3), ('->', ('telling-truth', 0), ('telling-truth', 2)))", "index": 274}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Michael, Ava, Sebastian, Grace, Logan, Benjamin, William, and Isabella. Michael said, \"William is a knave or Ava is a knave.\" Ava expressed that Grace is a knave. Sebastian said, \"William is not a knave.\" Grace said that Sebastian is not a knave. As Logan put it, \"William is a knave and Sebastian is a knave\". Benjamin said, \"Sebastian is not a knave.\" \"William is a knight if and only if Logan is a knave,\" William claimed. Isabella commented, \"If Logan is a knave then Benjamin is a knight\". So who is a knight and who is a knave?", "names": ["Michael", "Ava", "Sebastian", "Grace", "Logan", "Benjamin", "William", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true, true, true], "solution_text": "Michael is a knight, Ava is a knave, Sebastian is a knight, Grace is a knight, Logan is a knave, Benjamin is a knight, William is a knight, and Isabella is a knight.", "solution_text_format": "(1) Michael is a knight\n(2) Ava is a knave\n(3) Sebastian is a knight\n(4) Grace is a knight\n(5) Logan is a knave\n(6) Benjamin is a knight\n(7) William is a knight\n(8) Isabella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that William is a knave or Ava is a knave.", "Assume William is a knight. No contradiction is found in their claim that William is a knight if and only if Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of their own that William is a knave and Sebastian is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that William is a knave and Sebastian is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that William is not a knave.", "Ava cannot be a knight, because this would contradict the claim of Michael that William is a knave or Ava is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Grace is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Sebastian is not a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Sebastian is not a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that If Logan is a knave then Benjamin is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 6), ('lying', 1)), ('lying', 3), ('not', ('lying', 6)), ('not', ('lying', 2)), ('and', ('lying', 6), ('lying', 2)), ('not', ('lying', 2)), ('<=>', ('telling-truth', 6), ('lying', 4)), ('->', ('lying', 4), ('telling-truth', 5)))", "index": 275}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sebastian, Henry, Joseph, Owen, Aiden, David, Avery, and Emily. \"Aiden is a knave or David is a knight,\" Sebastian mentioned. Henry was heard saying, \"Henry is a knight or Owen is a knight\". Joseph was heard saying, \"David is a knave if and only if Sebastian is a knave\". In Owen's words: \"David is a knight if and only if Emily is a knight\". Aiden remarked, \"Sebastian is not a knave\". According to David, \"Sebastian is a knave or David is a knight\". In Avery's words: \"Aiden is a knight or Sebastian is a knave\". \"David is a knave if and only if Avery is a knave\" - Emily. So who is a knight and who is a knave?", "names": ["Sebastian", "Henry", "Joseph", "Owen", "Aiden", "David", "Avery", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true, true, true], "solution_text": "Sebastian is a knight, Henry is a knight, Joseph is a knight, Owen is a knight, Aiden is a knight, David is a knight, Avery is a knight, and Emily is a knight.", "solution_text_format": "(1) Sebastian is a knight\n(2) Henry is a knight\n(3) Joseph is a knight\n(4) Owen is a knight\n(5) Aiden is a knight\n(6) David is a knight\n(7) Avery is a knight\n(8) Emily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that Aiden is a knave or David is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Sebastian is not a knave.", "Assume David is a knight. No contradiction is found in their claim that Sebastian is a knave or David is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Henry is a knight or Owen is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that David is a knight if and only if Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that David is a knave if and only if Avery is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Aiden is a knight or Sebastian is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that David is a knave if and only if Sebastian is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 4), ('telling-truth', 5)), ('or', ('telling-truth', 1), ('telling-truth', 3)), ('<=>', ('lying', 5), ('lying', 0)), ('<=>', ('telling-truth', 5), ('telling-truth', 7)), ('not', ('lying', 0)), ('or', ('lying', 0), ('telling-truth', 5)), ('or', ('telling-truth', 4), ('lying', 0)), ('<=>', ('lying', 5), ('lying', 6)))", "index": 276}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jack, Ava, Aiden, Sophia, Aria, Isabella, Daniel, and Logan. According to Jack, \"If Daniel is a knave then Aria is a knight\". In Ava's words: \"Ava is a knight or Aiden is a knight\". \"Jack is a knave or Isabella is a knight,\" Aiden declared. Sophia was heard saying, \"Aria is a knave or Daniel is a knave\". Aria noted, \"Aiden is a knave if and only if Ava is a knave\". Isabella asserted: \"If Logan is a knight then Daniel is a knave\". Daniel asserted: \"Jack is a knight or Logan is a knight\". Logan noted, \"Sophia is a knight or Aiden is a knight\". So who is a knight and who is a knave?", "names": ["Jack", "Ava", "Aiden", "Sophia", "Aria", "Isabella", "Daniel", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false, true, true], "solution_text": "Jack is a knight, Ava is a knight, Aiden is a knave, Sophia is a knight, Aria is a knave, Isabella is a knave, Daniel is a knight, and Logan is a knight.", "solution_text_format": "(1) Jack is a knight\n(2) Ava is a knight\n(3) Aiden is a knave\n(4) Sophia is a knight\n(5) Aria is a knave\n(6) Isabella is a knave\n(7) Daniel is a knight\n(8) Logan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that If Daniel is a knave then Aria is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Jack is a knight or Logan is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Sophia is a knight or Aiden is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Aria is a knave or Daniel is a knave.", "Aria cannot be a knight, because this would contradict the claim of Sophia that Aria is a knave or Daniel is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if Ava is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Jack is a knave or Isabella is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that If Logan is a knight then Daniel is a knave.", "Isabella cannot be a knave, because this would contradict the claim of Aiden that Jack is a knave or Isabella is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Jack is a knave or Isabella is a knight.", "Isabella cannot be a knight, because this would contradict the false claim of Aiden that Jack is a knave or Isabella is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that If Logan is a knight then Daniel is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Ava is a knight or Aiden is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 6), ('telling-truth', 4)), ('or', ('telling-truth', 1), ('telling-truth', 2)), ('or', ('lying', 0), ('telling-truth', 5)), ('or', ('lying', 4), ('lying', 6)), ('<=>', ('lying', 2), ('lying', 1)), ('->', ('telling-truth', 7), ('lying', 6)), ('or', ('telling-truth', 0), ('telling-truth', 7)), ('or', ('telling-truth', 3), ('telling-truth', 2)))", "index": 277}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: David, Aria, Logan, Matthew, Alexander, Owen, Benjamin, and Emily. In David's words: \"Benjamin is a knight or Matthew is a knight\". Aria remarked, \"Owen is a knave or Alexander is a knight\". \"David is not a knave,\" Logan declared. Matthew said, \"Aria is a knight and Benjamin is a knave.\" Alexander said, \"Benjamin is a knight and David is a knight.\" \"Benjamin is a knight and David is a knight,\" Owen declared. Benjamin asserted: \"Matthew is a knight if and only if Alexander is a knave\". Emily noted, \"If Matthew is a knave then Alexander is a knave\". So who is a knight and who is a knave?", "names": ["David", "Aria", "Logan", "Matthew", "Alexander", "Owen", "Benjamin", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true, true, false], "solution_text": "David is a knight, Aria is a knight, Logan is a knight, Matthew is a knave, Alexander is a knight, Owen is a knight, Benjamin is a knight, and Emily is a knave.", "solution_text_format": "(1) David is a knight\n(2) Aria is a knight\n(3) Logan is a knight\n(4) Matthew is a knave\n(5) Alexander is a knight\n(6) Owen is a knight\n(7) Benjamin is a knight\n(8) Emily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Benjamin is a knight or Matthew is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Matthew is a knight if and only if Alexander is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Aria is a knight and Benjamin is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Aria is a knight and Benjamin is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Owen is a knave or Alexander is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Benjamin is a knight and David is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Benjamin is a knight and David is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that David is not a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that If Matthew is a knave then Alexander is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that If Matthew is a knave then Alexander is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 6), ('telling-truth', 3)), ('or', ('lying', 5), ('telling-truth', 4)), ('not', ('lying', 0)), ('and', ('telling-truth', 1), ('lying', 6)), ('and', ('telling-truth', 6), ('telling-truth', 0)), ('and', ('telling-truth', 6), ('telling-truth', 0)), ('<=>', ('telling-truth', 3), ('lying', 4)), ('->', ('lying', 3), ('lying', 4)))", "index": 278}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mason, David, Avery, Isabella, Harper, Sophia, Oliver, and Joseph. Mason asserted: \"If David is a knight then Joseph is a knight\". As David put it, \"Sophia is a knave\". Avery expressed that Isabella is a knave and Joseph is a knave. Isabella asserted: \"If Sophia is a knave then David is a knight\". Harper said, \"David is not a knight.\" Sophia told you that Mason is a knave and Isabella is a knave. Oliver noted, \"If Sophia is a knight then Sophia is a knave\". \"Isabella is a knight or David is a knave,\" Joseph claimed. So who is a knight and who is a knave?", "names": ["Mason", "David", "Avery", "Isabella", "Harper", "Sophia", "Oliver", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false, true, true], "solution_text": "Mason is a knight, David is a knight, Avery is a knave, Isabella is a knight, Harper is a knave, Sophia is a knave, Oliver is a knight, and Joseph is a knight.", "solution_text_format": "(1) Mason is a knight\n(2) David is a knight\n(3) Avery is a knave\n(4) Isabella is a knight\n(5) Harper is a knave\n(6) Sophia is a knave\n(7) Oliver is a knight\n(8) Joseph is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that If David is a knight then Joseph is a knight.", "Assume David is a knight. No contradiction is found in their claim that Sophia is a knave.", "Sophia cannot be a knight, because this would contradict the claim of David that Sophia is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Mason is a knave and Isabella is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that If Sophia is a knave then David is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Isabella is a knight or David is a knave.", "Avery cannot be a knight, because this would contradict the claim of their own that Isabella is a knave and Joseph is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Isabella is a knave and Joseph is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that David is not a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that David is not a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that If Sophia is a knight then Sophia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 1), ('telling-truth', 7)), ('lying', 5), ('and', ('lying', 3), ('lying', 7)), ('->', ('lying', 5), ('telling-truth', 1)), ('not', ('telling-truth', 1)), ('and', ('lying', 0), ('lying', 3)), ('->', ('telling-truth', 5), ('lying', 5)), ('or', ('telling-truth', 3), ('lying', 1)))", "index": 279}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: James, David, Harper, Matthew, Luke, Daniel, Avery, and Sofia. \"Daniel is a knight,\" James declared. David told you that Sofia is a knave if and only if James is a knave. Harper remarked, \"Daniel is not a knight\". Matthew told you that If James is a knight then James is a knave. \"If Sofia is a knight then Avery is a knave,\" Luke claimed. Daniel expressed that Sofia is a knave. According to Avery, \"Harper is not a knight\". Sofia expressed that Luke is not a knight. So who is a knight and who is a knave?", "names": ["James", "David", "Harper", "Matthew", "Luke", "Daniel", "Avery", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true, true, false], "solution_text": "James is a knight, David is a knave, Harper is a knave, Matthew is a knave, Luke is a knight, Daniel is a knight, Avery is a knight, and Sofia is a knave.", "solution_text_format": "(1) James is a knight\n(2) David is a knave\n(3) Harper is a knave\n(4) Matthew is a knave\n(5) Luke is a knight\n(6) Daniel is a knight\n(7) Avery is a knight\n(8) Sofia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Daniel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Daniel that Sofia is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Luke is not a knight.", "Assume Luke is a knight. No contradiction is found in their claim that If Sofia is a knight then Avery is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Harper is not a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that Daniel is not a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Daniel is not a knight.", "David cannot be a knight, because this would contradict the claim of their own that Sofia is a knave if and only if James is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Sofia is a knave if and only if James is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that If James is a knight then James is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that If James is a knight then James is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 5), ('<=>', ('lying', 7), ('lying', 0)), ('not', ('telling-truth', 5)), ('->', ('telling-truth', 0), ('lying', 0)), ('->', ('telling-truth', 7), ('lying', 6)), ('lying', 7), ('not', ('telling-truth', 2)), ('not', ('telling-truth', 4)))", "index": 280}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ella, Jacob, Matthew, Emma, Emily, Harper, Lily, and Avery. Ella noted, \"Lily is a knight or Jacob is a knight\". Jacob commented, \"Emma is a knave or Harper is a knight\". Matthew asserted: \"Ella is a knight and Jacob is a knight\". As Emma put it, \"Lily is a knave if and only if Lily is a knight\". In Emily's words: \"Ella is not a knight\". \"Ella is not a knight\" - Harper. Lily was heard saying, \"If Emma is a knight then Emily is a knave\". Avery noted, \"Jacob is a knave\". So who is a knight and who is a knave?", "names": ["Ella", "Jacob", "Matthew", "Emma", "Emily", "Harper", "Lily", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false, true, false], "solution_text": "Ella is a knight, Jacob is a knight, Matthew is a knight, Emma is a knave, Emily is a knave, Harper is a knave, Lily is a knight, and Avery is a knave.", "solution_text_format": "(1) Ella is a knight\n(2) Jacob is a knight\n(3) Matthew is a knight\n(4) Emma is a knave\n(5) Emily is a knave\n(6) Harper is a knave\n(7) Lily is a knight\n(8) Avery is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Lily is a knight or Jacob is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that If Emma is a knight then Emily is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Lily is a knave if and only if Lily is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Lily is a knave if and only if Lily is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Ella is not a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Ella is not a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Emma is a knave or Harper is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that Ella is not a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Ella is not a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Ella is a knight and Jacob is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Jacob is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Jacob is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 6), ('telling-truth', 1)), ('or', ('lying', 3), ('telling-truth', 5)), ('and', ('telling-truth', 0), ('telling-truth', 1)), ('<=>', ('lying', 6), ('telling-truth', 6)), ('not', ('telling-truth', 0)), ('not', ('telling-truth', 0)), ('->', ('telling-truth', 3), ('lying', 4)), ('lying', 1))", "index": 281}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Scarlett, Penelope, Luke, Sophia, Chloe, Daniel, Joseph, and Alexander. Scarlett said, \"Scarlett is a knight and Chloe is a knave.\" Penelope told you that Alexander is a knight or Joseph is a knave. In Luke's words: \"Scarlett is a knight if and only if Sophia is a knight\". Sophia told you that Alexander is a knight and Luke is a knight. As Chloe put it, \"Scarlett is a knave or Scarlett is a knight\". In a statement by Daniel: \"If Daniel is a knight then Alexander is a knave\". Joseph stated, \"Sophia is a knight and Penelope is a knight\". Alexander remarked, \"Sophia is a knight or Luke is a knave\". So who is a knight and who is a knave?", "names": ["Scarlett", "Penelope", "Luke", "Sophia", "Chloe", "Daniel", "Joseph", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true, false, false], "solution_text": "Scarlett is a knave, Penelope is a knight, Luke is a knight, Sophia is a knave, Chloe is a knight, Daniel is a knight, Joseph is a knave, and Alexander is a knave.", "solution_text_format": "(1) Scarlett is a knave\n(2) Penelope is a knight\n(3) Luke is a knight\n(4) Sophia is a knave\n(5) Chloe is a knight\n(6) Daniel is a knight\n(7) Joseph is a knave\n(8) Alexander is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Scarlett is a knight and Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Scarlett that Scarlett is a knight and Chloe is a knave.", "Chloe cannot be a knave, because this would contradict the false claim of their own that Scarlett is a knave or Scarlett is a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Scarlett is a knight and Chloe is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Scarlett is a knave or Scarlett is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Alexander is a knight or Joseph is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Sophia is a knight or Luke is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Alexander is a knight and Luke is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight if and only if Sophia is a knight.", "Luke cannot be a knave, because this would contradict the claim of Sophia that Alexander is a knight and Luke is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Alexander is a knight and Luke is a knight.", "Luke cannot be a knight, because this would contradict the false claim of Sophia that Alexander is a knight and Luke is a knight.", "Luke cannot be a knave, because this would contradict the false claim of their own that Scarlett is a knight if and only if Sophia is a knight.", "We have exhausted all possibilities for Luke and Sophia, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Sophia is a knight or Luke is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that Alexander is a knight and Luke is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Alexander is a knight and Luke is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Scarlett is a knight if and only if Sophia is a knight.", "Joseph cannot be a knight, because this would contradict the claim of Penelope that Alexander is a knight or Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Sophia is a knight and Penelope is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that If Daniel is a knight then Alexander is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 0), ('lying', 4)), ('or', ('telling-truth', 7), ('lying', 6)), ('<=>', ('telling-truth', 0), ('telling-truth', 3)), ('and', ('telling-truth', 7), ('telling-truth', 2)), ('or', ('lying', 0), ('telling-truth', 0)), ('->', ('telling-truth', 5), ('lying', 7)), ('and', ('telling-truth', 3), ('telling-truth', 1)), ('or', ('telling-truth', 3), ('lying', 2)))", "index": 282}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mason, Avery, Mia, Noah, Daniel, Oliver, Joseph, and Ella. According to Mason, \"If Mia is a knight then Ella is a knave\". In Avery's words: \"Mason is a knave or Ella is a knight\". As Mia put it, \"Noah is a knight\". In Noah's words: \"Joseph is a knave and Noah is a knight\". Daniel expressed that If Joseph is a knave then Oliver is a knave. In Oliver's words: \"Ella is a knight\". Joseph commented, \"Daniel is a knight\". \"Mia is a knave if and only if Oliver is a knave,\" Ella claimed. So who is a knight and who is a knave?", "names": ["Mason", "Avery", "Mia", "Noah", "Daniel", "Oliver", "Joseph", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true, false, true], "solution_text": "Mason is a knave, Avery is a knight, Mia is a knight, Noah is a knight, Daniel is a knave, Oliver is a knight, Joseph is a knave, and Ella is a knight.", "solution_text_format": "(1) Mason is a knave\n(2) Avery is a knight\n(3) Mia is a knight\n(4) Noah is a knight\n(5) Daniel is a knave\n(6) Oliver is a knight\n(7) Joseph is a knave\n(8) Ella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that If Mia is a knight then Ella is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Noah is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Joseph is a knave and Noah is a knight.", "Joseph cannot be a knight, because this would contradict the claim of Noah that Joseph is a knave and Noah is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of Joseph that Daniel is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that If Joseph is a knave then Oliver is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Ella is a knight.", "Ella cannot be a knight, because this would contradict the claim of Mason that If Mia is a knight then Ella is a knave.", "Ella cannot be a knave, because this would contradict the claim of Oliver that Ella is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the false claim of Daniel that If Joseph is a knave then Oliver is a knave.", "We have exhausted all possibilities for Oliver, Daniel, and Joseph, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the claim of Mia that Noah is a knight.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Noah is a knight.", "Noah cannot be a knight, because this would contradict the false claim of Mia that Noah is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Joseph is a knave and Noah is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Daniel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that If Joseph is a knave then Oliver is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Ella is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Mia is a knave if and only if Oliver is a knave.", "Ella cannot be a knave, because this would contradict the claim of Oliver that Ella is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Ella is a knight.", "Ella cannot be a knight, because this would contradict the false claim of Oliver that Ella is a knight.", "Ella cannot be a knave, because this would contradict the false claim of their own that Mia is a knave if and only if Oliver is a knave.", "We have exhausted all possibilities for Ella and Oliver, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the false claim of their own that If Joseph is a knave then Oliver is a knave.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of Joseph that Daniel is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that If Joseph is a knave then Oliver is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Ella is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Mia is a knave if and only if Oliver is a knave.", "Ella cannot be a knave, because this would contradict the claim of Oliver that Ella is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the false claim of Daniel that If Joseph is a knave then Oliver is a knave.", "We have exhausted all possibilities for Oliver, Daniel, Joseph, Noah, and Mia, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that If Mia is a knight then Ella is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Noah is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Joseph is a knave and Noah is a knight.", "Joseph cannot be a knight, because this would contradict the claim of Noah that Joseph is a knave and Noah is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of Joseph that Daniel is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that If Joseph is a knave then Oliver is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Mia is a knave if and only if Oliver is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Mason is a knave or Ella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('lying', 7)), ('or', ('lying', 0), ('telling-truth', 7)), ('telling-truth', 3), ('and', ('lying', 6), ('telling-truth', 3)), ('->', ('lying', 6), ('lying', 5)), ('telling-truth', 7), ('telling-truth', 4), ('<=>', ('lying', 2), ('lying', 5)))", "index": 283}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ethan, Lucas, Alexander, Amelia, Logan, Mason, William, and Liam. Ethan said that Amelia is a knight if and only if Alexander is a knave. Lucas told you that Ethan is a knight or Mason is a knave. Alexander noted, \"Logan is a knight and Ethan is a knight\". Amelia noted, \"Mason is a knave and William is a knave\". \"Alexander is not a knight,\" Logan declared. Mason told you that Lucas is not a knight. William remarked, \"Mason is a knight or Logan is a knave\". In a statement by Liam: \"Ethan is a knight\". So who is a knight and who is a knave?", "names": ["Ethan", "Lucas", "Alexander", "Amelia", "Logan", "Mason", "William", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, true, true, false], "solution_text": "Ethan is a knave, Lucas is a knave, Alexander is a knave, Amelia is a knave, Logan is a knight, Mason is a knight, William is a knight, and Liam is a knave.", "solution_text_format": "(1) Ethan is a knave\n(2) Lucas is a knave\n(3) Alexander is a knave\n(4) Amelia is a knave\n(5) Logan is a knight\n(6) Mason is a knight\n(7) William is a knight\n(8) Liam is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Amelia is a knight if and only if Alexander is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Mason is a knave and William is a knave.", "Mason cannot be a knight, because this would contradict the claim of Amelia that Mason is a knave and William is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Lucas is not a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Ethan is a knight or Mason is a knave.", "William cannot be a knight, because this would contradict the claim of Amelia that Mason is a knave and William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Mason is a knight or Logan is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of Ethan that Amelia is a knight if and only if Alexander is a knave.", "Alexander cannot be a knave, because this would contradict the false claim of their own that Logan is a knight and Ethan is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the false claim of William that Mason is a knight or Logan is a knave.", "We have exhausted all possibilities for Logan and William, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the false claim of their own that Ethan is a knight or Mason is a knave.", "We have exhausted all possibilities for Lucas and Mason, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Mason is a knave and William is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Lucas is not a knight.", "Lucas cannot be a knight, because this would contradict the claim of Mason that Lucas is not a knight.", "Lucas cannot be a knave, because this would contradict the false claim of their own that Ethan is a knight or Mason is a knave.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Lucas is not a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Ethan is a knight or Mason is a knave.", "Assume William is a knight. No contradiction is found in their claim that Mason is a knight or Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of William that Mason is a knight or Logan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that Logan is a knight and Ethan is a knight.", "Alexander cannot be a knave, because this would contradict the claim of Ethan that Amelia is a knight if and only if Alexander is a knave.", "We have exhausted all possibilities for Alexander and Logan, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the false claim of Amelia that Mason is a knave and William is a knave.", "We have exhausted all possibilities for William, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the false claim of their own that Ethan is a knight or Mason is a knave.", "We have exhausted all possibilities for Lucas, Mason, and Amelia, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Amelia is a knight if and only if Alexander is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Mason is a knave and William is a knave.", "Mason cannot be a knight, because this would contradict the claim of Amelia that Mason is a knave and William is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Lucas is not a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Ethan is a knight or Mason is a knave.", "William cannot be a knight, because this would contradict the claim of Amelia that Mason is a knave and William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Mason is a knight or Logan is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that Logan is a knight and Ethan is a knight.", "Alexander cannot be a knave, because this would contradict the false claim of Ethan that Amelia is a knight if and only if Alexander is a knave.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the false claim of William that Mason is a knight or Logan is a knave.", "We have exhausted all possibilities for Logan and William, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the false claim of their own that Ethan is a knight or Mason is a knave.", "We have exhausted all possibilities for Lucas and Mason, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Mason is a knave and William is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Lucas is not a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Ethan is a knight or Mason is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Ethan is a knight or Mason is a knave.", "Assume William is a knight. No contradiction is found in their claim that Mason is a knight or Logan is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the false claim of Ethan that Amelia is a knight if and only if Alexander is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Logan is a knight and Ethan is a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that Ethan is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Ethan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 3), ('lying', 2)), ('or', ('telling-truth', 0), ('lying', 5)), ('and', ('telling-truth', 4), ('telling-truth', 0)), ('and', ('lying', 5), ('lying', 6)), ('not', ('telling-truth', 2)), ('not', ('telling-truth', 1)), ('or', ('telling-truth', 5), ('lying', 4)), ('telling-truth', 0))", "index": 284}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Isabella, Emma, Penelope, Alexander, Ethan, Logan, Harper, and Samuel. In Isabella's words: \"Ethan is a knight and Alexander is a knave\". Emma commented, \"Isabella is a knave\". Penelope asserted: \"Alexander is a knight and Harper is a knight\". Alexander was heard saying, \"Samuel is a knight if and only if Alexander is a knight\". Ethan noted, \"Logan is a knight if and only if Isabella is a knave\". Logan commented, \"Isabella is a knight\". In a statement by Harper: \"Alexander is a knave if and only if Ethan is a knight\". Samuel noted, \"Logan is a knight or Penelope is a knight\". So who is a knight and who is a knave?", "names": ["Isabella", "Emma", "Penelope", "Alexander", "Ethan", "Logan", "Harper", "Samuel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false, true, true], "solution_text": "Isabella is a knave, Emma is a knight, Penelope is a knight, Alexander is a knight, Ethan is a knave, Logan is a knave, Harper is a knight, and Samuel is a knight.", "solution_text_format": "(1) Isabella is a knave\n(2) Emma is a knight\n(3) Penelope is a knight\n(4) Alexander is a knight\n(5) Ethan is a knave\n(6) Logan is a knave\n(7) Harper is a knight\n(8) Samuel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Ethan is a knight and Alexander is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Logan is a knight if and only if Isabella is a knave.", "Logan cannot be a knight, because this would contradict the claim of Ethan that Logan is a knight if and only if Isabella is a knave.", "Logan cannot be a knave, because this would contradict the false claim of their own that Isabella is a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the claim of Isabella that Ethan is a knight and Alexander is a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Ethan is a knight and Alexander is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Logan is a knight if and only if Isabella is a knave.", "Logan cannot be a knight, because this would contradict the claim of their own that Isabella is a knight.", "Logan cannot be a knave, because this would contradict the claim of Ethan that Logan is a knight if and only if Isabella is a knave.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Logan is a knight if and only if Isabella is a knave.", "Logan cannot be a knight, because this would contradict the false claim of Ethan that Logan is a knight if and only if Isabella is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Isabella is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Samuel is a knight if and only if Alexander is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Logan is a knight or Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Alexander is a knight and Harper is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Alexander is a knave if and only if Ethan is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Isabella is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 4), ('lying', 3)), ('lying', 0), ('and', ('telling-truth', 3), ('telling-truth', 6)), ('<=>', ('telling-truth', 7), ('telling-truth', 3)), ('<=>', ('telling-truth', 5), ('lying', 0)), ('telling-truth', 0), ('<=>', ('lying', 3), ('telling-truth', 4)), ('or', ('telling-truth', 5), ('telling-truth', 2)))", "index": 285}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: David, Matthew, Logan, Scarlett, Olivia, Ava, Evelyn, and Benjamin. David told you that Logan is not a knave. Matthew told you that Scarlett is a knight if and only if David is a knave. According to Logan, \"Scarlett is not a knave\". Scarlett said that Evelyn is a knight or Ava is a knight. Olivia was heard saying, \"If Benjamin is a knave then Olivia is a knight\". \"David is a knight,\" Ava claimed. In a statement by Evelyn: \"Matthew is a knave if and only if Scarlett is a knave\". According to Benjamin, \"Logan is a knight and David is a knight\". So who is a knight and who is a knave?", "names": ["David", "Matthew", "Logan", "Scarlett", "Olivia", "Ava", "Evelyn", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true, false, true], "solution_text": "David is a knight, Matthew is a knave, Logan is a knight, Scarlett is a knight, Olivia is a knight, Ava is a knight, Evelyn is a knave, and Benjamin is a knight.", "solution_text_format": "(1) David is a knight\n(2) Matthew is a knave\n(3) Logan is a knight\n(4) Scarlett is a knight\n(5) Olivia is a knight\n(6) Ava is a knight\n(7) Evelyn is a knave\n(8) Benjamin is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Logan is not a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Evelyn is a knight or Ava is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Matthew is a knave if and only if Scarlett is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight if and only if David is a knave.", "Matthew cannot be a knave, because this would contradict the claim of Evelyn that Matthew is a knave if and only if Scarlett is a knave.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Matthew is a knave if and only if Scarlett is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight if and only if David is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Scarlett is a knight if and only if David is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that David is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that If Benjamin is a knave then Olivia is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Logan is a knight and David is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('<=>', ('telling-truth', 3), ('lying', 0)), ('not', ('lying', 3)), ('or', ('telling-truth', 6), ('telling-truth', 5)), ('->', ('lying', 7), ('telling-truth', 4)), ('telling-truth', 0), ('<=>', ('lying', 1), ('lying', 3)), ('and', ('telling-truth', 2), ('telling-truth', 0)))", "index": 286}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lucas, Jackson, Evelyn, Michael, Sebastian, Mia, Ava, and Lily. \"Mia is a knave,\" Lucas claimed. \"Lucas is a knave and Lucas is a knight,\" Jackson mentioned. \"Jackson is not a knight,\" Evelyn mentioned. Michael noted, \"Lucas is a knave or Michael is a knight\". According to Sebastian, \"Lily is a knight\". \"If Jackson is a knight then Mia is a knight,\" Mia mentioned. \"Lily is a knave or Lucas is a knight,\" Ava declared. \"If Evelyn is a knight then Jackson is a knight,\" Lily claimed. So who is a knight and who is a knave?", "names": ["Lucas", "Jackson", "Evelyn", "Michael", "Sebastian", "Mia", "Ava", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, true, true, false], "solution_text": "Lucas is a knave, Jackson is a knave, Evelyn is a knight, Michael is a knight, Sebastian is a knave, Mia is a knight, Ava is a knight, and Lily is a knave.", "solution_text_format": "(1) Lucas is a knave\n(2) Jackson is a knave\n(3) Evelyn is a knight\n(4) Michael is a knight\n(5) Sebastian is a knave\n(6) Mia is a knight\n(7) Ava is a knight\n(8) Lily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that Mia is a knave.", "Mia cannot be a knight, because this would contradict the claim of Lucas that Mia is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that If Jackson is a knight then Mia is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Lucas is a knave and Lucas is a knight.", "Jackson cannot be a knave, because this would contradict the false claim of Mia that If Jackson is a knight then Mia is a knight.", "We have exhausted all possibilities for Jackson and Mia, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Mia is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that If Jackson is a knight then Mia is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Lucas is a knave and Lucas is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Lucas is a knave and Lucas is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Jackson is not a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Lucas is a knave or Michael is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Lily is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that If Evelyn is a knight then Jackson is a knight.", "Lily cannot be a knave, because this would contradict the claim of Sebastian that Lily is a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Lily is a knight.", "Lily cannot be a knight, because this would contradict the false claim of Sebastian that Lily is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that If Evelyn is a knight then Jackson is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Lily is a knave or Lucas is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 5), ('and', ('lying', 0), ('telling-truth', 0)), ('not', ('telling-truth', 1)), ('or', ('lying', 0), ('telling-truth', 3)), ('telling-truth', 7), ('->', ('telling-truth', 1), ('telling-truth', 5)), ('or', ('lying', 7), ('telling-truth', 0)), ('->', ('telling-truth', 2), ('telling-truth', 1)))", "index": 287}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sofia, Noah, Scarlett, Jackson, Avery, Daniel, Abigail, and Grace. Sofia was heard saying, \"Sofia is a knight or Abigail is a knave\". Noah noted, \"Sofia is a knave if and only if Grace is a knave\". Scarlett said that Grace is a knave and Jackson is a knave. \"Sofia is not a knight,\" Jackson claimed. \"If Grace is a knave then Daniel is a knave,\" Avery declared. Daniel said that Scarlett is a knight. Abigail noted, \"Scarlett is a knight\". As Grace put it, \"Jackson is not a knave\". So who is a knight and who is a knave?", "names": ["Sofia", "Noah", "Scarlett", "Jackson", "Avery", "Daniel", "Abigail", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true, true, false], "solution_text": "Sofia is a knight, Noah is a knave, Scarlett is a knight, Jackson is a knave, Avery is a knave, Daniel is a knight, Abigail is a knight, and Grace is a knave.", "solution_text_format": "(1) Sofia is a knight\n(2) Noah is a knave\n(3) Scarlett is a knight\n(4) Jackson is a knave\n(5) Avery is a knave\n(6) Daniel is a knight\n(7) Abigail is a knight\n(8) Grace is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Sofia is a knight or Abigail is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Grace is a knave and Jackson is a knave.", "Grace cannot be a knight, because this would contradict the claim of Scarlett that Grace is a knave and Jackson is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Jackson is not a knave.", "Jackson cannot be a knight, because this would contradict the claim of Scarlett that Grace is a knave and Jackson is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Sofia is not a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that Sofia is a knave if and only if Grace is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Sofia is a knave if and only if Grace is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that If Grace is a knave then Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of Avery that If Grace is a knave then Daniel is a knave.", "Daniel cannot be a knave, because this would contradict the false claim of their own that Scarlett is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that If Grace is a knave then Daniel is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Scarlett is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 0), ('lying', 6)), ('<=>', ('lying', 0), ('lying', 7)), ('and', ('lying', 7), ('lying', 3)), ('not', ('telling-truth', 0)), ('->', ('lying', 7), ('lying', 5)), ('telling-truth', 2), ('telling-truth', 2), ('not', ('lying', 3)))", "index": 288}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Evelyn, Jacob, Alexander, Henry, Elizabeth, Aria, Lily, and Ethan. Evelyn expressed that Jacob is not a knight. In a statement by Jacob: \"Ethan is not a knave\". In a statement by Alexander: \"Jacob is a knight if and only if Jacob is a knave\". Henry expressed that Elizabeth is a knight. In Elizabeth's words: \"Evelyn is a knight if and only if Ethan is a knave\". Aria commented, \"Ethan is a knave\". \"Ethan is a knave if and only if Evelyn is a knave,\" Lily mentioned. In a statement by Ethan: \"If Lily is a knight then Alexander is a knight\". So who is a knight and who is a knave?", "names": ["Evelyn", "Jacob", "Alexander", "Henry", "Elizabeth", "Aria", "Lily", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false, false, true], "solution_text": "Evelyn is a knave, Jacob is a knight, Alexander is a knave, Henry is a knight, Elizabeth is a knight, Aria is a knave, Lily is a knave, and Ethan is a knight.", "solution_text_format": "(1) Evelyn is a knave\n(2) Jacob is a knight\n(3) Alexander is a knave\n(4) Henry is a knight\n(5) Elizabeth is a knight\n(6) Aria is a knave\n(7) Lily is a knave\n(8) Ethan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Jacob is not a knight.", "Jacob cannot be a knight, because this would contradict the claim of Evelyn that Jacob is not a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Ethan is not a knave.", "Ethan cannot be a knight, because this would contradict the false claim of Jacob that Ethan is not a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that If Lily is a knight then Alexander is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Ethan is a knave if and only if Evelyn is a knave.", "Lily cannot be a knave, because this would contradict the false claim of Ethan that If Lily is a knight then Alexander is a knight.", "We have exhausted all possibilities for Lily, Ethan, and Jacob, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Jacob is not a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Ethan is not a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that If Lily is a knight then Alexander is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Ethan is a knave if and only if Evelyn is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Ethan is a knave if and only if Evelyn is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that Jacob is a knight if and only if Jacob is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Jacob is a knight if and only if Jacob is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Evelyn is a knight if and only if Ethan is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Ethan is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Ethan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 1)), ('not', ('lying', 7)), ('<=>', ('telling-truth', 1), ('lying', 1)), ('telling-truth', 4), ('<=>', ('telling-truth', 0), ('lying', 7)), ('lying', 7), ('<=>', ('lying', 7), ('lying', 0)), ('->', ('telling-truth', 6), ('telling-truth', 2)))", "index": 289}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Matthew, Sebastian, Noah, Zoey, Elizabeth, Amelia, Lily, and Sofia. Matthew said that Amelia is a knight and Sofia is a knave. Sebastian said, \"Noah is a knave or Noah is a knight.\" Noah said, \"Amelia is a knight if and only if Sofia is a knave.\" In a statement by Zoey: \"Lily is a knave if and only if Sofia is a knight\". Elizabeth said, \"Sofia is a knight and Noah is a knight.\" \"Noah is a knave and Noah is a knight\" - Amelia. Lily remarked, \"Noah is a knave if and only if Zoey is a knight\". Sofia noted, \"Noah is a knave or Lily is a knave\". So who is a knight and who is a knave?", "names": ["Matthew", "Sebastian", "Noah", "Zoey", "Elizabeth", "Amelia", "Lily", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false, false, true], "solution_text": "Matthew is a knave, Sebastian is a knight, Noah is a knight, Zoey is a knight, Elizabeth is a knight, Amelia is a knave, Lily is a knave, and Sofia is a knight.", "solution_text_format": "(1) Matthew is a knave\n(2) Sebastian is a knight\n(3) Noah is a knight\n(4) Zoey is a knight\n(5) Elizabeth is a knight\n(6) Amelia is a knave\n(7) Lily is a knave\n(8) Sofia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that Amelia is a knight and Sofia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Noah is a knave and Noah is a knight.", "Amelia cannot be a knave, because this would contradict the claim of Matthew that Amelia is a knight and Sofia is a knave.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Amelia is a knight and Sofia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Noah is a knave and Noah is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Noah is a knave and Noah is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Amelia is a knight if and only if Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Noah is a knave or Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of Sofia that Noah is a knave or Lily is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Noah is a knave if and only if Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Lily is a knave if and only if Sofia is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Noah is a knave or Noah is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Sofia is a knight and Noah is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('lying', 7)), ('or', ('lying', 2), ('telling-truth', 2)), ('<=>', ('telling-truth', 5), ('lying', 7)), ('<=>', ('lying', 6), ('telling-truth', 7)), ('and', ('telling-truth', 7), ('telling-truth', 2)), ('and', ('lying', 2), ('telling-truth', 2)), ('<=>', ('lying', 2), ('telling-truth', 3)), ('or', ('lying', 2), ('lying', 6)))", "index": 290}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Benjamin, Sofia, Liam, David, Joseph, Oliver, Sophia, and Noah. In Benjamin's words: \"If Sophia is a knight then Noah is a knave\". Sofia said, \"David is not a knave.\" According to Liam, \"Joseph is a knave if and only if Noah is a knave\". \"Liam is a knight\" - David. Joseph commented, \"Benjamin is not a knight\". In Oliver's words: \"Joseph is a knave or Liam is a knave\". Sophia expressed that Oliver is a knave and Sofia is a knave. Noah stated, \"Oliver is a knave\". So who is a knight and who is a knave?", "names": ["Benjamin", "Sofia", "Liam", "David", "Joseph", "Oliver", "Sophia", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true, false, false], "solution_text": "Benjamin is a knight, Sofia is a knight, Liam is a knight, David is a knight, Joseph is a knave, Oliver is a knight, Sophia is a knave, and Noah is a knave.", "solution_text_format": "(1) Benjamin is a knight\n(2) Sofia is a knight\n(3) Liam is a knight\n(4) David is a knight\n(5) Joseph is a knave\n(6) Oliver is a knight\n(7) Sophia is a knave\n(8) Noah is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that If Sophia is a knight then Noah is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Oliver is a knave and Sofia is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Sophia that Oliver is a knave and Sofia is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Joseph is a knave or Liam is a knave.", "Joseph cannot be a knight, because this would contradict the claim of their own that Benjamin is not a knight.", "Joseph cannot be a knave, because this would contradict the false claim of Oliver that Joseph is a knave or Liam is a knave.", "We have exhausted all possibilities for Joseph and Oliver, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Oliver is a knave and Sofia is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Joseph is a knave or Liam is a knave.", "Joseph cannot be a knight, because this would contradict the claim of their own that Benjamin is not a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Benjamin is not a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Joseph is a knave if and only if Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of Liam that Joseph is a knave if and only if Noah is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Oliver is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that David is not a knave.", "Assume David is a knight. No contradiction is found in their claim that Liam is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 6), ('lying', 7)), ('not', ('lying', 3)), ('<=>', ('lying', 4), ('lying', 7)), ('telling-truth', 2), ('not', ('telling-truth', 0)), ('or', ('lying', 4), ('lying', 2)), ('and', ('lying', 5), ('lying', 1)), ('lying', 5))", "index": 291}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lily, Noah, Evelyn, Lucas, Victoria, Chloe, Mason, and Avery. As Lily put it, \"Chloe is a knave or Chloe is a knight\". \"Victoria is not a knave,\" Noah claimed. Evelyn noted, \"Mason is not a knave\". Lucas was heard saying, \"Chloe is a knave and Mason is a knight\". \"Evelyn is a knave if and only if Lily is a knight,\" Victoria declared. Chloe commented, \"Evelyn is a knight and Noah is a knight\". As Mason put it, \"Avery is a knight and Mason is a knight\". \"Mason is a knight and Evelyn is a knave,\" Avery claimed. So who is a knight and who is a knave?", "names": ["Lily", "Noah", "Evelyn", "Lucas", "Victoria", "Chloe", "Mason", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, false, false, false], "solution_text": "Lily is a knight, Noah is a knight, Evelyn is a knave, Lucas is a knave, Victoria is a knight, Chloe is a knave, Mason is a knave, and Avery is a knave.", "solution_text_format": "(1) Lily is a knight\n(2) Noah is a knight\n(3) Evelyn is a knave\n(4) Lucas is a knave\n(5) Victoria is a knight\n(6) Chloe is a knave\n(7) Mason is a knave\n(8) Avery is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that Chloe is a knave or Chloe is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Evelyn is a knight and Noah is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Mason is not a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Avery is a knight and Mason is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Mason is a knight and Evelyn is a knave.", "Avery cannot be a knave, because this would contradict the claim of Mason that Avery is a knight and Mason is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Mason.", "Mason cannot be a knave, because this would contradict the claim of Evelyn that Mason is not a knave.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the claim of Chloe that Evelyn is a knight and Noah is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Evelyn is a knight and Noah is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Mason is not a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Avery is a knight and Mason is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Mason is a knight and Evelyn is a knave.", "Avery cannot be a knave, because this would contradict the claim of Mason that Avery is a knight and Mason is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Mason.", "Mason cannot be a knave, because this would contradict the claim of Evelyn that Mason is not a knave.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Mason is not a knave.", "Mason cannot be a knight, because this would contradict the false claim of Evelyn that Mason is not a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Avery is a knight and Mason is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Mason is a knight and Evelyn is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Mason is a knight and Evelyn is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Victoria is not a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Evelyn is a knave if and only if Lily is a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Chloe is a knave and Mason is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Chloe is a knave and Mason is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 5), ('telling-truth', 5)), ('not', ('lying', 4)), ('not', ('lying', 6)), ('and', ('lying', 5), ('telling-truth', 6)), ('<=>', ('lying', 2), ('telling-truth', 0)), ('and', ('telling-truth', 2), ('telling-truth', 1)), ('and', ('telling-truth', 7), ('telling-truth', 6)), ('and', ('telling-truth', 6), ('lying', 2)))", "index": 292}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Isabella, Sophia, Abigail, Aria, Emma, Daniel, Scarlett, and Owen. Isabella commented, \"Sophia is a knight or Aria is a knave\". Sophia said that Abigail is a knight and Emma is a knave. Abigail said that Scarlett is a knave if and only if Aria is a knave. Aria asserted: \"If Scarlett is a knight then Sophia is a knave\". Emma commented, \"Owen is a knight and Isabella is a knave\". In a statement by Daniel: \"Isabella is a knave\". Scarlett was heard saying, \"Aria is a knight or Sophia is a knight\". Owen was heard saying, \"Scarlett is a knight and Aria is a knight\". So who is a knight and who is a knave?", "names": ["Isabella", "Sophia", "Abigail", "Aria", "Emma", "Daniel", "Scarlett", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true, true, true], "solution_text": "Isabella is a knave, Sophia is a knave, Abigail is a knight, Aria is a knight, Emma is a knight, Daniel is a knight, Scarlett is a knight, and Owen is a knight.", "solution_text_format": "(1) Isabella is a knave\n(2) Sophia is a knave\n(3) Abigail is a knight\n(4) Aria is a knight\n(5) Emma is a knight\n(6) Daniel is a knight\n(7) Scarlett is a knight\n(8) Owen is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Sophia is a knight or Aria is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Abigail is a knight and Emma is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Scarlett is a knave if and only if Aria is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Aria is a knight or Sophia is a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that If Scarlett is a knight then Sophia is a knave.", "Aria cannot be a knave, because this would contradict the claim of Abigail that Scarlett is a knave if and only if Aria is a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the false claim of their own that Aria is a knight or Sophia is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the claim of Sophia that Abigail is a knight and Emma is a knave.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Abigail is a knight and Emma is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Scarlett is a knave if and only if Aria is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Aria is a knight or Sophia is a knight.", "Aria cannot be a knight, because this would contradict the claim of Isabella that Sophia is a knight or Aria is a knave.", "Aria cannot be a knave, because this would contradict the claim of Abigail that Scarlett is a knave if and only if Aria is a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Aria is a knight or Sophia is a knight.", "Aria cannot be a knight, because this would contradict the claim of Isabella that Sophia is a knight or Aria is a knave.", "Aria cannot be a knave, because this would contradict the false claim of their own that If Scarlett is a knight then Sophia is a knave.", "We have exhausted all possibilities for Aria and Scarlett, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Scarlett is a knave if and only if Aria is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Aria is a knight or Sophia is a knight.", "Aria cannot be a knight, because this would contradict the claim of Isabella that Sophia is a knight or Aria is a knave.", "Aria cannot be a knave, because this would contradict the false claim of their own that If Scarlett is a knight then Sophia is a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Aria is a knight or Sophia is a knight.", "Aria cannot be a knight, because this would contradict the claim of Isabella that Sophia is a knight or Aria is a knave.", "Aria cannot be a knave, because this would contradict the false claim of Abigail that Scarlett is a knave if and only if Aria is a knave.", "We have exhausted all possibilities for Aria, Scarlett, Abigail, and Sophia, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Sophia is a knight or Aria is a knave.", "Sophia cannot be a knight, because this would contradict the false claim of Isabella that Sophia is a knight or Aria is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Abigail is a knight and Emma is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Scarlett is a knave if and only if Aria is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Aria is a knight or Sophia is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that If Scarlett is a knight then Sophia is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Owen is a knight and Isabella is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Scarlett is a knight and Aria is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Isabella is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('lying', 3)), ('and', ('telling-truth', 2), ('lying', 4)), ('<=>', ('lying', 6), ('lying', 3)), ('->', ('telling-truth', 6), ('lying', 1)), ('and', ('telling-truth', 7), ('lying', 0)), ('lying', 0), ('or', ('telling-truth', 3), ('telling-truth', 1)), ('and', ('telling-truth', 6), ('telling-truth', 3)))", "index": 293}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lily, Joseph, Jackson, Jacob, Sofia, Aiden, Ethan, and David. Lily said that Jackson is a knight. \"Jackson is not a knave,\" Joseph claimed. Jackson commented, \"Ethan is a knight or Ethan is a knave\". \"Sofia is a knave and Aiden is a knight,\" Jacob claimed. Sofia noted, \"Joseph is a knight\". Aiden said that Jackson is a knave and Jackson is a knight. In Ethan's words: \"Lily is a knave or Aiden is a knight\". \"Aiden is a knave and Aiden is a knight,\" David mentioned. So who is a knight and who is a knave?", "names": ["Lily", "Joseph", "Jackson", "Jacob", "Sofia", "Aiden", "Ethan", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false, false, false], "solution_text": "Lily is a knight, Joseph is a knight, Jackson is a knight, Jacob is a knave, Sofia is a knight, Aiden is a knave, Ethan is a knave, and David is a knave.", "solution_text_format": "(1) Lily is a knight\n(2) Joseph is a knight\n(3) Jackson is a knight\n(4) Jacob is a knave\n(5) Sofia is a knight\n(6) Aiden is a knave\n(7) Ethan is a knave\n(8) David is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that Jackson is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Ethan is a knight or Ethan is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Lily is a knave or Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Jackson is a knave and Jackson is a knight.", "Aiden cannot be a knave, because this would contradict the claim of Ethan that Lily is a knave or Aiden is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Lily is a knave or Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Jackson is a knave and Jackson is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Jackson is a knave and Jackson is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Jackson is not a knave.", "Jacob cannot be a knight, because this would contradict the claim of their own that Sofia is a knave and Aiden is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Sofia is a knave and Aiden is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Joseph is a knight.", "David cannot be a knight, because this would contradict the claim of their own that Aiden is a knave and Aiden is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Aiden is a knave and Aiden is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('not', ('lying', 2)), ('or', ('telling-truth', 6), ('lying', 6)), ('and', ('lying', 4), ('telling-truth', 5)), ('telling-truth', 1), ('and', ('lying', 2), ('telling-truth', 2)), ('or', ('lying', 0), ('telling-truth', 5)), ('and', ('lying', 5), ('telling-truth', 5)))", "index": 294}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mia, Michael, Avery, Abigail, Lucas, Charlotte, Harper, and Alexander. \"If Mia is a knight then Alexander is a knight,\" Mia claimed. Michael said that Abigail is a knave and Harper is a knight. In Avery's words: \"Lucas is a knave if and only if Michael is a knight\". \"Michael is a knave,\" Abigail mentioned. Lucas expressed that Charlotte is not a knight. In a statement by Charlotte: \"Harper is a knight or Michael is a knave\". \"Abigail is not a knave,\" Harper mentioned. Alexander stated, \"Lucas is a knave and Charlotte is a knight\". So who is a knight and who is a knave?", "names": ["Mia", "Michael", "Avery", "Abigail", "Lucas", "Charlotte", "Harper", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, true, true, true], "solution_text": "Mia is a knight, Michael is a knave, Avery is a knave, Abigail is a knight, Lucas is a knave, Charlotte is a knight, Harper is a knight, and Alexander is a knight.", "solution_text_format": "(1) Mia is a knight\n(2) Michael is a knave\n(3) Avery is a knave\n(4) Abigail is a knight\n(5) Lucas is a knave\n(6) Charlotte is a knight\n(7) Harper is a knight\n(8) Alexander is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that If Mia is a knight then Alexander is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Lucas is a knave and Charlotte is a knight.", "Lucas cannot be a knight, because this would contradict the claim of Alexander that Lucas is a knave and Charlotte is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Charlotte is not a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Harper is a knight or Michael is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Abigail is not a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Abigail is a knave and Harper is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Abigail is a knave and Harper is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Lucas is a knave if and only if Michael is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Lucas is a knave if and only if Michael is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 0), ('telling-truth', 7)), ('and', ('lying', 3), ('telling-truth', 6)), ('<=>', ('lying', 4), ('telling-truth', 1)), ('lying', 1), ('not', ('telling-truth', 5)), ('or', ('telling-truth', 6), ('lying', 1)), ('not', ('lying', 3)), ('and', ('lying', 4), ('telling-truth', 5)))", "index": 295}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ella, Lucas, Benjamin, Chloe, Michael, Jacob, Emma, and Joseph. Ella told you that Michael is a knight. Lucas stated, \"Michael is a knave or Emma is a knight\". Benjamin was heard saying, \"Ella is a knave if and only if Jacob is a knave\". \"Joseph is a knight if and only if Michael is a knave,\" Chloe declared. Michael expressed that If Jacob is a knight then Chloe is a knight. In a statement by Jacob: \"Chloe is a knave and Lucas is a knave\". Emma was heard saying, \"Chloe is not a knight\". \"If Emma is a knight then Michael is a knight,\" Joseph claimed. So who is a knight and who is a knave?", "names": ["Ella", "Lucas", "Benjamin", "Chloe", "Michael", "Jacob", "Emma", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, false, true, true], "solution_text": "Ella is a knight, Lucas is a knight, Benjamin is a knave, Chloe is a knave, Michael is a knight, Jacob is a knave, Emma is a knight, and Joseph is a knight.", "solution_text_format": "(1) Ella is a knight\n(2) Lucas is a knight\n(3) Benjamin is a knave\n(4) Chloe is a knave\n(5) Michael is a knight\n(6) Jacob is a knave\n(7) Emma is a knight\n(8) Joseph is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Michael is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that If Jacob is a knight then Chloe is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Chloe is a knave and Lucas is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Jacob that Chloe is a knave and Lucas is a knave.", "Chloe cannot be a knave, because this would contradict the claim of Michael that If Jacob is a knight then Chloe is a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Chloe is a knave and Lucas is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Joseph is a knight if and only if Michael is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Chloe that Joseph is a knight if and only if Michael is a knave.", "Joseph cannot be a knave, because this would contradict the false claim of their own that If Emma is a knight then Michael is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Joseph is a knight if and only if Michael is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that If Emma is a knight then Michael is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Chloe is not a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Michael is a knave or Emma is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Ella is a knave if and only if Jacob is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Ella is a knave if and only if Jacob is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('or', ('lying', 4), ('telling-truth', 6)), ('<=>', ('lying', 0), ('lying', 5)), ('<=>', ('telling-truth', 7), ('lying', 4)), ('->', ('telling-truth', 5), ('telling-truth', 3)), ('and', ('lying', 3), ('lying', 1)), ('not', ('telling-truth', 3)), ('->', ('telling-truth', 6), ('telling-truth', 4)))", "index": 296}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emma, Ava, Sofia, Lucas, Aria, Penelope, Aiden, and Joseph. \"Aiden is a knight,\" Emma declared. In Ava's words: \"Penelope is a knave if and only if Emma is a knight\". Sofia noted, \"Ava is a knight and Penelope is a knave\". In a statement by Lucas: \"Sofia is not a knight\". Aria said that If Aiden is a knave then Lucas is a knight. \"Aria is a knave,\" Penelope mentioned. \"If Emma is a knave then Penelope is a knave,\" Aiden claimed. \"Ava is a knave and Sofia is a knight,\" Joseph claimed. So who is a knight and who is a knave?", "names": ["Emma", "Ava", "Sofia", "Lucas", "Aria", "Penelope", "Aiden", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false, true, false], "solution_text": "Emma is a knight, Ava is a knight, Sofia is a knight, Lucas is a knave, Aria is a knight, Penelope is a knave, Aiden is a knight, and Joseph is a knave.", "solution_text_format": "(1) Emma is a knight\n(2) Ava is a knight\n(3) Sofia is a knight\n(4) Lucas is a knave\n(5) Aria is a knight\n(6) Penelope is a knave\n(7) Aiden is a knight\n(8) Joseph is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that If Emma is a knave then Penelope is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of Penelope that Aria is a knave.", "Aria cannot be a knave, because this would contradict the false claim of their own that If Aiden is a knave then Lucas is a knight.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Aria is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that If Aiden is a knave then Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Sofia is not a knight.", "Sofia cannot be a knight, because this would contradict the claim of Lucas that Sofia is not a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Ava is a knight and Penelope is a knave.", "Ava cannot be a knight, because this would contradict the false claim of Sofia that Ava is a knight and Penelope is a knave.", "Ava cannot be a knave, because this would contradict the false claim of their own that Penelope is a knave if and only if Emma is a knight.", "We have exhausted all possibilities for Ava and Sofia, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Sofia is not a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Ava is a knight and Penelope is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Penelope is a knave if and only if Emma is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Ava is a knave and Sofia is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Ava is a knave and Sofia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 6), ('<=>', ('lying', 5), ('telling-truth', 0)), ('and', ('telling-truth', 1), ('lying', 5)), ('not', ('telling-truth', 2)), ('->', ('lying', 6), ('telling-truth', 3)), ('lying', 4), ('->', ('lying', 0), ('lying', 5)), ('and', ('lying', 1), ('telling-truth', 2)))", "index": 297}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Luke, Aria, Emma, Liam, Sophia, Grace, Aiden, and Oliver. According to Luke, \"If Sophia is a knight then Emma is a knight\". Aria said that Aiden is a knave and Liam is a knight. Emma asserted: \"Luke is not a knave\". \"Aria is a knave or Sophia is a knight,\" Liam mentioned. According to Sophia, \"Liam is a knight if and only if Oliver is a knave\". In a statement by Grace: \"Grace is a knight and Oliver is a knave\". Aiden noted, \"Liam is a knight or Grace is a knave\". Oliver was heard saying, \"Liam is a knight or Luke is a knight\". So who is a knight and who is a knave?", "names": ["Luke", "Aria", "Emma", "Liam", "Sophia", "Grace", "Aiden", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, false, true, true], "solution_text": "Luke is a knight, Aria is a knave, Emma is a knight, Liam is a knight, Sophia is a knave, Grace is a knave, Aiden is a knight, and Oliver is a knight.", "solution_text_format": "(1) Luke is a knight\n(2) Aria is a knave\n(3) Emma is a knight\n(4) Liam is a knight\n(5) Sophia is a knave\n(6) Grace is a knave\n(7) Aiden is a knight\n(8) Oliver is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that If Sophia is a knight then Emma is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Liam is a knight if and only if Oliver is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Aria is a knave or Sophia is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Aiden is a knave and Liam is a knight.", "Aiden cannot be a knight, because this would contradict the claim of Aria that Aiden is a knave and Liam is a knight.", "Aiden cannot be a knave, because this would contradict the false claim of their own that Liam is a knight or Grace is a knave.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Aiden is a knave and Liam is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Liam is a knight or Grace is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Grace is a knight and Oliver is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Sophia that Liam is a knight if and only if Oliver is a knave.", "Oliver cannot be a knave, because this would contradict the false claim of their own that Liam is a knight or Luke is a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Grace is a knight and Oliver is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Sophia that Liam is a knight if and only if Oliver is a knave.", "Oliver cannot be a knave, because this would contradict the false claim of their own that Liam is a knight or Luke is a knight.", "We have exhausted all possibilities for Oliver and Grace, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the false claim of Aria that Aiden is a knave and Liam is a knight.", "We have exhausted all possibilities for Aiden and Aria, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the false claim of their own that Aria is a knave or Sophia is a knight.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Liam is a knight if and only if Oliver is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Aria is a knave or Sophia is a knight.", "Aria cannot be a knight, because this would contradict the claim of Liam that Aria is a knave or Sophia is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Aiden is a knave and Liam is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Liam is a knight or Grace is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Grace is a knight and Oliver is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Grace that Grace is a knight and Oliver is a knave.", "Oliver cannot be a knave, because this would contradict the false claim of Sophia that Liam is a knight if and only if Oliver is a knave.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Grace is a knight and Oliver is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Liam is a knight or Luke is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Luke is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 4), ('telling-truth', 2)), ('and', ('lying', 6), ('telling-truth', 3)), ('not', ('lying', 0)), ('or', ('lying', 1), ('telling-truth', 4)), ('<=>', ('telling-truth', 3), ('lying', 7)), ('and', ('telling-truth', 5), ('lying', 7)), ('or', ('telling-truth', 3), ('lying', 5)), ('or', ('telling-truth', 3), ('telling-truth', 0)))", "index": 298}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Olivia, James, Joseph, Samuel, Sophia, Ethan, Emily, and Jackson. In a statement by Olivia: \"Emily is not a knave\". James asserted: \"Emily is a knight and Samuel is a knight\". Joseph expressed that Samuel is a knight or Emily is a knave. Samuel was heard saying, \"James is a knave\". Sophia was heard saying, \"Olivia is a knave and Emily is a knave\". Ethan said that Emily is a knave if and only if Samuel is a knave. Emily expressed that Joseph is a knave and Samuel is a knight. According to Jackson, \"If Jackson is a knight then Joseph is a knight\". So who is a knight and who is a knave?", "names": ["Olivia", "James", "Joseph", "Samuel", "Sophia", "Ethan", "Emily", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false, false, true], "solution_text": "Olivia is a knave, James is a knave, Joseph is a knight, Samuel is a knight, Sophia is a knight, Ethan is a knave, Emily is a knave, and Jackson is a knight.", "solution_text_format": "(1) Olivia is a knave\n(2) James is a knave\n(3) Joseph is a knight\n(4) Samuel is a knight\n(5) Sophia is a knight\n(6) Ethan is a knave\n(7) Emily is a knave\n(8) Jackson is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Emily is not a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Joseph is a knave and Samuel is a knight.", "Joseph cannot be a knight, because this would contradict the claim of Emily that Joseph is a knave and Samuel is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Samuel is a knight or Emily is a knave.", "Samuel cannot be a knight, because this would contradict the false claim of Joseph that Samuel is a knight or Emily is a knave.", "Samuel cannot be a knave, because this would contradict the claim of Emily that Joseph is a knave and Samuel is a knight.", "We have exhausted all possibilities for Samuel and Joseph, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the claim of Olivia that Emily is not a knave.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Emily is not a knave.", "Emily cannot be a knight, because this would contradict the false claim of Olivia that Emily is not a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Joseph is a knave and Samuel is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Samuel is a knight or Emily is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that James is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Emily is a knight and Samuel is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Emily is a knight and Samuel is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Olivia is a knave and Emily is a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Emily is a knave if and only if Samuel is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Emily is a knave if and only if Samuel is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that If Jackson is a knight then Joseph is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 6)), ('and', ('telling-truth', 6), ('telling-truth', 3)), ('or', ('telling-truth', 3), ('lying', 6)), ('lying', 1), ('and', ('lying', 0), ('lying', 6)), ('<=>', ('lying', 6), ('lying', 3)), ('and', ('lying', 2), ('telling-truth', 3)), ('->', ('telling-truth', 7), ('telling-truth', 2)))", "index": 299}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aria, Matthew, Chloe, Ava, Scarlett, Noah, Liam, and Riley. Aria told you that Aria is a knight if and only if Scarlett is a knave. In a statement by Matthew: \"Riley is a knight\". \"Ava is a knave or Scarlett is a knight\" - Chloe. \"Riley is a knight and Scarlett is a knave,\" Ava mentioned. Scarlett asserted: \"Liam is a knight if and only if Aria is a knave\". Noah told you that Matthew is a knight if and only if Aria is a knave. \"Liam is a knight and Riley is a knight\" - Liam. As Riley put it, \"Liam is a knight or Matthew is a knave\". So who is a knight and who is a knave?", "names": ["Aria", "Matthew", "Chloe", "Ava", "Scarlett", "Noah", "Liam", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false, true, true], "solution_text": "Aria is a knight, Matthew is a knight, Chloe is a knave, Ava is a knight, Scarlett is a knave, Noah is a knave, Liam is a knight, and Riley is a knight.", "solution_text_format": "(1) Aria is a knight\n(2) Matthew is a knight\n(3) Chloe is a knave\n(4) Ava is a knight\n(5) Scarlett is a knave\n(6) Noah is a knave\n(7) Liam is a knight\n(8) Riley is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that Aria is a knight if and only if Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Aria that Aria is a knight if and only if Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Liam is a knight if and only if Aria is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Liam is a knight and Riley is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Liam is a knight or Matthew is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Riley is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Ava is a knave or Scarlett is a knight.", "Ava cannot be a knight, because this would contradict the claim of Chloe that Ava is a knave or Scarlett is a knight.", "Ava cannot be a knave, because this would contradict the false claim of their own that Riley is a knight and Scarlett is a knave.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Ava is a knave or Scarlett is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Riley is a knight and Scarlett is a knave.", "Noah cannot be a knight, because this would contradict the claim of their own that Matthew is a knight if and only if Aria is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Matthew is a knight if and only if Aria is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 0), ('lying', 4)), ('telling-truth', 7), ('or', ('lying', 3), ('telling-truth', 4)), ('and', ('telling-truth', 7), ('lying', 4)), ('<=>', ('telling-truth', 6), ('lying', 0)), ('<=>', ('telling-truth', 1), ('lying', 0)), ('and', ('telling-truth', 6), ('telling-truth', 7)), ('or', ('telling-truth', 6), ('lying', 1)))", "index": 300}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Scarlett, Daniel, Owen, Avery, Joseph, Lily, David, and Henry. \"Owen is a knave\" - Scarlett. According to Daniel, \"Henry is a knight if and only if Avery is a knight\". \"Daniel is not a knave,\" Owen claimed. \"Daniel is a knave or Daniel is a knight,\" Avery claimed. \"Lily is a knight and Henry is a knight,\" Joseph declared. \"If Daniel is a knight then Henry is a knight,\" Lily mentioned. David said that If Joseph is a knight then Lily is a knave. Henry asserted: \"Joseph is a knight or David is a knight\". So who is a knight and who is a knave?", "names": ["Scarlett", "Daniel", "Owen", "Avery", "Joseph", "Lily", "David", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true, false, true], "solution_text": "Scarlett is a knave, Daniel is a knight, Owen is a knight, Avery is a knight, Joseph is a knight, Lily is a knight, David is a knave, and Henry is a knight.", "solution_text_format": "(1) Scarlett is a knave\n(2) Daniel is a knight\n(3) Owen is a knight\n(4) Avery is a knight\n(5) Joseph is a knight\n(6) Lily is a knight\n(7) David is a knave\n(8) Henry is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of Scarlett that Owen is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Daniel is not a knave.", "Daniel cannot be a knight, because this would contradict the false claim of Owen that Daniel is not a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Henry is a knight if and only if Avery is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Joseph is a knight or David is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Lily is a knight and Henry is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that If Daniel is a knight then Henry is a knight.", "David cannot be a knight, because this would contradict the claim of their own that If Joseph is a knight then Lily is a knave.", "Assume David is a knave. No contradiction is found in their false claim that If Joseph is a knight then Lily is a knave.", "Avery cannot be a knight, because this would contradict the false claim of Daniel that Henry is a knight if and only if Avery is a knight.", "Avery cannot be a knave, because this would contradict the false claim of their own that Daniel is a knave or Daniel is a knight.", "We have exhausted all possibilities for Avery and David, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the claim of Joseph that Lily is a knight and Henry is a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Lily is a knight and Henry is a knight.", "Lily cannot be a knight, because this would contradict the false claim of Joseph that Lily is a knight and Henry is a knight.", "Lily cannot be a knave, because this would contradict the false claim of their own that If Daniel is a knight then Henry is a knight.", "We have exhausted all possibilities for Lily and Joseph, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Joseph is a knight or David is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Lily is a knight and Henry is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Lily is a knight and Henry is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that If Daniel is a knight then Henry is a knight.", "David cannot be a knight, because this would contradict the false claim of Henry that Joseph is a knight or David is a knight.", "David cannot be a knave, because this would contradict the false claim of their own that If Joseph is a knight then Lily is a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the false claim of their own that If Daniel is a knight then Henry is a knight.", "We have exhausted all possibilities for Lily, Joseph, Henry, Daniel, and Owen, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Owen is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Daniel is not a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Henry is a knight if and only if Avery is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Joseph is a knight or David is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Lily is a knight and Henry is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that If Daniel is a knight then Henry is a knight.", "David cannot be a knight, because this would contradict the claim of their own that If Joseph is a knight then Lily is a knave.", "Assume David is a knave. No contradiction is found in their false claim that If Joseph is a knight then Lily is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Daniel is a knave or Daniel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('<=>', ('telling-truth', 7), ('telling-truth', 3)), ('not', ('lying', 1)), ('or', ('lying', 1), ('telling-truth', 1)), ('and', ('telling-truth', 5), ('telling-truth', 7)), ('->', ('telling-truth', 1), ('telling-truth', 7)), ('->', ('telling-truth', 4), ('lying', 5)), ('or', ('telling-truth', 4), ('telling-truth', 6)))", "index": 301}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sebastian, Amelia, Alexander, Charlotte, Aria, Sofia, Oliver, and Michael. Sebastian stated, \"If Sofia is a knave then Charlotte is a knight\". According to Amelia, \"Alexander is a knave and Charlotte is a knight\". As Alexander put it, \"Sofia is a knave and Sebastian is a knave\". \"Alexander is a knight if and only if Charlotte is a knight,\" Charlotte mentioned. Aria expressed that If Michael is a knave then Oliver is a knave. \"Amelia is a knight,\" Sofia claimed. Oliver asserted: \"Charlotte is a knight and Alexander is a knave\". As Michael put it, \"Alexander is a knight or Aria is a knave\". So who is a knight and who is a knave?", "names": ["Sebastian", "Amelia", "Alexander", "Charlotte", "Aria", "Sofia", "Oliver", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, false, false, true], "solution_text": "Sebastian is a knave, Amelia is a knave, Alexander is a knight, Charlotte is a knave, Aria is a knight, Sofia is a knave, Oliver is a knave, and Michael is a knight.", "solution_text_format": "(1) Sebastian is a knave\n(2) Amelia is a knave\n(3) Alexander is a knight\n(4) Charlotte is a knave\n(5) Aria is a knight\n(6) Sofia is a knave\n(7) Oliver is a knave\n(8) Michael is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that If Sofia is a knave then Charlotte is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Amelia is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Alexander is a knave and Charlotte is a knight.", "Alexander cannot be a knight, because this would contradict the claim of Amelia that Alexander is a knave and Charlotte is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Sofia is a knave and Sebastian is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Alexander is a knight if and only if Charlotte is a knight.", "Charlotte cannot be a knave, because this would contradict the claim of Amelia that Alexander is a knave and Charlotte is a knight.", "We have exhausted all possibilities for Charlotte and Alexander, so let us go back and reconsider Amelia.", "Amelia cannot be a knave, because this would contradict the claim of Sofia that Amelia is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Amelia is a knight.", "Amelia cannot be a knight, because this would contradict the false claim of Sofia that Amelia is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Alexander is a knave and Charlotte is a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that Sofia is a knave and Sebastian is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Sofia is a knave and Sebastian is a knave.", "Charlotte cannot be a knight, because this would contradict the false claim of Amelia that Alexander is a knave and Charlotte is a knight.", "Charlotte cannot be a knave, because this would contradict the claim of Sebastian that If Sofia is a knave then Charlotte is a knight.", "We have exhausted all possibilities for Charlotte, Alexander, Amelia, and Sofia, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that If Sofia is a knave then Charlotte is a knight.", "Sofia cannot be a knight, because this would contradict the false claim of Sebastian that If Sofia is a knave then Charlotte is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Amelia is a knight.", "Amelia cannot be a knight, because this would contradict the false claim of Sofia that Amelia is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Alexander is a knave and Charlotte is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Sofia is a knave and Sebastian is a knave.", "Charlotte cannot be a knight, because this would contradict the false claim of Sebastian that If Sofia is a knave then Charlotte is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Alexander is a knight if and only if Charlotte is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that If Michael is a knave then Oliver is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Alexander is a knight or Aria is a knave.", "Oliver cannot be a knight, because this would contradict the claim of their own that Charlotte is a knight and Alexander is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Charlotte is a knight and Alexander is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('telling-truth', 3)), ('and', ('lying', 2), ('telling-truth', 3)), ('and', ('lying', 5), ('lying', 0)), ('<=>', ('telling-truth', 2), ('telling-truth', 3)), ('->', ('lying', 7), ('lying', 6)), ('telling-truth', 1), ('and', ('telling-truth', 3), ('lying', 2)), ('or', ('telling-truth', 2), ('lying', 4)))", "index": 302}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lily, Scarlett, James, Riley, Aiden, Jack, Olivia, and Oliver. Lily said, \"James is a knight or Jack is a knight.\" In Scarlett's words: \"Oliver is a knave or Jack is a knight\". James remarked, \"Scarlett is not a knight\". \"Aiden is a knave\" - Riley. Aiden told you that Oliver is a knave and Jack is a knave. \"Olivia is a knight if and only if Olivia is a knave,\" Jack claimed. As Olivia put it, \"Oliver is not a knight\". Oliver asserted: \"Olivia is a knight if and only if Aiden is a knave\". So who is a knight and who is a knave?", "names": ["Lily", "Scarlett", "James", "Riley", "Aiden", "Jack", "Olivia", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, false, true, false], "solution_text": "Lily is a knave, Scarlett is a knight, James is a knave, Riley is a knave, Aiden is a knight, Jack is a knave, Olivia is a knight, and Oliver is a knave.", "solution_text_format": "(1) Lily is a knave\n(2) Scarlett is a knight\n(3) James is a knave\n(4) Riley is a knave\n(5) Aiden is a knight\n(6) Jack is a knave\n(7) Olivia is a knight\n(8) Oliver is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that James is a knight or Jack is a knight.", "Assume James is a knight. No contradiction is found in their claim that Scarlett is not a knight.", "Scarlett cannot be a knight, because this would contradict the claim of James that Scarlett is not a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Oliver is a knave or Jack is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Aiden is a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that Oliver is not a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Oliver is not a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Oliver is a knave and Jack is a knave.", "Aiden cannot be a knave, because this would contradict the claim of Oliver that Olivia is a knight if and only if Aiden is a knave.", "We have exhausted all possibilities for Aiden and Olivia, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the false claim of Scarlett that Oliver is a knave or Jack is a knight.", "We have exhausted all possibilities for Oliver and Scarlett, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Scarlett is not a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Oliver is a knave or Jack is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Aiden is a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that Oliver is not a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Oliver is not a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Oliver is a knave and Jack is a knave.", "Aiden cannot be a knave, because this would contradict the claim of Oliver that Olivia is a knight if and only if Aiden is a knave.", "We have exhausted all possibilities for Aiden and Olivia, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Olivia is a knight if and only if Aiden is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Oliver is not a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Oliver is a knave and Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of Aiden that Oliver is a knave and Jack is a knave.", "Jack cannot be a knave, because this would contradict the claim of Lily that James is a knight or Jack is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the false claim of Oliver that Olivia is a knight if and only if Aiden is a knave.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the false claim of their own that Oliver is not a knight.", "We have exhausted all possibilities for Olivia and Oliver, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the false claim of James that Scarlett is not a knight.", "We have exhausted all possibilities for Scarlett and James, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that James is a knight or Jack is a knight.", "James cannot be a knight, because this would contradict the false claim of Lily that James is a knight or Jack is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Scarlett is not a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Oliver is a knave or Jack is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Aiden is a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that Oliver is not a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Oliver is not a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Oliver is a knave and Jack is a knave.", "Aiden cannot be a knave, because this would contradict the claim of Oliver that Olivia is a knight if and only if Aiden is a knave.", "We have exhausted all possibilities for Aiden and Olivia, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Olivia is a knight if and only if Aiden is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Oliver is not a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Oliver is a knave and Jack is a knave.", "Jack cannot be a knight, because this would contradict the false claim of Lily that James is a knight or Jack is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Olivia is a knight if and only if Olivia is a knave.", "Riley cannot be a knight, because this would contradict the claim of their own that Aiden is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Aiden is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('telling-truth', 5)), ('or', ('lying', 7), ('telling-truth', 5)), ('not', ('telling-truth', 1)), ('lying', 4), ('and', ('lying', 7), ('lying', 5)), ('<=>', ('telling-truth', 6), ('lying', 6)), ('not', ('telling-truth', 7)), ('<=>', ('telling-truth', 6), ('lying', 4)))", "index": 303}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Liam, Michael, Ella, David, Charlotte, Elizabeth, Mia, and Benjamin. Liam expressed that Ella is a knight if and only if Elizabeth is a knave. In Michael's words: \"Benjamin is a knave and Ella is a knave\". \"If Charlotte is a knight then Benjamin is a knave,\" Ella claimed. David said, \"Michael is not a knave.\" Charlotte noted, \"Elizabeth is a knight if and only if Ella is a knave\". Elizabeth commented, \"If David is a knave then Liam is a knight\". \"Charlotte is not a knave,\" Mia declared. Benjamin said that Elizabeth is a knight if and only if Mia is a knight. So who is a knight and who is a knave?", "names": ["Liam", "Michael", "Ella", "David", "Charlotte", "Elizabeth", "Mia", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true, true, true], "solution_text": "Liam is a knight, Michael is a knave, Ella is a knave, David is a knave, Charlotte is a knight, Elizabeth is a knight, Mia is a knight, and Benjamin is a knight.", "solution_text_format": "(1) Liam is a knight\n(2) Michael is a knave\n(3) Ella is a knave\n(4) David is a knave\n(5) Charlotte is a knight\n(6) Elizabeth is a knight\n(7) Mia is a knight\n(8) Benjamin is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Ella is a knight if and only if Elizabeth is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that If Charlotte is a knight then Benjamin is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Elizabeth is a knight if and only if Ella is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of Liam that Ella is a knight if and only if Elizabeth is a knave.", "Elizabeth cannot be a knave, because this would contradict the false claim of their own that If David is a knave then Liam is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Elizabeth is a knight if and only if Ella is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of Liam that Ella is a knight if and only if Elizabeth is a knave.", "Elizabeth cannot be a knave, because this would contradict the false claim of Charlotte that Elizabeth is a knight if and only if Ella is a knave.", "We have exhausted all possibilities for Elizabeth and Charlotte, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that If Charlotte is a knight then Benjamin is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Elizabeth is a knight if and only if Ella is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If David is a knave then Liam is a knight.", "Assume David is a knight. No contradiction is found in their claim that Michael is not a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Benjamin is a knave and Ella is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Michael that Benjamin is a knave and Ella is a knave.", "Benjamin cannot be a knave, because this would contradict the false claim of Ella that If Charlotte is a knight then Benjamin is a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Michael.", "Michael cannot be a knave, because this would contradict the claim of David that Michael is not a knave.", "We have exhausted all possibilities for Michael, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Michael is not a knave.", "Michael cannot be a knight, because this would contradict the false claim of David that Michael is not a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Benjamin is a knave and Ella is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Elizabeth is a knight if and only if Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Charlotte is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('lying', 5)), ('and', ('lying', 7), ('lying', 2)), ('->', ('telling-truth', 4), ('lying', 7)), ('not', ('lying', 1)), ('<=>', ('telling-truth', 5), ('lying', 2)), ('->', ('lying', 3), ('telling-truth', 0)), ('not', ('lying', 4)), ('<=>', ('telling-truth', 5), ('telling-truth', 6)))", "index": 304}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Grace, Daniel, Owen, Abigail, Sofia, Joseph, Evelyn, and Zoey. Grace told you that Evelyn is a knight. Daniel stated, \"Grace is a knave if and only if Evelyn is a knave\". Owen remarked, \"Daniel is not a knight\". Abigail said that Evelyn is a knight and Grace is a knave. \"Abigail is a knight if and only if Joseph is a knave,\" Sofia mentioned. As Joseph put it, \"Abigail is a knave or Abigail is a knight\". \"Owen is not a knight,\" Evelyn claimed. Zoey remarked, \"Daniel is a knave\". So who is a knight and who is a knave?", "names": ["Grace", "Daniel", "Owen", "Abigail", "Sofia", "Joseph", "Evelyn", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true, true, false], "solution_text": "Grace is a knight, Daniel is a knight, Owen is a knave, Abigail is a knave, Sofia is a knight, Joseph is a knight, Evelyn is a knight, and Zoey is a knave.", "solution_text_format": "(1) Grace is a knight\n(2) Daniel is a knight\n(3) Owen is a knave\n(4) Abigail is a knave\n(5) Sofia is a knight\n(6) Joseph is a knight\n(7) Evelyn is a knight\n(8) Zoey is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Evelyn is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Owen is not a knight.", "Owen cannot be a knight, because this would contradict the claim of Evelyn that Owen is not a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Daniel is not a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Grace is a knave if and only if Evelyn is a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Evelyn is a knight and Grace is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Evelyn is a knight and Grace is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Abigail is a knight if and only if Joseph is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Abigail is a knave or Abigail is a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that Daniel is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Daniel is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 6), ('<=>', ('lying', 0), ('lying', 6)), ('not', ('telling-truth', 1)), ('and', ('telling-truth', 6), ('lying', 0)), ('<=>', ('telling-truth', 3), ('lying', 5)), ('or', ('lying', 3), ('telling-truth', 3)), ('not', ('telling-truth', 2)), ('lying', 1))", "index": 305}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mason, Abigail, Riley, Charlotte, Harper, Benjamin, Henry, and Alexander. Mason commented, \"Harper is a knight or Alexander is a knight\". Abigail noted, \"If Riley is a knight then Mason is a knight\". Riley commented, \"If Alexander is a knave then Abigail is a knave\". According to Charlotte, \"Riley is a knight or Alexander is a knight\". \"If Abigail is a knight then Mason is a knave,\" Harper mentioned. Benjamin told you that Abigail is not a knave. Henry noted, \"If Alexander is a knight then Mason is a knight\". As Alexander put it, \"Henry is a knave or Benjamin is a knight\". So who is a knight and who is a knave?", "names": ["Mason", "Abigail", "Riley", "Charlotte", "Harper", "Benjamin", "Henry", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true, true, true], "solution_text": "Mason is a knight, Abigail is a knight, Riley is a knight, Charlotte is a knight, Harper is a knave, Benjamin is a knight, Henry is a knight, and Alexander is a knight.", "solution_text_format": "(1) Mason is a knight\n(2) Abigail is a knight\n(3) Riley is a knight\n(4) Charlotte is a knight\n(5) Harper is a knave\n(6) Benjamin is a knight\n(7) Henry is a knight\n(8) Alexander is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Harper is a knight or Alexander is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that If Abigail is a knight then Mason is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Harper that If Abigail is a knight then Mason is a knave.", "Abigail cannot be a knave, because this would contradict the false claim of their own that If Riley is a knight then Mason is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that If Abigail is a knight then Mason is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that If Riley is a knight then Mason is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that If Alexander is a knave then Abigail is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Henry is a knave or Benjamin is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that If Alexander is a knight then Mason is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Abigail is not a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Riley is a knight or Alexander is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('telling-truth', 7)), ('->', ('telling-truth', 2), ('telling-truth', 0)), ('->', ('lying', 7), ('lying', 1)), ('or', ('telling-truth', 2), ('telling-truth', 7)), ('->', ('telling-truth', 1), ('lying', 0)), ('not', ('lying', 1)), ('->', ('telling-truth', 7), ('telling-truth', 0)), ('or', ('lying', 6), ('telling-truth', 5)))", "index": 306}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Matthew, Olivia, Abigail, Emma, Jacob, Joseph, Jackson, and Victoria. \"Victoria is not a knave,\" Matthew claimed. Olivia said that Jacob is a knave if and only if Emma is a knave. Abigail was heard saying, \"Victoria is a knight\". Emma expressed that Jackson is a knave. Jacob noted, \"Abigail is a knight\". \"If Emma is a knight then Olivia is a knight,\" Joseph declared. Jackson was heard saying, \"Abigail is a knight and Joseph is a knight\". Victoria noted, \"Jackson is a knight and Olivia is a knight\". So who is a knight and who is a knave?", "names": ["Matthew", "Olivia", "Abigail", "Emma", "Jacob", "Joseph", "Jackson", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, false, false, false], "solution_text": "Matthew is a knave, Olivia is a knave, Abigail is a knave, Emma is a knight, Jacob is a knave, Joseph is a knave, Jackson is a knave, and Victoria is a knave.", "solution_text_format": "(1) Matthew is a knave\n(2) Olivia is a knave\n(3) Abigail is a knave\n(4) Emma is a knight\n(5) Jacob is a knave\n(6) Joseph is a knave\n(7) Jackson is a knave\n(8) Victoria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that Victoria is not a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Jackson is a knight and Olivia is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Abigail is a knight and Joseph is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Victoria is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Emma is a knight then Olivia is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Jackson is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Jackson is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Jacob is a knave if and only if Emma is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Olivia that Jacob is a knave if and only if Emma is a knave.", "Jacob cannot be a knave, because this would contradict the false claim of their own that Abigail is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the claim of Victoria that Jackson is a knight and Olivia is a knight.", "We have exhausted all possibilities for Olivia and Emma, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of Jackson that Abigail is a knight and Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the false claim of their own that Victoria is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Jackson.", "Jackson cannot be a knave, because this would contradict the claim of Victoria that Jackson is a knight and Olivia is a knight.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Victoria.", "Victoria cannot be a knave, because this would contradict the claim of Matthew that Victoria is not a knave.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Victoria is not a knave.", "Victoria cannot be a knight, because this would contradict the false claim of Matthew that Victoria is not a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Jackson is a knight and Olivia is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Abigail is a knight and Joseph is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Victoria is a knight.", "Abigail cannot be a knave, because this would contradict the claim of Jackson that Abigail is a knight and Joseph is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Abigail is a knight and Joseph is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Victoria is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Victoria is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Emma is a knight then Olivia is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Jackson is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Jacob is a knave if and only if Emma is a knave.", "Jacob cannot be a knight, because this would contradict the claim of their own that Abigail is a knight.", "Jacob cannot be a knave, because this would contradict the claim of Olivia that Jacob is a knave if and only if Emma is a knave.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the claim of Joseph that If Emma is a knight then Olivia is a knight.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Emma.", "Emma cannot be a knave, because this would contradict the false claim of their own that Jackson is a knave.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that If Emma is a knight then Olivia is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Jackson is a knave.", "Olivia cannot be a knight, because this would contradict the false claim of Joseph that If Emma is a knight then Olivia is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Jacob is a knave if and only if Emma is a knave.", "Jacob cannot be a knight, because this would contradict the false claim of Olivia that Jacob is a knave if and only if Emma is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Abigail is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 7)), ('<=>', ('lying', 4), ('lying', 3)), ('telling-truth', 7), ('lying', 6), ('telling-truth', 2), ('->', ('telling-truth', 3), ('telling-truth', 1)), ('and', ('telling-truth', 2), ('telling-truth', 5)), ('and', ('telling-truth', 6), ('telling-truth', 1)))", "index": 307}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Henry, Benjamin, Olivia, Scarlett, Michael, Riley, David, and Victoria. Henry said that David is a knight or Olivia is a knave. In Benjamin's words: \"Riley is not a knight\". In Olivia's words: \"Henry is a knave and Michael is a knight\". \"David is a knight or Victoria is a knight,\" Scarlett claimed. Michael noted, \"David is a knight or Riley is a knave\". Riley noted, \"If Olivia is a knight then Olivia is a knave\". David told you that Scarlett is a knight if and only if Benjamin is a knave. Victoria stated, \"Henry is not a knave\". So who is a knight and who is a knave?", "names": ["Henry", "Benjamin", "Olivia", "Scarlett", "Michael", "Riley", "David", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true, true, true], "solution_text": "Henry is a knight, Benjamin is a knave, Olivia is a knave, Scarlett is a knight, Michael is a knight, Riley is a knight, David is a knight, and Victoria is a knight.", "solution_text_format": "(1) Henry is a knight\n(2) Benjamin is a knave\n(3) Olivia is a knave\n(4) Scarlett is a knight\n(5) Michael is a knight\n(6) Riley is a knight\n(7) David is a knight\n(8) Victoria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that David is a knight or Olivia is a knave.", "Assume David is a knight. No contradiction is found in their claim that Scarlett is a knight if and only if Benjamin is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that David is a knight or Victoria is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Henry is not a knave.", "Benjamin cannot be a knight, because this would contradict the claim of David that Scarlett is a knight if and only if Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Riley is not a knight.", "Assume Riley is a knight. No contradiction is found in their claim that If Olivia is a knight then Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that Henry is a knave and Michael is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Henry is a knave and Michael is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that David is a knight or Riley is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 6), ('lying', 2)), ('not', ('telling-truth', 5)), ('and', ('lying', 0), ('telling-truth', 4)), ('or', ('telling-truth', 6), ('telling-truth', 7)), ('or', ('telling-truth', 6), ('lying', 5)), ('->', ('telling-truth', 2), ('lying', 2)), ('<=>', ('telling-truth', 3), ('lying', 1)), ('not', ('lying', 0)))", "index": 308}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Noah, Scarlett, Lily, Grace, Benjamin, Jack, Aiden, and Luke. Noah commented, \"Aiden is not a knave\". \"Benjamin is a knight and Grace is a knave,\" Scarlett declared. Lily told you that Aiden is a knight and Luke is a knave. \"Luke is a knave,\" Grace declared. Benjamin stated, \"Noah is a knight or Jack is a knight\". Jack expressed that Benjamin is a knave. In Aiden's words: \"Lily is a knight and Aiden is a knight\". Luke commented, \"Lily is a knave and Aiden is a knight\". So who is a knight and who is a knave?", "names": ["Noah", "Scarlett", "Lily", "Grace", "Benjamin", "Jack", "Aiden", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false, true, false], "solution_text": "Noah is a knight, Scarlett is a knave, Lily is a knight, Grace is a knight, Benjamin is a knight, Jack is a knave, Aiden is a knight, and Luke is a knave.", "solution_text_format": "(1) Noah is a knight\n(2) Scarlett is a knave\n(3) Lily is a knight\n(4) Grace is a knight\n(5) Benjamin is a knight\n(6) Jack is a knave\n(7) Aiden is a knight\n(8) Luke is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Noah is a knight. No contradiction is found in their claim that Aiden is not a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Lily is a knight and Aiden is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Aiden is a knight and Luke is a knave.", "Luke cannot be a knight, because this would contradict the claim of Lily that Aiden is a knight and Luke is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Lily is a knave and Aiden is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Benjamin is a knight and Grace is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Noah is a knight or Jack is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Benjamin is a knave.", "Grace cannot be a knight, because this would contradict the claim of Scarlett that Benjamin is a knight and Grace is a knave.", "Grace cannot be a knave, because this would contradict the false claim of their own that Luke is a knave.", "We have exhausted all possibilities for Grace and Jack, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the claim of Scarlett that Benjamin is a knight and Grace is a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Benjamin is a knight and Grace is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Noah is a knight or Jack is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Benjamin is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Luke is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 6)), ('and', ('telling-truth', 4), ('lying', 3)), ('and', ('telling-truth', 6), ('lying', 7)), ('lying', 7), ('or', ('telling-truth', 0), ('telling-truth', 5)), ('lying', 4), ('and', ('telling-truth', 2), ('telling-truth', 6)), ('and', ('lying', 2), ('telling-truth', 6)))", "index": 309}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Scarlett, Sofia, Mia, Sebastian, Abigail, Ethan, William, and Harper. As Scarlett put it, \"Sofia is a knave or William is a knave\". Sofia asserted: \"Scarlett is a knight\". \"Abigail is a knave,\" Mia declared. \"Sofia is a knave and Ethan is a knave,\" Sebastian declared. In a statement by Abigail: \"Ethan is not a knave\". Ethan stated, \"If Abigail is a knight then Sebastian is a knave\". In a statement by William: \"Harper is a knight and Sebastian is a knave\". \"Ethan is a knight if and only if Harper is a knight,\" Harper claimed. So who is a knight and who is a knave?", "names": ["Scarlett", "Sofia", "Mia", "Sebastian", "Abigail", "Ethan", "William", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true, false, false], "solution_text": "Scarlett is a knight, Sofia is a knight, Mia is a knave, Sebastian is a knave, Abigail is a knight, Ethan is a knight, William is a knave, and Harper is a knave.", "solution_text_format": "(1) Scarlett is a knight\n(2) Sofia is a knight\n(3) Mia is a knave\n(4) Sebastian is a knave\n(5) Abigail is a knight\n(6) Ethan is a knight\n(7) William is a knave\n(8) Harper is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Sofia is a knave or William is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Scarlett is a knight.", "William cannot be a knight, because this would contradict the claim of Scarlett that Sofia is a knave or William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Harper is a knight and Sebastian is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Ethan is a knight if and only if Harper is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If Abigail is a knight then Sebastian is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Ethan is not a knave.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Sofia is a knave and Ethan is a knave.", "Sebastian cannot be a knave, because this would contradict the false claim of William that Harper is a knight and Sebastian is a knave.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the false claim of their own that Ethan is not a knave.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the claim of Harper that Ethan is a knight if and only if Harper is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Ethan is a knight if and only if Harper is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If Abigail is a knight then Sebastian is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Ethan is not a knave.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Sofia is a knave and Ethan is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Sofia is a knave and Ethan is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Abigail is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Abigail is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('lying', 6)), ('telling-truth', 0), ('lying', 4), ('and', ('lying', 1), ('lying', 5)), ('not', ('lying', 5)), ('->', ('telling-truth', 4), ('lying', 3)), ('and', ('telling-truth', 7), ('lying', 3)), ('<=>', ('telling-truth', 5), ('telling-truth', 7)))", "index": 310}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sophia, Mia, Zoey, Avery, Liam, Harper, James, and Sebastian. Sophia noted, \"Harper is a knight and Avery is a knight\". Mia commented, \"Zoey is a knave\". Zoey asserted: \"Liam is a knight if and only if Mia is a knight\". Avery stated, \"Liam is a knave\". Liam said that If James is a knight then James is a knave. Harper asserted: \"Zoey is a knight or James is a knave\". James expressed that Mia is not a knave. Sebastian told you that Avery is a knight. So who is a knight and who is a knave?", "names": ["Sophia", "Mia", "Zoey", "Avery", "Liam", "Harper", "James", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, false, true, true], "solution_text": "Sophia is a knave, Mia is a knight, Zoey is a knave, Avery is a knight, Liam is a knave, Harper is a knave, James is a knight, and Sebastian is a knight.", "solution_text_format": "(1) Sophia is a knave\n(2) Mia is a knight\n(3) Zoey is a knave\n(4) Avery is a knight\n(5) Liam is a knave\n(6) Harper is a knave\n(7) James is a knight\n(8) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Harper is a knight and Avery is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Zoey is a knight or James is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Liam is a knight if and only if Mia is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that If James is a knight then James is a knave.", "James cannot be a knight, because this would contradict the claim of Liam that If James is a knight then James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Mia is not a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Zoey is a knave.", "Mia cannot be a knave, because this would contradict the claim of Zoey that Liam is a knight if and only if Mia is a knight.", "We have exhausted all possibilities for Mia and James, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that If James is a knight then James is a knave.", "Assume James is a knight. No contradiction is found in their claim that Mia is not a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Zoey is a knave.", "Mia cannot be a knave, because this would contradict the claim of James that Mia is not a knave.", "We have exhausted all possibilities for Mia, so let us go back and reconsider James.", "James cannot be a knave, because this would contradict the false claim of Liam that If James is a knight then James is a knave.", "We have exhausted all possibilities for James and Liam, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Liam is a knight if and only if Mia is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that If James is a knight then James is a knave.", "James cannot be a knight, because this would contradict the claim of Liam that If James is a knight then James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Mia is not a knave.", "Mia cannot be a knight, because this would contradict the false claim of Zoey that Liam is a knight if and only if Mia is a knight.", "Mia cannot be a knave, because this would contradict the false claim of their own that Zoey is a knave.", "We have exhausted all possibilities for Mia and James, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that If James is a knight then James is a knave.", "James cannot be a knight, because this would contradict the claim of Harper that Zoey is a knight or James is a knave.", "James cannot be a knave, because this would contradict the false claim of Liam that If James is a knight then James is a knave.", "We have exhausted all possibilities for James, Liam, and Zoey, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the claim of Sophia that Harper is a knight and Avery is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Harper is a knight and Avery is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Zoey is a knight or James is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Liam is a knight if and only if Mia is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that If James is a knight then James is a knave.", "James cannot be a knight, because this would contradict the claim of Liam that If James is a knight then James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Mia is not a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Zoey is a knave.", "Mia cannot be a knave, because this would contradict the claim of Zoey that Liam is a knight if and only if Mia is a knight.", "We have exhausted all possibilities for Mia and James, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that If James is a knight then James is a knave.", "Assume James is a knight. No contradiction is found in their claim that Mia is not a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Zoey is a knave.", "Mia cannot be a knave, because this would contradict the claim of James that Mia is not a knave.", "We have exhausted all possibilities for Mia, so let us go back and reconsider James.", "James cannot be a knave, because this would contradict the false claim of Liam that If James is a knight then James is a knave.", "We have exhausted all possibilities for James and Liam, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Liam is a knight if and only if Mia is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that If James is a knight then James is a knave.", "James cannot be a knight, because this would contradict the claim of Liam that If James is a knight then James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Mia is not a knave.", "Mia cannot be a knight, because this would contradict the false claim of Zoey that Liam is a knight if and only if Mia is a knight.", "Mia cannot be a knave, because this would contradict the false claim of their own that Zoey is a knave.", "We have exhausted all possibilities for Mia and James, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that If James is a knight then James is a knave.", "James cannot be a knight, because this would contradict the claim of Harper that Zoey is a knight or James is a knave.", "James cannot be a knave, because this would contradict the false claim of Liam that If James is a knight then James is a knave.", "We have exhausted all possibilities for James, Liam, and Zoey, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Zoey is a knight or James is a knave.", "Zoey cannot be a knight, because this would contradict the false claim of Harper that Zoey is a knight or James is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Liam is a knight if and only if Mia is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that If James is a knight then James is a knave.", "James cannot be a knight, because this would contradict the claim of Liam that If James is a knight then James is a knave.", "James cannot be a knave, because this would contradict the false claim of Harper that Zoey is a knight or James is a knave.", "We have exhausted all possibilities for James, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that If James is a knight then James is a knave.", "Assume James is a knight. No contradiction is found in their claim that Mia is not a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Zoey is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Liam is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Avery is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('telling-truth', 3)), ('lying', 2), ('<=>', ('telling-truth', 4), ('telling-truth', 1)), ('lying', 4), ('->', ('telling-truth', 6), ('lying', 6)), ('or', ('telling-truth', 2), ('lying', 6)), ('not', ('lying', 1)), ('telling-truth', 3))", "index": 311}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sofia, Benjamin, Charlotte, Aurora, Lucas, Matthew, Daniel, and David. \"If Daniel is a knight then Charlotte is a knave,\" Sofia claimed. Benjamin asserted: \"Daniel is a knave if and only if David is a knave\". \"Lucas is not a knight,\" Charlotte declared. Aurora remarked, \"Charlotte is a knave\". \"Matthew is not a knave,\" Lucas mentioned. \"If Charlotte is a knave then David is a knight\" - Matthew. Daniel commented, \"If Charlotte is a knight then Benjamin is a knight\". David was heard saying, \"Aurora is a knight or Sofia is a knave\". So who is a knight and who is a knave?", "names": ["Sofia", "Benjamin", "Charlotte", "Aurora", "Lucas", "Matthew", "Daniel", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true, true, true], "solution_text": "Sofia is a knight, Benjamin is a knight, Charlotte is a knave, Aurora is a knight, Lucas is a knight, Matthew is a knight, Daniel is a knight, and David is a knight.", "solution_text_format": "(1) Sofia is a knight\n(2) Benjamin is a knight\n(3) Charlotte is a knave\n(4) Aurora is a knight\n(5) Lucas is a knight\n(6) Matthew is a knight\n(7) Daniel is a knight\n(8) David is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that If Daniel is a knight then Charlotte is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that If Charlotte is a knight then Benjamin is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Sofia that If Daniel is a knight then Charlotte is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Lucas is not a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Matthew is not a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that If Charlotte is a knave then David is a knight.", "Assume David is a knight. No contradiction is found in their claim that Aurora is a knight or Sofia is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Charlotte is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Daniel is a knave if and only if David is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 6), ('lying', 2)), ('<=>', ('lying', 6), ('lying', 7)), ('not', ('telling-truth', 4)), ('lying', 2), ('not', ('lying', 5)), ('->', ('lying', 2), ('telling-truth', 7)), ('->', ('telling-truth', 2), ('telling-truth', 1)), ('or', ('telling-truth', 3), ('lying', 0)))", "index": 312}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aiden, Emma, Ella, Daniel, Luke, Henry, Sofia, and Owen. In Aiden's words: \"Emma is a knight or Henry is a knight\". Emma was heard saying, \"If Luke is a knight then Sofia is a knave\". Ella remarked, \"Owen is a knight\". Daniel said, \"If Sofia is a knight then Emma is a knave.\" As Luke put it, \"Daniel is a knight\". \"Daniel is a knave or Aiden is a knave,\" Henry claimed. Sofia commented, \"If Luke is a knave then Emma is a knight\". Owen was heard saying, \"Emma is a knave\". So who is a knight and who is a knave?", "names": ["Aiden", "Emma", "Ella", "Daniel", "Luke", "Henry", "Sofia", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, true, true, false], "solution_text": "Aiden is a knight, Emma is a knight, Ella is a knave, Daniel is a knave, Luke is a knave, Henry is a knight, Sofia is a knight, and Owen is a knave.", "solution_text_format": "(1) Aiden is a knight\n(2) Emma is a knight\n(3) Ella is a knave\n(4) Daniel is a knave\n(5) Luke is a knave\n(6) Henry is a knight\n(7) Sofia is a knight\n(8) Owen is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Emma is a knight or Henry is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If Luke is a knight then Sofia is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Daniel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that If Sofia is a knight then Emma is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Emma that If Luke is a knight then Sofia is a knave.", "Sofia cannot be a knave, because this would contradict the false claim of their own that If Luke is a knave then Emma is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the claim of Luke that Daniel is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of Luke that Daniel is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that If Sofia is a knight then Emma is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that If Luke is a knave then Emma is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Daniel is a knave or Aiden is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Owen is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Emma is a knave.", "Owen cannot be a knave, because this would contradict the claim of Ella that Owen is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Owen is a knight.", "Owen cannot be a knight, because this would contradict the false claim of Ella that Owen is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Emma is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('telling-truth', 5)), ('->', ('telling-truth', 4), ('lying', 6)), ('telling-truth', 7), ('->', ('telling-truth', 6), ('lying', 1)), ('telling-truth', 3), ('or', ('lying', 3), ('lying', 0)), ('->', ('lying', 4), ('telling-truth', 1)), ('lying', 1))", "index": 313}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Avery, Isabella, Olivia, Victoria, David, Penelope, Mason, and Riley. Avery noted, \"Mason is a knave and Riley is a knave\". \"Olivia is a knight or Penelope is a knight,\" Isabella declared. According to Olivia, \"Riley is a knave\". Victoria asserted: \"David is a knight and David is a knave\". David said that Mason is not a knave. \"Victoria is a knight if and only if Riley is a knave,\" Penelope claimed. \"Olivia is a knight or David is a knave\" - Mason. Riley stated, \"Olivia is a knight if and only if Avery is a knight\". So who is a knight and who is a knave?", "names": ["Avery", "Isabella", "Olivia", "Victoria", "David", "Penelope", "Mason", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, false, true, false], "solution_text": "Avery is a knave, Isabella is a knight, Olivia is a knight, Victoria is a knave, David is a knight, Penelope is a knave, Mason is a knight, and Riley is a knave.", "solution_text_format": "(1) Avery is a knave\n(2) Isabella is a knight\n(3) Olivia is a knight\n(4) Victoria is a knave\n(5) David is a knight\n(6) Penelope is a knave\n(7) Mason is a knight\n(8) Riley is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Mason is a knave and Riley is a knave.", "Mason cannot be a knight, because this would contradict the claim of Avery that Mason is a knave and Riley is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Olivia is a knight or David is a knave.", "Olivia cannot be a knight, because this would contradict the false claim of Mason that Olivia is a knight or David is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Riley is a knave.", "Riley cannot be a knight, because this would contradict the claim of Avery that Mason is a knave and Riley is a knave.", "Riley cannot be a knave, because this would contradict the false claim of Olivia that Riley is a knave.", "We have exhausted all possibilities for Riley, Olivia, and Mason, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Mason is a knave and Riley is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Olivia is a knight or David is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Riley is a knave.", "Riley cannot be a knight, because this would contradict the claim of Olivia that Riley is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Olivia is a knight if and only if Avery is a knight.", "Assume David is a knight. No contradiction is found in their claim that Mason is not a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Olivia is a knight or Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Riley is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that David is a knight and David is a knave.", "Victoria cannot be a knave, because this would contradict the claim of Penelope that Victoria is a knight if and only if Riley is a knave.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Victoria is a knight if and only if Riley is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that David is a knight and David is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that David is a knight and David is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 6), ('lying', 7)), ('or', ('telling-truth', 2), ('telling-truth', 5)), ('lying', 7), ('and', ('telling-truth', 4), ('lying', 4)), ('not', ('lying', 6)), ('<=>', ('telling-truth', 3), ('lying', 7)), ('or', ('telling-truth', 2), ('lying', 4)), ('<=>', ('telling-truth', 2), ('telling-truth', 0)))", "index": 314}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sophia, Isabella, Olivia, James, Riley, Evelyn, Jackson, and Scarlett. Sophia stated, \"Jackson is a knave\". Isabella asserted: \"Olivia is a knave\". Olivia said, \"Jackson is a knight and Jackson is a knave.\" James told you that Sophia is not a knave. Riley stated, \"Isabella is a knight if and only if Isabella is a knave\". According to Evelyn, \"James is a knight if and only if Sophia is a knight\". In Jackson's words: \"If Riley is a knight then James is a knave\". Scarlett remarked, \"If Sophia is a knight then Riley is a knight\". So who is a knight and who is a knave?", "names": ["Sophia", "Isabella", "Olivia", "James", "Riley", "Evelyn", "Jackson", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, true, true, true], "solution_text": "Sophia is a knave, Isabella is a knight, Olivia is a knave, James is a knave, Riley is a knave, Evelyn is a knight, Jackson is a knight, and Scarlett is a knight.", "solution_text_format": "(1) Sophia is a knave\n(2) Isabella is a knight\n(3) Olivia is a knave\n(4) James is a knave\n(5) Riley is a knave\n(6) Evelyn is a knight\n(7) Jackson is a knight\n(8) Scarlett is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Jackson is a knave.", "Jackson cannot be a knight, because this would contradict the claim of Sophia that Jackson is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that If Riley is a knight then James is a knave.", "Riley cannot be a knight, because this would contradict the claim of their own that Isabella is a knight if and only if Isabella is a knave.", "Riley cannot be a knave, because this would contradict the false claim of Jackson that If Riley is a knight then James is a knave.", "We have exhausted all possibilities for Riley and Jackson, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Jackson is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that If Riley is a knight then James is a knave.", "Riley cannot be a knight, because this would contradict the claim of their own that Isabella is a knight if and only if Isabella is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Isabella is a knight if and only if Isabella is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Isabella that Olivia is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Jackson is a knight and Jackson is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Sophia is not a knave.", "Assume James is a knave. No contradiction is found in their false claim that Sophia is not a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that James is a knight if and only if Sophia is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Sophia is a knight then Riley is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 6), ('lying', 2), ('and', ('telling-truth', 6), ('lying', 6)), ('not', ('lying', 0)), ('<=>', ('telling-truth', 1), ('lying', 1)), ('<=>', ('telling-truth', 3), ('telling-truth', 0)), ('->', ('telling-truth', 4), ('lying', 3)), ('->', ('telling-truth', 0), ('telling-truth', 4)))", "index": 315}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Alexander, Avery, Grace, Owen, Joseph, Aria, Liam, and Aiden. Alexander commented, \"If Joseph is a knave then Avery is a knave\". \"Aria is a knave or Liam is a knight,\" Avery mentioned. Grace remarked, \"Liam is a knave if and only if Joseph is a knave\". Owen noted, \"Aria is not a knight\". Joseph commented, \"Liam is a knave and Aiden is a knave\". Aria remarked, \"If Grace is a knight then Liam is a knave\". Liam said that Grace is a knave and Alexander is a knight. \"Aiden is a knight,\" Aiden declared. So who is a knight and who is a knave?", "names": ["Alexander", "Avery", "Grace", "Owen", "Joseph", "Aria", "Liam", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true, false, true], "solution_text": "Alexander is a knight, Avery is a knave, Grace is a knight, Owen is a knave, Joseph is a knave, Aria is a knight, Liam is a knave, and Aiden is a knight.", "solution_text_format": "(1) Alexander is a knight\n(2) Avery is a knave\n(3) Grace is a knight\n(4) Owen is a knave\n(5) Joseph is a knave\n(6) Aria is a knight\n(7) Liam is a knave\n(8) Aiden is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that If Joseph is a knave then Avery is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Liam is a knave and Aiden is a knave.", "Liam cannot be a knight, because this would contradict the claim of Joseph that Liam is a knave and Aiden is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Grace is a knave and Alexander is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Liam is a knave if and only if Joseph is a knave.", "Grace cannot be a knave, because this would contradict the false claim of Liam that Grace is a knave and Alexander is a knight.", "We have exhausted all possibilities for Grace and Liam, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Liam is a knave and Aiden is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Grace is a knave and Alexander is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Liam is a knave if and only if Joseph is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Liam is a knave if and only if Joseph is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Aiden is a knight.", "Avery cannot be a knight, because this would contradict the claim of Alexander that If Joseph is a knave then Avery is a knave.", "Avery cannot be a knave, because this would contradict the false claim of their own that Aria is a knave or Liam is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Aiden is a knight.", "Avery cannot be a knight, because this would contradict the claim of Alexander that If Joseph is a knave then Avery is a knave.", "Avery cannot be a knave, because this would contradict the false claim of their own that Aria is a knave or Liam is a knight.", "We have exhausted all possibilities for Avery, Aiden, and Grace, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Grace is a knave and Alexander is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Liam is a knave if and only if Joseph is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Aiden is a knight.", "Avery cannot be a knight, because this would contradict the claim of Alexander that If Joseph is a knave then Avery is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Aria is a knave or Liam is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that If Grace is a knight then Liam is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Aria is not a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Aria is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 4), ('lying', 1)), ('or', ('lying', 5), ('telling-truth', 6)), ('<=>', ('lying', 6), ('lying', 4)), ('not', ('telling-truth', 5)), ('and', ('lying', 6), ('lying', 7)), ('->', ('telling-truth', 2), ('lying', 6)), ('and', ('lying', 2), ('telling-truth', 0)), ('telling-truth', 7))", "index": 316}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aria, William, Ava, Daniel, Ethan, Owen, Joseph, and David. Aria commented, \"Owen is a knight if and only if Ethan is a knave\". In a statement by William: \"Joseph is a knight\". Ava noted, \"David is a knight and William is a knave\". \"Ethan is a knave\" - Daniel. Ethan told you that David is not a knave. Owen commented, \"Joseph is not a knave\". Joseph commented, \"William is a knight if and only if David is a knight\". \"Aria is a knave or Daniel is a knight,\" David claimed. So who is a knight and who is a knave?", "names": ["Aria", "William", "Ava", "Daniel", "Ethan", "Owen", "Joseph", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true, true, true], "solution_text": "Aria is a knave, William is a knight, Ava is a knave, Daniel is a knave, Ethan is a knight, Owen is a knight, Joseph is a knight, and David is a knight.", "solution_text_format": "(1) Aria is a knave\n(2) William is a knight\n(3) Ava is a knave\n(4) Daniel is a knave\n(5) Ethan is a knight\n(6) Owen is a knight\n(7) Joseph is a knight\n(8) David is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that Owen is a knight if and only if Ethan is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Joseph is not a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that William is a knight if and only if David is a knight.", "Assume William is a knight. No contradiction is found in their claim that Joseph is a knight.", "Assume David is a knight. No contradiction is found in their claim that Aria is a knave or Daniel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Ethan is a knave.", "Ethan cannot be a knight, because this would contradict the claim of Aria that Owen is a knight if and only if Ethan is a knave.", "Ethan cannot be a knave, because this would contradict the false claim of their own that David is not a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the claim of David that Aria is a knave or Daniel is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the claim of Joseph that William is a knight if and only if David is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the false claim of their own that Joseph is a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of Owen that Joseph is not a knave.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Joseph is not a knave.", "Joseph cannot be a knight, because this would contradict the false claim of Owen that Joseph is not a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that William is a knight if and only if David is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Joseph is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Joseph is a knight.", "Assume David is a knight. No contradiction is found in their claim that Aria is a knave or Daniel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Ethan is a knave.", "Ethan cannot be a knight, because this would contradict the claim of Daniel that Ethan is a knave.", "Ethan cannot be a knave, because this would contradict the claim of Aria that Owen is a knight if and only if Ethan is a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the claim of David that Aria is a knave or Daniel is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the false claim of Joseph that William is a knight if and only if David is a knight.", "We have exhausted all possibilities for David, William, Joseph, and Owen, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Owen is a knight if and only if Ethan is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Joseph is not a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that William is a knight if and only if David is a knight.", "Assume William is a knight. No contradiction is found in their claim that Joseph is a knight.", "Assume David is a knight. No contradiction is found in their claim that Aria is a knave or Daniel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Ethan is a knave.", "Ethan cannot be a knight, because this would contradict the claim of Daniel that Ethan is a knave.", "Ethan cannot be a knave, because this would contradict the false claim of Aria that Owen is a knight if and only if Ethan is a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Ethan is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that David is not a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that David is a knight and William is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that David is a knight and William is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 5), ('lying', 4)), ('telling-truth', 6), ('and', ('telling-truth', 7), ('lying', 1)), ('lying', 4), ('not', ('lying', 7)), ('not', ('lying', 6)), ('<=>', ('telling-truth', 1), ('telling-truth', 7)), ('or', ('lying', 0), ('telling-truth', 3)))", "index": 317}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Chloe, Elizabeth, Zoey, Victoria, Ethan, Ava, Alexander, and James. In Chloe's words: \"James is a knight\". Elizabeth stated, \"If Alexander is a knave then Victoria is a knave\". In a statement by Zoey: \"Ava is not a knave\". Victoria asserted: \"Zoey is a knight or Zoey is a knave\". \"If Elizabeth is a knave then James is a knight,\" Ethan declared. According to Ava, \"Elizabeth is not a knight\". Alexander asserted: \"Ava is a knight or Zoey is a knave\". James was heard saying, \"Ethan is a knave or Zoey is a knave\". So who is a knight and who is a knave?", "names": ["Chloe", "Elizabeth", "Zoey", "Victoria", "Ethan", "Ava", "Alexander", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false, true, true], "solution_text": "Chloe is a knight, Elizabeth is a knight, Zoey is a knave, Victoria is a knight, Ethan is a knight, Ava is a knave, Alexander is a knight, and James is a knight.", "solution_text_format": "(1) Chloe is a knight\n(2) Elizabeth is a knight\n(3) Zoey is a knave\n(4) Victoria is a knight\n(5) Ethan is a knight\n(6) Ava is a knave\n(7) Alexander is a knight\n(8) James is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that James is a knight.", "Assume James is a knight. No contradiction is found in their claim that Ethan is a knave or Zoey is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that If Elizabeth is a knave then James is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Alexander is a knave then Victoria is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Ava is a knight or Zoey is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Elizabeth is not a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Elizabeth is not a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that Ava is not a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Ava is not a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Zoey is a knight or Zoey is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 7), ('->', ('lying', 6), ('lying', 3)), ('not', ('lying', 5)), ('or', ('telling-truth', 2), ('lying', 2)), ('->', ('lying', 1), ('telling-truth', 7)), ('not', ('telling-truth', 1)), ('or', ('telling-truth', 5), ('lying', 2)), ('or', ('lying', 4), ('lying', 2)))", "index": 318}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lucas, Elizabeth, Sophia, Grace, Sofia, Benjamin, Emma, and Ethan. Lucas stated, \"Grace is a knight or Ethan is a knight\". Elizabeth expressed that Sofia is a knave or Sophia is a knight. \"If Sofia is a knight then Ethan is a knave,\" Sophia declared. \"Ethan is a knave\" - Grace. Sofia said, \"Benjamin is a knave and Ethan is a knave.\" In Benjamin's words: \"Emma is a knight\". According to Emma, \"Ethan is not a knight\". \"Emma is a knave if and only if Benjamin is a knight\" - Ethan. So who is a knight and who is a knave?", "names": ["Lucas", "Elizabeth", "Sophia", "Grace", "Sofia", "Benjamin", "Emma", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true, true, false], "solution_text": "Lucas is a knight, Elizabeth is a knight, Sophia is a knight, Grace is a knight, Sofia is a knave, Benjamin is a knight, Emma is a knight, and Ethan is a knave.", "solution_text_format": "(1) Lucas is a knight\n(2) Elizabeth is a knight\n(3) Sophia is a knight\n(4) Grace is a knight\n(5) Sofia is a knave\n(6) Benjamin is a knight\n(7) Emma is a knight\n(8) Ethan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that Grace is a knight or Ethan is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Ethan is a knave.", "Ethan cannot be a knight, because this would contradict the claim of Grace that Ethan is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Emma is a knave if and only if Benjamin is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Ethan is not a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Emma is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Sofia is a knave or Sophia is a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave and Ethan is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Benjamin is a knave and Ethan is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that If Sofia is a knight then Ethan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('telling-truth', 7)), ('or', ('lying', 4), ('telling-truth', 2)), ('->', ('telling-truth', 4), ('lying', 7)), ('lying', 7), ('and', ('lying', 5), ('lying', 7)), ('telling-truth', 6), ('not', ('telling-truth', 7)), ('<=>', ('lying', 6), ('telling-truth', 5)))", "index": 319}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lily, Benjamin, Joseph, Logan, Isabella, Sebastian, William, and Penelope. Lily stated, \"Penelope is a knave if and only if Logan is a knight\". In Benjamin's words: \"Logan is a knight or Lily is a knave\". Joseph was heard saying, \"Penelope is not a knave\". \"William is a knave if and only if Joseph is a knight,\" Logan claimed. Isabella expressed that Penelope is a knight and Isabella is a knight. Sebastian asserted: \"Logan is a knave and Penelope is a knight\". William asserted: \"Benjamin is a knight or Logan is a knave\". As Penelope put it, \"Isabella is a knight if and only if Lily is a knave\". So who is a knight and who is a knave?", "names": ["Lily", "Benjamin", "Joseph", "Logan", "Isabella", "Sebastian", "William", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true, true, true], "solution_text": "Lily is a knight, Benjamin is a knave, Joseph is a knight, Logan is a knave, Isabella is a knave, Sebastian is a knight, William is a knight, and Penelope is a knight.", "solution_text_format": "(1) Lily is a knight\n(2) Benjamin is a knave\n(3) Joseph is a knight\n(4) Logan is a knave\n(5) Isabella is a knave\n(6) Sebastian is a knight\n(7) William is a knight\n(8) Penelope is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that Penelope is a knave if and only if Logan is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Lily is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Penelope that Isabella is a knight if and only if Lily is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Penelope is a knight and Isabella is a knight.", "Logan cannot be a knight, because this would contradict the claim of Lily that Penelope is a knave if and only if Logan is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that William is a knave if and only if Joseph is a knight.", "Assume William is a knight. No contradiction is found in their claim that Benjamin is a knight or Logan is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Logan is a knight or Lily is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Logan is a knight or Lily is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Penelope is not a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Logan is a knave and Penelope is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 7), ('telling-truth', 3)), ('or', ('telling-truth', 3), ('lying', 0)), ('not', ('lying', 7)), ('<=>', ('lying', 6), ('telling-truth', 2)), ('and', ('telling-truth', 7), ('telling-truth', 4)), ('and', ('lying', 3), ('telling-truth', 7)), ('or', ('telling-truth', 1), ('lying', 3)), ('<=>', ('telling-truth', 4), ('lying', 0)))", "index": 320}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Harper, Joseph, Avery, Jackson, Scarlett, Liam, Mia, and Daniel. In a statement by Harper: \"Liam is not a knave\". Joseph asserted: \"Avery is a knave if and only if Jackson is a knight\". Avery asserted: \"Scarlett is a knight or Daniel is a knight\". Jackson told you that Joseph is a knight or Scarlett is a knight. Scarlett told you that Jackson is not a knight. Liam commented, \"Daniel is a knight and Joseph is a knave\". Mia remarked, \"Harper is a knight if and only if Liam is a knave\". Daniel expressed that Mia is a knight and Harper is a knave. So who is a knight and who is a knave?", "names": ["Harper", "Joseph", "Avery", "Jackson", "Scarlett", "Liam", "Mia", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, false, false, false], "solution_text": "Harper is a knave, Joseph is a knight, Avery is a knave, Jackson is a knight, Scarlett is a knave, Liam is a knave, Mia is a knave, and Daniel is a knave.", "solution_text_format": "(1) Harper is a knave\n(2) Joseph is a knight\n(3) Avery is a knave\n(4) Jackson is a knight\n(5) Scarlett is a knave\n(6) Liam is a knave\n(7) Mia is a knave\n(8) Daniel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that Liam is not a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Daniel is a knight and Joseph is a knave.", "Daniel cannot be a knight, because this would contradict the claim of their own that Mia is a knight and Harper is a knave.", "Daniel cannot be a knave, because this would contradict the claim of Liam that Daniel is a knight and Joseph is a knave.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the claim of Harper that Liam is not a knave.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Liam is not a knave.", "Liam cannot be a knight, because this would contradict the false claim of Harper that Liam is not a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Daniel is a knight and Joseph is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Mia is a knight and Harper is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Harper is a knight if and only if Liam is a knave.", "Mia cannot be a knave, because this would contradict the claim of Daniel that Mia is a knight and Harper is a knave.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Mia is a knight and Harper is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Harper is a knight if and only if Liam is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Harper is a knight if and only if Liam is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Avery is a knave if and only if Jackson is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Scarlett is a knight or Daniel is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Jackson is not a knight.", "Jackson cannot be a knight, because this would contradict the claim of Joseph that Avery is a knave if and only if Jackson is a knight.", "Jackson cannot be a knave, because this would contradict the false claim of their own that Joseph is a knight or Scarlett is a knight.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the claim of Avery that Scarlett is a knight or Daniel is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Scarlett is a knight or Daniel is a knight.", "Scarlett cannot be a knight, because this would contradict the false claim of Avery that Scarlett is a knight or Daniel is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Jackson is not a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Joseph is a knight or Scarlett is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 5)), ('<=>', ('lying', 2), ('telling-truth', 3)), ('or', ('telling-truth', 4), ('telling-truth', 7)), ('or', ('telling-truth', 1), ('telling-truth', 4)), ('not', ('telling-truth', 3)), ('and', ('telling-truth', 7), ('lying', 1)), ('<=>', ('telling-truth', 0), ('lying', 5)), ('and', ('telling-truth', 6), ('lying', 0)))", "index": 321}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aiden, Logan, Jacob, Scarlett, Evelyn, Sebastian, Mia, and William. Aiden told you that Sebastian is a knave or Sebastian is a knight. Logan expressed that Scarlett is not a knave. Jacob was heard saying, \"William is a knave if and only if Mia is a knight\". Scarlett stated, \"Aiden is not a knight\". According to Evelyn, \"Sebastian is a knave if and only if Scarlett is a knight\". According to Sebastian, \"Scarlett is a knave or Logan is a knave\". Mia commented, \"If William is a knave then Sebastian is a knave\". William asserted: \"William is a knight and Aiden is a knave\". So who is a knight and who is a knave?", "names": ["Aiden", "Logan", "Jacob", "Scarlett", "Evelyn", "Sebastian", "Mia", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true, false, false], "solution_text": "Aiden is a knight, Logan is a knave, Jacob is a knave, Scarlett is a knave, Evelyn is a knight, Sebastian is a knight, Mia is a knave, and William is a knave.", "solution_text_format": "(1) Aiden is a knight\n(2) Logan is a knave\n(3) Jacob is a knave\n(4) Scarlett is a knave\n(5) Evelyn is a knight\n(6) Sebastian is a knight\n(7) Mia is a knave\n(8) William is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Sebastian is a knave or Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Scarlett is a knave or Logan is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Aiden is not a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Aiden is not a knight.", "Logan cannot be a knight, because this would contradict the claim of their own that Scarlett is not a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Scarlett is not a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that William is a knave if and only if Mia is a knight.", "William cannot be a knight, because this would contradict the claim of their own that William is a knight and Aiden is a knave.", "Assume William is a knave. No contradiction is found in their false claim that William is a knight and Aiden is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that If William is a knave then Sebastian is a knave.", "Mia cannot be a knave, because this would contradict the claim of Jacob that William is a knave if and only if Mia is a knight.", "We have exhausted all possibilities for Mia and William, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that William is a knave if and only if Mia is a knight.", "William cannot be a knight, because this would contradict the claim of their own that William is a knight and Aiden is a knave.", "Assume William is a knave. No contradiction is found in their false claim that William is a knight and Aiden is a knave.", "Mia cannot be a knight, because this would contradict the false claim of Jacob that William is a knave if and only if Mia is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that If William is a knave then Sebastian is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Sebastian is a knave if and only if Scarlett is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 5), ('telling-truth', 5)), ('not', ('lying', 3)), ('<=>', ('lying', 7), ('telling-truth', 6)), ('not', ('telling-truth', 0)), ('<=>', ('lying', 5), ('telling-truth', 3)), ('or', ('lying', 3), ('lying', 1)), ('->', ('lying', 7), ('lying', 5)), ('and', ('telling-truth', 7), ('lying', 0)))", "index": 322}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Chloe, Riley, Joseph, Evelyn, Penelope, Henry, Mason, and Grace. In Chloe's words: \"Evelyn is not a knight\". Riley commented, \"Penelope is a knight and Chloe is a knight\". Joseph said, \"Penelope is a knight and Mason is a knight.\" Evelyn commented, \"Chloe is a knight if and only if Riley is a knight\". Penelope remarked, \"Joseph is a knave\". In Henry's words: \"If Joseph is a knave then Chloe is a knave\". According to Mason, \"If Joseph is a knave then Joseph is a knight\". Grace stated, \"Henry is a knave\". So who is a knight and who is a knave?", "names": ["Chloe", "Riley", "Joseph", "Evelyn", "Penelope", "Henry", "Mason", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true, false, false], "solution_text": "Chloe is a knave, Riley is a knave, Joseph is a knave, Evelyn is a knight, Penelope is a knight, Henry is a knight, Mason is a knave, and Grace is a knave.", "solution_text_format": "(1) Chloe is a knave\n(2) Riley is a knave\n(3) Joseph is a knave\n(4) Evelyn is a knight\n(5) Penelope is a knight\n(6) Henry is a knight\n(7) Mason is a knave\n(8) Grace is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Evelyn is not a knight.", "Evelyn cannot be a knight, because this would contradict the claim of Chloe that Evelyn is not a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Chloe is a knight if and only if Riley is a knight.", "Riley cannot be a knight, because this would contradict the false claim of Evelyn that Chloe is a knight if and only if Riley is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Penelope is a knight and Chloe is a knight.", "Penelope cannot be a knight, because this would contradict the false claim of Riley that Penelope is a knight and Chloe is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of their own that Penelope is a knight and Mason is a knight.", "Joseph cannot be a knave, because this would contradict the false claim of Penelope that Joseph is a knave.", "We have exhausted all possibilities for Joseph, Penelope, Riley, and Evelyn, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Evelyn is not a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Chloe is a knight if and only if Riley is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Penelope is a knight and Chloe is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Penelope is a knight and Chloe is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Penelope that Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Penelope is a knight and Mason is a knight.", "Mason cannot be a knight, because this would contradict the false claim of Joseph that Penelope is a knight and Mason is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that If Joseph is a knave then Joseph is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that If Joseph is a knave then Chloe is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Henry is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Henry is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 3)), ('and', ('telling-truth', 4), ('telling-truth', 0)), ('and', ('telling-truth', 4), ('telling-truth', 6)), ('<=>', ('telling-truth', 0), ('telling-truth', 1)), ('lying', 2), ('->', ('lying', 2), ('lying', 0)), ('->', ('lying', 2), ('telling-truth', 2)), ('lying', 5))", "index": 323}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Charlotte, Victoria, Alexander, Ava, Luke, Abigail, Elizabeth, and Jacob. In Charlotte's words: \"Alexander is a knight if and only if Abigail is a knave\". \"Elizabeth is a knight,\" Victoria mentioned. Alexander said, \"Charlotte is a knight or Jacob is a knight.\" Ava remarked, \"Elizabeth is a knight or Jacob is a knight\". In a statement by Luke: \"Abigail is a knight and Alexander is a knave\". \"Jacob is a knave if and only if Alexander is a knight,\" Abigail mentioned. According to Elizabeth, \"Luke is a knight\". \"Luke is not a knight,\" Jacob mentioned. So who is a knight and who is a knave?", "names": ["Charlotte", "Victoria", "Alexander", "Ava", "Luke", "Abigail", "Elizabeth", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, false, false, true], "solution_text": "Charlotte is a knight, Victoria is a knave, Alexander is a knight, Ava is a knight, Luke is a knave, Abigail is a knave, Elizabeth is a knave, and Jacob is a knight.", "solution_text_format": "(1) Charlotte is a knight\n(2) Victoria is a knave\n(3) Alexander is a knight\n(4) Ava is a knight\n(5) Luke is a knave\n(6) Abigail is a knave\n(7) Elizabeth is a knave\n(8) Jacob is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that Alexander is a knight if and only if Abigail is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Charlotte is a knight or Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Luke is not a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Abigail is a knight and Alexander is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Abigail is a knight and Alexander is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Charlotte that Alexander is a knight if and only if Abigail is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Jacob is a knave if and only if Alexander is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Luke is a knight.", "Elizabeth cannot be a knave, because this would contradict the claim of Victoria that Elizabeth is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the false claim of Victoria that Elizabeth is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Luke is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Elizabeth is a knight or Jacob is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('lying', 5)), ('telling-truth', 6), ('or', ('telling-truth', 0), ('telling-truth', 7)), ('or', ('telling-truth', 6), ('telling-truth', 7)), ('and', ('telling-truth', 5), ('lying', 2)), ('<=>', ('lying', 7), ('telling-truth', 2)), ('telling-truth', 4), ('not', ('telling-truth', 4)))", "index": 324}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Benjamin, Amelia, Ava, Aurora, Oliver, Sebastian, Charlotte, and Noah. Benjamin was heard saying, \"Ava is a knave\". Amelia asserted: \"Amelia is a knight if and only if Charlotte is a knave\". Ava expressed that Aurora is a knave or Sebastian is a knight. Aurora expressed that Charlotte is a knight. In a statement by Oliver: \"Noah is a knight\". Sebastian commented, \"Aurora is a knight and Ava is a knight\". In Charlotte's words: \"Amelia is a knight\". Noah told you that Benjamin is a knight if and only if Charlotte is a knave. So who is a knight and who is a knave?", "names": ["Benjamin", "Amelia", "Ava", "Aurora", "Oliver", "Sebastian", "Charlotte", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, false, false, false], "solution_text": "Benjamin is a knave, Amelia is a knave, Ava is a knight, Aurora is a knave, Oliver is a knave, Sebastian is a knave, Charlotte is a knave, and Noah is a knave.", "solution_text_format": "(1) Benjamin is a knave\n(2) Amelia is a knave\n(3) Ava is a knight\n(4) Aurora is a knave\n(5) Oliver is a knave\n(6) Sebastian is a knave\n(7) Charlotte is a knave\n(8) Noah is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of Benjamin that Ava is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Aurora is a knave or Sebastian is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Amelia is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Amelia is a knight if and only if Charlotte is a knave.", "Amelia cannot be a knave, because this would contradict the false claim of their own that Amelia is a knight if and only if Charlotte is a knave.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the claim of Aurora that Charlotte is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the false claim of Ava that Aurora is a knave or Sebastian is a knight.", "We have exhausted all possibilities for Aurora and Ava, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Ava is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Aurora is a knave or Sebastian is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Amelia is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Amelia is a knight if and only if Charlotte is a knave.", "Amelia cannot be a knave, because this would contradict the false claim of their own that Amelia is a knight if and only if Charlotte is a knave.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the claim of Aurora that Charlotte is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of Aurora that Charlotte is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Amelia is a knight.", "Amelia cannot be a knight, because this would contradict the false claim of Charlotte that Amelia is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Amelia is a knight if and only if Charlotte is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Aurora is a knight and Ava is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Aurora is a knight and Ava is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Noah is a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight if and only if Charlotte is a knave.", "Noah cannot be a knave, because this would contradict the claim of Oliver that Noah is a knight.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Noah is a knight.", "Noah cannot be a knight, because this would contradict the false claim of Oliver that Noah is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Benjamin is a knight if and only if Charlotte is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('<=>', ('telling-truth', 1), ('lying', 6)), ('or', ('lying', 3), ('telling-truth', 5)), ('telling-truth', 6), ('telling-truth', 7), ('and', ('telling-truth', 3), ('telling-truth', 2)), ('telling-truth', 1), ('<=>', ('telling-truth', 0), ('lying', 6)))", "index": 325}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Oliver, William, Noah, Chloe, Jackson, Harper, Logan, and Emily. Oliver noted, \"Emily is a knight if and only if Harper is a knave\". William expressed that Oliver is a knight or Jackson is a knave. In a statement by Noah: \"Emily is a knave and Chloe is a knave\". \"William is not a knight,\" Chloe mentioned. Jackson remarked, \"Emily is a knight or Chloe is a knave\". Harper stated, \"Noah is not a knave\". As Logan put it, \"Oliver is not a knave\". Emily commented, \"William is not a knight\". So who is a knight and who is a knave?", "names": ["Oliver", "William", "Noah", "Chloe", "Jackson", "Harper", "Logan", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true, true, false], "solution_text": "Oliver is a knight, William is a knight, Noah is a knight, Chloe is a knave, Jackson is a knight, Harper is a knight, Logan is a knight, and Emily is a knave.", "solution_text_format": "(1) Oliver is a knight\n(2) William is a knight\n(3) Noah is a knight\n(4) Chloe is a knave\n(5) Jackson is a knight\n(6) Harper is a knight\n(7) Logan is a knight\n(8) Emily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Emily is a knight if and only if Harper is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that William is not a knight.", "William cannot be a knight, because this would contradict the claim of Emily that William is not a knight.", "William cannot be a knave, because this would contradict the false claim of their own that Oliver is a knight or Jackson is a knave.", "We have exhausted all possibilities for William, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that William is not a knight.", "Assume William is a knight. No contradiction is found in their claim that Oliver is a knight or Jackson is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Emily is a knight or Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that William is not a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that William is not a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Noah is not a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Emily is a knave and Chloe is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Oliver is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 7), ('lying', 5)), ('or', ('telling-truth', 0), ('lying', 4)), ('and', ('lying', 7), ('lying', 3)), ('not', ('telling-truth', 1)), ('or', ('telling-truth', 7), ('lying', 3)), ('not', ('lying', 2)), ('not', ('lying', 0)), ('not', ('telling-truth', 1)))", "index": 326}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Michael, Daniel, Mia, Logan, Scarlett, Grace, Penelope, and William. \"Logan is a knave if and only if Scarlett is a knave,\" Michael mentioned. \"Mia is a knight,\" Daniel claimed. In a statement by Mia: \"Michael is a knave or Scarlett is a knave\". Logan said, \"Grace is a knight or Michael is a knight.\" Scarlett commented, \"Mia is a knight or Grace is a knave\". \"Michael is not a knight,\" Grace claimed. Penelope stated, \"Mia is not a knave\". William said that Mia is a knight or Mia is a knave. So who is a knight and who is a knave?", "names": ["Michael", "Daniel", "Mia", "Logan", "Scarlett", "Grace", "Penelope", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false, false, true], "solution_text": "Michael is a knight, Daniel is a knave, Mia is a knave, Logan is a knight, Scarlett is a knight, Grace is a knave, Penelope is a knave, and William is a knight.", "solution_text_format": "(1) Michael is a knight\n(2) Daniel is a knave\n(3) Mia is a knave\n(4) Logan is a knight\n(5) Scarlett is a knight\n(6) Grace is a knave\n(7) Penelope is a knave\n(8) William is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Logan is a knave if and only if Scarlett is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Grace is a knight or Michael is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Michael is not a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Michael is not a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Mia is a knight or Grace is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Michael is a knave or Scarlett is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Michael is a knave or Scarlett is a knave.", "Daniel cannot be a knight, because this would contradict the claim of their own that Mia is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Mia is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Mia is not a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Mia is not a knave.", "Assume William is a knight. No contradiction is found in their claim that Mia is a knight or Mia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('lying', 4)), ('telling-truth', 2), ('or', ('lying', 0), ('lying', 4)), ('or', ('telling-truth', 5), ('telling-truth', 0)), ('or', ('telling-truth', 2), ('lying', 5)), ('not', ('telling-truth', 0)), ('not', ('lying', 2)), ('or', ('telling-truth', 2), ('lying', 2)))", "index": 327}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jackson, Michael, Lily, Sofia, Henry, Noah, Ethan, and Charlotte. Jackson expressed that Sofia is a knight or Ethan is a knight. Michael was heard saying, \"Ethan is a knight or Ethan is a knave\". Lily was heard saying, \"Charlotte is a knave or Henry is a knave\". Sofia remarked, \"Charlotte is a knave if and only if Jackson is a knight\". Henry said that Michael is a knight and Sofia is a knave. \"If Jackson is a knight then Henry is a knight\" - Noah. \"Ethan is a knight or Michael is a knave,\" Ethan claimed. As Charlotte put it, \"Noah is not a knight\". So who is a knight and who is a knave?", "names": ["Jackson", "Michael", "Lily", "Sofia", "Henry", "Noah", "Ethan", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true, false, false], "solution_text": "Jackson is a knave, Michael is a knight, Lily is a knight, Sofia is a knave, Henry is a knight, Noah is a knight, Ethan is a knave, and Charlotte is a knave.", "solution_text_format": "(1) Jackson is a knave\n(2) Michael is a knight\n(3) Lily is a knight\n(4) Sofia is a knave\n(5) Henry is a knight\n(6) Noah is a knight\n(7) Ethan is a knave\n(8) Charlotte is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Sofia is a knight or Ethan is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Charlotte is a knave if and only if Jackson is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Sofia that Charlotte is a knave if and only if Jackson is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Noah is not a knight.", "Assume Noah is a knight. No contradiction is found in their claim that If Jackson is a knight then Henry is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Michael is a knight and Sofia is a knave.", "Henry cannot be a knave, because this would contradict the claim of Noah that If Jackson is a knight then Henry is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the false claim of Charlotte that Noah is not a knight.", "We have exhausted all possibilities for Noah and Charlotte, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Charlotte is a knave if and only if Jackson is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Noah is not a knight.", "Noah cannot be a knight, because this would contradict the claim of Charlotte that Noah is not a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that If Jackson is a knight then Henry is a knight.", "Henry cannot be a knight, because this would contradict the false claim of Noah that If Jackson is a knight then Henry is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Michael is a knight and Sofia is a knave.", "Michael cannot be a knight, because this would contradict the false claim of Henry that Michael is a knight and Sofia is a knave.", "Michael cannot be a knave, because this would contradict the false claim of their own that Ethan is a knight or Ethan is a knave.", "We have exhausted all possibilities for Michael, Henry, and Noah, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the false claim of Sofia that Charlotte is a knave if and only if Jackson is a knight.", "We have exhausted all possibilities for Charlotte and Sofia, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Sofia is a knight or Ethan is a knight.", "Sofia cannot be a knight, because this would contradict the false claim of Jackson that Sofia is a knight or Ethan is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Charlotte is a knave if and only if Jackson is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of Sofia that Charlotte is a knave if and only if Jackson is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Noah is not a knight.", "Assume Noah is a knight. No contradiction is found in their claim that If Jackson is a knight then Henry is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Michael is a knight and Sofia is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Ethan is a knight or Ethan is a knave.", "Ethan cannot be a knight, because this would contradict the false claim of Jackson that Sofia is a knight or Ethan is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Ethan is a knight or Michael is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Charlotte is a knave or Henry is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('telling-truth', 6)), ('or', ('telling-truth', 6), ('lying', 6)), ('or', ('lying', 7), ('lying', 4)), ('<=>', ('lying', 7), ('telling-truth', 0)), ('and', ('telling-truth', 1), ('lying', 3)), ('->', ('telling-truth', 0), ('telling-truth', 4)), ('or', ('telling-truth', 6), ('lying', 1)), ('not', ('telling-truth', 5)))", "index": 328}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Elizabeth, Charlotte, James, Ella, Harper, Olivia, Victoria, and Luke. \"Ella is a knight or Luke is a knight,\" Elizabeth declared. \"If Ella is a knave then Harper is a knight,\" Charlotte claimed. James remarked, \"Luke is not a knight\". Ella commented, \"Charlotte is not a knight\". \"Luke is a knave and Charlotte is a knight,\" Harper claimed. In Olivia's words: \"Victoria is a knave and Victoria is a knight\". \"James is a knave or Olivia is a knight,\" Victoria mentioned. Luke expressed that Harper is a knight if and only if James is a knave. So who is a knight and who is a knave?", "names": ["Elizabeth", "Charlotte", "James", "Ella", "Harper", "Olivia", "Victoria", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, false, false, false], "solution_text": "Elizabeth is a knave, Charlotte is a knight, James is a knight, Ella is a knave, Harper is a knight, Olivia is a knave, Victoria is a knave, and Luke is a knave.", "solution_text_format": "(1) Elizabeth is a knave\n(2) Charlotte is a knight\n(3) James is a knight\n(4) Ella is a knave\n(5) Harper is a knight\n(6) Olivia is a knave\n(7) Victoria is a knave\n(8) Luke is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Ella is a knight or Luke is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Charlotte is not a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Ella that Charlotte is not a knight.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that If Ella is a knave then Harper is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Charlotte is not a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Ella is a knave then Harper is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Luke is a knave and Charlotte is a knight.", "Luke cannot be a knight, because this would contradict the claim of Harper that Luke is a knave and Charlotte is a knight.", "Luke cannot be a knave, because this would contradict the claim of Elizabeth that Ella is a knight or Luke is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the claim of Charlotte that If Ella is a knave then Harper is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the false claim of Ella that Charlotte is not a knight.", "We have exhausted all possibilities for Charlotte and Ella, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Ella is a knight or Luke is a knight.", "Ella cannot be a knight, because this would contradict the false claim of Elizabeth that Ella is a knight or Luke is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Charlotte is not a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Ella is a knave then Harper is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Luke is a knave and Charlotte is a knight.", "Luke cannot be a knight, because this would contradict the false claim of Elizabeth that Ella is a knight or Luke is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Harper is a knight if and only if James is a knave.", "Assume James is a knight. No contradiction is found in their claim that Luke is not a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that Victoria is a knave and Victoria is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Victoria is a knave and Victoria is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that James is a knave or Olivia is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that James is a knave or Olivia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('telling-truth', 7)), ('->', ('lying', 3), ('telling-truth', 4)), ('not', ('telling-truth', 7)), ('not', ('telling-truth', 1)), ('and', ('lying', 7), ('telling-truth', 1)), ('and', ('lying', 6), ('telling-truth', 6)), ('or', ('lying', 2), ('telling-truth', 5)), ('<=>', ('telling-truth', 4), ('lying', 2)))", "index": 329}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mason, Samuel, Penelope, Avery, Grace, James, Henry, and Aurora. In Mason's words: \"Grace is a knight or Penelope is a knave\". According to Samuel, \"Henry is a knight if and only if Mason is a knight\". \"If Penelope is a knight then Henry is a knight\" - Penelope. Avery expressed that James is a knave. Grace told you that Aurora is a knave if and only if Henry is a knight. \"Henry is a knave and Aurora is a knight,\" James mentioned. Henry expressed that If Grace is a knight then Avery is a knight. Aurora expressed that If James is a knave then Avery is a knave. So who is a knight and who is a knave?", "names": ["Mason", "Samuel", "Penelope", "Avery", "Grace", "James", "Henry", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false, true, false], "solution_text": "Mason is a knight, Samuel is a knight, Penelope is a knight, Avery is a knight, Grace is a knight, James is a knave, Henry is a knight, and Aurora is a knave.", "solution_text_format": "(1) Mason is a knight\n(2) Samuel is a knight\n(3) Penelope is a knight\n(4) Avery is a knight\n(5) Grace is a knight\n(6) James is a knave\n(7) Henry is a knight\n(8) Aurora is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Grace is a knight or Penelope is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Aurora is a knave if and only if Henry is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that If James is a knave then Avery is a knave.", "Assume James is a knight. No contradiction is found in their claim that Henry is a knave and Aurora is a knight.", "Henry cannot be a knight, because this would contradict the claim of Grace that Aurora is a knave if and only if Henry is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that If Grace is a knight then Avery is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that James is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that James is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that If Penelope is a knight then Henry is a knight.", "Penelope cannot be a knave, because this would contradict the false claim of their own that If Penelope is a knight then Henry is a knight.", "We have exhausted all possibilities for Penelope, Avery, and Henry, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Henry is a knave and Aurora is a knight.", "Henry cannot be a knight, because this would contradict the claim of Grace that Aurora is a knave if and only if Henry is a knight.", "Henry cannot be a knave, because this would contradict the false claim of James that Henry is a knave and Aurora is a knight.", "We have exhausted all possibilities for Henry and James, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that If James is a knave then Avery is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Henry is a knave and Aurora is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Henry is a knave and Aurora is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that If Grace is a knight then Avery is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that James is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that If Penelope is a knight then Henry is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Henry is a knight if and only if Mason is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('lying', 2)), ('<=>', ('telling-truth', 6), ('telling-truth', 0)), ('->', ('telling-truth', 2), ('telling-truth', 6)), ('lying', 5), ('<=>', ('lying', 7), ('telling-truth', 6)), ('and', ('lying', 6), ('telling-truth', 7)), ('->', ('telling-truth', 4), ('telling-truth', 3)), ('->', ('lying', 5), ('lying', 3)))", "index": 330}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: William, Aurora, Joseph, Daniel, Grace, Abigail, Jack, and Charlotte. William said that If Abigail is a knight then Jack is a knight. As Aurora put it, \"Daniel is a knight and Joseph is a knight\". According to Joseph, \"Abigail is a knight or Jack is a knight\". \"William is a knave and Daniel is a knight,\" Daniel mentioned. As Grace put it, \"Abigail is not a knave\". \"William is a knave and Jack is a knight,\" Abigail mentioned. Jack said that If Abigail is a knave then William is a knave. Charlotte remarked, \"If Joseph is a knave then Jack is a knight\". So who is a knight and who is a knave?", "names": ["William", "Aurora", "Joseph", "Daniel", "Grace", "Abigail", "Jack", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, false, false, false], "solution_text": "William is a knight, Aurora is a knave, Joseph is a knave, Daniel is a knave, Grace is a knave, Abigail is a knave, Jack is a knave, and Charlotte is a knave.", "solution_text_format": "(1) William is a knight\n(2) Aurora is a knave\n(3) Joseph is a knave\n(4) Daniel is a knave\n(5) Grace is a knave\n(6) Abigail is a knave\n(7) Jack is a knave\n(8) Charlotte is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that If Abigail is a knight then Jack is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that William is a knave and Jack is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that William is a knave and Jack is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that If Abigail is a knave then William is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that If Abigail is a knave then William is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Daniel is a knight and Joseph is a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that William is a knave and Daniel is a knight.", "Daniel cannot be a knave, because this would contradict the claim of Aurora that Daniel is a knight and Joseph is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Daniel is a knight and Joseph is a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that William is a knave and Daniel is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that William is a knave and Daniel is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Abigail is a knight or Jack is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Abigail is a knight or Jack is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Abigail is not a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Abigail is not a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that If Joseph is a knave then Jack is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that If Joseph is a knave then Jack is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 5), ('telling-truth', 6)), ('and', ('telling-truth', 3), ('telling-truth', 2)), ('or', ('telling-truth', 5), ('telling-truth', 6)), ('and', ('lying', 0), ('telling-truth', 3)), ('not', ('lying', 5)), ('and', ('lying', 0), ('telling-truth', 6)), ('->', ('lying', 5), ('lying', 0)), ('->', ('lying', 2), ('telling-truth', 6)))", "index": 331}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lucas, David, Michael, Avery, Elizabeth, Isabella, Victoria, and Aiden. Lucas said that Aiden is a knight or Michael is a knight. As David put it, \"Avery is a knave\". Michael commented, \"Elizabeth is a knight\". \"Victoria is a knave,\" Avery claimed. Elizabeth stated, \"David is a knave\". Isabella was heard saying, \"Avery is not a knave\". Victoria stated, \"Elizabeth is a knave if and only if Avery is a knight\". Aiden said, \"If Michael is a knave then Elizabeth is a knight.\" So who is a knight and who is a knave?", "names": ["Lucas", "David", "Michael", "Avery", "Elizabeth", "Isabella", "Victoria", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true, false, true], "solution_text": "Lucas is a knight, David is a knave, Michael is a knight, Avery is a knight, Elizabeth is a knight, Isabella is a knight, Victoria is a knave, and Aiden is a knight.", "solution_text_format": "(1) Lucas is a knight\n(2) David is a knave\n(3) Michael is a knight\n(4) Avery is a knight\n(5) Elizabeth is a knight\n(6) Isabella is a knight\n(7) Victoria is a knave\n(8) Aiden is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that Aiden is a knight or Michael is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that If Michael is a knave then Elizabeth is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that David is a knave.", "David cannot be a knight, because this would contradict the claim of Elizabeth that David is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Avery is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Victoria is a knave.", "Victoria cannot be a knight, because this would contradict the claim of Avery that Victoria is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Elizabeth is a knave if and only if Avery is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Avery is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 7), ('telling-truth', 2)), ('lying', 3), ('telling-truth', 4), ('lying', 6), ('lying', 1), ('not', ('lying', 3)), ('<=>', ('lying', 4), ('telling-truth', 3)), ('->', ('lying', 2), ('telling-truth', 4)))", "index": 332}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Michael, Isabella, Sebastian, Ethan, Emily, Zoey, Charlotte, and Sofia. In Michael's words: \"Sebastian is a knight if and only if Zoey is a knave\". Isabella asserted: \"If Sofia is a knave then Sebastian is a knight\". Sebastian noted, \"Charlotte is a knave or Michael is a knave\". Ethan commented, \"Isabella is a knave if and only if Emily is a knight\". As Emily put it, \"Emily is a knight if and only if Michael is a knight\". Zoey said, \"Emily is a knight if and only if Michael is a knave.\" \"Zoey is not a knave,\" Charlotte claimed. Sofia stated, \"Isabella is not a knight\". So who is a knight and who is a knave?", "names": ["Michael", "Isabella", "Sebastian", "Ethan", "Emily", "Zoey", "Charlotte", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false, false, false], "solution_text": "Michael is a knight, Isabella is a knight, Sebastian is a knight, Ethan is a knave, Emily is a knight, Zoey is a knave, Charlotte is a knave, and Sofia is a knave.", "solution_text_format": "(1) Michael is a knight\n(2) Isabella is a knight\n(3) Sebastian is a knight\n(4) Ethan is a knave\n(5) Emily is a knight\n(6) Zoey is a knave\n(7) Charlotte is a knave\n(8) Sofia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Sebastian is a knight if and only if Zoey is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Charlotte is a knave or Michael is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Sebastian that Charlotte is a knave or Michael is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Zoey is not a knave.", "Zoey cannot be a knight, because this would contradict the claim of Michael that Sebastian is a knight if and only if Zoey is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Emily is a knight if and only if Michael is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Emily is a knight if and only if Michael is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that If Sofia is a knave then Sebastian is a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that Isabella is not a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Isabella is not a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Isabella is a knave if and only if Emily is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Isabella is a knave if and only if Emily is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('lying', 5)), ('->', ('lying', 7), ('telling-truth', 2)), ('or', ('lying', 6), ('lying', 0)), ('<=>', ('lying', 1), ('telling-truth', 4)), ('<=>', ('telling-truth', 4), ('telling-truth', 0)), ('<=>', ('telling-truth', 4), ('lying', 0)), ('not', ('lying', 5)), ('not', ('telling-truth', 1)))", "index": 333}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aurora, Michael, Abigail, James, Penelope, Victoria, Lucas, and Aiden. \"Penelope is not a knight,\" Aurora declared. Michael stated, \"If Abigail is a knave then Aiden is a knave\". Abigail remarked, \"James is a knave or Penelope is a knight\". \"Michael is a knave or Michael is a knight,\" James claimed. Penelope noted, \"Aiden is not a knave\". Victoria was heard saying, \"James is a knave\". \"Penelope is a knight,\" Lucas claimed. Aiden commented, \"Victoria is a knight and Penelope is a knight\". So who is a knight and who is a knave?", "names": ["Aurora", "Michael", "Abigail", "James", "Penelope", "Victoria", "Lucas", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false, false, false], "solution_text": "Aurora is a knight, Michael is a knight, Abigail is a knave, James is a knight, Penelope is a knave, Victoria is a knave, Lucas is a knave, and Aiden is a knave.", "solution_text_format": "(1) Aurora is a knight\n(2) Michael is a knight\n(3) Abigail is a knave\n(4) James is a knight\n(5) Penelope is a knave\n(6) Victoria is a knave\n(7) Lucas is a knave\n(8) Aiden is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Penelope cannot be a knight, because this would contradict the claim of Aurora that Penelope is not a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Aiden is not a knave.", "Aiden cannot be a knight, because this would contradict the false claim of Penelope that Aiden is not a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Victoria is a knight and Penelope is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that James is a knave.", "James cannot be a knight, because this would contradict the claim of Victoria that James is a knave.", "James cannot be a knave, because this would contradict the false claim of their own that Michael is a knave or Michael is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that James is a knave.", "Assume James is a knight. No contradiction is found in their claim that Michael is a knave or Michael is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that If Abigail is a knave then Aiden is a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that James is a knave or Penelope is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that James is a knave or Penelope is a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Penelope is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Penelope is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 4)), ('->', ('lying', 2), ('lying', 7)), ('or', ('lying', 3), ('telling-truth', 4)), ('or', ('lying', 1), ('telling-truth', 1)), ('not', ('lying', 7)), ('lying', 3), ('telling-truth', 4), ('and', ('telling-truth', 5), ('telling-truth', 4)))", "index": 334}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jacob, Victoria, Mia, William, Alexander, James, Owen, and Avery. Jacob commented, \"Owen is a knight and Mia is a knave\". In a statement by Victoria: \"Alexander is not a knight\". Mia was heard saying, \"If Victoria is a knight then Owen is a knight\". \"Victoria is a knave or Owen is a knave,\" William mentioned. \"William is a knave and Owen is a knave,\" Alexander declared. James stated, \"Alexander is a knave and Avery is a knight\". \"Avery is not a knight,\" Owen claimed. Avery expressed that Victoria is not a knave. So who is a knight and who is a knave?", "names": ["Jacob", "Victoria", "Mia", "William", "Alexander", "James", "Owen", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, true, false, true], "solution_text": "Jacob is a knave, Victoria is a knight, Mia is a knave, William is a knight, Alexander is a knave, James is a knight, Owen is a knave, and Avery is a knight.", "solution_text_format": "(1) Jacob is a knave\n(2) Victoria is a knight\n(3) Mia is a knave\n(4) William is a knight\n(5) Alexander is a knave\n(6) James is a knight\n(7) Owen is a knave\n(8) Avery is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that Owen is a knight and Mia is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Avery is not a knight.", "Avery cannot be a knight, because this would contradict the claim of Owen that Avery is not a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Victoria is not a knave.", "Victoria cannot be a knight, because this would contradict the false claim of Avery that Victoria is not a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that William is a knave and Owen is a knave.", "Alexander cannot be a knave, because this would contradict the false claim of Victoria that Alexander is not a knight.", "We have exhausted all possibilities for Alexander, Victoria, and Avery, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the claim of Jacob that Owen is a knight and Mia is a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Owen is a knight and Mia is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Avery is not a knight.", "Avery cannot be a knight, because this would contradict the claim of Owen that Avery is not a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Victoria is not a knave.", "Victoria cannot be a knight, because this would contradict the false claim of Avery that Victoria is not a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that William is a knave and Owen is a knave.", "Alexander cannot be a knave, because this would contradict the false claim of Victoria that Alexander is not a knight.", "We have exhausted all possibilities for Alexander, Victoria, and Avery, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Avery is not a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Victoria is not a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of Victoria that Alexander is not a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that William is a knave and Owen is a knave.", "Assume William is a knight. No contradiction is found in their claim that Victoria is a knave or Owen is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that If Victoria is a knight then Owen is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that If Victoria is a knight then Owen is a knight.", "Assume James is a knight. No contradiction is found in their claim that Alexander is a knave and Avery is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 6), ('lying', 2)), ('not', ('telling-truth', 4)), ('->', ('telling-truth', 1), ('telling-truth', 6)), ('or', ('lying', 1), ('lying', 6)), ('and', ('lying', 3), ('lying', 6)), ('and', ('lying', 4), ('telling-truth', 7)), ('not', ('telling-truth', 7)), ('not', ('lying', 1)))", "index": 335}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emily, Mason, Noah, Harper, Grace, Michael, David, and William. Emily remarked, \"If William is a knight then Harper is a knight\". Mason said, \"Michael is a knave and Noah is a knight.\" Noah told you that Michael is a knave and Noah is a knight. Harper remarked, \"William is a knave\". In Grace's words: \"David is not a knave\". Michael was heard saying, \"Mason is a knight\". \"Mason is not a knave,\" David claimed. According to William, \"If Noah is a knight then William is a knight\". So who is a knight and who is a knave?", "names": ["Emily", "Mason", "Noah", "Harper", "Grace", "Michael", "David", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, false, false, true], "solution_text": "Emily is a knave, Mason is a knave, Noah is a knave, Harper is a knave, Grace is a knave, Michael is a knave, David is a knave, and William is a knight.", "solution_text_format": "(1) Emily is a knave\n(2) Mason is a knave\n(3) Noah is a knave\n(4) Harper is a knave\n(5) Grace is a knave\n(6) Michael is a knave\n(7) David is a knave\n(8) William is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that If William is a knight then Harper is a knight.", "Assume William is a knight. No contradiction is found in their claim that If Noah is a knight then William is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Michael is a knave and Noah is a knight.", "Michael cannot be a knight, because this would contradict the claim of Noah that Michael is a knave and Noah is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Mason is a knight.", "Mason cannot be a knight, because this would contradict the false claim of Michael that Mason is a knight.", "Mason cannot be a knave, because this would contradict the false claim of their own that Michael is a knave and Noah is a knight.", "We have exhausted all possibilities for Mason and Michael, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Michael is a knave and Noah is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Mason is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Noah is a knight.", "Mason cannot be a knave, because this would contradict the claim of Michael that Mason is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Mason is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Noah is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Michael is a knave and Noah is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that William is a knave.", "Harper cannot be a knave, because this would contradict the claim of Emily that If William is a knight then Harper is a knight.", "We have exhausted all possibilities for Harper, Mason, Michael, and Noah, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that If Noah is a knight then William is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Michael is a knave and Noah is a knight.", "Michael cannot be a knight, because this would contradict the claim of Noah that Michael is a knave and Noah is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Mason is a knight.", "Mason cannot be a knight, because this would contradict the false claim of Michael that Mason is a knight.", "Mason cannot be a knave, because this would contradict the false claim of their own that Michael is a knave and Noah is a knight.", "We have exhausted all possibilities for Mason and Michael, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the false claim of William that If Noah is a knight then William is a knight.", "We have exhausted all possibilities for Noah and William, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that If William is a knight then Harper is a knight.", "Assume William is a knight. No contradiction is found in their claim that If Noah is a knight then William is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Michael is a knave and Noah is a knight.", "Michael cannot be a knight, because this would contradict the claim of Noah that Michael is a knave and Noah is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Mason is a knight.", "Mason cannot be a knight, because this would contradict the false claim of Michael that Mason is a knight.", "Mason cannot be a knave, because this would contradict the false claim of their own that Michael is a knave and Noah is a knight.", "We have exhausted all possibilities for Mason and Michael, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Michael is a knave and Noah is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Mason is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Noah is a knight.", "Mason cannot be a knave, because this would contradict the claim of Michael that Mason is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Mason is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Noah is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Michael is a knave and Noah is a knight.", "Harper cannot be a knight, because this would contradict the false claim of Emily that If William is a knight then Harper is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that William is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that David is not a knave.", "David cannot be a knight, because this would contradict the claim of their own that Mason is not a knave.", "David cannot be a knave, because this would contradict the claim of Grace that David is not a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that David is not a knave.", "David cannot be a knight, because this would contradict the false claim of Grace that David is not a knave.", "Assume David is a knave. No contradiction is found in their false claim that Mason is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 7), ('telling-truth', 3)), ('and', ('lying', 5), ('telling-truth', 2)), ('and', ('lying', 5), ('telling-truth', 2)), ('lying', 7), ('not', ('lying', 6)), ('telling-truth', 1), ('not', ('lying', 1)), ('->', ('telling-truth', 2), ('telling-truth', 7)))", "index": 336}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Grace, Henry, Emma, Oliver, Abigail, Amelia, Aria, and David. \"If Emma is a knave then Grace is a knight\" - Grace. Henry said, \"Amelia is a knight.\" As Emma put it, \"Amelia is a knave and Grace is a knight\". Oliver said that Aria is a knight or David is a knave. As Abigail put it, \"Oliver is not a knave\". Amelia commented, \"Emma is a knight or David is a knave\". Aria noted, \"Abigail is a knight if and only if Aria is a knight\". David asserted: \"Emma is a knave or Abigail is a knave\". So who is a knight and who is a knave?", "names": ["Grace", "Henry", "Emma", "Oliver", "Abigail", "Amelia", "Aria", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, false, true, true], "solution_text": "Grace is a knave, Henry is a knave, Emma is a knave, Oliver is a knight, Abigail is a knight, Amelia is a knave, Aria is a knight, and David is a knight.", "solution_text_format": "(1) Grace is a knave\n(2) Henry is a knave\n(3) Emma is a knave\n(4) Oliver is a knight\n(5) Abigail is a knight\n(6) Amelia is a knave\n(7) Aria is a knight\n(8) David is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that If Emma is a knave then Grace is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Amelia is a knave and Grace is a knight.", "Amelia cannot be a knight, because this would contradict the claim of Emma that Amelia is a knave and Grace is a knight.", "Amelia cannot be a knave, because this would contradict the false claim of their own that Emma is a knight or David is a knave.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Amelia is a knave and Grace is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Emma is a knight or David is a knave.", "David cannot be a knight, because this would contradict the claim of Amelia that Emma is a knight or David is a knave.", "David cannot be a knave, because this would contradict the false claim of their own that Emma is a knave or Abigail is a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Amelia.", "Amelia cannot be a knave, because this would contradict the false claim of Emma that Amelia is a knave and Grace is a knight.", "We have exhausted all possibilities for Amelia and Emma, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that If Emma is a knave then Grace is a knight.", "Emma cannot be a knight, because this would contradict the false claim of Grace that If Emma is a knave then Grace is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Amelia is a knave and Grace is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Emma is a knight or David is a knave.", "David cannot be a knight, because this would contradict the claim of Amelia that Emma is a knight or David is a knave.", "David cannot be a knave, because this would contradict the false claim of their own that Emma is a knave or Abigail is a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Emma is a knight or David is a knave.", "Assume David is a knight. No contradiction is found in their claim that Emma is a knave or Abigail is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Oliver is not a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Aria is a knight or David is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Abigail is a knight if and only if Aria is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Amelia is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Amelia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 2), ('telling-truth', 0)), ('telling-truth', 5), ('and', ('lying', 5), ('telling-truth', 0)), ('or', ('telling-truth', 6), ('lying', 7)), ('not', ('lying', 3)), ('or', ('telling-truth', 2), ('lying', 7)), ('<=>', ('telling-truth', 4), ('telling-truth', 6)), ('or', ('lying', 2), ('lying', 4)))", "index": 337}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Avery, Riley, Aiden, William, Jack, Amelia, Scarlett, and Lily. Avery stated, \"If William is a knave then Avery is a knight\". Riley said that Jack is a knight. Aiden was heard saying, \"Amelia is a knight or William is a knight\". William noted, \"Avery is a knave and Amelia is a knight\". Jack remarked, \"Lily is not a knight\". \"If Jack is a knight then Riley is a knight,\" Amelia claimed. Scarlett said that Amelia is a knight. In a statement by Lily: \"Avery is a knight and Scarlett is a knight\". So who is a knight and who is a knave?", "names": ["Avery", "Riley", "Aiden", "William", "Jack", "Amelia", "Scarlett", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true, true, true], "solution_text": "Avery is a knight, Riley is a knave, Aiden is a knight, William is a knave, Jack is a knave, Amelia is a knight, Scarlett is a knight, and Lily is a knight.", "solution_text_format": "(1) Avery is a knight\n(2) Riley is a knave\n(3) Aiden is a knight\n(4) William is a knave\n(5) Jack is a knave\n(6) Amelia is a knight\n(7) Scarlett is a knight\n(8) Lily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that If William is a knave then Avery is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Avery is a knave and Amelia is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Avery is a knave and Amelia is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that If Jack is a knight then Riley is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Lily is not a knight.", "Lily cannot be a knight, because this would contradict the claim of Jack that Lily is not a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Avery is a knight and Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the false claim of Lily that Avery is a knight and Scarlett is a knight.", "Scarlett cannot be a knave, because this would contradict the false claim of their own that Amelia is a knight.", "We have exhausted all possibilities for Scarlett and Lily, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Lily is not a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Avery is a knight and Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Amelia is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Jack is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Jack is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Amelia is a knight or William is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('telling-truth', 0)), ('telling-truth', 4), ('or', ('telling-truth', 5), ('telling-truth', 3)), ('and', ('lying', 0), ('telling-truth', 5)), ('not', ('telling-truth', 7)), ('->', ('telling-truth', 4), ('telling-truth', 1)), ('telling-truth', 5), ('and', ('telling-truth', 0), ('telling-truth', 6)))", "index": 338}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: James, Victoria, Liam, Ella, Ethan, Elizabeth, Aiden, and Logan. James remarked, \"Ethan is not a knight\". Victoria expressed that Ella is a knight. \"Aiden is a knight if and only if Ella is a knave,\" Liam mentioned. \"Aiden is a knight or Liam is a knight\" - Ella. Ethan commented, \"Elizabeth is a knight\". Elizabeth said, \"Liam is a knave if and only if Aiden is a knave.\" \"James is a knight or Logan is a knight\" - Aiden. Logan remarked, \"James is a knave\". So who is a knight and who is a knave?", "names": ["James", "Victoria", "Liam", "Ella", "Ethan", "Elizabeth", "Aiden", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false, true, false], "solution_text": "James is a knight, Victoria is a knight, Liam is a knave, Ella is a knight, Ethan is a knave, Elizabeth is a knave, Aiden is a knight, and Logan is a knave.", "solution_text_format": "(1) James is a knight\n(2) Victoria is a knight\n(3) Liam is a knave\n(4) Ella is a knight\n(5) Ethan is a knave\n(6) Elizabeth is a knave\n(7) Aiden is a knight\n(8) Logan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Ethan is not a knight.", "Ethan cannot be a knight, because this would contradict the claim of James that Ethan is not a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the false claim of Ethan that Elizabeth is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Liam is a knave if and only if Aiden is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Aiden is a knight if and only if Ella is a knave.", "Aiden cannot be a knight, because this would contradict the false claim of Elizabeth that Liam is a knave if and only if Aiden is a knave.", "Aiden cannot be a knave, because this would contradict the false claim of their own that James is a knight or Logan is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Aiden is a knight if and only if Ella is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that James is a knight or Logan is a knight.", "Logan cannot be a knight, because this would contradict the claim of their own that James is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that James is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Aiden is a knight or Liam is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Ella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 4)), ('telling-truth', 3), ('<=>', ('telling-truth', 6), ('lying', 3)), ('or', ('telling-truth', 6), ('telling-truth', 2)), ('telling-truth', 5), ('<=>', ('lying', 2), ('lying', 6)), ('or', ('telling-truth', 0), ('telling-truth', 7)), ('lying', 0))", "index": 339}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Victoria, Oliver, Emily, Mason, Lucas, Amelia, Avery, and Sophia. Victoria said that Mason is a knight if and only if Sophia is a knight. Oliver asserted: \"Mason is a knight\". Emily commented, \"Sophia is not a knave\". Mason remarked, \"Avery is a knight and Amelia is a knave\". Lucas was heard saying, \"Mason is not a knave\". Amelia asserted: \"Avery is a knight\". \"Emily is not a knight,\" Avery declared. \"Lucas is a knight if and only if Mason is a knave,\" Sophia declared. So who is a knight and who is a knave?", "names": ["Victoria", "Oliver", "Emily", "Mason", "Lucas", "Amelia", "Avery", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, true, true, false], "solution_text": "Victoria is a knight, Oliver is a knave, Emily is a knave, Mason is a knave, Lucas is a knave, Amelia is a knight, Avery is a knight, and Sophia is a knave.", "solution_text_format": "(1) Victoria is a knight\n(2) Oliver is a knave\n(3) Emily is a knave\n(4) Mason is a knave\n(5) Lucas is a knave\n(6) Amelia is a knight\n(7) Avery is a knight\n(8) Sophia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that Mason is a knight if and only if Sophia is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Avery is a knight and Amelia is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Emily is not a knight.", "Emily cannot be a knight, because this would contradict the claim of Avery that Emily is not a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Sophia is not a knave.", "Sophia cannot be a knight, because this would contradict the false claim of Emily that Sophia is not a knave.", "Sophia cannot be a knave, because this would contradict the claim of Victoria that Mason is a knight if and only if Sophia is a knight.", "We have exhausted all possibilities for Sophia and Emily, so let us go back and reconsider Avery.", "Avery cannot be a knave, because this would contradict the claim of Mason that Avery is a knight and Amelia is a knave.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Avery is a knight and Amelia is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Emily is not a knight.", "Emily cannot be a knight, because this would contradict the claim of Avery that Emily is not a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Sophia is not a knave.", "Sophia cannot be a knight, because this would contradict the claim of Victoria that Mason is a knight if and only if Sophia is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Lucas is a knight if and only if Mason is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Mason is not a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Mason is not a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Avery is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Mason is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Mason is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 3), ('telling-truth', 7)), ('telling-truth', 3), ('not', ('lying', 7)), ('and', ('telling-truth', 6), ('lying', 5)), ('not', ('lying', 3)), ('telling-truth', 6), ('not', ('telling-truth', 2)), ('<=>', ('telling-truth', 4), ('lying', 3)))", "index": 340}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Henry, Sophia, Oliver, Michael, William, Scarlett, Emma, and Chloe. As Henry put it, \"Henry is a knight if and only if Scarlett is a knave\". \"Michael is a knave and Sophia is a knight,\" Sophia mentioned. Oliver told you that Chloe is not a knave. According to Michael, \"Oliver is not a knave\". William was heard saying, \"Sophia is a knight or Henry is a knight\". Scarlett said, \"Chloe is a knave and William is a knight.\" In Emma's words: \"Oliver is not a knave\". Chloe noted, \"William is a knight if and only if Sophia is a knight\". So who is a knight and who is a knave?", "names": ["Henry", "Sophia", "Oliver", "Michael", "William", "Scarlett", "Emma", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false, true, true], "solution_text": "Henry is a knave, Sophia is a knave, Oliver is a knight, Michael is a knight, William is a knave, Scarlett is a knave, Emma is a knight, and Chloe is a knight.", "solution_text_format": "(1) Henry is a knave\n(2) Sophia is a knave\n(3) Oliver is a knight\n(4) Michael is a knight\n(5) William is a knave\n(6) Scarlett is a knave\n(7) Emma is a knight\n(8) Chloe is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that Henry is a knight if and only if Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Henry that Henry is a knight if and only if Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Chloe is a knave and William is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that William is a knight if and only if Sophia is a knight.", "Assume William is a knight. No contradiction is found in their claim that Sophia is a knight or Henry is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Michael is a knave and Sophia is a knight.", "Michael cannot be a knight, because this would contradict the claim of Sophia that Michael is a knave and Sophia is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Oliver is not a knave.", "Oliver cannot be a knight, because this would contradict the false claim of Michael that Oliver is not a knave.", "Oliver cannot be a knave, because this would contradict the false claim of their own that Chloe is not a knave.", "We have exhausted all possibilities for Oliver and Michael, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the claim of Chloe that William is a knight if and only if Sophia is a knight.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the false claim of their own that Sophia is a knight or Henry is a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that William is a knight if and only if Sophia is a knight.", "William cannot be a knight, because this would contradict the false claim of Scarlett that Chloe is a knave and William is a knight.", "William cannot be a knave, because this would contradict the false claim of their own that Sophia is a knight or Henry is a knight.", "We have exhausted all possibilities for William, Chloe, and Scarlett, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Henry is a knight if and only if Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the false claim of Henry that Henry is a knight if and only if Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Chloe is a knave and William is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that William is a knight if and only if Sophia is a knight.", "Assume William is a knight. No contradiction is found in their claim that Sophia is a knight or Henry is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Michael is a knave and Sophia is a knight.", "Michael cannot be a knight, because this would contradict the claim of Sophia that Michael is a knave and Sophia is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Oliver is not a knave.", "Oliver cannot be a knight, because this would contradict the false claim of Michael that Oliver is not a knave.", "Oliver cannot be a knave, because this would contradict the false claim of their own that Chloe is not a knave.", "We have exhausted all possibilities for Oliver and Michael, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the claim of William that Sophia is a knight or Henry is a knight.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Sophia is a knight or Henry is a knight.", "Sophia cannot be a knight, because this would contradict the false claim of William that Sophia is a knight or Henry is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Michael is a knave and Sophia is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Oliver is not a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Chloe is not a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Oliver is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 0), ('lying', 5)), ('and', ('lying', 3), ('telling-truth', 1)), ('not', ('lying', 7)), ('not', ('lying', 2)), ('or', ('telling-truth', 1), ('telling-truth', 0)), ('and', ('lying', 7), ('telling-truth', 4)), ('not', ('lying', 2)), ('<=>', ('telling-truth', 4), ('telling-truth', 1)))", "index": 341}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Michael, Aiden, Evelyn, Jackson, Joseph, Benjamin, Oliver, and James. In Michael's words: \"If Aiden is a knave then Joseph is a knave\". Aiden remarked, \"Benjamin is not a knave\". \"Aiden is a knight and James is a knave,\" Evelyn declared. Jackson noted, \"If James is a knight then Michael is a knave\". Joseph commented, \"Aiden is not a knight\". Benjamin stated, \"James is a knight and Aiden is a knight\". \"Michael is a knave or Joseph is a knave,\" Oliver declared. \"Michael is a knave,\" James mentioned. So who is a knight and who is a knave?", "names": ["Michael", "Aiden", "Evelyn", "Jackson", "Joseph", "Benjamin", "Oliver", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, false, true, true], "solution_text": "Michael is a knave, Aiden is a knave, Evelyn is a knave, Jackson is a knight, Joseph is a knight, Benjamin is a knave, Oliver is a knight, and James is a knight.", "solution_text_format": "(1) Michael is a knave\n(2) Aiden is a knave\n(3) Evelyn is a knave\n(4) Jackson is a knight\n(5) Joseph is a knight\n(6) Benjamin is a knave\n(7) Oliver is a knight\n(8) James is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that If Aiden is a knave then Joseph is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Benjamin is not a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that James is a knight and Aiden is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Michael is a knave.", "James cannot be a knave, because this would contradict the claim of Benjamin that James is a knight and Aiden is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the claim of Aiden that Benjamin is not a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Benjamin is not a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Aiden that Benjamin is not a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that James is a knight and Aiden is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Michael is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Michael is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Michael that If Aiden is a knave then Joseph is a knave.", "Joseph cannot be a knave, because this would contradict the false claim of their own that Aiden is not a knight.", "We have exhausted all possibilities for Joseph, James, Benjamin, and Aiden, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that If Aiden is a knave then Joseph is a knave.", "Aiden cannot be a knight, because this would contradict the false claim of Michael that If Aiden is a knave then Joseph is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Benjamin is not a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Aiden that Benjamin is not a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that James is a knight and Aiden is a knight.", "Assume James is a knight. No contradiction is found in their claim that Michael is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Aiden is not a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Aiden is a knight and James is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Aiden is a knight and James is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that If James is a knight then Michael is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Michael is a knave or Joseph is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 1), ('lying', 4)), ('not', ('lying', 5)), ('and', ('telling-truth', 1), ('lying', 7)), ('->', ('telling-truth', 7), ('lying', 0)), ('not', ('telling-truth', 1)), ('and', ('telling-truth', 7), ('telling-truth', 1)), ('or', ('lying', 0), ('lying', 4)), ('lying', 0))", "index": 342}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mia, Noah, Grace, Luke, Logan, Aiden, Abigail, and Harper. Mia was heard saying, \"If Mia is a knight then Grace is a knight\". \"If Aiden is a knight then Luke is a knight\" - Noah. Grace told you that Aiden is a knave. As Luke put it, \"Noah is a knave or Harper is a knave\". \"Abigail is not a knave,\" Logan declared. Aiden said, \"Logan is not a knave.\" In Abigail's words: \"Logan is a knight if and only if Aiden is a knave\". Harper asserted: \"Abigail is a knight if and only if Abigail is a knave\". So who is a knight and who is a knave?", "names": ["Mia", "Noah", "Grace", "Luke", "Logan", "Aiden", "Abigail", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false, false, false], "solution_text": "Mia is a knight, Noah is a knight, Grace is a knight, Luke is a knight, Logan is a knave, Aiden is a knave, Abigail is a knave, and Harper is a knave.", "solution_text_format": "(1) Mia is a knight\n(2) Noah is a knight\n(3) Grace is a knight\n(4) Luke is a knight\n(5) Logan is a knave\n(6) Aiden is a knave\n(7) Abigail is a knave\n(8) Harper is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that If Mia is a knight then Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Aiden is a knave.", "Aiden cannot be a knight, because this would contradict the claim of Grace that Aiden is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Logan is not a knave.", "Logan cannot be a knight, because this would contradict the false claim of Aiden that Logan is not a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Abigail is not a knave.", "Abigail cannot be a knight, because this would contradict the false claim of Logan that Abigail is not a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Logan is a knight if and only if Aiden is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that If Aiden is a knight then Luke is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Noah is a knave or Harper is a knave.", "Harper cannot be a knight, because this would contradict the claim of Luke that Noah is a knave or Harper is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Abigail is a knight if and only if Abigail is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 0), ('telling-truth', 2)), ('->', ('telling-truth', 5), ('telling-truth', 3)), ('lying', 5), ('or', ('lying', 1), ('lying', 7)), ('not', ('lying', 6)), ('not', ('lying', 4)), ('<=>', ('telling-truth', 4), ('lying', 5)), ('<=>', ('telling-truth', 6), ('lying', 6)))", "index": 343}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Luke, Victoria, James, Aria, Evelyn, Ethan, Sophia, and David. \"Aria is a knight or David is a knave,\" Luke claimed. In a statement by Victoria: \"David is a knight or Ethan is a knave\". James expressed that Ethan is a knight and James is a knight. Aria told you that Victoria is not a knave. Evelyn remarked, \"If James is a knight then David is a knave\". According to Ethan, \"Ethan is a knight and Luke is a knave\". In Sophia's words: \"David is not a knight\". David remarked, \"If Ethan is a knave then Luke is a knight\". So who is a knight and who is a knave?", "names": ["Luke", "Victoria", "James", "Aria", "Evelyn", "Ethan", "Sophia", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false, false, true], "solution_text": "Luke is a knight, Victoria is a knight, James is a knave, Aria is a knight, Evelyn is a knight, Ethan is a knave, Sophia is a knave, and David is a knight.", "solution_text_format": "(1) Luke is a knight\n(2) Victoria is a knight\n(3) James is a knave\n(4) Aria is a knight\n(5) Evelyn is a knight\n(6) Ethan is a knave\n(7) Sophia is a knave\n(8) David is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Aria is a knight or David is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Victoria is not a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that David is a knight or Ethan is a knave.", "Assume David is a knight. No contradiction is found in their claim that If Ethan is a knave then Luke is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Ethan is a knight and Luke is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Ethan is a knight and Luke is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Ethan is a knight and James is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Ethan is a knight and James is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If James is a knight then David is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that David is not a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that David is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('lying', 7)), ('or', ('telling-truth', 7), ('lying', 5)), ('and', ('telling-truth', 5), ('telling-truth', 2)), ('not', ('lying', 1)), ('->', ('telling-truth', 2), ('lying', 7)), ('and', ('telling-truth', 5), ('lying', 0)), ('not', ('telling-truth', 7)), ('->', ('lying', 5), ('telling-truth', 0)))", "index": 344}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Abigail, James, Charlotte, Owen, Sophia, Elizabeth, Joseph, and Henry. Abigail remarked, \"Henry is a knight\". \"Henry is a knave if and only if Owen is a knave,\" James declared. Charlotte said, \"If Owen is a knight then Elizabeth is a knave.\" Owen remarked, \"Elizabeth is a knight\". Sophia commented, \"Charlotte is a knight and Elizabeth is a knave\". \"Charlotte is a knave if and only if Charlotte is a knight\" - Elizabeth. \"Sophia is not a knight,\" Joseph declared. Henry told you that If Joseph is a knave then Sophia is a knave. So who is a knight and who is a knave?", "names": ["Abigail", "James", "Charlotte", "Owen", "Sophia", "Elizabeth", "Joseph", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, false, false, false], "solution_text": "Abigail is a knave, James is a knight, Charlotte is a knight, Owen is a knave, Sophia is a knight, Elizabeth is a knave, Joseph is a knave, and Henry is a knave.", "solution_text_format": "(1) Abigail is a knave\n(2) James is a knight\n(3) Charlotte is a knight\n(4) Owen is a knave\n(5) Sophia is a knight\n(6) Elizabeth is a knave\n(7) Joseph is a knave\n(8) Henry is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Henry is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that If Joseph is a knave then Sophia is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Sophia is not a knight.", "Sophia cannot be a knight, because this would contradict the claim of Joseph that Sophia is not a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Charlotte is a knight and Elizabeth is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Owen is a knight then Elizabeth is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Charlotte that If Owen is a knight then Elizabeth is a knave.", "Elizabeth cannot be a knave, because this would contradict the claim of Owen that Elizabeth is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the false claim of Owen that Elizabeth is a knight.", "Elizabeth cannot be a knave, because this would contradict the false claim of Sophia that Charlotte is a knight and Elizabeth is a knave.", "We have exhausted all possibilities for Elizabeth and Owen, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that If Owen is a knight then Elizabeth is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Charlotte is a knave if and only if Charlotte is a knight.", "Elizabeth cannot be a knave, because this would contradict the false claim of Charlotte that If Owen is a knight then Elizabeth is a knave.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the false claim of Charlotte that If Owen is a knight then Elizabeth is a knave.", "We have exhausted all possibilities for Owen, Charlotte, and Sophia, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Sophia is not a knight.", "Sophia cannot be a knight, because this would contradict the claim of Henry that If Joseph is a knave then Sophia is a knave.", "Sophia cannot be a knave, because this would contradict the false claim of Joseph that Sophia is not a knight.", "We have exhausted all possibilities for Sophia and Joseph, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the claim of Abigail that Henry is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Henry is a knight.", "Henry cannot be a knight, because this would contradict the false claim of Abigail that Henry is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that If Joseph is a knave then Sophia is a knave.", "Joseph cannot be a knight, because this would contradict the false claim of Henry that If Joseph is a knave then Sophia is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Sophia is not a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Charlotte is a knight and Elizabeth is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Owen is a knight then Elizabeth is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Charlotte that If Owen is a knight then Elizabeth is a knave.", "Elizabeth cannot be a knave, because this would contradict the claim of Owen that Elizabeth is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the false claim of Owen that Elizabeth is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Charlotte is a knave if and only if Charlotte is a knight.", "Assume James is a knight. No contradiction is found in their claim that Henry is a knave if and only if Owen is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 7), ('<=>', ('lying', 7), ('lying', 3)), ('->', ('telling-truth', 3), ('lying', 5)), ('telling-truth', 5), ('and', ('telling-truth', 2), ('lying', 5)), ('<=>', ('lying', 2), ('telling-truth', 2)), ('not', ('telling-truth', 4)), ('->', ('lying', 6), ('lying', 4)))", "index": 345}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Olivia, Aria, Daniel, Alexander, Aiden, Ella, Joseph, and Sophia. As Olivia put it, \"Aiden is a knight if and only if Aria is a knight\". Aria was heard saying, \"Aiden is a knight if and only if Aria is a knight\". Daniel asserted: \"Olivia is not a knight\". In Alexander's words: \"If Alexander is a knight then Aiden is a knight\". Aiden remarked, \"Joseph is not a knight\". Ella told you that Aria is a knave or Daniel is a knight. \"If Ella is a knight then Sophia is a knight,\" Joseph mentioned. \"Ella is a knight if and only if Aiden is a knave,\" Sophia declared. So who is a knight and who is a knave?", "names": ["Olivia", "Aria", "Daniel", "Alexander", "Aiden", "Ella", "Joseph", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true, false, false], "solution_text": "Olivia is a knave, Aria is a knave, Daniel is a knight, Alexander is a knight, Aiden is a knight, Ella is a knight, Joseph is a knave, and Sophia is a knave.", "solution_text_format": "(1) Olivia is a knave\n(2) Aria is a knave\n(3) Daniel is a knight\n(4) Alexander is a knight\n(5) Aiden is a knight\n(6) Ella is a knight\n(7) Joseph is a knave\n(8) Sophia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Aiden is a knight if and only if Aria is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Joseph is not a knight.", "Joseph cannot be a knight, because this would contradict the claim of Aiden that Joseph is not a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that If Ella is a knight then Sophia is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Aria is a knave or Daniel is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Aiden is a knight if and only if Aria is a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that Olivia is not a knight.", "Daniel cannot be a knave, because this would contradict the claim of Ella that Aria is a knave or Daniel is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Aria.", "Aria cannot be a knave, because this would contradict the claim of Olivia that Aiden is a knight if and only if Aria is a knight.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the false claim of Joseph that If Ella is a knight then Sophia is a knight.", "We have exhausted all possibilities for Ella and Joseph, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Joseph is not a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Ella is a knight then Sophia is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Aria is a knave or Daniel is a knight.", "Aria cannot be a knight, because this would contradict the claim of Olivia that Aiden is a knight if and only if Aria is a knight.", "Aria cannot be a knave, because this would contradict the false claim of their own that Aiden is a knight if and only if Aria is a knight.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Aria is a knave or Daniel is a knight.", "Aria cannot be a knight, because this would contradict the claim of Olivia that Aiden is a knight if and only if Aria is a knight.", "Aria cannot be a knave, because this would contradict the false claim of their own that Aiden is a knight if and only if Aria is a knight.", "We have exhausted all possibilities for Aria and Ella, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the false claim of Aiden that Joseph is not a knight.", "We have exhausted all possibilities for Joseph and Aiden, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Aiden is a knight if and only if Aria is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Joseph is not a knight.", "Joseph cannot be a knight, because this would contradict the claim of Aiden that Joseph is not a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that If Ella is a knight then Sophia is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Aria is a knave or Daniel is a knight.", "Aria cannot be a knight, because this would contradict the false claim of Olivia that Aiden is a knight if and only if Aria is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Aiden is a knight if and only if Aria is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Olivia is not a knight.", "Sophia cannot be a knight, because this would contradict the false claim of Joseph that If Ella is a knight then Sophia is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Ella is a knight if and only if Aiden is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that If Alexander is a knight then Aiden is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 4), ('telling-truth', 1)), ('<=>', ('telling-truth', 4), ('telling-truth', 1)), ('not', ('telling-truth', 0)), ('->', ('telling-truth', 3), ('telling-truth', 4)), ('not', ('telling-truth', 6)), ('or', ('lying', 1), ('telling-truth', 2)), ('->', ('telling-truth', 5), ('telling-truth', 7)), ('<=>', ('telling-truth', 5), ('lying', 4)))", "index": 346}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Benjamin, Liam, Aurora, Amelia, Luke, Daniel, Abigail, and Penelope. Benjamin was heard saying, \"Luke is a knight or Daniel is a knave\". As Liam put it, \"Abigail is a knave and Aurora is a knave\". Aurora stated, \"Benjamin is a knight if and only if Abigail is a knight\". Amelia was heard saying, \"Abigail is a knave if and only if Aurora is a knight\". \"Amelia is a knight\" - Luke. According to Daniel, \"Amelia is a knave if and only if Aurora is a knight\". Abigail told you that Aurora is a knight if and only if Daniel is a knave. As Penelope put it, \"If Luke is a knave then Abigail is a knight\". So who is a knight and who is a knave?", "names": ["Benjamin", "Liam", "Aurora", "Amelia", "Luke", "Daniel", "Abigail", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, false, false, false], "solution_text": "Benjamin is a knight, Liam is a knight, Aurora is a knave, Amelia is a knave, Luke is a knave, Daniel is a knave, Abigail is a knave, and Penelope is a knave.", "solution_text_format": "(1) Benjamin is a knight\n(2) Liam is a knight\n(3) Aurora is a knave\n(4) Amelia is a knave\n(5) Luke is a knave\n(6) Daniel is a knave\n(7) Abigail is a knave\n(8) Penelope is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Luke is a knight or Daniel is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Amelia is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Abigail is a knave if and only if Aurora is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Aurora is a knight if and only if Daniel is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Amelia that Abigail is a knave if and only if Aurora is a knight.", "Aurora cannot be a knave, because this would contradict the false claim of their own that Benjamin is a knight if and only if Abigail is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Aurora is a knight if and only if Daniel is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight if and only if Abigail is a knight.", "Aurora cannot be a knave, because this would contradict the claim of Amelia that Abigail is a knave if and only if Aurora is a knight.", "We have exhausted all possibilities for Aurora and Abigail, so let us go back and reconsider Amelia.", "Amelia cannot be a knave, because this would contradict the claim of Luke that Amelia is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Amelia is a knight.", "Amelia cannot be a knight, because this would contradict the false claim of Luke that Amelia is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Abigail is a knave if and only if Aurora is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Aurora is a knight if and only if Daniel is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Benjamin is a knight if and only if Abigail is a knight.", "Daniel cannot be a knight, because this would contradict the claim of Benjamin that Luke is a knight or Daniel is a knave.", "Daniel cannot be a knave, because this would contradict the false claim of their own that Amelia is a knave if and only if Aurora is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the false claim of their own that Benjamin is a knight if and only if Abigail is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Aurora is a knight if and only if Daniel is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight if and only if Abigail is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Benjamin is a knight if and only if Abigail is a knight.", "Daniel cannot be a knight, because this would contradict the claim of Benjamin that Luke is a knight or Daniel is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Amelia is a knave if and only if Aurora is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Abigail is a knave and Aurora is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that If Luke is a knave then Abigail is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that If Luke is a knave then Abigail is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('lying', 5)), ('and', ('lying', 6), ('lying', 2)), ('<=>', ('telling-truth', 0), ('telling-truth', 6)), ('<=>', ('lying', 6), ('telling-truth', 2)), ('telling-truth', 3), ('<=>', ('lying', 3), ('telling-truth', 2)), ('<=>', ('telling-truth', 2), ('lying', 5)), ('->', ('lying', 4), ('telling-truth', 6)))", "index": 347}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: William, Riley, Logan, Luke, Aiden, Abigail, Aurora, and Matthew. William commented, \"Aiden is not a knight\". In Riley's words: \"Aiden is a knave or Matthew is a knight\". \"Matthew is a knight or William is a knight,\" Logan claimed. \"Abigail is a knave and Matthew is a knave,\" Luke declared. Aiden was heard saying, \"Aurora is a knight and Matthew is a knight\". According to Abigail, \"Riley is a knight if and only if Riley is a knave\". \"Abigail is a knave,\" Aurora mentioned. As Matthew put it, \"Riley is a knave if and only if Abigail is a knave\". So who is a knight and who is a knave?", "names": ["William", "Riley", "Logan", "Luke", "Aiden", "Abigail", "Aurora", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false, true, false], "solution_text": "William is a knight, Riley is a knight, Logan is a knight, Luke is a knight, Aiden is a knave, Abigail is a knave, Aurora is a knight, and Matthew is a knave.", "solution_text_format": "(1) William is a knight\n(2) Riley is a knight\n(3) Logan is a knight\n(4) Luke is a knight\n(5) Aiden is a knave\n(6) Abigail is a knave\n(7) Aurora is a knight\n(8) Matthew is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Aiden is not a knight.", "Aiden cannot be a knight, because this would contradict the claim of William that Aiden is not a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Aurora is a knight and Matthew is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Riley is a knight if and only if Riley is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Riley is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Aiden is a knave or Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the false claim of Aiden that Aurora is a knight and Matthew is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Riley is a knave if and only if Abigail is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Matthew is a knight or William is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Abigail is a knave and Matthew is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 4)), ('or', ('lying', 4), ('telling-truth', 7)), ('or', ('telling-truth', 7), ('telling-truth', 0)), ('and', ('lying', 5), ('lying', 7)), ('and', ('telling-truth', 6), ('telling-truth', 7)), ('<=>', ('telling-truth', 1), ('lying', 1)), ('lying', 5), ('<=>', ('lying', 1), ('lying', 5)))", "index": 348}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jack, David, Logan, Zoey, Elizabeth, Matthew, Sophia, and William. \"Logan is not a knight\" - Jack. David commented, \"If Elizabeth is a knave then Sophia is a knight\". Logan stated, \"Elizabeth is a knave if and only if Jack is a knave\". Zoey stated, \"Jack is a knight\". As Elizabeth put it, \"Sophia is not a knight\". Matthew noted, \"Sophia is a knave\". \"Logan is not a knave,\" Sophia mentioned. William said, \"Zoey is a knight if and only if David is a knave.\" So who is a knight and who is a knave?", "names": ["Jack", "David", "Logan", "Zoey", "Elizabeth", "Matthew", "Sophia", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false, true, true], "solution_text": "Jack is a knave, David is a knight, Logan is a knight, Zoey is a knave, Elizabeth is a knave, Matthew is a knave, Sophia is a knight, and William is a knight.", "solution_text_format": "(1) Jack is a knave\n(2) David is a knight\n(3) Logan is a knight\n(4) Zoey is a knave\n(5) Elizabeth is a knave\n(6) Matthew is a knave\n(7) Sophia is a knight\n(8) William is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Logan is not a knight.", "Logan cannot be a knight, because this would contradict the claim of Jack that Logan is not a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Elizabeth is a knave if and only if Jack is a knave.", "Elizabeth cannot be a knight, because this would contradict the false claim of Logan that Elizabeth is a knave if and only if Jack is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Sophia is not a knight.", "Sophia cannot be a knight, because this would contradict the claim of their own that Logan is not a knave.", "Sophia cannot be a knave, because this would contradict the false claim of Elizabeth that Sophia is not a knight.", "We have exhausted all possibilities for Sophia, Elizabeth, and Logan, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Logan is not a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Elizabeth is a knave if and only if Jack is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of Logan that Elizabeth is a knave if and only if Jack is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Sophia is not a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Logan is not a knave.", "Assume David is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Sophia is a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that Jack is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Jack is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Sophia is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Sophia is a knave.", "Assume William is a knight. No contradiction is found in their claim that Zoey is a knight if and only if David is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('->', ('lying', 4), ('telling-truth', 6)), ('<=>', ('lying', 4), ('lying', 0)), ('telling-truth', 0), ('not', ('telling-truth', 6)), ('lying', 6), ('not', ('lying', 2)), ('<=>', ('telling-truth', 3), ('lying', 1)))", "index": 349}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: David, Zoey, Elizabeth, Grace, Owen, Michael, Charlotte, and Penelope. In a statement by David: \"Michael is a knave or Grace is a knight\". \"Elizabeth is a knight and Owen is a knight,\" Zoey declared. Elizabeth said that Grace is a knight if and only if Owen is a knave. \"Michael is a knight and David is a knave,\" Grace claimed. In Owen's words: \"Penelope is a knight or Elizabeth is a knight\". In a statement by Michael: \"Penelope is a knight if and only if Owen is a knight\". Charlotte noted, \"Zoey is a knight if and only if Michael is a knight\". Penelope expressed that David is a knave. So who is a knight and who is a knave?", "names": ["David", "Zoey", "Elizabeth", "Grace", "Owen", "Michael", "Charlotte", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false, false, false], "solution_text": "David is a knight, Zoey is a knight, Elizabeth is a knight, Grace is a knave, Owen is a knight, Michael is a knave, Charlotte is a knave, and Penelope is a knave.", "solution_text_format": "(1) David is a knight\n(2) Zoey is a knight\n(3) Elizabeth is a knight\n(4) Grace is a knave\n(5) Owen is a knight\n(6) Michael is a knave\n(7) Charlotte is a knave\n(8) Penelope is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Michael is a knave or Grace is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Penelope is a knight if and only if Owen is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that David is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that David is a knave.", "Owen cannot be a knight, because this would contradict the claim of Michael that Penelope is a knight if and only if Owen is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Penelope is a knight or Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the false claim of Owen that Penelope is a knight or Elizabeth is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Grace is a knight if and only if Owen is a knave.", "Grace cannot be a knight, because this would contradict the false claim of Elizabeth that Grace is a knight if and only if Owen is a knave.", "Grace cannot be a knave, because this would contradict the claim of David that Michael is a knave or Grace is a knight.", "We have exhausted all possibilities for Grace, Elizabeth, Owen, and Penelope, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Penelope is a knight if and only if Owen is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that David is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that David is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Penelope is a knight or Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Grace is a knight if and only if Owen is a knave.", "Grace cannot be a knight, because this would contradict the claim of Elizabeth that Grace is a knight if and only if Owen is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Michael is a knight and David is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Elizabeth is a knight and Owen is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Zoey is a knight if and only if Michael is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Zoey is a knight if and only if Michael is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 5), ('telling-truth', 3)), ('and', ('telling-truth', 2), ('telling-truth', 4)), ('<=>', ('telling-truth', 3), ('lying', 4)), ('and', ('telling-truth', 5), ('lying', 0)), ('or', ('telling-truth', 7), ('telling-truth', 2)), ('<=>', ('telling-truth', 7), ('telling-truth', 4)), ('<=>', ('telling-truth', 1), ('telling-truth', 5)), ('lying', 0))", "index": 350}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Riley, Penelope, Ella, Evelyn, Mia, Joseph, Lucas, and Ava. Riley said that Ava is a knave and Evelyn is a knave. Penelope said, \"If Joseph is a knave then Mia is a knave.\" Ella noted, \"Ava is a knave or Lucas is a knight\". \"If Lucas is a knave then Ella is a knight,\" Evelyn declared. Mia commented, \"Ella is not a knave\". \"Riley is a knight if and only if Penelope is a knight,\" Joseph claimed. According to Lucas, \"Riley is a knight\". Ava asserted: \"If Ella is a knight then Lucas is a knave\". So who is a knight and who is a knave?", "names": ["Riley", "Penelope", "Ella", "Evelyn", "Mia", "Joseph", "Lucas", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, false, false, true], "solution_text": "Riley is a knave, Penelope is a knight, Ella is a knave, Evelyn is a knave, Mia is a knave, Joseph is a knave, Lucas is a knave, and Ava is a knight.", "solution_text_format": "(1) Riley is a knave\n(2) Penelope is a knight\n(3) Ella is a knave\n(4) Evelyn is a knave\n(5) Mia is a knave\n(6) Joseph is a knave\n(7) Lucas is a knave\n(8) Ava is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Ava is a knave and Evelyn is a knave.", "Ava cannot be a knight, because this would contradict the claim of Riley that Ava is a knave and Evelyn is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that If Ella is a knight then Lucas is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Ava is a knave or Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Riley is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of Riley that Ava is a knave and Evelyn is a knave.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that If Lucas is a knave then Ella is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the false claim of their own that Riley is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the false claim of their own that Ava is a knave or Lucas is a knight.", "We have exhausted all possibilities for Ella and Ava, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Ava is a knave and Evelyn is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that If Ella is a knight then Lucas is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Ava is a knave or Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Riley is a knight.", "Lucas cannot be a knave, because this would contradict the claim of Ella that Ava is a knave or Lucas is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Ava is a knave or Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of Ella that Ava is a knave or Lucas is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Riley is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that If Lucas is a knave then Ella is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that If Lucas is a knave then Ella is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that If Joseph is a knave then Mia is a knave.", "Joseph cannot be a knight, because this would contradict the claim of their own that Riley is a knight if and only if Penelope is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Penelope is a knight.", "Mia cannot be a knight, because this would contradict the claim of Penelope that If Joseph is a knave then Mia is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Ella is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 7), ('lying', 3)), ('->', ('lying', 5), ('lying', 4)), ('or', ('lying', 7), ('telling-truth', 6)), ('->', ('lying', 6), ('telling-truth', 2)), ('not', ('lying', 2)), ('<=>', ('telling-truth', 0), ('telling-truth', 1)), ('telling-truth', 0), ('->', ('telling-truth', 2), ('lying', 6)))", "index": 351}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Michael, Noah, Jacob, Scarlett, Chloe, Joseph, Ethan, and Samuel. Michael expressed that Jacob is a knight if and only if Chloe is a knight. As Noah put it, \"Samuel is a knight or Joseph is a knight\". In a statement by Jacob: \"Joseph is a knight if and only if Chloe is a knight\". Scarlett asserted: \"If Jacob is a knave then Michael is a knight\". \"If Scarlett is a knight then Ethan is a knave\" - Chloe. \"Scarlett is a knight and Ethan is a knight\" - Joseph. \"Michael is a knight if and only if Michael is a knave,\" Ethan mentioned. \"Jacob is a knight\" - Samuel. So who is a knight and who is a knave?", "names": ["Michael", "Noah", "Jacob", "Scarlett", "Chloe", "Joseph", "Ethan", "Samuel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, false, false, false], "solution_text": "Michael is a knave, Noah is a knave, Jacob is a knave, Scarlett is a knave, Chloe is a knight, Joseph is a knave, Ethan is a knave, and Samuel is a knave.", "solution_text_format": "(1) Michael is a knave\n(2) Noah is a knave\n(3) Jacob is a knave\n(4) Scarlett is a knave\n(5) Chloe is a knight\n(6) Joseph is a knave\n(7) Ethan is a knave\n(8) Samuel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Jacob is a knight if and only if Chloe is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Joseph is a knight if and only if Chloe is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Scarlett is a knight and Ethan is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Jacob is a knave then Michael is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Michael is a knight if and only if Michael is a knave.", "Ethan cannot be a knave, because this would contradict the claim of Joseph that Scarlett is a knight and Ethan is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the false claim of their own that If Jacob is a knave then Michael is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Scarlett is a knight and Ethan is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Jacob is a knave then Michael is a knight.", "Ethan cannot be a knight, because this would contradict the false claim of Joseph that Scarlett is a knight and Ethan is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Michael is a knight if and only if Michael is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Jacob that Joseph is a knight if and only if Chloe is a knight.", "Chloe cannot be a knave, because this would contradict the claim of Michael that Jacob is a knight if and only if Chloe is a knight.", "We have exhausted all possibilities for Chloe and Ethan, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the false claim of their own that If Jacob is a knave then Michael is a knight.", "We have exhausted all possibilities for Scarlett and Joseph, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Joseph is a knight if and only if Chloe is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Scarlett is a knight and Ethan is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Jacob is a knave then Michael is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Michael is a knight if and only if Michael is a knave.", "Ethan cannot be a knave, because this would contradict the claim of Joseph that Scarlett is a knight and Ethan is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the false claim of their own that If Jacob is a knave then Michael is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Scarlett is a knight and Ethan is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Jacob is a knave then Michael is a knight.", "Ethan cannot be a knight, because this would contradict the false claim of Joseph that Scarlett is a knight and Ethan is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Michael is a knight if and only if Michael is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Michael that Jacob is a knight if and only if Chloe is a knight.", "Chloe cannot be a knave, because this would contradict the false claim of Jacob that Joseph is a knight if and only if Chloe is a knight.", "We have exhausted all possibilities for Chloe and Ethan, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the false claim of their own that If Jacob is a knave then Michael is a knight.", "We have exhausted all possibilities for Scarlett, Joseph, and Jacob, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Jacob is a knight if and only if Chloe is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Joseph is a knight if and only if Chloe is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Scarlett is a knight and Ethan is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Jacob is a knave then Michael is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Michael is a knight if and only if Michael is a knave.", "Ethan cannot be a knave, because this would contradict the claim of Joseph that Scarlett is a knight and Ethan is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the false claim of their own that If Jacob is a knave then Michael is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Scarlett is a knight and Ethan is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Jacob is a knave then Michael is a knight.", "Ethan cannot be a knight, because this would contradict the false claim of Joseph that Scarlett is a knight and Ethan is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Michael is a knight if and only if Michael is a knave.", "Chloe cannot be a knight, because this would contradict the false claim of Michael that Jacob is a knight if and only if Chloe is a knight.", "Chloe cannot be a knave, because this would contradict the false claim of their own that If Scarlett is a knight then Ethan is a knave.", "We have exhausted all possibilities for Chloe and Ethan, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the false claim of their own that If Jacob is a knave then Michael is a knight.", "We have exhausted all possibilities for Scarlett and Joseph, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Joseph is a knight if and only if Chloe is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Scarlett is a knight and Ethan is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that If Jacob is a knave then Michael is a knight.", "Scarlett cannot be a knave, because this would contradict the claim of Joseph that Scarlett is a knight and Ethan is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Scarlett is a knight and Ethan is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that If Jacob is a knave then Michael is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that If Jacob is a knave then Michael is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Michael is a knight if and only if Michael is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Michael is a knight if and only if Michael is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that If Scarlett is a knight then Ethan is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Samuel is a knight or Joseph is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Jacob is a knight.", "Samuel cannot be a knave, because this would contradict the claim of Noah that Samuel is a knight or Joseph is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Samuel is a knight or Joseph is a knight.", "Samuel cannot be a knight, because this would contradict the false claim of Noah that Samuel is a knight or Joseph is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Jacob is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('telling-truth', 4)), ('or', ('telling-truth', 7), ('telling-truth', 5)), ('<=>', ('telling-truth', 5), ('telling-truth', 4)), ('->', ('lying', 2), ('telling-truth', 0)), ('->', ('telling-truth', 3), ('lying', 6)), ('and', ('telling-truth', 3), ('telling-truth', 6)), ('<=>', ('telling-truth', 0), ('lying', 0)), ('telling-truth', 2))", "index": 352}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Luke, Emily, Oliver, Jack, Sebastian, Lily, Samuel, and Jacob. In a statement by Luke: \"Samuel is a knight if and only if Jack is a knight\". \"Samuel is not a knight,\" Emily mentioned. Oliver noted, \"If Emily is a knave then Samuel is a knight\". According to Jack, \"Sebastian is a knight\". \"Emily is a knight\" - Sebastian. \"Samuel is a knave or Samuel is a knight\" - Lily. Samuel expressed that Luke is a knight and Jacob is a knave. As Jacob put it, \"Sebastian is a knave or Lily is a knight\". So who is a knight and who is a knave?", "names": ["Luke", "Emily", "Oliver", "Jack", "Sebastian", "Lily", "Samuel", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true, false, true], "solution_text": "Luke is a knave, Emily is a knight, Oliver is a knight, Jack is a knight, Sebastian is a knight, Lily is a knight, Samuel is a knave, and Jacob is a knight.", "solution_text_format": "(1) Luke is a knave\n(2) Emily is a knight\n(3) Oliver is a knight\n(4) Jack is a knight\n(5) Sebastian is a knight\n(6) Lily is a knight\n(7) Samuel is a knave\n(8) Jacob is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Samuel is a knight if and only if Jack is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Luke is a knight and Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Samuel that Luke is a knight and Jacob is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Sebastian is a knave or Lily is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Emily is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Samuel is not a knight.", "Emily cannot be a knave, because this would contradict the claim of Sebastian that Emily is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the false claim of Jacob that Sebastian is a knave or Lily is a knight.", "We have exhausted all possibilities for Sebastian and Jacob, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Luke is a knight and Jacob is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Sebastian is a knave or Lily is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Samuel is not a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Samuel is a knave or Samuel is a knight.", "Jack cannot be a knight, because this would contradict the claim of Luke that Samuel is a knight if and only if Jack is a knight.", "Jack cannot be a knave, because this would contradict the false claim of their own that Sebastian is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the false claim of their own that Samuel is a knave or Samuel is a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the false claim of their own that Samuel is not a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Emily is a knight.", "Emily cannot be a knight, because this would contradict the false claim of Sebastian that Emily is a knight.", "Emily cannot be a knave, because this would contradict the false claim of their own that Samuel is not a knight.", "We have exhausted all possibilities for Emily and Sebastian, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the false claim of Samuel that Luke is a knight and Jacob is a knave.", "We have exhausted all possibilities for Jacob and Samuel, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Samuel is a knight if and only if Jack is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Luke is a knight and Jacob is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Luke is a knight and Jacob is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Sebastian is a knave or Lily is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Samuel is not a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Samuel is a knave or Samuel is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Sebastian is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that If Emily is a knave then Samuel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 6), ('telling-truth', 3)), ('not', ('telling-truth', 6)), ('->', ('lying', 1), ('telling-truth', 6)), ('telling-truth', 4), ('telling-truth', 1), ('or', ('lying', 6), ('telling-truth', 6)), ('and', ('telling-truth', 0), ('lying', 7)), ('or', ('lying', 4), ('telling-truth', 5)))", "index": 353}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Michael, Penelope, Matthew, Sebastian, Aurora, Avery, Luke, and Riley. \"Matthew is a knave and Penelope is a knave\" - Michael. Penelope stated, \"Avery is not a knave\". Matthew remarked, \"Luke is a knave and Michael is a knave\". Sebastian was heard saying, \"Matthew is a knave if and only if Aurora is a knave\". Aurora said, \"Avery is a knave and Riley is a knight.\" Avery expressed that Riley is a knave. \"Penelope is a knight and Riley is a knave\" - Luke. \"Aurora is a knave and Sebastian is a knave,\" Riley mentioned. So who is a knight and who is a knave?", "names": ["Michael", "Penelope", "Matthew", "Sebastian", "Aurora", "Avery", "Luke", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, true, true, false], "solution_text": "Michael is a knave, Penelope is a knight, Matthew is a knave, Sebastian is a knight, Aurora is a knave, Avery is a knight, Luke is a knight, and Riley is a knave.", "solution_text_format": "(1) Michael is a knave\n(2) Penelope is a knight\n(3) Matthew is a knave\n(4) Sebastian is a knight\n(5) Aurora is a knave\n(6) Avery is a knight\n(7) Luke is a knight\n(8) Riley is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Matthew is a knave and Penelope is a knave.", "Matthew cannot be a knight, because this would contradict the claim of Michael that Matthew is a knave and Penelope is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Luke is a knave and Michael is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Penelope is a knight and Riley is a knave.", "Penelope cannot be a knight, because this would contradict the claim of Michael that Matthew is a knave and Penelope is a knave.", "Penelope cannot be a knave, because this would contradict the claim of Luke that Penelope is a knight and Riley is a knave.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Penelope is a knight and Riley is a knave.", "Penelope cannot be a knight, because this would contradict the claim of Michael that Matthew is a knave and Penelope is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Avery is not a knave.", "Avery cannot be a knight, because this would contradict the false claim of Penelope that Avery is not a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Riley is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Aurora is a knave and Sebastian is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Riley that Aurora is a knave and Sebastian is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of their own that Avery is a knave and Riley is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Riley.", "Riley cannot be a knave, because this would contradict the false claim of Avery that Riley is a knave.", "We have exhausted all possibilities for Riley, Avery, Penelope, Luke, and Matthew, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Matthew is a knave and Penelope is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Luke is a knave and Michael is a knave.", "Luke cannot be a knight, because this would contradict the claim of Matthew that Luke is a knave and Michael is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Penelope is a knight and Riley is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Avery is not a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Riley is a knave.", "Riley cannot be a knight, because this would contradict the claim of Avery that Riley is a knave.", "Riley cannot be a knave, because this would contradict the false claim of Luke that Penelope is a knight and Riley is a knave.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Avery.", "Avery cannot be a knave, because this would contradict the claim of Penelope that Avery is not a knave.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Avery is not a knave.", "Avery cannot be a knight, because this would contradict the false claim of Penelope that Avery is not a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Riley is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Aurora is a knave and Sebastian is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Riley that Aurora is a knave and Sebastian is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of their own that Avery is a knave and Riley is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Riley.", "Riley cannot be a knave, because this would contradict the false claim of Avery that Riley is a knave.", "We have exhausted all possibilities for Riley, Avery, Penelope, and Luke, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Luke is a knave and Michael is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Penelope is a knight and Riley is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Avery is not a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Riley is a knave.", "Riley cannot be a knight, because this would contradict the claim of Avery that Riley is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Aurora is a knave and Sebastian is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Avery is a knave and Riley is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Avery is a knave and Riley is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Matthew is a knave if and only if Aurora is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('lying', 1)), ('not', ('lying', 5)), ('and', ('lying', 6), ('lying', 0)), ('<=>', ('lying', 2), ('lying', 4)), ('and', ('lying', 5), ('telling-truth', 7)), ('lying', 7), ('and', ('telling-truth', 1), ('lying', 7)), ('and', ('lying', 4), ('lying', 3)))", "index": 354}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: James, Chloe, Aiden, Joseph, Scarlett, Michael, Avery, and Sophia. According to James, \"Sophia is a knave or Chloe is a knight\". \"James is a knight or Michael is a knight,\" Chloe claimed. Aiden said that Joseph is a knight and Scarlett is a knight. Joseph remarked, \"If Scarlett is a knight then Scarlett is a knave\". \"Chloe is not a knave,\" Scarlett mentioned. Michael told you that Scarlett is not a knight. \"Joseph is not a knight,\" Avery claimed. Sophia stated, \"Michael is a knight\". So who is a knight and who is a knave?", "names": ["James", "Chloe", "Aiden", "Joseph", "Scarlett", "Michael", "Avery", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, false, true, false], "solution_text": "James is a knight, Chloe is a knight, Aiden is a knave, Joseph is a knave, Scarlett is a knight, Michael is a knave, Avery is a knight, and Sophia is a knave.", "solution_text_format": "(1) James is a knight\n(2) Chloe is a knight\n(3) Aiden is a knave\n(4) Joseph is a knave\n(5) Scarlett is a knight\n(6) Michael is a knave\n(7) Avery is a knight\n(8) Sophia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Sophia is a knave or Chloe is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Michael is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Scarlett is not a knight.", "Scarlett cannot be a knight, because this would contradict the claim of Michael that Scarlett is not a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Chloe is not a knave.", "Chloe cannot be a knight, because this would contradict the false claim of Scarlett that Chloe is not a knave.", "Chloe cannot be a knave, because this would contradict the claim of James that Sophia is a knave or Chloe is a knight.", "We have exhausted all possibilities for Chloe and Scarlett, so let us go back and reconsider Michael.", "Michael cannot be a knave, because this would contradict the claim of Sophia that Michael is a knight.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Michael is a knight.", "Michael cannot be a knight, because this would contradict the false claim of Sophia that Michael is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Scarlett is not a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Chloe is not a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that James is a knight or Michael is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Joseph is a knight and Scarlett is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that If Scarlett is a knight then Scarlett is a knave.", "Joseph cannot be a knave, because this would contradict the claim of Aiden that Joseph is a knight and Scarlett is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Joseph is a knight and Scarlett is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of Aiden that Joseph is a knight and Scarlett is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that If Scarlett is a knight then Scarlett is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Joseph is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 7), ('telling-truth', 1)), ('or', ('telling-truth', 0), ('telling-truth', 5)), ('and', ('telling-truth', 3), ('telling-truth', 4)), ('->', ('telling-truth', 4), ('lying', 4)), ('not', ('lying', 1)), ('not', ('telling-truth', 4)), ('not', ('telling-truth', 3)), ('telling-truth', 5))", "index": 355}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Scarlett, Alexander, Ella, Jack, Harper, Sophia, Logan, and Abigail. Scarlett remarked, \"Harper is a knave and Abigail is a knave\". According to Alexander, \"If Scarlett is a knave then Jack is a knight\". \"Scarlett is a knight if and only if Logan is a knave,\" Ella claimed. \"Logan is a knave and Ella is a knave,\" Jack claimed. In Harper's words: \"If Jack is a knight then Sophia is a knight\". According to Sophia, \"Harper is a knight\". \"Jack is a knave if and only if Alexander is a knave,\" Logan mentioned. Abigail expressed that Sophia is not a knave. So who is a knight and who is a knave?", "names": ["Scarlett", "Alexander", "Ella", "Jack", "Harper", "Sophia", "Logan", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true, true, true], "solution_text": "Scarlett is a knave, Alexander is a knave, Ella is a knight, Jack is a knave, Harper is a knight, Sophia is a knight, Logan is a knight, and Abigail is a knight.", "solution_text_format": "(1) Scarlett is a knave\n(2) Alexander is a knave\n(3) Ella is a knight\n(4) Jack is a knave\n(5) Harper is a knight\n(6) Sophia is a knight\n(7) Logan is a knight\n(8) Abigail is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Harper is a knave and Abigail is a knave.", "Harper cannot be a knight, because this would contradict the claim of Scarlett that Harper is a knave and Abigail is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that If Jack is a knight then Sophia is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Logan is a knave and Ella is a knave.", "Logan cannot be a knight, because this would contradict the claim of Jack that Logan is a knave and Ella is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Jack is a knave if and only if Alexander is a knave.", "Alexander cannot be a knight, because this would contradict the false claim of Logan that Jack is a knave if and only if Alexander is a knave.", "Alexander cannot be a knave, because this would contradict the false claim of their own that If Scarlett is a knave then Jack is a knight.", "We have exhausted all possibilities for Alexander and Logan, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the false claim of Harper that If Jack is a knight then Sophia is a knight.", "We have exhausted all possibilities for Jack and Harper, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Harper is a knave and Abigail is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that If Jack is a knight then Sophia is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Logan is a knave and Ella is a knave.", "Logan cannot be a knight, because this would contradict the claim of Jack that Logan is a knave and Ella is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Jack is a knave if and only if Alexander is a knave.", "Alexander cannot be a knight, because this would contradict the false claim of Logan that Jack is a knave if and only if Alexander is a knave.", "Alexander cannot be a knave, because this would contradict the false claim of their own that If Scarlett is a knave then Jack is a knight.", "We have exhausted all possibilities for Alexander and Logan, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Logan is a knave and Ella is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Jack is a knave if and only if Alexander is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that If Scarlett is a knave then Jack is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that If Scarlett is a knave then Jack is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Scarlett is a knight if and only if Logan is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Harper is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Sophia is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('lying', 7)), ('->', ('lying', 0), ('telling-truth', 3)), ('<=>', ('telling-truth', 0), ('lying', 6)), ('and', ('lying', 6), ('lying', 2)), ('->', ('telling-truth', 3), ('telling-truth', 5)), ('telling-truth', 4), ('<=>', ('lying', 3), ('lying', 1)), ('not', ('lying', 5)))", "index": 356}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: James, Mason, Riley, Chloe, Samuel, David, Joseph, and Victoria. James was heard saying, \"Samuel is not a knave\". Mason was heard saying, \"Samuel is a knave if and only if Riley is a knave\". Riley was heard saying, \"Joseph is a knave\". As Chloe put it, \"Mason is a knight\". Samuel stated, \"Joseph is a knight if and only if Samuel is a knight\". \"If Riley is a knave then Riley is a knight,\" David claimed. As Joseph put it, \"Mason is not a knight\". According to Victoria, \"Chloe is not a knight\". So who is a knight and who is a knave?", "names": ["James", "Mason", "Riley", "Chloe", "Samuel", "David", "Joseph", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, false, true, true], "solution_text": "James is a knight, Mason is a knave, Riley is a knave, Chloe is a knave, Samuel is a knight, David is a knave, Joseph is a knight, and Victoria is a knight.", "solution_text_format": "(1) James is a knight\n(2) Mason is a knave\n(3) Riley is a knave\n(4) Chloe is a knave\n(5) Samuel is a knight\n(6) David is a knave\n(7) Joseph is a knight\n(8) Victoria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Samuel is not a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Joseph is a knight if and only if Samuel is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Mason is not a knight.", "Mason cannot be a knight, because this would contradict the claim of Joseph that Mason is not a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Samuel is a knave if and only if Riley is a knave.", "Riley cannot be a knight, because this would contradict the false claim of Mason that Samuel is a knave if and only if Riley is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Joseph is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Mason is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Mason is a knight.", "David cannot be a knight, because this would contradict the claim of their own that If Riley is a knave then Riley is a knight.", "Assume David is a knave. No contradiction is found in their false claim that If Riley is a knave then Riley is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Chloe is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('<=>', ('lying', 4), ('lying', 2)), ('lying', 6), ('telling-truth', 1), ('<=>', ('telling-truth', 6), ('telling-truth', 4)), ('->', ('lying', 2), ('telling-truth', 2)), ('not', ('telling-truth', 1)), ('not', ('telling-truth', 3)))", "index": 357}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Logan, Sofia, Oliver, Luke, Michael, Victoria, Liam, and Benjamin. Logan expressed that Victoria is not a knight. Sofia commented, \"If Benjamin is a knave then Logan is a knave\". Oliver expressed that If Luke is a knave then Benjamin is a knave. \"Benjamin is a knight or Sofia is a knave\" - Luke. According to Michael, \"Logan is a knight and Victoria is a knight\". \"Michael is a knight and Liam is a knight,\" Victoria mentioned. In a statement by Liam: \"If Luke is a knave then Benjamin is a knave\". \"Michael is a knight if and only if Luke is a knave\" - Benjamin. So who is a knight and who is a knave?", "names": ["Logan", "Sofia", "Oliver", "Luke", "Michael", "Victoria", "Liam", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false, true, true], "solution_text": "Logan is a knight, Sofia is a knight, Oliver is a knight, Luke is a knight, Michael is a knave, Victoria is a knave, Liam is a knight, and Benjamin is a knight.", "solution_text_format": "(1) Logan is a knight\n(2) Sofia is a knight\n(3) Oliver is a knight\n(4) Luke is a knight\n(5) Michael is a knave\n(6) Victoria is a knave\n(7) Liam is a knight\n(8) Benjamin is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that Victoria is not a knight.", "Victoria cannot be a knight, because this would contradict the claim of Logan that Victoria is not a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Michael is a knight and Liam is a knight.", "Michael cannot be a knight, because this would contradict the claim of their own that Logan is a knight and Victoria is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Logan is a knight and Victoria is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that If Luke is a knave then Benjamin is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Benjamin is a knight or Sofia is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Michael is a knight if and only if Luke is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that If Benjamin is a knave then Logan is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that If Luke is a knave then Benjamin is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 5)), ('->', ('lying', 7), ('lying', 0)), ('->', ('lying', 3), ('lying', 7)), ('or', ('telling-truth', 7), ('lying', 1)), ('and', ('telling-truth', 0), ('telling-truth', 5)), ('and', ('telling-truth', 4), ('telling-truth', 6)), ('->', ('lying', 3), ('lying', 7)), ('<=>', ('telling-truth', 4), ('lying', 3)))", "index": 358}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Daniel, Emma, Grace, Oliver, David, Liam, Victoria, and Sofia. Daniel stated, \"Grace is a knave if and only if Sofia is a knight\". As Emma put it, \"Grace is not a knight\". As Grace put it, \"Victoria is a knight\". According to Oliver, \"David is a knave and Liam is a knight\". David said, \"Victoria is not a knave.\" As Liam put it, \"David is a knave or Grace is a knight\". \"Sofia is a knight or Sofia is a knave,\" Victoria mentioned. Sofia said, \"Liam is a knave and Sofia is a knight.\" So who is a knight and who is a knave?", "names": ["Daniel", "Emma", "Grace", "Oliver", "David", "Liam", "Victoria", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true, true, false], "solution_text": "Daniel is a knight, Emma is a knave, Grace is a knight, Oliver is a knave, David is a knight, Liam is a knight, Victoria is a knight, and Sofia is a knave.", "solution_text_format": "(1) Daniel is a knight\n(2) Emma is a knave\n(3) Grace is a knight\n(4) Oliver is a knave\n(5) David is a knight\n(6) Liam is a knight\n(7) Victoria is a knight\n(8) Sofia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that Grace is a knave if and only if Sofia is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Victoria is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Sofia is a knight or Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Daniel that Grace is a knave if and only if Sofia is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Liam is a knave and Sofia is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that David is a knave or Grace is a knight.", "Assume David is a knight. No contradiction is found in their claim that Victoria is not a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Grace is not a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Grace is not a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that David is a knave and Liam is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that David is a knave and Liam is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('telling-truth', 7)), ('not', ('telling-truth', 2)), ('telling-truth', 6), ('and', ('lying', 4), ('telling-truth', 5)), ('not', ('lying', 6)), ('or', ('lying', 4), ('telling-truth', 2)), ('or', ('telling-truth', 7), ('lying', 7)), ('and', ('lying', 5), ('telling-truth', 7)))", "index": 359}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Zoey, Elizabeth, Victoria, Jack, Ella, Noah, Owen, and Ethan. \"Elizabeth is a knight or Owen is a knave,\" Zoey mentioned. Elizabeth told you that Jack is a knave. Victoria said that Ethan is a knave or Noah is a knight. Jack asserted: \"Victoria is not a knave\". According to Ella, \"Zoey is not a knave\". In a statement by Noah: \"Zoey is a knave and Victoria is a knight\". Owen said that Jack is a knave or Elizabeth is a knight. Ethan stated, \"Elizabeth is a knight or Elizabeth is a knave\". So who is a knight and who is a knave?", "names": ["Zoey", "Elizabeth", "Victoria", "Jack", "Ella", "Noah", "Owen", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, false, true, true], "solution_text": "Zoey is a knight, Elizabeth is a knight, Victoria is a knave, Jack is a knave, Ella is a knight, Noah is a knave, Owen is a knight, and Ethan is a knight.", "solution_text_format": "(1) Zoey is a knight\n(2) Elizabeth is a knight\n(3) Victoria is a knave\n(4) Jack is a knave\n(5) Ella is a knight\n(6) Noah is a knave\n(7) Owen is a knight\n(8) Ethan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Zoey is a knight. No contradiction is found in their claim that Elizabeth is a knight or Owen is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of Elizabeth that Jack is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Victoria is not a knave.", "Victoria cannot be a knight, because this would contradict the false claim of Jack that Victoria is not a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Ethan is a knave or Noah is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Elizabeth is a knight or Elizabeth is a knave.", "Noah cannot be a knight, because this would contradict the false claim of Victoria that Ethan is a knave or Noah is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Zoey is a knave and Victoria is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Jack is a knave or Elizabeth is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Zoey is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('lying', 6)), ('lying', 3), ('or', ('lying', 7), ('telling-truth', 5)), ('not', ('lying', 2)), ('not', ('lying', 0)), ('and', ('lying', 0), ('telling-truth', 2)), ('or', ('lying', 3), ('telling-truth', 1)), ('or', ('telling-truth', 1), ('lying', 1)))", "index": 360}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Michael, Aiden, Owen, Victoria, Abigail, Amelia, Liam, and Jack. Michael commented, \"Liam is a knight and Victoria is a knave\". Aiden said, \"Owen is a knave and Amelia is a knave.\" Owen said that Victoria is a knight and Liam is a knave. In a statement by Victoria: \"Amelia is not a knight\". In Abigail's words: \"Liam is a knave and Aiden is a knight\". In Amelia's words: \"Owen is a knight and Jack is a knave\". Liam expressed that Victoria is a knave if and only if Amelia is a knight. Jack told you that Abigail is a knight or Michael is a knight. So who is a knight and who is a knave?", "names": ["Michael", "Aiden", "Owen", "Victoria", "Abigail", "Amelia", "Liam", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, false, true, false], "solution_text": "Michael is a knave, Aiden is a knight, Owen is a knave, Victoria is a knight, Abigail is a knave, Amelia is a knave, Liam is a knight, and Jack is a knave.", "solution_text_format": "(1) Michael is a knave\n(2) Aiden is a knight\n(3) Owen is a knave\n(4) Victoria is a knight\n(5) Abigail is a knave\n(6) Amelia is a knave\n(7) Liam is a knight\n(8) Jack is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Liam is a knight and Victoria is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Victoria is a knave if and only if Amelia is a knight.", "Victoria cannot be a knight, because this would contradict the claim of Michael that Liam is a knight and Victoria is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Amelia is not a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Owen is a knight and Jack is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Victoria is a knight and Liam is a knave.", "Owen cannot be a knave, because this would contradict the claim of Amelia that Owen is a knight and Jack is a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Amelia.", "Amelia cannot be a knave, because this would contradict the false claim of Victoria that Amelia is not a knight.", "We have exhausted all possibilities for Amelia and Victoria, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the claim of Michael that Liam is a knight and Victoria is a knave.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Liam is a knight and Victoria is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Victoria is a knave if and only if Amelia is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Amelia is not a knight.", "Amelia cannot be a knight, because this would contradict the claim of Victoria that Amelia is not a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Owen is a knight and Jack is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Victoria is a knight and Liam is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Victoria is a knight and Liam is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Abigail is a knight or Michael is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Liam is a knave and Aiden is a knight.", "Abigail cannot be a knave, because this would contradict the claim of Jack that Abigail is a knight or Michael is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Abigail is a knight or Michael is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Liam is a knave and Aiden is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Liam is a knave and Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Owen is a knave and Amelia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 6), ('lying', 3)), ('and', ('lying', 2), ('lying', 5)), ('and', ('telling-truth', 3), ('lying', 6)), ('not', ('telling-truth', 5)), ('and', ('lying', 6), ('telling-truth', 1)), ('and', ('telling-truth', 2), ('lying', 7)), ('<=>', ('lying', 3), ('telling-truth', 5)), ('or', ('telling-truth', 4), ('telling-truth', 0)))", "index": 361}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jack, Luke, Lily, Riley, Samuel, Sophia, Joseph, and David. Jack asserted: \"If Lily is a knight then Luke is a knave\". Luke asserted: \"Joseph is a knight\". In Lily's words: \"Riley is a knave and Luke is a knave\". Riley stated, \"Samuel is a knave or Jack is a knight\". Samuel commented, \"Riley is a knave if and only if Riley is a knight\". Sophia remarked, \"If David is a knave then Samuel is a knave\". Joseph stated, \"Samuel is a knight\". David commented, \"If Joseph is a knave then Luke is a knave\". So who is a knight and who is a knave?", "names": ["Jack", "Luke", "Lily", "Riley", "Samuel", "Sophia", "Joseph", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, true, false, true], "solution_text": "Jack is a knight, Luke is a knave, Lily is a knave, Riley is a knight, Samuel is a knave, Sophia is a knight, Joseph is a knave, and David is a knight.", "solution_text_format": "(1) Jack is a knight\n(2) Luke is a knave\n(3) Lily is a knave\n(4) Riley is a knight\n(5) Samuel is a knave\n(6) Sophia is a knight\n(7) Joseph is a knave\n(8) David is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that If Lily is a knight then Luke is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Riley is a knave and Luke is a knave.", "Riley cannot be a knight, because this would contradict the claim of Lily that Riley is a knave and Luke is a knave.", "Riley cannot be a knave, because this would contradict the false claim of their own that Samuel is a knave or Jack is a knight.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Riley is a knave and Luke is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Samuel is a knave or Jack is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Riley is a knave if and only if Riley is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Riley is a knave if and only if Riley is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Samuel is a knight.", "Joseph cannot be a knave, because this would contradict the claim of Luke that Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of Luke that Joseph is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Samuel is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that If David is a knave then Samuel is a knave.", "Assume David is a knight. No contradiction is found in their claim that If Joseph is a knave then Luke is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('lying', 1)), ('telling-truth', 6), ('and', ('lying', 3), ('lying', 1)), ('or', ('lying', 4), ('telling-truth', 0)), ('<=>', ('lying', 3), ('telling-truth', 3)), ('->', ('lying', 7), ('lying', 4)), ('telling-truth', 4), ('->', ('lying', 6), ('lying', 1)))", "index": 362}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aiden, Mia, Alexander, Emily, Elizabeth, Lily, Luke, and Amelia. \"Amelia is a knight if and only if Mia is a knave,\" Aiden claimed. In Mia's words: \"Amelia is a knight or Luke is a knight\". Alexander said that Amelia is a knight. According to Emily, \"If Mia is a knave then Elizabeth is a knave\". Elizabeth noted, \"Emily is not a knave\". Lily expressed that Alexander is a knight or Aiden is a knight. \"Emily is a knave,\" Luke declared. Amelia was heard saying, \"Alexander is a knight if and only if Emily is a knight\". So who is a knight and who is a knave?", "names": ["Aiden", "Mia", "Alexander", "Emily", "Elizabeth", "Lily", "Luke", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true, false, true], "solution_text": "Aiden is a knave, Mia is a knight, Alexander is a knight, Emily is a knight, Elizabeth is a knight, Lily is a knight, Luke is a knave, and Amelia is a knight.", "solution_text_format": "(1) Aiden is a knave\n(2) Mia is a knight\n(3) Alexander is a knight\n(4) Emily is a knight\n(5) Elizabeth is a knight\n(6) Lily is a knight\n(7) Luke is a knave\n(8) Amelia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Amelia is a knight if and only if Mia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Alexander is a knight if and only if Emily is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Amelia is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that If Mia is a knave then Elizabeth is a knave.", "Mia cannot be a knight, because this would contradict the claim of Aiden that Amelia is a knight if and only if Mia is a knave.", "Mia cannot be a knave, because this would contradict the false claim of their own that Amelia is a knight or Luke is a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the claim of Amelia that Alexander is a knight if and only if Emily is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Alexander.", "Alexander cannot be a knave, because this would contradict the false claim of their own that Amelia is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Alexander is a knight if and only if Emily is a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that Amelia is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Amelia is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that If Mia is a knave then Elizabeth is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Amelia is a knight or Luke is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Emily is a knave.", "Luke cannot be a knave, because this would contradict the claim of Mia that Amelia is a knight or Luke is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the claim of Aiden that Amelia is a knight if and only if Mia is a knave.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the false claim of Amelia that Alexander is a knight if and only if Emily is a knight.", "We have exhausted all possibilities for Emily, Alexander, and Amelia, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Amelia is a knight if and only if Mia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Alexander is a knight if and only if Emily is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Amelia is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that If Mia is a knave then Elizabeth is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Amelia is a knight or Luke is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Emily is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Emily is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Emily is not a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Alexander is a knight or Aiden is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 7), ('lying', 1)), ('or', ('telling-truth', 7), ('telling-truth', 6)), ('telling-truth', 7), ('->', ('lying', 1), ('lying', 4)), ('not', ('lying', 3)), ('or', ('telling-truth', 2), ('telling-truth', 0)), ('lying', 3), ('<=>', ('telling-truth', 2), ('telling-truth', 3)))", "index": 363}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Isabella, Matthew, Jack, Amelia, Emily, Riley, Elizabeth, and Lucas. Isabella expressed that Amelia is a knave or Matthew is a knight. Matthew said, \"If Jack is a knight then Matthew is a knight.\" Jack expressed that Riley is a knight if and only if Jack is a knight. In Amelia's words: \"Lucas is a knave or Isabella is a knight\". Emily was heard saying, \"Jack is a knave and Riley is a knave\". According to Riley, \"Jack is a knight if and only if Riley is a knight\". Elizabeth remarked, \"Matthew is not a knave\". \"Jack is a knight,\" Lucas declared. So who is a knight and who is a knave?", "names": ["Isabella", "Matthew", "Jack", "Amelia", "Emily", "Riley", "Elizabeth", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true, true, true], "solution_text": "Isabella is a knight, Matthew is a knight, Jack is a knight, Amelia is a knight, Emily is a knave, Riley is a knight, Elizabeth is a knight, and Lucas is a knight.", "solution_text_format": "(1) Isabella is a knight\n(2) Matthew is a knight\n(3) Jack is a knight\n(4) Amelia is a knight\n(5) Emily is a knave\n(6) Riley is a knight\n(7) Elizabeth is a knight\n(8) Lucas is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Amelia is a knave or Matthew is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Lucas is a knave or Isabella is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Riley is a knight if and only if Jack is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Jack is a knight if and only if Riley is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that If Jack is a knight then Matthew is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Jack is a knave and Riley is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Jack is a knave and Riley is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Matthew is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('telling-truth', 1)), ('->', ('telling-truth', 2), ('telling-truth', 1)), ('<=>', ('telling-truth', 5), ('telling-truth', 2)), ('or', ('lying', 7), ('telling-truth', 0)), ('and', ('lying', 2), ('lying', 5)), ('<=>', ('telling-truth', 2), ('telling-truth', 5)), ('not', ('lying', 1)), ('telling-truth', 2))", "index": 364}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Amelia, Avery, David, Ethan, Alexander, Michael, Zoey, and Riley. Amelia noted, \"Michael is a knave\". Avery remarked, \"Zoey is a knight if and only if Zoey is a knave\". David told you that Michael is not a knight. Ethan said that Zoey is not a knave. \"Ethan is a knight if and only if Alexander is a knight,\" Alexander declared. Michael was heard saying, \"If Ethan is a knight then Zoey is a knave\". \"Alexander is a knight or Michael is a knight,\" Zoey mentioned. Riley told you that Alexander is not a knave. So who is a knight and who is a knave?", "names": ["Amelia", "Avery", "David", "Ethan", "Alexander", "Michael", "Zoey", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false, true, true], "solution_text": "Amelia is a knight, Avery is a knave, David is a knight, Ethan is a knight, Alexander is a knight, Michael is a knave, Zoey is a knight, and Riley is a knight.", "solution_text_format": "(1) Amelia is a knight\n(2) Avery is a knave\n(3) David is a knight\n(4) Ethan is a knight\n(5) Alexander is a knight\n(6) Michael is a knave\n(7) Zoey is a knight\n(8) Riley is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Amelia is a knight. No contradiction is found in their claim that Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of Amelia that Michael is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that If Ethan is a knight then Zoey is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Zoey is not a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Alexander is a knight or Michael is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Ethan is a knight if and only if Alexander is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Zoey is a knight if and only if Zoey is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Zoey is a knight if and only if Zoey is a knave.", "Assume David is a knight. No contradiction is found in their claim that Michael is not a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Alexander is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 5), ('<=>', ('telling-truth', 6), ('lying', 6)), ('not', ('telling-truth', 5)), ('not', ('lying', 6)), ('<=>', ('telling-truth', 3), ('telling-truth', 4)), ('->', ('telling-truth', 3), ('lying', 6)), ('or', ('telling-truth', 4), ('telling-truth', 5)), ('not', ('lying', 4)))", "index": 365}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aurora, Lucas, Benjamin, Ella, Logan, Henry, Olivia, and Penelope. In a statement by Aurora: \"Benjamin is a knight or Olivia is a knave\". Lucas remarked, \"Olivia is a knight\". Benjamin said, \"If Olivia is a knave then Ella is a knave.\" In Ella's words: \"If Lucas is a knight then Henry is a knave\". As Logan put it, \"If Penelope is a knight then Aurora is a knave\". Henry noted, \"Lucas is a knave and Penelope is a knave\". Olivia said that Aurora is a knave. \"Olivia is a knave or Benjamin is a knave,\" Penelope declared. So who is a knight and who is a knave?", "names": ["Aurora", "Lucas", "Benjamin", "Ella", "Logan", "Henry", "Olivia", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, false, false, true], "solution_text": "Aurora is a knight, Lucas is a knave, Benjamin is a knave, Ella is a knight, Logan is a knave, Henry is a knave, Olivia is a knave, and Penelope is a knight.", "solution_text_format": "(1) Aurora is a knight\n(2) Lucas is a knave\n(3) Benjamin is a knave\n(4) Ella is a knight\n(5) Logan is a knave\n(6) Henry is a knave\n(7) Olivia is a knave\n(8) Penelope is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that Benjamin is a knight or Olivia is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Olivia is a knave then Ella is a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that Aurora is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Aurora is a knave.", "Ella cannot be a knight, because this would contradict the claim of Benjamin that If Olivia is a knave then Ella is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that If Lucas is a knight then Henry is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Olivia is a knight.", "Lucas cannot be a knave, because this would contradict the false claim of Ella that If Lucas is a knight then Henry is a knave.", "We have exhausted all possibilities for Lucas, Ella, and Olivia, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that If Olivia is a knave then Ella is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Aurora that Benjamin is a knight or Olivia is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Aurora is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that If Lucas is a knight then Henry is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Olivia is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Olivia is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Lucas is a knave and Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the claim of Henry that Lucas is a knave and Penelope is a knave.", "Penelope cannot be a knave, because this would contradict the false claim of their own that Olivia is a knave or Benjamin is a knave.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Lucas is a knave and Penelope is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Olivia is a knave or Benjamin is a knave.", "Logan cannot be a knight, because this would contradict the claim of their own that If Penelope is a knight then Aurora is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that If Penelope is a knight then Aurora is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('lying', 6)), ('telling-truth', 6), ('->', ('lying', 6), ('lying', 3)), ('->', ('telling-truth', 1), ('lying', 5)), ('->', ('telling-truth', 7), ('lying', 0)), ('and', ('lying', 1), ('lying', 7)), ('lying', 0), ('or', ('lying', 6), ('lying', 2)))", "index": 366}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ella, Chloe, Charlotte, Samuel, Mia, Emma, Emily, and Grace. \"Grace is a knave,\" Ella declared. Chloe asserted: \"Chloe is a knight or Mia is a knight\". \"Grace is a knave and Emily is a knave,\" Charlotte claimed. Samuel remarked, \"Emma is a knave\". According to Mia, \"Grace is a knight if and only if Emily is a knave\". Emma commented, \"Chloe is not a knight\". According to Emily, \"Ella is a knight or Samuel is a knight\". In a statement by Grace: \"Emily is a knave and Chloe is a knave\". So who is a knight and who is a knave?", "names": ["Ella", "Chloe", "Charlotte", "Samuel", "Mia", "Emma", "Emily", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false, true, false], "solution_text": "Ella is a knight, Chloe is a knight, Charlotte is a knave, Samuel is a knight, Mia is a knight, Emma is a knave, Emily is a knight, and Grace is a knave.", "solution_text_format": "(1) Ella is a knight\n(2) Chloe is a knight\n(3) Charlotte is a knave\n(4) Samuel is a knight\n(5) Mia is a knight\n(6) Emma is a knave\n(7) Emily is a knight\n(8) Grace is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Grace is a knave.", "Grace cannot be a knight, because this would contradict the claim of Ella that Grace is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Emily is a knave and Chloe is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Ella is a knight or Samuel is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of Samuel that Emma is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Chloe is not a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Chloe is a knight or Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Grace is a knight if and only if Emily is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Grace is a knave and Emily is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Grace is a knave and Emily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 7), ('or', ('telling-truth', 1), ('telling-truth', 4)), ('and', ('lying', 7), ('lying', 6)), ('lying', 5), ('<=>', ('telling-truth', 7), ('lying', 6)), ('not', ('telling-truth', 1)), ('or', ('telling-truth', 0), ('telling-truth', 3)), ('and', ('lying', 6), ('lying', 1)))", "index": 367}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ethan, Samuel, Lily, Sophia, David, Grace, Jack, and Evelyn. \"Grace is a knight and Jack is a knave,\" Ethan mentioned. According to Samuel, \"Lily is a knight\". As Lily put it, \"Ethan is not a knave\". Sophia said that Jack is a knave if and only if Grace is a knight. David commented, \"If Lily is a knave then Ethan is a knight\". Grace said that If Samuel is a knight then Sophia is a knave. Jack said, \"Grace is a knight.\" \"Lily is a knight and Sophia is a knave\" - Evelyn. So who is a knight and who is a knave?", "names": ["Ethan", "Samuel", "Lily", "Sophia", "David", "Grace", "Jack", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, true, true, false], "solution_text": "Ethan is a knave, Samuel is a knave, Lily is a knave, Sophia is a knave, David is a knave, Grace is a knight, Jack is a knight, and Evelyn is a knave.", "solution_text_format": "(1) Ethan is a knave\n(2) Samuel is a knave\n(3) Lily is a knave\n(4) Sophia is a knave\n(5) David is a knave\n(6) Grace is a knight\n(7) Jack is a knight\n(8) Evelyn is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Grace is a knight and Jack is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that If Samuel is a knight then Sophia is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Lily is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Ethan is not a knave.", "Sophia cannot be a knight, because this would contradict the claim of Grace that If Samuel is a knight then Sophia is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Jack is a knave if and only if Grace is a knight.", "Jack cannot be a knight, because this would contradict the claim of Ethan that Grace is a knight and Jack is a knave.", "Jack cannot be a knave, because this would contradict the false claim of Sophia that Jack is a knave if and only if Grace is a knight.", "We have exhausted all possibilities for Jack and Sophia, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the claim of Samuel that Lily is a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Lily is a knight.", "Lily cannot be a knight, because this would contradict the false claim of Samuel that Lily is a knight.", "Lily cannot be a knave, because this would contradict the false claim of their own that Ethan is not a knave.", "We have exhausted all possibilities for Lily and Samuel, so let us go back and reconsider Grace.", "Grace cannot be a knave, because this would contradict the claim of Ethan that Grace is a knight and Jack is a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Grace is a knight and Jack is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that If Samuel is a knight then Sophia is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Lily is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Ethan is not a knave.", "Lily cannot be a knave, because this would contradict the claim of Samuel that Lily is a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Lily is a knight.", "Lily cannot be a knight, because this would contradict the false claim of Samuel that Lily is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Ethan is not a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Jack is a knave if and only if Grace is a knight.", "Jack cannot be a knight, because this would contradict the claim of Sophia that Jack is a knave if and only if Grace is a knight.", "Jack cannot be a knave, because this would contradict the false claim of Ethan that Grace is a knight and Jack is a knave.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Jack is a knave if and only if Grace is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Grace is a knight.", "David cannot be a knight, because this would contradict the claim of their own that If Lily is a knave then Ethan is a knight.", "Assume David is a knave. No contradiction is found in their false claim that If Lily is a knave then Ethan is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Lily is a knight and Sophia is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Lily is a knight and Sophia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('lying', 6)), ('telling-truth', 2), ('not', ('lying', 0)), ('<=>', ('lying', 6), ('telling-truth', 5)), ('->', ('lying', 2), ('telling-truth', 0)), ('->', ('telling-truth', 1), ('lying', 3)), ('telling-truth', 5), ('and', ('telling-truth', 2), ('lying', 3)))", "index": 368}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Riley, Matthew, Penelope, Sofia, Chloe, Ava, Samuel, and Aurora. \"Sofia is a knave if and only if Riley is a knight,\" Riley declared. As Matthew put it, \"Penelope is a knave\". Penelope expressed that Riley is not a knave. According to Sofia, \"If Chloe is a knight then Riley is a knight\". Chloe asserted: \"Riley is a knight or Matthew is a knight\". Ava noted, \"Aurora is a knight\". \"If Chloe is a knave then Ava is a knight,\" Samuel declared. Aurora expressed that Samuel is not a knave. So who is a knight and who is a knave?", "names": ["Riley", "Matthew", "Penelope", "Sofia", "Chloe", "Ava", "Samuel", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true, true, true], "solution_text": "Riley is a knave, Matthew is a knight, Penelope is a knave, Sofia is a knave, Chloe is a knight, Ava is a knight, Samuel is a knight, and Aurora is a knight.", "solution_text_format": "(1) Riley is a knave\n(2) Matthew is a knight\n(3) Penelope is a knave\n(4) Sofia is a knave\n(5) Chloe is a knight\n(6) Ava is a knight\n(7) Samuel is a knight\n(8) Aurora is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Sofia is a knave if and only if Riley is a knight.", "Sofia cannot be a knight, because this would contradict the claim of Riley that Sofia is a knave if and only if Riley is a knight.", "Sofia cannot be a knave, because this would contradict the false claim of their own that If Chloe is a knight then Riley is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Sofia is a knave if and only if Riley is a knight.", "Sofia cannot be a knight, because this would contradict the false claim of Riley that Sofia is a knave if and only if Riley is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that If Chloe is a knight then Riley is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Riley is a knight or Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the claim of Matthew that Penelope is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Riley is not a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Aurora is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Samuel is not a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that If Chloe is a knave then Ava is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('telling-truth', 0)), ('lying', 2), ('not', ('lying', 0)), ('->', ('telling-truth', 4), ('telling-truth', 0)), ('or', ('telling-truth', 0), ('telling-truth', 1)), ('telling-truth', 7), ('->', ('lying', 4), ('telling-truth', 5)), ('not', ('lying', 6)))", "index": 369}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Grace, Michael, Joseph, Logan, Aurora, Jacob, Matthew, and Sophia. Grace expressed that Jacob is a knave and Michael is a knight. In a statement by Michael: \"Sophia is a knight if and only if Joseph is a knave\". According to Joseph, \"Michael is a knave and Jacob is a knight\". Logan asserted: \"Jacob is a knight if and only if Joseph is a knave\". Aurora was heard saying, \"Matthew is a knight and Sophia is a knave\". Jacob said that Michael is a knight if and only if Grace is a knave. Matthew asserted: \"Sophia is not a knave\". \"Aurora is a knave and Joseph is a knight,\" Sophia mentioned. So who is a knight and who is a knave?", "names": ["Grace", "Michael", "Joseph", "Logan", "Aurora", "Jacob", "Matthew", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, false, false, false], "solution_text": "Grace is a knave, Michael is a knave, Joseph is a knave, Logan is a knave, Aurora is a knave, Jacob is a knave, Matthew is a knave, and Sophia is a knave.", "solution_text_format": "(1) Grace is a knave\n(2) Michael is a knave\n(3) Joseph is a knave\n(4) Logan is a knave\n(5) Aurora is a knave\n(6) Jacob is a knave\n(7) Matthew is a knave\n(8) Sophia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Jacob is a knave and Michael is a knight.", "Jacob cannot be a knight, because this would contradict the claim of Grace that Jacob is a knave and Michael is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Michael is a knight if and only if Grace is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Sophia is a knight if and only if Joseph is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Aurora is a knave and Joseph is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Matthew is a knight and Sophia is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Matthew is a knight and Sophia is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Sophia is not a knave.", "Joseph cannot be a knight, because this would contradict the claim of Michael that Sophia is a knight if and only if Joseph is a knave.", "Joseph cannot be a knave, because this would contradict the claim of Sophia that Aurora is a knave and Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the false claim of their own that Sophia is not a knave.", "We have exhausted all possibilities for Matthew and Aurora, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Aurora is a knave and Joseph is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Matthew is a knight and Sophia is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Sophia is not a knave.", "Matthew cannot be a knave, because this would contradict the claim of Aurora that Matthew is a knight and Sophia is a knave.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Matthew is a knight and Sophia is a knave.", "Matthew cannot be a knight, because this would contradict the false claim of Aurora that Matthew is a knight and Sophia is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Sophia is not a knave.", "Joseph cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Jacob is a knight.", "Joseph cannot be a knave, because this would contradict the claim of Michael that Sophia is a knight if and only if Joseph is a knave.", "We have exhausted all possibilities for Joseph, Matthew, Aurora, and Sophia, so let us go back and reconsider Michael.", "Michael cannot be a knave, because this would contradict the claim of Grace that Jacob is a knave and Michael is a knight.", "We have exhausted all possibilities for Michael and Jacob, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Jacob is a knave and Michael is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Michael is a knight if and only if Grace is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Sophia is a knight if and only if Joseph is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Aurora is a knave and Joseph is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Matthew is a knight and Sophia is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Matthew is a knight and Sophia is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Sophia is not a knave.", "Joseph cannot be a knight, because this would contradict the claim of Michael that Sophia is a knight if and only if Joseph is a knave.", "Joseph cannot be a knave, because this would contradict the claim of Sophia that Aurora is a knave and Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the false claim of their own that Sophia is not a knave.", "We have exhausted all possibilities for Matthew and Aurora, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Aurora is a knave and Joseph is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Matthew is a knight and Sophia is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Sophia is not a knave.", "Matthew cannot be a knave, because this would contradict the claim of Aurora that Matthew is a knight and Sophia is a knave.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Matthew is a knight and Sophia is a knave.", "Matthew cannot be a knight, because this would contradict the false claim of Aurora that Matthew is a knight and Sophia is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Sophia is not a knave.", "Joseph cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Jacob is a knight.", "Joseph cannot be a knave, because this would contradict the claim of Michael that Sophia is a knight if and only if Joseph is a knave.", "We have exhausted all possibilities for Joseph, Matthew, Aurora, and Sophia, so let us go back and reconsider Michael.", "Michael cannot be a knave, because this would contradict the claim of Jacob that Michael is a knight if and only if Grace is a knave.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Michael is a knight if and only if Grace is a knave.", "Michael cannot be a knight, because this would contradict the false claim of Grace that Jacob is a knave and Michael is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Sophia is a knight if and only if Joseph is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Aurora is a knave and Joseph is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Matthew is a knight and Sophia is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Matthew is a knight and Sophia is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Sophia is not a knave.", "Joseph cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Jacob is a knight.", "Joseph cannot be a knave, because this would contradict the false claim of Michael that Sophia is a knight if and only if Joseph is a knave.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the false claim of their own that Sophia is not a knave.", "We have exhausted all possibilities for Matthew and Aurora, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Aurora is a knave and Joseph is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Matthew is a knight and Sophia is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Sophia is not a knave.", "Matthew cannot be a knave, because this would contradict the claim of Aurora that Matthew is a knight and Sophia is a knave.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Matthew is a knight and Sophia is a knave.", "Matthew cannot be a knight, because this would contradict the false claim of Aurora that Matthew is a knight and Sophia is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Sophia is not a knave.", "Joseph cannot be a knight, because this would contradict the false claim of Michael that Sophia is a knight if and only if Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Michael is a knave and Jacob is a knight.", "Logan cannot be a knight, because this would contradict the claim of their own that Jacob is a knight if and only if Joseph is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Jacob is a knight if and only if Joseph is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 5), ('telling-truth', 1)), ('<=>', ('telling-truth', 7), ('lying', 2)), ('and', ('lying', 1), ('telling-truth', 5)), ('<=>', ('telling-truth', 5), ('lying', 2)), ('and', ('telling-truth', 6), ('lying', 7)), ('<=>', ('telling-truth', 1), ('lying', 0)), ('not', ('lying', 7)), ('and', ('lying', 4), ('telling-truth', 2)))", "index": 370}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Victoria, Riley, Luke, Jacob, Chloe, Noah, Harper, and Owen. Victoria said that Jacob is a knave if and only if Jacob is a knight. In Riley's words: \"If Harper is a knave then Riley is a knight\". Luke said, \"Riley is a knave if and only if Chloe is a knave.\" \"Harper is not a knight,\" Jacob declared. Chloe remarked, \"Victoria is not a knight\". Noah said, \"Noah is a knight if and only if Jacob is a knave.\" \"Noah is a knave or Jacob is a knight,\" Harper claimed. As Owen put it, \"Chloe is a knave if and only if Riley is a knight\". So who is a knight and who is a knave?", "names": ["Victoria", "Riley", "Luke", "Jacob", "Chloe", "Noah", "Harper", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, false, true, false], "solution_text": "Victoria is a knave, Riley is a knight, Luke is a knight, Jacob is a knave, Chloe is a knight, Noah is a knave, Harper is a knight, and Owen is a knave.", "solution_text_format": "(1) Victoria is a knave\n(2) Riley is a knight\n(3) Luke is a knight\n(4) Jacob is a knave\n(5) Chloe is a knight\n(6) Noah is a knave\n(7) Harper is a knight\n(8) Owen is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Victoria cannot be a knight, because this would contradict the claim of their own that Jacob is a knave if and only if Jacob is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Jacob is a knave if and only if Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Harper is not a knight.", "Harper cannot be a knight, because this would contradict the claim of Jacob that Harper is not a knight.", "Harper cannot be a knave, because this would contradict the false claim of their own that Noah is a knave or Jacob is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Harper is not a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Noah is a knave or Jacob is a knight.", "Noah cannot be a knight, because this would contradict the claim of Harper that Noah is a knave or Jacob is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Noah is a knight if and only if Jacob is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that If Harper is a knave then Riley is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Riley is a knave if and only if Chloe is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Victoria is not a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Chloe is a knave if and only if Riley is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Chloe is a knave if and only if Riley is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('telling-truth', 3)), ('->', ('lying', 6), ('telling-truth', 1)), ('<=>', ('lying', 1), ('lying', 4)), ('not', ('telling-truth', 6)), ('not', ('telling-truth', 0)), ('<=>', ('telling-truth', 5), ('lying', 3)), ('or', ('lying', 5), ('telling-truth', 3)), ('<=>', ('lying', 4), ('telling-truth', 1)))", "index": 371}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jackson, Amelia, Logan, Penelope, Owen, Sophia, Benjamin, and Sofia. In a statement by Jackson: \"Owen is a knave if and only if Benjamin is a knave\". Amelia was heard saying, \"Sophia is a knave if and only if Benjamin is a knight\". In Logan's words: \"Benjamin is a knave\". Penelope asserted: \"Benjamin is a knave and Amelia is a knight\". Owen said, \"If Sophia is a knave then Benjamin is a knave.\" In Sophia's words: \"If Logan is a knight then Amelia is a knight\". Benjamin noted, \"Sophia is a knight and Amelia is a knight\". Sofia told you that If Sophia is a knight then Benjamin is a knight. So who is a knight and who is a knave?", "names": ["Jackson", "Amelia", "Logan", "Penelope", "Owen", "Sophia", "Benjamin", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, false, false, true], "solution_text": "Jackson is a knave, Amelia is a knave, Logan is a knight, Penelope is a knave, Owen is a knight, Sophia is a knave, Benjamin is a knave, and Sofia is a knight.", "solution_text_format": "(1) Jackson is a knave\n(2) Amelia is a knave\n(3) Logan is a knight\n(4) Penelope is a knave\n(5) Owen is a knight\n(6) Sophia is a knave\n(7) Benjamin is a knave\n(8) Sofia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Owen is a knave if and only if Benjamin is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that If Sophia is a knave then Benjamin is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that If Logan is a knight then Amelia is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Logan that Benjamin is a knave.", "Benjamin cannot be a knave, because this would contradict the claim of Jackson that Owen is a knave if and only if Benjamin is a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Benjamin is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Sophia is a knight and Amelia is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Sophia is a knave if and only if Benjamin is a knight.", "Amelia cannot be a knave, because this would contradict the claim of Benjamin that Sophia is a knight and Amelia is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the claim of Jackson that Owen is a knave if and only if Benjamin is a knave.", "We have exhausted all possibilities for Benjamin and Logan, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that If Logan is a knight then Amelia is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Logan that Benjamin is a knave.", "Benjamin cannot be a knave, because this would contradict the claim of Jackson that Owen is a knave if and only if Benjamin is a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the false claim of Sophia that If Logan is a knight then Amelia is a knight.", "We have exhausted all possibilities for Logan and Sophia, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that If Sophia is a knave then Benjamin is a knave.", "Sophia cannot be a knight, because this would contradict the false claim of Owen that If Sophia is a knave then Benjamin is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that If Logan is a knight then Amelia is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Jackson that Owen is a knave if and only if Benjamin is a knave.", "Benjamin cannot be a knave, because this would contradict the false claim of Owen that If Sophia is a knave then Benjamin is a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the false claim of Sophia that If Logan is a knight then Amelia is a knight.", "We have exhausted all possibilities for Logan, Sophia, and Owen, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Owen is a knave if and only if Benjamin is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that If Sophia is a knave then Benjamin is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that If Logan is a knight then Amelia is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Jackson that Owen is a knave if and only if Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Sophia is a knight and Amelia is a knight.", "Amelia cannot be a knight, because this would contradict the false claim of Benjamin that Sophia is a knight and Amelia is a knight.", "Amelia cannot be a knave, because this would contradict the false claim of their own that Sophia is a knave if and only if Benjamin is a knight.", "We have exhausted all possibilities for Amelia and Benjamin, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Jackson that Owen is a knave if and only if Benjamin is a knave.", "Benjamin cannot be a knave, because this would contradict the false claim of Logan that Benjamin is a knave.", "We have exhausted all possibilities for Benjamin and Logan, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that If Logan is a knight then Amelia is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Jackson that Owen is a knave if and only if Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Sophia is a knight and Amelia is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Sophia is a knave if and only if Benjamin is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Sophia is a knave if and only if Benjamin is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave and Amelia is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Benjamin is a knave and Amelia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that If Sophia is a knight then Benjamin is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 4), ('lying', 6)), ('<=>', ('lying', 5), ('telling-truth', 6)), ('lying', 6), ('and', ('lying', 6), ('telling-truth', 1)), ('->', ('lying', 5), ('lying', 6)), ('->', ('telling-truth', 2), ('telling-truth', 1)), ('and', ('telling-truth', 5), ('telling-truth', 1)), ('->', ('telling-truth', 5), ('telling-truth', 6)))", "index": 372}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Olivia, Daniel, Jack, Sofia, Evelyn, Charlotte, Ella, and Emma. Olivia commented, \"Sofia is a knight\". As Daniel put it, \"Jack is a knave or Olivia is a knight\". Jack said that Daniel is not a knave. \"Olivia is not a knave,\" Sofia declared. \"Charlotte is not a knight,\" Evelyn declared. Charlotte said, \"Sofia is a knave and Jack is a knave.\" Ella said, \"Daniel is not a knave.\" Emma expressed that If Jack is a knave then Jack is a knight. So who is a knight and who is a knave?", "names": ["Olivia", "Daniel", "Jack", "Sofia", "Evelyn", "Charlotte", "Ella", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false, true, true], "solution_text": "Olivia is a knight, Daniel is a knight, Jack is a knight, Sofia is a knight, Evelyn is a knight, Charlotte is a knave, Ella is a knight, and Emma is a knight.", "solution_text_format": "(1) Olivia is a knight\n(2) Daniel is a knight\n(3) Jack is a knight\n(4) Sofia is a knight\n(5) Evelyn is a knight\n(6) Charlotte is a knave\n(7) Ella is a knight\n(8) Emma is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Sofia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Olivia is not a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Jack is a knave or Olivia is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Daniel is not a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Charlotte is not a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Evelyn that Charlotte is not a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Sofia is a knave and Jack is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Daniel is not a knave.", "Assume Emma is a knight. No contradiction is found in their claim that If Jack is a knave then Jack is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 3), ('or', ('lying', 2), ('telling-truth', 0)), ('not', ('lying', 1)), ('not', ('lying', 0)), ('not', ('telling-truth', 5)), ('and', ('lying', 3), ('lying', 2)), ('not', ('lying', 1)), ('->', ('lying', 2), ('telling-truth', 2)))", "index": 373}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Henry, Sophia, Amelia, Charlotte, James, Evelyn, Mia, and Victoria. Henry stated, \"Sophia is a knave and Henry is a knight\". Sophia commented, \"Mia is a knave\". Amelia commented, \"Evelyn is a knave and Sophia is a knave\". In a statement by Charlotte: \"James is a knave or Amelia is a knave\". James commented, \"Henry is a knight if and only if Charlotte is a knave\". \"Victoria is a knight or Mia is a knave,\" Evelyn claimed. Mia said that James is a knight or Amelia is a knight. \"Henry is a knight or Mia is a knight,\" Victoria claimed. So who is a knight and who is a knave?", "names": ["Henry", "Sophia", "Amelia", "Charlotte", "James", "Evelyn", "Mia", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true, true, true], "solution_text": "Henry is a knave, Sophia is a knave, Amelia is a knave, Charlotte is a knight, James is a knight, Evelyn is a knight, Mia is a knight, and Victoria is a knight.", "solution_text_format": "(1) Henry is a knave\n(2) Sophia is a knave\n(3) Amelia is a knave\n(4) Charlotte is a knight\n(5) James is a knight\n(6) Evelyn is a knight\n(7) Mia is a knight\n(8) Victoria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that Sophia is a knave and Henry is a knight.", "Sophia cannot be a knight, because this would contradict the claim of Henry that Sophia is a knave and Henry is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Mia is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that James is a knight or Amelia is a knight.", "Assume James is a knight. No contradiction is found in their claim that Henry is a knight if and only if Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of James that Henry is a knight if and only if Charlotte is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that James is a knave or Amelia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Evelyn is a knave and Sophia is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of Amelia that Evelyn is a knave and Sophia is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Victoria is a knight or Mia is a knave.", "Victoria cannot be a knight, because this would contradict the false claim of Evelyn that Victoria is a knight or Mia is a knave.", "Victoria cannot be a knave, because this would contradict the false claim of their own that Henry is a knight or Mia is a knight.", "We have exhausted all possibilities for Victoria and Evelyn, so let us go back and reconsider Amelia.", "Amelia cannot be a knave, because this would contradict the false claim of Charlotte that James is a knave or Amelia is a knave.", "We have exhausted all possibilities for Amelia and Charlotte, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Henry is a knight if and only if Charlotte is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that James is a knave or Amelia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Evelyn is a knave and Sophia is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of Amelia that Evelyn is a knave and Sophia is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Victoria is a knight or Mia is a knave.", "Victoria cannot be a knight, because this would contradict the false claim of Evelyn that Victoria is a knight or Mia is a knave.", "Victoria cannot be a knave, because this would contradict the false claim of their own that Henry is a knight or Mia is a knight.", "We have exhausted all possibilities for Victoria and Evelyn, so let us go back and reconsider Amelia.", "Amelia cannot be a knave, because this would contradict the claim of Mia that James is a knight or Amelia is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that James is a knave or Amelia is a knave.", "We have exhausted all possibilities for Charlotte and James, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the false claim of Sophia that Mia is a knave.", "We have exhausted all possibilities for Mia and Sophia, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Sophia is a knave and Henry is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Mia is a knave.", "Mia cannot be a knight, because this would contradict the claim of Sophia that Mia is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that James is a knight or Amelia is a knight.", "James cannot be a knight, because this would contradict the false claim of Mia that James is a knight or Amelia is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Henry is a knight if and only if Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the false claim of James that Henry is a knight if and only if Charlotte is a knave.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that James is a knave or Amelia is a knave.", "We have exhausted all possibilities for Charlotte, James, and Mia, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Mia is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that James is a knight or Amelia is a knight.", "Assume James is a knight. No contradiction is found in their claim that Henry is a knight if and only if Charlotte is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that James is a knave or Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Charlotte that James is a knave or Amelia is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Evelyn is a knave and Sophia is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Victoria is a knight or Mia is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Henry is a knight or Mia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 1), ('telling-truth', 0)), ('lying', 6), ('and', ('lying', 5), ('lying', 1)), ('or', ('lying', 4), ('lying', 2)), ('<=>', ('telling-truth', 0), ('lying', 3)), ('or', ('telling-truth', 7), ('lying', 6)), ('or', ('telling-truth', 4), ('telling-truth', 2)), ('or', ('telling-truth', 0), ('telling-truth', 6)))", "index": 374}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lucas, David, Ella, Abigail, Mason, Amelia, Samuel, and Alexander. Lucas was heard saying, \"Ella is not a knave\". David was heard saying, \"Amelia is a knight\". Ella noted, \"Mason is a knight and David is a knight\". Abigail said that Abigail is a knight and Alexander is a knight. Mason said that Samuel is a knave and Amelia is a knave. Amelia remarked, \"Mason is a knight\". Samuel remarked, \"Amelia is a knight or Abigail is a knave\". \"Mason is not a knight\" - Alexander. So who is a knight and who is a knave?", "names": ["Lucas", "David", "Ella", "Abigail", "Mason", "Amelia", "Samuel", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, false, true, true], "solution_text": "Lucas is a knave, David is a knave, Ella is a knave, Abigail is a knave, Mason is a knave, Amelia is a knave, Samuel is a knight, and Alexander is a knight.", "solution_text_format": "(1) Lucas is a knave\n(2) David is a knave\n(3) Ella is a knave\n(4) Abigail is a knave\n(5) Mason is a knave\n(6) Amelia is a knave\n(7) Samuel is a knight\n(8) Alexander is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that Ella is not a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Mason is a knight and David is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Samuel is a knave and Amelia is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Mason that Samuel is a knave and Amelia is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Amelia is a knight or Abigail is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Mason that Samuel is a knave and Amelia is a knave.", "Amelia cannot be a knave, because this would contradict the false claim of their own that Mason is a knight.", "We have exhausted all possibilities for Amelia and Samuel, so let us go back and reconsider Mason.", "Mason cannot be a knave, because this would contradict the claim of Ella that Mason is a knight and David is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the claim of Lucas that Ella is not a knave.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Ella is not a knave.", "Ella cannot be a knight, because this would contradict the false claim of Lucas that Ella is not a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Mason is a knight and David is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Samuel is a knave and Amelia is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Mason that Samuel is a knave and Amelia is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Amelia is a knight or Abigail is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Mason that Samuel is a knave and Amelia is a knave.", "Amelia cannot be a knave, because this would contradict the false claim of their own that Mason is a knight.", "We have exhausted all possibilities for Amelia and Samuel, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Samuel is a knave and Amelia is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Amelia is a knight or Abigail is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Mason is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Mason is a knight.", "Abigail cannot be a knight, because this would contradict the claim of Samuel that Amelia is a knight or Abigail is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Abigail is a knight and Alexander is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Mason is not a knight.", "David cannot be a knight, because this would contradict the claim of their own that Amelia is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Amelia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('telling-truth', 5), ('and', ('telling-truth', 4), ('telling-truth', 1)), ('and', ('telling-truth', 3), ('telling-truth', 7)), ('and', ('lying', 6), ('lying', 5)), ('telling-truth', 4), ('or', ('telling-truth', 5), ('lying', 3)), ('not', ('telling-truth', 4)))", "index": 375}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: William, Ava, James, Mia, Avery, Liam, Penelope, and Aiden. \"James is a knave,\" William mentioned. \"James is a knight if and only if Liam is a knight,\" Ava declared. James expressed that Avery is a knight if and only if Ava is a knave. \"Avery is a knave if and only if James is a knave,\" Mia claimed. Avery remarked, \"Aiden is a knight or Penelope is a knight\". Liam asserted: \"Ava is not a knight\". Penelope remarked, \"Aiden is not a knave\". Aiden told you that Mia is a knight and Liam is a knave. So who is a knight and who is a knave?", "names": ["William", "Ava", "James", "Mia", "Avery", "Liam", "Penelope", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, true, false, false], "solution_text": "William is a knight, Ava is a knave, James is a knave, Mia is a knight, Avery is a knave, Liam is a knight, Penelope is a knave, and Aiden is a knave.", "solution_text_format": "(1) William is a knight\n(2) Ava is a knave\n(3) James is a knave\n(4) Mia is a knight\n(5) Avery is a knave\n(6) Liam is a knight\n(7) Penelope is a knave\n(8) Aiden is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that James is a knave.", "James cannot be a knight, because this would contradict the claim of William that James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Avery is a knight if and only if Ava is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Aiden is a knight or Penelope is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Mia is a knight and Liam is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Avery is a knave if and only if James is a knave.", "Mia cannot be a knave, because this would contradict the claim of Aiden that Mia is a knight and Liam is a knave.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Mia is a knight and Liam is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Avery is a knave if and only if James is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Avery is a knave if and only if James is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Ava is not a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that James is a knight if and only if Liam is a knight.", "Ava cannot be a knave, because this would contradict the false claim of James that Avery is a knight if and only if Ava is a knave.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Ava is not a knight.", "Assume Ava is a knight. No contradiction is found in their claim that James is a knight if and only if Liam is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Aiden is not a knave.", "Penelope cannot be a knave, because this would contradict the claim of Avery that Aiden is a knight or Penelope is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the false claim of their own that James is a knight if and only if Liam is a knight.", "We have exhausted all possibilities for Ava, Liam, Mia, and Aiden, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Aiden is a knight or Penelope is a knight.", "Aiden cannot be a knight, because this would contradict the false claim of Avery that Aiden is a knight or Penelope is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Mia is a knight and Liam is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Avery is a knave if and only if James is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Ava is not a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that James is a knight if and only if Liam is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that James is a knight if and only if Liam is a knight.", "Penelope cannot be a knight, because this would contradict the false claim of Avery that Aiden is a knight or Penelope is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Aiden is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('<=>', ('telling-truth', 2), ('telling-truth', 5)), ('<=>', ('telling-truth', 4), ('lying', 1)), ('<=>', ('lying', 4), ('lying', 2)), ('or', ('telling-truth', 7), ('telling-truth', 6)), ('not', ('telling-truth', 1)), ('not', ('lying', 7)), ('and', ('telling-truth', 3), ('lying', 5)))", "index": 376}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aurora, Owen, Luke, Ethan, Victoria, Elizabeth, Sebastian, and Olivia. Aurora remarked, \"If Owen is a knave then Olivia is a knight\". Owen told you that Victoria is a knave if and only if Olivia is a knight. Luke stated, \"If Ethan is a knight then Olivia is a knave\". Ethan was heard saying, \"Sebastian is a knight\". Victoria commented, \"If Elizabeth is a knight then Luke is a knight\". Elizabeth commented, \"Owen is a knave or Olivia is a knave\". In a statement by Sebastian: \"Luke is a knight or Olivia is a knight\". Olivia commented, \"Sebastian is not a knight\". So who is a knight and who is a knave?", "names": ["Aurora", "Owen", "Luke", "Ethan", "Victoria", "Elizabeth", "Sebastian", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true, true, false], "solution_text": "Aurora is a knight, Owen is a knight, Luke is a knight, Ethan is a knight, Victoria is a knight, Elizabeth is a knight, Sebastian is a knight, and Olivia is a knave.", "solution_text_format": "(1) Aurora is a knight\n(2) Owen is a knight\n(3) Luke is a knight\n(4) Ethan is a knight\n(5) Victoria is a knight\n(6) Elizabeth is a knight\n(7) Sebastian is a knight\n(8) Olivia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that If Owen is a knave then Olivia is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Victoria is a knave if and only if Olivia is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that If Elizabeth is a knight then Luke is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Owen is a knave or Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Owen that Victoria is a knave if and only if Olivia is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Sebastian is not a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Luke is a knight or Olivia is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that If Ethan is a knight then Olivia is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Sebastian is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 1), ('telling-truth', 7)), ('<=>', ('lying', 4), ('telling-truth', 7)), ('->', ('telling-truth', 3), ('lying', 7)), ('telling-truth', 6), ('->', ('telling-truth', 5), ('telling-truth', 2)), ('or', ('lying', 1), ('lying', 7)), ('or', ('telling-truth', 2), ('telling-truth', 7)), ('not', ('telling-truth', 6)))", "index": 377}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sophia, Avery, Emma, Matthew, Mason, Oliver, Chloe, and Mia. Sophia remarked, \"Mason is a knave\". Avery said that Mia is a knight or Sophia is a knave. Emma was heard saying, \"Chloe is a knave or Chloe is a knight\". Matthew said that Oliver is not a knave. Mason noted, \"Chloe is a knight\". Oliver asserted: \"Mason is a knave or Mia is a knave\". According to Chloe, \"Emma is not a knight\". Mia expressed that If Chloe is a knight then Mia is a knight. So who is a knight and who is a knave?", "names": ["Sophia", "Avery", "Emma", "Matthew", "Mason", "Oliver", "Chloe", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true, false, true], "solution_text": "Sophia is a knight, Avery is a knight, Emma is a knight, Matthew is a knight, Mason is a knave, Oliver is a knight, Chloe is a knave, and Mia is a knight.", "solution_text_format": "(1) Sophia is a knight\n(2) Avery is a knight\n(3) Emma is a knight\n(4) Matthew is a knight\n(5) Mason is a knave\n(6) Oliver is a knight\n(7) Chloe is a knave\n(8) Mia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of Sophia that Mason is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Chloe is a knight.", "Chloe cannot be a knight, because this would contradict the false claim of Mason that Chloe is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Emma is not a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Chloe is a knave or Chloe is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Mia is a knight or Sophia is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that If Chloe is a knight then Mia is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Oliver is not a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Mason is a knave or Mia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('or', ('telling-truth', 7), ('lying', 0)), ('or', ('lying', 6), ('telling-truth', 6)), ('not', ('lying', 5)), ('telling-truth', 6), ('or', ('lying', 4), ('lying', 7)), ('not', ('telling-truth', 2)), ('->', ('telling-truth', 6), ('telling-truth', 7)))", "index": 378}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Luke, Sofia, James, Isabella, Oliver, Abigail, Aria, and Aiden. Luke said, \"If James is a knight then Isabella is a knight.\" Sofia told you that Aria is not a knight. As James put it, \"If Oliver is a knave then Luke is a knave\". Isabella was heard saying, \"Isabella is a knight and Aria is a knave\". Oliver was heard saying, \"Aiden is not a knight\". In a statement by Abigail: \"If Luke is a knave then Aria is a knight\". Aria expressed that Oliver is a knave and Luke is a knight. \"Sofia is a knave if and only if Aiden is a knight\" - Aiden. So who is a knight and who is a knave?", "names": ["Luke", "Sofia", "James", "Isabella", "Oliver", "Abigail", "Aria", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, true, true, true], "solution_text": "Luke is a knight, Sofia is a knave, James is a knave, Isabella is a knave, Oliver is a knave, Abigail is a knight, Aria is a knight, and Aiden is a knight.", "solution_text_format": "(1) Luke is a knight\n(2) Sofia is a knave\n(3) James is a knave\n(4) Isabella is a knave\n(5) Oliver is a knave\n(6) Abigail is a knight\n(7) Aria is a knight\n(8) Aiden is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that If James is a knight then Isabella is a knight.", "Assume James is a knight. No contradiction is found in their claim that If Oliver is a knave then Luke is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Aiden is not a knight.", "Aiden cannot be a knight, because this would contradict the claim of Oliver that Aiden is not a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Sofia is a knave if and only if Aiden is a knight.", "Sofia cannot be a knight, because this would contradict the false claim of Aiden that Sofia is a knave if and only if Aiden is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Aria is not a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that Oliver is a knave and Luke is a knight.", "Aria cannot be a knave, because this would contradict the false claim of Sofia that Aria is not a knight.", "We have exhausted all possibilities for Aria, Sofia, and Aiden, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the claim of James that If Oliver is a knave then Luke is a knave.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that If Oliver is a knave then Luke is a knave.", "Oliver cannot be a knight, because this would contradict the false claim of James that If Oliver is a knave then Luke is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Aiden is not a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Sofia is a knave if and only if Aiden is a knight.", "Sofia cannot be a knight, because this would contradict the claim of Aiden that Sofia is a knave if and only if Aiden is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Aria is not a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Oliver is a knave and Luke is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Isabella is a knight and Aria is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Isabella is a knight and Aria is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that If Luke is a knave then Aria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('telling-truth', 3)), ('not', ('telling-truth', 6)), ('->', ('lying', 4), ('lying', 0)), ('and', ('telling-truth', 3), ('lying', 6)), ('not', ('telling-truth', 7)), ('->', ('lying', 0), ('telling-truth', 6)), ('and', ('lying', 4), ('telling-truth', 0)), ('<=>', ('lying', 1), ('telling-truth', 7)))", "index": 379}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Grace, Owen, James, Lucas, Jacob, Zoey, Olivia, and Penelope. \"Olivia is a knight if and only if Penelope is a knight,\" Grace mentioned. As Owen put it, \"Zoey is not a knave\". James was heard saying, \"Lucas is a knave if and only if James is a knight\". Lucas commented, \"Penelope is a knave if and only if Olivia is a knight\". As Jacob put it, \"Penelope is a knight or Jacob is a knight\". Zoey was heard saying, \"Owen is a knight or Olivia is a knight\". Olivia commented, \"Lucas is a knave or Owen is a knight\". Penelope commented, \"James is a knave\". So who is a knight and who is a knave?", "names": ["Grace", "Owen", "James", "Lucas", "Jacob", "Zoey", "Olivia", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true, true, true], "solution_text": "Grace is a knight, Owen is a knight, James is a knave, Lucas is a knave, Jacob is a knight, Zoey is a knight, Olivia is a knight, and Penelope is a knight.", "solution_text_format": "(1) Grace is a knight\n(2) Owen is a knight\n(3) James is a knave\n(4) Lucas is a knave\n(5) Jacob is a knight\n(6) Zoey is a knight\n(7) Olivia is a knight\n(8) Penelope is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Penelope is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Lucas is a knave or Owen is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Penelope is a knave if and only if Olivia is a knight.", "Penelope cannot be a knight, because this would contradict the claim of Lucas that Penelope is a knave if and only if Olivia is a knight.", "Penelope cannot be a knave, because this would contradict the claim of Grace that Olivia is a knight if and only if Penelope is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Penelope is a knave if and only if Olivia is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that James is a knave.", "James cannot be a knight, because this would contradict the claim of Penelope that James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Lucas is a knave if and only if James is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Zoey is not a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Owen is a knight or Olivia is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Penelope is a knight or Jacob is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 6), ('telling-truth', 7)), ('not', ('lying', 5)), ('<=>', ('lying', 3), ('telling-truth', 2)), ('<=>', ('lying', 7), ('telling-truth', 6)), ('or', ('telling-truth', 7), ('telling-truth', 4)), ('or', ('telling-truth', 1), ('telling-truth', 6)), ('or', ('lying', 3), ('telling-truth', 1)), ('lying', 2))", "index": 380}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Victoria, Logan, Sophia, Ella, Joseph, Lily, Mason, and Aria. Victoria stated, \"Ella is a knight if and only if Victoria is a knight\". \"Sophia is a knight,\" Logan mentioned. In a statement by Sophia: \"Victoria is a knight and Joseph is a knave\". Ella said that Lily is a knight or Logan is a knight. Joseph was heard saying, \"Mason is not a knight\". Lily noted, \"If Lily is a knight then Sophia is a knight\". \"Ella is a knight if and only if Mason is a knight\" - Mason. Aria commented, \"If Ella is a knave then Joseph is a knight\". So who is a knight and who is a knave?", "names": ["Victoria", "Logan", "Sophia", "Ella", "Joseph", "Lily", "Mason", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true, true, true], "solution_text": "Victoria is a knight, Logan is a knight, Sophia is a knight, Ella is a knight, Joseph is a knave, Lily is a knight, Mason is a knight, and Aria is a knight.", "solution_text_format": "(1) Victoria is a knight\n(2) Logan is a knight\n(3) Sophia is a knight\n(4) Ella is a knight\n(5) Joseph is a knave\n(6) Lily is a knight\n(7) Mason is a knight\n(8) Aria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that Ella is a knight if and only if Victoria is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Lily is a knight or Logan is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that If Lily is a knight then Sophia is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Victoria is a knight and Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Sophia that Victoria is a knight and Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Mason is not a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Ella is a knight if and only if Mason is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Sophia is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that If Ella is a knave then Joseph is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 3), ('telling-truth', 0)), ('telling-truth', 2), ('and', ('telling-truth', 0), ('lying', 4)), ('or', ('telling-truth', 5), ('telling-truth', 1)), ('not', ('telling-truth', 6)), ('->', ('telling-truth', 5), ('telling-truth', 2)), ('<=>', ('telling-truth', 3), ('telling-truth', 6)), ('->', ('lying', 3), ('telling-truth', 4)))", "index": 381}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Alexander, Emily, Jackson, Evelyn, Jacob, Penelope, Sebastian, and James. Alexander stated, \"Evelyn is a knight if and only if James is a knave\". Emily told you that Sebastian is a knight. Jackson was heard saying, \"Alexander is a knight or Evelyn is a knight\". \"If Penelope is a knave then Alexander is a knight,\" Evelyn mentioned. Jacob noted, \"Sebastian is a knight and Emily is a knight\". \"Jackson is not a knight,\" Penelope declared. In Sebastian's words: \"If Jackson is a knave then Penelope is a knave\". According to James, \"Jacob is not a knight\". So who is a knight and who is a knave?", "names": ["Alexander", "Emily", "Jackson", "Evelyn", "Jacob", "Penelope", "Sebastian", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false, true, false], "solution_text": "Alexander is a knight, Emily is a knight, Jackson is a knight, Evelyn is a knight, Jacob is a knight, Penelope is a knave, Sebastian is a knight, and James is a knave.", "solution_text_format": "(1) Alexander is a knight\n(2) Emily is a knight\n(3) Jackson is a knight\n(4) Evelyn is a knight\n(5) Jacob is a knight\n(6) Penelope is a knave\n(7) Sebastian is a knight\n(8) James is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that Evelyn is a knight if and only if James is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Penelope is a knave then Alexander is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Jackson is not a knight.", "Jackson cannot be a knight, because this would contradict the claim of Penelope that Jackson is not a knight.", "Jackson cannot be a knave, because this would contradict the false claim of their own that Alexander is a knight or Evelyn is a knight.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Jackson is not a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Alexander is a knight or Evelyn is a knight.", "James cannot be a knight, because this would contradict the claim of Alexander that Evelyn is a knight if and only if James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Jacob is not a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Sebastian is a knight and Emily is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Jackson is a knave then Penelope is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Sebastian is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 3), ('lying', 7)), ('telling-truth', 6), ('or', ('telling-truth', 0), ('telling-truth', 3)), ('->', ('lying', 5), ('telling-truth', 0)), ('and', ('telling-truth', 6), ('telling-truth', 1)), ('not', ('telling-truth', 2)), ('->', ('lying', 2), ('lying', 5)), ('not', ('telling-truth', 4)))", "index": 382}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Penelope, Mia, Aiden, Emily, Matthew, Sophia, Victoria, and Ava. \"If Sophia is a knave then Emily is a knight\" - Penelope. Mia asserted: \"If Victoria is a knight then Sophia is a knave\". In Aiden's words: \"If Penelope is a knave then Sophia is a knave\". \"Aiden is a knave or Sophia is a knave,\" Emily mentioned. Matthew asserted: \"Aiden is a knight\". Sophia was heard saying, \"Aiden is a knave if and only if Penelope is a knave\". Victoria remarked, \"Mia is a knave and Penelope is a knave\". In a statement by Ava: \"Penelope is a knave if and only if Sophia is a knave\". So who is a knight and who is a knave?", "names": ["Penelope", "Mia", "Aiden", "Emily", "Matthew", "Sophia", "Victoria", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true, false, true], "solution_text": "Penelope is a knight, Mia is a knight, Aiden is a knight, Emily is a knave, Matthew is a knight, Sophia is a knight, Victoria is a knave, and Ava is a knight.", "solution_text_format": "(1) Penelope is a knight\n(2) Mia is a knight\n(3) Aiden is a knight\n(4) Emily is a knave\n(5) Matthew is a knight\n(6) Sophia is a knight\n(7) Victoria is a knave\n(8) Ava is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that If Sophia is a knave then Emily is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Aiden is a knave if and only if Penelope is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Penelope is a knave then Sophia is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Aiden is a knave or Sophia is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Aiden is a knave or Sophia is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that If Victoria is a knight then Sophia is a knave.", "Victoria cannot be a knight, because this would contradict the claim of Mia that If Victoria is a knight then Sophia is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Mia is a knave and Penelope is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Aiden is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Penelope is a knave if and only if Sophia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('telling-truth', 3)), ('->', ('telling-truth', 6), ('lying', 5)), ('->', ('lying', 0), ('lying', 5)), ('or', ('lying', 2), ('lying', 5)), ('telling-truth', 2), ('<=>', ('lying', 2), ('lying', 0)), ('and', ('lying', 1), ('lying', 0)), ('<=>', ('lying', 0), ('lying', 5)))", "index": 383}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Riley, David, Owen, Luke, Joseph, Grace, Abigail, and Sofia. Riley stated, \"Owen is a knight\". David remarked, \"Owen is a knave or Joseph is a knave\". As Owen put it, \"Grace is a knight\". \"David is a knave or Owen is a knight,\" Luke declared. In a statement by Joseph: \"If Owen is a knight then Grace is a knave\". Grace commented, \"If Sofia is a knight then Abigail is a knight\". In a statement by Abigail: \"Joseph is a knave or Abigail is a knight\". In Sofia's words: \"David is a knave and Riley is a knave\". So who is a knight and who is a knave?", "names": ["Riley", "David", "Owen", "Luke", "Joseph", "Grace", "Abigail", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true, true, false], "solution_text": "Riley is a knight, David is a knight, Owen is a knight, Luke is a knight, Joseph is a knave, Grace is a knight, Abigail is a knight, and Sofia is a knave.", "solution_text_format": "(1) Riley is a knight\n(2) David is a knight\n(3) Owen is a knight\n(4) Luke is a knight\n(5) Joseph is a knave\n(6) Grace is a knight\n(7) Abigail is a knight\n(8) Sofia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Owen is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that If Sofia is a knight then Abigail is a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that David is a knave and Riley is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that David is a knave and Riley is a knave.", "Assume David is a knight. No contradiction is found in their claim that Owen is a knave or Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of David that Owen is a knave or Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that If Owen is a knight then Grace is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Joseph is a knave or Abigail is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that David is a knave or Owen is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('or', ('lying', 2), ('lying', 4)), ('telling-truth', 5), ('or', ('lying', 1), ('telling-truth', 2)), ('->', ('telling-truth', 2), ('lying', 5)), ('->', ('telling-truth', 7), ('telling-truth', 6)), ('or', ('lying', 4), ('telling-truth', 6)), ('and', ('lying', 1), ('lying', 0)))", "index": 384}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emma, Sebastian, Matthew, Zoey, Sofia, Isabella, William, and Henry. \"Isabella is a knight or William is a knight,\" Emma claimed. In a statement by Sebastian: \"Henry is a knight\". Matthew was heard saying, \"Henry is a knight and Henry is a knave\". According to Zoey, \"Zoey is a knight or Sofia is a knight\". Sofia stated, \"Sebastian is a knave or Henry is a knight\". Isabella said that Sofia is a knave and William is a knight. William stated, \"Sofia is a knave if and only if Isabella is a knave\". Henry said, \"Emma is a knight and Zoey is a knave.\" So who is a knight and who is a knave?", "names": ["Emma", "Sebastian", "Matthew", "Zoey", "Sofia", "Isabella", "William", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, false, false, false], "solution_text": "Emma is a knave, Sebastian is a knave, Matthew is a knave, Zoey is a knight, Sofia is a knight, Isabella is a knave, William is a knave, and Henry is a knave.", "solution_text_format": "(1) Emma is a knave\n(2) Sebastian is a knave\n(3) Matthew is a knave\n(4) Zoey is a knight\n(5) Sofia is a knight\n(6) Isabella is a knave\n(7) William is a knave\n(8) Henry is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Isabella is a knight or William is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Sofia is a knave and William is a knight.", "Sofia cannot be a knight, because this would contradict the claim of Isabella that Sofia is a knave and William is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Sebastian is a knave or Henry is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Henry is a knight.", "Henry cannot be a knight, because this would contradict the false claim of Sofia that Sebastian is a knave or Henry is a knight.", "Henry cannot be a knave, because this would contradict the claim of Sebastian that Henry is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the false claim of Sofia that Sebastian is a knave or Henry is a knight.", "We have exhausted all possibilities for Sebastian and Sofia, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Sofia is a knave and William is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Sebastian is a knave or Henry is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Henry is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Emma is a knight and Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Henry that Emma is a knight and Zoey is a knave.", "Zoey cannot be a knave, because this would contradict the false claim of their own that Zoey is a knight or Sofia is a knight.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the claim of Sebastian that Henry is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Henry is a knight.", "Henry cannot be a knight, because this would contradict the false claim of Sebastian that Henry is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Emma is a knight and Zoey is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Zoey is a knight or Sofia is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Sofia is a knave if and only if Isabella is a knave.", "William cannot be a knave, because this would contradict the claim of Emma that Isabella is a knight or William is a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider Zoey.", "Zoey cannot be a knave, because this would contradict the false claim of their own that Zoey is a knight or Sofia is a knight.", "We have exhausted all possibilities for Zoey, Henry, and Sebastian, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Sebastian is a knave or Henry is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Henry is a knight.", "Henry cannot be a knight, because this would contradict the false claim of Sofia that Sebastian is a knave or Henry is a knight.", "Henry cannot be a knave, because this would contradict the claim of Sebastian that Henry is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the false claim of Sofia that Sebastian is a knave or Henry is a knight.", "We have exhausted all possibilities for Sebastian, Sofia, and Isabella, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Isabella is a knight or William is a knight.", "Isabella cannot be a knight, because this would contradict the false claim of Emma that Isabella is a knight or William is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Sofia is a knave and William is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Sebastian is a knave or Henry is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Henry is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Emma is a knight and Zoey is a knave.", "Henry cannot be a knave, because this would contradict the claim of Sebastian that Henry is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Henry is a knight.", "Henry cannot be a knight, because this would contradict the false claim of Sebastian that Henry is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Emma is a knight and Zoey is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Zoey is a knight or Sofia is a knight.", "William cannot be a knight, because this would contradict the false claim of Emma that Isabella is a knight or William is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Sofia is a knave if and only if Isabella is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Henry is a knight and Henry is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Henry is a knight and Henry is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('telling-truth', 6)), ('telling-truth', 7), ('and', ('telling-truth', 7), ('lying', 7)), ('or', ('telling-truth', 3), ('telling-truth', 4)), ('or', ('lying', 1), ('telling-truth', 7)), ('and', ('lying', 4), ('telling-truth', 6)), ('<=>', ('lying', 4), ('lying', 5)), ('and', ('telling-truth', 0), ('lying', 3)))", "index": 385}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jack, Henry, Mason, Elizabeth, Zoey, Luke, Mia, and Jacob. Jack stated, \"Henry is not a knave\". Henry expressed that Jacob is a knight if and only if Elizabeth is a knave. Mason stated, \"Henry is a knave and Henry is a knight\". \"Jacob is not a knight,\" Elizabeth declared. \"Henry is a knave,\" Zoey mentioned. Luke expressed that Elizabeth is a knave. Mia was heard saying, \"Jacob is a knave and Jack is a knight\". Jacob was heard saying, \"Mason is a knight and Luke is a knight\". So who is a knight and who is a knave?", "names": ["Jack", "Henry", "Mason", "Elizabeth", "Zoey", "Luke", "Mia", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false, true, false], "solution_text": "Jack is a knight, Henry is a knight, Mason is a knave, Elizabeth is a knight, Zoey is a knave, Luke is a knave, Mia is a knight, and Jacob is a knave.", "solution_text_format": "(1) Jack is a knight\n(2) Henry is a knight\n(3) Mason is a knave\n(4) Elizabeth is a knight\n(5) Zoey is a knave\n(6) Luke is a knave\n(7) Mia is a knight\n(8) Jacob is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Henry is not a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Jacob is a knight if and only if Elizabeth is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Mason is a knight and Luke is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Henry is a knave and Henry is a knight.", "Mason cannot be a knave, because this would contradict the claim of Jacob that Mason is a knight and Luke is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Mason is a knight and Luke is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Henry is a knave and Henry is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Henry is a knave and Henry is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Elizabeth is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of Luke that Elizabeth is a knave.", "Elizabeth cannot be a knave, because this would contradict the claim of Henry that Jacob is a knight if and only if Elizabeth is a knave.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Elizabeth is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Jacob is not a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that Henry is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Henry is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Jacob is a knave and Jack is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('<=>', ('telling-truth', 7), ('lying', 3)), ('and', ('lying', 1), ('telling-truth', 1)), ('not', ('telling-truth', 7)), ('lying', 1), ('lying', 3), ('and', ('lying', 7), ('telling-truth', 0)), ('and', ('telling-truth', 2), ('telling-truth', 5)))", "index": 386}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Evelyn, Isabella, Sebastian, Penelope, Mason, Joseph, Owen, and Matthew. \"Evelyn is a knight if and only if Owen is a knight,\" Evelyn claimed. Isabella remarked, \"Owen is a knight and Evelyn is a knight\". Sebastian said that Sebastian is a knight or Mason is a knave. In a statement by Penelope: \"Matthew is a knave if and only if Joseph is a knave\". Mason commented, \"Matthew is a knight\". Joseph commented, \"Joseph is a knight and Mason is a knight\". Owen commented, \"Mason is not a knight\". Matthew expressed that Evelyn is a knave if and only if Sebastian is a knight. So who is a knight and who is a knave?", "names": ["Evelyn", "Isabella", "Sebastian", "Penelope", "Mason", "Joseph", "Owen", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false, true, false], "solution_text": "Evelyn is a knight, Isabella is a knight, Sebastian is a knight, Penelope is a knight, Mason is a knave, Joseph is a knave, Owen is a knight, and Matthew is a knave.", "solution_text_format": "(1) Evelyn is a knight\n(2) Isabella is a knight\n(3) Sebastian is a knight\n(4) Penelope is a knight\n(5) Mason is a knave\n(6) Joseph is a knave\n(7) Owen is a knight\n(8) Matthew is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Evelyn is a knight if and only if Owen is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Mason is not a knight.", "Mason cannot be a knight, because this would contradict the claim of Owen that Mason is not a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the false claim of Mason that Matthew is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Evelyn is a knave if and only if Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Sebastian is a knight or Mason is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Owen is a knight and Evelyn is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Matthew is a knave if and only if Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Penelope that Matthew is a knave if and only if Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Joseph is a knight and Mason is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 0), ('telling-truth', 6)), ('and', ('telling-truth', 6), ('telling-truth', 0)), ('or', ('telling-truth', 2), ('lying', 4)), ('<=>', ('lying', 7), ('lying', 5)), ('telling-truth', 7), ('and', ('telling-truth', 5), ('telling-truth', 4)), ('not', ('telling-truth', 4)), ('<=>', ('lying', 0), ('telling-truth', 2)))", "index": 387}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Harper, Samuel, Emma, Alexander, Victoria, David, Mason, and Elizabeth. In a statement by Harper: \"Samuel is not a knave\". Samuel told you that Mason is a knave and Victoria is a knight. \"Victoria is not a knight,\" Emma mentioned. \"Alexander is a knight or Emma is a knave,\" Alexander declared. Victoria remarked, \"If Harper is a knave then Samuel is a knave\". David said, \"If Emma is a knight then Emma is a knave.\" Mason noted, \"If David is a knight then Alexander is a knight\". Elizabeth asserted: \"Samuel is a knave or Emma is a knave\". So who is a knight and who is a knave?", "names": ["Harper", "Samuel", "Emma", "Alexander", "Victoria", "David", "Mason", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true, true, true], "solution_text": "Harper is a knave, Samuel is a knave, Emma is a knave, Alexander is a knight, Victoria is a knight, David is a knight, Mason is a knight, and Elizabeth is a knight.", "solution_text_format": "(1) Harper is a knave\n(2) Samuel is a knave\n(3) Emma is a knave\n(4) Alexander is a knight\n(5) Victoria is a knight\n(6) David is a knight\n(7) Mason is a knight\n(8) Elizabeth is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that Samuel is not a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Mason is a knave and Victoria is a knight.", "Mason cannot be a knight, because this would contradict the claim of Samuel that Mason is a knave and Victoria is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that If David is a knight then Alexander is a knight.", "Assume David is a knight. No contradiction is found in their claim that If Emma is a knight then Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of David that If Emma is a knight then Emma is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Victoria is not a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that If Harper is a knave then Samuel is a knave.", "Alexander cannot be a knight, because this would contradict the false claim of Mason that If David is a knight then Alexander is a knight.", "Alexander cannot be a knave, because this would contradict the false claim of their own that Alexander is a knight or Emma is a knave.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Victoria.", "Victoria cannot be a knave, because this would contradict the claim of Samuel that Mason is a knave and Victoria is a knight.", "We have exhausted all possibilities for Victoria and Emma, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the false claim of Mason that If David is a knight then Alexander is a knight.", "We have exhausted all possibilities for David and Mason, so let us go back and reconsider Samuel.", "Samuel cannot be a knave, because this would contradict the claim of Harper that Samuel is not a knave.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Samuel is not a knave.", "Samuel cannot be a knight, because this would contradict the false claim of Harper that Samuel is not a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Mason is a knave and Victoria is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that If David is a knight then Alexander is a knight.", "Assume David is a knight. No contradiction is found in their claim that If Emma is a knight then Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of David that If Emma is a knight then Emma is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Victoria is not a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that If Harper is a knave then Samuel is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Alexander is a knight or Emma is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Samuel is a knave or Emma is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('and', ('lying', 6), ('telling-truth', 4)), ('not', ('telling-truth', 4)), ('or', ('telling-truth', 3), ('lying', 2)), ('->', ('lying', 0), ('lying', 1)), ('->', ('telling-truth', 2), ('lying', 2)), ('->', ('telling-truth', 5), ('telling-truth', 3)), ('or', ('lying', 1), ('lying', 2)))", "index": 388}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Avery, Owen, Oliver, Ella, Emma, Noah, Ethan, and Luke. According to Avery, \"Emma is a knight and Ethan is a knave\". \"Ethan is not a knave\" - Owen. Oliver said that Luke is a knave and Avery is a knave. As Ella put it, \"If Owen is a knave then Luke is a knight\". Emma said, \"Avery is a knight and Owen is a knight.\" Noah said, \"Luke is a knight or Noah is a knight.\" \"If Noah is a knave then Ethan is a knight,\" Ethan declared. Luke was heard saying, \"If Emma is a knight then Avery is a knave\". So who is a knight and who is a knave?", "names": ["Avery", "Owen", "Oliver", "Ella", "Emma", "Noah", "Ethan", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, true, true, true], "solution_text": "Avery is a knave, Owen is a knight, Oliver is a knave, Ella is a knight, Emma is a knave, Noah is a knight, Ethan is a knight, and Luke is a knight.", "solution_text_format": "(1) Avery is a knave\n(2) Owen is a knight\n(3) Oliver is a knave\n(4) Ella is a knight\n(5) Emma is a knave\n(6) Noah is a knight\n(7) Ethan is a knight\n(8) Luke is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Emma is a knight and Ethan is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Avery is a knight and Owen is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Ethan is not a knave.", "Ethan cannot be a knight, because this would contradict the claim of Avery that Emma is a knight and Ethan is a knave.", "Ethan cannot be a knave, because this would contradict the claim of Owen that Ethan is not a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the claim of Emma that Avery is a knight and Owen is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Emma.", "Emma cannot be a knave, because this would contradict the claim of Avery that Emma is a knight and Ethan is a knave.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Emma is a knight and Ethan is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Avery is a knight and Owen is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Avery is a knight and Owen is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Ethan is not a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that If Noah is a knave then Ethan is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Luke is a knight or Noah is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that If Emma is a knight then Avery is a knave.", "Oliver cannot be a knight, because this would contradict the claim of their own that Luke is a knave and Avery is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Luke is a knave and Avery is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that If Owen is a knave then Luke is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 4), ('lying', 6)), ('not', ('lying', 6)), ('and', ('lying', 7), ('lying', 0)), ('->', ('lying', 1), ('telling-truth', 7)), ('and', ('telling-truth', 0), ('telling-truth', 1)), ('or', ('telling-truth', 7), ('telling-truth', 5)), ('->', ('lying', 5), ('telling-truth', 6)), ('->', ('telling-truth', 4), ('lying', 0)))", "index": 389}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Penelope, Sophia, Lucas, Owen, Charlotte, Sofia, Lily, and Ava. Penelope stated, \"Sofia is a knight if and only if Sofia is a knave\". Sophia told you that Ava is not a knight. Lucas told you that Owen is a knight and Penelope is a knave. As Owen put it, \"If Sofia is a knave then Sofia is a knight\". Charlotte noted, \"Lily is a knave or Owen is a knight\". \"Sofia is a knight if and only if Lily is a knight,\" Sofia declared. Lily commented, \"If Sophia is a knave then Owen is a knave\". Ava remarked, \"Sofia is a knight or Charlotte is a knight\". So who is a knight and who is a knave?", "names": ["Penelope", "Sophia", "Lucas", "Owen", "Charlotte", "Sofia", "Lily", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, false, true, false], "solution_text": "Penelope is a knave, Sophia is a knight, Lucas is a knave, Owen is a knave, Charlotte is a knave, Sofia is a knave, Lily is a knight, and Ava is a knave.", "solution_text_format": "(1) Penelope is a knave\n(2) Sophia is a knight\n(3) Lucas is a knave\n(4) Owen is a knave\n(5) Charlotte is a knave\n(6) Sofia is a knave\n(7) Lily is a knight\n(8) Ava is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Penelope cannot be a knight, because this would contradict the claim of their own that Sofia is a knight if and only if Sofia is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Sofia is a knight if and only if Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Sofia is a knight if and only if Lily is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that If Sophia is a knave then Owen is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Ava is not a knight.", "Ava cannot be a knight, because this would contradict the claim of Sophia that Ava is not a knight.", "Ava cannot be a knave, because this would contradict the false claim of their own that Sofia is a knight or Charlotte is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Ava is not a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Sofia is a knight or Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Lily is a knave or Owen is a knight.", "Owen cannot be a knight, because this would contradict the claim of Lily that If Sophia is a knave then Owen is a knave.", "Owen cannot be a knave, because this would contradict the false claim of their own that If Sofia is a knave then Sofia is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Lily is a knave or Owen is a knight.", "Owen cannot be a knight, because this would contradict the false claim of Charlotte that Lily is a knave or Owen is a knight.", "Owen cannot be a knave, because this would contradict the false claim of their own that If Sofia is a knave then Sofia is a knight.", "We have exhausted all possibilities for Owen and Charlotte, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the false claim of Sophia that Ava is not a knight.", "We have exhausted all possibilities for Ava and Sophia, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the claim of Sofia that Sofia is a knight if and only if Lily is a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Sofia is a knight if and only if Lily is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that If Sophia is a knave then Owen is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Ava is not a knight.", "Ava cannot be a knight, because this would contradict the claim of Sophia that Ava is not a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Sofia is a knight or Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of Ava that Sofia is a knight or Charlotte is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Lily is a knave or Owen is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that If Sofia is a knave then Sofia is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that If Sofia is a knave then Sofia is a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Owen is a knight and Penelope is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Owen is a knight and Penelope is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 5), ('lying', 5)), ('not', ('telling-truth', 7)), ('and', ('telling-truth', 3), ('lying', 0)), ('->', ('lying', 5), ('telling-truth', 5)), ('or', ('lying', 6), ('telling-truth', 3)), ('<=>', ('telling-truth', 5), ('telling-truth', 6)), ('->', ('lying', 1), ('lying', 3)), ('or', ('telling-truth', 5), ('telling-truth', 4)))", "index": 390}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lucas, Ella, Jacob, Evelyn, Emily, Isabella, Aurora, and Samuel. According to Lucas, \"Isabella is not a knave\". \"Isabella is a knight or Evelyn is a knave\" - Ella. Jacob said, \"Aurora is not a knave.\" \"Ella is not a knight,\" Evelyn declared. Emily expressed that Evelyn is a knight. Isabella was heard saying, \"Jacob is a knight if and only if Aurora is a knight\". According to Aurora, \"If Emily is a knave then Evelyn is a knight\". In a statement by Samuel: \"Ella is a knight if and only if Isabella is a knight\". So who is a knight and who is a knave?", "names": ["Lucas", "Ella", "Jacob", "Evelyn", "Emily", "Isabella", "Aurora", "Samuel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, true, false, true], "solution_text": "Lucas is a knight, Ella is a knight, Jacob is a knave, Evelyn is a knave, Emily is a knave, Isabella is a knight, Aurora is a knave, and Samuel is a knight.", "solution_text_format": "(1) Lucas is a knight\n(2) Ella is a knight\n(3) Jacob is a knave\n(4) Evelyn is a knave\n(5) Emily is a knave\n(6) Isabella is a knight\n(7) Aurora is a knave\n(8) Samuel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that Isabella is not a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Jacob is a knight if and only if Aurora is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Aurora is not a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that If Emily is a knave then Evelyn is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Evelyn is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Ella is not a knight.", "Ella cannot be a knight, because this would contradict the claim of Evelyn that Ella is not a knight.", "Ella cannot be a knave, because this would contradict the false claim of their own that Isabella is a knight or Evelyn is a knave.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the claim of Emily that Evelyn is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Evelyn is a knight.", "Evelyn cannot be a knight, because this would contradict the false claim of Emily that Evelyn is a knight.", "Evelyn cannot be a knave, because this would contradict the claim of Aurora that If Emily is a knave then Evelyn is a knight.", "We have exhausted all possibilities for Evelyn and Emily, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the claim of Jacob that Aurora is not a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Aurora is not a knave.", "Aurora cannot be a knight, because this would contradict the false claim of Jacob that Aurora is not a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that If Emily is a knave then Evelyn is a knight.", "Emily cannot be a knight, because this would contradict the false claim of Aurora that If Emily is a knave then Evelyn is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Evelyn is a knight.", "Evelyn cannot be a knight, because this would contradict the false claim of Emily that Evelyn is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Ella is not a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Isabella is a knight or Evelyn is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Ella is a knight if and only if Isabella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 5)), ('or', ('telling-truth', 5), ('lying', 3)), ('not', ('lying', 6)), ('not', ('telling-truth', 1)), ('telling-truth', 3), ('<=>', ('telling-truth', 2), ('telling-truth', 6)), ('->', ('lying', 4), ('telling-truth', 3)), ('<=>', ('telling-truth', 1), ('telling-truth', 5)))", "index": 391}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Liam, Aurora, Benjamin, Jack, Michael, Charlotte, Victoria, and Henry. Liam expressed that Michael is a knave and Jack is a knight. Aurora asserted: \"Benjamin is a knave and Liam is a knave\". Benjamin told you that Aurora is not a knave. Jack expressed that Liam is a knave if and only if Aurora is a knight. Michael was heard saying, \"Benjamin is a knight or Charlotte is a knave\". \"Victoria is a knight if and only if Aurora is a knave,\" Charlotte claimed. \"Jack is not a knave,\" Victoria claimed. Henry was heard saying, \"Michael is a knave if and only if Charlotte is a knave\". So who is a knight and who is a knave?", "names": ["Liam", "Aurora", "Benjamin", "Jack", "Michael", "Charlotte", "Victoria", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, true, true, false], "solution_text": "Liam is a knight, Aurora is a knave, Benjamin is a knave, Jack is a knight, Michael is a knave, Charlotte is a knight, Victoria is a knight, and Henry is a knave.", "solution_text_format": "(1) Liam is a knight\n(2) Aurora is a knave\n(3) Benjamin is a knave\n(4) Jack is a knight\n(5) Michael is a knave\n(6) Charlotte is a knight\n(7) Victoria is a knight\n(8) Henry is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Michael is a knave and Jack is a knight.", "Michael cannot be a knight, because this would contradict the claim of Liam that Michael is a knave and Jack is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Benjamin is a knight or Charlotte is a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Michael that Benjamin is a knight or Charlotte is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Aurora is not a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave and Liam is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Benjamin is a knave and Liam is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Aurora is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Jack is not a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Liam is a knave if and only if Aurora is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Michael is a knave if and only if Charlotte is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Michael is a knave if and only if Charlotte is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('telling-truth', 3)), ('and', ('lying', 2), ('lying', 0)), ('not', ('lying', 1)), ('<=>', ('lying', 0), ('telling-truth', 1)), ('or', ('telling-truth', 2), ('lying', 5)), ('<=>', ('telling-truth', 6), ('lying', 1)), ('not', ('lying', 3)), ('<=>', ('lying', 4), ('lying', 5)))", "index": 392}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jacob, Chloe, Lily, Henry, David, Olivia, Owen, and Elizabeth. In Jacob's words: \"Elizabeth is not a knave\". Chloe said that David is a knight. As Lily put it, \"Jacob is a knave if and only if Owen is a knight\". Henry commented, \"Elizabeth is a knave if and only if David is a knave\". \"David is a knight or Lily is a knight,\" David declared. Olivia was heard saying, \"Elizabeth is a knave and Chloe is a knave\". In a statement by Owen: \"Chloe is not a knight\". Elizabeth was heard saying, \"Lily is not a knight\". So who is a knight and who is a knave?", "names": ["Jacob", "Chloe", "Lily", "Henry", "David", "Olivia", "Owen", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, false, true, true], "solution_text": "Jacob is a knight, Chloe is a knave, Lily is a knave, Henry is a knave, David is a knave, Olivia is a knave, Owen is a knight, and Elizabeth is a knight.", "solution_text_format": "(1) Jacob is a knight\n(2) Chloe is a knave\n(3) Lily is a knave\n(4) Henry is a knave\n(5) David is a knave\n(6) Olivia is a knave\n(7) Owen is a knight\n(8) Elizabeth is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that Elizabeth is not a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Lily is not a knight.", "Lily cannot be a knight, because this would contradict the claim of Elizabeth that Lily is not a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Jacob is a knave if and only if Owen is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Chloe is not a knight.", "Chloe cannot be a knight, because this would contradict the claim of Owen that Chloe is not a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that David is a knight.", "David cannot be a knight, because this would contradict the false claim of Chloe that David is a knight.", "Assume David is a knave. No contradiction is found in their false claim that David is a knight or Lily is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave if and only if David is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Elizabeth is a knave if and only if David is a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave and Chloe is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Elizabeth is a knave and Chloe is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 7)), ('telling-truth', 4), ('<=>', ('lying', 0), ('telling-truth', 6)), ('<=>', ('lying', 7), ('lying', 4)), ('or', ('telling-truth', 4), ('telling-truth', 2)), ('and', ('lying', 7), ('lying', 1)), ('not', ('telling-truth', 1)), ('not', ('telling-truth', 2)))", "index": 393}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Riley, Scarlett, Emma, Grace, Owen, Penelope, Jack, and Ethan. Riley stated, \"Scarlett is a knave and Penelope is a knave\". According to Scarlett, \"If Riley is a knave then Emma is a knave\". As Emma put it, \"Jack is a knight and Scarlett is a knight\". Grace said, \"Emma is a knave.\" In a statement by Owen: \"Grace is a knave and Grace is a knight\". Penelope stated, \"Scarlett is a knave if and only if Grace is a knight\". \"Scarlett is a knave and Jack is a knight,\" Jack mentioned. Ethan told you that Jack is a knave and Grace is a knight. So who is a knight and who is a knave?", "names": ["Riley", "Scarlett", "Emma", "Grace", "Owen", "Penelope", "Jack", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, false, false, true], "solution_text": "Riley is a knave, Scarlett is a knight, Emma is a knave, Grace is a knight, Owen is a knave, Penelope is a knave, Jack is a knave, and Ethan is a knight.", "solution_text_format": "(1) Riley is a knave\n(2) Scarlett is a knight\n(3) Emma is a knave\n(4) Grace is a knight\n(5) Owen is a knave\n(6) Penelope is a knave\n(7) Jack is a knave\n(8) Ethan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Scarlett is a knave and Penelope is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Riley that Scarlett is a knave and Penelope is a knave.", "Scarlett cannot be a knave, because this would contradict the false claim of their own that If Riley is a knave then Emma is a knave.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Scarlett is a knave and Penelope is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Riley is a knave then Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of Scarlett that If Riley is a knave then Emma is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Jack is a knight and Scarlett is a knight.", "Jack cannot be a knight, because this would contradict the false claim of Emma that Jack is a knight and Scarlett is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Scarlett is a knave and Jack is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Scarlett is a knave if and only if Grace is a knight.", "Grace cannot be a knight, because this would contradict the claim of Penelope that Scarlett is a knave if and only if Grace is a knight.", "Grace cannot be a knave, because this would contradict the false claim of their own that Emma is a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Scarlett is a knave if and only if Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Emma is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Grace is a knave and Grace is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Grace is a knave and Grace is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Jack is a knave and Grace is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 1), ('lying', 5)), ('->', ('lying', 0), ('lying', 2)), ('and', ('telling-truth', 6), ('telling-truth', 1)), ('lying', 2), ('and', ('lying', 3), ('telling-truth', 3)), ('<=>', ('lying', 1), ('telling-truth', 3)), ('and', ('lying', 1), ('telling-truth', 6)), ('and', ('lying', 6), ('telling-truth', 3)))", "index": 394}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Grace, Samuel, Mia, Olivia, Ava, James, Scarlett, and Lucas. In Grace's words: \"Samuel is a knave if and only if Olivia is a knight\". In a statement by Samuel: \"Grace is a knave or Mia is a knave\". Mia commented, \"Grace is a knight and Lucas is a knave\". Olivia stated, \"If James is a knave then Mia is a knight\". \"Samuel is not a knave,\" Ava declared. \"Olivia is not a knight,\" James mentioned. \"Lucas is a knight if and only if Ava is a knight,\" Scarlett mentioned. Lucas said, \"Grace is a knight and Ava is a knight.\" So who is a knight and who is a knave?", "names": ["Grace", "Samuel", "Mia", "Olivia", "Ava", "James", "Scarlett", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, false, true, false], "solution_text": "Grace is a knight, Samuel is a knave, Mia is a knight, Olivia is a knight, Ava is a knave, James is a knave, Scarlett is a knight, and Lucas is a knave.", "solution_text_format": "(1) Grace is a knight\n(2) Samuel is a knave\n(3) Mia is a knight\n(4) Olivia is a knight\n(5) Ava is a knave\n(6) James is a knave\n(7) Scarlett is a knight\n(8) Lucas is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Olivia is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Grace is a knave or Mia is a knave.", "Mia cannot be a knight, because this would contradict the claim of Samuel that Grace is a knave or Mia is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Grace is a knight and Lucas is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Grace is a knight and Ava is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Samuel is not a knave.", "Olivia cannot be a knight, because this would contradict the claim of Grace that Samuel is a knave if and only if Olivia is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that If James is a knave then Mia is a knight.", "James cannot be a knight, because this would contradict the false claim of Olivia that If James is a knave then Mia is a knight.", "James cannot be a knave, because this would contradict the false claim of their own that Olivia is not a knight.", "We have exhausted all possibilities for James and Olivia, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the false claim of their own that Samuel is not a knave.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the false claim of Mia that Grace is a knight and Lucas is a knave.", "We have exhausted all possibilities for Lucas and Mia, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Grace is a knave or Mia is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Grace is a knight and Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the claim of Mia that Grace is a knight and Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Grace is a knight and Ava is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Samuel is not a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Samuel is not a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that If James is a knave then Mia is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Olivia is not a knight.", "Assume James is a knave. No contradiction is found in their false claim that Olivia is not a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Lucas is a knight if and only if Ava is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('telling-truth', 3)), ('or', ('lying', 0), ('lying', 2)), ('and', ('telling-truth', 0), ('lying', 7)), ('->', ('lying', 5), ('telling-truth', 2)), ('not', ('lying', 1)), ('not', ('telling-truth', 3)), ('<=>', ('telling-truth', 7), ('telling-truth', 4)), ('and', ('telling-truth', 0), ('telling-truth', 4)))", "index": 395}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Amelia, Luke, Ethan, Grace, Samuel, Olivia, Evelyn, and Aiden. \"Luke is a knave or Luke is a knight,\" Amelia mentioned. Luke commented, \"Samuel is a knave and Grace is a knight\". As Ethan put it, \"Luke is a knight and Grace is a knight\". As Grace put it, \"If Samuel is a knight then Evelyn is a knave\". \"If Amelia is a knave then Luke is a knight,\" Samuel declared. In Olivia's words: \"If Samuel is a knight then Ethan is a knight\". In a statement by Evelyn: \"Amelia is a knight\". \"Ethan is a knave,\" Aiden claimed. So who is a knight and who is a knave?", "names": ["Amelia", "Luke", "Ethan", "Grace", "Samuel", "Olivia", "Evelyn", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, false, true, true], "solution_text": "Amelia is a knight, Luke is a knave, Ethan is a knave, Grace is a knave, Samuel is a knight, Olivia is a knave, Evelyn is a knight, and Aiden is a knight.", "solution_text_format": "(1) Amelia is a knight\n(2) Luke is a knave\n(3) Ethan is a knave\n(4) Grace is a knave\n(5) Samuel is a knight\n(6) Olivia is a knave\n(7) Evelyn is a knight\n(8) Aiden is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Amelia is a knight. No contradiction is found in their claim that Luke is a knave or Luke is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Samuel is a knave and Grace is a knight.", "Samuel cannot be a knight, because this would contradict the claim of Luke that Samuel is a knave and Grace is a knight.", "Samuel cannot be a knave, because this would contradict the false claim of their own that If Amelia is a knave then Luke is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Samuel is a knave and Grace is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that If Amelia is a knave then Luke is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that If Samuel is a knight then Evelyn is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of Grace that If Samuel is a knight then Evelyn is a knave.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that Amelia is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that If Samuel is a knight then Evelyn is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Amelia is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Luke is a knight and Grace is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Luke is a knight and Grace is a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that If Samuel is a knight then Ethan is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that If Samuel is a knight then Ethan is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Ethan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('telling-truth', 1)), ('and', ('lying', 4), ('telling-truth', 3)), ('and', ('telling-truth', 1), ('telling-truth', 3)), ('->', ('telling-truth', 4), ('lying', 6)), ('->', ('lying', 0), ('telling-truth', 1)), ('->', ('telling-truth', 4), ('telling-truth', 2)), ('telling-truth', 0), ('lying', 2))", "index": 396}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sebastian, Alexander, Aiden, James, Lucas, Liam, David, and Elizabeth. \"Liam is a knave and David is a knight,\" Sebastian mentioned. \"Aiden is not a knight,\" Alexander declared. \"Alexander is a knave,\" Aiden mentioned. James told you that Sebastian is a knave and Elizabeth is a knave. \"Aiden is a knave,\" Lucas mentioned. Liam told you that If Elizabeth is a knave then David is a knave. David said, \"James is a knave or Lucas is a knave.\" Elizabeth remarked, \"Sebastian is not a knave\". So who is a knight and who is a knave?", "names": ["Sebastian", "Alexander", "Aiden", "James", "Lucas", "Liam", "David", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true, false, false], "solution_text": "Sebastian is a knave, Alexander is a knight, Aiden is a knave, James is a knight, Lucas is a knight, Liam is a knight, David is a knave, and Elizabeth is a knave.", "solution_text_format": "(1) Sebastian is a knave\n(2) Alexander is a knight\n(3) Aiden is a knave\n(4) James is a knight\n(5) Lucas is a knight\n(6) Liam is a knight\n(7) David is a knave\n(8) Elizabeth is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that Liam is a knave and David is a knight.", "Liam cannot be a knight, because this would contradict the claim of Sebastian that Liam is a knave and David is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that If Elizabeth is a knave then David is a knave.", "Elizabeth cannot be a knight, because this would contradict the false claim of Liam that If Elizabeth is a knave then David is a knave.", "Elizabeth cannot be a knave, because this would contradict the false claim of their own that Sebastian is not a knave.", "We have exhausted all possibilities for Elizabeth and Liam, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Liam is a knave and David is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that If Elizabeth is a knave then David is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Sebastian is not a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Sebastian is not a knave.", "David cannot be a knight, because this would contradict the claim of Liam that If Elizabeth is a knave then David is a knave.", "Assume David is a knave. No contradiction is found in their false claim that James is a knave or Lucas is a knave.", "Assume James is a knight. No contradiction is found in their claim that Sebastian is a knave and Elizabeth is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Aiden is a knave.", "Aiden cannot be a knight, because this would contradict the claim of Lucas that Aiden is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Alexander is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Aiden is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 5), ('telling-truth', 6)), ('not', ('telling-truth', 2)), ('lying', 1), ('and', ('lying', 0), ('lying', 7)), ('lying', 2), ('->', ('lying', 7), ('lying', 6)), ('or', ('lying', 3), ('lying', 4)), ('not', ('lying', 0)))", "index": 397}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Isabella, Olivia, Harper, James, Jack, Sebastian, Chloe, and Henry. Isabella was heard saying, \"James is not a knave\". Olivia told you that Chloe is a knave and Sebastian is a knave. In Harper's words: \"Jack is a knight or Harper is a knight\". \"Jack is a knight if and only if Henry is a knight,\" James declared. Jack was heard saying, \"Isabella is not a knight\". Sebastian commented, \"If Isabella is a knight then Chloe is a knight\". Chloe noted, \"Henry is a knight and Sebastian is a knight\". Henry remarked, \"Harper is a knight or Jack is a knight\". So who is a knight and who is a knave?", "names": ["Isabella", "Olivia", "Harper", "James", "Jack", "Sebastian", "Chloe", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false, false, false], "solution_text": "Isabella is a knight, Olivia is a knight, Harper is a knave, James is a knight, Jack is a knave, Sebastian is a knave, Chloe is a knave, and Henry is a knave.", "solution_text_format": "(1) Isabella is a knight\n(2) Olivia is a knight\n(3) Harper is a knave\n(4) James is a knight\n(5) Jack is a knave\n(6) Sebastian is a knave\n(7) Chloe is a knave\n(8) Henry is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that James is not a knave.", "Assume James is a knight. No contradiction is found in their claim that Jack is a knight if and only if Henry is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Isabella is not a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Isabella is not a knight.", "Henry cannot be a knight, because this would contradict the claim of James that Jack is a knight if and only if Henry is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Harper is a knight or Jack is a knight.", "Harper cannot be a knight, because this would contradict the false claim of Henry that Harper is a knight or Jack is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Jack is a knight or Harper is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Chloe is a knave and Sebastian is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Olivia that Chloe is a knave and Sebastian is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Henry is a knight and Sebastian is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of Olivia that Chloe is a knave and Sebastian is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that If Isabella is a knight then Chloe is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 3)), ('and', ('lying', 6), ('lying', 5)), ('or', ('telling-truth', 4), ('telling-truth', 2)), ('<=>', ('telling-truth', 4), ('telling-truth', 7)), ('not', ('telling-truth', 0)), ('->', ('telling-truth', 0), ('telling-truth', 6)), ('and', ('telling-truth', 7), ('telling-truth', 5)), ('or', ('telling-truth', 2), ('telling-truth', 4)))", "index": 398}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sophia, Emma, Olivia, Mia, Isabella, Henry, Oliver, and Matthew. \"Oliver is a knave,\" Sophia declared. \"Sophia is a knight or Mia is a knight,\" Emma claimed. Olivia asserted: \"Henry is a knave if and only if Matthew is a knave\". Mia was heard saying, \"Isabella is a knave\". Isabella said that Emma is a knight. \"Olivia is a knight,\" Henry mentioned. Oliver noted, \"Henry is a knave\". Matthew said that Oliver is a knave or Emma is a knight. So who is a knight and who is a knave?", "names": ["Sophia", "Emma", "Olivia", "Mia", "Isabella", "Henry", "Oliver", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true, false, true], "solution_text": "Sophia is a knight, Emma is a knight, Olivia is a knight, Mia is a knave, Isabella is a knight, Henry is a knight, Oliver is a knave, and Matthew is a knight.", "solution_text_format": "(1) Sophia is a knight\n(2) Emma is a knight\n(3) Olivia is a knight\n(4) Mia is a knave\n(5) Isabella is a knight\n(6) Henry is a knight\n(7) Oliver is a knave\n(8) Matthew is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Oliver is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Sophia that Oliver is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Henry is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Olivia is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Henry is a knave if and only if Matthew is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Oliver is a knave or Emma is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Sophia is a knight or Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Isabella is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Mia that Isabella is a knave.", "Isabella cannot be a knave, because this would contradict the false claim of their own that Emma is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Isabella is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Emma is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 6), ('or', ('telling-truth', 0), ('telling-truth', 3)), ('<=>', ('lying', 5), ('lying', 7)), ('lying', 4), ('telling-truth', 1), ('telling-truth', 2), ('lying', 5), ('or', ('lying', 6), ('telling-truth', 1)))", "index": 399}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Noah, Aiden, Logan, Liam, Riley, Lucas, Mia, and Ella. \"Logan is a knave,\" Noah mentioned. Aiden commented, \"Lucas is a knave or Ella is a knave\". In a statement by Logan: \"Liam is a knight if and only if Liam is a knave\". According to Liam, \"If Logan is a knave then Lucas is a knight\". Riley asserted: \"Aiden is a knave if and only if Liam is a knave\". \"Liam is a knight or Logan is a knave,\" Lucas mentioned. Mia said, \"Noah is a knave and Logan is a knight.\" \"Lucas is a knave and Logan is a knave,\" Ella declared. So who is a knight and who is a knave?", "names": ["Noah", "Aiden", "Logan", "Liam", "Riley", "Lucas", "Mia", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true, false, false], "solution_text": "Noah is a knight, Aiden is a knight, Logan is a knave, Liam is a knight, Riley is a knight, Lucas is a knight, Mia is a knave, and Ella is a knave.", "solution_text_format": "(1) Noah is a knight\n(2) Aiden is a knight\n(3) Logan is a knave\n(4) Liam is a knight\n(5) Riley is a knight\n(6) Lucas is a knight\n(7) Mia is a knave\n(8) Ella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Noah is a knight. No contradiction is found in their claim that Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of Noah that Logan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Liam is a knight if and only if Liam is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that If Logan is a knave then Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Liam is a knight or Logan is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Lucas is a knave or Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of Aiden that Lucas is a knave or Ella is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Lucas is a knave and Logan is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Aiden is a knave if and only if Liam is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Noah is a knave and Logan is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Noah is a knave and Logan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('or', ('lying', 5), ('lying', 7)), ('<=>', ('telling-truth', 3), ('lying', 3)), ('->', ('lying', 2), ('telling-truth', 5)), ('<=>', ('lying', 1), ('lying', 3)), ('or', ('telling-truth', 3), ('lying', 2)), ('and', ('lying', 0), ('telling-truth', 2)), ('and', ('lying', 5), ('lying', 2)))", "index": 400}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mia, Elizabeth, William, Henry, Liam, Charlotte, Chloe, and Michael. \"Michael is a knave,\" Mia claimed. Elizabeth remarked, \"Mia is a knave and Liam is a knight\". According to William, \"If Henry is a knave then Liam is a knave\". Henry commented, \"Mia is a knight\". Liam noted, \"Henry is a knave if and only if William is a knave\". \"William is a knight if and only if Mia is a knight,\" Charlotte claimed. \"Mia is a knave and Henry is a knight,\" Chloe mentioned. In Michael's words: \"Chloe is a knave if and only if Charlotte is a knight\". So who is a knight and who is a knave?", "names": ["Mia", "Elizabeth", "William", "Henry", "Liam", "Charlotte", "Chloe", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true, false, true], "solution_text": "Mia is a knave, Elizabeth is a knight, William is a knave, Henry is a knave, Liam is a knight, Charlotte is a knight, Chloe is a knave, and Michael is a knight.", "solution_text_format": "(1) Mia is a knave\n(2) Elizabeth is a knight\n(3) William is a knave\n(4) Henry is a knave\n(5) Liam is a knight\n(6) Charlotte is a knight\n(7) Chloe is a knave\n(8) Michael is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of Mia that Michael is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Chloe is a knave if and only if Charlotte is a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Mia is a knave and Henry is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Mia is a knave and Henry is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Mia is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of Michael that Chloe is a knave if and only if Charlotte is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that William is a knight if and only if Mia is a knight.", "William cannot be a knight, because this would contradict the false claim of Charlotte that William is a knight if and only if Mia is a knight.", "William cannot be a knave, because this would contradict the false claim of their own that If Henry is a knave then Liam is a knave.", "We have exhausted all possibilities for William and Charlotte, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the false claim of their own that Mia is a knight.", "We have exhausted all possibilities for Henry, Chloe, and Michael, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Michael is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Chloe is a knave if and only if Charlotte is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Mia is a knave and Henry is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Mia is a knight.", "Henry cannot be a knave, because this would contradict the claim of Chloe that Mia is a knave and Henry is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Mia is a knave and Henry is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Mia is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Mia is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that William is a knight if and only if Mia is a knight.", "William cannot be a knight, because this would contradict the claim of Charlotte that William is a knight if and only if Mia is a knight.", "Assume William is a knave. No contradiction is found in their false claim that If Henry is a knave then Liam is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Henry is a knave if and only if William is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Mia is a knave and Liam is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 7), ('and', ('lying', 0), ('telling-truth', 4)), ('->', ('lying', 3), ('lying', 4)), ('telling-truth', 0), ('<=>', ('lying', 3), ('lying', 2)), ('<=>', ('telling-truth', 2), ('telling-truth', 0)), ('and', ('lying', 0), ('telling-truth', 3)), ('<=>', ('lying', 6), ('telling-truth', 5)))", "index": 401}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Alexander, Sophia, Ella, Zoey, Oliver, Abigail, Ethan, and Henry. Alexander commented, \"Ella is a knight\". \"If Oliver is a knave then Ella is a knave\" - Sophia. As Ella put it, \"Oliver is a knight if and only if Ethan is a knave\". \"Ethan is a knight and Abigail is a knight,\" Zoey claimed. \"If Ethan is a knight then Sophia is a knight,\" Oliver claimed. In Abigail's words: \"If Zoey is a knight then Ethan is a knave\". In Ethan's words: \"Abigail is not a knight\". Henry said, \"Oliver is a knight.\" So who is a knight and who is a knave?", "names": ["Alexander", "Sophia", "Ella", "Zoey", "Oliver", "Abigail", "Ethan", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true, false, true], "solution_text": "Alexander is a knight, Sophia is a knight, Ella is a knight, Zoey is a knave, Oliver is a knight, Abigail is a knight, Ethan is a knave, and Henry is a knight.", "solution_text_format": "(1) Alexander is a knight\n(2) Sophia is a knight\n(3) Ella is a knight\n(4) Zoey is a knave\n(5) Oliver is a knight\n(6) Abigail is a knight\n(7) Ethan is a knave\n(8) Henry is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Oliver is a knight if and only if Ethan is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that If Ethan is a knight then Sophia is a knight.", "Ethan cannot be a knight, because this would contradict the claim of Ella that Oliver is a knight if and only if Ethan is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Abigail is not a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If Zoey is a knight then Ethan is a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that Ethan is a knight and Abigail is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Ethan is a knight and Abigail is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that If Oliver is a knave then Ella is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Oliver is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('->', ('lying', 4), ('lying', 2)), ('<=>', ('telling-truth', 4), ('lying', 6)), ('and', ('telling-truth', 6), ('telling-truth', 5)), ('->', ('telling-truth', 6), ('telling-truth', 1)), ('->', ('telling-truth', 3), ('lying', 6)), ('not', ('telling-truth', 5)), ('telling-truth', 4))", "index": 402}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ethan, Riley, Daniel, Oliver, Henry, Sophia, Benjamin, and Harper. \"Daniel is not a knave,\" Ethan claimed. \"If Ethan is a knave then Oliver is a knave\" - Riley. Daniel asserted: \"Oliver is a knight and Harper is a knight\". \"Riley is not a knight\" - Oliver. Henry noted, \"Daniel is not a knave\". Sophia was heard saying, \"Henry is a knight or Harper is a knight\". \"Harper is a knave if and only if Henry is a knave,\" Benjamin declared. Harper told you that Harper is a knight or Daniel is a knave. So who is a knight and who is a knave?", "names": ["Ethan", "Riley", "Daniel", "Oliver", "Henry", "Sophia", "Benjamin", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, true, false, true], "solution_text": "Ethan is a knave, Riley is a knight, Daniel is a knave, Oliver is a knave, Henry is a knave, Sophia is a knight, Benjamin is a knave, and Harper is a knight.", "solution_text_format": "(1) Ethan is a knave\n(2) Riley is a knight\n(3) Daniel is a knave\n(4) Oliver is a knave\n(5) Henry is a knave\n(6) Sophia is a knight\n(7) Benjamin is a knave\n(8) Harper is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Daniel is not a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Oliver is a knight and Harper is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Riley is not a knight.", "Riley cannot be a knight, because this would contradict the claim of Oliver that Riley is not a knight.", "Riley cannot be a knave, because this would contradict the false claim of their own that If Ethan is a knave then Oliver is a knave.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the claim of Daniel that Oliver is a knight and Harper is a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the claim of Ethan that Daniel is not a knave.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Daniel is not a knave.", "Daniel cannot be a knight, because this would contradict the false claim of Ethan that Daniel is not a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Oliver is a knight and Harper is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Riley is not a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that If Ethan is a knave then Oliver is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that If Ethan is a knave then Oliver is a knave.", "Harper cannot be a knight, because this would contradict the false claim of Daniel that Oliver is a knight and Harper is a knight.", "Harper cannot be a knave, because this would contradict the false claim of their own that Harper is a knight or Daniel is a knave.", "We have exhausted all possibilities for Harper and Riley, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Riley is not a knight.", "Assume Riley is a knight. No contradiction is found in their claim that If Ethan is a knave then Oliver is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Harper is a knight or Daniel is a knave.", "Henry cannot be a knight, because this would contradict the claim of their own that Daniel is not a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Daniel is not a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Henry is a knight or Harper is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Harper is a knave if and only if Henry is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Harper is a knave if and only if Henry is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('->', ('lying', 0), ('lying', 3)), ('and', ('telling-truth', 3), ('telling-truth', 7)), ('not', ('telling-truth', 1)), ('not', ('lying', 2)), ('or', ('telling-truth', 4), ('telling-truth', 7)), ('<=>', ('lying', 7), ('lying', 4)), ('or', ('telling-truth', 7), ('lying', 2)))", "index": 403}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Evelyn, Michael, Penelope, Aurora, Daniel, Aria, Benjamin, and Olivia. According to Evelyn, \"Aurora is a knave or Aria is a knight\". Michael expressed that Olivia is a knight if and only if Olivia is a knave. Penelope was heard saying, \"If Aria is a knight then Olivia is a knight\". \"Penelope is a knight and Aria is a knight,\" Aurora mentioned. \"Olivia is a knave if and only if Aurora is a knave,\" Daniel claimed. Aria remarked, \"Olivia is a knave or Benjamin is a knight\". Benjamin remarked, \"Olivia is a knave\". Olivia said that Aurora is a knight. So who is a knight and who is a knave?", "names": ["Evelyn", "Michael", "Penelope", "Aurora", "Daniel", "Aria", "Benjamin", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true, true, false], "solution_text": "Evelyn is a knight, Michael is a knave, Penelope is a knave, Aurora is a knave, Daniel is a knight, Aria is a knight, Benjamin is a knight, and Olivia is a knave.", "solution_text_format": "(1) Evelyn is a knight\n(2) Michael is a knave\n(3) Penelope is a knave\n(4) Aurora is a knave\n(5) Daniel is a knight\n(6) Aria is a knight\n(7) Benjamin is a knight\n(8) Olivia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Aurora is a knave or Aria is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Penelope is a knight and Aria is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that If Aria is a knight then Olivia is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Olivia is a knave or Benjamin is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Aurora is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Olivia is a knave.", "Benjamin cannot be a knave, because this would contradict the claim of Aria that Olivia is a knave or Benjamin is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the claim of Penelope that If Aria is a knight then Olivia is a knight.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Aria.", "Aria cannot be a knave, because this would contradict the claim of Evelyn that Aurora is a knave or Aria is a knight.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the claim of Aurora that Penelope is a knight and Aria is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Penelope is a knight and Aria is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that If Aria is a knight then Olivia is a knight.", "Aria cannot be a knight, because this would contradict the false claim of Aurora that Penelope is a knight and Aria is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Olivia is a knave or Benjamin is a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that Aurora is a knight.", "Olivia cannot be a knave, because this would contradict the false claim of Aria that Olivia is a knave or Benjamin is a knight.", "We have exhausted all possibilities for Olivia and Aria, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that If Aria is a knight then Olivia is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Olivia is a knave or Benjamin is a knight.", "Olivia cannot be a knight, because this would contradict the false claim of Penelope that If Aria is a knight then Olivia is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Aurora is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Olivia is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Olivia is a knight if and only if Olivia is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Olivia is a knight if and only if Olivia is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Olivia is a knave if and only if Aurora is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('telling-truth', 5)), ('<=>', ('telling-truth', 7), ('lying', 7)), ('->', ('telling-truth', 5), ('telling-truth', 7)), ('and', ('telling-truth', 2), ('telling-truth', 5)), ('<=>', ('lying', 7), ('lying', 3)), ('or', ('lying', 7), ('telling-truth', 6)), ('lying', 7), ('telling-truth', 3))", "index": 404}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Benjamin, Sofia, James, Sophia, Scarlett, Isabella, Lily, and Penelope. As Benjamin put it, \"If Sophia is a knight then Sofia is a knight\". In Sofia's words: \"Isabella is not a knight\". James expressed that Isabella is a knave. \"Sophia is a knight or Sofia is a knight,\" Sophia mentioned. \"Lily is a knight and James is a knight,\" Scarlett declared. \"Sofia is a knight or Sophia is a knave,\" Isabella declared. Lily commented, \"Sophia is a knight and Sophia is a knave\". Penelope said, \"Lily is a knave or Sophia is a knave.\" So who is a knight and who is a knave?", "names": ["Benjamin", "Sofia", "James", "Sophia", "Scarlett", "Isabella", "Lily", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, true, false, true], "solution_text": "Benjamin is a knight, Sofia is a knave, James is a knave, Sophia is a knave, Scarlett is a knave, Isabella is a knight, Lily is a knave, and Penelope is a knight.", "solution_text_format": "(1) Benjamin is a knight\n(2) Sofia is a knave\n(3) James is a knave\n(4) Sophia is a knave\n(5) Scarlett is a knave\n(6) Isabella is a knight\n(7) Lily is a knave\n(8) Penelope is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that If Sophia is a knight then Sofia is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Sophia is a knight or Sofia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Isabella is not a knight.", "Isabella cannot be a knight, because this would contradict the claim of Sofia that Isabella is not a knight.", "Isabella cannot be a knave, because this would contradict the false claim of their own that Sofia is a knight or Sophia is a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Sofia.", "Sofia cannot be a knave, because this would contradict the claim of Benjamin that If Sophia is a knight then Sofia is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Sophia is a knight or Sofia is a knight.", "Sofia cannot be a knight, because this would contradict the false claim of Sophia that Sophia is a knight or Sofia is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Isabella is not a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Sofia is a knight or Sophia is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Isabella is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Isabella is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Lily is a knight and James is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Lily is a knight and James is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Sophia is a knight and Sophia is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Sophia is a knight and Sophia is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Lily is a knave or Sophia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('telling-truth', 1)), ('not', ('telling-truth', 5)), ('lying', 5), ('or', ('telling-truth', 3), ('telling-truth', 1)), ('and', ('telling-truth', 6), ('telling-truth', 2)), ('or', ('telling-truth', 1), ('lying', 3)), ('and', ('telling-truth', 3), ('lying', 3)), ('or', ('lying', 6), ('lying', 3)))", "index": 405}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Grace, Henry, Lily, Liam, Michael, Sophia, Daniel, and Joseph. Grace told you that If Liam is a knave then Sophia is a knave. Henry expressed that Michael is a knave and Lily is a knight. \"Henry is a knave and Liam is a knave,\" Lily claimed. Liam said, \"Henry is a knave.\" Michael commented, \"Henry is a knave and Liam is a knight\". Sophia expressed that Lily is not a knight. Daniel noted, \"Lily is a knave\". In Joseph's words: \"Grace is a knight\". So who is a knight and who is a knave?", "names": ["Grace", "Henry", "Lily", "Liam", "Michael", "Sophia", "Daniel", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true, true, true], "solution_text": "Grace is a knight, Henry is a knave, Lily is a knave, Liam is a knight, Michael is a knight, Sophia is a knight, Daniel is a knight, and Joseph is a knight.", "solution_text_format": "(1) Grace is a knight\n(2) Henry is a knave\n(3) Lily is a knave\n(4) Liam is a knight\n(5) Michael is a knight\n(6) Sophia is a knight\n(7) Daniel is a knight\n(8) Joseph is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that If Liam is a knave then Sophia is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of Liam that Henry is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Michael is a knave and Lily is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Henry is a knave and Liam is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Henry is a knave and Liam is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Henry is a knave and Liam is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Lily is not a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Lily is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Grace is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('lying', 5)), ('and', ('lying', 4), ('telling-truth', 2)), ('and', ('lying', 1), ('lying', 3)), ('lying', 1), ('and', ('lying', 1), ('telling-truth', 3)), ('not', ('telling-truth', 2)), ('lying', 2), ('telling-truth', 0))", "index": 406}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Samuel, Amelia, Elizabeth, Isabella, Joseph, Emma, Mia, and Jacob. In Samuel's words: \"Elizabeth is a knave if and only if Jacob is a knave\". \"Emma is a knight if and only if Isabella is a knight,\" Amelia mentioned. As Elizabeth put it, \"If Samuel is a knight then Mia is a knight\". Isabella said, \"Emma is a knight and Elizabeth is a knight.\" According to Joseph, \"Amelia is a knave and Mia is a knave\". Emma stated, \"Joseph is a knight and Emma is a knight\". \"Samuel is not a knave,\" Mia mentioned. Jacob stated, \"Joseph is a knight\". So who is a knight and who is a knave?", "names": ["Samuel", "Amelia", "Elizabeth", "Isabella", "Joseph", "Emma", "Mia", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false, false, false], "solution_text": "Samuel is a knave, Amelia is a knight, Elizabeth is a knight, Isabella is a knave, Joseph is a knave, Emma is a knave, Mia is a knave, and Jacob is a knave.", "solution_text_format": "(1) Samuel is a knave\n(2) Amelia is a knight\n(3) Elizabeth is a knight\n(4) Isabella is a knave\n(5) Joseph is a knave\n(6) Emma is a knave\n(7) Mia is a knave\n(8) Jacob is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that Elizabeth is a knave if and only if Jacob is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Samuel is a knight then Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Samuel is not a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Amelia is a knave and Mia is a knave.", "Joseph cannot be a knave, because this would contradict the claim of Jacob that Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the claim of Samuel that Elizabeth is a knave if and only if Jacob is a knave.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the claim of Elizabeth that If Samuel is a knight then Mia is a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that If Samuel is a knight then Mia is a knight.", "Mia cannot be a knight, because this would contradict the false claim of Elizabeth that If Samuel is a knight then Mia is a knight.", "Mia cannot be a knave, because this would contradict the false claim of their own that Samuel is not a knave.", "We have exhausted all possibilities for Mia and Elizabeth, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Elizabeth is a knave if and only if Jacob is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Samuel is a knight then Mia is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that Samuel is not a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Samuel is not a knave.", "Jacob cannot be a knight, because this would contradict the false claim of Samuel that Elizabeth is a knave if and only if Jacob is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of Jacob that Joseph is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Amelia is a knave and Mia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Emma is a knight if and only if Isabella is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Joseph is a knight and Emma is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Joseph is a knight and Emma is a knight.", "Isabella cannot be a knight, because this would contradict the claim of Amelia that Emma is a knight if and only if Isabella is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Emma is a knight and Elizabeth is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('lying', 7)), ('<=>', ('telling-truth', 5), ('telling-truth', 3)), ('->', ('telling-truth', 0), ('telling-truth', 6)), ('and', ('telling-truth', 5), ('telling-truth', 2)), ('and', ('lying', 1), ('lying', 6)), ('and', ('telling-truth', 4), ('telling-truth', 5)), ('not', ('lying', 0)), ('telling-truth', 4))", "index": 407}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Henry, Sebastian, Scarlett, Penelope, Ella, Benjamin, Victoria, and Daniel. \"Victoria is not a knight,\" Henry claimed. Sebastian commented, \"Victoria is a knight\". Scarlett expressed that If Victoria is a knight then Penelope is a knight. Penelope was heard saying, \"Sebastian is a knave or Ella is a knight\". Ella expressed that Scarlett is not a knave. \"Sebastian is a knight or Ella is a knight\" - Benjamin. As Victoria put it, \"Daniel is a knight and Benjamin is a knight\". Daniel noted, \"Scarlett is a knight\". So who is a knight and who is a knave?", "names": ["Henry", "Sebastian", "Scarlett", "Penelope", "Ella", "Benjamin", "Victoria", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true, true, true], "solution_text": "Henry is a knave, Sebastian is a knight, Scarlett is a knight, Penelope is a knight, Ella is a knight, Benjamin is a knight, Victoria is a knight, and Daniel is a knight.", "solution_text_format": "(1) Henry is a knave\n(2) Sebastian is a knight\n(3) Scarlett is a knight\n(4) Penelope is a knight\n(5) Ella is a knight\n(6) Benjamin is a knight\n(7) Victoria is a knight\n(8) Daniel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that Victoria is not a knight.", "Victoria cannot be a knight, because this would contradict the claim of Henry that Victoria is not a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Daniel is a knight and Benjamin is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Victoria is a knight then Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Sebastian is a knave or Ella is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Victoria is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Victoria is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Victoria that Daniel is a knight and Benjamin is a knight.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that Sebastian is a knight or Ella is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the false claim of their own that Scarlett is not a knave.", "We have exhausted all possibilities for Ella and Sebastian, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Sebastian is a knave or Ella is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Victoria is a knight.", "Sebastian cannot be a knave, because this would contradict the false claim of Penelope that Sebastian is a knave or Ella is a knight.", "We have exhausted all possibilities for Sebastian and Penelope, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the false claim of their own that If Victoria is a knight then Penelope is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the false claim of Daniel that Scarlett is a knight.", "Scarlett cannot be a knave, because this would contradict the false claim of their own that If Victoria is a knight then Penelope is a knight.", "We have exhausted all possibilities for Scarlett, Daniel, and Victoria, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Victoria is not a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Daniel is a knight and Benjamin is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Victoria is a knight then Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Sebastian is a knave or Ella is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Victoria is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Sebastian is a knight or Ella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 6)), ('telling-truth', 6), ('->', ('telling-truth', 6), ('telling-truth', 3)), ('or', ('lying', 1), ('telling-truth', 4)), ('not', ('lying', 2)), ('or', ('telling-truth', 1), ('telling-truth', 4)), ('and', ('telling-truth', 7), ('telling-truth', 5)), ('telling-truth', 2))", "index": 408}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Charlotte, Luke, Aiden, Riley, Evelyn, Sofia, Jack, and Penelope. \"Riley is a knave or Luke is a knight,\" Charlotte mentioned. In Luke's words: \"Riley is a knave or Penelope is a knight\". Aiden noted, \"Jack is a knave or Evelyn is a knave\". Riley remarked, \"Jack is not a knave\". Evelyn remarked, \"Riley is a knave\". Sofia asserted: \"Penelope is a knight if and only if Jack is a knave\". \"If Aiden is a knave then Evelyn is a knave,\" Jack declared. Penelope told you that Riley is not a knave. So who is a knight and who is a knave?", "names": ["Charlotte", "Luke", "Aiden", "Riley", "Evelyn", "Sofia", "Jack", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false, true, true], "solution_text": "Charlotte is a knight, Luke is a knight, Aiden is a knight, Riley is a knight, Evelyn is a knave, Sofia is a knave, Jack is a knight, and Penelope is a knight.", "solution_text_format": "(1) Charlotte is a knight\n(2) Luke is a knight\n(3) Aiden is a knight\n(4) Riley is a knight\n(5) Evelyn is a knave\n(6) Sofia is a knave\n(7) Jack is a knight\n(8) Penelope is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that Riley is a knave or Luke is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Jack is not a knave.", "Assume Jack is a knight. No contradiction is found in their claim that If Aiden is a knave then Evelyn is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Jack is a knave or Evelyn is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of Aiden that Jack is a knave or Evelyn is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Riley is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Riley is a knave or Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Riley is not a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Penelope is a knight if and only if Jack is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Penelope is a knight if and only if Jack is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('telling-truth', 1)), ('or', ('lying', 3), ('telling-truth', 7)), ('or', ('lying', 6), ('lying', 4)), ('not', ('lying', 6)), ('lying', 3), ('<=>', ('telling-truth', 7), ('lying', 6)), ('->', ('lying', 2), ('lying', 4)), ('not', ('lying', 3)))", "index": 409}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Liam, Samuel, Scarlett, Grace, Joseph, Charlotte, Chloe, and Owen. According to Liam, \"Charlotte is a knave if and only if Owen is a knave\". \"Grace is a knight or Liam is a knave\" - Samuel. In Scarlett's words: \"If Liam is a knight then Owen is a knave\". \"Liam is a knave\" - Grace. Joseph commented, \"If Charlotte is a knave then Scarlett is a knight\". In Charlotte's words: \"Scarlett is a knave or Owen is a knave\". Chloe told you that Scarlett is a knight if and only if Owen is a knight. In Owen's words: \"Joseph is a knave and Grace is a knight\". So who is a knight and who is a knave?", "names": ["Liam", "Samuel", "Scarlett", "Grace", "Joseph", "Charlotte", "Chloe", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true, false, false], "solution_text": "Liam is a knave, Samuel is a knight, Scarlett is a knight, Grace is a knight, Joseph is a knight, Charlotte is a knight, Chloe is a knave, and Owen is a knave.", "solution_text_format": "(1) Liam is a knave\n(2) Samuel is a knight\n(3) Scarlett is a knight\n(4) Grace is a knight\n(5) Joseph is a knight\n(6) Charlotte is a knight\n(7) Chloe is a knave\n(8) Owen is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Charlotte is a knave if and only if Owen is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Scarlett is a knave or Owen is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Liam is a knight then Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of Scarlett that If Liam is a knight then Owen is a knave.", "Owen cannot be a knave, because this would contradict the claim of Liam that Charlotte is a knave if and only if Owen is a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that If Liam is a knight then Owen is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Joseph is a knave and Grace is a knight.", "Joseph cannot be a knight, because this would contradict the claim of Owen that Joseph is a knave and Grace is a knight.", "Joseph cannot be a knave, because this would contradict the false claim of their own that If Charlotte is a knave then Scarlett is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the claim of Liam that Charlotte is a knave if and only if Owen is a knave.", "We have exhausted all possibilities for Owen and Scarlett, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Scarlett is a knave or Owen is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Liam is a knight then Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of Liam that Charlotte is a knave if and only if Owen is a knave.", "Owen cannot be a knave, because this would contradict the false claim of Charlotte that Scarlett is a knave or Owen is a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the false claim of Charlotte that Scarlett is a knave or Owen is a knave.", "We have exhausted all possibilities for Scarlett and Charlotte, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Charlotte is a knave if and only if Owen is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Scarlett is a knave or Owen is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Liam is a knight then Owen is a knave.", "Owen cannot be a knight, because this would contradict the false claim of Liam that Charlotte is a knave if and only if Owen is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Joseph is a knave and Grace is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Charlotte is a knave then Scarlett is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Liam is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Grace is a knight or Liam is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight if and only if Owen is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Scarlett is a knight if and only if Owen is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 5), ('lying', 7)), ('or', ('telling-truth', 3), ('lying', 0)), ('->', ('telling-truth', 0), ('lying', 7)), ('lying', 0), ('->', ('lying', 5), ('telling-truth', 2)), ('or', ('lying', 2), ('lying', 7)), ('<=>', ('telling-truth', 2), ('telling-truth', 7)), ('and', ('lying', 4), ('telling-truth', 3)))", "index": 410}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jack, Jackson, Charlotte, Sophia, Victoria, Emily, Evelyn, and Elizabeth. \"Sophia is a knave if and only if Jackson is a knave,\" Jack claimed. Jackson noted, \"Sophia is a knave or Evelyn is a knave\". Charlotte was heard saying, \"Jackson is a knave if and only if Jack is a knave\". Sophia remarked, \"Elizabeth is a knight and Elizabeth is a knave\". In a statement by Victoria: \"Charlotte is not a knight\". \"If Jackson is a knave then Evelyn is a knight,\" Emily mentioned. Evelyn expressed that Charlotte is a knight. \"Sophia is a knight and Jack is a knight,\" Elizabeth mentioned. So who is a knight and who is a knave?", "names": ["Jack", "Jackson", "Charlotte", "Sophia", "Victoria", "Emily", "Evelyn", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true, false, false], "solution_text": "Jack is a knave, Jackson is a knight, Charlotte is a knave, Sophia is a knave, Victoria is a knight, Emily is a knight, Evelyn is a knave, and Elizabeth is a knave.", "solution_text_format": "(1) Jack is a knave\n(2) Jackson is a knight\n(3) Charlotte is a knave\n(4) Sophia is a knave\n(5) Victoria is a knight\n(6) Emily is a knight\n(7) Evelyn is a knave\n(8) Elizabeth is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Sophia is a knave if and only if Jackson is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight and Elizabeth is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Elizabeth is a knight and Elizabeth is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Sophia is a knight and Jack is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Sophia is a knight and Jack is a knight.", "Jackson cannot be a knight, because this would contradict the claim of Jack that Sophia is a knave if and only if Jackson is a knave.", "Jackson cannot be a knave, because this would contradict the false claim of their own that Sophia is a knave or Evelyn is a knave.", "We have exhausted all possibilities for Jackson, Elizabeth, and Sophia, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Sophia is a knave if and only if Jackson is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight and Elizabeth is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Elizabeth is a knight and Elizabeth is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Sophia is a knight and Jack is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Sophia is a knight and Jack is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Sophia is a knave or Evelyn is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Jackson is a knave if and only if Jack is a knave.", "Charlotte cannot be a knave, because this would contradict the claim of Evelyn that Charlotte is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Jackson is a knave if and only if Jack is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Jackson is a knave if and only if Jack is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Charlotte is not a knight.", "Assume Emily is a knight. No contradiction is found in their claim that If Jackson is a knave then Evelyn is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('lying', 1)), ('or', ('lying', 3), ('lying', 6)), ('<=>', ('lying', 1), ('lying', 0)), ('and', ('telling-truth', 7), ('lying', 7)), ('not', ('telling-truth', 2)), ('->', ('lying', 1), ('telling-truth', 6)), ('telling-truth', 2), ('and', ('telling-truth', 3), ('telling-truth', 0)))", "index": 411}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Grace, Avery, Benjamin, Chloe, Zoey, David, Evelyn, and Aurora. Grace was heard saying, \"If Benjamin is a knave then Zoey is a knave\". As Avery put it, \"David is not a knight\". \"Aurora is a knight if and only if Grace is a knave\" - Benjamin. \"Grace is a knave or Evelyn is a knave,\" Chloe mentioned. In Zoey's words: \"Chloe is a knight or David is a knight\". David expressed that Benjamin is a knight. Evelyn commented, \"Aurora is a knave and Zoey is a knight\". Aurora remarked, \"Evelyn is a knave or Avery is a knave\". So who is a knight and who is a knave?", "names": ["Grace", "Avery", "Benjamin", "Chloe", "Zoey", "David", "Evelyn", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false, true, false], "solution_text": "Grace is a knave, Avery is a knight, Benjamin is a knave, Chloe is a knight, Zoey is a knight, David is a knave, Evelyn is a knight, and Aurora is a knave.", "solution_text_format": "(1) Grace is a knave\n(2) Avery is a knight\n(3) Benjamin is a knave\n(4) Chloe is a knight\n(5) Zoey is a knight\n(6) David is a knave\n(7) Evelyn is a knight\n(8) Aurora is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that If Benjamin is a knave then Zoey is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Aurora is a knight if and only if Grace is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Benjamin that Aurora is a knight if and only if Grace is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Evelyn is a knave or Avery is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Aurora is a knave and Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Chloe is a knight or David is a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Grace is a knave or Evelyn is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Grace is a knave or Evelyn is a knave.", "Assume David is a knight. No contradiction is found in their claim that Benjamin is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that David is not a knight.", "Avery cannot be a knave, because this would contradict the false claim of Aurora that Evelyn is a knave or Avery is a knave.", "We have exhausted all possibilities for Avery, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the claim of Zoey that Chloe is a knight or David is a knight.", "We have exhausted all possibilities for David and Chloe, so let us go back and reconsider Zoey.", "Zoey cannot be a knave, because this would contradict the claim of Evelyn that Aurora is a knave and Zoey is a knight.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the false claim of Aurora that Evelyn is a knave or Avery is a knave.", "We have exhausted all possibilities for Evelyn and Aurora, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Aurora is a knight if and only if Grace is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Evelyn is a knave or Avery is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Aurora is a knave and Zoey is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Aurora is a knave and Zoey is a knight.", "Zoey cannot be a knight, because this would contradict the claim of Grace that If Benjamin is a knave then Zoey is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Chloe is a knight or David is a knight.", "Chloe cannot be a knight, because this would contradict the false claim of Zoey that Chloe is a knight or David is a knight.", "Chloe cannot be a knave, because this would contradict the false claim of their own that Grace is a knave or Evelyn is a knave.", "We have exhausted all possibilities for Chloe, Zoey, and Evelyn, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the false claim of Benjamin that Aurora is a knight if and only if Grace is a knave.", "We have exhausted all possibilities for Aurora and Benjamin, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that If Benjamin is a knave then Zoey is a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Grace that If Benjamin is a knave then Zoey is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Aurora is a knight if and only if Grace is a knave.", "Aurora cannot be a knight, because this would contradict the false claim of Benjamin that Aurora is a knight if and only if Grace is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Evelyn is a knave or Avery is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Aurora is a knave and Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Chloe is a knight or David is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Grace is a knave or Evelyn is a knave.", "David cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Benjamin is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that David is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 2), ('lying', 4)), ('not', ('telling-truth', 5)), ('<=>', ('telling-truth', 7), ('lying', 0)), ('or', ('lying', 0), ('lying', 6)), ('or', ('telling-truth', 3), ('telling-truth', 5)), ('telling-truth', 2), ('and', ('lying', 7), ('telling-truth', 4)), ('or', ('lying', 6), ('lying', 1)))", "index": 412}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Matthew, Charlotte, Isabella, Elizabeth, Michael, Chloe, Harper, and Lily. Matthew was heard saying, \"Charlotte is not a knave\". \"Elizabeth is a knave and Michael is a knight,\" Charlotte mentioned. According to Isabella, \"If Harper is a knight then Matthew is a knave\". In a statement by Elizabeth: \"Isabella is a knight if and only if Matthew is a knave\". \"If Matthew is a knight then Matthew is a knave,\" Michael mentioned. Chloe was heard saying, \"Harper is a knight and Harper is a knave\". Harper was heard saying, \"Isabella is a knave and Elizabeth is a knight\". Lily commented, \"Charlotte is a knave or Isabella is a knight\". So who is a knight and who is a knave?", "names": ["Matthew", "Charlotte", "Isabella", "Elizabeth", "Michael", "Chloe", "Harper", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false, false, true], "solution_text": "Matthew is a knave, Charlotte is a knave, Isabella is a knight, Elizabeth is a knight, Michael is a knight, Chloe is a knave, Harper is a knave, and Lily is a knight.", "solution_text_format": "(1) Matthew is a knave\n(2) Charlotte is a knave\n(3) Isabella is a knight\n(4) Elizabeth is a knight\n(5) Michael is a knight\n(6) Chloe is a knave\n(7) Harper is a knave\n(8) Lily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that Charlotte is not a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Elizabeth is a knave and Michael is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Charlotte that Elizabeth is a knave and Michael is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Isabella is a knight if and only if Matthew is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that If Harper is a knight then Matthew is a knave.", "Harper cannot be a knight, because this would contradict the claim of Isabella that If Harper is a knight then Matthew is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Isabella is a knave and Elizabeth is a knight.", "Michael cannot be a knight, because this would contradict the claim of their own that If Matthew is a knight then Matthew is a knave.", "Michael cannot be a knave, because this would contradict the claim of Charlotte that Elizabeth is a knave and Michael is a knight.", "We have exhausted all possibilities for Michael and Harper, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the false claim of Elizabeth that Isabella is a knight if and only if Matthew is a knave.", "We have exhausted all possibilities for Isabella and Elizabeth, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the claim of Matthew that Charlotte is not a knave.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Charlotte is not a knave.", "Charlotte cannot be a knight, because this would contradict the false claim of Matthew that Charlotte is not a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Elizabeth is a knave and Michael is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Matthew is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that If Harper is a knight then Matthew is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Isabella is a knave and Elizabeth is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Isabella is a knave and Elizabeth is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that If Matthew is a knight then Matthew is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Harper is a knight and Harper is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Harper is a knight and Harper is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Charlotte is a knave or Isabella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('and', ('lying', 3), ('telling-truth', 4)), ('->', ('telling-truth', 6), ('lying', 0)), ('<=>', ('telling-truth', 2), ('lying', 0)), ('->', ('telling-truth', 0), ('lying', 0)), ('and', ('telling-truth', 6), ('lying', 6)), ('and', ('lying', 2), ('telling-truth', 3)), ('or', ('lying', 1), ('telling-truth', 2)))", "index": 413}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lucas, Jacob, Lily, Benjamin, Ava, Aurora, Liam, and Oliver. Lucas remarked, \"Lily is a knight if and only if Ava is a knight\". \"Lucas is not a knave\" - Jacob. In a statement by Lily: \"Ava is a knight or Oliver is a knave\". Benjamin noted, \"Lily is a knight\". Ava said, \"Jacob is a knave.\" According to Aurora, \"Liam is a knave or Aurora is a knight\". Liam noted, \"Benjamin is not a knave\". As Oliver put it, \"Oliver is a knight and Jacob is a knight\". So who is a knight and who is a knave?", "names": ["Lucas", "Jacob", "Lily", "Benjamin", "Ava", "Aurora", "Liam", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, true, false, true], "solution_text": "Lucas is a knight, Jacob is a knight, Lily is a knave, Benjamin is a knave, Ava is a knave, Aurora is a knight, Liam is a knave, and Oliver is a knight.", "solution_text_format": "(1) Lucas is a knight\n(2) Jacob is a knight\n(3) Lily is a knave\n(4) Benjamin is a knave\n(5) Ava is a knave\n(6) Aurora is a knight\n(7) Liam is a knave\n(8) Oliver is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that Lily is a knight if and only if Ava is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Ava is a knight or Oliver is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Ava that Jacob is a knave.", "Jacob cannot be a knave, because this would contradict the false claim of their own that Lucas is not a knave.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the claim of Lucas that Lily is a knight if and only if Ava is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Ava is a knight or Oliver is a knave.", "Ava cannot be a knight, because this would contradict the claim of Lucas that Lily is a knight if and only if Ava is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Jacob is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Lucas is not a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Oliver is a knight and Jacob is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Lily is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Lily is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Liam is a knave or Aurora is a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that Benjamin is not a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Benjamin is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('telling-truth', 4)), ('not', ('lying', 0)), ('or', ('telling-truth', 4), ('lying', 7)), ('telling-truth', 2), ('lying', 1), ('or', ('lying', 6), ('telling-truth', 5)), ('not', ('lying', 3)), ('and', ('telling-truth', 7), ('telling-truth', 1)))", "index": 414}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jackson, Chloe, Logan, Liam, Jacob, Alexander, Emily, and Sebastian. Jackson said that Alexander is a knave. Chloe was heard saying, \"Jackson is a knight or Sebastian is a knave\". \"Alexander is a knave or Emily is a knave\" - Logan. Liam remarked, \"Chloe is a knave or Chloe is a knight\". Jacob expressed that Chloe is a knave. \"Sebastian is not a knight,\" Alexander mentioned. In Emily's words: \"If Sebastian is a knight then Jacob is a knight\". As Sebastian put it, \"Liam is a knight or Liam is a knave\". So who is a knight and who is a knave?", "names": ["Jackson", "Chloe", "Logan", "Liam", "Jacob", "Alexander", "Emily", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false, false, true], "solution_text": "Jackson is a knight, Chloe is a knight, Logan is a knight, Liam is a knight, Jacob is a knave, Alexander is a knave, Emily is a knave, and Sebastian is a knight.", "solution_text_format": "(1) Jackson is a knight\n(2) Chloe is a knight\n(3) Logan is a knight\n(4) Liam is a knight\n(5) Jacob is a knave\n(6) Alexander is a knave\n(7) Emily is a knave\n(8) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Alexander is a knave.", "Alexander cannot be a knight, because this would contradict the claim of Jackson that Alexander is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Sebastian is not a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Liam is a knight or Liam is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Chloe is a knave or Chloe is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Jackson is a knight or Sebastian is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Alexander is a knave or Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that If Sebastian is a knight then Jacob is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Chloe is a knave.", "Jacob cannot be a knave, because this would contradict the claim of Emily that If Sebastian is a knight then Jacob is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that If Sebastian is a knight then Jacob is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Chloe is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Chloe is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 5), ('or', ('telling-truth', 0), ('lying', 7)), ('or', ('lying', 5), ('lying', 6)), ('or', ('lying', 1), ('telling-truth', 1)), ('lying', 1), ('not', ('telling-truth', 7)), ('->', ('telling-truth', 7), ('telling-truth', 4)), ('or', ('telling-truth', 3), ('lying', 3)))", "index": 415}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: James, Jack, Amelia, Scarlett, Ava, Sebastian, Emily, and Aurora. James stated, \"If Scarlett is a knight then Ava is a knave\". Jack remarked, \"Ava is a knave or Scarlett is a knight\". As Amelia put it, \"James is not a knave\". Scarlett was heard saying, \"If Ava is a knight then Sebastian is a knave\". Ava noted, \"Jack is not a knave\". In a statement by Sebastian: \"James is a knight\". As Emily put it, \"Amelia is a knave or Aurora is a knight\". \"Sebastian is a knave or Amelia is a knight,\" Aurora declared. So who is a knight and who is a knave?", "names": ["James", "Jack", "Amelia", "Scarlett", "Ava", "Sebastian", "Emily", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false, true, true], "solution_text": "James is a knave, Jack is a knight, Amelia is a knave, Scarlett is a knight, Ava is a knight, Sebastian is a knave, Emily is a knight, and Aurora is a knight.", "solution_text_format": "(1) James is a knave\n(2) Jack is a knight\n(3) Amelia is a knave\n(4) Scarlett is a knight\n(5) Ava is a knight\n(6) Sebastian is a knave\n(7) Emily is a knight\n(8) Aurora is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that If Scarlett is a knight then Ava is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Ava is a knight then Sebastian is a knave.", "Ava cannot be a knight, because this would contradict the claim of James that If Scarlett is a knight then Ava is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Jack is not a knave.", "Jack cannot be a knight, because this would contradict the false claim of Ava that Jack is not a knave.", "Jack cannot be a knave, because this would contradict the false claim of their own that Ava is a knave or Scarlett is a knight.", "We have exhausted all possibilities for Jack and Ava, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that If Ava is a knight then Sebastian is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Jack is not a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Ava is a knave or Scarlett is a knight.", "Jack cannot be a knave, because this would contradict the claim of Ava that Jack is not a knave.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the false claim of Scarlett that If Ava is a knight then Sebastian is a knave.", "We have exhausted all possibilities for Ava and Scarlett, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that If Scarlett is a knight then Ava is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Ava is a knight then Sebastian is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Jack is not a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Ava is a knave or Scarlett is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of Scarlett that If Ava is a knight then Sebastian is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that James is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that James is not a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that James is not a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Amelia is a knave or Aurora is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Sebastian is a knave or Amelia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('lying', 4)), ('or', ('lying', 4), ('telling-truth', 3)), ('not', ('lying', 0)), ('->', ('telling-truth', 4), ('lying', 5)), ('not', ('lying', 1)), ('telling-truth', 0), ('or', ('lying', 2), ('telling-truth', 7)), ('or', ('lying', 5), ('telling-truth', 2)))", "index": 416}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mia, Emily, Emma, Owen, Aurora, Oliver, Abigail, and Sophia. \"Owen is a knave and Abigail is a knave,\" Mia declared. As Emily put it, \"Emma is a knight if and only if Owen is a knight\". Emma said, \"Emily is a knight if and only if Emma is a knight.\" Owen expressed that Mia is not a knave. Aurora told you that Oliver is a knave. Oliver remarked, \"Mia is a knight\". Abigail told you that Emma is a knave and Aurora is a knight. Sophia asserted: \"Aurora is a knight and Oliver is a knave\". So who is a knight and who is a knave?", "names": ["Mia", "Emily", "Emma", "Owen", "Aurora", "Oliver", "Abigail", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, false, true, true], "solution_text": "Mia is a knave, Emily is a knight, Emma is a knave, Owen is a knave, Aurora is a knight, Oliver is a knave, Abigail is a knight, and Sophia is a knight.", "solution_text_format": "(1) Mia is a knave\n(2) Emily is a knight\n(3) Emma is a knave\n(4) Owen is a knave\n(5) Aurora is a knight\n(6) Oliver is a knave\n(7) Abigail is a knight\n(8) Sophia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Owen is a knave and Abigail is a knave.", "Owen cannot be a knight, because this would contradict the claim of Mia that Owen is a knave and Abigail is a knave.", "Owen cannot be a knave, because this would contradict the false claim of their own that Mia is not a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Owen is a knave and Abigail is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Mia is not a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Mia is not a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Emma is a knave and Aurora is a knight.", "Emma cannot be a knight, because this would contradict the claim of Abigail that Emma is a knave and Aurora is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Emily is a knight if and only if Emma is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Emma is a knight if and only if Owen is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Oliver is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Aurora that Oliver is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Mia is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Aurora is a knight and Oliver is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('lying', 6)), ('<=>', ('telling-truth', 2), ('telling-truth', 3)), ('<=>', ('telling-truth', 1), ('telling-truth', 2)), ('not', ('lying', 0)), ('lying', 5), ('telling-truth', 0), ('and', ('lying', 2), ('telling-truth', 4)), ('and', ('telling-truth', 4), ('lying', 5)))", "index": 417}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Scarlett, Emma, Abigail, Zoey, Penelope, Ava, Alexander, and Michael. Scarlett told you that If Zoey is a knave then Michael is a knave. According to Emma, \"Penelope is a knight and Michael is a knave\". Abigail told you that If Emma is a knave then Ava is a knight. Zoey asserted: \"Scarlett is a knave and Abigail is a knave\". Penelope said that If Alexander is a knave then Ava is a knave. In Ava's words: \"Emma is not a knave\". Alexander told you that Abigail is a knave or Emma is a knight. In Michael's words: \"Michael is a knight\". So who is a knight and who is a knave?", "names": ["Scarlett", "Emma", "Abigail", "Zoey", "Penelope", "Ava", "Alexander", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true, true, false], "solution_text": "Scarlett is a knight, Emma is a knight, Abigail is a knight, Zoey is a knave, Penelope is a knight, Ava is a knight, Alexander is a knight, and Michael is a knave.", "solution_text_format": "(1) Scarlett is a knight\n(2) Emma is a knight\n(3) Abigail is a knight\n(4) Zoey is a knave\n(5) Penelope is a knight\n(6) Ava is a knight\n(7) Alexander is a knight\n(8) Michael is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that If Zoey is a knave then Michael is a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that Scarlett is a knave and Abigail is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Scarlett is a knave and Abigail is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that If Emma is a knave then Ava is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Penelope is a knight and Michael is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that If Alexander is a knave then Ava is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Abigail is a knave or Emma is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Emma is not a knave.", "Michael cannot be a knight, because this would contradict the claim of Scarlett that If Zoey is a knave then Michael is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Michael is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('lying', 7)), ('and', ('telling-truth', 4), ('lying', 7)), ('->', ('lying', 1), ('telling-truth', 5)), ('and', ('lying', 0), ('lying', 2)), ('->', ('lying', 6), ('lying', 5)), ('not', ('lying', 1)), ('or', ('lying', 2), ('telling-truth', 1)), ('telling-truth', 7))", "index": 418}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emily, Evelyn, James, Penelope, Luke, Oliver, Emma, and Michael. In Emily's words: \"Emma is a knight or Emily is a knight\". \"If Emily is a knave then Penelope is a knave\" - Evelyn. In a statement by James: \"Emma is a knave if and only if Luke is a knight\". Penelope stated, \"Luke is not a knight\". Luke expressed that If Oliver is a knave then Michael is a knight. Oliver told you that Emma is not a knight. Emma remarked, \"Emily is a knight\". Michael noted, \"James is a knight if and only if Evelyn is a knight\". So who is a knight and who is a knave?", "names": ["Emily", "Evelyn", "James", "Penelope", "Luke", "Oliver", "Emma", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true, false, true], "solution_text": "Emily is a knave, Evelyn is a knight, James is a knight, Penelope is a knave, Luke is a knight, Oliver is a knight, Emma is a knave, and Michael is a knight.", "solution_text_format": "(1) Emily is a knave\n(2) Evelyn is a knight\n(3) James is a knight\n(4) Penelope is a knave\n(5) Luke is a knight\n(6) Oliver is a knight\n(7) Emma is a knave\n(8) Michael is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Emma is a knight or Emily is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Emily is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Emily is a knave then Penelope is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Luke is not a knight.", "Luke cannot be a knight, because this would contradict the claim of Penelope that Luke is not a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that If Oliver is a knave then Michael is a knight.", "Oliver cannot be a knight, because this would contradict the false claim of Luke that If Oliver is a knave then Michael is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Emma is not a knight.", "Michael cannot be a knight, because this would contradict the false claim of Luke that If Oliver is a knave then Michael is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that James is a knight if and only if Evelyn is a knight.", "James cannot be a knight, because this would contradict the false claim of Michael that James is a knight if and only if Evelyn is a knight.", "James cannot be a knave, because this would contradict the false claim of their own that Emma is a knave if and only if Luke is a knight.", "We have exhausted all possibilities for James, Michael, Oliver, and Luke, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Luke is not a knight.", "Assume Luke is a knight. No contradiction is found in their claim that If Oliver is a knave then Michael is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Emma is not a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Emma is not a knight.", "Assume Michael is a knight. No contradiction is found in their claim that James is a knight if and only if Evelyn is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Emma is a knave if and only if Luke is a knight.", "James cannot be a knave, because this would contradict the claim of Michael that James is a knight if and only if Evelyn is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Michael.", "Michael cannot be a knave, because this would contradict the claim of Luke that If Oliver is a knave then Michael is a knight.", "We have exhausted all possibilities for Michael and Oliver, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the false claim of Penelope that Luke is not a knight.", "We have exhausted all possibilities for Luke and Penelope, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that If Emily is a knave then Penelope is a knave.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Emma.", "Emma cannot be a knave, because this would contradict the false claim of their own that Emily is a knight.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Emma is a knight or Emily is a knight.", "Emma cannot be a knight, because this would contradict the false claim of Emily that Emma is a knight or Emily is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Emily is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Emily is a knave then Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the claim of Evelyn that If Emily is a knave then Penelope is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Luke is not a knight.", "Assume Luke is a knight. No contradiction is found in their claim that If Oliver is a knave then Michael is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Emma is not a knight.", "Assume Michael is a knight. No contradiction is found in their claim that James is a knight if and only if Evelyn is a knight.", "Assume James is a knight. No contradiction is found in their claim that Emma is a knave if and only if Luke is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 6), ('telling-truth', 0)), ('->', ('lying', 0), ('lying', 3)), ('<=>', ('lying', 6), ('telling-truth', 4)), ('not', ('telling-truth', 4)), ('->', ('lying', 5), ('telling-truth', 7)), ('not', ('telling-truth', 6)), ('telling-truth', 0), ('<=>', ('telling-truth', 2), ('telling-truth', 1)))", "index": 419}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Owen, Benjamin, Ava, Lucas, Mia, Aiden, Isabella, and Olivia. Owen told you that Olivia is a knight or Isabella is a knave. \"Aiden is a knave and Isabella is a knave\" - Benjamin. In a statement by Ava: \"Isabella is not a knight\". \"Olivia is a knave or Owen is a knave,\" Lucas declared. Mia said that If Aiden is a knave then Lucas is a knight. \"Olivia is a knight and Mia is a knight,\" Aiden declared. Isabella was heard saying, \"Lucas is a knight or Olivia is a knave\". In Olivia's words: \"Mia is not a knave\". So who is a knight and who is a knave?", "names": ["Owen", "Benjamin", "Ava", "Lucas", "Mia", "Aiden", "Isabella", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true, false, true], "solution_text": "Owen is a knight, Benjamin is a knave, Ava is a knight, Lucas is a knave, Mia is a knight, Aiden is a knight, Isabella is a knave, and Olivia is a knight.", "solution_text_format": "(1) Owen is a knight\n(2) Benjamin is a knave\n(3) Ava is a knight\n(4) Lucas is a knave\n(5) Mia is a knight\n(6) Aiden is a knight\n(7) Isabella is a knave\n(8) Olivia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Olivia is a knight or Isabella is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Mia is not a knave.", "Assume Mia is a knight. No contradiction is found in their claim that If Aiden is a knave then Lucas is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Olivia is a knight and Mia is a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Olivia is a knave or Owen is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Olivia is a knave or Owen is a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that Lucas is a knight or Olivia is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Lucas is a knight or Olivia is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Aiden is a knave and Isabella is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Aiden is a knave and Isabella is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Isabella is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 7), ('lying', 6)), ('and', ('lying', 5), ('lying', 6)), ('not', ('telling-truth', 6)), ('or', ('lying', 7), ('lying', 0)), ('->', ('lying', 5), ('telling-truth', 3)), ('and', ('telling-truth', 7), ('telling-truth', 4)), ('or', ('telling-truth', 3), ('lying', 7)), ('not', ('lying', 4)))", "index": 420}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: David, Ella, Aurora, Emma, Joseph, Victoria, James, and Alexander. \"If Ella is a knight then Emma is a knight,\" David declared. \"James is a knight or David is a knave,\" Ella claimed. Aurora noted, \"David is a knave if and only if Alexander is a knave\". Emma expressed that James is a knave or Alexander is a knight. Joseph expressed that If Victoria is a knight then Alexander is a knave. Victoria remarked, \"Alexander is not a knight\". James asserted: \"Victoria is a knave\". Alexander stated, \"Ella is a knight if and only if James is a knave\". So who is a knight and who is a knave?", "names": ["David", "Ella", "Aurora", "Emma", "Joseph", "Victoria", "James", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true, false, false], "solution_text": "David is a knight, Ella is a knave, Aurora is a knave, Emma is a knight, Joseph is a knight, Victoria is a knight, James is a knave, and Alexander is a knave.", "solution_text_format": "(1) David is a knight\n(2) Ella is a knave\n(3) Aurora is a knave\n(4) Emma is a knight\n(5) Joseph is a knight\n(6) Victoria is a knight\n(7) James is a knave\n(8) Alexander is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that If Ella is a knight then Emma is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that James is a knight or David is a knave.", "Assume James is a knight. No contradiction is found in their claim that Victoria is a knave.", "Victoria cannot be a knight, because this would contradict the claim of James that Victoria is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that Ella is a knight if and only if James is a knave.", "Alexander cannot be a knave, because this would contradict the false claim of Victoria that Alexander is not a knight.", "We have exhausted all possibilities for Alexander and Victoria, so let us go back and reconsider James.", "James cannot be a knave, because this would contradict the claim of Ella that James is a knight or David is a knave.", "We have exhausted all possibilities for James, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that James is a knight or David is a knave.", "James cannot be a knight, because this would contradict the false claim of Ella that James is a knight or David is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of Victoria that Alexander is not a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Ella is a knight if and only if James is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that James is a knave or Alexander is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that David is a knave if and only if Alexander is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that David is a knave if and only if Alexander is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that If Victoria is a knight then Alexander is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 1), ('telling-truth', 3)), ('or', ('telling-truth', 6), ('lying', 0)), ('<=>', ('lying', 0), ('lying', 7)), ('or', ('lying', 6), ('telling-truth', 7)), ('->', ('telling-truth', 5), ('lying', 7)), ('not', ('telling-truth', 7)), ('lying', 5), ('<=>', ('telling-truth', 1), ('lying', 6)))", "index": 421}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Owen, Chloe, Charlotte, Elizabeth, Matthew, Aria, Samuel, and Avery. As Owen put it, \"Samuel is a knight if and only if Elizabeth is a knave\". Chloe commented, \"Elizabeth is a knight and Samuel is a knight\". Charlotte commented, \"Chloe is a knave and Matthew is a knave\". In Elizabeth's words: \"Owen is a knave\". Matthew said, \"Aria is a knave.\" In Aria's words: \"Owen is a knave if and only if Elizabeth is a knight\". Samuel noted, \"Chloe is a knight\". Avery expressed that If Charlotte is a knave then Owen is a knight. So who is a knight and who is a knave?", "names": ["Owen", "Chloe", "Charlotte", "Elizabeth", "Matthew", "Aria", "Samuel", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, true, true, false], "solution_text": "Owen is a knave, Chloe is a knight, Charlotte is a knave, Elizabeth is a knight, Matthew is a knave, Aria is a knight, Samuel is a knight, and Avery is a knave.", "solution_text_format": "(1) Owen is a knave\n(2) Chloe is a knight\n(3) Charlotte is a knave\n(4) Elizabeth is a knight\n(5) Matthew is a knave\n(6) Aria is a knight\n(7) Samuel is a knight\n(8) Avery is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Samuel is a knight if and only if Elizabeth is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Chloe is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Elizabeth is a knight and Samuel is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Owen that Samuel is a knight if and only if Elizabeth is a knave.", "Elizabeth cannot be a knave, because this would contradict the claim of Chloe that Elizabeth is a knight and Samuel is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the claim of Samuel that Chloe is a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Chloe is a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight and Samuel is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Elizabeth is a knight and Samuel is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Owen is a knave.", "Elizabeth cannot be a knave, because this would contradict the claim of Owen that Samuel is a knight if and only if Elizabeth is a knave.", "We have exhausted all possibilities for Elizabeth, Chloe, and Samuel, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Samuel is a knight if and only if Elizabeth is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Chloe is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Elizabeth is a knight and Samuel is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Owen is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Chloe is a knave and Matthew is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Chloe is a knave and Matthew is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of Matthew that Aria is a knave.", "Aria cannot be a knave, because this would contradict the false claim of their own that Owen is a knave if and only if Elizabeth is a knight.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Aria is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Owen is a knave if and only if Elizabeth is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that If Charlotte is a knave then Owen is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that If Charlotte is a knave then Owen is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 6), ('lying', 3)), ('and', ('telling-truth', 3), ('telling-truth', 6)), ('and', ('lying', 1), ('lying', 4)), ('lying', 0), ('lying', 5), ('<=>', ('lying', 0), ('telling-truth', 3)), ('telling-truth', 1), ('->', ('lying', 2), ('telling-truth', 0)))", "index": 422}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Noah, Ethan, Daniel, Samuel, Jacob, Sofia, Aiden, and Joseph. \"Daniel is a knight or Sofia is a knight,\" Noah claimed. Ethan stated, \"Joseph is a knight or Samuel is a knave\". Daniel was heard saying, \"Aiden is a knight if and only if Noah is a knave\". In a statement by Samuel: \"Noah is a knave if and only if Joseph is a knave\". Jacob stated, \"Joseph is a knave if and only if Sofia is a knave\". \"Joseph is not a knave,\" Sofia declared. Aiden said, \"Ethan is a knave and Samuel is a knight.\" \"Ethan is a knave if and only if Aiden is a knight,\" Joseph claimed. So who is a knight and who is a knave?", "names": ["Noah", "Ethan", "Daniel", "Samuel", "Jacob", "Sofia", "Aiden", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true, false, true], "solution_text": "Noah is a knight, Ethan is a knight, Daniel is a knight, Samuel is a knight, Jacob is a knight, Sofia is a knight, Aiden is a knave, and Joseph is a knight.", "solution_text_format": "(1) Noah is a knight\n(2) Ethan is a knight\n(3) Daniel is a knight\n(4) Samuel is a knight\n(5) Jacob is a knight\n(6) Sofia is a knight\n(7) Aiden is a knave\n(8) Joseph is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Noah is a knight. No contradiction is found in their claim that Daniel is a knight or Sofia is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Aiden is a knight if and only if Noah is a knave.", "Aiden cannot be a knight, because this would contradict the claim of Daniel that Aiden is a knight if and only if Noah is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Ethan is a knave and Samuel is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Joseph is a knight or Samuel is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Ethan is a knave if and only if Aiden is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Noah is a knave if and only if Joseph is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Joseph is not a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Joseph is a knave if and only if Sofia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('telling-truth', 5)), ('or', ('telling-truth', 7), ('lying', 3)), ('<=>', ('telling-truth', 6), ('lying', 0)), ('<=>', ('lying', 0), ('lying', 7)), ('<=>', ('lying', 7), ('lying', 5)), ('not', ('lying', 7)), ('and', ('lying', 1), ('telling-truth', 3)), ('<=>', ('lying', 1), ('telling-truth', 6)))", "index": 423}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jack, Joseph, Chloe, Matthew, Luke, James, Victoria, and Evelyn. Jack remarked, \"Matthew is not a knave\". Joseph asserted: \"Jack is a knight and Jack is a knave\". Chloe expressed that Jack is a knave. \"Matthew is a knight or Jack is a knight,\" Matthew declared. Luke commented, \"If Luke is a knight then Matthew is a knave\". James noted, \"If Chloe is a knight then Chloe is a knave\". Victoria stated, \"James is a knave or Jack is a knight\". In a statement by Evelyn: \"James is a knight if and only if Joseph is a knave\". So who is a knight and who is a knave?", "names": ["Jack", "Joseph", "Chloe", "Matthew", "Luke", "James", "Victoria", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, false, true, false], "solution_text": "Jack is a knave, Joseph is a knave, Chloe is a knight, Matthew is a knave, Luke is a knight, James is a knave, Victoria is a knight, and Evelyn is a knave.", "solution_text_format": "(1) Jack is a knave\n(2) Joseph is a knave\n(3) Chloe is a knight\n(4) Matthew is a knave\n(5) Luke is a knight\n(6) James is a knave\n(7) Victoria is a knight\n(8) Evelyn is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Matthew is not a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Matthew is a knight or Jack is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Jack is a knight and Jack is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Jack is a knight and Jack is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Jack is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Jack is a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that If Luke is a knight then Matthew is a knave.", "Luke cannot be a knave, because this would contradict the false claim of their own that If Luke is a knight then Matthew is a knave.", "We have exhausted all possibilities for Luke, Chloe, and Joseph, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the claim of Jack that Matthew is not a knave.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Matthew is not a knave.", "Matthew cannot be a knight, because this would contradict the false claim of Jack that Matthew is not a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Matthew is a knight or Jack is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Jack is a knight and Jack is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Jack is a knight and Jack is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Jack is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that If Luke is a knight then Matthew is a knave.", "James cannot be a knight, because this would contradict the claim of their own that If Chloe is a knight then Chloe is a knave.", "Assume James is a knave. No contradiction is found in their false claim that If Chloe is a knight then Chloe is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that James is a knave or Jack is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that James is a knight if and only if Joseph is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that James is a knight if and only if Joseph is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 3)), ('and', ('telling-truth', 0), ('lying', 0)), ('lying', 0), ('or', ('telling-truth', 3), ('telling-truth', 0)), ('->', ('telling-truth', 4), ('lying', 3)), ('->', ('telling-truth', 2), ('lying', 2)), ('or', ('lying', 5), ('telling-truth', 0)), ('<=>', ('telling-truth', 5), ('lying', 1)))", "index": 424}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jacob, Lucas, Evelyn, Chloe, Jack, Olivia, Aria, and Samuel. In Jacob's words: \"If Jacob is a knight then Samuel is a knight\". Lucas remarked, \"Jack is a knave and Evelyn is a knave\". Evelyn stated, \"Jacob is a knave or Evelyn is a knight\". In a statement by Chloe: \"Evelyn is a knave\". Jack was heard saying, \"Evelyn is a knave if and only if Olivia is a knave\". \"Evelyn is a knave,\" Olivia claimed. \"Lucas is a knave or Jack is a knight,\" Aria mentioned. In Samuel's words: \"Lucas is a knight\". So who is a knight and who is a knave?", "names": ["Jacob", "Lucas", "Evelyn", "Chloe", "Jack", "Olivia", "Aria", "Samuel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true, false, true], "solution_text": "Jacob is a knight, Lucas is a knight, Evelyn is a knave, Chloe is a knight, Jack is a knave, Olivia is a knight, Aria is a knave, and Samuel is a knight.", "solution_text_format": "(1) Jacob is a knight\n(2) Lucas is a knight\n(3) Evelyn is a knave\n(4) Chloe is a knight\n(5) Jack is a knave\n(6) Olivia is a knight\n(7) Aria is a knave\n(8) Samuel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that If Jacob is a knight then Samuel is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Jack is a knave and Evelyn is a knave.", "Jack cannot be a knight, because this would contradict the claim of Lucas that Jack is a knave and Evelyn is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Evelyn is a knave if and only if Olivia is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of Lucas that Jack is a knave and Evelyn is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Jacob is a knave or Evelyn is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Evelyn is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Evelyn is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Lucas is a knave or Jack is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Lucas is a knave or Jack is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 0), ('telling-truth', 7)), ('and', ('lying', 4), ('lying', 2)), ('or', ('lying', 0), ('telling-truth', 2)), ('lying', 2), ('<=>', ('lying', 2), ('lying', 5)), ('lying', 2), ('or', ('lying', 1), ('telling-truth', 4)), ('telling-truth', 1))", "index": 425}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Luke, Alexander, Jackson, Henry, Evelyn, Owen, Aiden, and Penelope. In a statement by Luke: \"Jackson is a knight or Aiden is a knave\". \"If Evelyn is a knave then Henry is a knight,\" Alexander claimed. \"Owen is not a knave,\" Jackson claimed. Henry stated, \"If Owen is a knave then Penelope is a knave\". In a statement by Evelyn: \"Alexander is a knave or Penelope is a knave\". Owen was heard saying, \"Evelyn is not a knight\". Aiden said that If Owen is a knave then Jackson is a knave. As Penelope put it, \"Penelope is a knight or Luke is a knave\". So who is a knight and who is a knave?", "names": ["Luke", "Alexander", "Jackson", "Henry", "Evelyn", "Owen", "Aiden", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true, true, true], "solution_text": "Luke is a knight, Alexander is a knight, Jackson is a knight, Henry is a knight, Evelyn is a knave, Owen is a knight, Aiden is a knight, and Penelope is a knight.", "solution_text_format": "(1) Luke is a knight\n(2) Alexander is a knight\n(3) Jackson is a knight\n(4) Henry is a knight\n(5) Evelyn is a knave\n(6) Owen is a knight\n(7) Aiden is a knight\n(8) Penelope is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Jackson is a knight or Aiden is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Owen is not a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Evelyn is not a knight.", "Evelyn cannot be a knight, because this would contradict the claim of Owen that Evelyn is not a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Alexander is a knave or Penelope is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that If Evelyn is a knave then Henry is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that If Owen is a knave then Penelope is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Penelope is a knight or Luke is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Owen is a knave then Jackson is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('lying', 6)), ('->', ('lying', 4), ('telling-truth', 3)), ('not', ('lying', 5)), ('->', ('lying', 5), ('lying', 7)), ('or', ('lying', 1), ('lying', 7)), ('not', ('telling-truth', 4)), ('->', ('lying', 5), ('lying', 2)), ('or', ('telling-truth', 7), ('lying', 0)))", "index": 426}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aurora, Sophia, Lucas, Avery, Riley, Ella, Benjamin, and Liam. Aurora asserted: \"Avery is a knave\". Sophia remarked, \"Aurora is a knave if and only if Avery is a knight\". \"Benjamin is not a knight\" - Lucas. Avery noted, \"Liam is a knave\". \"If Avery is a knight then Sophia is a knave,\" Riley declared. Ella commented, \"Aurora is not a knave\". Benjamin stated, \"If Avery is a knave then Sophia is a knave\". Liam commented, \"If Sophia is a knave then Ella is a knight\". So who is a knight and who is a knave?", "names": ["Aurora", "Sophia", "Lucas", "Avery", "Riley", "Ella", "Benjamin", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true, false, true], "solution_text": "Aurora is a knight, Sophia is a knight, Lucas is a knight, Avery is a knave, Riley is a knight, Ella is a knight, Benjamin is a knave, and Liam is a knight.", "solution_text_format": "(1) Aurora is a knight\n(2) Sophia is a knight\n(3) Lucas is a knight\n(4) Avery is a knave\n(5) Riley is a knight\n(6) Ella is a knight\n(7) Benjamin is a knave\n(8) Liam is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that Avery is a knave.", "Avery cannot be a knight, because this would contradict the claim of Aurora that Avery is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Liam is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that If Sophia is a knave then Ella is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Aurora is a knave if and only if Avery is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Aurora is not a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Benjamin is not a knight.", "Benjamin cannot be a knight, because this would contradict the claim of Lucas that Benjamin is not a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that If Avery is a knave then Sophia is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that If Avery is a knight then Sophia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('<=>', ('lying', 0), ('telling-truth', 3)), ('not', ('telling-truth', 6)), ('lying', 7), ('->', ('telling-truth', 3), ('lying', 1)), ('not', ('lying', 0)), ('->', ('lying', 3), ('lying', 1)), ('->', ('lying', 1), ('telling-truth', 5)))", "index": 427}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: James, Liam, Aurora, Jacob, Jack, Emma, Daniel, and Harper. According to James, \"Jack is not a knave\". Liam said that Emma is not a knave. Aurora remarked, \"Daniel is a knight\". Jacob told you that Jack is a knight or Emma is a knight. \"Liam is a knight or Emma is a knave,\" Jack mentioned. Emma told you that Jacob is a knave and James is a knave. Daniel noted, \"Harper is a knight and Jacob is a knave\". Harper remarked, \"If Jack is a knight then Aurora is a knight\". So who is a knight and who is a knave?", "names": ["James", "Liam", "Aurora", "Jacob", "Jack", "Emma", "Daniel", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false, false, false], "solution_text": "James is a knight, Liam is a knave, Aurora is a knave, Jacob is a knight, Jack is a knight, Emma is a knave, Daniel is a knave, and Harper is a knave.", "solution_text_format": "(1) James is a knight\n(2) Liam is a knave\n(3) Aurora is a knave\n(4) Jacob is a knight\n(5) Jack is a knight\n(6) Emma is a knave\n(7) Daniel is a knave\n(8) Harper is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Jack is not a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Liam is a knight or Emma is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Emma is not a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Jacob is a knave and James is a knave.", "Emma cannot be a knave, because this would contradict the claim of Liam that Emma is not a knave.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Emma is not a knave.", "Emma cannot be a knight, because this would contradict the false claim of Liam that Emma is not a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Jacob is a knave and James is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Jack is a knight or Emma is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that Harper is a knight and Jacob is a knave.", "Daniel cannot be a knave, because this would contradict the claim of Aurora that Daniel is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of Aurora that Daniel is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Harper is a knight and Jacob is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that If Jack is a knight then Aurora is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that If Jack is a knight then Aurora is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('not', ('lying', 5)), ('telling-truth', 6), ('or', ('telling-truth', 4), ('telling-truth', 5)), ('or', ('telling-truth', 1), ('lying', 5)), ('and', ('lying', 3), ('lying', 0)), ('and', ('telling-truth', 7), ('lying', 3)), ('->', ('telling-truth', 4), ('telling-truth', 2)))", "index": 428}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jackson, Avery, Abigail, Sebastian, Emily, Jacob, Sophia, and Chloe. Jackson noted, \"Abigail is a knave\". Avery was heard saying, \"Chloe is not a knave\". Abigail noted, \"Avery is not a knight\". Sebastian remarked, \"Jackson is not a knight\". Emily expressed that Abigail is a knight if and only if Avery is a knave. Jacob said that Sophia is not a knave. Sophia told you that Emily is not a knave. Chloe expressed that Jacob is a knave. So who is a knight and who is a knave?", "names": ["Jackson", "Avery", "Abigail", "Sebastian", "Emily", "Jacob", "Sophia", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true, true, false], "solution_text": "Jackson is a knave, Avery is a knave, Abigail is a knight, Sebastian is a knight, Emily is a knight, Jacob is a knight, Sophia is a knight, and Chloe is a knave.", "solution_text_format": "(1) Jackson is a knave\n(2) Avery is a knave\n(3) Abigail is a knight\n(4) Sebastian is a knight\n(5) Emily is a knight\n(6) Jacob is a knight\n(7) Sophia is a knight\n(8) Chloe is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Jackson that Abigail is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Avery is not a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Chloe is not a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Chloe that Jacob is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Sophia is not a knave.", "Sophia cannot be a knight, because this would contradict the false claim of Jacob that Sophia is not a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Emily is not a knave.", "Emily cannot be a knight, because this would contradict the false claim of Sophia that Emily is not a knave.", "Emily cannot be a knave, because this would contradict the false claim of their own that Abigail is a knight if and only if Avery is a knave.", "We have exhausted all possibilities for Emily, Sophia, and Jacob, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the claim of Avery that Chloe is not a knave.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Avery.", "Avery cannot be a knave, because this would contradict the false claim of Abigail that Avery is not a knight.", "We have exhausted all possibilities for Avery and Abigail, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Abigail is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Avery is not a knight.", "Avery cannot be a knight, because this would contradict the claim of Abigail that Avery is not a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Chloe is not a knave.", "Chloe cannot be a knight, because this would contradict the false claim of Avery that Chloe is not a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Jacob is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Sophia is not a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Emily is not a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Abigail is a knight if and only if Avery is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Jackson is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('not', ('lying', 7)), ('not', ('telling-truth', 1)), ('not', ('telling-truth', 0)), ('<=>', ('telling-truth', 2), ('lying', 1)), ('not', ('lying', 6)), ('not', ('lying', 4)), ('lying', 5))", "index": 429}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Matthew, Isabella, Scarlett, Oliver, Emma, Aria, Olivia, and Emily. Matthew stated, \"If Oliver is a knave then Emma is a knight\". In a statement by Isabella: \"Olivia is not a knight\". In Scarlett's words: \"If Matthew is a knight then Aria is a knave\". Oliver told you that Emma is a knave or Matthew is a knave. Emma said, \"Aria is a knave.\" \"Emily is a knave or Isabella is a knave,\" Aria mentioned. \"Emma is a knight and Oliver is a knave\" - Olivia. Emily asserted: \"Aria is a knave and Oliver is a knight\". So who is a knight and who is a knave?", "names": ["Matthew", "Isabella", "Scarlett", "Oliver", "Emma", "Aria", "Olivia", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true, false, false], "solution_text": "Matthew is a knight, Isabella is a knight, Scarlett is a knave, Oliver is a knight, Emma is a knave, Aria is a knight, Olivia is a knave, and Emily is a knave.", "solution_text_format": "(1) Matthew is a knight\n(2) Isabella is a knight\n(3) Scarlett is a knave\n(4) Oliver is a knight\n(5) Emma is a knave\n(6) Aria is a knight\n(7) Olivia is a knave\n(8) Emily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that If Oliver is a knave then Emma is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Emma is a knave or Matthew is a knave.", "Emma cannot be a knight, because this would contradict the claim of Oliver that Emma is a knave or Matthew is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Aria is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Emily is a knave or Isabella is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Aria is a knave and Oliver is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Aria is a knave and Oliver is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Olivia is not a knight.", "Olivia cannot be a knight, because this would contradict the claim of Isabella that Olivia is not a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Emma is a knight and Oliver is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that If Matthew is a knight then Aria is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that If Matthew is a knight then Aria is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('telling-truth', 4)), ('not', ('telling-truth', 6)), ('->', ('telling-truth', 0), ('lying', 5)), ('or', ('lying', 4), ('lying', 0)), ('lying', 5), ('or', ('lying', 7), ('lying', 1)), ('and', ('telling-truth', 4), ('lying', 3)), ('and', ('lying', 5), ('telling-truth', 3)))", "index": 430}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emma, Logan, William, Liam, Emily, Scarlett, Benjamin, and Michael. Emma told you that Scarlett is not a knave. Logan stated, \"Michael is not a knight\". William remarked, \"Logan is not a knight\". In a statement by Liam: \"Logan is a knight\". Emily noted, \"Michael is a knave\". Scarlett said that Michael is not a knave. According to Benjamin, \"Logan is a knave or Liam is a knave\". \"If Scarlett is a knave then Emily is a knight,\" Michael declared. So who is a knight and who is a knave?", "names": ["Emma", "Logan", "William", "Liam", "Emily", "Scarlett", "Benjamin", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true, true, true], "solution_text": "Emma is a knight, Logan is a knave, William is a knight, Liam is a knave, Emily is a knave, Scarlett is a knight, Benjamin is a knight, and Michael is a knight.", "solution_text_format": "(1) Emma is a knight\n(2) Logan is a knave\n(3) William is a knight\n(4) Liam is a knave\n(5) Emily is a knave\n(6) Scarlett is a knight\n(7) Benjamin is a knight\n(8) Michael is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Michael is not a knave.", "Assume Michael is a knight. No contradiction is found in their claim that If Scarlett is a knave then Emily is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Michael is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Michael is a knave.", "Logan cannot be a knight, because this would contradict the claim of their own that Michael is not a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Michael is not a knight.", "Assume William is a knight. No contradiction is found in their claim that Logan is not a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that Logan is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Logan is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Logan is a knave or Liam is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 5)), ('not', ('telling-truth', 7)), ('not', ('telling-truth', 1)), ('telling-truth', 1), ('lying', 7), ('not', ('lying', 7)), ('or', ('lying', 1), ('lying', 3)), ('->', ('lying', 5), ('telling-truth', 4)))", "index": 431}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Isabella, Riley, Mia, Aiden, Zoey, David, William, and Avery. Isabella said, \"If Avery is a knight then Zoey is a knave.\" Riley expressed that Aiden is not a knave. \"Zoey is a knight\" - Mia. Aiden asserted: \"Mia is a knight if and only if David is a knight\". Zoey was heard saying, \"Aiden is a knight or Isabella is a knight\". David asserted: \"Zoey is not a knight\". William commented, \"David is a knave and Aiden is a knight\". In Avery's words: \"If Zoey is a knight then Zoey is a knave\". So who is a knight and who is a knave?", "names": ["Isabella", "Riley", "Mia", "Aiden", "Zoey", "David", "William", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, false, false, false], "solution_text": "Isabella is a knight, Riley is a knave, Mia is a knight, Aiden is a knave, Zoey is a knight, David is a knave, William is a knave, and Avery is a knave.", "solution_text_format": "(1) Isabella is a knight\n(2) Riley is a knave\n(3) Mia is a knight\n(4) Aiden is a knave\n(5) Zoey is a knight\n(6) David is a knave\n(7) William is a knave\n(8) Avery is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that If Avery is a knight then Zoey is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that If Zoey is a knight then Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Isabella that If Avery is a knight then Zoey is a knave.", "Zoey cannot be a knave, because this would contradict the false claim of their own that Aiden is a knight or Isabella is a knight.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that If Zoey is a knight then Zoey is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Aiden is a knight or Isabella is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Mia is a knight if and only if David is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Zoey is a knight.", "David cannot be a knight, because this would contradict the claim of their own that Zoey is not a knight.", "David cannot be a knave, because this would contradict the claim of Aiden that Mia is a knight if and only if David is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the false claim of their own that Zoey is a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Mia is a knight if and only if David is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Zoey is a knight.", "David cannot be a knight, because this would contradict the false claim of Aiden that Mia is a knight if and only if David is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Zoey is not a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Aiden is not a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Aiden is not a knave.", "William cannot be a knight, because this would contradict the claim of their own that David is a knave and Aiden is a knight.", "Assume William is a knave. No contradiction is found in their false claim that David is a knave and Aiden is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 7), ('lying', 4)), ('not', ('lying', 3)), ('telling-truth', 4), ('<=>', ('telling-truth', 2), ('telling-truth', 5)), ('or', ('telling-truth', 3), ('telling-truth', 0)), ('not', ('telling-truth', 4)), ('and', ('lying', 5), ('telling-truth', 3)), ('->', ('telling-truth', 4), ('lying', 4)))", "index": 432}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Zoey, Olivia, Scarlett, Aiden, Samuel, Victoria, Benjamin, and Michael. According to Zoey, \"Samuel is a knave and Michael is a knight\". Olivia was heard saying, \"Victoria is a knight if and only if Benjamin is a knight\". \"Benjamin is not a knave,\" Scarlett declared. \"Benjamin is a knight and Scarlett is a knight,\" Aiden mentioned. \"If Olivia is a knight then Zoey is a knight\" - Samuel. Victoria remarked, \"Victoria is a knight and Samuel is a knight\". In a statement by Benjamin: \"Scarlett is a knight and Victoria is a knight\". In Michael's words: \"Olivia is a knave or Victoria is a knave\". So who is a knight and who is a knave?", "names": ["Zoey", "Olivia", "Scarlett", "Aiden", "Samuel", "Victoria", "Benjamin", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, true, false, true], "solution_text": "Zoey is a knave, Olivia is a knave, Scarlett is a knave, Aiden is a knave, Samuel is a knight, Victoria is a knight, Benjamin is a knave, and Michael is a knight.", "solution_text_format": "(1) Zoey is a knave\n(2) Olivia is a knave\n(3) Scarlett is a knave\n(4) Aiden is a knave\n(5) Samuel is a knight\n(6) Victoria is a knight\n(7) Benjamin is a knave\n(8) Michael is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Zoey is a knight. No contradiction is found in their claim that Samuel is a knave and Michael is a knight.", "Samuel cannot be a knight, because this would contradict the claim of Zoey that Samuel is a knave and Michael is a knight.", "Samuel cannot be a knave, because this would contradict the false claim of their own that If Olivia is a knight then Zoey is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Samuel is a knave and Michael is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that If Olivia is a knight then Zoey is a knight.", "Olivia cannot be a knight, because this would contradict the claim of Samuel that If Olivia is a knight then Zoey is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Victoria is a knight if and only if Benjamin is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Victoria is a knight and Samuel is a knight.", "Benjamin cannot be a knight, because this would contradict the false claim of Olivia that Victoria is a knight if and only if Benjamin is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Scarlett is a knight and Victoria is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Benjamin is not a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Benjamin is not a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Olivia is a knave or Victoria is a knave.", "Aiden cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight and Scarlett is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Benjamin is a knight and Scarlett is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('telling-truth', 7)), ('<=>', ('telling-truth', 5), ('telling-truth', 6)), ('not', ('lying', 6)), ('and', ('telling-truth', 6), ('telling-truth', 2)), ('->', ('telling-truth', 1), ('telling-truth', 0)), ('and', ('telling-truth', 5), ('telling-truth', 4)), ('and', ('telling-truth', 2), ('telling-truth', 5)), ('or', ('lying', 1), ('lying', 5)))", "index": 433}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Benjamin, Grace, Avery, Mason, William, Victoria, Sophia, and Ella. Benjamin said, \"Avery is not a knight.\" Grace was heard saying, \"William is a knight and Ella is a knave\". Avery stated, \"William is not a knight\". In a statement by Mason: \"William is not a knight\". In a statement by William: \"If Victoria is a knave then Mason is a knave\". Victoria remarked, \"Benjamin is a knave if and only if Mason is a knight\". Sophia was heard saying, \"Sophia is a knight or Avery is a knave\". As Ella put it, \"If Sophia is a knight then Victoria is a knave\". So who is a knight and who is a knave?", "names": ["Benjamin", "Grace", "Avery", "Mason", "William", "Victoria", "Sophia", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true, true, false], "solution_text": "Benjamin is a knight, Grace is a knight, Avery is a knave, Mason is a knave, William is a knight, Victoria is a knight, Sophia is a knight, and Ella is a knave.", "solution_text_format": "(1) Benjamin is a knight\n(2) Grace is a knight\n(3) Avery is a knave\n(4) Mason is a knave\n(5) William is a knight\n(6) Victoria is a knight\n(7) Sophia is a knight\n(8) Ella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Avery is not a knight.", "Avery cannot be a knight, because this would contradict the claim of Benjamin that Avery is not a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that William is not a knight.", "Assume William is a knight. No contradiction is found in their claim that If Victoria is a knave then Mason is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Benjamin is a knave if and only if Mason is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that William is not a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that William is not a knight.", "Assume Grace is a knight. No contradiction is found in their claim that William is a knight and Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of Grace that William is a knight and Ella is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that If Sophia is a knight then Victoria is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Sophia is a knight or Avery is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('and', ('telling-truth', 4), ('lying', 7)), ('not', ('telling-truth', 4)), ('not', ('telling-truth', 4)), ('->', ('lying', 5), ('lying', 3)), ('<=>', ('lying', 0), ('telling-truth', 3)), ('or', ('telling-truth', 6), ('lying', 2)), ('->', ('telling-truth', 6), ('lying', 5)))", "index": 434}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Victoria, Jackson, Emma, Lucas, Oliver, Henry, Riley, and Emily. According to Victoria, \"Victoria is a knight if and only if Emily is a knight\". According to Jackson, \"Emily is a knave or Lucas is a knight\". In a statement by Emma: \"Victoria is a knight or Jackson is a knave\". Lucas asserted: \"Emily is a knight and Henry is a knight\". As Oliver put it, \"Riley is a knave if and only if Jackson is a knave\". Henry expressed that Oliver is a knight or Victoria is a knave. Riley said, \"Lucas is a knave and Lucas is a knight.\" Emily said that Emily is a knight if and only if Emma is a knave. So who is a knight and who is a knave?", "names": ["Victoria", "Jackson", "Emma", "Lucas", "Oliver", "Henry", "Riley", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, true, false, true], "solution_text": "Victoria is a knave, Jackson is a knight, Emma is a knave, Lucas is a knight, Oliver is a knave, Henry is a knight, Riley is a knave, and Emily is a knight.", "solution_text_format": "(1) Victoria is a knave\n(2) Jackson is a knight\n(3) Emma is a knave\n(4) Lucas is a knight\n(5) Oliver is a knave\n(6) Henry is a knight\n(7) Riley is a knave\n(8) Emily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Emily is a knight if and only if Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of Emily that Emily is a knight if and only if Emma is a knave.", "Emma cannot be a knave, because this would contradict the false claim of their own that Victoria is a knight or Jackson is a knave.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the claim of Victoria that Victoria is a knight if and only if Emily is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Victoria is a knight if and only if Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Emily is a knight if and only if Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of Emily that Emily is a knight if and only if Emma is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Victoria is a knight or Jackson is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Emily is a knave or Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Emily is a knight and Henry is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Oliver is a knight or Victoria is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Riley is a knave if and only if Jackson is a knave.", "Riley cannot be a knight, because this would contradict the claim of their own that Lucas is a knave and Lucas is a knight.", "Riley cannot be a knave, because this would contradict the claim of Oliver that Riley is a knave if and only if Jackson is a knave.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Riley is a knave if and only if Jackson is a knave.", "Riley cannot be a knight, because this would contradict the false claim of Oliver that Riley is a knave if and only if Jackson is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Lucas is a knave and Lucas is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 0), ('telling-truth', 7)), ('or', ('lying', 7), ('telling-truth', 3)), ('or', ('telling-truth', 0), ('lying', 1)), ('and', ('telling-truth', 7), ('telling-truth', 5)), ('<=>', ('lying', 6), ('lying', 1)), ('or', ('telling-truth', 4), ('lying', 0)), ('and', ('lying', 3), ('telling-truth', 3)), ('<=>', ('telling-truth', 7), ('lying', 2)))", "index": 435}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Riley, Grace, Scarlett, Jack, Avery, Ella, Luke, and Isabella. Riley said that Scarlett is a knave. As Grace put it, \"If Avery is a knight then Isabella is a knight\". \"Isabella is a knave,\" Scarlett declared. \"Isabella is a knave or Scarlett is a knave,\" Jack declared. According to Avery, \"Avery is a knight or Jack is a knight\". According to Ella, \"Jack is a knave or Grace is a knave\". \"If Grace is a knave then Avery is a knight,\" Luke claimed. Isabella noted, \"Isabella is a knight if and only if Ella is a knight\". So who is a knight and who is a knave?", "names": ["Riley", "Grace", "Scarlett", "Jack", "Avery", "Ella", "Luke", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true, true, false], "solution_text": "Riley is a knave, Grace is a knave, Scarlett is a knight, Jack is a knight, Avery is a knight, Ella is a knight, Luke is a knight, and Isabella is a knave.", "solution_text_format": "(1) Riley is a knave\n(2) Grace is a knave\n(3) Scarlett is a knight\n(4) Jack is a knight\n(5) Avery is a knight\n(6) Ella is a knight\n(7) Luke is a knight\n(8) Isabella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Riley that Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Isabella is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Jack is a knave or Grace is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Isabella is a knave or Scarlett is a knave.", "Grace cannot be a knight, because this would contradict the claim of Ella that Jack is a knave or Grace is a knave.", "Grace cannot be a knave, because this would contradict the false claim of their own that If Avery is a knight then Isabella is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the false claim of their own that Isabella is a knave or Scarlett is a knave.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the claim of Isabella that Isabella is a knight if and only if Ella is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the false claim of Scarlett that Isabella is a knave.", "We have exhausted all possibilities for Isabella and Scarlett, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Scarlett is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Isabella is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Scarlett that Isabella is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Isabella is a knight if and only if Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Jack is a knave or Grace is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Isabella is a knave or Scarlett is a knave.", "Grace cannot be a knight, because this would contradict the claim of Ella that Jack is a knave or Grace is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that If Avery is a knight then Isabella is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Avery is a knight or Jack is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that If Grace is a knave then Avery is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('->', ('telling-truth', 4), ('telling-truth', 7)), ('lying', 7), ('or', ('lying', 7), ('lying', 2)), ('or', ('telling-truth', 4), ('telling-truth', 3)), ('or', ('lying', 3), ('lying', 1)), ('->', ('lying', 1), ('telling-truth', 4)), ('<=>', ('telling-truth', 7), ('telling-truth', 5)))", "index": 436}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: William, Joseph, James, Michael, Liam, Abigail, Alexander, and Aurora. William was heard saying, \"Michael is not a knave\". According to Joseph, \"Alexander is a knave or William is a knight\". In James's words: \"Michael is a knight and William is a knight\". Michael was heard saying, \"Joseph is a knight or Aurora is a knave\". Liam was heard saying, \"Michael is a knave or Alexander is a knight\". \"Joseph is a knave and Michael is a knight,\" Abigail declared. As Alexander put it, \"Michael is not a knave\". Aurora commented, \"Abigail is a knight and Joseph is a knight\". So who is a knight and who is a knave?", "names": ["William", "Joseph", "James", "Michael", "Liam", "Abigail", "Alexander", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false, true, false], "solution_text": "William is a knight, Joseph is a knight, James is a knight, Michael is a knight, Liam is a knight, Abigail is a knave, Alexander is a knight, and Aurora is a knave.", "solution_text_format": "(1) William is a knight\n(2) Joseph is a knight\n(3) James is a knight\n(4) Michael is a knight\n(5) Liam is a knight\n(6) Abigail is a knave\n(7) Alexander is a knight\n(8) Aurora is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Michael is not a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Joseph is a knight or Aurora is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Alexander is a knave or William is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Michael is not a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Abigail is a knight and Joseph is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Joseph is a knave and Michael is a knight.", "Abigail cannot be a knave, because this would contradict the claim of Aurora that Abigail is a knight and Joseph is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Abigail is a knight and Joseph is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Joseph is a knave and Michael is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Joseph is a knave and Michael is a knight.", "Assume James is a knight. No contradiction is found in their claim that Michael is a knight and William is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Michael is a knave or Alexander is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 3)), ('or', ('lying', 6), ('telling-truth', 0)), ('and', ('telling-truth', 3), ('telling-truth', 0)), ('or', ('telling-truth', 1), ('lying', 7)), ('or', ('lying', 3), ('telling-truth', 6)), ('and', ('lying', 1), ('telling-truth', 3)), ('not', ('lying', 3)), ('and', ('telling-truth', 5), ('telling-truth', 1)))", "index": 437}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Logan, Alexander, Lucas, Avery, Matthew, Oliver, Scarlett, and Benjamin. Logan commented, \"Alexander is a knight and Lucas is a knave\". As Alexander put it, \"Avery is not a knave\". \"Logan is a knave or Scarlett is a knight,\" Lucas mentioned. \"Lucas is a knave or Matthew is a knave,\" Avery mentioned. Matthew noted, \"If Benjamin is a knight then Alexander is a knight\". Oliver expressed that If Matthew is a knave then Lucas is a knave. \"Avery is a knight and Benjamin is a knight,\" Scarlett mentioned. Benjamin told you that Oliver is a knight if and only if Avery is a knave. So who is a knight and who is a knave?", "names": ["Logan", "Alexander", "Lucas", "Avery", "Matthew", "Oliver", "Scarlett", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true, false, false], "solution_text": "Logan is a knight, Alexander is a knight, Lucas is a knave, Avery is a knight, Matthew is a knight, Oliver is a knight, Scarlett is a knave, and Benjamin is a knave.", "solution_text_format": "(1) Logan is a knight\n(2) Alexander is a knight\n(3) Lucas is a knave\n(4) Avery is a knight\n(5) Matthew is a knight\n(6) Oliver is a knight\n(7) Scarlett is a knave\n(8) Benjamin is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that Alexander is a knight and Lucas is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Avery is not a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Lucas is a knave or Matthew is a knave.", "Lucas cannot be a knight, because this would contradict the claim of Logan that Alexander is a knight and Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Logan is a knave or Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the false claim of Lucas that Logan is a knave or Scarlett is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Avery is a knight and Benjamin is a knight.", "Benjamin cannot be a knight, because this would contradict the false claim of Scarlett that Avery is a knight and Benjamin is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Oliver is a knight if and only if Avery is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that If Matthew is a knave then Lucas is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that If Benjamin is a knight then Alexander is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('lying', 2)), ('not', ('lying', 3)), ('or', ('lying', 0), ('telling-truth', 6)), ('or', ('lying', 2), ('lying', 4)), ('->', ('telling-truth', 7), ('telling-truth', 1)), ('->', ('lying', 4), ('lying', 2)), ('and', ('telling-truth', 3), ('telling-truth', 7)), ('<=>', ('telling-truth', 5), ('lying', 3)))", "index": 438}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Henry, Samuel, Ella, Sebastian, Olivia, James, Jack, and Jackson. In a statement by Henry: \"If Jackson is a knight then Sebastian is a knave\". Samuel stated, \"Ella is a knave or Ella is a knight\". According to Ella, \"Jackson is a knight and Jack is a knight\". According to Sebastian, \"James is a knave or Olivia is a knight\". \"Samuel is not a knight,\" Olivia claimed. As James put it, \"Jack is not a knight\". \"If Jackson is a knave then Olivia is a knave,\" Jack declared. As Jackson put it, \"If Jack is a knight then Samuel is a knight\". So who is a knight and who is a knave?", "names": ["Henry", "Samuel", "Ella", "Sebastian", "Olivia", "James", "Jack", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false, true, true], "solution_text": "Henry is a knave, Samuel is a knight, Ella is a knight, Sebastian is a knight, Olivia is a knave, James is a knave, Jack is a knight, and Jackson is a knight.", "solution_text_format": "(1) Henry is a knave\n(2) Samuel is a knight\n(3) Ella is a knight\n(4) Sebastian is a knight\n(5) Olivia is a knave\n(6) James is a knave\n(7) Jack is a knight\n(8) Jackson is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that If Jackson is a knight then Sebastian is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that If Jack is a knight then Samuel is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that If Jackson is a knave then Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Samuel is not a knight.", "Samuel cannot be a knight, because this would contradict the claim of Olivia that Samuel is not a knight.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Ella is a knave or Ella is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Samuel is not a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Ella is a knave or Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Jackson is a knight and Jack is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of Henry that If Jackson is a knight then Sebastian is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that James is a knave or Olivia is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Jack is not a knight.", "James cannot be a knave, because this would contradict the false claim of Sebastian that James is a knave or Olivia is a knight.", "We have exhausted all possibilities for James and Sebastian, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the false claim of their own that Jackson is a knight and Jack is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Samuel.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Ella is a knave or Ella is a knight.", "We have exhausted all possibilities for Samuel and Olivia, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the false claim of their own that If Jackson is a knave then Olivia is a knave.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that If Jack is a knight then Samuel is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that If Jackson is a knave then Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Jack that If Jackson is a knave then Olivia is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Samuel is not a knight.", "Samuel cannot be a knight, because this would contradict the false claim of Jackson that If Jack is a knight then Samuel is a knight.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Ella is a knave or Ella is a knight.", "We have exhausted all possibilities for Samuel and Olivia, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the false claim of Jackson that If Jack is a knight then Samuel is a knight.", "We have exhausted all possibilities for Jack and Jackson, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that If Jackson is a knight then Sebastian is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that If Jack is a knight then Samuel is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that If Jackson is a knave then Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Samuel is not a knight.", "Samuel cannot be a knight, because this would contradict the claim of Olivia that Samuel is not a knight.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Ella is a knave or Ella is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Samuel is not a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Ella is a knave or Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Jackson is a knight and Jack is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that James is a knave or Olivia is a knight.", "James cannot be a knight, because this would contradict the claim of Sebastian that James is a knave or Olivia is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Jack is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 7), ('lying', 3)), ('or', ('lying', 2), ('telling-truth', 2)), ('and', ('telling-truth', 7), ('telling-truth', 6)), ('or', ('lying', 5), ('telling-truth', 4)), ('not', ('telling-truth', 1)), ('not', ('telling-truth', 6)), ('->', ('lying', 7), ('lying', 4)), ('->', ('telling-truth', 6), ('telling-truth', 1)))", "index": 439}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: James, Sebastian, Luke, Riley, Sophia, Liam, Noah, and Michael. In a statement by James: \"Liam is a knight if and only if Noah is a knave\". Sebastian said, \"Luke is a knight or Noah is a knave.\" \"Sebastian is not a knight,\" Luke mentioned. \"Sophia is not a knave\" - Riley. Sophia expressed that Liam is a knave or Luke is a knight. \"Sebastian is a knight,\" Liam declared. Noah remarked, \"Liam is a knight and Riley is a knight\". Michael expressed that Liam is a knave and James is a knight. So who is a knight and who is a knave?", "names": ["James", "Sebastian", "Luke", "Riley", "Sophia", "Liam", "Noah", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, true, false, false], "solution_text": "James is a knight, Sebastian is a knight, Luke is a knave, Riley is a knave, Sophia is a knave, Liam is a knight, Noah is a knave, and Michael is a knave.", "solution_text_format": "(1) James is a knight\n(2) Sebastian is a knight\n(3) Luke is a knave\n(4) Riley is a knave\n(5) Sophia is a knave\n(6) Liam is a knight\n(7) Noah is a knave\n(8) Michael is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Liam is a knight if and only if Noah is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Luke is a knight or Noah is a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that Sebastian is not a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Sebastian is not a knight.", "Noah cannot be a knight, because this would contradict the claim of James that Liam is a knight if and only if Noah is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Liam is a knight and Riley is a knight.", "Riley cannot be a knight, because this would contradict the false claim of Noah that Liam is a knight and Riley is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Sophia is not a knave.", "Sophia cannot be a knight, because this would contradict the false claim of Riley that Sophia is not a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Liam is a knave or Luke is a knight.", "Michael cannot be a knight, because this would contradict the claim of their own that Liam is a knave and James is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Liam is a knave and James is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 5), ('lying', 6)), ('or', ('telling-truth', 2), ('lying', 6)), ('not', ('telling-truth', 1)), ('not', ('lying', 4)), ('or', ('lying', 5), ('telling-truth', 2)), ('telling-truth', 1), ('and', ('telling-truth', 5), ('telling-truth', 3)), ('and', ('lying', 5), ('telling-truth', 0)))", "index": 440}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Harper, Emma, Avery, Charlotte, Liam, Zoey, Olivia, and Matthew. As Harper put it, \"Avery is a knave if and only if Emma is a knight\". Emma noted, \"Harper is not a knave\". Avery said, \"Liam is a knight and Matthew is a knave.\" Charlotte remarked, \"If Emma is a knave then Harper is a knight\". In Liam's words: \"Charlotte is a knave\". Zoey remarked, \"If Olivia is a knight then Harper is a knight\". \"If Matthew is a knave then Avery is a knave\" - Olivia. Matthew stated, \"Harper is a knight\". So who is a knight and who is a knave?", "names": ["Harper", "Emma", "Avery", "Charlotte", "Liam", "Zoey", "Olivia", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true, true, true], "solution_text": "Harper is a knight, Emma is a knight, Avery is a knave, Charlotte is a knight, Liam is a knave, Zoey is a knight, Olivia is a knight, and Matthew is a knight.", "solution_text_format": "(1) Harper is a knight\n(2) Emma is a knight\n(3) Avery is a knave\n(4) Charlotte is a knight\n(5) Liam is a knave\n(6) Zoey is a knight\n(7) Olivia is a knight\n(8) Matthew is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that Avery is a knave if and only if Emma is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Liam is a knight and Matthew is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Liam that Charlotte is a knave.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that If Emma is a knave then Harper is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the claim of Avery that Liam is a knight and Matthew is a knave.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Liam is a knight and Matthew is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Liam that Charlotte is a knave.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that If Emma is a knave then Harper is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Charlotte is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Emma is a knave then Harper is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Harper is not a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Harper is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that If Olivia is a knight then Harper is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that If Matthew is a knave then Avery is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('telling-truth', 1)), ('not', ('lying', 0)), ('and', ('telling-truth', 4), ('lying', 7)), ('->', ('lying', 1), ('telling-truth', 0)), ('lying', 3), ('->', ('telling-truth', 6), ('telling-truth', 0)), ('->', ('lying', 7), ('lying', 2)), ('telling-truth', 0))", "index": 441}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Michael, Victoria, Chloe, Lucas, Ava, Oliver, Aurora, and Ethan. In Michael's words: \"If Ethan is a knight then Aurora is a knight\". According to Victoria, \"Ethan is a knight or Victoria is a knight\". As Chloe put it, \"Lucas is a knave if and only if Michael is a knave\". \"Ava is not a knight,\" Lucas claimed. \"Ava is a knight if and only if Chloe is a knave\" - Ava. According to Oliver, \"Aurora is a knave or Victoria is a knight\". \"Victoria is not a knave,\" Aurora mentioned. Ethan noted, \"Lucas is not a knight\". So who is a knight and who is a knave?", "names": ["Michael", "Victoria", "Chloe", "Lucas", "Ava", "Oliver", "Aurora", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true, true, true], "solution_text": "Michael is a knight, Victoria is a knight, Chloe is a knave, Lucas is a knave, Ava is a knight, Oliver is a knight, Aurora is a knight, and Ethan is a knight.", "solution_text_format": "(1) Michael is a knight\n(2) Victoria is a knight\n(3) Chloe is a knave\n(4) Lucas is a knave\n(5) Ava is a knight\n(6) Oliver is a knight\n(7) Aurora is a knight\n(8) Ethan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that If Ethan is a knight then Aurora is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Lucas is not a knight.", "Lucas cannot be a knight, because this would contradict the claim of Ethan that Lucas is not a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Ava is not a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Ava is a knight if and only if Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Lucas is a knave if and only if Michael is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Lucas is a knave if and only if Michael is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Victoria is not a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Ethan is a knight or Victoria is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Aurora is a knave or Victoria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 7), ('telling-truth', 6)), ('or', ('telling-truth', 7), ('telling-truth', 1)), ('<=>', ('lying', 3), ('lying', 0)), ('not', ('telling-truth', 4)), ('<=>', ('telling-truth', 4), ('lying', 2)), ('or', ('lying', 6), ('telling-truth', 1)), ('not', ('lying', 1)), ('not', ('telling-truth', 3)))", "index": 442}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Samuel, Victoria, Liam, Joseph, Olivia, Grace, James, and Daniel. Samuel was heard saying, \"James is not a knave\". According to Victoria, \"Daniel is a knave if and only if Liam is a knave\". \"Daniel is a knight and Joseph is a knave,\" Liam claimed. Joseph expressed that If James is a knight then Samuel is a knight. Olivia noted, \"If Victoria is a knave then Olivia is a knight\". Grace expressed that If Olivia is a knave then Olivia is a knight. James said that Joseph is not a knight. \"Joseph is a knight if and only if Joseph is a knave,\" Daniel claimed. So who is a knight and who is a knave?", "names": ["Samuel", "Victoria", "Liam", "Joseph", "Olivia", "Grace", "James", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true, false, false], "solution_text": "Samuel is a knave, Victoria is a knight, Liam is a knave, Joseph is a knight, Olivia is a knight, Grace is a knight, James is a knave, and Daniel is a knave.", "solution_text_format": "(1) Samuel is a knave\n(2) Victoria is a knight\n(3) Liam is a knave\n(4) Joseph is a knight\n(5) Olivia is a knight\n(6) Grace is a knight\n(7) James is a knave\n(8) Daniel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that James is not a knave.", "Assume James is a knight. No contradiction is found in their claim that Joseph is not a knight.", "Joseph cannot be a knight, because this would contradict the claim of James that Joseph is not a knight.", "Joseph cannot be a knave, because this would contradict the false claim of their own that If James is a knight then Samuel is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider James.", "James cannot be a knave, because this would contradict the claim of Samuel that James is not a knave.", "We have exhausted all possibilities for James, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that James is not a knave.", "James cannot be a knight, because this would contradict the false claim of Samuel that James is not a knave.", "Assume James is a knave. No contradiction is found in their false claim that Joseph is not a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If James is a knight then Samuel is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Daniel is a knave if and only if Liam is a knave.", "Daniel cannot be a knight, because this would contradict the claim of their own that Joseph is a knight if and only if Joseph is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Joseph is a knight if and only if Joseph is a knave.", "Liam cannot be a knight, because this would contradict the claim of Victoria that Daniel is a knave if and only if Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Daniel is a knight and Joseph is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that If Victoria is a knave then Olivia is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that If Olivia is a knave then Olivia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 6)), ('<=>', ('lying', 7), ('lying', 2)), ('and', ('telling-truth', 7), ('lying', 3)), ('->', ('telling-truth', 6), ('telling-truth', 0)), ('->', ('lying', 1), ('telling-truth', 4)), ('->', ('lying', 4), ('telling-truth', 4)), ('not', ('telling-truth', 3)), ('<=>', ('telling-truth', 3), ('lying', 3)))", "index": 443}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ethan, Olivia, Henry, Chloe, Lucas, Alexander, Logan, and Sebastian. Ethan expressed that Logan is a knave or Henry is a knight. Olivia asserted: \"Ethan is a knight if and only if Sebastian is a knave\". In Henry's words: \"If Olivia is a knave then Chloe is a knight\". Chloe stated, \"Sebastian is a knave if and only if Lucas is a knave\". Lucas was heard saying, \"Alexander is not a knight\". \"Chloe is a knave if and only if Logan is a knight\" - Alexander. In Logan's words: \"Chloe is a knight if and only if Sebastian is a knave\". Sebastian told you that Chloe is a knave and Olivia is a knave. So who is a knight and who is a knave?", "names": ["Ethan", "Olivia", "Henry", "Chloe", "Lucas", "Alexander", "Logan", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false, false, false], "solution_text": "Ethan is a knight, Olivia is a knight, Henry is a knight, Chloe is a knave, Lucas is a knight, Alexander is a knave, Logan is a knave, and Sebastian is a knave.", "solution_text_format": "(1) Ethan is a knight\n(2) Olivia is a knight\n(3) Henry is a knight\n(4) Chloe is a knave\n(5) Lucas is a knight\n(6) Alexander is a knave\n(7) Logan is a knave\n(8) Sebastian is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Logan is a knave or Henry is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Chloe is a knight if and only if Sebastian is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Sebastian is a knave if and only if Lucas is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Logan that Chloe is a knight if and only if Sebastian is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Chloe is a knave and Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Ethan is a knight if and only if Sebastian is a knave.", "Lucas cannot be a knight, because this would contradict the claim of Chloe that Sebastian is a knave if and only if Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that Chloe is a knave if and only if Logan is a knight.", "Alexander cannot be a knave, because this would contradict the false claim of Lucas that Alexander is not a knight.", "We have exhausted all possibilities for Alexander and Lucas, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the false claim of their own that Ethan is a knight if and only if Sebastian is a knave.", "We have exhausted all possibilities for Olivia and Sebastian, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Sebastian is a knave if and only if Lucas is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Chloe is a knave and Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that Ethan is a knight if and only if Sebastian is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Ethan is a knight if and only if Sebastian is a knave.", "Lucas cannot be a knight, because this would contradict the false claim of Chloe that Sebastian is a knave if and only if Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Alexander is not a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Chloe is a knave if and only if Logan is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that If Olivia is a knave then Chloe is a knight.", "Henry cannot be a knave, because this would contradict the claim of Ethan that Logan is a knave or Henry is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Alexander.", "Alexander cannot be a knave, because this would contradict the false claim of Lucas that Alexander is not a knight.", "We have exhausted all possibilities for Alexander, Lucas, and Olivia, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the claim of Logan that Chloe is a knight if and only if Sebastian is a knave.", "We have exhausted all possibilities for Sebastian and Chloe, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Chloe is a knight if and only if Sebastian is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Sebastian is a knave if and only if Lucas is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Chloe is a knave and Olivia is a knave.", "Sebastian cannot be a knave, because this would contradict the false claim of Logan that Chloe is a knight if and only if Sebastian is a knave.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Sebastian is a knave if and only if Lucas is a knave.", "Sebastian cannot be a knight, because this would contradict the false claim of Logan that Chloe is a knight if and only if Sebastian is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Chloe is a knave and Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Ethan is a knight if and only if Sebastian is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of Lucas that Alexander is not a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Chloe is a knave if and only if Logan is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that If Olivia is a knave then Chloe is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 6), ('telling-truth', 2)), ('<=>', ('telling-truth', 0), ('lying', 7)), ('->', ('lying', 1), ('telling-truth', 3)), ('<=>', ('lying', 7), ('lying', 4)), ('not', ('telling-truth', 5)), ('<=>', ('lying', 3), ('telling-truth', 6)), ('<=>', ('telling-truth', 3), ('lying', 7)), ('and', ('lying', 3), ('lying', 1)))", "index": 444}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Benjamin, Evelyn, Grace, Sofia, Scarlett, Owen, Mason, and Harper. Benjamin stated, \"If Mason is a knave then Scarlett is a knight\". \"Harper is a knight if and only if Scarlett is a knave\" - Evelyn. Grace stated, \"If Scarlett is a knave then Sofia is a knave\". According to Sofia, \"Scarlett is a knave or Harper is a knight\". Scarlett stated, \"Grace is a knave if and only if Mason is a knight\". According to Owen, \"If Benjamin is a knight then Owen is a knight\". Mason expressed that Owen is a knave if and only if Mason is a knight. Harper stated, \"Grace is a knight and Owen is a knave\". So who is a knight and who is a knave?", "names": ["Benjamin", "Evelyn", "Grace", "Sofia", "Scarlett", "Owen", "Mason", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false, false, true], "solution_text": "Benjamin is a knight, Evelyn is a knave, Grace is a knight, Sofia is a knight, Scarlett is a knight, Owen is a knave, Mason is a knave, and Harper is a knight.", "solution_text_format": "(1) Benjamin is a knight\n(2) Evelyn is a knave\n(3) Grace is a knight\n(4) Sofia is a knight\n(5) Scarlett is a knight\n(6) Owen is a knave\n(7) Mason is a knave\n(8) Harper is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that If Mason is a knave then Scarlett is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Owen is a knave if and only if Mason is a knight.", "Owen cannot be a knight, because this would contradict the claim of Mason that Owen is a knave if and only if Mason is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that If Benjamin is a knight then Owen is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Grace is a knave if and only if Mason is a knight.", "Grace cannot be a knight, because this would contradict the claim of Scarlett that Grace is a knave if and only if Mason is a knight.", "Grace cannot be a knave, because this would contradict the false claim of their own that If Scarlett is a knave then Sofia is a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Grace is a knave if and only if Mason is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that If Scarlett is a knave then Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Grace that If Scarlett is a knave then Sofia is a knave.", "Sofia cannot be a knave, because this would contradict the false claim of their own that Scarlett is a knave or Harper is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Grace.", "Grace cannot be a knave, because this would contradict the false claim of Scarlett that Grace is a knave if and only if Mason is a knight.", "We have exhausted all possibilities for Grace, Scarlett, and Owen, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Owen is a knave if and only if Mason is a knight.", "Owen cannot be a knight, because this would contradict the false claim of Mason that Owen is a knave if and only if Mason is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that If Benjamin is a knight then Owen is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Grace is a knave if and only if Mason is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that If Scarlett is a knave then Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Scarlett is a knave or Harper is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Grace is a knight and Owen is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Harper is a knight if and only if Scarlett is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Harper is a knight if and only if Scarlett is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 6), ('telling-truth', 4)), ('<=>', ('telling-truth', 7), ('lying', 4)), ('->', ('lying', 4), ('lying', 3)), ('or', ('lying', 4), ('telling-truth', 7)), ('<=>', ('lying', 2), ('telling-truth', 6)), ('->', ('telling-truth', 0), ('telling-truth', 5)), ('<=>', ('lying', 5), ('telling-truth', 6)), ('and', ('telling-truth', 2), ('lying', 5)))", "index": 445}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jackson, Lily, Emily, James, Liam, Scarlett, Ethan, and Matthew. \"Scarlett is a knight or Jackson is a knight,\" Jackson declared. According to Lily, \"James is a knight and Emily is a knave\". \"Ethan is a knight or Scarlett is a knight\" - Emily. James was heard saying, \"Scarlett is not a knight\". In Liam's words: \"Matthew is a knight and Scarlett is a knight\". \"Lily is not a knight,\" Scarlett claimed. Ethan noted, \"Matthew is a knave\". As Matthew put it, \"Scarlett is a knight\". So who is a knight and who is a knave?", "names": ["Jackson", "Lily", "Emily", "James", "Liam", "Scarlett", "Ethan", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true, false, true], "solution_text": "Jackson is a knight, Lily is a knave, Emily is a knight, James is a knave, Liam is a knight, Scarlett is a knight, Ethan is a knave, and Matthew is a knight.", "solution_text_format": "(1) Jackson is a knight\n(2) Lily is a knave\n(3) Emily is a knight\n(4) James is a knave\n(5) Liam is a knight\n(6) Scarlett is a knight\n(7) Ethan is a knave\n(8) Matthew is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Scarlett is a knight or Jackson is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Lily is not a knight.", "Lily cannot be a knight, because this would contradict the claim of Scarlett that Lily is not a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that James is a knight and Emily is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Scarlett is not a knight.", "Assume James is a knave. No contradiction is found in their false claim that Scarlett is not a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Ethan is a knight or Scarlett is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Matthew is a knave.", "Matthew cannot be a knight, because this would contradict the claim of Ethan that Matthew is a knave.", "Matthew cannot be a knave, because this would contradict the false claim of their own that Scarlett is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Matthew is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Scarlett is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Matthew is a knight and Scarlett is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('telling-truth', 0)), ('and', ('telling-truth', 3), ('lying', 2)), ('or', ('telling-truth', 6), ('telling-truth', 5)), ('not', ('telling-truth', 5)), ('and', ('telling-truth', 7), ('telling-truth', 5)), ('not', ('telling-truth', 1)), ('lying', 7), ('telling-truth', 5))", "index": 446}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mia, Harper, Jacob, Benjamin, Sebastian, Isabella, Aiden, and Evelyn. Mia expressed that Harper is a knight and Jacob is a knight. Harper was heard saying, \"Evelyn is not a knave\". Jacob remarked, \"Isabella is not a knave\". Benjamin expressed that Sebastian is a knave and Isabella is a knight. Sebastian remarked, \"If Isabella is a knight then Mia is a knave\". In Isabella's words: \"If Evelyn is a knave then Mia is a knave\". According to Aiden, \"Jacob is a knight if and only if Benjamin is a knight\". According to Evelyn, \"Jacob is not a knave\". So who is a knight and who is a knave?", "names": ["Mia", "Harper", "Jacob", "Benjamin", "Sebastian", "Isabella", "Aiden", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true, true, true], "solution_text": "Mia is a knight, Harper is a knight, Jacob is a knight, Benjamin is a knight, Sebastian is a knave, Isabella is a knight, Aiden is a knight, and Evelyn is a knight.", "solution_text_format": "(1) Mia is a knight\n(2) Harper is a knight\n(3) Jacob is a knight\n(4) Benjamin is a knight\n(5) Sebastian is a knave\n(6) Isabella is a knight\n(7) Aiden is a knight\n(8) Evelyn is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Harper is a knight and Jacob is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Evelyn is not a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Jacob is not a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Isabella is not a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that If Evelyn is a knave then Mia is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Sebastian is a knave and Isabella is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of Benjamin that Sebastian is a knave and Isabella is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that If Isabella is a knight then Mia is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Jacob is a knight if and only if Benjamin is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('telling-truth', 2)), ('not', ('lying', 7)), ('not', ('lying', 5)), ('and', ('lying', 4), ('telling-truth', 5)), ('->', ('telling-truth', 5), ('lying', 0)), ('->', ('lying', 7), ('lying', 0)), ('<=>', ('telling-truth', 2), ('telling-truth', 3)), ('not', ('lying', 2)))", "index": 447}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lily, Oliver, Mia, Lucas, Emily, Ava, Owen, and Avery. In Lily's words: \"Ava is not a knight\". As Oliver put it, \"Owen is a knave\". \"Oliver is a knave,\" Mia mentioned. \"Owen is not a knave,\" Lucas declared. According to Emily, \"Owen is not a knight\". Ava told you that Avery is a knight. \"Ava is a knight if and only if Ava is a knave,\" Owen claimed. In a statement by Avery: \"Oliver is a knight\". So who is a knight and who is a knave?", "names": ["Lily", "Oliver", "Mia", "Lucas", "Emily", "Ava", "Owen", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true, false, true], "solution_text": "Lily is a knave, Oliver is a knight, Mia is a knave, Lucas is a knave, Emily is a knight, Ava is a knight, Owen is a knave, and Avery is a knight.", "solution_text_format": "(1) Lily is a knave\n(2) Oliver is a knight\n(3) Mia is a knave\n(4) Lucas is a knave\n(5) Emily is a knight\n(6) Ava is a knight\n(7) Owen is a knave\n(8) Avery is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that Ava is not a knight.", "Ava cannot be a knight, because this would contradict the claim of Lily that Ava is not a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Avery is a knight.", "Avery cannot be a knight, because this would contradict the false claim of Ava that Avery is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Oliver is a knight.", "Oliver cannot be a knight, because this would contradict the false claim of Avery that Oliver is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Ava is a knight if and only if Ava is a knave.", "Owen cannot be a knave, because this would contradict the false claim of Oliver that Owen is a knave.", "We have exhausted all possibilities for Owen, Oliver, Avery, and Ava, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Ava is not a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Avery is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Oliver is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of Oliver that Owen is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Ava is a knight if and only if Ava is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Oliver is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Oliver is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Owen is not a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Owen is not a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Owen is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 5)), ('lying', 6), ('lying', 1), ('not', ('lying', 6)), ('not', ('telling-truth', 6)), ('telling-truth', 7), ('<=>', ('telling-truth', 5), ('lying', 5)), ('telling-truth', 1))", "index": 448}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Charlotte, Liam, Avery, Matthew, Sophia, Sebastian, Owen, and Noah. Charlotte told you that Owen is not a knave. According to Liam, \"Charlotte is a knave or Sophia is a knight\". According to Avery, \"Matthew is a knight and Noah is a knave\". In Matthew's words: \"Liam is a knight or Owen is a knight\". As Sophia put it, \"Avery is a knave if and only if Charlotte is a knave\". \"Charlotte is a knave and Sophia is a knight,\" Sebastian mentioned. \"Noah is a knave if and only if Liam is a knave\" - Owen. Noah was heard saying, \"Owen is a knight and Charlotte is a knight\". So who is a knight and who is a knave?", "names": ["Charlotte", "Liam", "Avery", "Matthew", "Sophia", "Sebastian", "Owen", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false, false, false], "solution_text": "Charlotte is a knave, Liam is a knight, Avery is a knight, Matthew is a knight, Sophia is a knave, Sebastian is a knave, Owen is a knave, and Noah is a knave.", "solution_text_format": "(1) Charlotte is a knave\n(2) Liam is a knight\n(3) Avery is a knight\n(4) Matthew is a knight\n(5) Sophia is a knave\n(6) Sebastian is a knave\n(7) Owen is a knave\n(8) Noah is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that Owen is not a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Noah is a knave if and only if Liam is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Owen is a knight and Charlotte is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Charlotte is a knave or Sophia is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Avery is a knave if and only if Charlotte is a knave.", "Avery cannot be a knight, because this would contradict the claim of their own that Matthew is a knight and Noah is a knave.", "Avery cannot be a knave, because this would contradict the claim of Sophia that Avery is a knave if and only if Charlotte is a knave.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the claim of Liam that Charlotte is a knave or Sophia is a knight.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the claim of Owen that Noah is a knave if and only if Liam is a knave.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the false claim of their own that Owen is a knight and Charlotte is a knight.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the claim of Charlotte that Owen is not a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Owen is not a knave.", "Owen cannot be a knight, because this would contradict the false claim of Charlotte that Owen is not a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Noah is a knave if and only if Liam is a knave.", "Noah cannot be a knight, because this would contradict the claim of their own that Owen is a knight and Charlotte is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Owen is a knight and Charlotte is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Charlotte is a knave or Sophia is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Avery is a knave if and only if Charlotte is a knave.", "Avery cannot be a knight, because this would contradict the claim of Sophia that Avery is a knave if and only if Charlotte is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Matthew is a knight and Noah is a knave.", "Matthew cannot be a knight, because this would contradict the false claim of Avery that Matthew is a knight and Noah is a knave.", "Matthew cannot be a knave, because this would contradict the false claim of their own that Liam is a knight or Owen is a knight.", "We have exhausted all possibilities for Matthew and Avery, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Avery is a knave if and only if Charlotte is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Matthew is a knight and Noah is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Liam is a knight or Owen is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Charlotte is a knave and Sophia is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Charlotte is a knave and Sophia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 6)), ('or', ('lying', 0), ('telling-truth', 4)), ('and', ('telling-truth', 3), ('lying', 7)), ('or', ('telling-truth', 1), ('telling-truth', 6)), ('<=>', ('lying', 2), ('lying', 0)), ('and', ('lying', 0), ('telling-truth', 4)), ('<=>', ('lying', 7), ('lying', 1)), ('and', ('telling-truth', 6), ('telling-truth', 0)))", "index": 449}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ethan, Alexander, Lily, Grace, Liam, Logan, Joseph, and Jack. Ethan said, \"Logan is a knave.\" In Alexander's words: \"Ethan is a knight or Logan is a knight\". Lily commented, \"If Grace is a knave then Alexander is a knight\". In a statement by Grace: \"Liam is a knave\". According to Liam, \"Alexander is a knight\". Logan asserted: \"Joseph is not a knight\". According to Joseph, \"Alexander is not a knight\". Jack said, \"Grace is not a knave.\" So who is a knight and who is a knave?", "names": ["Ethan", "Alexander", "Lily", "Grace", "Liam", "Logan", "Joseph", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true, false, false], "solution_text": "Ethan is a knave, Alexander is a knight, Lily is a knight, Grace is a knave, Liam is a knight, Logan is a knight, Joseph is a knave, and Jack is a knave.", "solution_text_format": "(1) Ethan is a knave\n(2) Alexander is a knight\n(3) Lily is a knight\n(4) Grace is a knave\n(5) Liam is a knight\n(6) Logan is a knight\n(7) Joseph is a knave\n(8) Jack is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of Ethan that Logan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Joseph is not a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of Joseph that Alexander is not a knight.", "Alexander cannot be a knave, because this would contradict the false claim of their own that Ethan is a knight or Logan is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the false claim of Logan that Joseph is not a knight.", "We have exhausted all possibilities for Joseph and Logan, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Logan is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Joseph is not a knight.", "Joseph cannot be a knight, because this would contradict the claim of Logan that Joseph is not a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Alexander is not a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Ethan is a knight or Logan is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that If Grace is a knave then Alexander is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of Grace that Liam is a knave.", "Liam cannot be a knave, because this would contradict the false claim of their own that Alexander is a knight.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Liam is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Alexander is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Grace is not a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Grace is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 5), ('or', ('telling-truth', 0), ('telling-truth', 5)), ('->', ('lying', 3), ('telling-truth', 1)), ('lying', 4), ('telling-truth', 1), ('not', ('telling-truth', 6)), ('not', ('telling-truth', 1)), ('not', ('lying', 3)))", "index": 450}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Alexander, Charlotte, Aria, Ethan, Michael, David, Owen, and Amelia. Alexander expressed that Charlotte is a knave if and only if Ethan is a knave. Charlotte noted, \"Alexander is a knave\". Aria told you that Ethan is a knight if and only if Owen is a knave. Ethan remarked, \"David is a knight\". Michael commented, \"David is not a knight\". \"If Charlotte is a knave then Owen is a knave,\" David mentioned. Owen said, \"If David is a knave then Charlotte is a knave.\" As Amelia put it, \"Charlotte is a knight or Alexander is a knight\". So who is a knight and who is a knave?", "names": ["Alexander", "Charlotte", "Aria", "Ethan", "Michael", "David", "Owen", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, false, true, true], "solution_text": "Alexander is a knight, Charlotte is a knave, Aria is a knight, Ethan is a knave, Michael is a knight, David is a knave, Owen is a knight, and Amelia is a knight.", "solution_text_format": "(1) Alexander is a knight\n(2) Charlotte is a knave\n(3) Aria is a knight\n(4) Ethan is a knave\n(5) Michael is a knight\n(6) David is a knave\n(7) Owen is a knight\n(8) Amelia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that Charlotte is a knave if and only if Ethan is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Alexander is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Alexander is a knave.", "Ethan cannot be a knight, because this would contradict the claim of Alexander that Charlotte is a knave if and only if Ethan is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that David is a knight.", "David cannot be a knight, because this would contradict the false claim of Ethan that David is a knight.", "Assume David is a knave. No contradiction is found in their false claim that If Charlotte is a knave then Owen is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that If David is a knave then Charlotte is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Ethan is a knight if and only if Owen is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that David is not a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Charlotte is a knight or Alexander is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('lying', 3)), ('lying', 0), ('<=>', ('telling-truth', 3), ('lying', 6)), ('telling-truth', 5), ('not', ('telling-truth', 5)), ('->', ('lying', 1), ('lying', 6)), ('->', ('lying', 5), ('lying', 1)), ('or', ('telling-truth', 1), ('telling-truth', 0)))", "index": 451}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Evelyn, Grace, Jackson, James, Luke, Zoey, Riley, and Lily. \"Grace is a knave\" - Evelyn. \"James is a knave,\" Grace mentioned. \"Riley is a knight,\" Jackson claimed. \"Luke is a knight if and only if Luke is a knave\" - James. Luke noted, \"Grace is a knave if and only if James is a knave\". Zoey noted, \"James is a knight if and only if Grace is a knave\". Riley was heard saying, \"Grace is a knight or James is a knight\". Lily told you that If Grace is a knight then Riley is a knight. So who is a knight and who is a knave?", "names": ["Evelyn", "Grace", "Jackson", "James", "Luke", "Zoey", "Riley", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true, true, true], "solution_text": "Evelyn is a knave, Grace is a knight, Jackson is a knight, James is a knave, Luke is a knave, Zoey is a knight, Riley is a knight, and Lily is a knight.", "solution_text_format": "(1) Evelyn is a knave\n(2) Grace is a knight\n(3) Jackson is a knight\n(4) James is a knave\n(5) Luke is a knave\n(6) Zoey is a knight\n(7) Riley is a knight\n(8) Lily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Grace is a knave.", "Grace cannot be a knight, because this would contradict the claim of Evelyn that Grace is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that James is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Luke is a knight if and only if Luke is a knave.", "James cannot be a knave, because this would contradict the false claim of Grace that James is a knave.", "We have exhausted all possibilities for James and Grace, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Grace is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that James is a knave.", "James cannot be a knight, because this would contradict the claim of Grace that James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Luke is a knight if and only if Luke is a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that Grace is a knave if and only if James is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Grace is a knave if and only if James is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Riley is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Grace is a knight or James is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that James is a knight if and only if Grace is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that If Grace is a knight then Riley is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 1), ('lying', 3), ('telling-truth', 6), ('<=>', ('telling-truth', 4), ('lying', 4)), ('<=>', ('lying', 1), ('lying', 3)), ('<=>', ('telling-truth', 3), ('lying', 1)), ('or', ('telling-truth', 1), ('telling-truth', 3)), ('->', ('telling-truth', 1), ('telling-truth', 6)))", "index": 452}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Elizabeth, Aurora, William, Noah, Ella, Victoria, Scarlett, and Zoey. According to Elizabeth, \"Noah is a knave\". Aurora said, \"Victoria is a knave.\" William asserted: \"Scarlett is a knight if and only if Elizabeth is a knave\". Noah said, \"If Victoria is a knight then Ella is a knave.\" In a statement by Ella: \"Scarlett is a knave\". Victoria said, \"If Elizabeth is a knight then William is a knight.\" Scarlett told you that If Ella is a knave then Victoria is a knight. Zoey remarked, \"If Ella is a knave then Aurora is a knave\". So who is a knight and who is a knave?", "names": ["Elizabeth", "Aurora", "William", "Noah", "Ella", "Victoria", "Scarlett", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, true, true, true], "solution_text": "Elizabeth is a knave, Aurora is a knave, William is a knight, Noah is a knight, Ella is a knave, Victoria is a knight, Scarlett is a knight, and Zoey is a knight.", "solution_text_format": "(1) Elizabeth is a knave\n(2) Aurora is a knave\n(3) William is a knight\n(4) Noah is a knight\n(5) Ella is a knave\n(6) Victoria is a knight\n(7) Scarlett is a knight\n(8) Zoey is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of Elizabeth that Noah is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that If Victoria is a knight then Ella is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that If Elizabeth is a knight then William is a knight.", "Assume William is a knight. No contradiction is found in their claim that Scarlett is a knight if and only if Elizabeth is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of William that Scarlett is a knight if and only if Elizabeth is a knave.", "Scarlett cannot be a knave, because this would contradict the false claim of their own that If Ella is a knave then Victoria is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the claim of Victoria that If Elizabeth is a knight then William is a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider Victoria.", "Victoria cannot be a knave, because this would contradict the false claim of Noah that If Victoria is a knight then Ella is a knave.", "We have exhausted all possibilities for Victoria and Noah, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Noah is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that If Victoria is a knight then Ella is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that If Elizabeth is a knight then William is a knight.", "Assume William is a knight. No contradiction is found in their claim that Scarlett is a knight if and only if Elizabeth is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Ella is a knave then Victoria is a knight.", "Ella cannot be a knight, because this would contradict the claim of Noah that If Victoria is a knight then Ella is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Scarlett is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Victoria is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Victoria is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that If Ella is a knave then Aurora is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('lying', 5), ('<=>', ('telling-truth', 6), ('lying', 0)), ('->', ('telling-truth', 5), ('lying', 4)), ('lying', 6), ('->', ('telling-truth', 0), ('telling-truth', 2)), ('->', ('lying', 4), ('telling-truth', 5)), ('->', ('lying', 4), ('lying', 1)))", "index": 453}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Samuel, Harper, Lucas, Aria, Ethan, Amelia, Abigail, and Logan. \"Aria is a knave,\" Samuel declared. Harper told you that If Aria is a knight then Ethan is a knight. In a statement by Lucas: \"Harper is a knight and Abigail is a knave\". Aria told you that Samuel is a knight if and only if Harper is a knave. Ethan expressed that Samuel is a knave if and only if Lucas is a knight. Amelia was heard saying, \"Abigail is not a knave\". \"Lucas is a knave or Amelia is a knave,\" Abigail declared. Logan was heard saying, \"Samuel is a knight or Ethan is a knave\". So who is a knight and who is a knave?", "names": ["Samuel", "Harper", "Lucas", "Aria", "Ethan", "Amelia", "Abigail", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true, true, true], "solution_text": "Samuel is a knight, Harper is a knight, Lucas is a knave, Aria is a knave, Ethan is a knight, Amelia is a knight, Abigail is a knight, and Logan is a knight.", "solution_text_format": "(1) Samuel is a knight\n(2) Harper is a knight\n(3) Lucas is a knave\n(4) Aria is a knave\n(5) Ethan is a knight\n(6) Amelia is a knight\n(7) Abigail is a knight\n(8) Logan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of Samuel that Aria is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Samuel is a knight if and only if Harper is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that If Aria is a knight then Ethan is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the claim of Ethan that Samuel is a knave if and only if Lucas is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Harper is a knight and Abigail is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Lucas is a knave or Amelia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Abigail is not a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Samuel is a knight or Ethan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('->', ('telling-truth', 3), ('telling-truth', 4)), ('and', ('telling-truth', 1), ('lying', 6)), ('<=>', ('telling-truth', 0), ('lying', 1)), ('<=>', ('lying', 0), ('telling-truth', 2)), ('not', ('lying', 6)), ('or', ('lying', 2), ('lying', 5)), ('or', ('telling-truth', 0), ('lying', 4)))", "index": 454}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Chloe, Sebastian, Lily, Sofia, Avery, Ella, Jacob, and Penelope. Chloe commented, \"Ella is not a knave\". \"If Chloe is a knave then Jacob is a knight,\" Sebastian claimed. Lily commented, \"Avery is not a knight\". Sofia commented, \"Ella is not a knave\". \"Jacob is a knave or Ella is a knight,\" Avery claimed. In a statement by Ella: \"Lily is a knight and Avery is a knave\". In Jacob's words: \"Penelope is a knave or Chloe is a knight\". Penelope remarked, \"Lily is a knave\". So who is a knight and who is a knave?", "names": ["Chloe", "Sebastian", "Lily", "Sofia", "Avery", "Ella", "Jacob", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, false, false, true], "solution_text": "Chloe is a knave, Sebastian is a knave, Lily is a knave, Sofia is a knave, Avery is a knight, Ella is a knave, Jacob is a knave, and Penelope is a knight.", "solution_text_format": "(1) Chloe is a knave\n(2) Sebastian is a knave\n(3) Lily is a knave\n(4) Sofia is a knave\n(5) Avery is a knight\n(6) Ella is a knave\n(7) Jacob is a knave\n(8) Penelope is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Ella is not a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Lily is a knight and Avery is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Avery is not a knight.", "Avery cannot be a knight, because this would contradict the claim of Lily that Avery is not a knight.", "Avery cannot be a knave, because this would contradict the false claim of their own that Jacob is a knave or Ella is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the claim of Ella that Lily is a knight and Avery is a knave.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the claim of Chloe that Ella is not a knave.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Ella is not a knave.", "Ella cannot be a knight, because this would contradict the false claim of Chloe that Ella is not a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Lily is a knight and Avery is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Avery is not a knight.", "Avery cannot be a knight, because this would contradict the claim of Lily that Avery is not a knight.", "Avery cannot be a knave, because this would contradict the false claim of Ella that Lily is a knight and Avery is a knave.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Avery is not a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Jacob is a knave or Ella is a knight.", "Jacob cannot be a knight, because this would contradict the claim of Avery that Jacob is a knave or Ella is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Penelope is a knave or Chloe is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Lily is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of their own that If Chloe is a knave then Jacob is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that If Chloe is a knave then Jacob is a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that Ella is not a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Ella is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 5)), ('->', ('lying', 0), ('telling-truth', 6)), ('not', ('telling-truth', 4)), ('not', ('lying', 5)), ('or', ('lying', 6), ('telling-truth', 5)), ('and', ('telling-truth', 2), ('lying', 4)), ('or', ('lying', 7), ('telling-truth', 0)), ('lying', 2))", "index": 455}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aria, Sophia, William, Aiden, Scarlett, Joseph, Benjamin, and Liam. \"Aiden is a knight if and only if Liam is a knave\" - Aria. Sophia expressed that Aiden is a knight or Sophia is a knight. William was heard saying, \"Scarlett is a knight\". As Aiden put it, \"Benjamin is a knave or Sophia is a knave\". Scarlett commented, \"Sophia is a knight or Liam is a knave\". In Joseph's words: \"If Aiden is a knave then Joseph is a knight\". \"Scarlett is a knave if and only if Aria is a knave,\" Benjamin mentioned. Liam said, \"Joseph is a knave.\" So who is a knight and who is a knave?", "names": ["Aria", "Sophia", "William", "Aiden", "Scarlett", "Joseph", "Benjamin", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false, true, true], "solution_text": "Aria is a knight, Sophia is a knight, William is a knight, Aiden is a knave, Scarlett is a knight, Joseph is a knave, Benjamin is a knight, and Liam is a knight.", "solution_text_format": "(1) Aria is a knight\n(2) Sophia is a knight\n(3) William is a knight\n(4) Aiden is a knave\n(5) Scarlett is a knight\n(6) Joseph is a knave\n(7) Benjamin is a knight\n(8) Liam is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that Aiden is a knight if and only if Liam is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Benjamin is a knave or Sophia is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Scarlett is a knave if and only if Aria is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Sophia is a knight or Liam is a knave.", "Sophia cannot be a knight, because this would contradict the claim of Aiden that Benjamin is a knave or Sophia is a knave.", "Sophia cannot be a knave, because this would contradict the false claim of their own that Aiden is a knight or Sophia is a knight.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the claim of Benjamin that Scarlett is a knave if and only if Aria is a knave.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Scarlett is a knave if and only if Aria is a knave.", "Scarlett cannot be a knight, because this would contradict the false claim of Benjamin that Scarlett is a knave if and only if Aria is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Sophia is a knight or Liam is a knave.", "Sophia cannot be a knight, because this would contradict the false claim of Scarlett that Sophia is a knight or Liam is a knave.", "Sophia cannot be a knave, because this would contradict the false claim of their own that Aiden is a knight or Sophia is a knight.", "We have exhausted all possibilities for Sophia, Scarlett, and Benjamin, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Benjamin is a knave or Sophia is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Scarlett is a knave if and only if Aria is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Sophia is a knight or Liam is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Aiden is a knight or Sophia is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Liam that Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that If Aiden is a knave then Joseph is a knight.", "Assume William is a knight. No contradiction is found in their claim that Scarlett is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 3), ('lying', 7)), ('or', ('telling-truth', 3), ('telling-truth', 1)), ('telling-truth', 4), ('or', ('lying', 6), ('lying', 1)), ('or', ('telling-truth', 1), ('lying', 7)), ('->', ('lying', 3), ('telling-truth', 5)), ('<=>', ('lying', 4), ('lying', 0)), ('lying', 5))", "index": 456}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jacob, Daniel, Scarlett, Ava, Emily, Oliver, Grace, and Aurora. \"Jacob is a knight or Aurora is a knight,\" Jacob mentioned. Daniel noted, \"Oliver is a knight or Emily is a knave\". Scarlett asserted: \"Jacob is a knight and Daniel is a knight\". Ava noted, \"Daniel is a knight or Emily is a knave\". Emily said, \"Oliver is a knight.\" \"If Ava is a knight then Aurora is a knight\" - Oliver. Grace remarked, \"Ava is a knave and Emily is a knight\". Aurora told you that Oliver is a knight or Daniel is a knight. So who is a knight and who is a knave?", "names": ["Jacob", "Daniel", "Scarlett", "Ava", "Emily", "Oliver", "Grace", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true, false, true], "solution_text": "Jacob is a knight, Daniel is a knight, Scarlett is a knight, Ava is a knight, Emily is a knight, Oliver is a knight, Grace is a knave, and Aurora is a knight.", "solution_text_format": "(1) Jacob is a knight\n(2) Daniel is a knight\n(3) Scarlett is a knight\n(4) Ava is a knight\n(5) Emily is a knight\n(6) Oliver is a knight\n(7) Grace is a knave\n(8) Aurora is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that Jacob is a knight or Aurora is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Oliver is a knight or Daniel is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that If Ava is a knight then Aurora is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Daniel is a knight or Emily is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Oliver is a knight or Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Oliver is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Jacob is a knight and Daniel is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Ava is a knave and Emily is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Ava is a knave and Emily is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 0), ('telling-truth', 7)), ('or', ('telling-truth', 5), ('lying', 4)), ('and', ('telling-truth', 0), ('telling-truth', 1)), ('or', ('telling-truth', 1), ('lying', 4)), ('telling-truth', 5), ('->', ('telling-truth', 3), ('telling-truth', 7)), ('and', ('lying', 3), ('telling-truth', 4)), ('or', ('telling-truth', 5), ('telling-truth', 1)))", "index": 457}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aiden, Henry, Sofia, Mason, Abigail, Logan, Olivia, and Aurora. In a statement by Aiden: \"Henry is a knight and Logan is a knave\". Henry stated, \"Aiden is a knave if and only if Olivia is a knave\". Sofia noted, \"Aiden is a knave if and only if Henry is a knave\". \"If Aurora is a knight then Abigail is a knave\" - Mason. \"Aurora is a knave and Aurora is a knight,\" Abigail mentioned. Logan stated, \"Sofia is a knight and Aiden is a knave\". According to Olivia, \"If Henry is a knave then Mason is a knave\". \"Olivia is a knight and Logan is a knave,\" Aurora declared. So who is a knight and who is a knave?", "names": ["Aiden", "Henry", "Sofia", "Mason", "Abigail", "Logan", "Olivia", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false, true, true], "solution_text": "Aiden is a knight, Henry is a knight, Sofia is a knight, Mason is a knight, Abigail is a knave, Logan is a knave, Olivia is a knight, and Aurora is a knight.", "solution_text_format": "(1) Aiden is a knight\n(2) Henry is a knight\n(3) Sofia is a knight\n(4) Mason is a knight\n(5) Abigail is a knave\n(6) Logan is a knave\n(7) Olivia is a knight\n(8) Aurora is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Henry is a knight and Logan is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Aiden is a knave if and only if Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that If Henry is a knave then Mason is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Aurora is a knight then Abigail is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Olivia is a knight and Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of Aiden that Henry is a knight and Logan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Sofia is a knight and Aiden is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Aiden is a knave if and only if Henry is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Mason that If Aurora is a knight then Abigail is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Aurora is a knave and Aurora is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('lying', 5)), ('<=>', ('lying', 0), ('lying', 6)), ('<=>', ('lying', 0), ('lying', 1)), ('->', ('telling-truth', 7), ('lying', 4)), ('and', ('lying', 7), ('telling-truth', 7)), ('and', ('telling-truth', 2), ('lying', 0)), ('->', ('lying', 1), ('lying', 3)), ('and', ('telling-truth', 6), ('lying', 5)))", "index": 458}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Henry, Sebastian, Olivia, Joseph, Penelope, William, Emily, and Chloe. As Henry put it, \"If Olivia is a knave then Penelope is a knave\". Sebastian said, \"Henry is a knave if and only if Penelope is a knave.\" Olivia said that Chloe is a knave if and only if Sebastian is a knight. Joseph asserted: \"Sebastian is a knave or Joseph is a knight\". As Penelope put it, \"Sebastian is a knight or William is a knight\". William said that Chloe is not a knight. As Emily put it, \"If Emily is a knight then Olivia is a knight\". Chloe noted, \"If William is a knight then Olivia is a knight\". So who is a knight and who is a knave?", "names": ["Henry", "Sebastian", "Olivia", "Joseph", "Penelope", "William", "Emily", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, false, true, true], "solution_text": "Henry is a knight, Sebastian is a knave, Olivia is a knight, Joseph is a knight, Penelope is a knave, William is a knave, Emily is a knight, and Chloe is a knight.", "solution_text_format": "(1) Henry is a knight\n(2) Sebastian is a knave\n(3) Olivia is a knight\n(4) Joseph is a knight\n(5) Penelope is a knave\n(6) William is a knave\n(7) Emily is a knight\n(8) Chloe is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that If Olivia is a knave then Penelope is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Chloe is a knave if and only if Sebastian is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that If William is a knight then Olivia is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Chloe is not a knight.", "Assume William is a knave. No contradiction is found in their false claim that Chloe is not a knight.", "Sebastian cannot be a knight, because this would contradict the claim of Olivia that Chloe is a knave if and only if Sebastian is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Henry is a knave if and only if Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the false claim of Sebastian that Henry is a knave if and only if Penelope is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Sebastian is a knight or William is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Sebastian is a knave or Joseph is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that If Emily is a knight then Olivia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 2), ('lying', 4)), ('<=>', ('lying', 0), ('lying', 4)), ('<=>', ('lying', 7), ('telling-truth', 1)), ('or', ('lying', 1), ('telling-truth', 3)), ('or', ('telling-truth', 1), ('telling-truth', 5)), ('not', ('telling-truth', 7)), ('->', ('telling-truth', 6), ('telling-truth', 2)), ('->', ('telling-truth', 5), ('telling-truth', 2)))", "index": 459}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: William, Samuel, Mason, Lily, Ava, Chloe, Owen, and Sofia. William stated, \"Sofia is a knight if and only if Chloe is a knight\". \"Mason is a knight and Chloe is a knight,\" Samuel claimed. \"William is not a knave,\" Mason mentioned. Lily remarked, \"If William is a knave then Ava is a knave\". Ava stated, \"Sofia is a knight and Samuel is a knight\". Chloe noted, \"Owen is a knight\". Owen stated, \"Lily is a knight if and only if Samuel is a knight\". Sofia said that Samuel is a knave. So who is a knight and who is a knave?", "names": ["William", "Samuel", "Mason", "Lily", "Ava", "Chloe", "Owen", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, false, false, true], "solution_text": "William is a knave, Samuel is a knave, Mason is a knave, Lily is a knight, Ava is a knave, Chloe is a knave, Owen is a knave, and Sofia is a knight.", "solution_text_format": "(1) William is a knave\n(2) Samuel is a knave\n(3) Mason is a knave\n(4) Lily is a knight\n(5) Ava is a knave\n(6) Chloe is a knave\n(7) Owen is a knave\n(8) Sofia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Sofia is a knight if and only if Chloe is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Sofia that Samuel is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Mason is a knight and Chloe is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that William is not a knave.", "Chloe cannot be a knight, because this would contradict the false claim of Samuel that Mason is a knight and Chloe is a knight.", "Chloe cannot be a knave, because this would contradict the claim of William that Sofia is a knight if and only if Chloe is a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Mason.", "Mason cannot be a knave, because this would contradict the false claim of their own that William is not a knave.", "We have exhausted all possibilities for Mason and Samuel, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Samuel is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Mason is a knight and Chloe is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that William is not a knave.", "Chloe cannot be a knight, because this would contradict the claim of William that Sofia is a knight if and only if Chloe is a knight.", "Chloe cannot be a knave, because this would contradict the claim of Samuel that Mason is a knight and Chloe is a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Mason.", "Mason cannot be a knave, because this would contradict the claim of Samuel that Mason is a knight and Chloe is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Samuel.", "Samuel cannot be a knave, because this would contradict the false claim of Sofia that Samuel is a knave.", "We have exhausted all possibilities for Samuel and Sofia, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Sofia is a knight if and only if Chloe is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Sofia that Samuel is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Mason is a knight and Chloe is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that William is not a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that William is not a knave.", "Chloe cannot be a knight, because this would contradict the false claim of William that Sofia is a knight if and only if Chloe is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Owen is a knight.", "Owen cannot be a knight, because this would contradict the false claim of Chloe that Owen is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Lily is a knight if and only if Samuel is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that If William is a knave then Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of Lily that If William is a knave then Ava is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Sofia is a knight and Samuel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 7), ('telling-truth', 5)), ('and', ('telling-truth', 2), ('telling-truth', 5)), ('not', ('lying', 0)), ('->', ('lying', 0), ('lying', 4)), ('and', ('telling-truth', 7), ('telling-truth', 1)), ('telling-truth', 6), ('<=>', ('telling-truth', 3), ('telling-truth', 1)), ('lying', 1))", "index": 460}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sophia, Samuel, Lucas, Jacob, David, Ethan, Grace, and Aiden. Sophia commented, \"Lucas is a knight and David is a knight\". Samuel commented, \"Aiden is a knave or Jacob is a knave\". Lucas expressed that Ethan is a knave if and only if Ethan is a knight. In a statement by Jacob: \"If Samuel is a knight then Grace is a knave\". David told you that Grace is a knave if and only if Ethan is a knave. Ethan noted, \"Sophia is a knave\". \"Sophia is a knight,\" Grace claimed. \"Sophia is not a knave,\" Aiden declared. So who is a knight and who is a knave?", "names": ["Sophia", "Samuel", "Lucas", "Jacob", "David", "Ethan", "Grace", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, true, false, false], "solution_text": "Sophia is a knave, Samuel is a knight, Lucas is a knave, Jacob is a knight, David is a knave, Ethan is a knight, Grace is a knave, and Aiden is a knave.", "solution_text_format": "(1) Sophia is a knave\n(2) Samuel is a knight\n(3) Lucas is a knave\n(4) Jacob is a knight\n(5) David is a knave\n(6) Ethan is a knight\n(7) Grace is a knave\n(8) Aiden is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Lucas is a knight and David is a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Ethan is a knave if and only if Ethan is a knight.", "Lucas cannot be a knave, because this would contradict the claim of Sophia that Lucas is a knight and David is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Lucas is a knight and David is a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Ethan is a knave if and only if Ethan is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Ethan is a knave if and only if Ethan is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Sophia is a knave.", "Assume David is a knight. No contradiction is found in their claim that Grace is a knave if and only if Ethan is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Sophia is a knight.", "Grace cannot be a knave, because this would contradict the claim of David that Grace is a knave if and only if Ethan is a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Grace is a knave if and only if Ethan is a knave.", "Grace cannot be a knight, because this would contradict the false claim of David that Grace is a knave if and only if Ethan is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Sophia is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Aiden is a knave or Jacob is a knave.", "Aiden cannot be a knight, because this would contradict the claim of their own that Sophia is not a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Sophia is not a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that If Samuel is a knight then Grace is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 2), ('telling-truth', 4)), ('or', ('lying', 7), ('lying', 3)), ('<=>', ('lying', 5), ('telling-truth', 5)), ('->', ('telling-truth', 1), ('lying', 6)), ('<=>', ('lying', 6), ('lying', 5)), ('lying', 0), ('telling-truth', 0), ('not', ('lying', 0)))", "index": 461}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Evelyn, Scarlett, Mia, Matthew, Aurora, Jack, Penelope, and Riley. \"If Riley is a knave then Penelope is a knave,\" Evelyn mentioned. In Scarlett's words: \"Evelyn is a knight if and only if Evelyn is a knave\". \"Aurora is a knave if and only if Jack is a knight\" - Mia. According to Matthew, \"If Matthew is a knight then Aurora is a knight\". Aurora said, \"Matthew is a knight.\" In Jack's words: \"Scarlett is not a knight\". Penelope said, \"Mia is a knight.\" Riley stated, \"Scarlett is a knave\". So who is a knight and who is a knave?", "names": ["Evelyn", "Scarlett", "Mia", "Matthew", "Aurora", "Jack", "Penelope", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true, false, true], "solution_text": "Evelyn is a knight, Scarlett is a knave, Mia is a knave, Matthew is a knight, Aurora is a knight, Jack is a knight, Penelope is a knave, and Riley is a knight.", "solution_text_format": "(1) Evelyn is a knight\n(2) Scarlett is a knave\n(3) Mia is a knave\n(4) Matthew is a knight\n(5) Aurora is a knight\n(6) Jack is a knight\n(7) Penelope is a knave\n(8) Riley is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that If Riley is a knave then Penelope is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Evelyn is a knight if and only if Evelyn is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Evelyn is a knight if and only if Evelyn is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Aurora is a knave if and only if Jack is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that If Matthew is a knight then Aurora is a knight.", "Jack cannot be a knight, because this would contradict the claim of Mia that Aurora is a knave if and only if Jack is a knight.", "Jack cannot be a knave, because this would contradict the false claim of their own that Scarlett is not a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the false claim of their own that If Matthew is a knight then Aurora is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that If Matthew is a knight then Aurora is a knight.", "Matthew cannot be a knave, because this would contradict the false claim of their own that If Matthew is a knight then Aurora is a knight.", "We have exhausted all possibilities for Matthew and Aurora, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the claim of Penelope that Mia is a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Mia is a knight.", "Mia cannot be a knight, because this would contradict the false claim of Penelope that Mia is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Aurora is a knave if and only if Jack is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that If Matthew is a knight then Aurora is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Scarlett is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 7), ('lying', 6)), ('<=>', ('telling-truth', 0), ('lying', 0)), ('<=>', ('lying', 4), ('telling-truth', 5)), ('->', ('telling-truth', 3), ('telling-truth', 4)), ('telling-truth', 3), ('not', ('telling-truth', 1)), ('telling-truth', 2), ('lying', 1))", "index": 462}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jack, Grace, Mason, Aiden, Noah, Harper, Ella, and Abigail. Jack said, \"Noah is a knave.\" In a statement by Grace: \"Ella is a knight if and only if Noah is a knave\". Mason commented, \"Mason is a knight and Noah is a knight\". \"Mason is a knight or Grace is a knight,\" Aiden claimed. Noah told you that Mason is a knave. Harper asserted: \"If Grace is a knight then Jack is a knave\". Ella was heard saying, \"Harper is a knave\". Abigail said that Jack is a knight and Mason is a knight. So who is a knight and who is a knave?", "names": ["Jack", "Grace", "Mason", "Aiden", "Noah", "Harper", "Ella", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true, false, false], "solution_text": "Jack is a knave, Grace is a knight, Mason is a knave, Aiden is a knight, Noah is a knight, Harper is a knight, Ella is a knave, and Abigail is a knave.", "solution_text_format": "(1) Jack is a knave\n(2) Grace is a knight\n(3) Mason is a knave\n(4) Aiden is a knight\n(5) Noah is a knight\n(6) Harper is a knight\n(7) Ella is a knave\n(8) Abigail is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of Jack that Noah is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Mason is a knight and Noah is a knight.", "Mason cannot be a knave, because this would contradict the false claim of Noah that Mason is a knave.", "We have exhausted all possibilities for Mason and Noah, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Noah is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of Noah that Mason is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Mason is a knight and Noah is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Ella is a knight if and only if Noah is a knave.", "Ella cannot be a knight, because this would contradict the claim of Grace that Ella is a knight if and only if Noah is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Harper is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that If Grace is a knight then Jack is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Mason is a knight or Grace is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Jack is a knight and Mason is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Jack is a knight and Mason is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('<=>', ('telling-truth', 6), ('lying', 4)), ('and', ('telling-truth', 2), ('telling-truth', 4)), ('or', ('telling-truth', 2), ('telling-truth', 1)), ('lying', 2), ('->', ('telling-truth', 1), ('lying', 0)), ('lying', 5), ('and', ('telling-truth', 0), ('telling-truth', 2)))", "index": 463}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: James, Jackson, Ella, William, Chloe, Noah, Samuel, and Alexander. James stated, \"Samuel is a knight or Chloe is a knight\". As Jackson put it, \"Noah is a knave or James is a knight\". Ella commented, \"Noah is a knave if and only if Jackson is a knight\". William said that Samuel is a knight if and only if Ella is a knight. Chloe said, \"Noah is a knave or Noah is a knight.\" Noah said that James is a knave or William is a knave. In Samuel's words: \"If William is a knight then William is a knave\". Alexander told you that Samuel is not a knight. So who is a knight and who is a knave?", "names": ["James", "Jackson", "Ella", "William", "Chloe", "Noah", "Samuel", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true, true, false], "solution_text": "James is a knight, Jackson is a knight, Ella is a knave, William is a knave, Chloe is a knight, Noah is a knight, Samuel is a knight, and Alexander is a knave.", "solution_text_format": "(1) James is a knight\n(2) Jackson is a knight\n(3) Ella is a knave\n(4) William is a knave\n(5) Chloe is a knight\n(6) Noah is a knight\n(7) Samuel is a knight\n(8) Alexander is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Samuel is a knight or Chloe is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that If William is a knight then William is a knave.", "William cannot be a knight, because this would contradict the claim of Samuel that If William is a knight then William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Samuel is a knight if and only if Ella is a knight.", "Ella cannot be a knight, because this would contradict the false claim of William that Samuel is a knight if and only if Ella is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Noah is a knave if and only if Jackson is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that James is a knave or William is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Noah is a knave or James is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Noah is a knave or Noah is a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that Samuel is not a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Samuel is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 6), ('telling-truth', 4)), ('or', ('lying', 5), ('telling-truth', 0)), ('<=>', ('lying', 5), ('telling-truth', 1)), ('<=>', ('telling-truth', 6), ('telling-truth', 2)), ('or', ('lying', 5), ('telling-truth', 5)), ('or', ('lying', 0), ('lying', 3)), ('->', ('telling-truth', 3), ('lying', 3)), ('not', ('telling-truth', 6)))", "index": 464}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: William, Jacob, Mia, Ella, Amelia, Samuel, Sofia, and Mason. William commented, \"If Amelia is a knight then Ella is a knave\". Jacob remarked, \"William is a knight\". \"Jacob is a knave or Mason is a knave,\" Mia mentioned. Ella expressed that If Amelia is a knight then Sofia is a knave. \"Jacob is a knave if and only if William is a knight,\" Amelia declared. Samuel noted, \"Jacob is a knight\". According to Sofia, \"William is a knight and Ella is a knave\". \"William is a knight or Amelia is a knight,\" Mason claimed. So who is a knight and who is a knave?", "names": ["William", "Jacob", "Mia", "Ella", "Amelia", "Samuel", "Sofia", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true, false, true], "solution_text": "William is a knight, Jacob is a knight, Mia is a knave, Ella is a knight, Amelia is a knave, Samuel is a knight, Sofia is a knave, and Mason is a knight.", "solution_text_format": "(1) William is a knight\n(2) Jacob is a knight\n(3) Mia is a knave\n(4) Ella is a knight\n(5) Amelia is a knave\n(6) Samuel is a knight\n(7) Sofia is a knave\n(8) Mason is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that If Amelia is a knight then Ella is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Jacob is a knave if and only if William is a knight.", "Jacob cannot be a knight, because this would contradict the claim of Amelia that Jacob is a knave if and only if William is a knight.", "Jacob cannot be a knave, because this would contradict the false claim of their own that William is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Jacob is a knave if and only if William is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that William is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that If Amelia is a knight then Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that William is a knight and Ella is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that William is a knight and Ella is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Jacob is a knave or Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of Mia that Jacob is a knave or Mason is a knave.", "Mason cannot be a knave, because this would contradict the false claim of their own that William is a knight or Amelia is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Jacob is a knave or Mason is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that William is a knight or Amelia is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Jacob is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 4), ('lying', 3)), ('telling-truth', 0), ('or', ('lying', 1), ('lying', 7)), ('->', ('telling-truth', 4), ('lying', 6)), ('<=>', ('lying', 1), ('telling-truth', 0)), ('telling-truth', 1), ('and', ('telling-truth', 0), ('lying', 3)), ('or', ('telling-truth', 0), ('telling-truth', 4)))", "index": 465}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Grace, Noah, Isabella, Amelia, Michael, Samuel, Emma, and Sofia. Grace asserted: \"Emma is a knight\". \"Grace is a knave if and only if Samuel is a knave,\" Noah declared. Isabella expressed that Grace is a knight or Emma is a knave. Amelia said that Emma is a knight and Samuel is a knave. Michael asserted: \"Isabella is a knave\". Samuel was heard saying, \"Emma is a knight or Grace is a knight\". \"If Amelia is a knave then Isabella is a knave\" - Emma. Sofia expressed that Noah is a knave or Michael is a knight. So who is a knight and who is a knave?", "names": ["Grace", "Noah", "Isabella", "Amelia", "Michael", "Samuel", "Emma", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false, false, false], "solution_text": "Grace is a knave, Noah is a knight, Isabella is a knight, Amelia is a knave, Michael is a knave, Samuel is a knave, Emma is a knave, and Sofia is a knave.", "solution_text_format": "(1) Grace is a knave\n(2) Noah is a knight\n(3) Isabella is a knight\n(4) Amelia is a knave\n(5) Michael is a knave\n(6) Samuel is a knave\n(7) Emma is a knave\n(8) Sofia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Emma is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If Amelia is a knave then Isabella is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Emma is a knight and Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Amelia that Emma is a knight and Samuel is a knave.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Emma is a knight or Grace is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Emma is a knight and Samuel is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Emma is a knight or Grace is a knight.", "Isabella cannot be a knight, because this would contradict the claim of Emma that If Amelia is a knave then Isabella is a knave.", "Isabella cannot be a knave, because this would contradict the false claim of their own that Grace is a knight or Emma is a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Samuel.", "Samuel cannot be a knave, because this would contradict the false claim of Amelia that Emma is a knight and Samuel is a knave.", "We have exhausted all possibilities for Samuel and Amelia, so let us go back and reconsider Emma.", "Emma cannot be a knave, because this would contradict the claim of Grace that Emma is a knight.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Emma is a knight.", "Emma cannot be a knight, because this would contradict the false claim of Grace that Emma is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that If Amelia is a knave then Isabella is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Emma is a knight and Samuel is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Emma is a knight and Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that Emma is a knight or Grace is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Emma is a knight or Grace is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Grace is a knight or Emma is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Grace is a knave if and only if Samuel is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Isabella is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Isabella is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Noah is a knave or Michael is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Noah is a knave or Michael is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 6), ('<=>', ('lying', 0), ('lying', 5)), ('or', ('telling-truth', 0), ('lying', 6)), ('and', ('telling-truth', 6), ('lying', 5)), ('lying', 2), ('or', ('telling-truth', 6), ('telling-truth', 0)), ('->', ('lying', 3), ('lying', 2)), ('or', ('lying', 1), ('telling-truth', 4)))", "index": 466}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Alexander, Victoria, Amelia, Evelyn, Samuel, Isabella, Jack, and Ava. Alexander told you that If Evelyn is a knave then Isabella is a knave. \"Evelyn is a knave\" - Victoria. \"Jack is a knight,\" Amelia claimed. \"Alexander is a knight and Samuel is a knave,\" Evelyn declared. Samuel remarked, \"Amelia is a knight if and only if Victoria is a knave\". Isabella expressed that Jack is a knave if and only if Evelyn is a knave. Jack expressed that Isabella is not a knave. Ava said that Jack is a knave. So who is a knight and who is a knave?", "names": ["Alexander", "Victoria", "Amelia", "Evelyn", "Samuel", "Isabella", "Jack", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, false, false, true], "solution_text": "Alexander is a knight, Victoria is a knave, Amelia is a knave, Evelyn is a knight, Samuel is a knave, Isabella is a knave, Jack is a knave, and Ava is a knight.", "solution_text_format": "(1) Alexander is a knight\n(2) Victoria is a knave\n(3) Amelia is a knave\n(4) Evelyn is a knight\n(5) Samuel is a knave\n(6) Isabella is a knave\n(7) Jack is a knave\n(8) Ava is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that If Evelyn is a knave then Isabella is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Alexander is a knight and Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Evelyn that Alexander is a knight and Samuel is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Amelia is a knight if and only if Victoria is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Isabella is not a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Jack is a knave if and only if Evelyn is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave.", "Victoria cannot be a knave, because this would contradict the false claim of Samuel that Amelia is a knight if and only if Victoria is a knave.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the false claim of their own that Jack is a knave if and only if Evelyn is a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the claim of Amelia that Jack is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Jack is a knight.", "Jack cannot be a knight, because this would contradict the false claim of Amelia that Jack is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Isabella is not a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that Jack is a knave if and only if Evelyn is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Jack is a knave if and only if Evelyn is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Evelyn is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Jack is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('lying', 5)), ('lying', 3), ('telling-truth', 6), ('and', ('telling-truth', 0), ('lying', 4)), ('<=>', ('telling-truth', 2), ('lying', 1)), ('<=>', ('lying', 6), ('lying', 3)), ('not', ('lying', 5)), ('lying', 6))", "index": 467}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Penelope, Liam, Benjamin, Matthew, William, Isabella, Ella, and Ava. Penelope commented, \"Isabella is a knave if and only if Isabella is a knight\". Liam commented, \"Benjamin is a knight or Matthew is a knave\". According to Benjamin, \"If Penelope is a knight then Ava is a knave\". In a statement by Matthew: \"Matthew is a knight or Ava is a knight\". William said, \"Penelope is not a knave.\" \"Ella is a knave and Benjamin is a knight,\" Isabella declared. \"Matthew is a knight,\" Ella mentioned. \"Ava is a knight if and only if Isabella is a knight\" - Ava. So who is a knight and who is a knave?", "names": ["Penelope", "Liam", "Benjamin", "Matthew", "William", "Isabella", "Ella", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true, false, false], "solution_text": "Penelope is a knave, Liam is a knight, Benjamin is a knight, Matthew is a knave, William is a knave, Isabella is a knight, Ella is a knave, and Ava is a knave.", "solution_text_format": "(1) Penelope is a knave\n(2) Liam is a knight\n(3) Benjamin is a knight\n(4) Matthew is a knave\n(5) William is a knave\n(6) Isabella is a knight\n(7) Ella is a knave\n(8) Ava is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Penelope cannot be a knight, because this would contradict the claim of their own that Isabella is a knave if and only if Isabella is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Isabella is a knave if and only if Isabella is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Ella is a knave and Benjamin is a knight.", "Ella cannot be a knight, because this would contradict the claim of Isabella that Ella is a knave and Benjamin is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the false claim of Ella that Matthew is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Matthew is a knight or Ava is a knight.", "Ava cannot be a knight, because this would contradict the false claim of Matthew that Matthew is a knight or Ava is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Ava is a knight if and only if Isabella is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Penelope is a knight then Ava is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Benjamin is a knight or Matthew is a knave.", "William cannot be a knight, because this would contradict the claim of their own that Penelope is not a knave.", "Assume William is a knave. No contradiction is found in their false claim that Penelope is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 5), ('telling-truth', 5)), ('or', ('telling-truth', 2), ('lying', 3)), ('->', ('telling-truth', 0), ('lying', 7)), ('or', ('telling-truth', 3), ('telling-truth', 7)), ('not', ('lying', 0)), ('and', ('lying', 6), ('telling-truth', 2)), ('telling-truth', 3), ('<=>', ('telling-truth', 7), ('telling-truth', 5)))", "index": 468}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Charlotte, Grace, Ava, Logan, Evelyn, Henry, Riley, and Aria. Charlotte asserted: \"Evelyn is a knave\". \"Henry is a knave or Evelyn is a knight,\" Grace declared. Ava noted, \"Grace is a knight if and only if Henry is a knight\". Logan stated, \"Riley is a knight\". \"If Grace is a knave then Aria is a knave,\" Evelyn declared. \"Ava is not a knave,\" Henry claimed. \"If Riley is a knight then Henry is a knight,\" Riley declared. Aria stated, \"Riley is not a knight\". So who is a knight and who is a knave?", "names": ["Charlotte", "Grace", "Ava", "Logan", "Evelyn", "Henry", "Riley", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true, true, false], "solution_text": "Charlotte is a knave, Grace is a knight, Ava is a knight, Logan is a knight, Evelyn is a knight, Henry is a knight, Riley is a knight, and Aria is a knave.", "solution_text_format": "(1) Charlotte is a knave\n(2) Grace is a knight\n(3) Ava is a knight\n(4) Logan is a knight\n(5) Evelyn is a knight\n(6) Henry is a knight\n(7) Riley is a knight\n(8) Aria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that Evelyn is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of Charlotte that Evelyn is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that If Grace is a knave then Aria is a knave.", "Grace cannot be a knight, because this would contradict the false claim of Evelyn that If Grace is a knave then Aria is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Henry is a knave or Evelyn is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Ava is not a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Grace is a knight if and only if Henry is a knight.", "Ava cannot be a knave, because this would contradict the claim of Henry that Ava is not a knave.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the false claim of Grace that Henry is a knave or Evelyn is a knight.", "We have exhausted all possibilities for Henry, Grace, and Evelyn, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Evelyn is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Grace is a knave then Aria is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Henry is a knave or Evelyn is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Ava is not a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Grace is a knight if and only if Henry is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Riley is not a knight.", "Riley cannot be a knight, because this would contradict the claim of Aria that Riley is not a knight.", "Riley cannot be a knave, because this would contradict the false claim of their own that If Riley is a knight then Henry is a knight.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Riley is not a knight.", "Assume Riley is a knight. No contradiction is found in their claim that If Riley is a knight then Henry is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Riley is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('or', ('lying', 5), ('telling-truth', 4)), ('<=>', ('telling-truth', 1), ('telling-truth', 5)), ('telling-truth', 6), ('->', ('lying', 1), ('lying', 7)), ('not', ('lying', 2)), ('->', ('telling-truth', 6), ('telling-truth', 5)), ('not', ('telling-truth', 6)))", "index": 469}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Riley, Olivia, Zoey, Luke, Daniel, Avery, Emma, and Michael. \"Olivia is a knave or Olivia is a knight,\" Riley declared. \"Emma is not a knight\" - Olivia. According to Zoey, \"Emma is a knave if and only if Michael is a knave\". In Luke's words: \"Olivia is not a knave\". \"Riley is not a knight\" - Daniel. Avery noted, \"Olivia is a knight or Luke is a knave\". In Emma's words: \"Olivia is a knave if and only if Zoey is a knave\". Michael noted, \"Zoey is a knave or Emma is a knave\". So who is a knight and who is a knave?", "names": ["Riley", "Olivia", "Zoey", "Luke", "Daniel", "Avery", "Emma", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true, false, true], "solution_text": "Riley is a knight, Olivia is a knight, Zoey is a knave, Luke is a knight, Daniel is a knave, Avery is a knight, Emma is a knave, and Michael is a knight.", "solution_text_format": "(1) Riley is a knight\n(2) Olivia is a knight\n(3) Zoey is a knave\n(4) Luke is a knight\n(5) Daniel is a knave\n(6) Avery is a knight\n(7) Emma is a knave\n(8) Michael is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Olivia is a knave or Olivia is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Emma is not a knight.", "Emma cannot be a knight, because this would contradict the claim of Olivia that Emma is not a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Olivia is a knave if and only if Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the false claim of Emma that Olivia is a knave if and only if Zoey is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Emma is a knave if and only if Michael is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Zoey is a knave or Emma is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Olivia is not a knave.", "Daniel cannot be a knight, because this would contradict the claim of their own that Riley is not a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Riley is not a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Olivia is a knight or Luke is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('telling-truth', 1)), ('not', ('telling-truth', 6)), ('<=>', ('lying', 6), ('lying', 7)), ('not', ('lying', 1)), ('not', ('telling-truth', 0)), ('or', ('telling-truth', 1), ('lying', 3)), ('<=>', ('lying', 1), ('lying', 2)), ('or', ('lying', 2), ('lying', 6)))", "index": 470}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aurora, Samuel, Elizabeth, Alexander, Oliver, Isabella, James, and Riley. Aurora was heard saying, \"Isabella is a knave if and only if James is a knight\". Samuel was heard saying, \"Alexander is not a knave\". \"Aurora is a knave\" - Elizabeth. Alexander commented, \"Samuel is a knave or James is a knight\". \"Riley is a knight if and only if Samuel is a knave,\" Oliver claimed. Isabella remarked, \"If James is a knight then Samuel is a knight\". James said that Riley is a knight if and only if Aurora is a knight. In Riley's words: \"James is not a knight\". So who is a knight and who is a knave?", "names": ["Aurora", "Samuel", "Elizabeth", "Alexander", "Oliver", "Isabella", "James", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true, true, false], "solution_text": "Aurora is a knave, Samuel is a knight, Elizabeth is a knight, Alexander is a knight, Oliver is a knight, Isabella is a knight, James is a knight, and Riley is a knave.", "solution_text_format": "(1) Aurora is a knave\n(2) Samuel is a knight\n(3) Elizabeth is a knight\n(4) Alexander is a knight\n(5) Oliver is a knight\n(6) Isabella is a knight\n(7) James is a knight\n(8) Riley is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that Isabella is a knave if and only if James is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that If James is a knight then Samuel is a knight.", "James cannot be a knight, because this would contradict the claim of Aurora that Isabella is a knave if and only if James is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Aurora is a knight.", "Riley cannot be a knight, because this would contradict the false claim of James that Riley is a knight if and only if Aurora is a knight.", "Riley cannot be a knave, because this would contradict the false claim of their own that James is not a knight.", "We have exhausted all possibilities for Riley and James, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that If James is a knight then Samuel is a knight.", "Assume James is a knight. No contradiction is found in their claim that Riley is a knight if and only if Aurora is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that James is not a knight.", "Riley cannot be a knave, because this would contradict the claim of James that Riley is a knight if and only if Aurora is a knight.", "We have exhausted all possibilities for Riley, so let us go back and reconsider James.", "James cannot be a knave, because this would contradict the claim of Aurora that Isabella is a knave if and only if James is a knight.", "We have exhausted all possibilities for James and Isabella, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Isabella is a knave if and only if James is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that If James is a knight then Samuel is a knight.", "Assume James is a knight. No contradiction is found in their claim that Riley is a knight if and only if Aurora is a knight.", "Riley cannot be a knight, because this would contradict the claim of James that Riley is a knight if and only if Aurora is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that James is not a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Alexander is not a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Samuel is a knave or James is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Aurora is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Riley is a knight if and only if Samuel is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 5), ('telling-truth', 6)), ('not', ('lying', 3)), ('lying', 0), ('or', ('lying', 1), ('telling-truth', 6)), ('<=>', ('telling-truth', 7), ('lying', 1)), ('->', ('telling-truth', 6), ('telling-truth', 1)), ('<=>', ('telling-truth', 7), ('telling-truth', 0)), ('not', ('telling-truth', 6)))", "index": 471}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ella, Joseph, Samuel, Emma, Henry, James, William, and Penelope. Ella told you that Ella is a knight if and only if Penelope is a knave. Joseph noted, \"William is a knight if and only if Samuel is a knight\". \"James is a knave and Henry is a knave,\" Samuel declared. \"If William is a knight then Penelope is a knight,\" Emma mentioned. Henry expressed that If Emma is a knave then Ella is a knight. James asserted: \"If William is a knight then Ella is a knight\". William said, \"Penelope is a knave and Joseph is a knight.\" \"James is a knave and Joseph is a knave\" - Penelope. So who is a knight and who is a knave?", "names": ["Ella", "Joseph", "Samuel", "Emma", "Henry", "James", "William", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false, true, false], "solution_text": "Ella is a knave, Joseph is a knight, Samuel is a knight, Emma is a knave, Henry is a knave, James is a knave, William is a knight, and Penelope is a knave.", "solution_text_format": "(1) Ella is a knave\n(2) Joseph is a knight\n(3) Samuel is a knight\n(4) Emma is a knave\n(5) Henry is a knave\n(6) James is a knave\n(7) William is a knight\n(8) Penelope is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Ella is a knight if and only if Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the claim of Ella that Ella is a knight if and only if Penelope is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that James is a knave and Joseph is a knave.", "Assume James is a knight. No contradiction is found in their claim that If William is a knight then Ella is a knight.", "Assume William is a knight. No contradiction is found in their claim that Penelope is a knave and Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that William is a knight if and only if Samuel is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that James is a knave and Henry is a knave.", "Samuel cannot be a knave, because this would contradict the claim of Joseph that William is a knight if and only if Samuel is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of William that Penelope is a knave and Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Penelope is a knave and Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of William that Penelope is a knave and Joseph is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that William is a knight if and only if Samuel is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that James is a knave and Henry is a knave.", "Samuel cannot be a knave, because this would contradict the false claim of Joseph that William is a knight if and only if Samuel is a knight.", "We have exhausted all possibilities for Samuel, Joseph, and William, so let us go back and reconsider James.", "James cannot be a knave, because this would contradict the false claim of their own that If William is a knight then Ella is a knight.", "We have exhausted all possibilities for James and Penelope, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Ella is a knight if and only if Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the false claim of Ella that Ella is a knight if and only if Penelope is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that James is a knave and Joseph is a knave.", "Assume James is a knight. No contradiction is found in their claim that If William is a knight then Ella is a knight.", "William cannot be a knight, because this would contradict the claim of James that If William is a knight then Ella is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Penelope is a knave and Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of William that Penelope is a knave and Joseph is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that William is a knight if and only if Samuel is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that James is a knave and Henry is a knave.", "Samuel cannot be a knave, because this would contradict the false claim of Joseph that William is a knight if and only if Samuel is a knight.", "We have exhausted all possibilities for Samuel, Joseph, and William, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that If William is a knight then Ella is a knight.", "Assume William is a knight. No contradiction is found in their claim that Penelope is a knave and Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that William is a knight if and only if Samuel is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that James is a knave and Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of Samuel that James is a knave and Henry is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that If Emma is a knave then Ella is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that If William is a knight then Penelope is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that If William is a knight then Penelope is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 0), ('lying', 7)), ('<=>', ('telling-truth', 6), ('telling-truth', 2)), ('and', ('lying', 5), ('lying', 4)), ('->', ('telling-truth', 6), ('telling-truth', 7)), ('->', ('lying', 3), ('telling-truth', 0)), ('->', ('telling-truth', 6), ('telling-truth', 0)), ('and', ('lying', 7), ('telling-truth', 1)), ('and', ('lying', 5), ('lying', 1)))", "index": 472}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Isabella, Henry, Lily, Mason, Michael, Jackson, Victoria, and Aria. \"Jackson is a knave if and only if Michael is a knight\" - Isabella. Henry commented, \"Jackson is a knight and Mason is a knave\". \"Lily is a knight or Aria is a knight\" - Lily. Mason said that Michael is a knave or Jackson is a knave. \"Jackson is a knave if and only if Jackson is a knight,\" Michael claimed. Jackson asserted: \"If Victoria is a knight then Henry is a knave\". In a statement by Victoria: \"Lily is a knight\". \"Michael is a knave,\" Aria mentioned. So who is a knight and who is a knave?", "names": ["Isabella", "Henry", "Lily", "Mason", "Michael", "Jackson", "Victoria", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true, true, true], "solution_text": "Isabella is a knight, Henry is a knave, Lily is a knight, Mason is a knight, Michael is a knave, Jackson is a knight, Victoria is a knight, and Aria is a knight.", "solution_text_format": "(1) Isabella is a knight\n(2) Henry is a knave\n(3) Lily is a knight\n(4) Mason is a knight\n(5) Michael is a knave\n(6) Jackson is a knight\n(7) Victoria is a knight\n(8) Aria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Jackson is a knave if and only if Michael is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that If Victoria is a knight then Henry is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Lily is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Lily is a knight or Aria is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of Isabella that Jackson is a knave if and only if Michael is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Jackson is a knave if and only if Jackson is a knight.", "Henry cannot be a knight, because this would contradict the claim of Jackson that If Victoria is a knight then Henry is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Jackson is a knight and Mason is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Michael is a knave or Jackson is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 5), ('telling-truth', 4)), ('and', ('telling-truth', 5), ('lying', 3)), ('or', ('telling-truth', 2), ('telling-truth', 7)), ('or', ('lying', 4), ('lying', 5)), ('<=>', ('lying', 5), ('telling-truth', 5)), ('->', ('telling-truth', 6), ('lying', 1)), ('telling-truth', 2), ('lying', 4))", "index": 473}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Benjamin, Isabella, Oliver, Noah, Henry, James, Grace, and Olivia. Benjamin told you that If James is a knave then Isabella is a knave. Isabella stated, \"Olivia is a knave if and only if Oliver is a knight\". Oliver remarked, \"If Olivia is a knight then James is a knave\". Noah asserted: \"Oliver is a knave\". \"James is a knave,\" Henry mentioned. James noted, \"James is a knight if and only if Grace is a knight\". In Grace's words: \"If Grace is a knight then Noah is a knight\". As Olivia put it, \"Grace is a knight and Henry is a knave\". So who is a knight and who is a knave?", "names": ["Benjamin", "Isabella", "Oliver", "Noah", "Henry", "James", "Grace", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true, true, true], "solution_text": "Benjamin is a knight, Isabella is a knight, Oliver is a knave, Noah is a knight, Henry is a knave, James is a knight, Grace is a knight, and Olivia is a knight.", "solution_text_format": "(1) Benjamin is a knight\n(2) Isabella is a knight\n(3) Oliver is a knave\n(4) Noah is a knight\n(5) Henry is a knave\n(6) James is a knight\n(7) Grace is a knight\n(8) Olivia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that If James is a knave then Isabella is a knave.", "Assume James is a knight. No contradiction is found in their claim that James is a knight if and only if Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that If Grace is a knight then Noah is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Oliver is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Noah that Oliver is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that If Olivia is a knight then James is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Grace is a knight and Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of their own that James is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that James is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Olivia is a knave if and only if Oliver is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('lying', 1)), ('<=>', ('lying', 7), ('telling-truth', 2)), ('->', ('telling-truth', 7), ('lying', 5)), ('lying', 2), ('lying', 5), ('<=>', ('telling-truth', 5), ('telling-truth', 6)), ('->', ('telling-truth', 6), ('telling-truth', 3)), ('and', ('telling-truth', 6), ('lying', 4)))", "index": 474}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Avery, Olivia, Jackson, Lily, Ava, William, Noah, and Riley. Avery noted, \"Jackson is a knave or Ava is a knave\". \"Riley is a knave\" - Olivia. \"Avery is a knave,\" Jackson declared. \"Riley is a knight and William is a knight,\" Lily declared. \"William is not a knight,\" Ava mentioned. \"Riley is a knave if and only if Riley is a knight,\" William declared. Noah said, \"If Noah is a knight then Avery is a knave.\" Riley noted, \"Noah is a knight or Avery is a knight\". So who is a knight and who is a knave?", "names": ["Avery", "Olivia", "Jackson", "Lily", "Ava", "William", "Noah", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, false, true, true], "solution_text": "Avery is a knave, Olivia is a knave, Jackson is a knight, Lily is a knave, Ava is a knight, William is a knave, Noah is a knight, and Riley is a knight.", "solution_text_format": "(1) Avery is a knave\n(2) Olivia is a knave\n(3) Jackson is a knight\n(4) Lily is a knave\n(5) Ava is a knight\n(6) William is a knave\n(7) Noah is a knight\n(8) Riley is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Jackson is a knave or Ava is a knave.", "Jackson cannot be a knight, because this would contradict the claim of their own that Avery is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Avery is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that William is not a knight.", "William cannot be a knight, because this would contradict the claim of Ava that William is not a knight.", "Assume William is a knave. No contradiction is found in their false claim that Riley is a knave if and only if Riley is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Noah is a knight or Avery is a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that If Noah is a knight then Avery is a knave.", "Noah cannot be a knave, because this would contradict the false claim of their own that If Noah is a knight then Avery is a knave.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Riley.", "Riley cannot be a knave, because this would contradict the false claim of their own that Noah is a knight or Avery is a knight.", "We have exhausted all possibilities for Riley and William, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that William is not a knight.", "William cannot be a knight, because this would contradict the claim of their own that Riley is a knave if and only if Riley is a knight.", "William cannot be a knave, because this would contradict the false claim of Ava that William is not a knight.", "We have exhausted all possibilities for William, Ava, and Jackson, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Jackson is a knave or Ava is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Avery is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that William is not a knight.", "William cannot be a knight, because this would contradict the claim of Ava that William is not a knight.", "Assume William is a knave. No contradiction is found in their false claim that Riley is a knave if and only if Riley is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Noah is a knight or Avery is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that If Noah is a knight then Avery is a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that Riley is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Riley is a knave.", "Lily cannot be a knight, because this would contradict the claim of their own that Riley is a knight and William is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Riley is a knight and William is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('lying', 4)), ('lying', 7), ('lying', 0), ('and', ('telling-truth', 7), ('telling-truth', 5)), ('not', ('telling-truth', 5)), ('<=>', ('lying', 7), ('telling-truth', 7)), ('->', ('telling-truth', 6), ('lying', 0)), ('or', ('telling-truth', 6), ('telling-truth', 0)))", "index": 475}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jackson, Charlotte, Avery, Sophia, Joseph, Samuel, Noah, and Grace. Jackson expressed that Charlotte is a knight or Grace is a knight. \"Noah is a knave and Sophia is a knight,\" Charlotte declared. Avery said, \"Sophia is a knight if and only if Avery is a knight.\" Sophia told you that Avery is not a knave. In a statement by Joseph: \"Samuel is a knave\". Samuel said that If Samuel is a knight then Avery is a knight. Noah asserted: \"Grace is a knave or Samuel is a knight\". Grace asserted: \"If Joseph is a knight then Sophia is a knave\". So who is a knight and who is a knave?", "names": ["Jackson", "Charlotte", "Avery", "Sophia", "Joseph", "Samuel", "Noah", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true, true, true], "solution_text": "Jackson is a knight, Charlotte is a knave, Avery is a knight, Sophia is a knight, Joseph is a knave, Samuel is a knight, Noah is a knight, and Grace is a knight.", "solution_text_format": "(1) Jackson is a knight\n(2) Charlotte is a knave\n(3) Avery is a knight\n(4) Sophia is a knight\n(5) Joseph is a knave\n(6) Samuel is a knight\n(7) Noah is a knight\n(8) Grace is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Charlotte is a knight or Grace is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Noah is a knave and Sophia is a knight.", "Noah cannot be a knight, because this would contradict the claim of Charlotte that Noah is a knave and Sophia is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Grace is a knave or Samuel is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that If Joseph is a knight then Sophia is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Joseph that Samuel is a knave.", "Samuel cannot be a knave, because this would contradict the false claim of their own that If Samuel is a knight then Avery is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the false claim of Noah that Grace is a knave or Samuel is a knight.", "Samuel cannot be a knave, because this would contradict the false claim of Joseph that Samuel is a knave.", "We have exhausted all possibilities for Samuel and Joseph, so let us go back and reconsider Grace.", "Grace cannot be a knave, because this would contradict the false claim of Noah that Grace is a knave or Samuel is a knight.", "We have exhausted all possibilities for Grace and Noah, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Noah is a knave and Sophia is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Grace is a knave or Samuel is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that If Joseph is a knight then Sophia is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Joseph that Samuel is a knave.", "Samuel cannot be a knave, because this would contradict the false claim of their own that If Samuel is a knight then Avery is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Samuel is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that If Samuel is a knight then Avery is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Sophia is a knight if and only if Avery is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Avery is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('telling-truth', 7)), ('and', ('lying', 6), ('telling-truth', 3)), ('<=>', ('telling-truth', 3), ('telling-truth', 2)), ('not', ('lying', 2)), ('lying', 5), ('->', ('telling-truth', 5), ('telling-truth', 2)), ('or', ('lying', 7), ('telling-truth', 5)), ('->', ('telling-truth', 4), ('lying', 3)))", "index": 476}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Abigail, Harper, Liam, Riley, Aiden, Victoria, Henry, and Mia. Abigail noted, \"Henry is a knight\". Harper told you that Abigail is a knave if and only if Aiden is a knight. According to Liam, \"Harper is a knight and Victoria is a knight\". According to Riley, \"If Victoria is a knave then Victoria is a knight\". Aiden expressed that Abigail is a knave if and only if Mia is a knight. \"If Mia is a knave then Henry is a knave\" - Victoria. Henry stated, \"Aiden is a knight and Victoria is a knight\". Mia asserted: \"Riley is not a knight\". So who is a knight and who is a knave?", "names": ["Abigail", "Harper", "Liam", "Riley", "Aiden", "Victoria", "Henry", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, true, false, false], "solution_text": "Abigail is a knave, Harper is a knave, Liam is a knave, Riley is a knight, Aiden is a knave, Victoria is a knight, Henry is a knave, and Mia is a knave.", "solution_text_format": "(1) Abigail is a knave\n(2) Harper is a knave\n(3) Liam is a knave\n(4) Riley is a knight\n(5) Aiden is a knave\n(6) Victoria is a knight\n(7) Henry is a knave\n(8) Mia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Henry is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Aiden is a knight and Victoria is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Abigail is a knave if and only if Mia is a knight.", "Mia cannot be a knight, because this would contradict the claim of Aiden that Abigail is a knave if and only if Mia is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Riley is not a knight.", "Assume Riley is a knight. No contradiction is found in their claim that If Victoria is a knave then Victoria is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that If Mia is a knave then Henry is a knave.", "Victoria cannot be a knave, because this would contradict the claim of Riley that If Victoria is a knave then Victoria is a knight.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Riley.", "Riley cannot be a knave, because this would contradict the false claim of Mia that Riley is not a knight.", "We have exhausted all possibilities for Riley and Mia, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the claim of Henry that Aiden is a knight and Victoria is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the claim of Abigail that Henry is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Henry is a knight.", "Henry cannot be a knight, because this would contradict the false claim of Abigail that Henry is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Aiden is a knight and Victoria is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Abigail is a knave if and only if Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Riley is not a knight.", "Riley cannot be a knight, because this would contradict the claim of Mia that Riley is not a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that If Victoria is a knave then Victoria is a knight.", "Victoria cannot be a knight, because this would contradict the false claim of Riley that If Victoria is a knave then Victoria is a knight.", "Victoria cannot be a knave, because this would contradict the false claim of their own that If Mia is a knave then Henry is a knave.", "We have exhausted all possibilities for Victoria and Riley, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the claim of Aiden that Abigail is a knave if and only if Mia is a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Abigail is a knave if and only if Mia is a knight.", "Mia cannot be a knight, because this would contradict the false claim of Aiden that Abigail is a knave if and only if Mia is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Riley is not a knight.", "Assume Riley is a knight. No contradiction is found in their claim that If Victoria is a knave then Victoria is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that If Mia is a knave then Henry is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Abigail is a knave if and only if Aiden is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Abigail is a knave if and only if Aiden is a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that Harper is a knight and Victoria is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Harper is a knight and Victoria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 6), ('<=>', ('lying', 0), ('telling-truth', 4)), ('and', ('telling-truth', 1), ('telling-truth', 5)), ('->', ('lying', 5), ('telling-truth', 5)), ('<=>', ('lying', 0), ('telling-truth', 7)), ('->', ('lying', 7), ('lying', 6)), ('and', ('telling-truth', 4), ('telling-truth', 5)), ('not', ('telling-truth', 3)))", "index": 477}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emma, Samuel, Riley, Oliver, Michael, Henry, Aurora, and Alexander. As Emma put it, \"Alexander is not a knight\". In Samuel's words: \"Alexander is a knave or Oliver is a knight\". Riley commented, \"Alexander is a knight and Henry is a knight\". Oliver told you that If Riley is a knave then Oliver is a knight. In Michael's words: \"Henry is a knight if and only if Michael is a knight\". Henry said, \"Michael is a knight and Aurora is a knave.\" Aurora said that Aurora is a knight. Alexander stated, \"Henry is a knave if and only if Samuel is a knave\". So who is a knight and who is a knave?", "names": ["Emma", "Samuel", "Riley", "Oliver", "Michael", "Henry", "Aurora", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true, false, true], "solution_text": "Emma is a knave, Samuel is a knight, Riley is a knight, Oliver is a knight, Michael is a knight, Henry is a knight, Aurora is a knave, and Alexander is a knight.", "solution_text_format": "(1) Emma is a knave\n(2) Samuel is a knight\n(3) Riley is a knight\n(4) Oliver is a knight\n(5) Michael is a knight\n(6) Henry is a knight\n(7) Aurora is a knave\n(8) Alexander is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of Emma that Alexander is not a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Henry is a knave if and only if Samuel is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Michael is a knight and Aurora is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Henry is a knight if and only if Michael is a knight.", "Aurora cannot be a knight, because this would contradict the claim of Henry that Michael is a knight and Aurora is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Aurora is a knight.", "Samuel cannot be a knight, because this would contradict the false claim of Alexander that Henry is a knave if and only if Samuel is a knave.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Alexander is a knave or Oliver is a knight.", "We have exhausted all possibilities for Samuel and Aurora, so let us go back and reconsider Michael.", "Michael cannot be a knave, because this would contradict the claim of Henry that Michael is a knight and Aurora is a knave.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Michael is a knight and Aurora is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Henry is a knight if and only if Michael is a knight.", "Michael cannot be a knave, because this would contradict the false claim of their own that Henry is a knight if and only if Michael is a knight.", "We have exhausted all possibilities for Michael, Henry, and Alexander, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Alexander is not a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Henry is a knave if and only if Samuel is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Michael is a knight and Aurora is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Henry is a knight if and only if Michael is a knight.", "Aurora cannot be a knight, because this would contradict the claim of Henry that Michael is a knight and Aurora is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Aurora is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Alexander is a knave or Oliver is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that If Riley is a knave then Oliver is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Alexander is a knight and Henry is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 7)), ('or', ('lying', 7), ('telling-truth', 3)), ('and', ('telling-truth', 7), ('telling-truth', 5)), ('->', ('lying', 2), ('telling-truth', 3)), ('<=>', ('telling-truth', 5), ('telling-truth', 4)), ('and', ('telling-truth', 4), ('lying', 6)), ('telling-truth', 6), ('<=>', ('lying', 5), ('lying', 1)))", "index": 478}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Joseph, Logan, Mason, Benjamin, Elizabeth, Alexander, Isabella, and Owen. Joseph said that If Benjamin is a knight then Alexander is a knave. According to Logan, \"Benjamin is not a knave\". \"Joseph is a knave,\" Mason claimed. In a statement by Benjamin: \"Logan is a knave if and only if Benjamin is a knight\". Elizabeth told you that Mason is a knight if and only if Joseph is a knight. Alexander expressed that Mason is not a knave. \"Alexander is a knight if and only if Mason is a knave,\" Isabella declared. Owen stated, \"Isabella is a knight\". So who is a knight and who is a knave?", "names": ["Joseph", "Logan", "Mason", "Benjamin", "Elizabeth", "Alexander", "Isabella", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, false, false, false], "solution_text": "Joseph is a knight, Logan is a knave, Mason is a knave, Benjamin is a knave, Elizabeth is a knave, Alexander is a knave, Isabella is a knave, and Owen is a knave.", "solution_text_format": "(1) Joseph is a knight\n(2) Logan is a knave\n(3) Mason is a knave\n(4) Benjamin is a knave\n(5) Elizabeth is a knave\n(6) Alexander is a knave\n(7) Isabella is a knave\n(8) Owen is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that If Benjamin is a knight then Alexander is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Logan is a knave if and only if Benjamin is a knight.", "Logan cannot be a knight, because this would contradict the claim of Benjamin that Logan is a knave if and only if Benjamin is a knight.", "Logan cannot be a knave, because this would contradict the false claim of their own that Benjamin is not a knave.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Logan is a knave if and only if Benjamin is a knight.", "Logan cannot be a knight, because this would contradict the claim of their own that Benjamin is not a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Benjamin is not a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Mason is not a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Joseph is a knave.", "Mason cannot be a knave, because this would contradict the claim of Alexander that Mason is not a knave.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Mason is not a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Joseph is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Joseph is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Mason is a knight if and only if Joseph is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Mason is a knight if and only if Joseph is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Alexander is a knight if and only if Mason is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Alexander is a knight if and only if Mason is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Isabella is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Isabella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('lying', 5)), ('not', ('lying', 3)), ('lying', 0), ('<=>', ('lying', 1), ('telling-truth', 3)), ('<=>', ('telling-truth', 2), ('telling-truth', 0)), ('not', ('lying', 2)), ('<=>', ('telling-truth', 5), ('lying', 2)), ('telling-truth', 6))", "index": 479}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Olivia, Ethan, Amelia, Ava, Scarlett, Matthew, Aria, and Isabella. In Olivia's words: \"Scarlett is a knight or Scarlett is a knave\". Ethan remarked, \"Olivia is a knight\". According to Amelia, \"If Isabella is a knight then Amelia is a knight\". Ava told you that Ethan is a knight if and only if Amelia is a knight. Scarlett was heard saying, \"Ava is not a knight\". \"Ethan is not a knight,\" Matthew mentioned. Aria expressed that Scarlett is a knight or Scarlett is a knave. \"Matthew is a knight and Scarlett is a knave\" - Isabella. So who is a knight and who is a knave?", "names": ["Olivia", "Ethan", "Amelia", "Ava", "Scarlett", "Matthew", "Aria", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false, true, false], "solution_text": "Olivia is a knight, Ethan is a knight, Amelia is a knight, Ava is a knight, Scarlett is a knave, Matthew is a knave, Aria is a knight, and Isabella is a knave.", "solution_text_format": "(1) Olivia is a knight\n(2) Ethan is a knight\n(3) Amelia is a knight\n(4) Ava is a knight\n(5) Scarlett is a knave\n(6) Matthew is a knave\n(7) Aria is a knight\n(8) Isabella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Scarlett is a knight or Scarlett is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Ava is not a knight.", "Ava cannot be a knight, because this would contradict the claim of Scarlett that Ava is not a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Ethan is a knight if and only if Amelia is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Olivia is a knight.", "Amelia cannot be a knight, because this would contradict the false claim of Ava that Ethan is a knight if and only if Amelia is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that If Isabella is a knight then Amelia is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Matthew is a knight and Scarlett is a knave.", "Isabella cannot be a knave, because this would contradict the false claim of Amelia that If Isabella is a knight then Amelia is a knight.", "We have exhausted all possibilities for Isabella and Amelia, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the false claim of their own that Olivia is a knight.", "We have exhausted all possibilities for Ethan and Ava, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Ava is not a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Ethan is a knight if and only if Amelia is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Olivia is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that If Isabella is a knight then Amelia is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Matthew is a knight and Scarlett is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Ethan is not a knight.", "Matthew cannot be a knave, because this would contradict the claim of Isabella that Matthew is a knight and Scarlett is a knave.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Matthew is a knight and Scarlett is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Ethan is not a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Ethan is not a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Scarlett is a knight or Scarlett is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('lying', 4)), ('telling-truth', 0), ('->', ('telling-truth', 7), ('telling-truth', 2)), ('<=>', ('telling-truth', 1), ('telling-truth', 2)), ('not', ('telling-truth', 3)), ('not', ('telling-truth', 1)), ('or', ('telling-truth', 4), ('lying', 4)), ('and', ('telling-truth', 5), ('lying', 4)))", "index": 480}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: David, Michael, Ethan, Olivia, Sebastian, Abigail, Aiden, and Joseph. David was heard saying, \"Michael is a knave or Michael is a knight\". \"David is a knight if and only if Joseph is a knight,\" Michael declared. According to Ethan, \"Abigail is a knave or Joseph is a knave\". Olivia told you that If Ethan is a knave then David is a knave. \"If Michael is a knight then David is a knight\" - Sebastian. Abigail noted, \"If Ethan is a knave then Sebastian is a knave\". Aiden stated, \"Sebastian is a knight if and only if Olivia is a knight\". Joseph told you that Olivia is a knave and Ethan is a knave. So who is a knight and who is a knave?", "names": ["David", "Michael", "Ethan", "Olivia", "Sebastian", "Abigail", "Aiden", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true, true, false], "solution_text": "David is a knight, Michael is a knave, Ethan is a knight, Olivia is a knight, Sebastian is a knight, Abigail is a knight, Aiden is a knight, and Joseph is a knave.", "solution_text_format": "(1) David is a knight\n(2) Michael is a knave\n(3) Ethan is a knight\n(4) Olivia is a knight\n(5) Sebastian is a knight\n(6) Abigail is a knight\n(7) Aiden is a knight\n(8) Joseph is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Michael is a knave or Michael is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that David is a knight if and only if Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Olivia is a knave and Ethan is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Joseph that Olivia is a knave and Ethan is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that If Ethan is a knave then David is a knave.", "Ethan cannot be a knight, because this would contradict the false claim of Olivia that If Ethan is a knave then David is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Abigail is a knave or Joseph is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that If Ethan is a knave then Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Abigail that If Ethan is a knave then Sebastian is a knave.", "Sebastian cannot be a knave, because this would contradict the false claim of their own that If Michael is a knight then David is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the false claim of Ethan that Abigail is a knave or Joseph is a knave.", "We have exhausted all possibilities for Abigail, Ethan, and Olivia, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of Michael that David is a knight if and only if Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that David is a knight if and only if Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of Michael that David is a knight if and only if Joseph is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Olivia is a knave and Ethan is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that If Ethan is a knave then David is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Abigail is a knave or Joseph is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that If Ethan is a knave then Sebastian is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Michael is a knight then David is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Sebastian is a knight if and only if Olivia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('telling-truth', 1)), ('<=>', ('telling-truth', 0), ('telling-truth', 7)), ('or', ('lying', 5), ('lying', 7)), ('->', ('lying', 2), ('lying', 0)), ('->', ('telling-truth', 1), ('telling-truth', 0)), ('->', ('lying', 2), ('lying', 4)), ('<=>', ('telling-truth', 4), ('telling-truth', 3)), ('and', ('lying', 3), ('lying', 2)))", "index": 481}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jack, David, Aurora, Harper, Abigail, Oliver, Luke, and Noah. Jack noted, \"Aurora is a knight and Luke is a knight\". David stated, \"Jack is a knight and Luke is a knight\". Aurora told you that Aurora is a knight. Harper said that Luke is a knight and Noah is a knight. Abigail noted, \"David is not a knave\". As Oliver put it, \"Luke is a knight and Aurora is a knight\". \"Harper is a knight if and only if Luke is a knight,\" Luke declared. \"David is not a knave,\" Noah claimed. So who is a knight and who is a knave?", "names": ["Jack", "David", "Aurora", "Harper", "Abigail", "Oliver", "Luke", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true, true, true], "solution_text": "Jack is a knight, David is a knight, Aurora is a knight, Harper is a knight, Abigail is a knight, Oliver is a knight, Luke is a knight, and Noah is a knight.", "solution_text_format": "(1) Jack is a knight\n(2) David is a knight\n(3) Aurora is a knight\n(4) Harper is a knight\n(5) Abigail is a knight\n(6) Oliver is a knight\n(7) Luke is a knight\n(8) Noah is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Aurora is a knight and Luke is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Aurora is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Harper is a knight if and only if Luke is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Luke is a knight and Noah is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that David is not a knave.", "Assume David is a knight. No contradiction is found in their claim that Jack is a knight and Luke is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that David is not a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Luke is a knight and Aurora is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 2), ('telling-truth', 6)), ('and', ('telling-truth', 0), ('telling-truth', 6)), ('telling-truth', 2), ('and', ('telling-truth', 6), ('telling-truth', 7)), ('not', ('lying', 1)), ('and', ('telling-truth', 6), ('telling-truth', 2)), ('<=>', ('telling-truth', 3), ('telling-truth', 6)), ('not', ('lying', 1)))", "index": 482}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Noah, Liam, Ethan, Evelyn, Luke, Chloe, Jack, and Mason. Noah stated, \"Mason is a knight\". In Liam's words: \"Jack is a knave\". Ethan commented, \"Jack is a knave\". In a statement by Evelyn: \"Mason is not a knight\". \"Ethan is a knight if and only if Liam is a knave,\" Luke claimed. Chloe said, \"Jack is a knight.\" Jack told you that Luke is a knight if and only if Mason is a knight. Mason remarked, \"Evelyn is a knight or Evelyn is a knave\". So who is a knight and who is a knave?", "names": ["Noah", "Liam", "Ethan", "Evelyn", "Luke", "Chloe", "Jack", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false, false, true], "solution_text": "Noah is a knight, Liam is a knight, Ethan is a knight, Evelyn is a knave, Luke is a knave, Chloe is a knave, Jack is a knave, and Mason is a knight.", "solution_text_format": "(1) Noah is a knight\n(2) Liam is a knight\n(3) Ethan is a knight\n(4) Evelyn is a knave\n(5) Luke is a knave\n(6) Chloe is a knave\n(7) Jack is a knave\n(8) Mason is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Noah is a knight. No contradiction is found in their claim that Mason is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Evelyn is a knight or Evelyn is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Mason is not a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Mason is not a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of Liam that Jack is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Luke is a knight if and only if Mason is a knight.", "Luke cannot be a knight, because this would contradict the false claim of Jack that Luke is a knight if and only if Mason is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Ethan is a knight if and only if Liam is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Jack is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Jack is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Jack is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 7), ('lying', 6), ('lying', 6), ('not', ('telling-truth', 7)), ('<=>', ('telling-truth', 2), ('lying', 1)), ('telling-truth', 6), ('<=>', ('telling-truth', 4), ('telling-truth', 7)), ('or', ('telling-truth', 3), ('lying', 3)))", "index": 483}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sebastian, Ethan, David, Ella, Mason, Elizabeth, Luke, and Oliver. Sebastian said, \"Ella is a knave.\" Ethan said, \"Luke is a knight or Elizabeth is a knight.\" According to David, \"Mason is a knight and Elizabeth is a knight\". Ella was heard saying, \"Ethan is a knave if and only if David is a knave\". Mason told you that Luke is a knave and David is a knave. \"Sebastian is a knight and Oliver is a knight,\" Elizabeth claimed. Luke asserted: \"Elizabeth is not a knight\". Oliver stated, \"Ethan is a knight and Sebastian is a knave\". So who is a knight and who is a knave?", "names": ["Sebastian", "Ethan", "David", "Ella", "Mason", "Elizabeth", "Luke", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, false, true, false], "solution_text": "Sebastian is a knight, Ethan is a knight, David is a knave, Ella is a knave, Mason is a knave, Elizabeth is a knave, Luke is a knight, and Oliver is a knave.", "solution_text_format": "(1) Sebastian is a knight\n(2) Ethan is a knight\n(3) David is a knave\n(4) Ella is a knave\n(5) Mason is a knave\n(6) Elizabeth is a knave\n(7) Luke is a knight\n(8) Oliver is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of Sebastian that Ella is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Ethan is a knave if and only if David is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Luke is a knight or Elizabeth is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Elizabeth is not a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Luke that Elizabeth is not a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Sebastian is a knight and Oliver is a knight.", "Oliver cannot be a knight, because this would contradict the false claim of Elizabeth that Sebastian is a knight and Oliver is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Ethan is a knight and Sebastian is a knave.", "David cannot be a knight, because this would contradict the claim of their own that Mason is a knight and Elizabeth is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Mason is a knight and Elizabeth is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Luke is a knave and David is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Luke is a knave and David is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('or', ('telling-truth', 6), ('telling-truth', 5)), ('and', ('telling-truth', 4), ('telling-truth', 5)), ('<=>', ('lying', 1), ('lying', 2)), ('and', ('lying', 6), ('lying', 2)), ('and', ('telling-truth', 0), ('telling-truth', 7)), ('not', ('telling-truth', 5)), ('and', ('telling-truth', 1), ('lying', 0)))", "index": 484}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Logan, Jackson, Aurora, Amelia, Joseph, Luke, Matthew, and Avery. Logan noted, \"Luke is a knight\". In Jackson's words: \"If Logan is a knight then Aurora is a knight\". \"Joseph is a knight or Aurora is a knight,\" Aurora declared. As Amelia put it, \"Aurora is a knight and Jackson is a knight\". Joseph said, \"Luke is a knave and Jackson is a knight.\" Luke said, \"Amelia is a knight.\" Matthew stated, \"Aurora is not a knave\". Avery was heard saying, \"If Luke is a knave then Matthew is a knave\". So who is a knight and who is a knave?", "names": ["Logan", "Jackson", "Aurora", "Amelia", "Joseph", "Luke", "Matthew", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true, true, true], "solution_text": "Logan is a knight, Jackson is a knight, Aurora is a knight, Amelia is a knight, Joseph is a knave, Luke is a knight, Matthew is a knight, and Avery is a knight.", "solution_text_format": "(1) Logan is a knight\n(2) Jackson is a knight\n(3) Aurora is a knight\n(4) Amelia is a knight\n(5) Joseph is a knave\n(6) Luke is a knight\n(7) Matthew is a knight\n(8) Avery is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that Luke is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Amelia is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Aurora is a knight and Jackson is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Joseph is a knight or Aurora is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Luke is a knave and Jackson is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Luke is a knave and Jackson is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that If Logan is a knight then Aurora is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Aurora is not a knave.", "Assume Avery is a knight. No contradiction is found in their claim that If Luke is a knave then Matthew is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 5), ('->', ('telling-truth', 0), ('telling-truth', 2)), ('or', ('telling-truth', 4), ('telling-truth', 2)), ('and', ('telling-truth', 2), ('telling-truth', 1)), ('and', ('lying', 5), ('telling-truth', 1)), ('telling-truth', 3), ('not', ('lying', 2)), ('->', ('lying', 5), ('lying', 6)))", "index": 485}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Liam, David, Lucas, James, Noah, Emily, Alexander, and Olivia. Liam expressed that Olivia is a knave or James is a knave. In David's words: \"Lucas is a knave or James is a knight\". In a statement by Lucas: \"Liam is a knight or Liam is a knave\". James remarked, \"Alexander is a knight\". Noah said that Emily is a knave or Alexander is a knave. \"Alexander is not a knight,\" Emily declared. In a statement by Alexander: \"Lucas is not a knave\". \"Lucas is a knight or Liam is a knight\" - Olivia. So who is a knight and who is a knave?", "names": ["Liam", "David", "Lucas", "James", "Noah", "Emily", "Alexander", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false, true, true], "solution_text": "Liam is a knave, David is a knight, Lucas is a knight, James is a knight, Noah is a knight, Emily is a knave, Alexander is a knight, and Olivia is a knight.", "solution_text_format": "(1) Liam is a knave\n(2) David is a knight\n(3) Lucas is a knight\n(4) James is a knight\n(5) Noah is a knight\n(6) Emily is a knave\n(7) Alexander is a knight\n(8) Olivia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Olivia is a knave or James is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Lucas is a knight or Liam is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Liam is a knight or Liam is a knave.", "James cannot be a knight, because this would contradict the claim of Liam that Olivia is a knave or James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Alexander is a knight.", "Alexander cannot be a knight, because this would contradict the false claim of James that Alexander is a knight.", "Alexander cannot be a knave, because this would contradict the false claim of their own that Lucas is not a knave.", "We have exhausted all possibilities for Alexander and James, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the false claim of their own that Liam is a knight or Liam is a knave.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the false claim of their own that Lucas is a knight or Liam is a knight.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Olivia is a knave or James is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Lucas is a knight or Liam is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Liam is a knight or Liam is a knave.", "Assume James is a knight. No contradiction is found in their claim that Alexander is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Lucas is not a knave.", "Assume David is a knight. No contradiction is found in their claim that Lucas is a knave or James is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Emily is a knave or Alexander is a knave.", "Emily cannot be a knight, because this would contradict the claim of Noah that Emily is a knave or Alexander is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Alexander is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 7), ('lying', 3)), ('or', ('lying', 2), ('telling-truth', 3)), ('or', ('telling-truth', 0), ('lying', 0)), ('telling-truth', 6), ('or', ('lying', 5), ('lying', 6)), ('not', ('telling-truth', 6)), ('not', ('lying', 2)), ('or', ('telling-truth', 2), ('telling-truth', 0)))", "index": 486}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Chloe, James, Sebastian, Aria, Benjamin, Sofia, Harper, and Joseph. Chloe expressed that Chloe is a knight or Joseph is a knight. James told you that If Benjamin is a knight then Sebastian is a knight. Sebastian remarked, \"Sofia is a knight or Chloe is a knave\". \"Sebastian is a knave if and only if Sofia is a knight,\" Aria mentioned. Benjamin expressed that Harper is a knave and Joseph is a knave. In Sofia's words: \"Chloe is not a knave\". Harper said, \"Joseph is a knight and James is a knight.\" According to Joseph, \"If James is a knave then Chloe is a knave\". So who is a knight and who is a knave?", "names": ["Chloe", "James", "Sebastian", "Aria", "Benjamin", "Sofia", "Harper", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true, true, true], "solution_text": "Chloe is a knight, James is a knight, Sebastian is a knight, Aria is a knave, Benjamin is a knave, Sofia is a knight, Harper is a knight, and Joseph is a knight.", "solution_text_format": "(1) Chloe is a knight\n(2) James is a knight\n(3) Sebastian is a knight\n(4) Aria is a knave\n(5) Benjamin is a knave\n(6) Sofia is a knight\n(7) Harper is a knight\n(8) Joseph is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Chloe is a knight or Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If James is a knave then Chloe is a knave.", "Assume James is a knight. No contradiction is found in their claim that If Benjamin is a knight then Sebastian is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Harper is a knave and Joseph is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Harper is a knave and Joseph is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Joseph is a knight and James is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Sofia is a knight or Chloe is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Chloe is not a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave if and only if Sofia is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Sebastian is a knave if and only if Sofia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 0), ('telling-truth', 7)), ('->', ('telling-truth', 4), ('telling-truth', 2)), ('or', ('telling-truth', 5), ('lying', 0)), ('<=>', ('lying', 2), ('telling-truth', 5)), ('and', ('lying', 6), ('lying', 7)), ('not', ('lying', 0)), ('and', ('telling-truth', 7), ('telling-truth', 1)), ('->', ('lying', 1), ('lying', 0)))", "index": 487}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Samuel, Olivia, Mia, Liam, Amelia, Benjamin, Aria, and Matthew. Samuel commented, \"Matthew is a knave\". Olivia commented, \"Amelia is a knight and Samuel is a knave\". Mia was heard saying, \"Amelia is a knave or Benjamin is a knave\". Liam remarked, \"If Olivia is a knight then Liam is a knight\". \"Aria is a knight\" - Amelia. Benjamin said, \"If Aria is a knave then Benjamin is a knight.\" Aria expressed that Liam is a knight if and only if Samuel is a knave. Matthew remarked, \"If Matthew is a knight then Samuel is a knave\". So who is a knight and who is a knave?", "names": ["Samuel", "Olivia", "Mia", "Liam", "Amelia", "Benjamin", "Aria", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true, true, true], "solution_text": "Samuel is a knave, Olivia is a knight, Mia is a knave, Liam is a knight, Amelia is a knight, Benjamin is a knight, Aria is a knight, and Matthew is a knight.", "solution_text_format": "(1) Samuel is a knave\n(2) Olivia is a knight\n(3) Mia is a knave\n(4) Liam is a knight\n(5) Amelia is a knight\n(6) Benjamin is a knight\n(7) Aria is a knight\n(8) Matthew is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that Matthew is a knave.", "Matthew cannot be a knight, because this would contradict the claim of Samuel that Matthew is a knave.", "Matthew cannot be a knave, because this would contradict the false claim of their own that If Matthew is a knight then Samuel is a knave.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Matthew is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that If Matthew is a knight then Samuel is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Amelia is a knight and Samuel is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Aria is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Liam is a knight if and only if Samuel is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that If Olivia is a knight then Liam is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Amelia is a knave or Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Mia that Amelia is a knave or Benjamin is a knave.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that If Aria is a knave then Benjamin is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Amelia is a knave or Benjamin is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Aria is a knave then Benjamin is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 7), ('and', ('telling-truth', 4), ('lying', 0)), ('or', ('lying', 4), ('lying', 5)), ('->', ('telling-truth', 1), ('telling-truth', 3)), ('telling-truth', 6), ('->', ('lying', 6), ('telling-truth', 5)), ('<=>', ('telling-truth', 3), ('lying', 0)), ('->', ('telling-truth', 7), ('lying', 0)))", "index": 488}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Avery, Benjamin, Harper, Amelia, Abigail, Jack, Mason, and Sofia. Avery stated, \"Amelia is a knave and Jack is a knave\". In a statement by Benjamin: \"If Avery is a knight then Mason is a knight\". Harper told you that Benjamin is a knight or Jack is a knight. \"If Benjamin is a knave then Avery is a knave,\" Amelia declared. \"Jack is a knave if and only if Amelia is a knight\" - Abigail. Jack asserted: \"Benjamin is a knave\". \"Benjamin is a knave\" - Mason. \"Amelia is a knight or Benjamin is a knave\" - Sofia. So who is a knight and who is a knave?", "names": ["Avery", "Benjamin", "Harper", "Amelia", "Abigail", "Jack", "Mason", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false, false, true], "solution_text": "Avery is a knave, Benjamin is a knight, Harper is a knight, Amelia is a knight, Abigail is a knight, Jack is a knave, Mason is a knave, and Sofia is a knight.", "solution_text_format": "(1) Avery is a knave\n(2) Benjamin is a knight\n(3) Harper is a knight\n(4) Amelia is a knight\n(5) Abigail is a knight\n(6) Jack is a knave\n(7) Mason is a knave\n(8) Sofia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Amelia is a knave and Jack is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Avery that Amelia is a knave and Jack is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that If Benjamin is a knave then Avery is a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Amelia that If Benjamin is a knave then Avery is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that If Avery is a knight then Mason is a knight.", "Mason cannot be a knight, because this would contradict the false claim of Benjamin that If Avery is a knight then Mason is a knight.", "Mason cannot be a knave, because this would contradict the false claim of their own that Benjamin is a knave.", "We have exhausted all possibilities for Mason, Benjamin, and Amelia, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Amelia is a knave and Jack is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that If Benjamin is a knave then Avery is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Avery is a knight then Mason is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Benjamin is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Benjamin is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Benjamin is a knight or Jack is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Jack is a knave if and only if Amelia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Amelia is a knight or Benjamin is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('lying', 5)), ('->', ('telling-truth', 0), ('telling-truth', 6)), ('or', ('telling-truth', 1), ('telling-truth', 5)), ('->', ('lying', 1), ('lying', 0)), ('<=>', ('lying', 5), ('telling-truth', 3)), ('lying', 1), ('lying', 1), ('or', ('telling-truth', 3), ('lying', 1)))", "index": 489}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Owen, Jack, Michael, Penelope, Liam, Ava, Sofia, and Grace. \"Owen is a knight and Michael is a knight,\" Owen mentioned. Jack said, \"Penelope is not a knight.\" According to Michael, \"Penelope is a knight or Owen is a knave\". Penelope remarked, \"Liam is a knight or Ava is a knight\". Liam said that Sofia is a knight or Penelope is a knave. Ava commented, \"Sofia is a knight and Penelope is a knave\". Sofia said, \"Owen is a knave.\" Grace remarked, \"Sofia is a knight if and only if Penelope is a knave\". So who is a knight and who is a knave?", "names": ["Owen", "Jack", "Michael", "Penelope", "Liam", "Ava", "Sofia", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false, true, false], "solution_text": "Owen is a knave, Jack is a knave, Michael is a knight, Penelope is a knight, Liam is a knight, Ava is a knave, Sofia is a knight, and Grace is a knave.", "solution_text_format": "(1) Owen is a knave\n(2) Jack is a knave\n(3) Michael is a knight\n(4) Penelope is a knight\n(5) Liam is a knight\n(6) Ava is a knave\n(7) Sofia is a knight\n(8) Grace is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Owen is a knight and Michael is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Penelope is a knight or Owen is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Liam is a knight or Ava is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Sofia is a knight or Penelope is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Owen is a knave.", "Sofia cannot be a knave, because this would contradict the claim of Liam that Sofia is a knight or Penelope is a knave.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Sofia is a knight or Penelope is a knave.", "Sofia cannot be a knight, because this would contradict the false claim of Liam that Sofia is a knight or Penelope is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Owen is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Sofia is a knight and Penelope is a knave.", "Ava cannot be a knave, because this would contradict the claim of Penelope that Liam is a knight or Ava is a knight.", "We have exhausted all possibilities for Ava, Sofia, and Liam, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the claim of Michael that Penelope is a knight or Owen is a knave.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Michael.", "Michael cannot be a knave, because this would contradict the claim of Owen that Owen is a knight and Michael is a knight.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Owen is a knight and Michael is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Penelope is a knight or Owen is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Liam is a knight or Ava is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Sofia is a knight or Penelope is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Owen is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Sofia is a knight and Penelope is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Sofia is a knight and Penelope is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Penelope is not a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Penelope is not a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Sofia is a knight if and only if Penelope is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Sofia is a knight if and only if Penelope is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 0), ('telling-truth', 2)), ('not', ('telling-truth', 3)), ('or', ('telling-truth', 3), ('lying', 0)), ('or', ('telling-truth', 4), ('telling-truth', 5)), ('or', ('telling-truth', 6), ('lying', 3)), ('and', ('telling-truth', 6), ('lying', 3)), ('lying', 0), ('<=>', ('telling-truth', 6), ('lying', 3)))", "index": 490}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Olivia, Jack, Charlotte, Aiden, Abigail, Mason, Oliver, and Aurora. Olivia commented, \"Aiden is a knave and Charlotte is a knight\". According to Jack, \"If Aiden is a knave then Olivia is a knave\". Charlotte was heard saying, \"Aurora is a knave or Abigail is a knight\". Aiden told you that If Jack is a knave then Aurora is a knight. Abigail stated, \"Jack is not a knave\". \"Oliver is a knight or Aurora is a knave,\" Mason declared. Oliver expressed that Aurora is not a knight. Aurora said, \"Abigail is a knave and Oliver is a knight.\" So who is a knight and who is a knave?", "names": ["Olivia", "Jack", "Charlotte", "Aiden", "Abigail", "Mason", "Oliver", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true, true, false], "solution_text": "Olivia is a knave, Jack is a knight, Charlotte is a knight, Aiden is a knight, Abigail is a knight, Mason is a knight, Oliver is a knight, and Aurora is a knave.", "solution_text_format": "(1) Olivia is a knave\n(2) Jack is a knight\n(3) Charlotte is a knight\n(4) Aiden is a knight\n(5) Abigail is a knight\n(6) Mason is a knight\n(7) Oliver is a knight\n(8) Aurora is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Aiden is a knave and Charlotte is a knight.", "Aiden cannot be a knight, because this would contradict the claim of Olivia that Aiden is a knave and Charlotte is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that If Jack is a knave then Aurora is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that If Aiden is a knave then Olivia is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that If Aiden is a knave then Olivia is a knave.", "Aurora cannot be a knight, because this would contradict the false claim of Aiden that If Jack is a knave then Aurora is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Abigail is a knave and Oliver is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Jack is not a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Jack is not a knave.", "Oliver cannot be a knight, because this would contradict the false claim of Aurora that Abigail is a knave and Oliver is a knight.", "Oliver cannot be a knave, because this would contradict the false claim of their own that Aurora is not a knight.", "We have exhausted all possibilities for Oliver, Abigail, Aurora, Jack, and Aiden, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Aiden is a knave and Charlotte is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that If Jack is a knave then Aurora is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that If Aiden is a knave then Olivia is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Abigail is a knave and Oliver is a knight.", "Abigail cannot be a knight, because this would contradict the claim of Aurora that Abigail is a knave and Oliver is a knight.", "Abigail cannot be a knave, because this would contradict the false claim of their own that Jack is not a knave.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Abigail is a knave and Oliver is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Jack is not a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Aurora is not a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Aurora is a knave or Abigail is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Oliver is a knight or Aurora is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('telling-truth', 2)), ('->', ('lying', 3), ('lying', 0)), ('or', ('lying', 7), ('telling-truth', 4)), ('->', ('lying', 1), ('telling-truth', 7)), ('not', ('lying', 1)), ('or', ('telling-truth', 6), ('lying', 7)), ('not', ('telling-truth', 7)), ('and', ('lying', 4), ('telling-truth', 6)))", "index": 491}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ava, Alexander, Michael, Benjamin, Henry, Aiden, Logan, and Chloe. In Ava's words: \"Alexander is a knight and Logan is a knight\". Alexander commented, \"Logan is a knave and Henry is a knave\". Michael remarked, \"Ava is not a knave\". \"If Henry is a knight then Ava is a knave,\" Benjamin declared. Henry commented, \"If Alexander is a knight then Ava is a knave\". Aiden expressed that Aiden is a knight or Alexander is a knave. Logan told you that Benjamin is a knight if and only if Michael is a knight. Chloe stated, \"Alexander is a knave if and only if Alexander is a knight\". So who is a knight and who is a knave?", "names": ["Ava", "Alexander", "Michael", "Benjamin", "Henry", "Aiden", "Logan", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true, false, false], "solution_text": "Ava is a knave, Alexander is a knave, Michael is a knave, Benjamin is a knight, Henry is a knight, Aiden is a knight, Logan is a knave, and Chloe is a knave.", "solution_text_format": "(1) Ava is a knave\n(2) Alexander is a knave\n(3) Michael is a knave\n(4) Benjamin is a knight\n(5) Henry is a knight\n(6) Aiden is a knight\n(7) Logan is a knave\n(8) Chloe is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Alexander is a knight and Logan is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Logan is a knave and Henry is a knave.", "Logan cannot be a knight, because this would contradict the claim of Alexander that Logan is a knave and Henry is a knave.", "Logan cannot be a knave, because this would contradict the claim of Ava that Alexander is a knight and Logan is a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Alexander.", "Alexander cannot be a knave, because this would contradict the claim of Ava that Alexander is a knight and Logan is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Alexander is a knight and Logan is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Logan is a knave and Henry is a knave.", "Logan cannot be a knight, because this would contradict the false claim of Ava that Alexander is a knight and Logan is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Benjamin is a knight if and only if Michael is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Henry is a knight then Ava is a knave.", "Henry cannot be a knight, because this would contradict the claim of Alexander that Logan is a knave and Henry is a knave.", "Henry cannot be a knave, because this would contradict the false claim of their own that If Alexander is a knight then Ava is a knave.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that If Henry is a knight then Ava is a knave.", "We have exhausted all possibilities for Benjamin and Logan, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Logan is a knave and Henry is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Benjamin is a knight if and only if Michael is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Henry is a knight then Ava is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Alexander is a knight then Ava is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Ava is not a knave.", "Michael cannot be a knave, because this would contradict the claim of Logan that Benjamin is a knight if and only if Michael is a knight.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the false claim of their own that If Alexander is a knight then Ava is a knave.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that If Henry is a knight then Ava is a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Benjamin is a knight if and only if Michael is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Henry is a knight then Ava is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Alexander is a knight then Ava is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Ava is not a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Ava is not a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Aiden is a knight or Alexander is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Alexander is a knave if and only if Alexander is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Alexander is a knave if and only if Alexander is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('telling-truth', 6)), ('and', ('lying', 6), ('lying', 4)), ('not', ('lying', 0)), ('->', ('telling-truth', 4), ('lying', 0)), ('->', ('telling-truth', 1), ('lying', 0)), ('or', ('telling-truth', 5), ('lying', 1)), ('<=>', ('telling-truth', 3), ('telling-truth', 2)), ('<=>', ('lying', 1), ('telling-truth', 1)))", "index": 492}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lily, Daniel, Evelyn, William, Alexander, Henry, Olivia, and Emma. Lily remarked, \"William is a knave and Daniel is a knave\". \"Alexander is a knight if and only if Daniel is a knight\" - Daniel. Evelyn noted, \"If Henry is a knave then Daniel is a knave\". \"If Alexander is a knave then Olivia is a knight\" - William. Alexander was heard saying, \"Henry is a knight if and only if Emma is a knight\". Henry noted, \"William is a knave or Olivia is a knave\". Olivia expressed that Daniel is a knight or William is a knight. As Emma put it, \"Lily is a knight if and only if Daniel is a knave\". So who is a knight and who is a knave?", "names": ["Lily", "Daniel", "Evelyn", "William", "Alexander", "Henry", "Olivia", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false, true, false], "solution_text": "Lily is a knave, Daniel is a knave, Evelyn is a knight, William is a knight, Alexander is a knight, Henry is a knave, Olivia is a knight, and Emma is a knave.", "solution_text_format": "(1) Lily is a knave\n(2) Daniel is a knave\n(3) Evelyn is a knight\n(4) William is a knight\n(5) Alexander is a knight\n(6) Henry is a knave\n(7) Olivia is a knight\n(8) Emma is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that William is a knave and Daniel is a knave.", "William cannot be a knight, because this would contradict the claim of Lily that William is a knave and Daniel is a knave.", "Assume William is a knave. No contradiction is found in their false claim that If Alexander is a knave then Olivia is a knight.", "Alexander cannot be a knight, because this would contradict the false claim of William that If Alexander is a knave then Olivia is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Henry is a knight if and only if Emma is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that William is a knave or Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the false claim of William that If Alexander is a knave then Olivia is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Daniel is a knight or William is a knight.", "Daniel cannot be a knight, because this would contradict the claim of Lily that William is a knave and Daniel is a knave.", "Daniel cannot be a knave, because this would contradict the false claim of their own that Alexander is a knight if and only if Daniel is a knight.", "We have exhausted all possibilities for Daniel and Olivia, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the false claim of their own that William is a knave or Olivia is a knave.", "We have exhausted all possibilities for Henry, Alexander, and William, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that William is a knave and Daniel is a knave.", "Assume William is a knight. No contradiction is found in their claim that If Alexander is a knave then Olivia is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Henry is a knight if and only if Emma is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that William is a knave or Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Henry that William is a knave or Olivia is a knave.", "Olivia cannot be a knave, because this would contradict the false claim of their own that Daniel is a knight or William is a knight.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that William is a knave or Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Daniel is a knight or William is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Alexander is a knight if and only if Daniel is a knight.", "Emma cannot be a knight, because this would contradict the claim of Alexander that Henry is a knight if and only if Emma is a knight.", "Emma cannot be a knave, because this would contradict the false claim of their own that Lily is a knight if and only if Daniel is a knave.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Alexander is a knight if and only if Daniel is a knight.", "Emma cannot be a knight, because this would contradict the claim of Alexander that Henry is a knight if and only if Emma is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Lily is a knight if and only if Daniel is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Henry is a knave then Daniel is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('lying', 1)), ('<=>', ('telling-truth', 4), ('telling-truth', 1)), ('->', ('lying', 5), ('lying', 1)), ('->', ('lying', 4), ('telling-truth', 6)), ('<=>', ('telling-truth', 5), ('telling-truth', 7)), ('or', ('lying', 3), ('lying', 6)), ('or', ('telling-truth', 1), ('telling-truth', 3)), ('<=>', ('telling-truth', 0), ('lying', 1)))", "index": 493}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Chloe, Scarlett, Sofia, Sophia, Grace, Lily, Joseph, and Amelia. Chloe told you that Amelia is a knave or Joseph is a knave. Scarlett remarked, \"If Sofia is a knight then Sophia is a knave\". \"Joseph is a knave and Lily is a knave,\" Sofia claimed. In Sophia's words: \"Joseph is a knave or Sofia is a knight\". Grace remarked, \"Sophia is a knave\". \"Amelia is a knave\" - Lily. Joseph was heard saying, \"Sophia is a knight and Grace is a knight\". Amelia told you that Chloe is not a knave. So who is a knight and who is a knave?", "names": ["Chloe", "Scarlett", "Sofia", "Sophia", "Grace", "Lily", "Joseph", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, false, false, true], "solution_text": "Chloe is a knight, Scarlett is a knave, Sofia is a knight, Sophia is a knight, Grace is a knave, Lily is a knave, Joseph is a knave, and Amelia is a knight.", "solution_text_format": "(1) Chloe is a knight\n(2) Scarlett is a knave\n(3) Sofia is a knight\n(4) Sophia is a knight\n(5) Grace is a knave\n(6) Lily is a knave\n(7) Joseph is a knave\n(8) Amelia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Amelia is a knave or Joseph is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Chloe is not a knave.", "Joseph cannot be a knight, because this would contradict the claim of Chloe that Amelia is a knave or Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Sophia is a knight and Grace is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Joseph is a knave or Sofia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Joseph is a knave and Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of Sofia that Joseph is a knave and Lily is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Amelia is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Sophia is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Sophia is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that If Sofia is a knight then Sophia is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that If Sofia is a knight then Sophia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 7), ('lying', 6)), ('->', ('telling-truth', 2), ('lying', 3)), ('and', ('lying', 6), ('lying', 5)), ('or', ('lying', 6), ('telling-truth', 2)), ('lying', 3), ('lying', 7), ('and', ('telling-truth', 3), ('telling-truth', 4)), ('not', ('lying', 0)))", "index": 494}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mason, Noah, Liam, Jack, Jackson, Harper, Amelia, and David. Mason said, \"If Jack is a knave then Jackson is a knight.\" Noah said, \"If Liam is a knight then Jackson is a knight.\" Liam noted, \"David is not a knight\". Jack was heard saying, \"David is a knave\". Jackson remarked, \"Harper is a knight and David is a knave\". Harper said, \"If Amelia is a knave then Jack is a knight.\" Amelia said that If Mason is a knave then Jack is a knight. \"Liam is a knight if and only if Mason is a knight\" - David. So who is a knight and who is a knave?", "names": ["Mason", "Noah", "Liam", "Jack", "Jackson", "Harper", "Amelia", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, false, false, true], "solution_text": "Mason is a knave, Noah is a knight, Liam is a knave, Jack is a knave, Jackson is a knave, Harper is a knave, Amelia is a knave, and David is a knight.", "solution_text_format": "(1) Mason is a knave\n(2) Noah is a knight\n(3) Liam is a knave\n(4) Jack is a knave\n(5) Jackson is a knave\n(6) Harper is a knave\n(7) Amelia is a knave\n(8) David is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that If Jack is a knave then Jackson is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that David is a knave.", "David cannot be a knight, because this would contradict the claim of Jack that David is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Liam is a knight if and only if Mason is a knight.", "Liam cannot be a knight, because this would contradict the false claim of David that Liam is a knight if and only if Mason is a knight.", "Liam cannot be a knave, because this would contradict the false claim of their own that David is not a knight.", "We have exhausted all possibilities for Liam and David, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that David is a knave.", "Assume David is a knight. No contradiction is found in their claim that Liam is a knight if and only if Mason is a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that David is not a knight.", "Liam cannot be a knave, because this would contradict the claim of David that Liam is a knight if and only if Mason is a knight.", "We have exhausted all possibilities for Liam, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the false claim of Jack that David is a knave.", "We have exhausted all possibilities for David and Jack, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that If Jack is a knave then Jackson is a knight.", "Jack cannot be a knight, because this would contradict the false claim of Mason that If Jack is a knave then Jackson is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that David is a knave.", "Assume David is a knight. No contradiction is found in their claim that Liam is a knight if and only if Mason is a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that David is not a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that David is not a knight.", "Jackson cannot be a knight, because this would contradict the false claim of Mason that If Jack is a knave then Jackson is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Harper is a knight and David is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that If Amelia is a knave then Jack is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that If Mason is a knave then Jack is a knight.", "Amelia cannot be a knave, because this would contradict the claim of Harper that If Amelia is a knave then Jack is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that If Amelia is a knave then Jack is a knight.", "Amelia cannot be a knight, because this would contradict the false claim of Harper that If Amelia is a knave then Jack is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that If Mason is a knave then Jack is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that If Liam is a knight then Jackson is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('telling-truth', 4)), ('->', ('telling-truth', 2), ('telling-truth', 4)), ('not', ('telling-truth', 7)), ('lying', 7), ('and', ('telling-truth', 5), ('lying', 7)), ('->', ('lying', 6), ('telling-truth', 3)), ('->', ('lying', 0), ('telling-truth', 3)), ('<=>', ('telling-truth', 2), ('telling-truth', 0)))", "index": 495}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Abigail, Jackson, Luke, Emma, Jack, Michael, Henry, and Grace. In Abigail's words: \"Jackson is a knave and Emma is a knave\". \"Jack is not a knight,\" Jackson declared. In Luke's words: \"Jack is a knight\". According to Emma, \"Abigail is not a knight\". In Jack's words: \"Grace is a knight or Henry is a knave\". Michael remarked, \"Grace is a knight and Henry is a knight\". Henry told you that Abigail is a knave and Emma is a knight. According to Grace, \"Jackson is a knight and Luke is a knave\". So who is a knight and who is a knave?", "names": ["Abigail", "Jackson", "Luke", "Emma", "Jack", "Michael", "Henry", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, false, false, false], "solution_text": "Abigail is a knight, Jackson is a knave, Luke is a knight, Emma is a knave, Jack is a knight, Michael is a knave, Henry is a knave, and Grace is a knave.", "solution_text_format": "(1) Abigail is a knight\n(2) Jackson is a knave\n(3) Luke is a knight\n(4) Emma is a knave\n(5) Jack is a knight\n(6) Michael is a knave\n(7) Henry is a knave\n(8) Grace is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Jackson is a knave and Emma is a knave.", "Jackson cannot be a knight, because this would contradict the claim of Abigail that Jackson is a knave and Emma is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Jack is not a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Grace is a knight or Henry is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Jackson is a knight and Luke is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Jackson is a knight and Luke is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Jack is a knight.", "Henry cannot be a knight, because this would contradict the claim of Jack that Grace is a knight or Henry is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Abigail is a knave and Emma is a knight.", "Emma cannot be a knight, because this would contradict the claim of Abigail that Jackson is a knave and Emma is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Abigail is not a knight.", "Michael cannot be a knight, because this would contradict the claim of their own that Grace is a knight and Henry is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Grace is a knight and Henry is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 1), ('lying', 3)), ('not', ('telling-truth', 4)), ('telling-truth', 4), ('not', ('telling-truth', 0)), ('or', ('telling-truth', 7), ('lying', 6)), ('and', ('telling-truth', 7), ('telling-truth', 6)), ('and', ('lying', 0), ('telling-truth', 3)), ('and', ('telling-truth', 1), ('lying', 2)))", "index": 496}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mia, Joseph, Sofia, Evelyn, Luke, Elizabeth, Lucas, and Aurora. Mia told you that Aurora is a knave and Luke is a knight. According to Joseph, \"Mia is not a knight\". As Sofia put it, \"Luke is not a knave\". \"Joseph is a knave,\" Evelyn mentioned. Luke expressed that Mia is a knave and Evelyn is a knight. As Elizabeth put it, \"Mia is not a knave\". Lucas said that Evelyn is a knight. \"Sofia is not a knave,\" Aurora mentioned. So who is a knight and who is a knave?", "names": ["Mia", "Joseph", "Sofia", "Evelyn", "Luke", "Elizabeth", "Lucas", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, false, false, false], "solution_text": "Mia is a knave, Joseph is a knight, Sofia is a knave, Evelyn is a knave, Luke is a knave, Elizabeth is a knave, Lucas is a knave, and Aurora is a knave.", "solution_text_format": "(1) Mia is a knave\n(2) Joseph is a knight\n(3) Sofia is a knave\n(4) Evelyn is a knave\n(5) Luke is a knave\n(6) Elizabeth is a knave\n(7) Lucas is a knave\n(8) Aurora is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Aurora is a knave and Luke is a knight.", "Aurora cannot be a knight, because this would contradict the claim of Mia that Aurora is a knave and Luke is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Sofia is not a knave.", "Sofia cannot be a knight, because this would contradict the false claim of Aurora that Sofia is not a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Luke is not a knave.", "Luke cannot be a knight, because this would contradict the false claim of Sofia that Luke is not a knave.", "Luke cannot be a knave, because this would contradict the claim of Mia that Aurora is a knave and Luke is a knight.", "We have exhausted all possibilities for Luke, Sofia, and Aurora, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Aurora is a knave and Luke is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Sofia is not a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Luke is not a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Mia is a knave and Evelyn is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Evelyn that Joseph is a knave.", "Joseph cannot be a knave, because this would contradict the false claim of their own that Mia is not a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the claim of Luke that Mia is a knave and Evelyn is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the claim of Sofia that Luke is not a knave.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Sofia.", "Sofia cannot be a knave, because this would contradict the claim of Aurora that Sofia is not a knave.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Sofia is not a knave.", "Sofia cannot be a knight, because this would contradict the false claim of Aurora that Sofia is not a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Luke is not a knave.", "Luke cannot be a knight, because this would contradict the false claim of Mia that Aurora is a knave and Luke is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Mia is a knave and Evelyn is a knight.", "Evelyn cannot be a knight, because this would contradict the false claim of Luke that Mia is a knave and Evelyn is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Joseph is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Mia is not a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Mia is not a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Mia is not a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Evelyn is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Evelyn is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 7), ('telling-truth', 4)), ('not', ('telling-truth', 0)), ('not', ('lying', 4)), ('lying', 1), ('and', ('lying', 0), ('telling-truth', 3)), ('not', ('lying', 0)), ('telling-truth', 3), ('not', ('lying', 2)))", "index": 497}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Penelope, Lucas, Ella, Samuel, David, Noah, Liam, and Sebastian. \"Ella is a knight or Samuel is a knight,\" Penelope declared. \"Sebastian is a knave and Liam is a knight\" - Lucas. According to Ella, \"If Samuel is a knight then Noah is a knave\". Samuel commented, \"If David is a knight then Ella is a knight\". David told you that David is a knight or Ella is a knave. According to Noah, \"David is not a knight\". Liam said, \"If Sebastian is a knave then Penelope is a knave.\" Sebastian said, \"David is not a knight.\" So who is a knight and who is a knave?", "names": ["Penelope", "Lucas", "Ella", "Samuel", "David", "Noah", "Liam", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false, false, false], "solution_text": "Penelope is a knight, Lucas is a knave, Ella is a knight, Samuel is a knight, David is a knight, Noah is a knave, Liam is a knave, and Sebastian is a knave.", "solution_text_format": "(1) Penelope is a knight\n(2) Lucas is a knave\n(3) Ella is a knight\n(4) Samuel is a knight\n(5) David is a knight\n(6) Noah is a knave\n(7) Liam is a knave\n(8) Sebastian is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that Ella is a knight or Samuel is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that If Samuel is a knight then Noah is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that If David is a knight then Ella is a knight.", "Assume David is a knight. No contradiction is found in their claim that David is a knight or Ella is a knave.", "Noah cannot be a knight, because this would contradict the claim of Ella that If Samuel is a knight then Noah is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that David is not a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Sebastian is a knave and Liam is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of Lucas that Sebastian is a knave and Liam is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that David is not a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that If Sebastian is a knave then Penelope is a knave.", "Liam cannot be a knave, because this would contradict the claim of Lucas that Sebastian is a knave and Liam is a knight.", "We have exhausted all possibilities for Liam and Sebastian, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Sebastian is a knave and Liam is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that David is not a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that David is not a knight.", "Liam cannot be a knight, because this would contradict the false claim of Lucas that Sebastian is a knave and Liam is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that If Sebastian is a knave then Penelope is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('telling-truth', 3)), ('and', ('lying', 7), ('telling-truth', 6)), ('->', ('telling-truth', 3), ('lying', 5)), ('->', ('telling-truth', 4), ('telling-truth', 2)), ('or', ('telling-truth', 4), ('lying', 2)), ('not', ('telling-truth', 4)), ('->', ('lying', 7), ('lying', 0)), ('not', ('telling-truth', 4)))", "index": 498}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lily, Emily, Isabella, Luke, Abigail, Sophia, Owen, and James. Lily asserted: \"Abigail is a knight\". Emily said, \"Lily is a knight.\" Isabella said that Emily is a knave. \"Isabella is a knave and Emily is a knight,\" Luke mentioned. In Abigail's words: \"James is a knave\". As Sophia put it, \"Isabella is not a knight\". \"Isabella is a knave if and only if Sophia is a knight,\" Owen mentioned. James asserted: \"If Sophia is a knight then Luke is a knight\". So who is a knight and who is a knave?", "names": ["Lily", "Emily", "Isabella", "Luke", "Abigail", "Sophia", "Owen", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, false, true, true], "solution_text": "Lily is a knave, Emily is a knave, Isabella is a knight, Luke is a knave, Abigail is a knave, Sophia is a knave, Owen is a knight, and James is a knight.", "solution_text_format": "(1) Lily is a knave\n(2) Emily is a knave\n(3) Isabella is a knight\n(4) Luke is a knave\n(5) Abigail is a knave\n(6) Sophia is a knave\n(7) Owen is a knight\n(8) James is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that James is a knave.", "James cannot be a knight, because this would contradict the claim of Abigail that James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that If Sophia is a knight then Luke is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Isabella is not a knight.", "Isabella cannot be a knight, because this would contradict the claim of Sophia that Isabella is not a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Lily is a knight.", "Luke cannot be a knight, because this would contradict the false claim of James that If Sophia is a knight then Luke is a knight.", "Luke cannot be a knave, because this would contradict the false claim of their own that Isabella is a knave and Emily is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the false claim of their own that Lily is a knight.", "We have exhausted all possibilities for Emily and Isabella, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the false claim of James that If Sophia is a knight then Luke is a knight.", "We have exhausted all possibilities for Sophia and James, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the claim of Lily that Abigail is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Abigail is a knight.", "Abigail cannot be a knight, because this would contradict the false claim of Lily that Abigail is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that James is a knave.", "Assume James is a knight. No contradiction is found in their claim that If Sophia is a knight then Luke is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Isabella is not a knight.", "Isabella cannot be a knight, because this would contradict the claim of Sophia that Isabella is not a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Lily is a knight.", "Emily cannot be a knave, because this would contradict the false claim of Isabella that Emily is a knave.", "We have exhausted all possibilities for Emily and Isabella, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Isabella is not a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Lily is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Lily is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Isabella is a knave and Emily is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Isabella is a knave and Emily is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Isabella is a knave if and only if Sophia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('telling-truth', 0), ('lying', 1), ('and', ('lying', 2), ('telling-truth', 1)), ('lying', 7), ('not', ('telling-truth', 2)), ('<=>', ('lying', 2), ('telling-truth', 5)), ('->', ('telling-truth', 5), ('telling-truth', 3)))", "index": 499}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ethan, Harper, Isabella, Logan, Jack, Daniel, Elizabeth, and David. As Ethan put it, \"Isabella is a knight if and only if David is a knave\". Harper stated, \"Jack is not a knave\". Isabella expressed that Ethan is not a knave. Logan noted, \"Ethan is a knave or Harper is a knave\". As Jack put it, \"Isabella is a knave if and only if David is a knave\". Daniel told you that If David is a knight then Logan is a knight. \"Isabella is a knight and Ethan is a knight\" - Elizabeth. According to David, \"Isabella is a knight if and only if Daniel is a knave\". So who is a knight and who is a knave?", "names": ["Ethan", "Harper", "Isabella", "Logan", "Jack", "Daniel", "Elizabeth", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true, true, false], "solution_text": "Ethan is a knight, Harper is a knave, Isabella is a knight, Logan is a knight, Jack is a knave, Daniel is a knight, Elizabeth is a knight, and David is a knave.", "solution_text_format": "(1) Ethan is a knight\n(2) Harper is a knave\n(3) Isabella is a knight\n(4) Logan is a knight\n(5) Jack is a knave\n(6) Daniel is a knight\n(7) Elizabeth is a knight\n(8) David is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Isabella is a knight if and only if David is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Ethan is not a knave.", "David cannot be a knight, because this would contradict the claim of Ethan that Isabella is a knight if and only if David is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Isabella is a knight if and only if Daniel is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that If David is a knight then Logan is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Ethan is a knave or Harper is a knave.", "Harper cannot be a knight, because this would contradict the claim of Logan that Ethan is a knave or Harper is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Jack is not a knave.", "Jack cannot be a knight, because this would contradict the false claim of Harper that Jack is not a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Isabella is a knave if and only if David is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Isabella is a knight and Ethan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('lying', 7)), ('not', ('lying', 4)), ('not', ('lying', 0)), ('or', ('lying', 0), ('lying', 1)), ('<=>', ('lying', 2), ('lying', 7)), ('->', ('telling-truth', 7), ('telling-truth', 3)), ('and', ('telling-truth', 2), ('telling-truth', 0)), ('<=>', ('telling-truth', 2), ('lying', 5)))", "index": 500}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Amelia, Logan, Abigail, Noah, Grace, Sophia, Lily, and Scarlett. \"Lily is not a knight,\" Amelia declared. Logan commented, \"Lily is not a knave\". Abigail remarked, \"If Logan is a knave then Sophia is a knight\". In Noah's words: \"Grace is a knave or Sophia is a knave\". Grace asserted: \"Amelia is a knight\". \"Amelia is a knight if and only if Grace is a knight,\" Sophia claimed. According to Lily, \"If Scarlett is a knight then Amelia is a knave\". In Scarlett's words: \"Grace is a knight and Lily is a knight\". So who is a knight and who is a knave?", "names": ["Amelia", "Logan", "Abigail", "Noah", "Grace", "Sophia", "Lily", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true, true, false], "solution_text": "Amelia is a knave, Logan is a knight, Abigail is a knight, Noah is a knight, Grace is a knave, Sophia is a knight, Lily is a knight, and Scarlett is a knave.", "solution_text_format": "(1) Amelia is a knave\n(2) Logan is a knight\n(3) Abigail is a knight\n(4) Noah is a knight\n(5) Grace is a knave\n(6) Sophia is a knight\n(7) Lily is a knight\n(8) Scarlett is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Amelia is a knight. No contradiction is found in their claim that Lily is not a knight.", "Lily cannot be a knight, because this would contradict the claim of Amelia that Lily is not a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that If Scarlett is a knight then Amelia is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Grace is a knight and Lily is a knight.", "Scarlett cannot be a knave, because this would contradict the false claim of Lily that If Scarlett is a knight then Amelia is a knave.", "We have exhausted all possibilities for Scarlett and Lily, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Lily is not a knight.", "Assume Lily is a knight. No contradiction is found in their claim that If Scarlett is a knight then Amelia is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Grace is a knight and Lily is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Amelia is a knight.", "Grace cannot be a knave, because this would contradict the claim of Scarlett that Grace is a knight and Lily is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Grace is a knight and Lily is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Amelia is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Amelia is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Lily is not a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that If Logan is a knave then Sophia is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Amelia is a knight if and only if Grace is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Grace is a knave or Sophia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 6)), ('not', ('lying', 6)), ('->', ('lying', 1), ('telling-truth', 5)), ('or', ('lying', 4), ('lying', 5)), ('telling-truth', 0), ('<=>', ('telling-truth', 0), ('telling-truth', 4)), ('->', ('telling-truth', 7), ('lying', 0)), ('and', ('telling-truth', 4), ('telling-truth', 6)))", "index": 501}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Amelia, Harper, David, Ethan, Penelope, Emily, Joseph, and Sofia. Amelia remarked, \"If Ethan is a knave then Ethan is a knight\". Harper asserted: \"Amelia is a knight and Joseph is a knight\". David stated, \"Joseph is a knave or Harper is a knight\". According to Ethan, \"Sofia is not a knave\". Penelope told you that Harper is not a knight. Emily said, \"Emily is a knight or David is a knight.\" Joseph was heard saying, \"If Emily is a knave then Joseph is a knight\". As Sofia put it, \"Harper is a knight if and only if Ethan is a knight\". So who is a knight and who is a knave?", "names": ["Amelia", "Harper", "David", "Ethan", "Penelope", "Emily", "Joseph", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true, true, true], "solution_text": "Amelia is a knight, Harper is a knight, David is a knight, Ethan is a knight, Penelope is a knave, Emily is a knight, Joseph is a knight, and Sofia is a knight.", "solution_text_format": "(1) Amelia is a knight\n(2) Harper is a knight\n(3) David is a knight\n(4) Ethan is a knight\n(5) Penelope is a knave\n(6) Emily is a knight\n(7) Joseph is a knight\n(8) Sofia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Amelia is a knight. No contradiction is found in their claim that If Ethan is a knave then Ethan is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Sofia is not a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Harper is a knight if and only if Ethan is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Amelia is a knight and Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Emily is a knave then Joseph is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Emily is a knight or David is a knight.", "Assume David is a knight. No contradiction is found in their claim that Joseph is a knave or Harper is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Harper is not a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Harper is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('telling-truth', 3)), ('and', ('telling-truth', 0), ('telling-truth', 6)), ('or', ('lying', 6), ('telling-truth', 1)), ('not', ('lying', 7)), ('not', ('telling-truth', 1)), ('or', ('telling-truth', 5), ('telling-truth', 2)), ('->', ('lying', 5), ('telling-truth', 6)), ('<=>', ('telling-truth', 1), ('telling-truth', 3)))", "index": 502}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Isabella, Ella, David, Victoria, Sebastian, Henry, Avery, and Joseph. In Isabella's words: \"Avery is not a knight\". Ella remarked, \"Joseph is a knight and Avery is a knave\". \"Joseph is a knave if and only if Avery is a knight,\" David mentioned. Victoria said, \"Sebastian is a knave if and only if Avery is a knave.\" In Sebastian's words: \"Joseph is a knight if and only if Ella is a knight\". Henry commented, \"Sebastian is a knight and Joseph is a knave\". \"David is a knight,\" Avery claimed. Joseph said that David is a knight. So who is a knight and who is a knave?", "names": ["Isabella", "Ella", "David", "Victoria", "Sebastian", "Henry", "Avery", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true, false, false], "solution_text": "Isabella is a knight, Ella is a knave, David is a knave, Victoria is a knave, Sebastian is a knight, Henry is a knight, Avery is a knave, and Joseph is a knave.", "solution_text_format": "(1) Isabella is a knight\n(2) Ella is a knave\n(3) David is a knave\n(4) Victoria is a knave\n(5) Sebastian is a knight\n(6) Henry is a knight\n(7) Avery is a knave\n(8) Joseph is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Avery is not a knight.", "Avery cannot be a knight, because this would contradict the claim of Isabella that Avery is not a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that David is a knight.", "David cannot be a knight, because this would contradict the false claim of Avery that David is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Joseph is a knave if and only if Avery is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of David that Joseph is a knave if and only if Avery is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that David is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Joseph is a knight and Avery is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Joseph is a knight and Avery is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Sebastian is a knave if and only if Avery is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Victoria that Sebastian is a knave if and only if Avery is a knave.", "Sebastian cannot be a knave, because this would contradict the false claim of their own that Joseph is a knight if and only if Ella is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Sebastian is a knave if and only if Avery is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Joseph is a knight if and only if Ella is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Sebastian is a knight and Joseph is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 6)), ('and', ('telling-truth', 7), ('lying', 6)), ('<=>', ('lying', 7), ('telling-truth', 6)), ('<=>', ('lying', 4), ('lying', 6)), ('<=>', ('telling-truth', 7), ('telling-truth', 1)), ('and', ('telling-truth', 4), ('lying', 7)), ('telling-truth', 2), ('telling-truth', 2))", "index": 503}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Victoria, Matthew, Samuel, Olivia, Oliver, Mia, Joseph, and Chloe. Victoria was heard saying, \"Chloe is a knight\". \"Chloe is a knave and Olivia is a knave,\" Matthew mentioned. \"Oliver is a knave if and only if Joseph is a knave,\" Samuel declared. Olivia was heard saying, \"Oliver is a knight\". \"Samuel is a knave and Samuel is a knight,\" Oliver declared. Mia was heard saying, \"Mia is a knight and Chloe is a knave\". \"Oliver is a knight or Olivia is a knight\" - Joseph. Chloe stated, \"Samuel is a knave or Olivia is a knave\". So who is a knight and who is a knave?", "names": ["Victoria", "Matthew", "Samuel", "Olivia", "Oliver", "Mia", "Joseph", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, false, false, true], "solution_text": "Victoria is a knight, Matthew is a knave, Samuel is a knight, Olivia is a knave, Oliver is a knave, Mia is a knave, Joseph is a knave, and Chloe is a knight.", "solution_text_format": "(1) Victoria is a knight\n(2) Matthew is a knave\n(3) Samuel is a knight\n(4) Olivia is a knave\n(5) Oliver is a knave\n(6) Mia is a knave\n(7) Joseph is a knave\n(8) Chloe is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that Chloe is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Samuel is a knave or Olivia is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Oliver is a knave if and only if Joseph is a knave.", "Oliver cannot be a knight, because this would contradict the claim of their own that Samuel is a knave and Samuel is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Samuel is a knave and Samuel is a knight.", "Joseph cannot be a knight, because this would contradict the claim of Samuel that Oliver is a knave if and only if Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Oliver is a knight or Olivia is a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that Oliver is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Oliver is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Chloe is a knave and Olivia is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Chloe is a knave and Olivia is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Mia is a knight and Chloe is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Mia is a knight and Chloe is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 7), ('and', ('lying', 7), ('lying', 3)), ('<=>', ('lying', 4), ('lying', 6)), ('telling-truth', 4), ('and', ('lying', 2), ('telling-truth', 2)), ('and', ('telling-truth', 5), ('lying', 7)), ('or', ('telling-truth', 4), ('telling-truth', 3)), ('or', ('lying', 2), ('lying', 3)))", "index": 504}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sofia, Henry, Ava, Victoria, Abigail, Avery, Jacob, and Charlotte. Sofia asserted: \"Victoria is a knave\". \"Victoria is not a knave,\" Henry claimed. \"Abigail is a knave\" - Ava. Victoria stated, \"If Avery is a knave then Charlotte is a knave\". Abigail said, \"Victoria is a knight if and only if Avery is a knight.\" \"Charlotte is a knave or Abigail is a knight,\" Avery declared. Jacob was heard saying, \"Ava is a knave if and only if Charlotte is a knave\". Charlotte said, \"Victoria is not a knave.\" So who is a knight and who is a knave?", "names": ["Sofia", "Henry", "Ava", "Victoria", "Abigail", "Avery", "Jacob", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true, false, true], "solution_text": "Sofia is a knave, Henry is a knight, Ava is a knave, Victoria is a knight, Abigail is a knight, Avery is a knight, Jacob is a knave, and Charlotte is a knight.", "solution_text_format": "(1) Sofia is a knave\n(2) Henry is a knight\n(3) Ava is a knave\n(4) Victoria is a knight\n(5) Abigail is a knight\n(6) Avery is a knight\n(7) Jacob is a knave\n(8) Charlotte is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Victoria is a knave.", "Victoria cannot be a knight, because this would contradict the claim of Sofia that Victoria is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that If Avery is a knave then Charlotte is a knave.", "Avery cannot be a knight, because this would contradict the false claim of Victoria that If Avery is a knave then Charlotte is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Charlotte is a knave or Abigail is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Victoria is not a knave.", "Charlotte cannot be a knave, because this would contradict the false claim of Victoria that If Avery is a knave then Charlotte is a knave.", "We have exhausted all possibilities for Charlotte, Avery, and Victoria, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that If Avery is a knave then Charlotte is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Charlotte is a knave or Abigail is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Victoria is not a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Avery is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Victoria is not a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Abigail is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Abigail is a knave.", "Jacob cannot be a knight, because this would contradict the claim of their own that Ava is a knave if and only if Charlotte is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Ava is a knave if and only if Charlotte is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('not', ('lying', 3)), ('lying', 4), ('->', ('lying', 5), ('lying', 7)), ('<=>', ('telling-truth', 3), ('telling-truth', 5)), ('or', ('lying', 7), ('telling-truth', 4)), ('<=>', ('lying', 2), ('lying', 7)), ('not', ('lying', 3)))", "index": 505}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Michael, Sophia, Victoria, Owen, David, Henry, Avery, and Evelyn. \"Victoria is a knave,\" Michael mentioned. \"Victoria is a knight\" - Sophia. Victoria was heard saying, \"If Owen is a knight then Henry is a knight\". Owen asserted: \"Sophia is a knave\". David stated, \"Owen is a knave and Michael is a knave\". Henry said that Owen is not a knave. Avery told you that Victoria is a knave or Victoria is a knight. Evelyn remarked, \"If Owen is a knight then Henry is a knave\". So who is a knight and who is a knave?", "names": ["Michael", "Sophia", "Victoria", "Owen", "David", "Henry", "Avery", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, false, true, true], "solution_text": "Michael is a knave, Sophia is a knight, Victoria is a knight, Owen is a knave, David is a knight, Henry is a knave, Avery is a knight, and Evelyn is a knight.", "solution_text_format": "(1) Michael is a knave\n(2) Sophia is a knight\n(3) Victoria is a knight\n(4) Owen is a knave\n(5) David is a knight\n(6) Henry is a knave\n(7) Avery is a knight\n(8) Evelyn is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Victoria is a knave.", "Victoria cannot be a knight, because this would contradict the claim of Michael that Victoria is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that If Owen is a knight then Henry is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Sophia is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that Victoria is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Victoria is a knight.", "Henry cannot be a knight, because this would contradict the false claim of Victoria that If Owen is a knight then Henry is a knight.", "Henry cannot be a knave, because this would contradict the false claim of their own that Owen is not a knave.", "We have exhausted all possibilities for Henry and Sophia, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the false claim of Victoria that If Owen is a knight then Henry is a knight.", "We have exhausted all possibilities for Owen and Victoria, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that If Owen is a knight then Henry is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Sophia is a knave.", "Sophia cannot be a knight, because this would contradict the claim of Owen that Sophia is a knave.", "Sophia cannot be a knave, because this would contradict the false claim of their own that Victoria is a knight.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Sophia is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Victoria is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Owen is not a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Owen is not a knave.", "Assume David is a knight. No contradiction is found in their claim that Owen is a knave and Michael is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Victoria is a knave or Victoria is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Owen is a knight then Henry is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('telling-truth', 2), ('->', ('telling-truth', 3), ('telling-truth', 5)), ('lying', 1), ('and', ('lying', 3), ('lying', 0)), ('not', ('lying', 3)), ('or', ('lying', 2), ('telling-truth', 2)), ('->', ('telling-truth', 3), ('lying', 5)))", "index": 506}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lucas, Zoey, Grace, Jacob, Luke, Liam, Lily, and Oliver. Lucas told you that Jacob is a knight if and only if Oliver is a knave. Zoey stated, \"Luke is a knave or Lucas is a knave\". Grace told you that Jacob is a knight. Jacob noted, \"Lucas is a knave\". Luke remarked, \"Oliver is a knave\". \"Luke is a knave if and only if Lily is a knight\" - Liam. According to Lily, \"Grace is a knave and Liam is a knight\". \"If Lucas is a knight then Zoey is a knave\" - Oliver. So who is a knight and who is a knave?", "names": ["Lucas", "Zoey", "Grace", "Jacob", "Luke", "Liam", "Lily", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false, false, true], "solution_text": "Lucas is a knave, Zoey is a knight, Grace is a knight, Jacob is a knight, Luke is a knave, Liam is a knave, Lily is a knave, and Oliver is a knight.", "solution_text_format": "(1) Lucas is a knave\n(2) Zoey is a knight\n(3) Grace is a knight\n(4) Jacob is a knight\n(5) Luke is a knave\n(6) Liam is a knave\n(7) Lily is a knave\n(8) Oliver is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that Jacob is a knight if and only if Oliver is a knave.", "Jacob cannot be a knight, because this would contradict the claim of their own that Lucas is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Lucas is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that If Lucas is a knight then Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Oliver that If Lucas is a knight then Zoey is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Luke is a knave or Lucas is a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that Oliver is a knave.", "Luke cannot be a knave, because this would contradict the false claim of Zoey that Luke is a knave or Lucas is a knave.", "We have exhausted all possibilities for Luke and Zoey, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the claim of Lucas that Jacob is a knight if and only if Oliver is a knave.", "We have exhausted all possibilities for Oliver and Jacob, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Jacob is a knight if and only if Oliver is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Lucas is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that If Lucas is a knight then Zoey is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Luke is a knave or Lucas is a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that Oliver is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Oliver is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Jacob is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Luke is a knave if and only if Lily is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Grace is a knave and Liam is a knight.", "Lily cannot be a knave, because this would contradict the claim of Liam that Luke is a knave if and only if Lily is a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Luke is a knave if and only if Lily is a knight.", "Lily cannot be a knight, because this would contradict the false claim of Liam that Luke is a knave if and only if Lily is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Grace is a knave and Liam is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 3), ('lying', 7)), ('or', ('lying', 4), ('lying', 0)), ('telling-truth', 3), ('lying', 0), ('lying', 7), ('<=>', ('lying', 4), ('telling-truth', 6)), ('and', ('lying', 2), ('telling-truth', 5)), ('->', ('telling-truth', 0), ('lying', 1)))", "index": 507}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Elizabeth, Avery, Harper, Luke, Jacob, Aiden, Samuel, and Jack. Elizabeth said, \"Luke is a knight and Samuel is a knight.\" According to Avery, \"Elizabeth is a knight\". Harper was heard saying, \"Samuel is a knight if and only if Avery is a knight\". In a statement by Luke: \"Samuel is a knight if and only if Samuel is a knave\". Jacob commented, \"Samuel is a knight or Luke is a knave\". Aiden remarked, \"If Luke is a knight then Harper is a knight\". Samuel said, \"Luke is a knight.\" Jack asserted: \"If Jacob is a knave then Aiden is a knight\". So who is a knight and who is a knave?", "names": ["Elizabeth", "Avery", "Harper", "Luke", "Jacob", "Aiden", "Samuel", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true, false, true], "solution_text": "Elizabeth is a knave, Avery is a knave, Harper is a knight, Luke is a knave, Jacob is a knight, Aiden is a knight, Samuel is a knave, and Jack is a knight.", "solution_text_format": "(1) Elizabeth is a knave\n(2) Avery is a knave\n(3) Harper is a knight\n(4) Luke is a knave\n(5) Jacob is a knight\n(6) Aiden is a knight\n(7) Samuel is a knave\n(8) Jack is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Luke is a knight and Samuel is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Samuel is a knight if and only if Samuel is a knave.", "Luke cannot be a knave, because this would contradict the claim of Elizabeth that Luke is a knight and Samuel is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Luke is a knight and Samuel is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Samuel is a knight if and only if Samuel is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Samuel is a knight if and only if Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that Luke is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Luke is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Elizabeth is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Samuel is a knight if and only if Avery is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Samuel is a knight or Luke is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Luke is a knight then Harper is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that If Jacob is a knave then Aiden is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('telling-truth', 6)), ('telling-truth', 0), ('<=>', ('telling-truth', 6), ('telling-truth', 1)), ('<=>', ('telling-truth', 6), ('lying', 6)), ('or', ('telling-truth', 6), ('lying', 3)), ('->', ('telling-truth', 3), ('telling-truth', 2)), ('telling-truth', 3), ('->', ('lying', 4), ('telling-truth', 5)))", "index": 508}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Harper, Charlotte, Penelope, Sofia, Jack, Chloe, Alexander, and Evelyn. Harper was heard saying, \"Charlotte is a knave and Sofia is a knave\". Charlotte told you that Jack is a knight and Alexander is a knight. \"Chloe is a knave and Jack is a knight,\" Penelope claimed. In a statement by Sofia: \"Alexander is not a knave\". \"If Harper is a knave then Charlotte is a knight\" - Jack. Chloe was heard saying, \"Sofia is a knave and Jack is a knave\". According to Alexander, \"Harper is a knight if and only if Alexander is a knight\". \"Jack is a knight and Sofia is a knight,\" Evelyn claimed. So who is a knight and who is a knave?", "names": ["Harper", "Charlotte", "Penelope", "Sofia", "Jack", "Chloe", "Alexander", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, false, false, false], "solution_text": "Harper is a knight, Charlotte is a knave, Penelope is a knight, Sofia is a knave, Jack is a knight, Chloe is a knave, Alexander is a knave, and Evelyn is a knave.", "solution_text_format": "(1) Harper is a knight\n(2) Charlotte is a knave\n(3) Penelope is a knight\n(4) Sofia is a knave\n(5) Jack is a knight\n(6) Chloe is a knave\n(7) Alexander is a knave\n(8) Evelyn is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that Charlotte is a knave and Sofia is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Harper that Charlotte is a knave and Sofia is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Jack is a knight and Alexander is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that If Harper is a knave then Charlotte is a knight.", "Alexander cannot be a knight, because this would contradict the false claim of Charlotte that Jack is a knight and Alexander is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Harper is a knight if and only if Alexander is a knight.", "Sofia cannot be a knight, because this would contradict the claim of Harper that Charlotte is a knave and Sofia is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Alexander is not a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Chloe is a knave and Jack is a knight.", "Chloe cannot be a knight, because this would contradict the claim of Penelope that Chloe is a knave and Jack is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Sofia is a knave and Jack is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Jack is a knight and Sofia is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Jack is a knight and Sofia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 1), ('lying', 3)), ('and', ('telling-truth', 4), ('telling-truth', 6)), ('and', ('lying', 5), ('telling-truth', 4)), ('not', ('lying', 6)), ('->', ('lying', 0), ('telling-truth', 1)), ('and', ('lying', 3), ('lying', 4)), ('<=>', ('telling-truth', 0), ('telling-truth', 6)), ('and', ('telling-truth', 4), ('telling-truth', 3)))", "index": 509}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ethan, Alexander, Benjamin, Luke, Aria, Olivia, Isabella, and Zoey. Ethan commented, \"Aria is a knight and Olivia is a knave\". Alexander asserted: \"Benjamin is not a knight\". According to Benjamin, \"Isabella is a knight and Olivia is a knight\". According to Luke, \"Aria is a knight if and only if Olivia is a knave\". According to Aria, \"If Ethan is a knave then Olivia is a knave\". Olivia commented, \"Benjamin is a knight and Alexander is a knight\". Isabella asserted: \"Alexander is a knight if and only if Ethan is a knight\". \"If Alexander is a knight then Isabella is a knight\" - Zoey. So who is a knight and who is a knave?", "names": ["Ethan", "Alexander", "Benjamin", "Luke", "Aria", "Olivia", "Isabella", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false, true, true], "solution_text": "Ethan is a knight, Alexander is a knight, Benjamin is a knave, Luke is a knight, Aria is a knight, Olivia is a knave, Isabella is a knight, and Zoey is a knight.", "solution_text_format": "(1) Ethan is a knight\n(2) Alexander is a knight\n(3) Benjamin is a knave\n(4) Luke is a knight\n(5) Aria is a knight\n(6) Olivia is a knave\n(7) Isabella is a knight\n(8) Zoey is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Aria is a knight and Olivia is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that If Ethan is a knave then Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Ethan that Aria is a knight and Olivia is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Benjamin is a knight and Alexander is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Isabella is a knight and Olivia is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Isabella is a knight and Olivia is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Alexander is a knight if and only if Ethan is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Benjamin is not a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Aria is a knight if and only if Olivia is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that If Alexander is a knight then Isabella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 4), ('lying', 5)), ('not', ('telling-truth', 2)), ('and', ('telling-truth', 6), ('telling-truth', 5)), ('<=>', ('telling-truth', 4), ('lying', 5)), ('->', ('lying', 0), ('lying', 5)), ('and', ('telling-truth', 2), ('telling-truth', 1)), ('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('->', ('telling-truth', 1), ('telling-truth', 6)))", "index": 510}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ava, Ella, Sebastian, Matthew, Zoey, Joseph, Luke, and Olivia. Ava said that Zoey is a knight. Ella said that Ava is a knave or Zoey is a knight. Sebastian stated, \"Ella is a knight and Ella is a knave\". In a statement by Matthew: \"Olivia is a knave if and only if Luke is a knight\". Zoey was heard saying, \"If Sebastian is a knight then Ella is a knave\". Joseph commented, \"Matthew is not a knight\". Luke commented, \"Ava is not a knight\". According to Olivia, \"Luke is not a knave\". So who is a knight and who is a knave?", "names": ["Ava", "Ella", "Sebastian", "Matthew", "Zoey", "Joseph", "Luke", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true, false, false], "solution_text": "Ava is a knight, Ella is a knight, Sebastian is a knave, Matthew is a knave, Zoey is a knight, Joseph is a knight, Luke is a knave, and Olivia is a knave.", "solution_text_format": "(1) Ava is a knight\n(2) Ella is a knight\n(3) Sebastian is a knave\n(4) Matthew is a knave\n(5) Zoey is a knight\n(6) Joseph is a knight\n(7) Luke is a knave\n(8) Olivia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that If Sebastian is a knight then Ella is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Ella is a knight and Ella is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Ella is a knight and Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Ava is a knave or Zoey is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Olivia is a knave if and only if Luke is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Luke is not a knave.", "Luke cannot be a knight, because this would contradict the claim of Matthew that Olivia is a knave if and only if Luke is a knight.", "Luke cannot be a knave, because this would contradict the claim of Olivia that Luke is not a knave.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Luke is not a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that Ava is not a knight.", "Luke cannot be a knave, because this would contradict the claim of Matthew that Olivia is a knave if and only if Luke is a knight.", "We have exhausted all possibilities for Luke and Olivia, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Olivia is a knave if and only if Luke is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Luke is not a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that Ava is not a knight.", "Luke cannot be a knave, because this would contradict the false claim of Matthew that Olivia is a knave if and only if Luke is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Luke is not a knave.", "Luke cannot be a knight, because this would contradict the false claim of Matthew that Olivia is a knave if and only if Luke is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Ava is not a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Matthew is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('or', ('lying', 0), ('telling-truth', 4)), ('and', ('telling-truth', 1), ('lying', 1)), ('<=>', ('lying', 7), ('telling-truth', 6)), ('->', ('telling-truth', 2), ('lying', 1)), ('not', ('telling-truth', 3)), ('not', ('telling-truth', 0)), ('not', ('lying', 6)))", "index": 511}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jack, Emma, Logan, Matthew, Mason, Grace, Amelia, and Oliver. Jack expressed that Emma is not a knight. \"If Matthew is a knight then Amelia is a knight,\" Emma claimed. Logan commented, \"Oliver is a knight if and only if Grace is a knave\". According to Matthew, \"If Grace is a knave then Jack is a knave\". Mason said that Oliver is a knight. \"Emma is a knave if and only if Amelia is a knight\" - Grace. In a statement by Amelia: \"If Grace is a knight then Matthew is a knight\". Oliver expressed that Matthew is a knight and Grace is a knave. So who is a knight and who is a knave?", "names": ["Jack", "Emma", "Logan", "Matthew", "Mason", "Grace", "Amelia", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false, true, true], "solution_text": "Jack is a knave, Emma is a knight, Logan is a knight, Matthew is a knight, Mason is a knight, Grace is a knave, Amelia is a knight, and Oliver is a knight.", "solution_text_format": "(1) Jack is a knave\n(2) Emma is a knight\n(3) Logan is a knight\n(4) Matthew is a knight\n(5) Mason is a knight\n(6) Grace is a knave\n(7) Amelia is a knight\n(8) Oliver is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Emma is not a knight.", "Emma cannot be a knight, because this would contradict the claim of Jack that Emma is not a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that If Matthew is a knight then Amelia is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that If Grace is a knave then Jack is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Emma is a knave if and only if Amelia is a knight.", "Amelia cannot be a knight, because this would contradict the false claim of Emma that If Matthew is a knight then Amelia is a knight.", "Amelia cannot be a knave, because this would contradict the claim of Grace that Emma is a knave if and only if Amelia is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Grace.", "Grace cannot be a knave, because this would contradict the claim of Matthew that If Grace is a knave then Jack is a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the false claim of Emma that If Matthew is a knight then Amelia is a knight.", "We have exhausted all possibilities for Matthew and Emma, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Emma is not a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If Matthew is a knight then Amelia is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that If Grace is a knave then Jack is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Emma is a knave if and only if Amelia is a knight.", "Amelia cannot be a knight, because this would contradict the claim of Grace that Emma is a knave if and only if Amelia is a knight.", "Amelia cannot be a knave, because this would contradict the claim of Emma that If Matthew is a knight then Amelia is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Emma is a knave if and only if Amelia is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that If Grace is a knight then Matthew is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Oliver is a knight if and only if Grace is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Matthew is a knight and Grace is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Oliver is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 1)), ('->', ('telling-truth', 3), ('telling-truth', 6)), ('<=>', ('telling-truth', 7), ('lying', 5)), ('->', ('lying', 5), ('lying', 0)), ('telling-truth', 7), ('<=>', ('lying', 1), ('telling-truth', 6)), ('->', ('telling-truth', 5), ('telling-truth', 3)), ('and', ('telling-truth', 3), ('lying', 5)))", "index": 512}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Luke, Avery, Samuel, Ella, Matthew, Penelope, Evelyn, and Noah. As Luke put it, \"If Noah is a knave then Samuel is a knave\". Avery expressed that Evelyn is a knight and Matthew is a knight. Samuel was heard saying, \"If Samuel is a knight then Noah is a knight\". \"Evelyn is a knight or Evelyn is a knave,\" Ella claimed. \"Penelope is a knave\" - Matthew. Penelope remarked, \"Luke is a knight or Avery is a knave\". \"Avery is a knight or Penelope is a knave,\" Evelyn declared. \"If Avery is a knave then Samuel is a knight,\" Noah declared. So who is a knight and who is a knave?", "names": ["Luke", "Avery", "Samuel", "Ella", "Matthew", "Penelope", "Evelyn", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true, false, true], "solution_text": "Luke is a knight, Avery is a knave, Samuel is a knight, Ella is a knight, Matthew is a knave, Penelope is a knight, Evelyn is a knave, and Noah is a knight.", "solution_text_format": "(1) Luke is a knight\n(2) Avery is a knave\n(3) Samuel is a knight\n(4) Ella is a knight\n(5) Matthew is a knave\n(6) Penelope is a knight\n(7) Evelyn is a knave\n(8) Noah is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that If Noah is a knave then Samuel is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that If Avery is a knave then Samuel is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Evelyn is a knight and Matthew is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Avery is a knight or Penelope is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Luke is a knight or Avery is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Penelope is a knave.", "Matthew cannot be a knave, because this would contradict the claim of Avery that Evelyn is a knight and Matthew is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the false claim of their own that Luke is a knight or Avery is a knave.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the claim of Avery that Evelyn is a knight and Matthew is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Evelyn is a knight and Matthew is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Avery is a knight or Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the claim of Evelyn that Avery is a knight or Penelope is a knave.", "Penelope cannot be a knave, because this would contradict the false claim of their own that Luke is a knight or Avery is a knave.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Avery is a knight or Penelope is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Luke is a knight or Avery is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Penelope is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Penelope is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that If Samuel is a knight then Noah is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Evelyn is a knight or Evelyn is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 7), ('lying', 2)), ('and', ('telling-truth', 6), ('telling-truth', 4)), ('->', ('telling-truth', 2), ('telling-truth', 7)), ('or', ('telling-truth', 6), ('lying', 6)), ('lying', 5), ('or', ('telling-truth', 0), ('lying', 1)), ('or', ('telling-truth', 1), ('lying', 5)), ('->', ('lying', 1), ('telling-truth', 2)))", "index": 513}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Benjamin, Jackson, Sebastian, James, Scarlett, Sofia, Victoria, and Noah. Benjamin expressed that Sebastian is a knight if and only if Benjamin is a knight. Jackson commented, \"Sebastian is a knight if and only if James is a knave\". Sebastian stated, \"Scarlett is a knave or Jackson is a knave\". James asserted: \"Sebastian is a knave or Victoria is a knight\". Scarlett asserted: \"Victoria is not a knight\". Sofia noted, \"Jackson is not a knave\". Victoria was heard saying, \"James is a knave if and only if Benjamin is a knight\". In a statement by Noah: \"Sofia is not a knight\". So who is a knight and who is a knave?", "names": ["Benjamin", "Jackson", "Sebastian", "James", "Scarlett", "Sofia", "Victoria", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false, true, true], "solution_text": "Benjamin is a knave, Jackson is a knave, Sebastian is a knight, James is a knight, Scarlett is a knave, Sofia is a knave, Victoria is a knight, and Noah is a knight.", "solution_text_format": "(1) Benjamin is a knave\n(2) Jackson is a knave\n(3) Sebastian is a knight\n(4) James is a knight\n(5) Scarlett is a knave\n(6) Sofia is a knave\n(7) Victoria is a knight\n(8) Noah is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Sebastian is a knight if and only if Benjamin is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Scarlett is a knave or Jackson is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Victoria is not a knight.", "Victoria cannot be a knight, because this would contradict the claim of Scarlett that Victoria is not a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that James is a knave if and only if Benjamin is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave or Victoria is a knight.", "James cannot be a knave, because this would contradict the false claim of Victoria that James is a knave if and only if Benjamin is a knight.", "We have exhausted all possibilities for James and Victoria, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Victoria is not a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that James is a knave if and only if Benjamin is a knight.", "James cannot be a knight, because this would contradict the claim of Victoria that James is a knave if and only if Benjamin is a knight.", "James cannot be a knave, because this would contradict the false claim of their own that Sebastian is a knave or Victoria is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Victoria.", "Victoria cannot be a knave, because this would contradict the false claim of Scarlett that Victoria is not a knight.", "We have exhausted all possibilities for Victoria and Scarlett, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the claim of Benjamin that Sebastian is a knight if and only if Benjamin is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Sebastian is a knight if and only if Benjamin is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Scarlett is a knave or Jackson is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Victoria is not a knight.", "Victoria cannot be a knight, because this would contradict the claim of Scarlett that Victoria is not a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that James is a knave if and only if Benjamin is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave or Victoria is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Sebastian is a knave or Victoria is a knight.", "Jackson cannot be a knight, because this would contradict the claim of Sebastian that Scarlett is a knave or Jackson is a knave.", "Jackson cannot be a knave, because this would contradict the false claim of their own that Sebastian is a knight if and only if James is a knave.", "We have exhausted all possibilities for Jackson, James, and Victoria, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Victoria is not a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that James is a knave if and only if Benjamin is a knight.", "Assume James is a knight. No contradiction is found in their claim that Sebastian is a knave or Victoria is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight if and only if James is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Sebastian is a knight if and only if James is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Jackson is not a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Jackson is not a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Sofia is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('telling-truth', 0)), ('<=>', ('telling-truth', 2), ('lying', 3)), ('or', ('lying', 4), ('lying', 1)), ('or', ('lying', 2), ('telling-truth', 6)), ('not', ('telling-truth', 6)), ('not', ('lying', 1)), ('<=>', ('lying', 3), ('telling-truth', 0)), ('not', ('telling-truth', 5)))", "index": 514}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lucas, Benjamin, Olivia, William, Chloe, Abigail, Joseph, and Ethan. Lucas said that Joseph is a knave and Olivia is a knight. \"Olivia is a knave if and only if Ethan is a knave,\" Benjamin declared. Olivia remarked, \"If Ethan is a knight then Benjamin is a knight\". \"Abigail is a knave or Chloe is a knave,\" William claimed. \"William is a knight,\" Chloe mentioned. Abigail remarked, \"Lucas is a knight or Benjamin is a knight\". As Joseph put it, \"Olivia is a knight if and only if Chloe is a knight\". \"If William is a knight then Abigail is a knight,\" Ethan claimed. So who is a knight and who is a knave?", "names": ["Lucas", "Benjamin", "Olivia", "William", "Chloe", "Abigail", "Joseph", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false, true, false], "solution_text": "Lucas is a knave, Benjamin is a knave, Olivia is a knight, William is a knight, Chloe is a knight, Abigail is a knave, Joseph is a knight, and Ethan is a knave.", "solution_text_format": "(1) Lucas is a knave\n(2) Benjamin is a knave\n(3) Olivia is a knight\n(4) William is a knight\n(5) Chloe is a knight\n(6) Abigail is a knave\n(7) Joseph is a knight\n(8) Ethan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that Joseph is a knave and Olivia is a knight.", "Joseph cannot be a knight, because this would contradict the claim of Lucas that Joseph is a knave and Olivia is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Olivia is a knight if and only if Chloe is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that If Ethan is a knight then Benjamin is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If William is a knight then Abigail is a knight.", "Assume William is a knight. No contradiction is found in their claim that Abigail is a knave or Chloe is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Lucas is a knight or Benjamin is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Olivia is a knave if and only if Ethan is a knave.", "Chloe cannot be a knight, because this would contradict the claim of William that Abigail is a knave or Chloe is a knave.", "Chloe cannot be a knave, because this would contradict the false claim of their own that William is a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that Olivia is a knave if and only if Ethan is a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the false claim of their own that Lucas is a knight or Benjamin is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Abigail is a knave or Chloe is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Lucas is a knight or Benjamin is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Olivia is a knave if and only if Ethan is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that William is a knight.", "Chloe cannot be a knave, because this would contradict the false claim of William that Abigail is a knave or Chloe is a knave.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that Olivia is a knave if and only if Ethan is a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the false claim of William that Abigail is a knave or Chloe is a knave.", "We have exhausted all possibilities for Abigail and William, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that If William is a knight then Abigail is a knight.", "Assume William is a knight. No contradiction is found in their claim that Abigail is a knave or Chloe is a knave.", "Abigail cannot be a knight, because this would contradict the false claim of Ethan that If William is a knight then Abigail is a knight.", "Abigail cannot be a knave, because this would contradict the false claim of their own that Lucas is a knight or Benjamin is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the false claim of Ethan that If William is a knight then Abigail is a knight.", "We have exhausted all possibilities for William and Ethan, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the claim of Lucas that Joseph is a knave and Olivia is a knight.", "We have exhausted all possibilities for Olivia and Joseph, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Joseph is a knave and Olivia is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Chloe is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that If Ethan is a knight then Benjamin is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If William is a knight then Abigail is a knight.", "Assume William is a knight. No contradiction is found in their claim that Abigail is a knave or Chloe is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Lucas is a knight or Benjamin is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Olivia is a knave if and only if Ethan is a knave.", "Chloe cannot be a knight, because this would contradict the claim of William that Abigail is a knave or Chloe is a knave.", "Chloe cannot be a knave, because this would contradict the false claim of their own that William is a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that Olivia is a knave if and only if Ethan is a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the claim of Ethan that If William is a knight then Abigail is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Abigail is a knave or Chloe is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Lucas is a knight or Benjamin is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Olivia is a knave if and only if Ethan is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that William is a knight.", "Chloe cannot be a knave, because this would contradict the false claim of William that Abigail is a knave or Chloe is a knave.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that Olivia is a knave if and only if Ethan is a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the false claim of William that Abigail is a knave or Chloe is a knave.", "We have exhausted all possibilities for Abigail and William, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that If William is a knight then Abigail is a knight.", "Assume William is a knight. No contradiction is found in their claim that Abigail is a knave or Chloe is a knave.", "Abigail cannot be a knight, because this would contradict the false claim of Ethan that If William is a knight then Abigail is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Lucas is a knight or Benjamin is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Olivia is a knave if and only if Ethan is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Olivia is a knave if and only if Ethan is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that William is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 6), ('telling-truth', 2)), ('<=>', ('lying', 2), ('lying', 7)), ('->', ('telling-truth', 7), ('telling-truth', 1)), ('or', ('lying', 5), ('lying', 4)), ('telling-truth', 3), ('or', ('telling-truth', 0), ('telling-truth', 1)), ('<=>', ('telling-truth', 2), ('telling-truth', 4)), ('->', ('telling-truth', 3), ('telling-truth', 5)))", "index": 515}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Riley, Oliver, Sophia, Victoria, Matthew, Michael, Ella, and Lucas. Riley was heard saying, \"Victoria is a knave\". Oliver noted, \"Sophia is a knave or Lucas is a knave\". \"Riley is a knave if and only if Ella is a knight,\" Sophia mentioned. \"Matthew is a knight,\" Victoria declared. Matthew expressed that Riley is a knight or Sophia is a knave. Michael said that Matthew is a knave if and only if Riley is a knight. Ella expressed that If Michael is a knight then Sophia is a knight. \"Ella is a knave if and only if Riley is a knave\" - Lucas. So who is a knight and who is a knave?", "names": ["Riley", "Oliver", "Sophia", "Victoria", "Matthew", "Michael", "Ella", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true, false, true], "solution_text": "Riley is a knave, Oliver is a knight, Sophia is a knave, Victoria is a knight, Matthew is a knight, Michael is a knight, Ella is a knave, and Lucas is a knight.", "solution_text_format": "(1) Riley is a knave\n(2) Oliver is a knight\n(3) Sophia is a knave\n(4) Victoria is a knight\n(5) Matthew is a knight\n(6) Michael is a knight\n(7) Ella is a knave\n(8) Lucas is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Victoria is a knave.", "Victoria cannot be a knight, because this would contradict the claim of Riley that Victoria is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the false claim of Victoria that Matthew is a knight.", "Matthew cannot be a knave, because this would contradict the false claim of their own that Riley is a knight or Sophia is a knave.", "We have exhausted all possibilities for Matthew and Victoria, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Riley is a knight or Sophia is a knave.", "Sophia cannot be a knight, because this would contradict the claim of Matthew that Riley is a knight or Sophia is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Riley is a knave if and only if Ella is a knight.", "Ella cannot be a knight, because this would contradict the false claim of Sophia that Riley is a knave if and only if Ella is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that If Michael is a knight then Sophia is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Matthew is a knave if and only if Riley is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Sophia is a knave or Lucas is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Ella is a knave if and only if Riley is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('or', ('lying', 2), ('lying', 7)), ('<=>', ('lying', 0), ('telling-truth', 6)), ('telling-truth', 4), ('or', ('telling-truth', 0), ('lying', 2)), ('<=>', ('lying', 4), ('telling-truth', 0)), ('->', ('telling-truth', 5), ('telling-truth', 2)), ('<=>', ('lying', 6), ('lying', 0)))", "index": 516}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Matthew, Victoria, Aurora, Evelyn, Jacob, Michael, Scarlett, and Emma. \"Aurora is a knight or Evelyn is a knave,\" Matthew claimed. \"If Jacob is a knight then Aurora is a knight,\" Victoria declared. Aurora remarked, \"Matthew is not a knave\". Evelyn expressed that Jacob is a knave or Michael is a knave. According to Jacob, \"If Scarlett is a knave then Scarlett is a knight\". Michael commented, \"If Evelyn is a knave then Aurora is a knave\". Scarlett said that Aurora is not a knave. In Emma's words: \"Aurora is a knight\". So who is a knight and who is a knave?", "names": ["Matthew", "Victoria", "Aurora", "Evelyn", "Jacob", "Michael", "Scarlett", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, true, false, false], "solution_text": "Matthew is a knave, Victoria is a knight, Aurora is a knave, Evelyn is a knight, Jacob is a knave, Michael is a knight, Scarlett is a knave, and Emma is a knave.", "solution_text_format": "(1) Matthew is a knave\n(2) Victoria is a knight\n(3) Aurora is a knave\n(4) Evelyn is a knight\n(5) Jacob is a knave\n(6) Michael is a knight\n(7) Scarlett is a knave\n(8) Emma is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that Aurora is a knight or Evelyn is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Matthew is not a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Jacob is a knave or Michael is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that If Scarlett is a knave then Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Aurora is not a knave.", "Michael cannot be a knight, because this would contradict the claim of Evelyn that Jacob is a knave or Michael is a knave.", "Michael cannot be a knave, because this would contradict the false claim of their own that If Evelyn is a knave then Aurora is a knave.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the claim of Jacob that If Scarlett is a knave then Scarlett is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that If Scarlett is a knave then Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the false claim of Jacob that If Scarlett is a knave then Scarlett is a knight.", "Scarlett cannot be a knave, because this would contradict the false claim of their own that Aurora is not a knave.", "We have exhausted all possibilities for Scarlett and Jacob, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Jacob is a knave or Michael is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that If Scarlett is a knave then Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Aurora is not a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that If Evelyn is a knave then Aurora is a knave.", "Michael cannot be a knave, because this would contradict the false claim of Evelyn that Jacob is a knave or Michael is a knave.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the claim of Jacob that If Scarlett is a knave then Scarlett is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the false claim of Evelyn that Jacob is a knave or Michael is a knave.", "We have exhausted all possibilities for Jacob and Evelyn, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the false claim of their own that Matthew is not a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Aurora is a knight or Evelyn is a knave.", "Aurora cannot be a knight, because this would contradict the false claim of Matthew that Aurora is a knight or Evelyn is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Matthew is not a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Jacob is a knave or Michael is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that If Scarlett is a knave then Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Aurora is not a knave.", "Scarlett cannot be a knave, because this would contradict the claim of Jacob that If Scarlett is a knave then Scarlett is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that If Scarlett is a knave then Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the false claim of Jacob that If Scarlett is a knave then Scarlett is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Aurora is not a knave.", "Assume Michael is a knight. No contradiction is found in their claim that If Evelyn is a knave then Aurora is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that If Jacob is a knight then Aurora is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Aurora is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Aurora is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('lying', 3)), ('->', ('telling-truth', 4), ('telling-truth', 2)), ('not', ('lying', 0)), ('or', ('lying', 4), ('lying', 5)), ('->', ('lying', 6), ('telling-truth', 6)), ('->', ('lying', 3), ('lying', 2)), ('not', ('lying', 2)), ('telling-truth', 2))", "index": 517}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Zoey, Sebastian, Isabella, Harper, Grace, Ava, Avery, and Mason. In a statement by Zoey: \"Mason is a knave and Harper is a knave\". In a statement by Sebastian: \"Ava is a knight if and only if Grace is a knight\". Isabella said that Avery is a knave. According to Harper, \"Avery is a knight and Zoey is a knight\". In a statement by Grace: \"Sebastian is a knight and Ava is a knave\". Ava expressed that If Harper is a knight then Sebastian is a knave. Avery noted, \"Grace is not a knight\". As Mason put it, \"If Avery is a knight then Harper is a knave\". So who is a knight and who is a knave?", "names": ["Zoey", "Sebastian", "Isabella", "Harper", "Grace", "Ava", "Avery", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, true, true, true], "solution_text": "Zoey is a knave, Sebastian is a knave, Isabella is a knave, Harper is a knave, Grace is a knave, Ava is a knight, Avery is a knight, and Mason is a knight.", "solution_text_format": "(1) Zoey is a knave\n(2) Sebastian is a knave\n(3) Isabella is a knave\n(4) Harper is a knave\n(5) Grace is a knave\n(6) Ava is a knight\n(7) Avery is a knight\n(8) Mason is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Zoey is a knight. No contradiction is found in their claim that Mason is a knave and Harper is a knave.", "Mason cannot be a knight, because this would contradict the claim of Zoey that Mason is a knave and Harper is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that If Avery is a knight then Harper is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Grace is not a knight.", "Grace cannot be a knight, because this would contradict the claim of Avery that Grace is not a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Sebastian is a knight and Ava is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Ava is a knight if and only if Grace is a knight.", "Ava cannot be a knight, because this would contradict the claim of Sebastian that Ava is a knight if and only if Grace is a knight.", "Ava cannot be a knave, because this would contradict the false claim of Grace that Sebastian is a knight and Ava is a knave.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Ava is a knight if and only if Grace is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that If Harper is a knight then Sebastian is a knave.", "Harper cannot be a knight, because this would contradict the claim of Zoey that Mason is a knave and Harper is a knave.", "Harper cannot be a knave, because this would contradict the false claim of their own that Avery is a knight and Zoey is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the false claim of Sebastian that Ava is a knight if and only if Grace is a knight.", "We have exhausted all possibilities for Ava, Sebastian, and Grace, so let us go back and reconsider Avery.", "Avery cannot be a knave, because this would contradict the false claim of Mason that If Avery is a knight then Harper is a knave.", "We have exhausted all possibilities for Avery and Mason, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Mason is a knave and Harper is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Avery is a knight then Harper is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Grace is not a knight.", "Grace cannot be a knight, because this would contradict the claim of Avery that Grace is not a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Sebastian is a knight and Ava is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Ava is a knight if and only if Grace is a knight.", "Ava cannot be a knight, because this would contradict the claim of Sebastian that Ava is a knight if and only if Grace is a knight.", "Ava cannot be a knave, because this would contradict the false claim of Grace that Sebastian is a knight and Ava is a knave.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Ava is a knight if and only if Grace is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that If Harper is a knight then Sebastian is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Avery is a knight and Zoey is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Avery is a knight and Zoey is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Avery is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Avery is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 7), ('lying', 3)), ('<=>', ('telling-truth', 5), ('telling-truth', 4)), ('lying', 6), ('and', ('telling-truth', 6), ('telling-truth', 0)), ('and', ('telling-truth', 1), ('lying', 5)), ('->', ('telling-truth', 3), ('lying', 1)), ('not', ('telling-truth', 4)), ('->', ('telling-truth', 6), ('lying', 3)))", "index": 518}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: William, Ella, Henry, Amelia, Sebastian, Penelope, Grace, and Sofia. \"Sofia is not a knight,\" William declared. Ella remarked, \"If Henry is a knight then Amelia is a knight\". Henry commented, \"Ella is a knight\". According to Amelia, \"Penelope is a knave or Henry is a knight\". Sebastian told you that Ella is a knight. Penelope stated, \"Ella is a knave and Henry is a knight\". \"Amelia is a knave and Henry is a knave,\" Grace declared. Sofia was heard saying, \"Henry is a knave or Henry is a knight\". So who is a knight and who is a knave?", "names": ["William", "Ella", "Henry", "Amelia", "Sebastian", "Penelope", "Grace", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false, false, true], "solution_text": "William is a knave, Ella is a knight, Henry is a knight, Amelia is a knight, Sebastian is a knight, Penelope is a knave, Grace is a knave, and Sofia is a knight.", "solution_text_format": "(1) William is a knave\n(2) Ella is a knight\n(3) Henry is a knight\n(4) Amelia is a knight\n(5) Sebastian is a knight\n(6) Penelope is a knave\n(7) Grace is a knave\n(8) Sofia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Sofia is not a knight.", "Sofia cannot be a knight, because this would contradict the claim of William that Sofia is not a knight.", "Sofia cannot be a knave, because this would contradict the false claim of their own that Henry is a knave or Henry is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Sofia is not a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Henry is a knave or Henry is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that If Henry is a knight then Amelia is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Penelope is a knave or Henry is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Ella is a knave and Henry is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Ella is a knave and Henry is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Ella is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Amelia is a knave and Henry is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Amelia is a knave and Henry is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 7)), ('->', ('telling-truth', 2), ('telling-truth', 3)), ('telling-truth', 1), ('or', ('lying', 5), ('telling-truth', 2)), ('telling-truth', 1), ('and', ('lying', 1), ('telling-truth', 2)), ('and', ('lying', 3), ('lying', 2)), ('or', ('lying', 2), ('telling-truth', 2)))", "index": 519}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Grace, Victoria, Charlotte, David, Mason, Benjamin, Logan, and Isabella. \"Charlotte is a knave,\" Grace declared. Victoria said, \"Benjamin is not a knight.\" Charlotte said, \"Charlotte is a knight if and only if Mason is a knave.\" David expressed that If David is a knight then Charlotte is a knight. According to Mason, \"Grace is not a knave\". Benjamin commented, \"David is a knave or Isabella is a knight\". Logan asserted: \"Grace is not a knight\". Isabella asserted: \"Logan is a knight\". So who is a knight and who is a knave?", "names": ["Grace", "Victoria", "Charlotte", "David", "Mason", "Benjamin", "Logan", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, true, true, true], "solution_text": "Grace is a knave, Victoria is a knave, Charlotte is a knight, David is a knight, Mason is a knave, Benjamin is a knight, Logan is a knight, and Isabella is a knight.", "solution_text_format": "(1) Grace is a knave\n(2) Victoria is a knave\n(3) Charlotte is a knight\n(4) David is a knight\n(5) Mason is a knave\n(6) Benjamin is a knight\n(7) Logan is a knight\n(8) Isabella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Grace that Charlotte is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Charlotte is a knight if and only if Mason is a knave.", "Mason cannot be a knight, because this would contradict the false claim of Charlotte that Charlotte is a knight if and only if Mason is a knave.", "Mason cannot be a knave, because this would contradict the false claim of their own that Grace is not a knave.", "We have exhausted all possibilities for Mason and Charlotte, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Charlotte is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Charlotte is a knight if and only if Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of Charlotte that Charlotte is a knight if and only if Mason is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Grace is not a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Benjamin is not a knight.", "Benjamin cannot be a knight, because this would contradict the claim of Victoria that Benjamin is not a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that David is a knave or Isabella is a knight.", "Assume David is a knight. No contradiction is found in their claim that If David is a knight then Charlotte is a knight.", "Isabella cannot be a knight, because this would contradict the false claim of Benjamin that David is a knave or Isabella is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Logan is a knight.", "Logan cannot be a knight, because this would contradict the false claim of Isabella that Logan is a knight.", "Logan cannot be a knave, because this would contradict the false claim of their own that Grace is not a knight.", "We have exhausted all possibilities for Logan and Isabella, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the false claim of their own that If David is a knight then Charlotte is a knight.", "We have exhausted all possibilities for David and Benjamin, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Benjamin is not a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that David is a knave or Isabella is a knight.", "Assume David is a knight. No contradiction is found in their claim that If David is a knight then Charlotte is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Logan is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Grace is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('not', ('telling-truth', 5)), ('<=>', ('telling-truth', 2), ('lying', 4)), ('->', ('telling-truth', 3), ('telling-truth', 2)), ('not', ('lying', 0)), ('or', ('lying', 3), ('telling-truth', 7)), ('not', ('telling-truth', 0)), ('telling-truth', 6))", "index": 520}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aiden, Evelyn, William, Zoey, Sofia, Mia, Lucas, and Riley. Aiden told you that Zoey is a knight or Evelyn is a knave. \"William is a knight if and only if Mia is a knight,\" Evelyn mentioned. William told you that Lucas is a knave if and only if William is a knight. \"William is a knave if and only if Mia is a knave,\" Zoey claimed. Sofia said that William is a knave and Aiden is a knight. Mia told you that Lucas is a knight and Evelyn is a knave. Lucas said, \"Zoey is a knave if and only if Aiden is a knight.\" Riley asserted: \"Evelyn is not a knave\". So who is a knight and who is a knave?", "names": ["Aiden", "Evelyn", "William", "Zoey", "Sofia", "Mia", "Lucas", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false, false, true], "solution_text": "Aiden is a knight, Evelyn is a knight, William is a knave, Zoey is a knight, Sofia is a knight, Mia is a knave, Lucas is a knave, and Riley is a knight.", "solution_text_format": "(1) Aiden is a knight\n(2) Evelyn is a knight\n(3) William is a knave\n(4) Zoey is a knight\n(5) Sofia is a knight\n(6) Mia is a knave\n(7) Lucas is a knave\n(8) Riley is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Zoey is a knight or Evelyn is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that William is a knave if and only if Mia is a knave.", "Assume William is a knight. No contradiction is found in their claim that Lucas is a knave if and only if William is a knight.", "Lucas cannot be a knight, because this would contradict the claim of William that Lucas is a knave if and only if William is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Zoey is a knave if and only if Aiden is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that Lucas is a knight and Evelyn is a knave.", "Mia cannot be a knave, because this would contradict the claim of Zoey that William is a knave if and only if Mia is a knave.", "We have exhausted all possibilities for Mia and Lucas, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Lucas is a knave if and only if William is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of William that Lucas is a knave if and only if William is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Zoey is a knave if and only if Aiden is a knight.", "Mia cannot be a knight, because this would contradict the claim of Zoey that William is a knave if and only if Mia is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Lucas is a knight and Evelyn is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that William is a knight if and only if Mia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that William is a knave and Aiden is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Evelyn is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('lying', 1)), ('<=>', ('telling-truth', 2), ('telling-truth', 5)), ('<=>', ('lying', 6), ('telling-truth', 2)), ('<=>', ('lying', 2), ('lying', 5)), ('and', ('lying', 2), ('telling-truth', 0)), ('and', ('telling-truth', 6), ('lying', 1)), ('<=>', ('lying', 3), ('telling-truth', 0)), ('not', ('lying', 1)))", "index": 521}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: William, Ethan, Lily, Jackson, Sebastian, Logan, Chloe, and Victoria. \"Lily is a knight and Logan is a knight\" - William. In a statement by Ethan: \"Jackson is not a knight\". Lily expressed that Victoria is a knight or Ethan is a knight. In a statement by Jackson: \"Logan is a knave and Logan is a knight\". Sebastian remarked, \"Jackson is a knight if and only if Lily is a knight\". Logan said, \"Sebastian is not a knave.\" Chloe said, \"Logan is a knave if and only if Sebastian is a knight.\" According to Victoria, \"Chloe is a knight and William is a knight\". So who is a knight and who is a knave?", "names": ["William", "Ethan", "Lily", "Jackson", "Sebastian", "Logan", "Chloe", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false, false, false], "solution_text": "William is a knave, Ethan is a knight, Lily is a knight, Jackson is a knave, Sebastian is a knave, Logan is a knave, Chloe is a knave, and Victoria is a knave.", "solution_text_format": "(1) William is a knave\n(2) Ethan is a knight\n(3) Lily is a knight\n(4) Jackson is a knave\n(5) Sebastian is a knave\n(6) Logan is a knave\n(7) Chloe is a knave\n(8) Victoria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Lily is a knight and Logan is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Victoria is a knight or Ethan is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Chloe is a knight and William is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Logan is a knave if and only if Sebastian is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Sebastian is not a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Chloe that Logan is a knave if and only if Sebastian is a knight.", "Sebastian cannot be a knave, because this would contradict the claim of Logan that Sebastian is not a knave.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the claim of William that Lily is a knight and Logan is a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the claim of Victoria that Chloe is a knight and William is a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Chloe is a knight and William is a knight.", "Chloe cannot be a knight, because this would contradict the false claim of Victoria that Chloe is a knight and William is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Logan is a knave if and only if Sebastian is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Sebastian is not a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Lily is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Logan is a knave and Logan is a knight.", "Jackson cannot be a knave, because this would contradict the claim of Sebastian that Jackson is a knight if and only if Lily is a knight.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the claim of Logan that Sebastian is not a knave.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the claim of William that Lily is a knight and Logan is a knight.", "We have exhausted all possibilities for Logan, Chloe, and Victoria, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the claim of William that Lily is a knight and Logan is a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Lily is a knight and Logan is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Victoria is a knight or Ethan is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Chloe is a knight and William is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Chloe is a knight and William is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Logan is a knave if and only if Sebastian is a knight.", "Logan cannot be a knight, because this would contradict the false claim of William that Lily is a knight and Logan is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Sebastian is not a knave.", "Sebastian cannot be a knight, because this would contradict the false claim of Logan that Sebastian is not a knave.", "Sebastian cannot be a knave, because this would contradict the claim of Chloe that Logan is a knave if and only if Sebastian is a knight.", "We have exhausted all possibilities for Sebastian and Logan, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Logan is a knave if and only if Sebastian is a knight.", "Logan cannot be a knight, because this would contradict the false claim of William that Lily is a knight and Logan is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Sebastian is not a knave.", "Sebastian cannot be a knight, because this would contradict the false claim of Logan that Sebastian is not a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Jackson is a knight if and only if Lily is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Logan is a knave and Logan is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Logan is a knave and Logan is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Jackson is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 2), ('telling-truth', 5)), ('not', ('telling-truth', 3)), ('or', ('telling-truth', 7), ('telling-truth', 1)), ('and', ('lying', 5), ('telling-truth', 5)), ('<=>', ('telling-truth', 3), ('telling-truth', 2)), ('not', ('lying', 4)), ('<=>', ('lying', 5), ('telling-truth', 4)), ('and', ('telling-truth', 6), ('telling-truth', 0)))", "index": 522}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ella, Evelyn, Elizabeth, Luke, Michael, Lily, Oliver, and Olivia. Ella expressed that Elizabeth is a knave and Elizabeth is a knight. According to Evelyn, \"Luke is a knave if and only if Michael is a knight\". According to Elizabeth, \"Evelyn is not a knave\". In a statement by Luke: \"If Lily is a knight then Oliver is a knight\". Michael commented, \"Olivia is a knave if and only if Elizabeth is a knight\". \"Olivia is a knight if and only if Elizabeth is a knight,\" Lily claimed. Oliver commented, \"Lily is a knight\". Olivia stated, \"Lily is a knave if and only if Olivia is a knight\". So who is a knight and who is a knave?", "names": ["Ella", "Evelyn", "Elizabeth", "Luke", "Michael", "Lily", "Oliver", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, false, false, true], "solution_text": "Ella is a knave, Evelyn is a knave, Elizabeth is a knave, Luke is a knight, Michael is a knight, Lily is a knave, Oliver is a knave, and Olivia is a knight.", "solution_text_format": "(1) Ella is a knave\n(2) Evelyn is a knave\n(3) Elizabeth is a knave\n(4) Luke is a knight\n(5) Michael is a knight\n(6) Lily is a knave\n(7) Oliver is a knave\n(8) Olivia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Ella cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave and Elizabeth is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Elizabeth is a knave and Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Evelyn is not a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Luke is a knave if and only if Michael is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that If Lily is a knight then Oliver is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Elizabeth is a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that Lily is a knave if and only if Olivia is a knight.", "Olivia cannot be a knave, because this would contradict the claim of Lily that Olivia is a knight if and only if Elizabeth is a knight.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Olivia is a knight if and only if Elizabeth is a knight.", "Olivia cannot be a knight, because this would contradict the false claim of Lily that Olivia is a knight if and only if Elizabeth is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Lily is a knave if and only if Olivia is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Lily is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Lily is a knight.", "Michael cannot be a knight, because this would contradict the claim of Evelyn that Luke is a knave if and only if Michael is a knight.", "Michael cannot be a knave, because this would contradict the false claim of their own that Olivia is a knave if and only if Elizabeth is a knight.", "We have exhausted all possibilities for Michael, Oliver, Olivia, and Lily, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that If Lily is a knight then Oliver is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Elizabeth is a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that Lily is a knave if and only if Olivia is a knight.", "Olivia cannot be a knave, because this would contradict the claim of Lily that Olivia is a knight if and only if Elizabeth is a knight.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the false claim of Luke that If Lily is a knight then Oliver is a knight.", "We have exhausted all possibilities for Lily and Luke, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the claim of Elizabeth that Evelyn is not a knave.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Evelyn is not a knave.", "Evelyn cannot be a knight, because this would contradict the false claim of Elizabeth that Evelyn is not a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Luke is a knave if and only if Michael is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that If Lily is a knight then Oliver is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Elizabeth is a knight.", "Olivia cannot be a knight, because this would contradict the claim of Lily that Olivia is a knight if and only if Elizabeth is a knight.", "Olivia cannot be a knave, because this would contradict the false claim of their own that Lily is a knave if and only if Olivia is a knight.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Olivia is a knight if and only if Elizabeth is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Lily is a knave if and only if Olivia is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Lily is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Lily is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Olivia is a knave if and only if Elizabeth is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('telling-truth', 2)), ('<=>', ('lying', 3), ('telling-truth', 4)), ('not', ('lying', 1)), ('->', ('telling-truth', 5), ('telling-truth', 6)), ('<=>', ('lying', 7), ('telling-truth', 2)), ('<=>', ('telling-truth', 7), ('telling-truth', 2)), ('telling-truth', 5), ('<=>', ('lying', 5), ('telling-truth', 7)))", "index": 523}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Grace, Isabella, Liam, Luke, Jack, Mia, Jacob, and Avery. Grace said that Luke is a knight. According to Isabella, \"Jacob is a knave if and only if Luke is a knight\". As Liam put it, \"Mia is not a knight\". Luke was heard saying, \"Liam is a knave or Isabella is a knave\". Jack commented, \"If Grace is a knave then Avery is a knight\". As Mia put it, \"Avery is a knave and Jack is a knight\". Jacob remarked, \"Jacob is a knight\". Avery said, \"Liam is not a knight.\" So who is a knight and who is a knave?", "names": ["Grace", "Isabella", "Liam", "Luke", "Jack", "Mia", "Jacob", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false, true, false], "solution_text": "Grace is a knave, Isabella is a knight, Liam is a knight, Luke is a knave, Jack is a knave, Mia is a knave, Jacob is a knight, and Avery is a knave.", "solution_text_format": "(1) Grace is a knave\n(2) Isabella is a knight\n(3) Liam is a knight\n(4) Luke is a knave\n(5) Jack is a knave\n(6) Mia is a knave\n(7) Jacob is a knight\n(8) Avery is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Luke is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Liam is a knave or Isabella is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Mia is not a knight.", "Mia cannot be a knight, because this would contradict the claim of Liam that Mia is not a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Avery is a knave and Jack is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Liam is not a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Liam is not a knight.", "Jack cannot be a knight, because this would contradict the false claim of Mia that Avery is a knave and Jack is a knight.", "Jack cannot be a knave, because this would contradict the false claim of their own that If Grace is a knave then Avery is a knight.", "We have exhausted all possibilities for Jack, Avery, and Mia, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Mia is not a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Avery is a knave and Jack is a knight.", "Avery cannot be a knight, because this would contradict the claim of Mia that Avery is a knave and Jack is a knight.", "Avery cannot be a knave, because this would contradict the false claim of their own that Liam is not a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the false claim of Liam that Mia is not a knight.", "We have exhausted all possibilities for Mia and Liam, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the claim of Grace that Luke is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Luke is a knight.", "Luke cannot be a knight, because this would contradict the false claim of Grace that Luke is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Liam is a knave or Isabella is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Mia is not a knight.", "Mia cannot be a knight, because this would contradict the claim of Liam that Mia is not a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Avery is a knave and Jack is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Liam is not a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Liam is not a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that If Grace is a knave then Avery is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that If Grace is a knave then Avery is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Jacob is a knave if and only if Luke is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Jacob is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 3), ('<=>', ('lying', 6), ('telling-truth', 3)), ('not', ('telling-truth', 5)), ('or', ('lying', 2), ('lying', 1)), ('->', ('lying', 0), ('telling-truth', 7)), ('and', ('lying', 7), ('telling-truth', 4)), ('telling-truth', 6), ('not', ('telling-truth', 2)))", "index": 524}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lily, Emily, Abigail, Charlotte, David, Daniel, Jackson, and Lucas. As Lily put it, \"Daniel is not a knave\". Emily remarked, \"Charlotte is not a knave\". Abigail said that Lucas is not a knave. As Charlotte put it, \"Lucas is a knight if and only if Emily is a knave\". David was heard saying, \"Abigail is a knave and Abigail is a knight\". According to Daniel, \"If Charlotte is a knight then Jackson is a knave\". \"David is a knave,\" Jackson mentioned. \"Emily is a knave\" - Lucas. So who is a knight and who is a knave?", "names": ["Lily", "Emily", "Abigail", "Charlotte", "David", "Daniel", "Jackson", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, false, true, false], "solution_text": "Lily is a knave, Emily is a knight, Abigail is a knave, Charlotte is a knight, David is a knave, Daniel is a knave, Jackson is a knight, and Lucas is a knave.", "solution_text_format": "(1) Lily is a knave\n(2) Emily is a knight\n(3) Abigail is a knave\n(4) Charlotte is a knight\n(5) David is a knave\n(6) Daniel is a knave\n(7) Jackson is a knight\n(8) Lucas is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that Daniel is not a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that If Charlotte is a knight then Jackson is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Lucas is a knight if and only if Emily is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of Charlotte that Lucas is a knight if and only if Emily is a knave.", "Emily cannot be a knave, because this would contradict the false claim of their own that Charlotte is not a knave.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Charlotte is not a knave.", "Jackson cannot be a knight, because this would contradict the claim of Daniel that If Charlotte is a knight then Jackson is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that David is a knave.", "David cannot be a knight, because this would contradict the claim of their own that Abigail is a knave and Abigail is a knight.", "David cannot be a knave, because this would contradict the false claim of Jackson that David is a knave.", "We have exhausted all possibilities for David and Jackson, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the false claim of their own that Charlotte is not a knave.", "We have exhausted all possibilities for Emily and Lucas, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Lucas is a knight if and only if Emily is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Charlotte is not a knave.", "Emily cannot be a knave, because this would contradict the false claim of Charlotte that Lucas is a knight if and only if Emily is a knave.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Charlotte is not a knave.", "Emily cannot be a knave, because this would contradict the false claim of Lucas that Emily is a knave.", "We have exhausted all possibilities for Emily, Lucas, and Charlotte, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the claim of Lily that Daniel is not a knave.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Daniel is not a knave.", "Daniel cannot be a knight, because this would contradict the false claim of Lily that Daniel is not a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that If Charlotte is a knight then Jackson is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Lucas is a knight if and only if Emily is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of Charlotte that Lucas is a knight if and only if Emily is a knave.", "Emily cannot be a knave, because this would contradict the false claim of their own that Charlotte is not a knave.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Charlotte is not a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that David is a knave.", "David cannot be a knight, because this would contradict the claim of their own that Abigail is a knave and Abigail is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Abigail is a knave and Abigail is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Lucas is not a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Lucas is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 5)), ('not', ('lying', 3)), ('not', ('lying', 7)), ('<=>', ('telling-truth', 7), ('lying', 1)), ('and', ('lying', 2), ('telling-truth', 2)), ('->', ('telling-truth', 3), ('lying', 6)), ('lying', 4), ('lying', 1))", "index": 525}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Henry, Oliver, Sebastian, Evelyn, Sophia, Grace, Liam, and James. \"Oliver is a knave,\" Henry mentioned. As Oliver put it, \"Sebastian is a knight and Sophia is a knight\". Sebastian told you that Evelyn is a knight if and only if Henry is a knight. Evelyn stated, \"Sophia is a knight if and only if Liam is a knave\". Sophia was heard saying, \"Sebastian is a knight if and only if Grace is a knave\". Grace remarked, \"Sebastian is not a knave\". Liam told you that Henry is a knight. James told you that Henry is not a knight. So who is a knight and who is a knave?", "names": ["Henry", "Oliver", "Sebastian", "Evelyn", "Sophia", "Grace", "Liam", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true, true, false], "solution_text": "Henry is a knight, Oliver is a knave, Sebastian is a knight, Evelyn is a knight, Sophia is a knave, Grace is a knight, Liam is a knight, and James is a knave.", "solution_text_format": "(1) Henry is a knight\n(2) Oliver is a knave\n(3) Sebastian is a knight\n(4) Evelyn is a knight\n(5) Sophia is a knave\n(6) Grace is a knight\n(7) Liam is a knight\n(8) James is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that Oliver is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Henry that Oliver is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Sebastian is a knight and Sophia is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Evelyn is a knight if and only if Henry is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Sophia is a knight if and only if Liam is a knave.", "Sophia cannot be a knight, because this would contradict the false claim of Oliver that Sebastian is a knight and Sophia is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Sebastian is a knight if and only if Grace is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Sebastian is not a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Henry is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Henry is not a knight.", "Assume James is a knave. No contradiction is found in their false claim that Henry is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 1), ('and', ('telling-truth', 2), ('telling-truth', 4)), ('<=>', ('telling-truth', 3), ('telling-truth', 0)), ('<=>', ('telling-truth', 4), ('lying', 6)), ('<=>', ('telling-truth', 2), ('lying', 5)), ('not', ('lying', 2)), ('telling-truth', 0), ('not', ('telling-truth', 0)))", "index": 526}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aria, Olivia, Emma, Chloe, Sofia, Aiden, Jackson, and William. Aria asserted: \"Olivia is a knight if and only if Chloe is a knave\". As Olivia put it, \"William is a knight if and only if Emma is a knave\". \"Sofia is a knave,\" Emma mentioned. \"Aiden is a knave or Sofia is a knave,\" Chloe mentioned. As Sofia put it, \"If Jackson is a knight then Aiden is a knave\". Aiden said that Aria is a knave. Jackson asserted: \"Chloe is a knight and Aiden is a knave\". William was heard saying, \"Chloe is not a knight\". So who is a knight and who is a knave?", "names": ["Aria", "Olivia", "Emma", "Chloe", "Sofia", "Aiden", "Jackson", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false, true, false], "solution_text": "Aria is a knight, Olivia is a knave, Emma is a knave, Chloe is a knight, Sofia is a knight, Aiden is a knave, Jackson is a knight, and William is a knave.", "solution_text_format": "(1) Aria is a knight\n(2) Olivia is a knave\n(3) Emma is a knave\n(4) Chloe is a knight\n(5) Sofia is a knight\n(6) Aiden is a knave\n(7) Jackson is a knight\n(8) William is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Chloe is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that William is a knight if and only if Emma is a knave.", "Assume William is a knight. No contradiction is found in their claim that Chloe is not a knight.", "Chloe cannot be a knight, because this would contradict the claim of Aria that Olivia is a knight if and only if Chloe is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Aiden is a knave or Sofia is a knave.", "Aiden cannot be a knight, because this would contradict the claim of their own that Aria is a knave.", "Aiden cannot be a knave, because this would contradict the false claim of Chloe that Aiden is a knave or Sofia is a knave.", "We have exhausted all possibilities for Aiden and Chloe, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Chloe is not a knight.", "Chloe cannot be a knight, because this would contradict the claim of Aria that Olivia is a knight if and only if Chloe is a knave.", "Chloe cannot be a knave, because this would contradict the false claim of William that Chloe is not a knight.", "We have exhausted all possibilities for Chloe and William, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that William is a knight if and only if Emma is a knave.", "Assume William is a knight. No contradiction is found in their claim that Chloe is not a knight.", "Chloe cannot be a knight, because this would contradict the claim of William that Chloe is not a knight.", "Chloe cannot be a knave, because this would contradict the claim of Aria that Olivia is a knight if and only if Chloe is a knave.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Chloe is not a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Aiden is a knave or Sofia is a knave.", "Aiden cannot be a knight, because this would contradict the claim of their own that Aria is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Aria is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that If Jackson is a knight then Aiden is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Chloe is a knight and Aiden is a knave.", "Emma cannot be a knight, because this would contradict the false claim of Olivia that William is a knight if and only if Emma is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Sofia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('lying', 3)), ('<=>', ('telling-truth', 7), ('lying', 2)), ('lying', 4), ('or', ('lying', 5), ('lying', 4)), ('->', ('telling-truth', 6), ('lying', 5)), ('lying', 0), ('and', ('telling-truth', 3), ('lying', 5)), ('not', ('telling-truth', 3)))", "index": 527}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sofia, Oliver, Daniel, Abigail, Noah, Lucas, Luke, and Ethan. Sofia said that If Luke is a knave then Noah is a knight. Oliver remarked, \"Lucas is a knave if and only if Luke is a knight\". Daniel was heard saying, \"Lucas is a knight if and only if Luke is a knave\". According to Abigail, \"Lucas is a knight if and only if Oliver is a knight\". Noah noted, \"Oliver is a knave or Ethan is a knight\". Lucas said that Sofia is not a knave. Luke expressed that Abigail is a knave and Sofia is a knight. Ethan remarked, \"If Lucas is a knight then Noah is a knave\". So who is a knight and who is a knave?", "names": ["Sofia", "Oliver", "Daniel", "Abigail", "Noah", "Lucas", "Luke", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true, true, false], "solution_text": "Sofia is a knight, Oliver is a knave, Daniel is a knave, Abigail is a knave, Noah is a knight, Lucas is a knight, Luke is a knight, and Ethan is a knave.", "solution_text_format": "(1) Sofia is a knight\n(2) Oliver is a knave\n(3) Daniel is a knave\n(4) Abigail is a knave\n(5) Noah is a knight\n(6) Lucas is a knight\n(7) Luke is a knight\n(8) Ethan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that If Luke is a knave then Noah is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Abigail is a knave and Sofia is a knight.", "Abigail cannot be a knight, because this would contradict the claim of Luke that Abigail is a knave and Sofia is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Lucas is a knight if and only if Oliver is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Sofia is not a knave.", "Oliver cannot be a knight, because this would contradict the claim of their own that Lucas is a knave if and only if Luke is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Lucas is a knave if and only if Luke is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Oliver is a knave or Ethan is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that If Lucas is a knight then Noah is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that If Lucas is a knight then Noah is a knave.", "Daniel cannot be a knight, because this would contradict the claim of their own that Lucas is a knight if and only if Luke is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Lucas is a knight if and only if Luke is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 6), ('telling-truth', 4)), ('<=>', ('lying', 5), ('telling-truth', 6)), ('<=>', ('telling-truth', 5), ('lying', 6)), ('<=>', ('telling-truth', 5), ('telling-truth', 1)), ('or', ('lying', 1), ('telling-truth', 7)), ('not', ('lying', 0)), ('and', ('lying', 3), ('telling-truth', 0)), ('->', ('telling-truth', 5), ('lying', 4)))", "index": 528}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Samuel, Jack, Ethan, Aurora, Harper, Daniel, Sophia, and Jackson. \"If Daniel is a knight then Harper is a knave,\" Samuel mentioned. \"Daniel is a knight and Aurora is a knight,\" Jack mentioned. Ethan was heard saying, \"Harper is a knight\". Aurora remarked, \"Daniel is a knave\". In a statement by Harper: \"Daniel is a knight or Jackson is a knight\". Daniel said that If Daniel is a knight then Jackson is a knight. According to Sophia, \"Harper is a knave\". Jackson was heard saying, \"Jackson is a knight or Harper is a knight\". So who is a knight and who is a knave?", "names": ["Samuel", "Jack", "Ethan", "Aurora", "Harper", "Daniel", "Sophia", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true, false, true], "solution_text": "Samuel is a knave, Jack is a knave, Ethan is a knight, Aurora is a knave, Harper is a knight, Daniel is a knight, Sophia is a knave, and Jackson is a knight.", "solution_text_format": "(1) Samuel is a knave\n(2) Jack is a knave\n(3) Ethan is a knight\n(4) Aurora is a knave\n(5) Harper is a knight\n(6) Daniel is a knight\n(7) Sophia is a knave\n(8) Jackson is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that If Daniel is a knight then Harper is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that If Daniel is a knight then Jackson is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Jackson is a knight or Harper is a knight.", "Harper cannot be a knight, because this would contradict the claim of Samuel that If Daniel is a knight then Harper is a knave.", "Harper cannot be a knave, because this would contradict the false claim of their own that Daniel is a knight or Jackson is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Jackson.", "Jackson cannot be a knave, because this would contradict the claim of Daniel that If Daniel is a knight then Jackson is a knight.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the false claim of their own that If Daniel is a knight then Jackson is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that If Daniel is a knight then Harper is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that If Daniel is a knight then Jackson is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Jackson is a knight or Harper is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Daniel is a knight or Jackson is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Daniel is a knight and Aurora is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Daniel is a knave.", "Aurora cannot be a knave, because this would contradict the claim of Jack that Daniel is a knight and Aurora is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Daniel is a knight and Aurora is a knight.", "Aurora cannot be a knight, because this would contradict the false claim of Jack that Daniel is a knight and Aurora is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Daniel is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Harper is a knight.", "Sophia cannot be a knight, because this would contradict the claim of their own that Harper is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Harper is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 5), ('lying', 4)), ('and', ('telling-truth', 5), ('telling-truth', 3)), ('telling-truth', 4), ('lying', 5), ('or', ('telling-truth', 5), ('telling-truth', 7)), ('->', ('telling-truth', 5), ('telling-truth', 7)), ('lying', 4), ('or', ('telling-truth', 7), ('telling-truth', 4)))", "index": 529}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ava, Jackson, James, Elizabeth, Charlotte, Ethan, Lucas, and Grace. As Ava put it, \"If Charlotte is a knight then Grace is a knave\". In Jackson's words: \"Lucas is not a knave\". James asserted: \"Ethan is a knight if and only if Lucas is a knight\". In Elizabeth's words: \"Jackson is a knave or Grace is a knave\". Charlotte said, \"Ava is a knave if and only if Charlotte is a knight.\" Ethan said that Grace is not a knight. Lucas said that Ethan is a knight and Charlotte is a knave. Grace said, \"If Ava is a knight then Ava is a knave.\" So who is a knight and who is a knave?", "names": ["Ava", "Jackson", "James", "Elizabeth", "Charlotte", "Ethan", "Lucas", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false, false, true], "solution_text": "Ava is a knave, Jackson is a knave, James is a knight, Elizabeth is a knight, Charlotte is a knight, Ethan is a knave, Lucas is a knave, and Grace is a knight.", "solution_text_format": "(1) Ava is a knave\n(2) Jackson is a knave\n(3) James is a knight\n(4) Elizabeth is a knight\n(5) Charlotte is a knight\n(6) Ethan is a knave\n(7) Lucas is a knave\n(8) Grace is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that If Charlotte is a knight then Grace is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Ava is a knave if and only if Charlotte is a knight.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that Ava is a knave if and only if Charlotte is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that If Charlotte is a knight then Grace is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Ava is a knave if and only if Charlotte is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that If Ava is a knight then Ava is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Lucas is not a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Ethan is a knight and Charlotte is a knave.", "Lucas cannot be a knave, because this would contradict the claim of Jackson that Lucas is not a knave.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Lucas is not a knave.", "Lucas cannot be a knight, because this would contradict the false claim of Jackson that Lucas is not a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Ethan is a knight and Charlotte is a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Grace is not a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Grace is not a knight.", "Assume James is a knight. No contradiction is found in their claim that Ethan is a knight if and only if Lucas is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Jackson is a knave or Grace is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 4), ('lying', 7)), ('not', ('lying', 6)), ('<=>', ('telling-truth', 5), ('telling-truth', 6)), ('or', ('lying', 1), ('lying', 7)), ('<=>', ('lying', 0), ('telling-truth', 4)), ('not', ('telling-truth', 7)), ('and', ('telling-truth', 5), ('lying', 4)), ('->', ('telling-truth', 0), ('lying', 0)))", "index": 530}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Harper, Isabella, Jackson, Chloe, Sofia, Charlotte, Jacob, and Emma. As Harper put it, \"Jacob is a knight\". Isabella noted, \"Sofia is a knave or Charlotte is a knight\". \"Emma is not a knave,\" Jackson claimed. Chloe commented, \"Jacob is a knave or Sofia is a knave\". Sofia expressed that Sofia is a knight and Chloe is a knight. Charlotte said, \"If Harper is a knave then Isabella is a knave.\" Jacob noted, \"Chloe is not a knight\". \"Chloe is a knight if and only if Jacob is a knight,\" Emma declared. So who is a knight and who is a knave?", "names": ["Harper", "Isabella", "Jackson", "Chloe", "Sofia", "Charlotte", "Jacob", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, false, false, false], "solution_text": "Harper is a knave, Isabella is a knight, Jackson is a knave, Chloe is a knight, Sofia is a knave, Charlotte is a knave, Jacob is a knave, and Emma is a knave.", "solution_text_format": "(1) Harper is a knave\n(2) Isabella is a knight\n(3) Jackson is a knave\n(4) Chloe is a knight\n(5) Sofia is a knave\n(6) Charlotte is a knave\n(7) Jacob is a knave\n(8) Emma is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Chloe is not a knight.", "Chloe cannot be a knight, because this would contradict the claim of Jacob that Chloe is not a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Jacob is a knave or Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Sofia is a knight and Chloe is a knight.", "Sofia cannot be a knave, because this would contradict the false claim of Chloe that Jacob is a knave or Sofia is a knave.", "We have exhausted all possibilities for Sofia and Chloe, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the claim of Harper that Jacob is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Jacob is a knight.", "Jacob cannot be a knight, because this would contradict the false claim of Harper that Jacob is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Chloe is not a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Jacob is a knave or Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Sofia is a knight and Chloe is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Sofia is a knave or Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that If Harper is a knave then Isabella is a knave.", "Charlotte cannot be a knave, because this would contradict the claim of Isabella that Sofia is a knave or Charlotte is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Sofia is a knave or Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of Isabella that Sofia is a knave or Charlotte is a knight.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that If Harper is a knave then Isabella is a knave.", "We have exhausted all possibilities for Charlotte and Isabella, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Sofia is a knight and Chloe is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Sofia is a knave or Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that If Harper is a knave then Isabella is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that If Harper is a knave then Isabella is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Emma is not a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Chloe is a knight if and only if Jacob is a knight.", "Emma cannot be a knave, because this would contradict the claim of Jackson that Emma is not a knave.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Emma is not a knave.", "Emma cannot be a knight, because this would contradict the false claim of Jackson that Emma is not a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Chloe is a knight if and only if Jacob is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 6), ('or', ('lying', 4), ('telling-truth', 5)), ('not', ('lying', 7)), ('or', ('lying', 6), ('lying', 4)), ('and', ('telling-truth', 4), ('telling-truth', 3)), ('->', ('lying', 0), ('lying', 1)), ('not', ('telling-truth', 3)), ('<=>', ('telling-truth', 3), ('telling-truth', 6)))", "index": 531}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Oliver, David, Mason, Benjamin, Aurora, Grace, Jackson, and Jack. Oliver said that If Jack is a knight then Jackson is a knave. According to David, \"If Benjamin is a knave then Jack is a knave\". \"If David is a knight then Benjamin is a knave\" - Mason. Benjamin told you that Grace is a knave if and only if Oliver is a knave. Aurora told you that Benjamin is not a knight. As Grace put it, \"Grace is a knight if and only if David is a knave\". \"If David is a knave then Jack is a knight,\" Jackson claimed. In a statement by Jack: \"David is a knave or Jackson is a knave\". So who is a knight and who is a knave?", "names": ["Oliver", "David", "Mason", "Benjamin", "Aurora", "Grace", "Jackson", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true, true, true], "solution_text": "Oliver is a knave, David is a knave, Mason is a knight, Benjamin is a knave, Aurora is a knight, Grace is a knight, Jackson is a knight, and Jack is a knight.", "solution_text_format": "(1) Oliver is a knave\n(2) David is a knave\n(3) Mason is a knight\n(4) Benjamin is a knave\n(5) Aurora is a knight\n(6) Grace is a knight\n(7) Jackson is a knight\n(8) Jack is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that If Jack is a knight then Jackson is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that David is a knave or Jackson is a knave.", "Assume David is a knight. No contradiction is found in their claim that If Benjamin is a knave then Jack is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Grace is a knave if and only if Oliver is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Grace is a knight if and only if David is a knave.", "Grace cannot be a knave, because this would contradict the claim of Benjamin that Grace is a knave if and only if Oliver is a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the claim of David that If Benjamin is a knave then Jack is a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that If Benjamin is a knave then Jack is a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of David that If Benjamin is a knave then Jack is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Grace is a knave if and only if Oliver is a knave.", "Grace cannot be a knight, because this would contradict the false claim of Benjamin that Grace is a knave if and only if Oliver is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Grace is a knight if and only if David is a knave.", "Jackson cannot be a knight, because this would contradict the claim of Oliver that If Jack is a knight then Jackson is a knave.", "Jackson cannot be a knave, because this would contradict the false claim of their own that If David is a knave then Jack is a knight.", "We have exhausted all possibilities for Jackson, Grace, Benjamin, and David, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that David is a knave or Jackson is a knave.", "Assume David is a knight. No contradiction is found in their claim that If Benjamin is a knave then Jack is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Grace is a knave if and only if Oliver is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Grace is a knight if and only if David is a knave.", "Grace cannot be a knave, because this would contradict the claim of Benjamin that Grace is a knave if and only if Oliver is a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Grace is a knave if and only if Oliver is a knave.", "Grace cannot be a knight, because this would contradict the false claim of Benjamin that Grace is a knave if and only if Oliver is a knave.", "Grace cannot be a knave, because this would contradict the false claim of their own that Grace is a knight if and only if David is a knave.", "We have exhausted all possibilities for Grace and Benjamin, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the false claim of their own that If Benjamin is a knave then Jack is a knave.", "We have exhausted all possibilities for David and Jack, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that If Jack is a knight then Jackson is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that David is a knave or Jackson is a knave.", "Assume David is a knight. No contradiction is found in their claim that If Benjamin is a knave then Jack is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Grace is a knave if and only if Oliver is a knave.", "Grace cannot be a knight, because this would contradict the claim of Benjamin that Grace is a knave if and only if Oliver is a knave.", "Grace cannot be a knave, because this would contradict the false claim of their own that Grace is a knight if and only if David is a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the claim of David that If Benjamin is a knave then Jack is a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that If Benjamin is a knave then Jack is a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of David that If Benjamin is a knave then Jack is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Grace is a knave if and only if Oliver is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Grace is a knight if and only if David is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that If David is a knave then Jack is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that If David is a knight then Benjamin is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Benjamin is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 7), ('lying', 6)), ('->', ('lying', 3), ('lying', 7)), ('->', ('telling-truth', 1), ('lying', 3)), ('<=>', ('lying', 5), ('lying', 0)), ('not', ('telling-truth', 3)), ('<=>', ('telling-truth', 5), ('lying', 1)), ('->', ('lying', 1), ('telling-truth', 7)), ('or', ('lying', 1), ('lying', 6)))", "index": 532}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Benjamin, Daniel, Charlotte, Penelope, Ella, Scarlett, Zoey, and Joseph. In a statement by Benjamin: \"Joseph is not a knave\". Daniel expressed that If Benjamin is a knave then Ella is a knave. According to Charlotte, \"Zoey is not a knave\". \"Benjamin is a knight,\" Penelope declared. In a statement by Ella: \"Joseph is a knight and Joseph is a knave\". In a statement by Scarlett: \"Penelope is not a knight\". Zoey said, \"Daniel is a knave if and only if Penelope is a knave.\" \"Zoey is a knight if and only if Charlotte is a knave,\" Joseph mentioned. So who is a knight and who is a knave?", "names": ["Benjamin", "Daniel", "Charlotte", "Penelope", "Ella", "Scarlett", "Zoey", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, true, false, false], "solution_text": "Benjamin is a knave, Daniel is a knight, Charlotte is a knave, Penelope is a knave, Ella is a knave, Scarlett is a knight, Zoey is a knave, and Joseph is a knave.", "solution_text_format": "(1) Benjamin is a knave\n(2) Daniel is a knight\n(3) Charlotte is a knave\n(4) Penelope is a knave\n(5) Ella is a knave\n(6) Scarlett is a knight\n(7) Zoey is a knave\n(8) Joseph is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Joseph is not a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Zoey is a knight if and only if Charlotte is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Daniel is a knave if and only if Penelope is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that If Benjamin is a knave then Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Joseph is a knight and Joseph is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Joseph is a knight and Joseph is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Benjamin is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Joseph that Zoey is a knight if and only if Charlotte is a knave.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that Zoey is not a knave.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the false claim of their own that Benjamin is a knight.", "We have exhausted all possibilities for Penelope and Ella, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the false claim of their own that If Benjamin is a knave then Ella is a knave.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Daniel is a knave if and only if Penelope is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that If Benjamin is a knave then Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Joseph is a knight and Joseph is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Joseph is a knight and Joseph is a knave.", "Penelope cannot be a knight, because this would contradict the false claim of Zoey that Daniel is a knave if and only if Penelope is a knave.", "Penelope cannot be a knave, because this would contradict the false claim of their own that Benjamin is a knight.", "We have exhausted all possibilities for Penelope and Ella, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the false claim of their own that If Benjamin is a knave then Ella is a knave.", "We have exhausted all possibilities for Daniel and Zoey, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of Benjamin that Joseph is not a knave.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Joseph is not a knave.", "Joseph cannot be a knight, because this would contradict the false claim of Benjamin that Joseph is not a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Zoey is a knight if and only if Charlotte is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Daniel is a knave if and only if Penelope is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that If Benjamin is a knave then Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of Daniel that If Benjamin is a knave then Ella is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Joseph is a knight and Joseph is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight.", "Penelope cannot be a knave, because this would contradict the claim of Zoey that Daniel is a knave if and only if Penelope is a knave.", "We have exhausted all possibilities for Penelope and Ella, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that If Benjamin is a knave then Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Joseph is a knight and Joseph is a knave.", "Ella cannot be a knave, because this would contradict the false claim of Daniel that If Benjamin is a knave then Ella is a knave.", "We have exhausted all possibilities for Ella and Daniel, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Daniel is a knave if and only if Penelope is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that If Benjamin is a knave then Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of Daniel that If Benjamin is a knave then Ella is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Joseph is a knight and Joseph is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Benjamin is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Zoey is not a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Zoey is not a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Penelope is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 7)), ('->', ('lying', 0), ('lying', 4)), ('not', ('lying', 6)), ('telling-truth', 0), ('and', ('telling-truth', 7), ('lying', 7)), ('not', ('telling-truth', 3)), ('<=>', ('lying', 1), ('lying', 3)), ('<=>', ('telling-truth', 6), ('lying', 2)))", "index": 533}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Charlotte, Lucas, Owen, Aiden, Avery, Ella, Olivia, and Noah. Charlotte expressed that Aiden is a knight if and only if Lucas is a knave. Lucas told you that Ella is a knave if and only if Charlotte is a knave. Owen commented, \"If Lucas is a knight then Olivia is a knave\". Aiden said that If Lucas is a knave then Charlotte is a knight. Avery asserted: \"Aiden is a knave or Owen is a knave\". Ella said, \"Charlotte is not a knave.\" \"Ella is a knight and Avery is a knave,\" Olivia claimed. In a statement by Noah: \"If Owen is a knight then Aiden is a knight\". So who is a knight and who is a knave?", "names": ["Charlotte", "Lucas", "Owen", "Aiden", "Avery", "Ella", "Olivia", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false, false, true], "solution_text": "Charlotte is a knave, Lucas is a knight, Owen is a knight, Aiden is a knight, Avery is a knave, Ella is a knave, Olivia is a knave, and Noah is a knight.", "solution_text_format": "(1) Charlotte is a knave\n(2) Lucas is a knight\n(3) Owen is a knight\n(4) Aiden is a knight\n(5) Avery is a knave\n(6) Ella is a knave\n(7) Olivia is a knave\n(8) Noah is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that Aiden is a knight if and only if Lucas is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Lucas is a knave then Charlotte is a knight.", "Lucas cannot be a knight, because this would contradict the claim of Charlotte that Aiden is a knight if and only if Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Ella is a knave if and only if Charlotte is a knave.", "Ella cannot be a knight, because this would contradict the false claim of Lucas that Ella is a knave if and only if Charlotte is a knave.", "Ella cannot be a knave, because this would contradict the false claim of their own that Charlotte is not a knave.", "We have exhausted all possibilities for Ella and Lucas, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the false claim of their own that If Lucas is a knave then Charlotte is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Aiden is a knight if and only if Lucas is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Lucas is a knave then Charlotte is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Ella is a knave if and only if Charlotte is a knave.", "Ella cannot be a knight, because this would contradict the claim of Lucas that Ella is a knave if and only if Charlotte is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Charlotte is not a knave.", "Assume Owen is a knight. No contradiction is found in their claim that If Lucas is a knight then Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Owen that If Lucas is a knight then Olivia is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Ella is a knight and Avery is a knave.", "Avery cannot be a knight, because this would contradict the claim of their own that Aiden is a knave or Owen is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Aiden is a knave or Owen is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that If Owen is a knight then Aiden is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 3), ('lying', 1)), ('<=>', ('lying', 5), ('lying', 0)), ('->', ('telling-truth', 1), ('lying', 6)), ('->', ('lying', 1), ('telling-truth', 0)), ('or', ('lying', 3), ('lying', 2)), ('not', ('lying', 0)), ('and', ('telling-truth', 5), ('lying', 4)), ('->', ('telling-truth', 2), ('telling-truth', 3)))", "index": 534}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lucas, David, Abigail, Lily, Amelia, Ethan, Ella, and Sofia. Lucas commented, \"David is a knight and Amelia is a knave\". According to David, \"Amelia is a knave\". \"Ethan is a knight\" - Abigail. Lily stated, \"Lucas is a knave or Abigail is a knight\". As Amelia put it, \"Amelia is a knight or Sofia is a knave\". \"Amelia is a knave and Ella is a knave,\" Ethan mentioned. \"Abigail is a knight if and only if David is a knight,\" Ella mentioned. Sofia said, \"Ella is a knave if and only if Lily is a knave.\" So who is a knight and who is a knave?", "names": ["Lucas", "David", "Abigail", "Lily", "Amelia", "Ethan", "Ella", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, false, true, true], "solution_text": "Lucas is a knave, David is a knave, Abigail is a knave, Lily is a knight, Amelia is a knight, Ethan is a knave, Ella is a knight, and Sofia is a knight.", "solution_text_format": "(1) Lucas is a knave\n(2) David is a knave\n(3) Abigail is a knave\n(4) Lily is a knight\n(5) Amelia is a knight\n(6) Ethan is a knave\n(7) Ella is a knight\n(8) Sofia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that David is a knight and Amelia is a knave.", "Assume David is a knight. No contradiction is found in their claim that Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Lucas that David is a knight and Amelia is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Amelia is a knight or Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Ella is a knave if and only if Lily is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Abigail is a knight if and only if David is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Ethan is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Amelia is a knave and Ella is a knave.", "Ethan cannot be a knave, because this would contradict the claim of Abigail that Ethan is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the claim of Ella that Abigail is a knight if and only if David is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Abigail is a knight if and only if David is a knight.", "Abigail cannot be a knight, because this would contradict the false claim of Ella that Abigail is a knight if and only if David is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Ethan is a knight.", "Ethan cannot be a knight, because this would contradict the false claim of Abigail that Ethan is a knight.", "Ethan cannot be a knave, because this would contradict the false claim of their own that Amelia is a knave and Ella is a knave.", "We have exhausted all possibilities for Ethan, Abigail, and Ella, so let us go back and reconsider Sofia.", "Sofia cannot be a knave, because this would contradict the false claim of Amelia that Amelia is a knight or Sofia is a knave.", "We have exhausted all possibilities for Sofia and Amelia, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the claim of Lucas that David is a knight and Amelia is a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that David is a knight and Amelia is a knave.", "Assume David is a knight. No contradiction is found in their claim that Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of David that Amelia is a knave.", "Amelia cannot be a knave, because this would contradict the false claim of Lucas that David is a knight and Amelia is a knave.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Amelia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Amelia is a knight or Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Ella is a knave if and only if Lily is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Abigail is a knight if and only if David is a knight.", "Abigail cannot be a knight, because this would contradict the claim of Ella that Abigail is a knight if and only if David is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Ethan is a knight.", "Ethan cannot be a knight, because this would contradict the false claim of Abigail that Ethan is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Amelia is a knave and Ella is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Lucas is a knave or Abigail is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('lying', 4)), ('lying', 4), ('telling-truth', 5), ('or', ('lying', 0), ('telling-truth', 2)), ('or', ('telling-truth', 4), ('lying', 7)), ('and', ('lying', 4), ('lying', 6)), ('<=>', ('telling-truth', 2), ('telling-truth', 1)), ('<=>', ('lying', 6), ('lying', 3)))", "index": 535}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Evelyn, Scarlett, Daniel, Elizabeth, Matthew, Harper, Noah, and Sebastian. Evelyn told you that Matthew is a knave or Harper is a knave. Scarlett was heard saying, \"Evelyn is a knave and Noah is a knight\". Daniel commented, \"Noah is a knight or Scarlett is a knight\". Elizabeth remarked, \"Noah is a knight if and only if Noah is a knave\". Matthew said that If Elizabeth is a knave then Noah is a knight. Harper was heard saying, \"Noah is a knave and Scarlett is a knight\". \"Noah is a knight and Scarlett is a knight,\" Noah claimed. \"If Harper is a knave then Noah is a knave\" - Sebastian. So who is a knight and who is a knave?", "names": ["Evelyn", "Scarlett", "Daniel", "Elizabeth", "Matthew", "Harper", "Noah", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, false, false, true], "solution_text": "Evelyn is a knight, Scarlett is a knave, Daniel is a knave, Elizabeth is a knave, Matthew is a knave, Harper is a knave, Noah is a knave, and Sebastian is a knight.", "solution_text_format": "(1) Evelyn is a knight\n(2) Scarlett is a knave\n(3) Daniel is a knave\n(4) Elizabeth is a knave\n(5) Matthew is a knave\n(6) Harper is a knave\n(7) Noah is a knave\n(8) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Matthew is a knave or Harper is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Noah is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Noah is a knight if and only if Noah is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Noah is a knight if and only if Noah is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Noah is a knight and Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave and Noah is a knight.", "Scarlett cannot be a knave, because this would contradict the claim of Noah that Noah is a knight and Scarlett is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the claim of Matthew that If Elizabeth is a knave then Noah is a knight.", "We have exhausted all possibilities for Noah and Elizabeth, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that If Elizabeth is a knave then Noah is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Noah is a knight if and only if Noah is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Noah is a knight if and only if Noah is a knave.", "Noah cannot be a knight, because this would contradict the false claim of Matthew that If Elizabeth is a knave then Noah is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Noah is a knight and Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave and Noah is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Evelyn is a knave and Noah is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that Noah is a knave and Scarlett is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Noah is a knave and Scarlett is a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that Noah is a knight or Scarlett is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Noah is a knight or Scarlett is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Harper is a knave then Noah is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 4), ('lying', 5)), ('and', ('lying', 0), ('telling-truth', 6)), ('or', ('telling-truth', 6), ('telling-truth', 1)), ('<=>', ('telling-truth', 6), ('lying', 6)), ('->', ('lying', 3), ('telling-truth', 6)), ('and', ('lying', 6), ('telling-truth', 1)), ('and', ('telling-truth', 6), ('telling-truth', 1)), ('->', ('lying', 5), ('lying', 6)))", "index": 536}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ella, Grace, Aiden, Liam, Sebastian, Alexander, Riley, and Michael. Ella was heard saying, \"Grace is a knight\". Grace expressed that If Alexander is a knight then Aiden is a knave. Aiden was heard saying, \"Grace is a knight\". Liam commented, \"If Aiden is a knight then Sebastian is a knight\". Sebastian was heard saying, \"If Riley is a knight then Sebastian is a knight\". Alexander remarked, \"Ella is a knave or Liam is a knight\". Riley remarked, \"Michael is a knave if and only if Ella is a knight\". In a statement by Michael: \"Ella is a knave\". So who is a knight and who is a knave?", "names": ["Ella", "Grace", "Aiden", "Liam", "Sebastian", "Alexander", "Riley", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false, true, false], "solution_text": "Ella is a knight, Grace is a knight, Aiden is a knight, Liam is a knave, Sebastian is a knave, Alexander is a knave, Riley is a knight, and Michael is a knave.", "solution_text_format": "(1) Ella is a knight\n(2) Grace is a knight\n(3) Aiden is a knight\n(4) Liam is a knave\n(5) Sebastian is a knave\n(6) Alexander is a knave\n(7) Riley is a knight\n(8) Michael is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that If Alexander is a knight then Aiden is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Ella is a knave or Liam is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that If Aiden is a knight then Sebastian is a knight.", "Aiden cannot be a knight, because this would contradict the claim of Grace that If Alexander is a knight then Aiden is a knave.", "Aiden cannot be a knave, because this would contradict the false claim of their own that Grace is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the claim of Alexander that Ella is a knave or Liam is a knight.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Ella is a knave or Liam is a knight.", "Liam cannot be a knight, because this would contradict the false claim of Alexander that Ella is a knave or Liam is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that If Aiden is a knight then Sebastian is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Grace is a knight.", "Sebastian cannot be a knight, because this would contradict the false claim of Liam that If Aiden is a knight then Sebastian is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that If Riley is a knight then Sebastian is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Michael is a knave if and only if Ella is a knight.", "Michael cannot be a knight, because this would contradict the claim of Riley that Michael is a knave if and only if Ella is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Ella is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('->', ('telling-truth', 5), ('lying', 2)), ('telling-truth', 1), ('->', ('telling-truth', 2), ('telling-truth', 4)), ('->', ('telling-truth', 6), ('telling-truth', 4)), ('or', ('lying', 0), ('telling-truth', 3)), ('<=>', ('lying', 7), ('telling-truth', 0)), ('lying', 0))", "index": 537}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Daniel, Jacob, Alexander, Sophia, David, Sofia, Logan, and Aria. Daniel was heard saying, \"Alexander is a knight if and only if Aria is a knight\". Jacob noted, \"Sofia is not a knave\". According to Alexander, \"David is a knave\". Sophia commented, \"Sophia is a knight and Jacob is a knight\". According to David, \"If Sophia is a knave then Logan is a knight\". Sofia said that If Sophia is a knave then Jacob is a knave. Logan said, \"Alexander is a knave.\" \"David is a knave and Jacob is a knave\" - Aria. So who is a knight and who is a knave?", "names": ["Daniel", "Jacob", "Alexander", "Sophia", "David", "Sofia", "Logan", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true, true, false], "solution_text": "Daniel is a knight, Jacob is a knight, Alexander is a knave, Sophia is a knight, David is a knight, Sofia is a knight, Logan is a knight, and Aria is a knave.", "solution_text_format": "(1) Daniel is a knight\n(2) Jacob is a knight\n(3) Alexander is a knave\n(4) Sophia is a knight\n(5) David is a knight\n(6) Sofia is a knight\n(7) Logan is a knight\n(8) Aria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that Alexander is a knight if and only if Aria is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that David is a knave.", "David cannot be a knight, because this would contradict the claim of Alexander that David is a knave.", "Assume David is a knave. No contradiction is found in their false claim that If Sophia is a knave then Logan is a knight.", "Sophia cannot be a knight, because this would contradict the false claim of David that If Sophia is a knave then Logan is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Sophia is a knight and Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Sofia is not a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that If Sophia is a knave then Jacob is a knave.", "Sofia cannot be a knave, because this would contradict the claim of Jacob that Sofia is not a knave.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Sofia is not a knave.", "Sofia cannot be a knight, because this would contradict the false claim of Jacob that Sofia is not a knave.", "Sofia cannot be a knave, because this would contradict the false claim of their own that If Sophia is a knave then Jacob is a knave.", "We have exhausted all possibilities for Sofia, Jacob, Sophia, and David, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that David is a knave.", "Assume David is a knight. No contradiction is found in their claim that If Sophia is a knave then Logan is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Sophia is a knight and Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Sofia is not a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that If Sophia is a knave then Jacob is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Alexander is a knave.", "Aria cannot be a knight, because this would contradict the claim of Daniel that Alexander is a knight if and only if Aria is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that David is a knave and Jacob is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('telling-truth', 7)), ('not', ('lying', 5)), ('lying', 4), ('and', ('telling-truth', 3), ('telling-truth', 1)), ('->', ('lying', 3), ('telling-truth', 6)), ('->', ('lying', 3), ('lying', 1)), ('lying', 2), ('and', ('lying', 4), ('lying', 1)))", "index": 538}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sophia, Aiden, Henry, Alexander, Ava, William, Amelia, and Noah. Sophia was heard saying, \"Noah is a knave or Henry is a knight\". Aiden was heard saying, \"If Noah is a knave then Noah is a knight\". According to Henry, \"Noah is a knight\". Alexander said that Noah is a knave if and only if Henry is a knave. Ava expressed that Amelia is a knave or Amelia is a knight. William asserted: \"Noah is a knight\". Amelia stated, \"Henry is not a knight\". Noah remarked, \"Alexander is a knave\". So who is a knight and who is a knave?", "names": ["Sophia", "Aiden", "Henry", "Alexander", "Ava", "William", "Amelia", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false, true, false], "solution_text": "Sophia is a knight, Aiden is a knave, Henry is a knave, Alexander is a knight, Ava is a knight, William is a knave, Amelia is a knight, and Noah is a knave.", "solution_text_format": "(1) Sophia is a knight\n(2) Aiden is a knave\n(3) Henry is a knave\n(4) Alexander is a knight\n(5) Ava is a knight\n(6) William is a knave\n(7) Amelia is a knight\n(8) Noah is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Noah is a knave or Henry is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Alexander is a knave.", "Alexander cannot be a knight, because this would contradict the claim of Noah that Alexander is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Noah is a knave if and only if Henry is a knave.", "Henry cannot be a knight, because this would contradict the false claim of Alexander that Noah is a knave if and only if Henry is a knave.", "Henry cannot be a knave, because this would contradict the claim of Sophia that Noah is a knave or Henry is a knight.", "We have exhausted all possibilities for Henry and Alexander, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Alexander is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Noah is a knave if and only if Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of their own that Noah is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Noah is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that If Noah is a knave then Noah is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that If Noah is a knave then Noah is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Amelia is a knave or Amelia is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Henry is not a knight.", "William cannot be a knight, because this would contradict the claim of their own that Noah is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Noah is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 7), ('telling-truth', 2)), ('->', ('lying', 7), ('telling-truth', 7)), ('telling-truth', 7), ('<=>', ('lying', 7), ('lying', 2)), ('or', ('lying', 6), ('telling-truth', 6)), ('telling-truth', 7), ('not', ('telling-truth', 2)), ('lying', 3))", "index": 539}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Logan, Luke, Emily, Joseph, Michael, Scarlett, Abigail, and Lily. \"Joseph is a knight and Scarlett is a knave,\" Logan mentioned. Luke expressed that Michael is a knave and Lily is a knight. \"Logan is a knight or Michael is a knave,\" Emily mentioned. In a statement by Joseph: \"Scarlett is not a knight\". Michael told you that Joseph is a knave if and only if Lily is a knight. According to Scarlett, \"Emily is a knight if and only if Luke is a knight\". \"Michael is a knave and Scarlett is a knave,\" Abigail mentioned. \"Luke is a knave\" - Lily. So who is a knight and who is a knave?", "names": ["Logan", "Luke", "Emily", "Joseph", "Michael", "Scarlett", "Abigail", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, true, false, true], "solution_text": "Logan is a knave, Luke is a knave, Emily is a knave, Joseph is a knave, Michael is a knight, Scarlett is a knight, Abigail is a knave, and Lily is a knight.", "solution_text_format": "(1) Logan is a knave\n(2) Luke is a knave\n(3) Emily is a knave\n(4) Joseph is a knave\n(5) Michael is a knight\n(6) Scarlett is a knight\n(7) Abigail is a knave\n(8) Lily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that Joseph is a knight and Scarlett is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Scarlett is not a knight.", "Scarlett cannot be a knight, because this would contradict the claim of Logan that Joseph is a knight and Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Emily is a knight if and only if Luke is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Logan is a knight or Michael is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Joseph is a knave if and only if Lily is a knight.", "Lily cannot be a knight, because this would contradict the claim of Michael that Joseph is a knave if and only if Lily is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Luke is a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Lily is a knight.", "Luke cannot be a knave, because this would contradict the false claim of Lily that Luke is a knave.", "We have exhausted all possibilities for Luke and Lily, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Joseph is a knave if and only if Lily is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Luke is a knave.", "Luke cannot be a knight, because this would contradict the false claim of Scarlett that Emily is a knight if and only if Luke is a knight.", "Luke cannot be a knave, because this would contradict the false claim of their own that Michael is a knave and Lily is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the false claim of Michael that Joseph is a knave if and only if Lily is a knight.", "We have exhausted all possibilities for Lily and Michael, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the false claim of their own that Logan is a knight or Michael is a knave.", "We have exhausted all possibilities for Emily and Scarlett, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of Logan that Joseph is a knight and Scarlett is a knave.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Joseph is a knight and Scarlett is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Scarlett is not a knight.", "Scarlett cannot be a knight, because this would contradict the claim of Joseph that Scarlett is not a knight.", "Scarlett cannot be a knave, because this would contradict the false claim of Logan that Joseph is a knight and Scarlett is a knave.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Scarlett is not a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Emily is a knight if and only if Luke is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Logan is a knight or Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of Emily that Logan is a knight or Michael is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Joseph is a knave if and only if Lily is a knight.", "Lily cannot be a knight, because this would contradict the false claim of Michael that Joseph is a knave if and only if Lily is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Luke is a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Lily is a knight.", "Luke cannot be a knave, because this would contradict the claim of Scarlett that Emily is a knight if and only if Luke is a knight.", "We have exhausted all possibilities for Luke, Lily, and Michael, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Logan is a knight or Michael is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Joseph is a knave if and only if Lily is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Luke is a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Lily is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Michael is a knave and Lily is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Scarlett is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Michael is a knave and Scarlett is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('lying', 5)), ('and', ('lying', 4), ('telling-truth', 7)), ('or', ('telling-truth', 0), ('lying', 4)), ('not', ('telling-truth', 5)), ('<=>', ('lying', 3), ('telling-truth', 7)), ('<=>', ('telling-truth', 2), ('telling-truth', 1)), ('and', ('lying', 4), ('lying', 5)), ('lying', 1))", "index": 540}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Logan, Benjamin, Isabella, Olivia, Aiden, Michael, Matthew, and Lucas. Logan asserted: \"Benjamin is a knight and Lucas is a knight\". Benjamin noted, \"Olivia is not a knave\". Isabella said, \"Michael is a knave if and only if Olivia is a knight.\" Olivia asserted: \"Logan is a knave if and only if Aiden is a knight\". Aiden commented, \"Olivia is a knave or Matthew is a knight\". \"Matthew is a knave if and only if Michael is a knight,\" Michael mentioned. In a statement by Matthew: \"Aiden is not a knave\". Lucas stated, \"If Aiden is a knave then Michael is a knight\". So who is a knight and who is a knave?", "names": ["Logan", "Benjamin", "Isabella", "Olivia", "Aiden", "Michael", "Matthew", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true, false, true], "solution_text": "Logan is a knight, Benjamin is a knight, Isabella is a knave, Olivia is a knight, Aiden is a knave, Michael is a knight, Matthew is a knave, and Lucas is a knight.", "solution_text_format": "(1) Logan is a knight\n(2) Benjamin is a knight\n(3) Isabella is a knave\n(4) Olivia is a knight\n(5) Aiden is a knave\n(6) Michael is a knight\n(7) Matthew is a knave\n(8) Lucas is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that Benjamin is a knight and Lucas is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Olivia is not a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Logan is a knave if and only if Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the claim of Olivia that Logan is a knave if and only if Aiden is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Olivia is a knave or Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the false claim of Aiden that Olivia is a knave or Matthew is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Aiden is not a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that If Aiden is a knave then Michael is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Matthew is a knave if and only if Michael is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Michael is a knave if and only if Olivia is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Michael is a knave if and only if Olivia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('telling-truth', 7)), ('not', ('lying', 3)), ('<=>', ('lying', 5), ('telling-truth', 3)), ('<=>', ('lying', 0), ('telling-truth', 4)), ('or', ('lying', 3), ('telling-truth', 6)), ('<=>', ('lying', 6), ('telling-truth', 5)), ('not', ('lying', 4)), ('->', ('lying', 4), ('telling-truth', 5)))", "index": 541}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Luke, Ella, Elizabeth, Evelyn, Ethan, William, Olivia, and James. Luke asserted: \"James is a knight if and only if Evelyn is a knave\". \"Ella is a knight or Evelyn is a knight\" - Ella. \"Ella is a knave and William is a knave\" - Elizabeth. Evelyn remarked, \"Elizabeth is a knave or Luke is a knight\". Ethan stated, \"Evelyn is a knave\". William asserted: \"Ethan is a knight\". Olivia noted, \"Evelyn is a knight and Ethan is a knight\". In a statement by James: \"Ella is a knight\". So who is a knight and who is a knave?", "names": ["Luke", "Ella", "Elizabeth", "Evelyn", "Ethan", "William", "Olivia", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, false, false, true], "solution_text": "Luke is a knave, Ella is a knight, Elizabeth is a knave, Evelyn is a knight, Ethan is a knave, William is a knave, Olivia is a knave, and James is a knight.", "solution_text_format": "(1) Luke is a knave\n(2) Ella is a knight\n(3) Elizabeth is a knave\n(4) Evelyn is a knight\n(5) Ethan is a knave\n(6) William is a knave\n(7) Olivia is a knave\n(8) James is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that James is a knight if and only if Evelyn is a knave.", "Assume James is a knight. No contradiction is found in their claim that Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Ella is a knight or Evelyn is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of Luke that James is a knight if and only if Evelyn is a knave.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that Elizabeth is a knave or Luke is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the claim of James that Ella is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Ella is a knight.", "Ella cannot be a knight, because this would contradict the false claim of James that Ella is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Ella is a knight or Evelyn is a knight.", "Evelyn cannot be a knight, because this would contradict the false claim of Ella that Ella is a knight or Evelyn is a knight.", "Evelyn cannot be a knave, because this would contradict the claim of Luke that James is a knight if and only if Evelyn is a knave.", "We have exhausted all possibilities for Evelyn, Ella, and James, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that James is a knight if and only if Evelyn is a knave.", "Assume James is a knight. No contradiction is found in their claim that Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Ella is a knight or Evelyn is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Elizabeth is a knave or Luke is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Ella is a knave and William is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Ella is a knave and William is a knave.", "Assume William is a knight. No contradiction is found in their claim that Ethan is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave.", "Ethan cannot be a knave, because this would contradict the claim of William that Ethan is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Ethan is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Evelyn is a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that Evelyn is a knight and Ethan is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Evelyn is a knight and Ethan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 7), ('lying', 3)), ('or', ('telling-truth', 1), ('telling-truth', 3)), ('and', ('lying', 1), ('lying', 5)), ('or', ('lying', 2), ('telling-truth', 0)), ('lying', 3), ('telling-truth', 4), ('and', ('telling-truth', 3), ('telling-truth', 4)), ('telling-truth', 1))", "index": 542}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mason, Luke, Abigail, Samuel, Elizabeth, Ella, Benjamin, and Daniel. Mason told you that Daniel is a knave if and only if Abigail is a knight. \"Elizabeth is a knight or Samuel is a knight\" - Luke. In a statement by Abigail: \"Mason is a knave\". Samuel told you that Benjamin is a knave and Ella is a knave. Elizabeth stated, \"Daniel is a knight or Mason is a knight\". \"Mason is not a knave,\" Ella declared. \"Ella is a knave and Abigail is a knave\" - Benjamin. Daniel stated, \"Elizabeth is a knight if and only if Abigail is a knight\". So who is a knight and who is a knave?", "names": ["Mason", "Luke", "Abigail", "Samuel", "Elizabeth", "Ella", "Benjamin", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false, false, true], "solution_text": "Mason is a knave, Luke is a knight, Abigail is a knight, Samuel is a knight, Elizabeth is a knight, Ella is a knave, Benjamin is a knave, and Daniel is a knight.", "solution_text_format": "(1) Mason is a knave\n(2) Luke is a knight\n(3) Abigail is a knight\n(4) Samuel is a knight\n(5) Elizabeth is a knight\n(6) Ella is a knave\n(7) Benjamin is a knave\n(8) Daniel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Daniel is a knave if and only if Abigail is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Elizabeth is a knight if and only if Abigail is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Daniel is a knight or Mason is a knight.", "Abigail cannot be a knight, because this would contradict the claim of Mason that Daniel is a knave if and only if Abigail is a knight.", "Abigail cannot be a knave, because this would contradict the claim of Daniel that Elizabeth is a knight if and only if Abigail is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Elizabeth.", "Elizabeth cannot be a knave, because this would contradict the false claim of their own that Daniel is a knight or Mason is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Elizabeth is a knight if and only if Abigail is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Daniel is a knight or Mason is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Mason is a knave.", "Abigail cannot be a knave, because this would contradict the claim of Mason that Daniel is a knave if and only if Abigail is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Elizabeth.", "Elizabeth cannot be a knave, because this would contradict the false claim of their own that Daniel is a knight or Mason is a knight.", "We have exhausted all possibilities for Elizabeth and Daniel, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Daniel is a knave if and only if Abigail is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Elizabeth is a knight if and only if Abigail is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Daniel is a knight or Mason is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Mason is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Elizabeth is a knight or Samuel is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Benjamin is a knave and Ella is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Samuel that Benjamin is a knave and Ella is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Ella is a knave and Abigail is a knave.", "Ella cannot be a knight, because this would contradict the claim of Samuel that Benjamin is a knave and Ella is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Mason is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 7), ('telling-truth', 2)), ('or', ('telling-truth', 4), ('telling-truth', 3)), ('lying', 0), ('and', ('lying', 6), ('lying', 5)), ('or', ('telling-truth', 7), ('telling-truth', 0)), ('not', ('lying', 0)), ('and', ('lying', 5), ('lying', 2)), ('<=>', ('telling-truth', 4), ('telling-truth', 2)))", "index": 543}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Alexander, Abigail, Mia, Zoey, James, Chloe, Charlotte, and Matthew. Alexander was heard saying, \"Charlotte is not a knave\". Abigail was heard saying, \"Charlotte is a knave or Zoey is a knight\". In Mia's words: \"If James is a knight then Abigail is a knave\". Zoey told you that Chloe is a knave. According to James, \"Charlotte is a knave if and only if Abigail is a knave\". According to Chloe, \"Abigail is a knave if and only if Matthew is a knight\". Charlotte expressed that Charlotte is a knight if and only if Zoey is a knight. Matthew asserted: \"Zoey is a knave or Charlotte is a knave\". So who is a knight and who is a knave?", "names": ["Alexander", "Abigail", "Mia", "Zoey", "James", "Chloe", "Charlotte", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false, false, true], "solution_text": "Alexander is a knave, Abigail is a knight, Mia is a knight, Zoey is a knight, James is a knave, Chloe is a knave, Charlotte is a knave, and Matthew is a knight.", "solution_text_format": "(1) Alexander is a knave\n(2) Abigail is a knight\n(3) Mia is a knight\n(4) Zoey is a knight\n(5) James is a knave\n(6) Chloe is a knave\n(7) Charlotte is a knave\n(8) Matthew is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that Charlotte is not a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Charlotte is a knight if and only if Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Zoey that Chloe is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Abigail is a knave if and only if Matthew is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Charlotte is a knave or Zoey is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Zoey is a knave or Charlotte is a knave.", "Matthew cannot be a knave, because this would contradict the false claim of Chloe that Abigail is a knave if and only if Matthew is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the false claim of their own that Charlotte is a knave or Zoey is a knight.", "We have exhausted all possibilities for Abigail and Chloe, so let us go back and reconsider Zoey.", "Zoey cannot be a knave, because this would contradict the claim of Charlotte that Charlotte is a knight if and only if Zoey is a knight.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the claim of Alexander that Charlotte is not a knave.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Charlotte is not a knave.", "Charlotte cannot be a knight, because this would contradict the false claim of Alexander that Charlotte is not a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Charlotte is a knight if and only if Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Zoey that Chloe is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Abigail is a knave if and only if Matthew is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Charlotte is a knave or Zoey is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Zoey is a knave or Charlotte is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that If James is a knight then Abigail is a knave.", "James cannot be a knight, because this would contradict the claim of Mia that If James is a knight then Abigail is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Charlotte is a knave if and only if Abigail is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 6)), ('or', ('lying', 6), ('telling-truth', 3)), ('->', ('telling-truth', 4), ('lying', 1)), ('lying', 5), ('<=>', ('lying', 6), ('lying', 1)), ('<=>', ('lying', 1), ('telling-truth', 7)), ('<=>', ('telling-truth', 6), ('telling-truth', 3)), ('or', ('lying', 3), ('lying', 6)))", "index": 544}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aria, Riley, Penelope, Ethan, Sebastian, Ella, Grace, and Jackson. Aria said, \"Grace is not a knight.\" Riley said that Sebastian is a knave if and only if Jackson is a knave. \"Aria is not a knave\" - Penelope. According to Ethan, \"Aria is a knave and Penelope is a knave\". \"If Ella is a knave then Grace is a knave\" - Sebastian. In a statement by Ella: \"Aria is not a knave\". Grace commented, \"If Sebastian is a knight then Ethan is a knave\". As Jackson put it, \"Ethan is a knight if and only if Sebastian is a knave\". So who is a knight and who is a knave?", "names": ["Aria", "Riley", "Penelope", "Ethan", "Sebastian", "Ella", "Grace", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, false, true, true], "solution_text": "Aria is a knave, Riley is a knave, Penelope is a knave, Ethan is a knight, Sebastian is a knave, Ella is a knave, Grace is a knight, and Jackson is a knight.", "solution_text_format": "(1) Aria is a knave\n(2) Riley is a knave\n(3) Penelope is a knave\n(4) Ethan is a knight\n(5) Sebastian is a knave\n(6) Ella is a knave\n(7) Grace is a knight\n(8) Jackson is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that Grace is not a knight.", "Grace cannot be a knight, because this would contradict the claim of Aria that Grace is not a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that If Sebastian is a knight then Ethan is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Ella is a knave then Grace is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Aria is not a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Aria is a knave and Penelope is a knave.", "Ethan cannot be a knave, because this would contradict the false claim of Grace that If Sebastian is a knight then Ethan is a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the false claim of their own that Aria is not a knave.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the false claim of their own that If Ella is a knave then Grace is a knave.", "We have exhausted all possibilities for Sebastian and Grace, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Grace is not a knight.", "Assume Grace is a knight. No contradiction is found in their claim that If Sebastian is a knight then Ethan is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Ella is a knave then Grace is a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Aria is not a knave.", "Ella cannot be a knave, because this would contradict the claim of Sebastian that If Ella is a knave then Grace is a knave.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that If Ella is a knave then Grace is a knave.", "Ella cannot be a knight, because this would contradict the false claim of Sebastian that If Ella is a knave then Grace is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Aria is not a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Aria is a knave and Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Aria is not a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Aria is not a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Sebastian is a knave if and only if Jackson is a knave.", "Jackson cannot be a knight, because this would contradict the claim of Riley that Sebastian is a knave if and only if Jackson is a knave.", "Jackson cannot be a knave, because this would contradict the false claim of their own that Ethan is a knight if and only if Sebastian is a knave.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Sebastian is a knave if and only if Jackson is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Ethan is a knight if and only if Sebastian is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 6)), ('<=>', ('lying', 4), ('lying', 7)), ('not', ('lying', 0)), ('and', ('lying', 0), ('lying', 2)), ('->', ('lying', 5), ('lying', 6)), ('not', ('lying', 0)), ('->', ('telling-truth', 4), ('lying', 3)), ('<=>', ('telling-truth', 3), ('lying', 4)))", "index": 545}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Alexander, Emily, Ava, Sophia, Owen, Jacob, Ethan, and Charlotte. In a statement by Alexander: \"Ava is a knight\". Emily noted, \"Jacob is a knave or Alexander is a knave\". \"If Owen is a knight then Jacob is a knave\" - Ava. Sophia said that Ava is a knight. Owen told you that If Ethan is a knight then Emily is a knave. In Jacob's words: \"Charlotte is not a knight\". Ethan expressed that Alexander is not a knave. Charlotte remarked, \"Charlotte is a knight or Sophia is a knave\". So who is a knight and who is a knave?", "names": ["Alexander", "Emily", "Ava", "Sophia", "Owen", "Jacob", "Ethan", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false, true, true], "solution_text": "Alexander is a knight, Emily is a knight, Ava is a knight, Sophia is a knight, Owen is a knave, Jacob is a knave, Ethan is a knight, and Charlotte is a knight.", "solution_text_format": "(1) Alexander is a knight\n(2) Emily is a knight\n(3) Ava is a knight\n(4) Sophia is a knight\n(5) Owen is a knave\n(6) Jacob is a knave\n(7) Ethan is a knight\n(8) Charlotte is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that Ava is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that If Owen is a knight then Jacob is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that If Ethan is a knight then Emily is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Alexander is not a knave.", "Emily cannot be a knight, because this would contradict the claim of Owen that If Ethan is a knight then Emily is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Jacob is a knave or Alexander is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Ava that If Owen is a knight then Jacob is a knave.", "Jacob cannot be a knave, because this would contradict the false claim of Emily that Jacob is a knave or Alexander is a knave.", "We have exhausted all possibilities for Jacob and Emily, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the false claim of their own that Alexander is not a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that If Ethan is a knight then Emily is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Alexander is not a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Jacob is a knave or Alexander is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Emily that Jacob is a knave or Alexander is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Charlotte is not a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Charlotte is a knight or Sophia is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Ava is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('or', ('lying', 5), ('lying', 0)), ('->', ('telling-truth', 4), ('lying', 5)), ('telling-truth', 2), ('->', ('telling-truth', 6), ('lying', 1)), ('not', ('telling-truth', 7)), ('not', ('lying', 0)), ('or', ('telling-truth', 7), ('lying', 3)))", "index": 546}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Owen, Matthew, Benjamin, Oliver, Lily, Aurora, Aria, and Chloe. Owen expressed that Chloe is not a knight. Matthew told you that Owen is a knight and Lily is a knight. Benjamin was heard saying, \"Oliver is a knave\". Oliver said, \"Owen is a knight.\" Lily stated, \"Oliver is not a knave\". \"Lily is a knave,\" Aurora claimed. Aria was heard saying, \"Aurora is a knight\". \"Aria is a knight or Aria is a knave\" - Chloe. So who is a knight and who is a knave?", "names": ["Owen", "Matthew", "Benjamin", "Oliver", "Lily", "Aurora", "Aria", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, true, true, true], "solution_text": "Owen is a knave, Matthew is a knave, Benjamin is a knight, Oliver is a knave, Lily is a knave, Aurora is a knight, Aria is a knight, and Chloe is a knight.", "solution_text_format": "(1) Owen is a knave\n(2) Matthew is a knave\n(3) Benjamin is a knight\n(4) Oliver is a knave\n(5) Lily is a knave\n(6) Aurora is a knight\n(7) Aria is a knight\n(8) Chloe is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Chloe is not a knight.", "Chloe cannot be a knight, because this would contradict the claim of Owen that Chloe is not a knight.", "Chloe cannot be a knave, because this would contradict the false claim of their own that Aria is a knight or Aria is a knave.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Chloe is not a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Aria is a knight or Aria is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Aurora is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of Aurora that Lily is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Oliver is not a knave.", "Oliver cannot be a knight, because this would contradict the claim of their own that Owen is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Owen is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Owen is a knight and Lily is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Owen is a knight and Lily is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Oliver is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 7)), ('and', ('telling-truth', 0), ('telling-truth', 4)), ('lying', 3), ('telling-truth', 0), ('not', ('lying', 3)), ('lying', 4), ('telling-truth', 5), ('or', ('telling-truth', 6), ('lying', 6)))", "index": 547}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sofia, Emily, David, Jack, Samuel, Victoria, Scarlett, and Charlotte. As Sofia put it, \"Jack is a knight\". Emily said that Sofia is a knight if and only if Charlotte is a knight. David noted, \"Victoria is a knave if and only if Scarlett is a knight\". As Jack put it, \"Victoria is a knave\". As Samuel put it, \"Sofia is a knight or Charlotte is a knight\". According to Victoria, \"Emily is a knave if and only if Scarlett is a knave\". Scarlett said, \"Jack is a knave.\" Charlotte remarked, \"David is not a knave\". So who is a knight and who is a knave?", "names": ["Sofia", "Emily", "David", "Jack", "Samuel", "Victoria", "Scarlett", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, true, true, false], "solution_text": "Sofia is a knave, Emily is a knight, David is a knave, Jack is a knave, Samuel is a knave, Victoria is a knight, Scarlett is a knight, and Charlotte is a knave.", "solution_text_format": "(1) Sofia is a knave\n(2) Emily is a knight\n(3) David is a knave\n(4) Jack is a knave\n(5) Samuel is a knave\n(6) Victoria is a knight\n(7) Scarlett is a knight\n(8) Charlotte is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Victoria is a knave.", "Victoria cannot be a knight, because this would contradict the claim of Jack that Victoria is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Emily is a knave if and only if Scarlett is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Sofia is a knight if and only if Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that David is not a knave.", "Assume David is a knight. No contradiction is found in their claim that Victoria is a knave if and only if Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the false claim of Victoria that Emily is a knave if and only if Scarlett is a knave.", "Scarlett cannot be a knave, because this would contradict the claim of David that Victoria is a knave if and only if Scarlett is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the claim of Charlotte that David is not a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the claim of Emily that Sofia is a knight if and only if Charlotte is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Sofia is a knight if and only if Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of Emily that Sofia is a knight if and only if Charlotte is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that David is not a knave.", "David cannot be a knight, because this would contradict the false claim of Charlotte that David is not a knave.", "Assume David is a knave. No contradiction is found in their false claim that Victoria is a knave if and only if Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the false claim of David that Victoria is a knave if and only if Scarlett is a knight.", "Scarlett cannot be a knave, because this would contradict the false claim of Victoria that Emily is a knave if and only if Scarlett is a knave.", "We have exhausted all possibilities for Scarlett, David, Charlotte, Emily, and Victoria, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the claim of Sofia that Jack is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Jack is a knight.", "Jack cannot be a knight, because this would contradict the false claim of Sofia that Jack is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Emily is a knave if and only if Scarlett is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Sofia is a knight if and only if Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Emily that Sofia is a knight if and only if Charlotte is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that David is not a knave.", "David cannot be a knight, because this would contradict the false claim of Charlotte that David is not a knave.", "Assume David is a knave. No contradiction is found in their false claim that Victoria is a knave if and only if Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Jack is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that Sofia is a knight or Charlotte is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Sofia is a knight or Charlotte is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 3), ('<=>', ('telling-truth', 0), ('telling-truth', 7)), ('<=>', ('lying', 5), ('telling-truth', 6)), ('lying', 5), ('or', ('telling-truth', 0), ('telling-truth', 7)), ('<=>', ('lying', 1), ('lying', 6)), ('lying', 3), ('not', ('lying', 2)))", "index": 548}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Oliver, Daniel, Isabella, Aiden, Avery, Luke, Lucas, and Jacob. Oliver stated, \"Daniel is a knight and Avery is a knave\". \"If Aiden is a knave then Luke is a knight,\" Daniel mentioned. Isabella was heard saying, \"Luke is a knight or Luke is a knave\". Aiden commented, \"Avery is a knave and Daniel is a knave\". In Avery's words: \"Luke is not a knight\". Luke noted, \"If Isabella is a knave then Aiden is a knave\". According to Lucas, \"Daniel is a knave if and only if Oliver is a knight\". Jacob said, \"Avery is a knave and Aiden is a knight.\" So who is a knight and who is a knave?", "names": ["Oliver", "Daniel", "Isabella", "Aiden", "Avery", "Luke", "Lucas", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true, false, false], "solution_text": "Oliver is a knight, Daniel is a knight, Isabella is a knight, Aiden is a knave, Avery is a knave, Luke is a knight, Lucas is a knave, and Jacob is a knave.", "solution_text_format": "(1) Oliver is a knight\n(2) Daniel is a knight\n(3) Isabella is a knight\n(4) Aiden is a knave\n(5) Avery is a knave\n(6) Luke is a knight\n(7) Lucas is a knave\n(8) Jacob is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Daniel is a knight and Avery is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that If Aiden is a knave then Luke is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Avery is a knave and Daniel is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Avery is a knave and Daniel is a knave.", "Avery cannot be a knight, because this would contradict the claim of Oliver that Daniel is a knight and Avery is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Luke is not a knight.", "Assume Luke is a knight. No contradiction is found in their claim that If Isabella is a knave then Aiden is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Luke is a knight or Luke is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Daniel is a knave if and only if Oliver is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Daniel is a knave if and only if Oliver is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Avery is a knave and Aiden is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Avery is a knave and Aiden is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('lying', 4)), ('->', ('lying', 3), ('telling-truth', 5)), ('or', ('telling-truth', 5), ('lying', 5)), ('and', ('lying', 4), ('lying', 1)), ('not', ('telling-truth', 5)), ('->', ('lying', 2), ('lying', 3)), ('<=>', ('lying', 1), ('telling-truth', 0)), ('and', ('lying', 4), ('telling-truth', 3)))", "index": 549}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Michael, Aiden, Oliver, Amelia, Alexander, Samuel, Noah, and Jack. In Michael's words: \"Jack is a knight\". Aiden was heard saying, \"Alexander is a knight and Noah is a knave\". Oliver was heard saying, \"Amelia is a knight if and only if Jack is a knight\". Amelia was heard saying, \"Aiden is a knight and Samuel is a knight\". In Alexander's words: \"Samuel is a knave and Amelia is a knight\". Samuel told you that Aiden is not a knight. Noah expressed that Oliver is a knight if and only if Jack is a knave. Jack noted, \"If Samuel is a knight then Samuel is a knave\". So who is a knight and who is a knave?", "names": ["Michael", "Aiden", "Oliver", "Amelia", "Alexander", "Samuel", "Noah", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, true, true, false], "solution_text": "Michael is a knave, Aiden is a knave, Oliver is a knight, Amelia is a knave, Alexander is a knave, Samuel is a knight, Noah is a knight, and Jack is a knave.", "solution_text_format": "(1) Michael is a knave\n(2) Aiden is a knave\n(3) Oliver is a knight\n(4) Amelia is a knave\n(5) Alexander is a knave\n(6) Samuel is a knight\n(7) Noah is a knight\n(8) Jack is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that If Samuel is a knight then Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Jack that If Samuel is a knight then Samuel is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Aiden is not a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Alexander is a knight and Noah is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Samuel is a knave and Amelia is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Aiden is a knight and Samuel is a knight.", "Amelia cannot be a knave, because this would contradict the claim of Alexander that Samuel is a knave and Amelia is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Alexander.", "Alexander cannot be a knave, because this would contradict the claim of Aiden that Alexander is a knight and Noah is a knave.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the false claim of Samuel that Aiden is not a knight.", "We have exhausted all possibilities for Aiden and Samuel, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the claim of Michael that Jack is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Jack is a knight.", "Jack cannot be a knight, because this would contradict the false claim of Michael that Jack is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that If Samuel is a knight then Samuel is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Aiden is not a knight.", "Aiden cannot be a knight, because this would contradict the claim of Samuel that Aiden is not a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Alexander is a knight and Noah is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that Samuel is a knave and Amelia is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Samuel is a knave and Amelia is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Aiden is a knight and Samuel is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Aiden is a knight and Samuel is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Oliver is a knight if and only if Jack is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Amelia is a knight if and only if Jack is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 7), ('and', ('telling-truth', 4), ('lying', 6)), ('<=>', ('telling-truth', 3), ('telling-truth', 7)), ('and', ('telling-truth', 1), ('telling-truth', 5)), ('and', ('lying', 5), ('telling-truth', 3)), ('not', ('telling-truth', 1)), ('<=>', ('telling-truth', 2), ('lying', 7)), ('->', ('telling-truth', 5), ('lying', 5)))", "index": 550}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ethan, Henry, Olivia, Aiden, Victoria, Liam, Daniel, and Avery. According to Ethan, \"Avery is a knight and Liam is a knight\". Henry noted, \"Ethan is a knight and Avery is a knight\". In a statement by Olivia: \"Victoria is a knave or Ethan is a knight\". \"Liam is a knave and Avery is a knave\" - Aiden. Victoria said, \"Avery is a knave if and only if Liam is a knight.\" Liam told you that If Daniel is a knight then Liam is a knight. \"Liam is not a knave,\" Daniel mentioned. Avery was heard saying, \"Victoria is a knave if and only if Avery is a knight\". So who is a knight and who is a knave?", "names": ["Ethan", "Henry", "Olivia", "Aiden", "Victoria", "Liam", "Daniel", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true, true, true], "solution_text": "Ethan is a knight, Henry is a knight, Olivia is a knight, Aiden is a knave, Victoria is a knave, Liam is a knight, Daniel is a knight, and Avery is a knight.", "solution_text_format": "(1) Ethan is a knight\n(2) Henry is a knight\n(3) Olivia is a knight\n(4) Aiden is a knave\n(5) Victoria is a knave\n(6) Liam is a knight\n(7) Daniel is a knight\n(8) Avery is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Avery is a knight and Liam is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Victoria is a knave if and only if Avery is a knight.", "Victoria cannot be a knight, because this would contradict the claim of Avery that Victoria is a knave if and only if Avery is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Avery is a knave if and only if Liam is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that If Daniel is a knight then Liam is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Liam is not a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Ethan is a knight and Avery is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Victoria is a knave or Ethan is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Liam is a knave and Avery is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Liam is a knave and Avery is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 7), ('telling-truth', 5)), ('and', ('telling-truth', 0), ('telling-truth', 7)), ('or', ('lying', 4), ('telling-truth', 0)), ('and', ('lying', 5), ('lying', 7)), ('<=>', ('lying', 7), ('telling-truth', 5)), ('->', ('telling-truth', 6), ('telling-truth', 5)), ('not', ('lying', 5)), ('<=>', ('lying', 4), ('telling-truth', 7)))", "index": 551}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aria, William, Harper, Chloe, Lucas, Aurora, Luke, and Scarlett. Aria noted, \"Aurora is a knight or Luke is a knight\". William said that If Scarlett is a knave then Scarlett is a knight. \"Chloe is a knave if and only if William is a knave,\" Harper mentioned. Chloe told you that If Scarlett is a knave then William is a knight. Lucas expressed that If Aria is a knave then William is a knave. According to Aurora, \"William is a knight if and only if Scarlett is a knave\". Luke told you that Harper is not a knave. \"Aria is a knight,\" Scarlett declared. So who is a knight and who is a knave?", "names": ["Aria", "William", "Harper", "Chloe", "Lucas", "Aurora", "Luke", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false, true, true], "solution_text": "Aria is a knight, William is a knight, Harper is a knight, Chloe is a knight, Lucas is a knight, Aurora is a knave, Luke is a knight, and Scarlett is a knight.", "solution_text_format": "(1) Aria is a knight\n(2) William is a knight\n(3) Harper is a knight\n(4) Chloe is a knight\n(5) Lucas is a knight\n(6) Aurora is a knave\n(7) Luke is a knight\n(8) Scarlett is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that Aurora is a knight or Luke is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that William is a knight if and only if Scarlett is a knave.", "Assume William is a knight. No contradiction is found in their claim that If Scarlett is a knave then Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of Aurora that William is a knight if and only if Scarlett is a knave.", "Scarlett cannot be a knave, because this would contradict the claim of William that If Scarlett is a knave then Scarlett is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that If Scarlett is a knave then Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the false claim of William that If Scarlett is a knave then Scarlett is a knight.", "Scarlett cannot be a knave, because this would contradict the claim of Aurora that William is a knight if and only if Scarlett is a knave.", "We have exhausted all possibilities for Scarlett and William, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that William is a knight if and only if Scarlett is a knave.", "Assume William is a knight. No contradiction is found in their claim that If Scarlett is a knave then Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Aria is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Harper is not a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Chloe is a knave if and only if William is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that If Scarlett is a knave then William is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that If Aria is a knave then William is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('telling-truth', 6)), ('->', ('lying', 7), ('telling-truth', 7)), ('<=>', ('lying', 3), ('lying', 1)), ('->', ('lying', 7), ('telling-truth', 1)), ('->', ('lying', 0), ('lying', 1)), ('<=>', ('telling-truth', 1), ('lying', 7)), ('not', ('lying', 2)), ('telling-truth', 0))", "index": 552}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Riley, Scarlett, Chloe, Sofia, William, Henry, Mason, and Jacob. Riley told you that Henry is a knight if and only if William is a knave. Scarlett noted, \"Henry is a knave\". As Chloe put it, \"Jacob is a knave if and only if Henry is a knave\". \"William is not a knave,\" Sofia claimed. William said, \"Riley is a knave.\" \"Henry is a knight if and only if William is a knave,\" Henry claimed. Mason commented, \"William is not a knight\". In Jacob's words: \"Henry is not a knave\". So who is a knight and who is a knave?", "names": ["Riley", "Scarlett", "Chloe", "Sofia", "William", "Henry", "Mason", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true, true, true], "solution_text": "Riley is a knight, Scarlett is a knave, Chloe is a knight, Sofia is a knave, William is a knave, Henry is a knight, Mason is a knight, and Jacob is a knight.", "solution_text_format": "(1) Riley is a knight\n(2) Scarlett is a knave\n(3) Chloe is a knight\n(4) Sofia is a knave\n(5) William is a knave\n(6) Henry is a knight\n(7) Mason is a knight\n(8) Jacob is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Henry is a knight if and only if William is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Henry is a knight if and only if William is a knave.", "William cannot be a knight, because this would contradict the claim of Riley that Henry is a knight if and only if William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Riley is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Henry is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Henry is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Jacob is a knave if and only if Henry is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Henry is not a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that William is not a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that William is not a knave.", "Assume Mason is a knight. No contradiction is found in their claim that William is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 5), ('lying', 4)), ('lying', 5), ('<=>', ('lying', 7), ('lying', 5)), ('not', ('lying', 4)), ('lying', 0), ('<=>', ('telling-truth', 5), ('lying', 4)), ('not', ('telling-truth', 4)), ('not', ('lying', 5)))", "index": 553}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lucas, Penelope, Emily, Olivia, Sebastian, James, Owen, and Zoey. In a statement by Lucas: \"Owen is a knight\". Penelope asserted: \"Sebastian is a knave\". Emily asserted: \"Zoey is a knave or Penelope is a knight\". Olivia said, \"Lucas is a knave and Owen is a knave.\" Sebastian told you that Zoey is a knave and Penelope is a knight. James expressed that If Lucas is a knave then Olivia is a knave. In Owen's words: \"Zoey is not a knave\". \"If Emily is a knave then Lucas is a knave,\" Zoey claimed. So who is a knight and who is a knave?", "names": ["Lucas", "Penelope", "Emily", "Olivia", "Sebastian", "James", "Owen", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true, true, true], "solution_text": "Lucas is a knight, Penelope is a knight, Emily is a knight, Olivia is a knave, Sebastian is a knave, James is a knight, Owen is a knight, and Zoey is a knight.", "solution_text_format": "(1) Lucas is a knight\n(2) Penelope is a knight\n(3) Emily is a knight\n(4) Olivia is a knave\n(5) Sebastian is a knave\n(6) James is a knight\n(7) Owen is a knight\n(8) Zoey is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that Owen is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Zoey is not a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that If Emily is a knave then Lucas is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Zoey is a knave or Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Penelope that Sebastian is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Zoey is a knave and Penelope is a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that Lucas is a knave and Owen is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Lucas is a knave and Owen is a knave.", "Assume James is a knight. No contradiction is found in their claim that If Lucas is a knave then Olivia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 6), ('lying', 4), ('or', ('lying', 7), ('telling-truth', 1)), ('and', ('lying', 0), ('lying', 6)), ('and', ('lying', 7), ('telling-truth', 1)), ('->', ('lying', 0), ('lying', 3)), ('not', ('lying', 7)), ('->', ('lying', 2), ('lying', 0)))", "index": 554}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emily, Victoria, Ella, Abigail, Elizabeth, Samuel, Scarlett, and Sebastian. Emily said that Victoria is a knight or Ella is a knave. Victoria told you that Samuel is a knave and Sebastian is a knave. Ella remarked, \"If Scarlett is a knave then Samuel is a knight\". Abigail noted, \"If Victoria is a knave then Scarlett is a knave\". In a statement by Elizabeth: \"If Victoria is a knave then Ella is a knight\". Samuel told you that Emily is not a knight. In a statement by Scarlett: \"Elizabeth is a knight or Ella is a knave\". \"Abigail is a knave or Elizabeth is a knight,\" Sebastian claimed. So who is a knight and who is a knave?", "names": ["Emily", "Victoria", "Ella", "Abigail", "Elizabeth", "Samuel", "Scarlett", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true, true, true], "solution_text": "Emily is a knave, Victoria is a knave, Ella is a knight, Abigail is a knave, Elizabeth is a knight, Samuel is a knight, Scarlett is a knight, and Sebastian is a knight.", "solution_text_format": "(1) Emily is a knave\n(2) Victoria is a knave\n(3) Ella is a knight\n(4) Abigail is a knave\n(5) Elizabeth is a knight\n(6) Samuel is a knight\n(7) Scarlett is a knight\n(8) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Victoria is a knight or Ella is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Samuel is a knave and Sebastian is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Victoria that Samuel is a knave and Sebastian is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Emily is not a knight.", "Sebastian cannot be a knight, because this would contradict the claim of Victoria that Samuel is a knave and Sebastian is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Abigail is a knave or Elizabeth is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If Victoria is a knave then Scarlett is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Elizabeth is a knight or Ella is a knave.", "Elizabeth cannot be a knight, because this would contradict the false claim of Sebastian that Abigail is a knave or Elizabeth is a knight.", "Elizabeth cannot be a knave, because this would contradict the false claim of their own that If Victoria is a knave then Ella is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Elizabeth is a knight or Ella is a knave.", "Elizabeth cannot be a knight, because this would contradict the false claim of Scarlett that Elizabeth is a knight or Ella is a knave.", "Elizabeth cannot be a knave, because this would contradict the false claim of their own that If Victoria is a knave then Ella is a knight.", "We have exhausted all possibilities for Elizabeth and Scarlett, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the false claim of their own that If Victoria is a knave then Scarlett is a knave.", "We have exhausted all possibilities for Abigail, Sebastian, and Samuel, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Samuel is a knave and Sebastian is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that Emily is not a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Emily is not a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Abigail is a knave or Elizabeth is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If Victoria is a knave then Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Abigail that If Victoria is a knave then Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Elizabeth is a knight or Ella is a knave.", "Elizabeth cannot be a knight, because this would contradict the false claim of Scarlett that Elizabeth is a knight or Ella is a knave.", "Elizabeth cannot be a knave, because this would contradict the claim of Sebastian that Abigail is a knave or Elizabeth is a knight.", "We have exhausted all possibilities for Elizabeth and Scarlett, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that If Victoria is a knave then Scarlett is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Elizabeth is a knight or Ella is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Victoria is a knave then Ella is a knight.", "Ella cannot be a knight, because this would contradict the claim of Emily that Victoria is a knight or Ella is a knave.", "Ella cannot be a knave, because this would contradict the false claim of their own that If Scarlett is a knave then Samuel is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that If Victoria is a knave then Ella is a knight.", "Ella cannot be a knight, because this would contradict the claim of Emily that Victoria is a knight or Ella is a knave.", "Ella cannot be a knave, because this would contradict the false claim of their own that If Scarlett is a knave then Samuel is a knight.", "We have exhausted all possibilities for Ella and Elizabeth, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the false claim of Abigail that If Victoria is a knave then Scarlett is a knave.", "We have exhausted all possibilities for Scarlett and Abigail, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the false claim of Victoria that Samuel is a knave and Sebastian is a knave.", "We have exhausted all possibilities for Sebastian, Samuel, and Victoria, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Victoria is a knight or Ella is a knave.", "Victoria cannot be a knight, because this would contradict the false claim of Emily that Victoria is a knight or Ella is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Samuel is a knave and Sebastian is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Emily is not a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Abigail is a knave or Elizabeth is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If Victoria is a knave then Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Abigail that If Victoria is a knave then Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Elizabeth is a knight or Ella is a knave.", "Elizabeth cannot be a knight, because this would contradict the false claim of Scarlett that Elizabeth is a knight or Ella is a knave.", "Elizabeth cannot be a knave, because this would contradict the claim of Sebastian that Abigail is a knave or Elizabeth is a knight.", "We have exhausted all possibilities for Elizabeth and Scarlett, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that If Victoria is a knave then Scarlett is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Elizabeth is a knight or Ella is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Victoria is a knave then Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that If Scarlett is a knave then Samuel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('lying', 2)), ('and', ('lying', 5), ('lying', 7)), ('->', ('lying', 6), ('telling-truth', 5)), ('->', ('lying', 1), ('lying', 6)), ('->', ('lying', 1), ('telling-truth', 2)), ('not', ('telling-truth', 0)), ('or', ('telling-truth', 4), ('lying', 2)), ('or', ('lying', 3), ('telling-truth', 4)))", "index": 555}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Evelyn, Joseph, Benjamin, Abigail, Chloe, Avery, Grace, and Scarlett. Evelyn expressed that Avery is not a knight. Joseph said that Chloe is a knight or Evelyn is a knight. As Benjamin put it, \"Scarlett is a knight or Abigail is a knave\". Abigail said that Benjamin is a knave if and only if Scarlett is a knight. In Chloe's words: \"Abigail is a knave\". \"Scarlett is a knight or Joseph is a knave,\" Avery claimed. Grace said, \"Chloe is not a knight.\" Scarlett commented, \"Joseph is a knight or Avery is a knight\". So who is a knight and who is a knave?", "names": ["Evelyn", "Joseph", "Benjamin", "Abigail", "Chloe", "Avery", "Grace", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true, false, true], "solution_text": "Evelyn is a knave, Joseph is a knight, Benjamin is a knight, Abigail is a knave, Chloe is a knight, Avery is a knight, Grace is a knave, and Scarlett is a knight.", "solution_text_format": "(1) Evelyn is a knave\n(2) Joseph is a knight\n(3) Benjamin is a knight\n(4) Abigail is a knave\n(5) Chloe is a knight\n(6) Avery is a knight\n(7) Grace is a knave\n(8) Scarlett is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Avery is not a knight.", "Avery cannot be a knight, because this would contradict the claim of Evelyn that Avery is not a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Scarlett is a knight or Joseph is a knave.", "Scarlett cannot be a knight, because this would contradict the false claim of Avery that Scarlett is a knight or Joseph is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Joseph is a knight or Avery is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of Scarlett that Joseph is a knight or Avery is a knight.", "Joseph cannot be a knave, because this would contradict the false claim of their own that Chloe is a knight or Evelyn is a knight.", "We have exhausted all possibilities for Joseph, Scarlett, and Avery, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Avery is not a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Scarlett is a knight or Joseph is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Joseph is a knight or Avery is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Chloe is a knight or Evelyn is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Chloe that Abigail is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Benjamin is a knave if and only if Scarlett is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Scarlett is a knight or Abigail is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Chloe is not a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Chloe is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 5)), ('or', ('telling-truth', 4), ('telling-truth', 0)), ('or', ('telling-truth', 7), ('lying', 3)), ('<=>', ('lying', 2), ('telling-truth', 7)), ('lying', 3), ('or', ('telling-truth', 7), ('lying', 1)), ('not', ('telling-truth', 4)), ('or', ('telling-truth', 1), ('telling-truth', 5)))", "index": 556}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Benjamin, Olivia, Elizabeth, Ethan, Matthew, Luke, Harper, and Evelyn. Benjamin commented, \"Harper is a knight or Harper is a knave\". \"If Benjamin is a knight then Harper is a knight,\" Olivia declared. Elizabeth noted, \"If Ethan is a knave then Evelyn is a knave\". Ethan was heard saying, \"If Harper is a knave then Olivia is a knight\". \"Luke is a knight or Olivia is a knave\" - Matthew. Luke noted, \"Luke is a knight or Olivia is a knight\". Harper commented, \"Elizabeth is a knight or Benjamin is a knight\". In Evelyn's words: \"If Harper is a knight then Elizabeth is a knave\". So who is a knight and who is a knave?", "names": ["Benjamin", "Olivia", "Elizabeth", "Ethan", "Matthew", "Luke", "Harper", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true, true, false], "solution_text": "Benjamin is a knight, Olivia is a knight, Elizabeth is a knight, Ethan is a knight, Matthew is a knight, Luke is a knight, Harper is a knight, and Evelyn is a knave.", "solution_text_format": "(1) Benjamin is a knight\n(2) Olivia is a knight\n(3) Elizabeth is a knight\n(4) Ethan is a knight\n(5) Matthew is a knight\n(6) Luke is a knight\n(7) Harper is a knight\n(8) Evelyn is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Harper is a knight or Harper is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Elizabeth is a knight or Benjamin is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Ethan is a knave then Evelyn is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that If Harper is a knave then Olivia is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that If Benjamin is a knight then Harper is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that If Harper is a knight then Elizabeth is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that If Harper is a knight then Elizabeth is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Luke is a knight or Olivia is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Luke is a knight or Olivia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 6), ('lying', 6)), ('->', ('telling-truth', 0), ('telling-truth', 6)), ('->', ('lying', 3), ('lying', 7)), ('->', ('lying', 6), ('telling-truth', 1)), ('or', ('telling-truth', 5), ('lying', 1)), ('or', ('telling-truth', 5), ('telling-truth', 1)), ('or', ('telling-truth', 2), ('telling-truth', 0)), ('->', ('telling-truth', 6), ('lying', 2)))", "index": 557}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Isabella, James, Sebastian, Emily, Jack, Amelia, Scarlett, and Emma. In a statement by Isabella: \"Jack is a knight if and only if James is a knave\". \"If Emma is a knave then Sebastian is a knight\" - James. Sebastian said, \"If Isabella is a knave then Emma is a knave.\" Emily commented, \"Scarlett is a knight if and only if Scarlett is a knave\". Jack asserted: \"Sebastian is not a knave\". Amelia said, \"If Sebastian is a knight then Emily is a knave.\" Scarlett told you that If Sebastian is a knight then Emma is a knave. According to Emma, \"James is a knave\". So who is a knight and who is a knave?", "names": ["Isabella", "James", "Sebastian", "Emily", "Jack", "Amelia", "Scarlett", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true, true, false], "solution_text": "Isabella is a knave, James is a knight, Sebastian is a knight, Emily is a knave, Jack is a knight, Amelia is a knight, Scarlett is a knight, and Emma is a knave.", "solution_text_format": "(1) Isabella is a knave\n(2) James is a knight\n(3) Sebastian is a knight\n(4) Emily is a knave\n(5) Jack is a knight\n(6) Amelia is a knight\n(7) Scarlett is a knight\n(8) Emma is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Jack is a knight if and only if James is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Sebastian is not a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Isabella is a knave then Emma is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that James is a knave.", "James cannot be a knight, because this would contradict the claim of Isabella that Jack is a knight if and only if James is a knave.", "James cannot be a knave, because this would contradict the false claim of their own that If Emma is a knave then Sebastian is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that James is a knave.", "James cannot be a knight, because this would contradict the claim of Isabella that Jack is a knight if and only if James is a knave.", "James cannot be a knave, because this would contradict the false claim of their own that If Emma is a knave then Sebastian is a knight.", "We have exhausted all possibilities for James and Emma, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the false claim of their own that If Isabella is a knave then Emma is a knave.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Sebastian is not a knave.", "Sebastian cannot be a knight, because this would contradict the false claim of Jack that Sebastian is not a knave.", "Sebastian cannot be a knave, because this would contradict the false claim of their own that If Isabella is a knave then Emma is a knave.", "We have exhausted all possibilities for Sebastian and Jack, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Jack is a knight if and only if James is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Sebastian is not a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Isabella is a knave then Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of Sebastian that If Isabella is a knave then Emma is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that James is a knave.", "Assume James is a knight. No contradiction is found in their claim that If Emma is a knave then Sebastian is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight if and only if Scarlett is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Scarlett is a knight if and only if Scarlett is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Sebastian is a knight then Emma is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that If Sebastian is a knight then Emily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 4), ('lying', 1)), ('->', ('lying', 7), ('telling-truth', 2)), ('->', ('lying', 0), ('lying', 7)), ('<=>', ('telling-truth', 6), ('lying', 6)), ('not', ('lying', 2)), ('->', ('telling-truth', 2), ('lying', 3)), ('->', ('telling-truth', 2), ('lying', 7)), ('lying', 1))", "index": 558}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ella, Sebastian, Luke, Jacob, Amelia, Daniel, Victoria, and Grace. Ella said, \"Sebastian is a knave or Jacob is a knave.\" Sebastian expressed that Victoria is a knave and Daniel is a knave. Luke asserted: \"Grace is a knave\". Jacob remarked, \"Ella is a knight or Grace is a knave\". Amelia told you that Luke is a knave and Sebastian is a knight. As Daniel put it, \"Grace is a knight\". In a statement by Victoria: \"Grace is a knave\". Grace expressed that Grace is a knight and Daniel is a knave. So who is a knight and who is a knave?", "names": ["Ella", "Sebastian", "Luke", "Jacob", "Amelia", "Daniel", "Victoria", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, false, true, false], "solution_text": "Ella is a knight, Sebastian is a knave, Luke is a knight, Jacob is a knight, Amelia is a knave, Daniel is a knave, Victoria is a knight, and Grace is a knave.", "solution_text_format": "(1) Ella is a knight\n(2) Sebastian is a knave\n(3) Luke is a knight\n(4) Jacob is a knight\n(5) Amelia is a knave\n(6) Daniel is a knave\n(7) Victoria is a knight\n(8) Grace is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Sebastian is a knave or Jacob is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Victoria is a knave and Daniel is a knave.", "Victoria cannot be a knight, because this would contradict the claim of Sebastian that Victoria is a knave and Daniel is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Grace is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Grace is a knight and Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of Sebastian that Victoria is a knave and Daniel is a knave.", "Daniel cannot be a knave, because this would contradict the false claim of their own that Grace is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Grace.", "Grace cannot be a knave, because this would contradict the false claim of Victoria that Grace is a knave.", "We have exhausted all possibilities for Grace and Victoria, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Victoria is a knave and Daniel is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Grace is a knave.", "Grace cannot be a knight, because this would contradict the claim of Victoria that Grace is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Grace is a knight and Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of their own that Grace is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Grace is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Ella is a knight or Grace is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Grace is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Luke is a knave and Sebastian is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Luke is a knave and Sebastian is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('lying', 3)), ('and', ('lying', 6), ('lying', 5)), ('lying', 7), ('or', ('telling-truth', 0), ('lying', 7)), ('and', ('lying', 2), ('telling-truth', 1)), ('telling-truth', 7), ('lying', 7), ('and', ('telling-truth', 7), ('lying', 5)))", "index": 559}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Olivia, James, Benjamin, Jackson, Penelope, Sebastian, Riley, and Victoria. Olivia expressed that Jackson is not a knight. According to James, \"Olivia is a knight\". Benjamin remarked, \"Riley is a knight or Victoria is a knight\". Jackson told you that If Benjamin is a knave then Penelope is a knight. Penelope was heard saying, \"Riley is a knight\". In a statement by Sebastian: \"Benjamin is a knight if and only if Benjamin is a knave\". Riley was heard saying, \"James is a knight and Sebastian is a knight\". As Victoria put it, \"Penelope is a knave and Sebastian is a knave\". So who is a knight and who is a knave?", "names": ["Olivia", "James", "Benjamin", "Jackson", "Penelope", "Sebastian", "Riley", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false, false, true], "solution_text": "Olivia is a knave, James is a knave, Benjamin is a knight, Jackson is a knight, Penelope is a knave, Sebastian is a knave, Riley is a knave, and Victoria is a knight.", "solution_text_format": "(1) Olivia is a knave\n(2) James is a knave\n(3) Benjamin is a knight\n(4) Jackson is a knight\n(5) Penelope is a knave\n(6) Sebastian is a knave\n(7) Riley is a knave\n(8) Victoria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Jackson is not a knight.", "Jackson cannot be a knight, because this would contradict the claim of Olivia that Jackson is not a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that If Benjamin is a knave then Penelope is a knight.", "Benjamin cannot be a knight, because this would contradict the false claim of Jackson that If Benjamin is a knave then Penelope is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Riley is a knight or Victoria is a knight.", "Riley cannot be a knight, because this would contradict the false claim of Benjamin that Riley is a knight or Victoria is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that James is a knight and Sebastian is a knight.", "Assume James is a knight. No contradiction is found in their claim that Olivia is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight if and only if Benjamin is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Benjamin is a knight if and only if Benjamin is a knave.", "Victoria cannot be a knight, because this would contradict the false claim of Benjamin that Riley is a knight or Victoria is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Penelope is a knave and Sebastian is a knave.", "Penelope cannot be a knight, because this would contradict the false claim of Jackson that If Benjamin is a knave then Penelope is a knight.", "Penelope cannot be a knave, because this would contradict the false claim of Victoria that Penelope is a knave and Sebastian is a knave.", "We have exhausted all possibilities for Penelope, Victoria, and Sebastian, so let us go back and reconsider James.", "James cannot be a knave, because this would contradict the false claim of their own that Olivia is a knight.", "We have exhausted all possibilities for James, Riley, Benjamin, and Jackson, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Jackson is not a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that If Benjamin is a knave then Penelope is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Riley is a knight or Victoria is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that James is a knight and Sebastian is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Olivia is a knight.", "James cannot be a knave, because this would contradict the claim of Riley that James is a knight and Sebastian is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that James is a knight and Sebastian is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Olivia is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Olivia is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight if and only if Benjamin is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Benjamin is a knight if and only if Benjamin is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Penelope is a knave and Sebastian is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Riley is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Riley is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 3)), ('telling-truth', 0), ('or', ('telling-truth', 6), ('telling-truth', 7)), ('->', ('lying', 2), ('telling-truth', 4)), ('telling-truth', 6), ('<=>', ('telling-truth', 2), ('lying', 2)), ('and', ('telling-truth', 1), ('telling-truth', 5)), ('and', ('lying', 4), ('lying', 5)))", "index": 560}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Abigail, Lucas, Luke, Ella, William, Riley, Zoey, and Avery. \"Riley is a knight or Riley is a knave\" - Abigail. Lucas stated, \"Riley is a knave if and only if Ella is a knave\". Luke commented, \"William is not a knight\". \"William is not a knight\" - Ella. According to William, \"Zoey is a knave if and only if Riley is a knave\". According to Riley, \"If Zoey is a knave then Ella is a knave\". Zoey noted, \"Luke is a knave if and only if Avery is a knave\". According to Avery, \"Lucas is a knight\". So who is a knight and who is a knave?", "names": ["Abigail", "Lucas", "Luke", "Ella", "William", "Riley", "Zoey", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true, true, false], "solution_text": "Abigail is a knight, Lucas is a knave, Luke is a knave, Ella is a knave, William is a knight, Riley is a knight, Zoey is a knight, and Avery is a knave.", "solution_text_format": "(1) Abigail is a knight\n(2) Lucas is a knave\n(3) Luke is a knave\n(4) Ella is a knave\n(5) William is a knight\n(6) Riley is a knight\n(7) Zoey is a knight\n(8) Avery is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Riley is a knight or Riley is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that If Zoey is a knave then Ella is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Luke is a knave if and only if Avery is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that William is not a knight.", "William cannot be a knight, because this would contradict the claim of Luke that William is not a knight.", "William cannot be a knave, because this would contradict the false claim of their own that Zoey is a knave if and only if Riley is a knave.", "We have exhausted all possibilities for William, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that William is not a knight.", "Assume William is a knight. No contradiction is found in their claim that Zoey is a knave if and only if Riley is a knave.", "Avery cannot be a knight, because this would contradict the claim of Zoey that Luke is a knave if and only if Avery is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of Avery that Lucas is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Riley is a knave if and only if Ella is a knave.", "Ella cannot be a knight, because this would contradict the false claim of Lucas that Riley is a knave if and only if Ella is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that William is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('lying', 5)), ('<=>', ('lying', 5), ('lying', 3)), ('not', ('telling-truth', 4)), ('not', ('telling-truth', 4)), ('<=>', ('lying', 6), ('lying', 5)), ('->', ('lying', 6), ('lying', 3)), ('<=>', ('lying', 2), ('lying', 7)), ('telling-truth', 1))", "index": 561}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Liam, Henry, Ava, Jack, Daniel, Lily, Ella, and Zoey. In a statement by Liam: \"Daniel is a knight\". Henry told you that Zoey is a knight. Ava commented, \"Zoey is a knight and Liam is a knave\". According to Jack, \"Zoey is a knave if and only if Ella is a knight\". According to Daniel, \"Ava is a knight\". Lily stated, \"Jack is a knave and Daniel is a knight\". \"If Liam is a knight then Ella is a knight,\" Ella declared. Zoey expressed that Ava is a knight and Lily is a knight. So who is a knight and who is a knave?", "names": ["Liam", "Henry", "Ava", "Jack", "Daniel", "Lily", "Ella", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, false, true, false], "solution_text": "Liam is a knave, Henry is a knave, Ava is a knave, Jack is a knight, Daniel is a knave, Lily is a knave, Ella is a knight, and Zoey is a knave.", "solution_text_format": "(1) Liam is a knave\n(2) Henry is a knave\n(3) Ava is a knave\n(4) Jack is a knight\n(5) Daniel is a knave\n(6) Lily is a knave\n(7) Ella is a knight\n(8) Zoey is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Daniel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Ava is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Zoey is a knight and Liam is a knave.", "Ava cannot be a knave, because this would contradict the claim of Daniel that Ava is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the claim of Liam that Daniel is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of Liam that Daniel is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Ava is a knight.", "Ava cannot be a knight, because this would contradict the false claim of Daniel that Ava is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Zoey is a knight and Liam is a knave.", "Zoey cannot be a knight, because this would contradict the false claim of Ava that Zoey is a knight and Liam is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Ava is a knight and Lily is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Jack is a knave and Daniel is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Jack is a knave and Daniel is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Zoey is a knave if and only if Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that If Liam is a knight then Ella is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Zoey is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Zoey is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('telling-truth', 7), ('and', ('telling-truth', 7), ('lying', 0)), ('<=>', ('lying', 7), ('telling-truth', 6)), ('telling-truth', 2), ('and', ('lying', 3), ('telling-truth', 4)), ('->', ('telling-truth', 0), ('telling-truth', 6)), ('and', ('telling-truth', 2), ('telling-truth', 5)))", "index": 562}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Michael, Jacob, Aiden, Alexander, Scarlett, Samuel, Lucas, and Riley. In Michael's words: \"Riley is a knave and Aiden is a knave\". Jacob said that If Jacob is a knight then Alexander is a knave. Aiden noted, \"Lucas is a knave and Alexander is a knight\". \"Scarlett is not a knight,\" Alexander claimed. Scarlett said, \"Lucas is a knave or Aiden is a knight.\" Samuel remarked, \"Jacob is not a knight\". Lucas asserted: \"Lucas is a knight and Jacob is a knave\". Riley expressed that If Scarlett is a knave then Samuel is a knight. So who is a knight and who is a knave?", "names": ["Michael", "Jacob", "Aiden", "Alexander", "Scarlett", "Samuel", "Lucas", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, false, false, true], "solution_text": "Michael is a knave, Jacob is a knight, Aiden is a knave, Alexander is a knave, Scarlett is a knight, Samuel is a knave, Lucas is a knave, and Riley is a knight.", "solution_text_format": "(1) Michael is a knave\n(2) Jacob is a knight\n(3) Aiden is a knave\n(4) Alexander is a knave\n(5) Scarlett is a knight\n(6) Samuel is a knave\n(7) Lucas is a knave\n(8) Riley is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Riley is a knave and Aiden is a knave.", "Riley cannot be a knight, because this would contradict the claim of Michael that Riley is a knave and Aiden is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that If Scarlett is a knave then Samuel is a knight.", "Scarlett cannot be a knight, because this would contradict the false claim of Riley that If Scarlett is a knave then Samuel is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Lucas is a knave or Aiden is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Lucas is a knight and Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Lucas that Lucas is a knight and Jacob is a knave.", "Jacob cannot be a knave, because this would contradict the false claim of their own that If Jacob is a knight then Alexander is a knave.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the false claim of Scarlett that Lucas is a knave or Aiden is a knight.", "We have exhausted all possibilities for Lucas, Scarlett, and Riley, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Riley is a knave and Aiden is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that If Scarlett is a knave then Samuel is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Lucas is a knave or Aiden is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Lucas is a knight and Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Lucas that Lucas is a knight and Jacob is a knave.", "Jacob cannot be a knave, because this would contradict the false claim of their own that If Jacob is a knight then Alexander is a knave.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Lucas is a knight and Jacob is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that If Jacob is a knight then Alexander is a knave.", "Alexander cannot be a knight, because this would contradict the claim of Jacob that If Jacob is a knight then Alexander is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Scarlett is not a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Lucas is a knave and Alexander is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Lucas is a knave and Alexander is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Jacob is not a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Jacob is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 7), ('lying', 2)), ('->', ('telling-truth', 1), ('lying', 3)), ('and', ('lying', 6), ('telling-truth', 3)), ('not', ('telling-truth', 4)), ('or', ('lying', 6), ('telling-truth', 2)), ('not', ('telling-truth', 1)), ('and', ('telling-truth', 6), ('lying', 1)), ('->', ('lying', 4), ('telling-truth', 5)))", "index": 563}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Alexander, Logan, Riley, Amelia, Chloe, Jacob, William, and Emily. As Alexander put it, \"If Logan is a knave then Chloe is a knave\". In a statement by Logan: \"Amelia is not a knave\". Riley asserted: \"If William is a knight then Jacob is a knight\". \"If Chloe is a knight then Jacob is a knight,\" Amelia declared. Chloe was heard saying, \"Riley is a knave if and only if Logan is a knight\". Jacob stated, \"Amelia is a knave or Riley is a knave\". William expressed that Alexander is a knave or Chloe is a knight. \"Chloe is a knave,\" Emily declared. So who is a knight and who is a knave?", "names": ["Alexander", "Logan", "Riley", "Amelia", "Chloe", "Jacob", "William", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false, false, true], "solution_text": "Alexander is a knight, Logan is a knight, Riley is a knight, Amelia is a knight, Chloe is a knave, Jacob is a knave, William is a knave, and Emily is a knight.", "solution_text_format": "(1) Alexander is a knight\n(2) Logan is a knight\n(3) Riley is a knight\n(4) Amelia is a knight\n(5) Chloe is a knave\n(6) Jacob is a knave\n(7) William is a knave\n(8) Emily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that If Logan is a knave then Chloe is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Amelia is not a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that If Chloe is a knight then Jacob is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Riley is a knave if and only if Logan is a knight.", "Riley cannot be a knight, because this would contradict the claim of Chloe that Riley is a knave if and only if Logan is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that If William is a knight then Jacob is a knight.", "Assume William is a knight. No contradiction is found in their claim that Alexander is a knave or Chloe is a knight.", "Jacob cannot be a knight, because this would contradict the false claim of Riley that If William is a knight then Jacob is a knight.", "Jacob cannot be a knave, because this would contradict the claim of Amelia that If Chloe is a knight then Jacob is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the false claim of Riley that If William is a knight then Jacob is a knight.", "We have exhausted all possibilities for William and Riley, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Riley is a knave if and only if Logan is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that If William is a knight then Jacob is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Alexander is a knave or Chloe is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Alexander is a knave or Chloe is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Amelia is a knave or Riley is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Amelia is a knave or Riley is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Chloe is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 1), ('lying', 4)), ('not', ('lying', 3)), ('->', ('telling-truth', 6), ('telling-truth', 5)), ('->', ('telling-truth', 4), ('telling-truth', 5)), ('<=>', ('lying', 2), ('telling-truth', 1)), ('or', ('lying', 3), ('lying', 2)), ('or', ('lying', 0), ('telling-truth', 4)), ('lying', 4))", "index": 564}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Luke, Jacob, Grace, Avery, Mia, Emily, Liam, and Michael. Luke told you that Mia is a knight. Jacob was heard saying, \"Emily is a knight\". Grace noted, \"Emily is a knave\". As Avery put it, \"Grace is not a knight\". Mia said that Luke is a knave and Emily is a knight. Emily was heard saying, \"Mia is a knave if and only if Jacob is a knight\". In Liam's words: \"Michael is a knight and Luke is a knave\". Michael remarked, \"If Liam is a knight then Grace is a knight\". So who is a knight and who is a knave?", "names": ["Luke", "Jacob", "Grace", "Avery", "Mia", "Emily", "Liam", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, false, true, true], "solution_text": "Luke is a knave, Jacob is a knave, Grace is a knight, Avery is a knave, Mia is a knave, Emily is a knave, Liam is a knight, and Michael is a knight.", "solution_text_format": "(1) Luke is a knave\n(2) Jacob is a knave\n(3) Grace is a knight\n(4) Avery is a knave\n(5) Mia is a knave\n(6) Emily is a knave\n(7) Liam is a knight\n(8) Michael is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Mia is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that Luke is a knave and Emily is a knight.", "Mia cannot be a knave, because this would contradict the claim of Luke that Mia is a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Mia is a knight.", "Mia cannot be a knight, because this would contradict the false claim of Luke that Mia is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Luke is a knave and Emily is a knight.", "Emily cannot be a knight, because this would contradict the false claim of Mia that Luke is a knave and Emily is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Mia is a knave if and only if Jacob is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Emily is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Emily is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Emily is a knave.", "Avery cannot be a knight, because this would contradict the claim of their own that Grace is not a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Grace is not a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Michael is a knight and Luke is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that If Liam is a knight then Grace is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('telling-truth', 5), ('lying', 5), ('not', ('telling-truth', 2)), ('and', ('lying', 0), ('telling-truth', 5)), ('<=>', ('lying', 4), ('telling-truth', 1)), ('and', ('telling-truth', 7), ('lying', 0)), ('->', ('telling-truth', 6), ('telling-truth', 2)))", "index": 565}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Riley, Jacob, Aurora, Samuel, David, Jack, Penelope, and Daniel. In Riley's words: \"Aurora is a knight\". \"Penelope is a knave or David is a knave,\" Jacob claimed. \"Daniel is a knave if and only if Jacob is a knight,\" Aurora mentioned. Samuel said, \"Jacob is a knave or Jack is a knight.\" \"If Riley is a knave then Samuel is a knave,\" David mentioned. Jack asserted: \"David is a knave or Samuel is a knight\". Penelope remarked, \"Daniel is a knave or Aurora is a knight\". \"Riley is a knave if and only if Jack is a knight,\" Daniel claimed. So who is a knight and who is a knave?", "names": ["Riley", "Jacob", "Aurora", "Samuel", "David", "Jack", "Penelope", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, true, false, true], "solution_text": "Riley is a knave, Jacob is a knight, Aurora is a knave, Samuel is a knight, David is a knave, Jack is a knight, Penelope is a knave, and Daniel is a knight.", "solution_text_format": "(1) Riley is a knave\n(2) Jacob is a knight\n(3) Aurora is a knave\n(4) Samuel is a knight\n(5) David is a knave\n(6) Jack is a knight\n(7) Penelope is a knave\n(8) Daniel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Aurora is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Daniel is a knave if and only if Jacob is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Riley is a knave if and only if Jack is a knight.", "Jack cannot be a knight, because this would contradict the claim of Daniel that Riley is a knave if and only if Jack is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that David is a knave or Samuel is a knight.", "Assume David is a knight. No contradiction is found in their claim that If Riley is a knave then Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the false claim of Jack that David is a knave or Samuel is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Jacob is a knave or Jack is a knight.", "Jacob cannot be a knight, because this would contradict the claim of Aurora that Daniel is a knave if and only if Jacob is a knight.", "Jacob cannot be a knave, because this would contradict the false claim of Samuel that Jacob is a knave or Jack is a knight.", "We have exhausted all possibilities for Jacob and Samuel, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the false claim of their own that If Riley is a knave then Samuel is a knave.", "We have exhausted all possibilities for David and Jack, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Riley is a knave if and only if Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that David is a knave or Samuel is a knight.", "Assume David is a knight. No contradiction is found in their claim that If Riley is a knave then Samuel is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Jacob is a knave or Jack is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Penelope is a knave or David is a knave.", "Penelope cannot be a knight, because this would contradict the claim of Jacob that Penelope is a knave or David is a knave.", "Penelope cannot be a knave, because this would contradict the false claim of their own that Daniel is a knave or Aurora is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the claim of Aurora that Daniel is a knave if and only if Jacob is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Samuel.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Jacob is a knave or Jack is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the false claim of their own that If Riley is a knave then Samuel is a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the false claim of Daniel that Riley is a knave if and only if Jack is a knight.", "We have exhausted all possibilities for Jack and Daniel, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the claim of Riley that Aurora is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Aurora is a knight.", "Aurora cannot be a knight, because this would contradict the false claim of Riley that Aurora is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Daniel is a knave if and only if Jacob is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Riley is a knave if and only if Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that David is a knave or Samuel is a knight.", "Assume David is a knight. No contradiction is found in their claim that If Riley is a knave then Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of David that If Riley is a knave then Samuel is a knave.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Jacob is a knave or Jack is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that If Riley is a knave then Samuel is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Jacob is a knave or Jack is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Penelope is a knave or David is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Daniel is a knave or Aurora is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Daniel is a knave or Aurora is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('or', ('lying', 6), ('lying', 4)), ('<=>', ('lying', 7), ('telling-truth', 1)), ('or', ('lying', 1), ('telling-truth', 5)), ('->', ('lying', 0), ('lying', 3)), ('or', ('lying', 4), ('telling-truth', 3)), ('or', ('lying', 7), ('telling-truth', 2)), ('<=>', ('lying', 0), ('telling-truth', 5)))", "index": 566}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Olivia, Elizabeth, Sophia, Michael, Owen, Jacob, Avery, and Ethan. According to Olivia, \"If Ethan is a knight then Elizabeth is a knight\". In Elizabeth's words: \"If Jacob is a knave then Michael is a knight\". Sophia stated, \"Olivia is a knight and Jacob is a knight\". Michael was heard saying, \"Olivia is a knave or Ethan is a knight\". \"Sophia is not a knight,\" Owen claimed. Jacob told you that If Michael is a knave then Olivia is a knave. Avery commented, \"If Ethan is a knave then Owen is a knave\". \"If Elizabeth is a knave then Jacob is a knave\" - Ethan. So who is a knight and who is a knave?", "names": ["Olivia", "Elizabeth", "Sophia", "Michael", "Owen", "Jacob", "Avery", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true, true, true], "solution_text": "Olivia is a knight, Elizabeth is a knight, Sophia is a knight, Michael is a knight, Owen is a knave, Jacob is a knight, Avery is a knight, and Ethan is a knight.", "solution_text_format": "(1) Olivia is a knight\n(2) Elizabeth is a knight\n(3) Sophia is a knight\n(4) Michael is a knight\n(5) Owen is a knave\n(6) Jacob is a knight\n(7) Avery is a knight\n(8) Ethan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that If Ethan is a knight then Elizabeth is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Jacob is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Jacob is a knave then Michael is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that If Michael is a knave then Olivia is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Olivia is a knave or Ethan is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Olivia is a knight and Jacob is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Sophia is not a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Sophia is not a knight.", "Assume Avery is a knight. No contradiction is found in their claim that If Ethan is a knave then Owen is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 7), ('telling-truth', 1)), ('->', ('lying', 5), ('telling-truth', 3)), ('and', ('telling-truth', 0), ('telling-truth', 5)), ('or', ('lying', 0), ('telling-truth', 7)), ('not', ('telling-truth', 2)), ('->', ('lying', 3), ('lying', 0)), ('->', ('lying', 7), ('lying', 4)), ('->', ('lying', 1), ('lying', 5)))", "index": 567}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Chloe, Avery, Logan, Olivia, Aria, Emily, Mia, and Scarlett. \"Scarlett is a knight\" - Chloe. Avery asserted: \"Logan is not a knight\". Logan expressed that Scarlett is not a knight. Olivia told you that Scarlett is a knave or Chloe is a knight. Aria said that Olivia is not a knave. According to Emily, \"If Mia is a knave then Olivia is a knight\". Mia was heard saying, \"If Chloe is a knave then Aria is a knave\". Scarlett noted, \"Avery is a knight or Emily is a knight\". So who is a knight and who is a knave?", "names": ["Chloe", "Avery", "Logan", "Olivia", "Aria", "Emily", "Mia", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true, true, true], "solution_text": "Chloe is a knight, Avery is a knight, Logan is a knave, Olivia is a knight, Aria is a knight, Emily is a knight, Mia is a knight, and Scarlett is a knight.", "solution_text_format": "(1) Chloe is a knight\n(2) Avery is a knight\n(3) Logan is a knave\n(4) Olivia is a knight\n(5) Aria is a knight\n(6) Emily is a knight\n(7) Mia is a knight\n(8) Scarlett is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Avery is a knight or Emily is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Logan is not a knight.", "Logan cannot be a knight, because this would contradict the claim of Avery that Logan is not a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Scarlett is not a knight.", "Assume Emily is a knight. No contradiction is found in their claim that If Mia is a knave then Olivia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that If Chloe is a knave then Aria is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Olivia is not a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Scarlett is a knave or Chloe is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 7), ('not', ('telling-truth', 2)), ('not', ('telling-truth', 7)), ('or', ('lying', 7), ('telling-truth', 0)), ('not', ('lying', 3)), ('->', ('lying', 6), ('telling-truth', 3)), ('->', ('lying', 0), ('lying', 4)), ('or', ('telling-truth', 1), ('telling-truth', 5)))", "index": 568}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emily, Jackson, Jack, Ava, Aiden, Amelia, Evelyn, and Aria. Emily noted, \"Jack is a knave and Aria is a knave\". \"If Aria is a knight then Jack is a knave\" - Jackson. In a statement by Jack: \"Aria is not a knave\". \"Evelyn is a knave if and only if Emily is a knave,\" Ava claimed. Aiden commented, \"If Jackson is a knave then Aria is a knight\". In Amelia's words: \"Ava is a knave or Aria is a knight\". \"Jack is a knave or Ava is a knight,\" Evelyn mentioned. \"Amelia is not a knave,\" Aria mentioned. So who is a knight and who is a knave?", "names": ["Emily", "Jackson", "Jack", "Ava", "Aiden", "Amelia", "Evelyn", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false, true, false], "solution_text": "Emily is a knight, Jackson is a knight, Jack is a knave, Ava is a knight, Aiden is a knight, Amelia is a knave, Evelyn is a knight, and Aria is a knave.", "solution_text_format": "(1) Emily is a knight\n(2) Jackson is a knight\n(3) Jack is a knave\n(4) Ava is a knight\n(5) Aiden is a knight\n(6) Amelia is a knave\n(7) Evelyn is a knight\n(8) Aria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Jack is a knave and Aria is a knave.", "Jack cannot be a knight, because this would contradict the claim of Emily that Jack is a knave and Aria is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Aria is not a knave.", "Aria cannot be a knight, because this would contradict the claim of Emily that Jack is a knave and Aria is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Amelia is not a knave.", "Amelia cannot be a knight, because this would contradict the false claim of Aria that Amelia is not a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Ava is a knave or Aria is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Evelyn is a knave if and only if Emily is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Jack is a knave or Ava is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that If Aria is a knight then Jack is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Jackson is a knave then Aria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('lying', 7)), ('->', ('telling-truth', 7), ('lying', 2)), ('not', ('lying', 7)), ('<=>', ('lying', 6), ('lying', 0)), ('->', ('lying', 1), ('telling-truth', 7)), ('or', ('lying', 3), ('telling-truth', 7)), ('or', ('lying', 2), ('telling-truth', 3)), ('not', ('lying', 5)))", "index": 569}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Michael, Samuel, Aiden, David, Matthew, Ethan, James, and Sofia. Michael was heard saying, \"Ethan is a knight or Aiden is a knight\". Samuel told you that Ethan is a knave if and only if Matthew is a knight. In a statement by Aiden: \"If Matthew is a knight then Samuel is a knave\". David commented, \"Michael is a knight if and only if James is a knave\". In Matthew's words: \"Aiden is a knight\". Ethan noted, \"Sofia is not a knave\". James told you that Ethan is a knave or Michael is a knight. Sofia expressed that Ethan is a knight or David is a knight. So who is a knight and who is a knave?", "names": ["Michael", "Samuel", "Aiden", "David", "Matthew", "Ethan", "James", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true, true, true], "solution_text": "Michael is a knight, Samuel is a knave, Aiden is a knight, David is a knave, Matthew is a knight, Ethan is a knight, James is a knight, and Sofia is a knight.", "solution_text_format": "(1) Michael is a knight\n(2) Samuel is a knave\n(3) Aiden is a knight\n(4) David is a knave\n(5) Matthew is a knight\n(6) Ethan is a knight\n(7) James is a knight\n(8) Sofia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Ethan is a knight or Aiden is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Sofia is not a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Ethan is a knight or David is a knight.", "Assume David is a knight. No contradiction is found in their claim that Michael is a knight if and only if James is a knave.", "James cannot be a knight, because this would contradict the claim of David that Michael is a knight if and only if James is a knave.", "James cannot be a knave, because this would contradict the false claim of their own that Ethan is a knave or Michael is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Michael is a knight if and only if James is a knave.", "Assume James is a knight. No contradiction is found in their claim that Ethan is a knave or Michael is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that If Matthew is a knight then Samuel is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Aiden is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Ethan is a knave if and only if Matthew is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Ethan is a knave if and only if Matthew is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('telling-truth', 2)), ('<=>', ('lying', 5), ('telling-truth', 4)), ('->', ('telling-truth', 4), ('lying', 1)), ('<=>', ('telling-truth', 0), ('lying', 6)), ('telling-truth', 2), ('not', ('lying', 7)), ('or', ('lying', 5), ('telling-truth', 0)), ('or', ('telling-truth', 5), ('telling-truth', 3)))", "index": 570}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Olivia, Samuel, William, Aiden, Elizabeth, Victoria, Lucas, and Aria. Olivia said, \"William is a knave if and only if Lucas is a knave.\" Samuel remarked, \"Olivia is a knight\". William told you that Elizabeth is a knight or William is a knight. \"Olivia is not a knave,\" Aiden declared. In a statement by Elizabeth: \"Aiden is a knave if and only if Olivia is a knave\". Victoria stated, \"Samuel is not a knight\". \"Aiden is a knave if and only if Olivia is a knight\" - Lucas. Aria said, \"If Aiden is a knight then Lucas is a knave.\" So who is a knight and who is a knave?", "names": ["Olivia", "Samuel", "William", "Aiden", "Elizabeth", "Victoria", "Lucas", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true, false, true], "solution_text": "Olivia is a knave, Samuel is a knave, William is a knight, Aiden is a knave, Elizabeth is a knight, Victoria is a knight, Lucas is a knave, and Aria is a knight.", "solution_text_format": "(1) Olivia is a knave\n(2) Samuel is a knave\n(3) William is a knight\n(4) Aiden is a knave\n(5) Elizabeth is a knight\n(6) Victoria is a knight\n(7) Lucas is a knave\n(8) Aria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that William is a knave if and only if Lucas is a knave.", "Assume William is a knight. No contradiction is found in their claim that Elizabeth is a knight or William is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Aiden is a knave if and only if Olivia is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Olivia is not a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Aiden is a knave if and only if Olivia is a knight.", "Lucas cannot be a knave, because this would contradict the claim of Olivia that William is a knave if and only if Lucas is a knave.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the false claim of their own that Olivia is not a knave.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if Olivia is a knave.", "Aiden cannot be a knight, because this would contradict the false claim of Elizabeth that Aiden is a knave if and only if Olivia is a knave.", "Aiden cannot be a knave, because this would contradict the false claim of their own that Olivia is not a knave.", "We have exhausted all possibilities for Aiden and Elizabeth, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Elizabeth is a knight or William is a knight.", "Elizabeth cannot be a knight, because this would contradict the false claim of William that Elizabeth is a knight or William is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if Olivia is a knave.", "Aiden cannot be a knight, because this would contradict the false claim of Elizabeth that Aiden is a knave if and only if Olivia is a knave.", "Aiden cannot be a knave, because this would contradict the false claim of their own that Olivia is not a knave.", "We have exhausted all possibilities for Aiden, Elizabeth, and William, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that William is a knave if and only if Lucas is a knave.", "Assume William is a knight. No contradiction is found in their claim that Elizabeth is a knight or William is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Aiden is a knave if and only if Olivia is a knave.", "Aiden cannot be a knight, because this would contradict the claim of their own that Olivia is not a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Olivia is not a knave.", "Lucas cannot be a knight, because this would contradict the false claim of Olivia that William is a knave if and only if Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if Olivia is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Olivia is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Olivia is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Samuel is not a knight.", "Assume Aria is a knight. No contradiction is found in their claim that If Aiden is a knight then Lucas is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('lying', 6)), ('telling-truth', 0), ('or', ('telling-truth', 4), ('telling-truth', 2)), ('not', ('lying', 0)), ('<=>', ('lying', 3), ('lying', 0)), ('not', ('telling-truth', 1)), ('<=>', ('lying', 3), ('telling-truth', 0)), ('->', ('telling-truth', 3), ('lying', 6)))", "index": 571}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Joseph, Sofia, Liam, William, Mia, Evelyn, Abigail, and Lucas. Joseph noted, \"Lucas is a knave if and only if Abigail is a knave\". Sofia was heard saying, \"If Sofia is a knight then Lucas is a knight\". Liam asserted: \"Mia is not a knight\". As William put it, \"If Liam is a knave then Abigail is a knight\". Mia told you that William is a knave. Evelyn asserted: \"Liam is not a knave\". Abigail said, \"Mia is a knight and Lucas is a knight.\" \"William is not a knave,\" Lucas claimed. So who is a knight and who is a knave?", "names": ["Joseph", "Sofia", "Liam", "William", "Mia", "Evelyn", "Abigail", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true, false, true], "solution_text": "Joseph is a knave, Sofia is a knight, Liam is a knight, William is a knight, Mia is a knave, Evelyn is a knight, Abigail is a knave, and Lucas is a knight.", "solution_text_format": "(1) Joseph is a knave\n(2) Sofia is a knight\n(3) Liam is a knight\n(4) William is a knight\n(5) Mia is a knave\n(6) Evelyn is a knight\n(7) Abigail is a knave\n(8) Lucas is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that Lucas is a knave if and only if Abigail is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that William is not a knave.", "Assume William is a knight. No contradiction is found in their claim that If Liam is a knave then Abigail is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Mia is not a knight.", "Mia cannot be a knight, because this would contradict the claim of Liam that Mia is not a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that William is a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Mia is a knight and Lucas is a knight.", "Abigail cannot be a knave, because this would contradict the claim of Joseph that Lucas is a knave if and only if Abigail is a knave.", "We have exhausted all possibilities for Abigail and Mia, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Mia is not a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that William is a knave.", "Mia cannot be a knave, because this would contradict the false claim of Liam that Mia is not a knight.", "We have exhausted all possibilities for Mia and Liam, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the claim of Lucas that William is not a knave.", "We have exhausted all possibilities for William, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that William is not a knave.", "William cannot be a knight, because this would contradict the false claim of Lucas that William is not a knave.", "Assume William is a knave. No contradiction is found in their false claim that If Liam is a knave then Abigail is a knight.", "Liam cannot be a knight, because this would contradict the false claim of William that If Liam is a knave then Abigail is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Mia is not a knight.", "Assume Mia is a knight. No contradiction is found in their claim that William is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Joseph that Lucas is a knave if and only if Abigail is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Mia is a knight and Lucas is a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that If Sofia is a knight then Lucas is a knight.", "Sofia cannot be a knave, because this would contradict the false claim of their own that If Sofia is a knight then Lucas is a knight.", "We have exhausted all possibilities for Sofia and Abigail, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the false claim of Liam that Mia is not a knight.", "We have exhausted all possibilities for Mia, Liam, William, and Lucas, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Lucas is a knave if and only if Abigail is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that William is not a knave.", "Assume William is a knight. No contradiction is found in their claim that If Liam is a knave then Abigail is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Mia is not a knight.", "Mia cannot be a knight, because this would contradict the claim of Liam that Mia is not a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that William is a knave.", "Abigail cannot be a knight, because this would contradict the false claim of Joseph that Lucas is a knave if and only if Abigail is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Mia is a knight and Lucas is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that If Sofia is a knight then Lucas is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Liam is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 7), ('lying', 6)), ('->', ('telling-truth', 1), ('telling-truth', 7)), ('not', ('telling-truth', 4)), ('->', ('lying', 2), ('telling-truth', 6)), ('lying', 3), ('not', ('lying', 2)), ('and', ('telling-truth', 4), ('telling-truth', 7)), ('not', ('lying', 3)))", "index": 572}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mia, Evelyn, Emma, Daniel, Henry, Ethan, Alexander, and Amelia. Mia commented, \"Amelia is a knight or Henry is a knave\". According to Evelyn, \"Emma is a knave\". Emma remarked, \"Amelia is a knave\". Daniel commented, \"If Henry is a knave then Ethan is a knave\". In Henry's words: \"Daniel is not a knave\". Ethan stated, \"Mia is a knave and Alexander is a knave\". Alexander was heard saying, \"Evelyn is a knave if and only if Daniel is a knight\". \"Mia is a knave if and only if Emma is a knight\" - Amelia. So who is a knight and who is a knave?", "names": ["Mia", "Evelyn", "Emma", "Daniel", "Henry", "Ethan", "Alexander", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false, false, true], "solution_text": "Mia is a knight, Evelyn is a knight, Emma is a knave, Daniel is a knight, Henry is a knight, Ethan is a knave, Alexander is a knave, and Amelia is a knight.", "solution_text_format": "(1) Mia is a knight\n(2) Evelyn is a knight\n(3) Emma is a knave\n(4) Daniel is a knight\n(5) Henry is a knight\n(6) Ethan is a knave\n(7) Alexander is a knave\n(8) Amelia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Amelia is a knight or Henry is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Mia is a knave if and only if Emma is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Amelia is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Amelia is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Daniel is not a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that If Henry is a knave then Ethan is a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Mia is a knave and Alexander is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Mia is a knave and Alexander is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Evelyn is a knave if and only if Daniel is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of Alexander that Evelyn is a knave if and only if Daniel is a knight.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that Emma is a knave.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Evelyn is a knave if and only if Daniel is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Emma is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 7), ('lying', 4)), ('lying', 2), ('lying', 7), ('->', ('lying', 4), ('lying', 5)), ('not', ('lying', 3)), ('and', ('lying', 0), ('lying', 6)), ('<=>', ('lying', 1), ('telling-truth', 3)), ('<=>', ('lying', 0), ('telling-truth', 2)))", "index": 573}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Joseph, Scarlett, Elizabeth, Grace, Jacob, Aiden, Emily, and Mia. Joseph expressed that Elizabeth is a knight or Elizabeth is a knave. Scarlett noted, \"Aiden is a knight or Jacob is a knight\". Elizabeth was heard saying, \"Joseph is a knight\". Grace was heard saying, \"Elizabeth is a knave\". Jacob commented, \"Aiden is a knight or Scarlett is a knight\". In Aiden's words: \"Grace is a knave\". Emily asserted: \"Joseph is not a knave\". \"If Jacob is a knight then Jacob is a knave,\" Mia mentioned. So who is a knight and who is a knave?", "names": ["Joseph", "Scarlett", "Elizabeth", "Grace", "Jacob", "Aiden", "Emily", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true, true, false], "solution_text": "Joseph is a knight, Scarlett is a knight, Elizabeth is a knight, Grace is a knave, Jacob is a knight, Aiden is a knight, Emily is a knight, and Mia is a knave.", "solution_text_format": "(1) Joseph is a knight\n(2) Scarlett is a knight\n(3) Elizabeth is a knight\n(4) Grace is a knave\n(5) Jacob is a knight\n(6) Aiden is a knight\n(7) Emily is a knight\n(8) Mia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that Elizabeth is a knight or Elizabeth is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Joseph is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Aiden is a knight or Jacob is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Grace is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Elizabeth is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Aiden is a knight or Scarlett is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Joseph is not a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that If Jacob is a knight then Jacob is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that If Jacob is a knight then Jacob is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('lying', 2)), ('or', ('telling-truth', 5), ('telling-truth', 4)), ('telling-truth', 0), ('lying', 2), ('or', ('telling-truth', 5), ('telling-truth', 1)), ('lying', 3), ('not', ('lying', 0)), ('->', ('telling-truth', 4), ('lying', 4)))", "index": 574}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Joseph, Owen, James, Sebastian, Jack, Matthew, Mia, and Isabella. In a statement by Joseph: \"Owen is a knave or Mia is a knave\". Owen noted, \"Joseph is not a knight\". \"Owen is not a knave,\" James mentioned. \"If Joseph is a knave then Matthew is a knave,\" Sebastian mentioned. Jack said that James is a knight. Matthew commented, \"James is a knave and Owen is a knave\". \"Matthew is a knight or Isabella is a knave,\" Mia claimed. Isabella remarked, \"If Jack is a knave then James is a knight\". So who is a knight and who is a knave?", "names": ["Joseph", "Owen", "James", "Sebastian", "Jack", "Matthew", "Mia", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, true, true, false], "solution_text": "Joseph is a knight, Owen is a knave, James is a knave, Sebastian is a knight, Jack is a knave, Matthew is a knight, Mia is a knight, and Isabella is a knave.", "solution_text_format": "(1) Joseph is a knight\n(2) Owen is a knave\n(3) James is a knave\n(4) Sebastian is a knight\n(5) Jack is a knave\n(6) Matthew is a knight\n(7) Mia is a knight\n(8) Isabella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that Owen is a knave or Mia is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Joseph is not a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Joseph is not a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Matthew is a knight or Isabella is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that James is a knave and Owen is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Owen is not a knave.", "Assume James is a knave. No contradiction is found in their false claim that Owen is not a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that If Jack is a knave then James is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that James is a knight.", "Jack cannot be a knave, because this would contradict the claim of Isabella that If Jack is a knave then James is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that If Jack is a knave then James is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that James is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that James is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Joseph is a knave then Matthew is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('lying', 6)), ('not', ('telling-truth', 0)), ('not', ('lying', 1)), ('->', ('lying', 0), ('lying', 5)), ('telling-truth', 2), ('and', ('lying', 2), ('lying', 1)), ('or', ('telling-truth', 5), ('lying', 7)), ('->', ('lying', 4), ('telling-truth', 2)))", "index": 575}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Joseph, Samuel, Henry, Oliver, Riley, Lily, Alexander, and Michael. Joseph said, \"Henry is a knight or Oliver is a knight.\" Samuel noted, \"Michael is not a knave\". Henry asserted: \"Riley is a knight and Riley is a knave\". Oliver asserted: \"If Alexander is a knight then Henry is a knave\". Riley remarked, \"Joseph is a knave if and only if Lily is a knight\". In Lily's words: \"Oliver is not a knight\". Alexander said, \"If Joseph is a knight then Oliver is a knave.\" In Michael's words: \"Joseph is not a knave\". So who is a knight and who is a knave?", "names": ["Joseph", "Samuel", "Henry", "Oliver", "Riley", "Lily", "Alexander", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false, false, true], "solution_text": "Joseph is a knight, Samuel is a knight, Henry is a knave, Oliver is a knight, Riley is a knight, Lily is a knave, Alexander is a knave, and Michael is a knight.", "solution_text_format": "(1) Joseph is a knight\n(2) Samuel is a knight\n(3) Henry is a knave\n(4) Oliver is a knight\n(5) Riley is a knight\n(6) Lily is a knave\n(7) Alexander is a knave\n(8) Michael is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that Henry is a knight or Oliver is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Riley is a knight and Riley is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Riley is a knight and Riley is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Joseph is a knave if and only if Lily is a knight.", "Lily cannot be a knight, because this would contradict the claim of Riley that Joseph is a knave if and only if Lily is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Oliver is not a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that If Alexander is a knight then Henry is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that If Joseph is a knight then Oliver is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that If Joseph is a knight then Oliver is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Michael is not a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Joseph is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('telling-truth', 3)), ('not', ('lying', 7)), ('and', ('telling-truth', 4), ('lying', 4)), ('->', ('telling-truth', 6), ('lying', 2)), ('<=>', ('lying', 0), ('telling-truth', 5)), ('not', ('telling-truth', 3)), ('->', ('telling-truth', 0), ('lying', 3)), ('not', ('lying', 0)))", "index": 576}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Samuel, Emily, Amelia, Lucas, Ella, Aiden, Riley, and Harper. Samuel said, \"Harper is not a knave.\" Emily commented, \"Harper is a knight or Riley is a knave\". \"Ella is a knight if and only if Riley is a knave,\" Amelia mentioned. Lucas said, \"Ella is a knight if and only if Harper is a knight.\" According to Ella, \"Aiden is a knave if and only if Riley is a knave\". \"Riley is a knight,\" Aiden claimed. Riley stated, \"Amelia is a knight if and only if Amelia is a knave\". In Harper's words: \"Ella is a knave\". So who is a knight and who is a knave?", "names": ["Samuel", "Emily", "Amelia", "Lucas", "Ella", "Aiden", "Riley", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, false, false, false], "solution_text": "Samuel is a knave, Emily is a knight, Amelia is a knight, Lucas is a knave, Ella is a knight, Aiden is a knave, Riley is a knave, and Harper is a knave.", "solution_text_format": "(1) Samuel is a knave\n(2) Emily is a knight\n(3) Amelia is a knight\n(4) Lucas is a knave\n(5) Ella is a knight\n(6) Aiden is a knave\n(7) Riley is a knave\n(8) Harper is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that Harper is not a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of Harper that Ella is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if Riley is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Riley is a knight.", "Riley cannot be a knight, because this would contradict the false claim of Ella that Aiden is a knave if and only if Riley is a knave.", "Riley cannot be a knave, because this would contradict the claim of Aiden that Riley is a knight.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Riley is a knight.", "Riley cannot be a knight, because this would contradict the false claim of Aiden that Riley is a knight.", "Riley cannot be a knave, because this would contradict the false claim of Ella that Aiden is a knave if and only if Riley is a knave.", "We have exhausted all possibilities for Riley, Aiden, and Ella, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the claim of Samuel that Harper is not a knave.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Harper is not a knave.", "Harper cannot be a knight, because this would contradict the false claim of Samuel that Harper is not a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Aiden is a knave if and only if Riley is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Riley is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Amelia is a knight if and only if Amelia is a knave.", "Riley cannot be a knave, because this would contradict the claim of Ella that Aiden is a knave if and only if Riley is a knave.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Riley is a knight.", "Riley cannot be a knight, because this would contradict the claim of Ella that Aiden is a knave if and only if Riley is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Amelia is a knight if and only if Amelia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Ella is a knight if and only if Riley is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Harper is a knight or Riley is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Ella is a knight if and only if Harper is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Ella is a knight if and only if Harper is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 7)), ('or', ('telling-truth', 7), ('lying', 6)), ('<=>', ('telling-truth', 4), ('lying', 6)), ('<=>', ('telling-truth', 4), ('telling-truth', 7)), ('<=>', ('lying', 5), ('lying', 6)), ('telling-truth', 6), ('<=>', ('telling-truth', 2), ('lying', 2)), ('lying', 4))", "index": 577}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jacob, Owen, David, Lily, Penelope, Sofia, Jackson, and Harper. Jacob said that Harper is a knave or Penelope is a knight. As Owen put it, \"David is a knave if and only if Sofia is a knave\". David noted, \"Penelope is not a knave\". \"Sofia is a knight if and only if Lily is a knight\" - Lily. Penelope was heard saying, \"If Harper is a knave then Sofia is a knight\". \"Harper is a knave,\" Sofia mentioned. Jackson stated, \"Jacob is a knight and Lily is a knave\". Harper said that Sofia is a knight if and only if Jackson is a knight. So who is a knight and who is a knave?", "names": ["Jacob", "Owen", "David", "Lily", "Penelope", "Sofia", "Jackson", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true, false, false], "solution_text": "Jacob is a knight, Owen is a knight, David is a knight, Lily is a knight, Penelope is a knight, Sofia is a knight, Jackson is a knave, and Harper is a knave.", "solution_text_format": "(1) Jacob is a knight\n(2) Owen is a knight\n(3) David is a knight\n(4) Lily is a knight\n(5) Penelope is a knight\n(6) Sofia is a knight\n(7) Jackson is a knave\n(8) Harper is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that Harper is a knave or Penelope is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Sofia is a knight if and only if Jackson is a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that Harper is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Harper is a knave.", "Jackson cannot be a knight, because this would contradict the claim of Harper that Sofia is a knight if and only if Jackson is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Jacob is a knight and Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of their own that Sofia is a knight if and only if Lily is a knight.", "Lily cannot be a knave, because this would contradict the false claim of their own that Sofia is a knight if and only if Lily is a knight.", "We have exhausted all possibilities for Lily, Jackson, and Sofia, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Sofia is a knight if and only if Jackson is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Harper is a knave.", "Jackson cannot be a knight, because this would contradict the false claim of Harper that Sofia is a knight if and only if Jackson is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Jacob is a knight and Lily is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Sofia is a knight if and only if Lily is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that If Harper is a knave then Sofia is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that David is a knave if and only if Sofia is a knave.", "Assume David is a knight. No contradiction is found in their claim that Penelope is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 7), ('telling-truth', 4)), ('<=>', ('lying', 2), ('lying', 5)), ('not', ('lying', 4)), ('<=>', ('telling-truth', 5), ('telling-truth', 3)), ('->', ('lying', 7), ('telling-truth', 5)), ('lying', 7), ('and', ('telling-truth', 0), ('lying', 3)), ('<=>', ('telling-truth', 5), ('telling-truth', 6)))", "index": 578}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mia, Amelia, Isabella, Ethan, Benjamin, Alexander, Harper, and Chloe. Mia commented, \"If Alexander is a knight then Benjamin is a knave\". Amelia stated, \"Mia is a knave and Benjamin is a knave\". Isabella asserted: \"If Ethan is a knave then Chloe is a knight\". Ethan was heard saying, \"Ethan is a knight if and only if Amelia is a knave\". \"Ethan is a knight if and only if Harper is a knave,\" Benjamin declared. \"Mia is a knight or Isabella is a knave\" - Alexander. As Harper put it, \"Isabella is a knave if and only if Alexander is a knave\". \"Isabella is a knave or Ethan is a knave,\" Chloe mentioned. So who is a knight and who is a knave?", "names": ["Mia", "Amelia", "Isabella", "Ethan", "Benjamin", "Alexander", "Harper", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true, true, false], "solution_text": "Mia is a knight, Amelia is a knave, Isabella is a knight, Ethan is a knight, Benjamin is a knave, Alexander is a knight, Harper is a knight, and Chloe is a knave.", "solution_text_format": "(1) Mia is a knight\n(2) Amelia is a knave\n(3) Isabella is a knight\n(4) Ethan is a knight\n(5) Benjamin is a knave\n(6) Alexander is a knight\n(7) Harper is a knight\n(8) Chloe is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that If Alexander is a knight then Benjamin is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Mia is a knight or Isabella is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that If Ethan is a knave then Chloe is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Ethan is a knight if and only if Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Mia is a knave and Benjamin is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Mia is a knave and Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Mia that If Alexander is a knight then Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Ethan is a knight if and only if Harper is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Isabella is a knave if and only if Alexander is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Isabella is a knave or Ethan is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Isabella is a knave or Ethan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 5), ('lying', 4)), ('and', ('lying', 0), ('lying', 4)), ('->', ('lying', 3), ('telling-truth', 7)), ('<=>', ('telling-truth', 3), ('lying', 1)), ('<=>', ('telling-truth', 3), ('lying', 6)), ('or', ('telling-truth', 0), ('lying', 2)), ('<=>', ('lying', 2), ('lying', 5)), ('or', ('lying', 2), ('lying', 3)))", "index": 579}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Harper, Grace, Elizabeth, Aiden, Lucas, Sebastian, Ella, and Riley. Harper said, \"Riley is a knight if and only if Sebastian is a knave.\" \"Aiden is a knave or Ella is a knave,\" Grace claimed. In Elizabeth's words: \"Riley is not a knave\". \"If Harper is a knight then Ella is a knight,\" Aiden mentioned. Lucas told you that If Sebastian is a knight then Ella is a knight. \"If Aiden is a knight then Grace is a knave\" - Sebastian. Ella remarked, \"Sebastian is a knight or Lucas is a knave\". Riley said that Grace is a knight if and only if Ella is a knave. So who is a knight and who is a knave?", "names": ["Harper", "Grace", "Elizabeth", "Aiden", "Lucas", "Sebastian", "Ella", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true, true, true], "solution_text": "Harper is a knave, Grace is a knave, Elizabeth is a knight, Aiden is a knight, Lucas is a knight, Sebastian is a knight, Ella is a knight, and Riley is a knight.", "solution_text_format": "(1) Harper is a knave\n(2) Grace is a knave\n(3) Elizabeth is a knight\n(4) Aiden is a knight\n(5) Lucas is a knight\n(6) Sebastian is a knight\n(7) Ella is a knight\n(8) Riley is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that Riley is a knight if and only if Sebastian is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Grace is a knight if and only if Ella is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Aiden is a knave or Ella is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Harper is a knight then Ella is a knight.", "Ella cannot be a knight, because this would contradict the claim of Grace that Aiden is a knave or Ella is a knave.", "Ella cannot be a knave, because this would contradict the claim of Aiden that If Harper is a knight then Ella is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that If Harper is a knight then Ella is a knight.", "Ella cannot be a knight, because this would contradict the false claim of Aiden that If Harper is a knight then Ella is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Sebastian is a knight or Lucas is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Harper that Riley is a knight if and only if Sebastian is a knave.", "Sebastian cannot be a knave, because this would contradict the false claim of their own that If Aiden is a knight then Grace is a knave.", "We have exhausted all possibilities for Sebastian, Ella, and Aiden, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Aiden is a knave or Ella is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Harper is a knight then Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Sebastian is a knight or Lucas is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Harper that Riley is a knight if and only if Sebastian is a knave.", "Sebastian cannot be a knave, because this would contradict the false claim of their own that If Aiden is a knight then Grace is a knave.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the false claim of Grace that Aiden is a knave or Ella is a knave.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the false claim of Grace that Aiden is a knave or Ella is a knave.", "We have exhausted all possibilities for Aiden and Grace, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Grace is a knight if and only if Ella is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Aiden is a knave or Ella is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Harper is a knight then Ella is a knight.", "Ella cannot be a knight, because this would contradict the claim of Grace that Aiden is a knave or Ella is a knave.", "Ella cannot be a knave, because this would contradict the claim of Aiden that If Harper is a knight then Ella is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that If Harper is a knight then Ella is a knight.", "Ella cannot be a knight, because this would contradict the false claim of Aiden that If Harper is a knight then Ella is a knight.", "Ella cannot be a knave, because this would contradict the false claim of Riley that Grace is a knight if and only if Ella is a knave.", "We have exhausted all possibilities for Ella and Aiden, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Aiden is a knave or Ella is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Harper is a knight then Ella is a knight.", "Ella cannot be a knight, because this would contradict the false claim of Riley that Grace is a knight if and only if Ella is a knave.", "Ella cannot be a knave, because this would contradict the false claim of Grace that Aiden is a knave or Ella is a knave.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the false claim of Grace that Aiden is a knave or Ella is a knave.", "We have exhausted all possibilities for Aiden, Grace, and Riley, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Sebastian is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Grace is a knight if and only if Ella is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Aiden is a knave or Ella is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Harper is a knight then Ella is a knight.", "Ella cannot be a knight, because this would contradict the claim of Grace that Aiden is a knave or Ella is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Sebastian is a knight or Lucas is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of their own that If Aiden is a knight then Grace is a knave.", "Sebastian cannot be a knave, because this would contradict the false claim of Harper that Riley is a knight if and only if Sebastian is a knave.", "We have exhausted all possibilities for Sebastian and Ella, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the false claim of their own that If Harper is a knight then Ella is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Aiden is a knave or Ella is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Harper is a knight then Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Sebastian is a knight or Lucas is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Aiden is a knight then Grace is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that If Sebastian is a knight then Ella is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Riley is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 7), ('lying', 5)), ('or', ('lying', 3), ('lying', 6)), ('not', ('lying', 7)), ('->', ('telling-truth', 0), ('telling-truth', 6)), ('->', ('telling-truth', 5), ('telling-truth', 6)), ('->', ('telling-truth', 3), ('lying', 1)), ('or', ('telling-truth', 5), ('lying', 4)), ('<=>', ('telling-truth', 1), ('lying', 6)))", "index": 580}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Benjamin, Avery, Sophia, James, Lily, Aurora, Penelope, and Noah. Benjamin said, \"Penelope is a knight.\" Avery expressed that Noah is a knave and James is a knight. Sophia said, \"Benjamin is a knave or Penelope is a knight.\" James expressed that Noah is a knight. Lily said that Benjamin is a knight or Noah is a knave. \"Lily is a knave and Aurora is a knight,\" Aurora claimed. According to Penelope, \"Lily is a knave\". Noah told you that Sophia is not a knight. So who is a knight and who is a knave?", "names": ["Benjamin", "Avery", "Sophia", "James", "Lily", "Aurora", "Penelope", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, false, false, false], "solution_text": "Benjamin is a knave, Avery is a knave, Sophia is a knight, James is a knave, Lily is a knight, Aurora is a knave, Penelope is a knave, and Noah is a knave.", "solution_text_format": "(1) Benjamin is a knave\n(2) Avery is a knave\n(3) Sophia is a knight\n(4) James is a knave\n(5) Lily is a knight\n(6) Aurora is a knave\n(7) Penelope is a knave\n(8) Noah is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of Penelope that Lily is a knave.", "Lily cannot be a knave, because this would contradict the false claim of their own that Benjamin is a knight or Noah is a knave.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the claim of Benjamin that Penelope is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Penelope is a knight.", "Penelope cannot be a knight, because this would contradict the false claim of Benjamin that Penelope is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Lily is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Benjamin is a knight or Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of Lily that Benjamin is a knight or Noah is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Sophia is not a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Benjamin is a knave or Penelope is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Noah is a knave and James is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Noah is a knight.", "James cannot be a knave, because this would contradict the claim of Avery that Noah is a knave and James is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Noah is a knave and James is a knight.", "James cannot be a knight, because this would contradict the false claim of Avery that Noah is a knave and James is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Noah is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Lily is a knave and Aurora is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Lily is a knave and Aurora is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 6), ('and', ('lying', 7), ('telling-truth', 3)), ('or', ('lying', 0), ('telling-truth', 6)), ('telling-truth', 7), ('or', ('telling-truth', 0), ('lying', 7)), ('and', ('lying', 4), ('telling-truth', 5)), ('lying', 4), ('not', ('telling-truth', 2)))", "index": 581}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Abigail, Chloe, Olivia, Jacob, Aria, Logan, Ella, and Victoria. Abigail said that If Chloe is a knight then Jacob is a knight. Chloe told you that Jacob is a knight or Ella is a knight. In Olivia's words: \"Aria is a knave or Ella is a knave\". Jacob said that Abigail is not a knight. Aria said that Chloe is a knave or Aria is a knight. Logan asserted: \"Aria is a knight or Chloe is a knave\". Ella said, \"If Victoria is a knave then Jacob is a knight.\" According to Victoria, \"Aria is not a knight\". So who is a knight and who is a knave?", "names": ["Abigail", "Chloe", "Olivia", "Jacob", "Aria", "Logan", "Ella", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true, false, false], "solution_text": "Abigail is a knight, Chloe is a knave, Olivia is a knight, Jacob is a knave, Aria is a knight, Logan is a knight, Ella is a knave, and Victoria is a knave.", "solution_text_format": "(1) Abigail is a knight\n(2) Chloe is a knave\n(3) Olivia is a knight\n(4) Jacob is a knave\n(5) Aria is a knight\n(6) Logan is a knight\n(7) Ella is a knave\n(8) Victoria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that If Chloe is a knight then Jacob is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Jacob is a knight or Ella is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Abigail is not a knight.", "Jacob cannot be a knave, because this would contradict the claim of Abigail that If Chloe is a knight then Jacob is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Jacob is a knight or Ella is a knight.", "Jacob cannot be a knight, because this would contradict the false claim of Chloe that Jacob is a knight or Ella is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Abigail is not a knight.", "Ella cannot be a knight, because this would contradict the false claim of Chloe that Jacob is a knight or Ella is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that If Victoria is a knave then Jacob is a knight.", "Victoria cannot be a knight, because this would contradict the false claim of Ella that If Victoria is a knave then Jacob is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Aria is not a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Chloe is a knave or Aria is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Aria is a knave or Ella is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Aria is a knight or Chloe is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 1), ('telling-truth', 3)), ('or', ('telling-truth', 3), ('telling-truth', 6)), ('or', ('lying', 4), ('lying', 6)), ('not', ('telling-truth', 0)), ('or', ('lying', 1), ('telling-truth', 4)), ('or', ('telling-truth', 4), ('lying', 1)), ('->', ('lying', 7), ('telling-truth', 3)), ('not', ('telling-truth', 4)))", "index": 582}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Scarlett, Jackson, Grace, Luke, Ella, Abigail, David, and Ethan. Scarlett told you that If Ella is a knight then David is a knave. Jackson expressed that David is a knight and Scarlett is a knave. Grace noted, \"Ella is a knave if and only if Luke is a knight\". In a statement by Luke: \"David is a knight or Ella is a knave\". Ella expressed that Jackson is a knave. \"Luke is a knight and Grace is a knight,\" Abigail declared. David was heard saying, \"Ethan is a knave and Grace is a knave\". \"Luke is not a knave,\" Ethan claimed. So who is a knight and who is a knave?", "names": ["Scarlett", "Jackson", "Grace", "Luke", "Ella", "Abigail", "David", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, false, false, false], "solution_text": "Scarlett is a knight, Jackson is a knave, Grace is a knight, Luke is a knave, Ella is a knight, Abigail is a knave, David is a knave, and Ethan is a knave.", "solution_text_format": "(1) Scarlett is a knight\n(2) Jackson is a knave\n(3) Grace is a knight\n(4) Luke is a knave\n(5) Ella is a knight\n(6) Abigail is a knave\n(7) David is a knave\n(8) Ethan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that If Ella is a knight then David is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Jackson is a knave.", "Jackson cannot be a knight, because this would contradict the claim of their own that David is a knight and Scarlett is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that David is a knight and Scarlett is a knave.", "David cannot be a knight, because this would contradict the claim of Scarlett that If Ella is a knight then David is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Ethan is a knave and Grace is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Luke is not a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that David is a knight or Ella is a knave.", "Luke cannot be a knave, because this would contradict the claim of Ethan that Luke is not a knave.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Luke is not a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that David is a knight or Ella is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that David is a knight or Ella is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Ella is a knave if and only if Luke is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Luke is a knight and Grace is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Luke is a knight and Grace is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 4), ('lying', 6)), ('and', ('telling-truth', 6), ('lying', 0)), ('<=>', ('lying', 4), ('telling-truth', 3)), ('or', ('telling-truth', 6), ('lying', 4)), ('lying', 1), ('and', ('telling-truth', 3), ('telling-truth', 2)), ('and', ('lying', 7), ('lying', 2)), ('not', ('lying', 3)))", "index": 583}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Logan, Oliver, Zoey, Olivia, Henry, Samuel, Chloe, and Isabella. Logan stated, \"Henry is a knave and Olivia is a knight\". According to Oliver, \"Olivia is not a knight\". Zoey commented, \"Logan is a knave or Henry is a knave\". \"If Logan is a knight then Olivia is a knight,\" Olivia mentioned. According to Henry, \"Oliver is a knight and Olivia is a knight\". Samuel noted, \"Oliver is a knave\". As Chloe put it, \"Samuel is a knight\". \"Chloe is a knave or Zoey is a knave,\" Isabella declared. So who is a knight and who is a knave?", "names": ["Logan", "Oliver", "Zoey", "Olivia", "Henry", "Samuel", "Chloe", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true, true, false], "solution_text": "Logan is a knight, Oliver is a knave, Zoey is a knight, Olivia is a knight, Henry is a knave, Samuel is a knight, Chloe is a knight, and Isabella is a knave.", "solution_text_format": "(1) Logan is a knight\n(2) Oliver is a knave\n(3) Zoey is a knight\n(4) Olivia is a knight\n(5) Henry is a knave\n(6) Samuel is a knight\n(7) Chloe is a knight\n(8) Isabella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that Henry is a knave and Olivia is a knight.", "Henry cannot be a knight, because this would contradict the claim of Logan that Henry is a knave and Olivia is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Oliver is a knight and Olivia is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Olivia is not a knight.", "Olivia cannot be a knight, because this would contradict the claim of Oliver that Olivia is not a knight.", "Olivia cannot be a knave, because this would contradict the claim of Logan that Henry is a knave and Olivia is a knight.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Olivia is not a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that If Logan is a knight then Olivia is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Logan is a knave or Henry is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Oliver is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Samuel is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Chloe is a knave or Zoey is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Chloe is a knave or Zoey is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('telling-truth', 3)), ('not', ('telling-truth', 3)), ('or', ('lying', 0), ('lying', 4)), ('->', ('telling-truth', 0), ('telling-truth', 3)), ('and', ('telling-truth', 1), ('telling-truth', 3)), ('lying', 1), ('telling-truth', 5), ('or', ('lying', 6), ('lying', 2)))", "index": 584}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Henry, Olivia, Daniel, Lily, Mia, Matthew, Harper, and Luke. \"Olivia is a knave\" - Henry. \"Lily is not a knave,\" Olivia declared. Daniel said that Lily is a knave if and only if Mia is a knight. Lily was heard saying, \"Olivia is a knight\". As Mia put it, \"Olivia is a knight and Daniel is a knight\". Matthew said that If Harper is a knave then Lily is a knave. \"Henry is a knight if and only if Lily is a knight\" - Harper. Luke was heard saying, \"Lily is a knave\". So who is a knight and who is a knave?", "names": ["Henry", "Olivia", "Daniel", "Lily", "Mia", "Matthew", "Harper", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, true, false, true], "solution_text": "Henry is a knight, Olivia is a knave, Daniel is a knave, Lily is a knave, Mia is a knave, Matthew is a knight, Harper is a knave, and Luke is a knight.", "solution_text_format": "(1) Henry is a knight\n(2) Olivia is a knave\n(3) Daniel is a knave\n(4) Lily is a knave\n(5) Mia is a knave\n(6) Matthew is a knight\n(7) Harper is a knave\n(8) Luke is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Henry that Olivia is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Lily is not a knave.", "Lily cannot be a knight, because this would contradict the false claim of Olivia that Lily is not a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Olivia is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Lily is a knave if and only if Mia is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that Olivia is a knight and Daniel is a knight.", "Mia cannot be a knave, because this would contradict the claim of Daniel that Lily is a knave if and only if Mia is a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Lily is a knave if and only if Mia is a knight.", "Mia cannot be a knight, because this would contradict the false claim of Daniel that Lily is a knave if and only if Mia is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Olivia is a knight and Daniel is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that If Harper is a knave then Lily is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Henry is a knight if and only if Lily is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Henry is a knight if and only if Lily is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Lily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 1), ('not', ('lying', 3)), ('<=>', ('lying', 3), ('telling-truth', 4)), ('telling-truth', 1), ('and', ('telling-truth', 1), ('telling-truth', 2)), ('->', ('lying', 6), ('lying', 3)), ('<=>', ('telling-truth', 0), ('telling-truth', 3)), ('lying', 3))", "index": 585}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ava, Abigail, Grace, Zoey, Aurora, Joseph, Samuel, and Avery. \"Avery is a knight and Grace is a knight,\" Ava mentioned. Abigail said that Aurora is a knave or Ava is a knight. As Grace put it, \"Abigail is a knight or Samuel is a knight\". Zoey told you that Zoey is a knight if and only if Aurora is a knight. According to Aurora, \"Zoey is not a knave\". Joseph asserted: \"Avery is a knave or Aurora is a knight\". In Samuel's words: \"Joseph is a knight or Samuel is a knight\". In a statement by Avery: \"Samuel is a knave and Ava is a knave\". So who is a knight and who is a knave?", "names": ["Ava", "Abigail", "Grace", "Zoey", "Aurora", "Joseph", "Samuel", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true, true, false], "solution_text": "Ava is a knave, Abigail is a knave, Grace is a knight, Zoey is a knight, Aurora is a knight, Joseph is a knight, Samuel is a knight, and Avery is a knave.", "solution_text_format": "(1) Ava is a knave\n(2) Abigail is a knave\n(3) Grace is a knight\n(4) Zoey is a knight\n(5) Aurora is a knight\n(6) Joseph is a knight\n(7) Samuel is a knight\n(8) Avery is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Avery is a knight and Grace is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Samuel is a knave and Ava is a knave.", "Avery cannot be a knave, because this would contradict the claim of Ava that Avery is a knight and Grace is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Avery is a knight and Grace is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Samuel is a knave and Ava is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Avery that Samuel is a knave and Ava is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Joseph is a knight or Samuel is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of Samuel that Joseph is a knight or Samuel is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Avery is a knave or Aurora is a knight.", "Aurora cannot be a knight, because this would contradict the false claim of Joseph that Avery is a knave or Aurora is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Zoey is not a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that Zoey is a knight if and only if Aurora is a knight.", "Zoey cannot be a knave, because this would contradict the false claim of their own that Zoey is a knight if and only if Aurora is a knight.", "We have exhausted all possibilities for Zoey, Aurora, Joseph, and Samuel, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Samuel is a knave and Ava is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Joseph is a knight or Samuel is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Avery is a knave or Aurora is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Zoey is not a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Zoey is a knight if and only if Aurora is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Abigail is a knight or Samuel is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Aurora is a knave or Ava is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Aurora is a knave or Ava is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 7), ('telling-truth', 2)), ('or', ('lying', 4), ('telling-truth', 0)), ('or', ('telling-truth', 1), ('telling-truth', 6)), ('<=>', ('telling-truth', 3), ('telling-truth', 4)), ('not', ('lying', 3)), ('or', ('lying', 7), ('telling-truth', 4)), ('or', ('telling-truth', 5), ('telling-truth', 6)), ('and', ('lying', 6), ('lying', 0)))", "index": 586}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jack, Evelyn, Mason, Henry, Victoria, Benjamin, Jacob, and Amelia. Jack remarked, \"Amelia is a knight and Mason is a knight\". Evelyn remarked, \"If Henry is a knight then Mason is a knight\". \"Victoria is a knight if and only if Jacob is a knight,\" Mason declared. Henry expressed that Victoria is a knight. As Victoria put it, \"If Jack is a knight then Mason is a knight\". In a statement by Benjamin: \"Amelia is a knave if and only if Henry is a knight\". Jacob was heard saying, \"Victoria is a knight\". \"If Jack is a knave then Evelyn is a knight,\" Amelia mentioned. So who is a knight and who is a knave?", "names": ["Jack", "Evelyn", "Mason", "Henry", "Victoria", "Benjamin", "Jacob", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false, true, true], "solution_text": "Jack is a knight, Evelyn is a knight, Mason is a knight, Henry is a knight, Victoria is a knight, Benjamin is a knave, Jacob is a knight, and Amelia is a knight.", "solution_text_format": "(1) Jack is a knight\n(2) Evelyn is a knight\n(3) Mason is a knight\n(4) Henry is a knight\n(5) Victoria is a knight\n(6) Benjamin is a knave\n(7) Jacob is a knight\n(8) Amelia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Amelia is a knight and Mason is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that If Jack is a knave then Evelyn is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Henry is a knight then Mason is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Victoria is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that If Jack is a knight then Mason is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Victoria is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Amelia is a knave if and only if Henry is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Amelia is a knave if and only if Henry is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 7), ('telling-truth', 2)), ('->', ('telling-truth', 3), ('telling-truth', 2)), ('<=>', ('telling-truth', 4), ('telling-truth', 6)), ('telling-truth', 4), ('->', ('telling-truth', 0), ('telling-truth', 2)), ('<=>', ('lying', 7), ('telling-truth', 3)), ('telling-truth', 4), ('->', ('lying', 0), ('telling-truth', 1)))", "index": 587}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Benjamin, Amelia, Chloe, Aria, David, Scarlett, Charlotte, and Jackson. Benjamin expressed that If Jackson is a knight then Chloe is a knight. Amelia told you that Benjamin is a knight and Chloe is a knave. Chloe expressed that Charlotte is not a knight. As Aria put it, \"David is a knight\". David was heard saying, \"David is a knight or Scarlett is a knight\". Scarlett commented, \"Amelia is a knave\". In Charlotte's words: \"Benjamin is a knave or Aria is a knight\". As Jackson put it, \"Scarlett is a knight if and only if Amelia is a knave\". So who is a knight and who is a knave?", "names": ["Benjamin", "Amelia", "Chloe", "Aria", "David", "Scarlett", "Charlotte", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true, true, true], "solution_text": "Benjamin is a knave, Amelia is a knave, Chloe is a knave, Aria is a knight, David is a knight, Scarlett is a knight, Charlotte is a knight, and Jackson is a knight.", "solution_text_format": "(1) Benjamin is a knave\n(2) Amelia is a knave\n(3) Chloe is a knave\n(4) Aria is a knight\n(5) David is a knight\n(6) Scarlett is a knight\n(7) Charlotte is a knight\n(8) Jackson is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that If Jackson is a knight then Chloe is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Scarlett is a knight if and only if Amelia is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Scarlett that Amelia is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Benjamin is a knight and Chloe is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Charlotte is not a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Chloe that Charlotte is not a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Benjamin is a knave or Aria is a knight.", "Aria cannot be a knight, because this would contradict the false claim of Charlotte that Benjamin is a knave or Aria is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that David is a knight.", "David cannot be a knight, because this would contradict the false claim of Aria that David is a knight.", "David cannot be a knave, because this would contradict the false claim of their own that David is a knight or Scarlett is a knight.", "We have exhausted all possibilities for David, Aria, and Charlotte, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the claim of Benjamin that If Jackson is a knight then Chloe is a knight.", "We have exhausted all possibilities for Chloe and Amelia, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Amelia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Benjamin is a knight and Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Amelia that Benjamin is a knight and Chloe is a knave.", "Chloe cannot be a knave, because this would contradict the claim of Benjamin that If Jackson is a knight then Chloe is a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Amelia.", "Amelia cannot be a knave, because this would contradict the false claim of Scarlett that Amelia is a knave.", "We have exhausted all possibilities for Amelia and Scarlett, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Scarlett is a knight if and only if Amelia is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Scarlett that Amelia is a knave.", "Amelia cannot be a knave, because this would contradict the false claim of Jackson that Scarlett is a knight if and only if Amelia is a knave.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the false claim of Jackson that Scarlett is a knight if and only if Amelia is a knave.", "Amelia cannot be a knave, because this would contradict the false claim of Scarlett that Amelia is a knave.", "We have exhausted all possibilities for Amelia, Scarlett, and Jackson, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that If Jackson is a knight then Chloe is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Scarlett is a knight if and only if Amelia is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight and Chloe is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Benjamin is a knight and Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the false claim of Benjamin that If Jackson is a knight then Chloe is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Charlotte is not a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Benjamin is a knave or Aria is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that David is a knight.", "Assume David is a knight. No contradiction is found in their claim that David is a knight or Scarlett is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 7), ('telling-truth', 2)), ('and', ('telling-truth', 0), ('lying', 2)), ('not', ('telling-truth', 6)), ('telling-truth', 4), ('or', ('telling-truth', 4), ('telling-truth', 5)), ('lying', 1), ('or', ('lying', 0), ('telling-truth', 3)), ('<=>', ('telling-truth', 5), ('lying', 1)))", "index": 588}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aurora, Alexander, Henry, Ethan, Joseph, James, Luke, and Jackson. \"Jackson is not a knave,\" Aurora declared. \"Joseph is not a knight,\" Alexander claimed. \"If Jackson is a knight then Aurora is a knight,\" Henry declared. According to Ethan, \"Aurora is a knave or Henry is a knave\". Joseph remarked, \"Henry is a knight and Aurora is a knave\". \"Ethan is a knight and Jackson is a knight,\" James declared. Luke was heard saying, \"Ethan is a knight if and only if Joseph is a knave\". \"If Joseph is a knave then James is a knave,\" Jackson mentioned. So who is a knight and who is a knave?", "names": ["Aurora", "Alexander", "Henry", "Ethan", "Joseph", "James", "Luke", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false, false, true], "solution_text": "Aurora is a knight, Alexander is a knight, Henry is a knight, Ethan is a knave, Joseph is a knave, James is a knave, Luke is a knave, and Jackson is a knight.", "solution_text_format": "(1) Aurora is a knight\n(2) Alexander is a knight\n(3) Henry is a knight\n(4) Ethan is a knave\n(5) Joseph is a knave\n(6) James is a knave\n(7) Luke is a knave\n(8) Jackson is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that Jackson is not a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that If Joseph is a knave then James is a knave.", "Joseph cannot be a knight, because this would contradict the claim of their own that Henry is a knight and Aurora is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Henry is a knight and Aurora is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Jackson is a knight then Aurora is a knight.", "James cannot be a knight, because this would contradict the claim of Jackson that If Joseph is a knave then James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Ethan is a knight and Jackson is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Aurora is a knave or Henry is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Aurora is a knave or Henry is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Joseph is not a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Ethan is a knight if and only if Joseph is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Ethan is a knight if and only if Joseph is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 7)), ('not', ('telling-truth', 4)), ('->', ('telling-truth', 7), ('telling-truth', 0)), ('or', ('lying', 0), ('lying', 2)), ('and', ('telling-truth', 2), ('lying', 0)), ('and', ('telling-truth', 3), ('telling-truth', 7)), ('<=>', ('telling-truth', 3), ('lying', 4)), ('->', ('lying', 4), ('lying', 5)))", "index": 589}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aurora, Sophia, Jackson, Isabella, Noah, Chloe, Ella, and Emily. In a statement by Aurora: \"Jackson is a knight if and only if Sophia is a knight\". Sophia commented, \"Chloe is a knave\". \"Noah is a knight and Aurora is a knave\" - Jackson. \"If Noah is a knave then Sophia is a knave,\" Isabella mentioned. Noah was heard saying, \"Isabella is a knight if and only if Jackson is a knave\". In a statement by Chloe: \"Aurora is a knave and Sophia is a knave\". As Ella put it, \"Isabella is a knave\". Emily said, \"Chloe is a knight if and only if Jackson is a knave.\" So who is a knight and who is a knave?", "names": ["Aurora", "Sophia", "Jackson", "Isabella", "Noah", "Chloe", "Ella", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, false, true, false], "solution_text": "Aurora is a knave, Sophia is a knight, Jackson is a knave, Isabella is a knave, Noah is a knave, Chloe is a knave, Ella is a knight, and Emily is a knave.", "solution_text_format": "(1) Aurora is a knave\n(2) Sophia is a knight\n(3) Jackson is a knave\n(4) Isabella is a knave\n(5) Noah is a knave\n(6) Chloe is a knave\n(7) Ella is a knight\n(8) Emily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Sophia is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Noah is a knight and Aurora is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Noah is a knight and Aurora is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Jackson is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that If Noah is a knave then Sophia is a knave.", "Sophia cannot be a knight, because this would contradict the claim of Aurora that Jackson is a knight if and only if Sophia is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Aurora is a knave and Sophia is a knave.", "Chloe cannot be a knave, because this would contradict the false claim of Sophia that Chloe is a knave.", "We have exhausted all possibilities for Chloe and Sophia, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the false claim of their own that If Noah is a knave then Sophia is a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Isabella is a knight if and only if Jackson is a knave.", "Isabella cannot be a knight, because this would contradict the false claim of Noah that Isabella is a knight if and only if Jackson is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that If Noah is a knave then Sophia is a knave.", "Sophia cannot be a knight, because this would contradict the claim of Aurora that Jackson is a knight if and only if Sophia is a knight.", "Sophia cannot be a knave, because this would contradict the false claim of Isabella that If Noah is a knave then Sophia is a knave.", "We have exhausted all possibilities for Sophia, Isabella, Noah, and Jackson, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Jackson is a knight if and only if Sophia is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Noah is a knight and Aurora is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Jackson is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Noah that Isabella is a knight if and only if Jackson is a knave.", "Isabella cannot be a knave, because this would contradict the false claim of their own that If Noah is a knave then Sophia is a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the claim of Jackson that Noah is a knight and Aurora is a knave.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Noah is a knight and Aurora is a knave.", "Noah cannot be a knight, because this would contradict the false claim of Jackson that Noah is a knight and Aurora is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Isabella is a knight if and only if Jackson is a knave.", "Isabella cannot be a knight, because this would contradict the false claim of Noah that Isabella is a knight if and only if Jackson is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that If Noah is a knave then Sophia is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Sophia that Chloe is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Aurora is a knave and Sophia is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Isabella is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Chloe is a knight if and only if Jackson is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Chloe is a knight if and only if Jackson is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('telling-truth', 1)), ('lying', 5), ('and', ('telling-truth', 4), ('lying', 0)), ('->', ('lying', 4), ('lying', 1)), ('<=>', ('telling-truth', 3), ('lying', 2)), ('and', ('lying', 0), ('lying', 1)), ('lying', 3), ('<=>', ('telling-truth', 5), ('lying', 2)))", "index": 590}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Daniel, Sebastian, Chloe, Lily, Amelia, Matthew, Joseph, and Ella. Daniel expressed that Ella is a knave if and only if Amelia is a knight. Sebastian noted, \"Daniel is a knave if and only if Lily is a knight\". In Chloe's words: \"Chloe is a knight or Amelia is a knave\". Lily stated, \"If Matthew is a knave then Joseph is a knave\". \"Chloe is a knight\" - Amelia. Matthew noted, \"Amelia is a knave if and only if Joseph is a knight\". \"If Amelia is a knave then Ella is a knight,\" Joseph mentioned. Ella expressed that Joseph is not a knave. So who is a knight and who is a knave?", "names": ["Daniel", "Sebastian", "Chloe", "Lily", "Amelia", "Matthew", "Joseph", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, false, true, true], "solution_text": "Daniel is a knave, Sebastian is a knave, Chloe is a knight, Lily is a knave, Amelia is a knight, Matthew is a knave, Joseph is a knight, and Ella is a knight.", "solution_text_format": "(1) Daniel is a knave\n(2) Sebastian is a knave\n(3) Chloe is a knight\n(4) Lily is a knave\n(5) Amelia is a knight\n(6) Matthew is a knave\n(7) Joseph is a knight\n(8) Ella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that Ella is a knave if and only if Amelia is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Joseph is not a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that If Amelia is a knave then Ella is a knight.", "Amelia cannot be a knight, because this would contradict the claim of Daniel that Ella is a knave if and only if Amelia is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Chloe is a knight.", "Chloe cannot be a knight, because this would contradict the false claim of Amelia that Chloe is a knight.", "Chloe cannot be a knave, because this would contradict the false claim of their own that Chloe is a knight or Amelia is a knave.", "We have exhausted all possibilities for Chloe and Amelia, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the false claim of their own that If Amelia is a knave then Ella is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Joseph is not a knave.", "Joseph cannot be a knight, because this would contradict the false claim of Ella that Joseph is not a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that If Amelia is a knave then Ella is a knight.", "Amelia cannot be a knight, because this would contradict the false claim of Joseph that If Amelia is a knave then Ella is a knight.", "Amelia cannot be a knave, because this would contradict the claim of Daniel that Ella is a knave if and only if Amelia is a knight.", "We have exhausted all possibilities for Amelia, Joseph, and Ella, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Ella is a knave if and only if Amelia is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Joseph is not a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that If Amelia is a knave then Ella is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Chloe is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Chloe is a knight or Amelia is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Daniel is a knave if and only if Lily is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that If Matthew is a knave then Joseph is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Amelia is a knave if and only if Joseph is a knight.", "Matthew cannot be a knave, because this would contradict the claim of Lily that If Matthew is a knave then Joseph is a knave.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the claim of Sebastian that Daniel is a knave if and only if Lily is a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Daniel is a knave if and only if Lily is a knight.", "Lily cannot be a knight, because this would contradict the false claim of Sebastian that Daniel is a knave if and only if Lily is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that If Matthew is a knave then Joseph is a knave.", "Matthew cannot be a knight, because this would contradict the false claim of Lily that If Matthew is a knave then Joseph is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Amelia is a knave if and only if Joseph is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 7), ('telling-truth', 4)), ('<=>', ('lying', 0), ('telling-truth', 3)), ('or', ('telling-truth', 2), ('lying', 4)), ('->', ('lying', 5), ('lying', 6)), ('telling-truth', 2), ('<=>', ('lying', 4), ('telling-truth', 6)), ('->', ('lying', 4), ('telling-truth', 7)), ('not', ('lying', 6)))", "index": 591}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aria, Oliver, Matthew, Liam, Avery, Owen, Logan, and Mason. Aria was heard saying, \"Matthew is a knave and Mason is a knave\". According to Oliver, \"Mason is a knave or Owen is a knight\". Matthew told you that Logan is a knave if and only if Avery is a knight. In Liam's words: \"Mason is a knight or Mason is a knave\". \"Oliver is a knave and Aria is a knight,\" Avery claimed. Owen noted, \"Aria is not a knave\". As Logan put it, \"Mason is not a knave\". In Mason's words: \"If Owen is a knave then Liam is a knight\". So who is a knight and who is a knave?", "names": ["Aria", "Oliver", "Matthew", "Liam", "Avery", "Owen", "Logan", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false, true, true], "solution_text": "Aria is a knave, Oliver is a knave, Matthew is a knight, Liam is a knight, Avery is a knave, Owen is a knave, Logan is a knight, and Mason is a knight.", "solution_text_format": "(1) Aria is a knave\n(2) Oliver is a knave\n(3) Matthew is a knight\n(4) Liam is a knight\n(5) Avery is a knave\n(6) Owen is a knave\n(7) Logan is a knight\n(8) Mason is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that Matthew is a knave and Mason is a knave.", "Matthew cannot be a knight, because this would contradict the claim of Aria that Matthew is a knave and Mason is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Logan is a knave if and only if Avery is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Mason is not a knave.", "Mason cannot be a knight, because this would contradict the claim of Aria that Matthew is a knave and Mason is a knave.", "Mason cannot be a knave, because this would contradict the claim of Logan that Mason is not a knave.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Mason is not a knave.", "Mason cannot be a knight, because this would contradict the claim of Aria that Matthew is a knave and Mason is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that If Owen is a knave then Liam is a knight.", "Owen cannot be a knight, because this would contradict the false claim of Mason that If Owen is a knave then Liam is a knight.", "Owen cannot be a knave, because this would contradict the false claim of their own that Aria is not a knave.", "We have exhausted all possibilities for Owen, Mason, Logan, and Matthew, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Matthew is a knave and Mason is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Logan is a knave if and only if Avery is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Mason is not a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Owen is a knave then Liam is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Aria is not a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Aria is not a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Mason is a knight or Mason is a knave.", "Avery cannot be a knight, because this would contradict the claim of Matthew that Logan is a knave if and only if Avery is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Oliver is a knave and Aria is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Mason is a knave or Owen is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Mason is a knave or Owen is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('lying', 7)), ('or', ('lying', 7), ('telling-truth', 5)), ('<=>', ('lying', 6), ('telling-truth', 4)), ('or', ('telling-truth', 7), ('lying', 7)), ('and', ('lying', 1), ('telling-truth', 0)), ('not', ('lying', 0)), ('not', ('lying', 7)), ('->', ('lying', 5), ('telling-truth', 3)))", "index": 592}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sophia, Penelope, Emma, Liam, Luke, Lily, Joseph, and Mia. \"Joseph is a knight and Lily is a knight,\" Sophia mentioned. \"Luke is a knave or Mia is a knight,\" Penelope claimed. As Emma put it, \"Penelope is a knight if and only if Lily is a knight\". Liam said, \"Luke is a knave.\" Luke said that Lily is a knight or Liam is a knight. Lily said, \"Penelope is a knave or Luke is a knight.\" Joseph said, \"If Liam is a knight then Joseph is a knight.\" \"Luke is a knave,\" Mia claimed. So who is a knight and who is a knave?", "names": ["Sophia", "Penelope", "Emma", "Liam", "Luke", "Lily", "Joseph", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true, true, false], "solution_text": "Sophia is a knight, Penelope is a knave, Emma is a knave, Liam is a knave, Luke is a knight, Lily is a knight, Joseph is a knight, and Mia is a knave.", "solution_text_format": "(1) Sophia is a knight\n(2) Penelope is a knave\n(3) Emma is a knave\n(4) Liam is a knave\n(5) Luke is a knight\n(6) Lily is a knight\n(7) Joseph is a knight\n(8) Mia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Joseph is a knight and Lily is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Liam is a knight then Joseph is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Luke is a knave.", "Luke cannot be a knight, because this would contradict the claim of Liam that Luke is a knave.", "Luke cannot be a knave, because this would contradict the false claim of their own that Lily is a knight or Liam is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Luke is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Lily is a knight or Liam is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Penelope is a knave or Luke is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Luke is a knave or Mia is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that Luke is a knave.", "Mia cannot be a knave, because this would contradict the claim of Penelope that Luke is a knave or Mia is a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Luke is a knave or Mia is a knight.", "Mia cannot be a knight, because this would contradict the false claim of Penelope that Luke is a knave or Mia is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Luke is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Penelope is a knight if and only if Lily is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Penelope is a knight if and only if Lily is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 6), ('telling-truth', 5)), ('or', ('lying', 4), ('telling-truth', 7)), ('<=>', ('telling-truth', 1), ('telling-truth', 5)), ('lying', 4), ('or', ('telling-truth', 5), ('telling-truth', 3)), ('or', ('lying', 1), ('telling-truth', 4)), ('->', ('telling-truth', 3), ('telling-truth', 6)), ('lying', 4))", "index": 593}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Daniel, Sebastian, David, Jacob, Harper, Victoria, Aurora, and Jack. \"Sebastian is not a knave,\" Daniel mentioned. \"David is a knight,\" Sebastian declared. In a statement by David: \"Daniel is a knave if and only if Aurora is a knight\". \"David is a knight and Aurora is a knight,\" Jacob claimed. In a statement by Harper: \"Aurora is a knight or Jack is a knave\". Victoria was heard saying, \"Daniel is a knave or Jacob is a knight\". As Aurora put it, \"Harper is a knight or David is a knight\". Jack remarked, \"Jack is a knight and Sebastian is a knave\". So who is a knight and who is a knave?", "names": ["Daniel", "Sebastian", "David", "Jacob", "Harper", "Victoria", "Aurora", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, true, false, true], "solution_text": "Daniel is a knave, Sebastian is a knave, David is a knave, Jacob is a knave, Harper is a knave, Victoria is a knight, Aurora is a knave, and Jack is a knight.", "solution_text_format": "(1) Daniel is a knave\n(2) Sebastian is a knave\n(3) David is a knave\n(4) Jacob is a knave\n(5) Harper is a knave\n(6) Victoria is a knight\n(7) Aurora is a knave\n(8) Jack is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that Sebastian is not a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that David is a knight.", "Assume David is a knight. No contradiction is found in their claim that Daniel is a knave if and only if Aurora is a knight.", "Aurora cannot be a knight, because this would contradict the claim of David that Daniel is a knave if and only if Aurora is a knight.", "Aurora cannot be a knave, because this would contradict the false claim of their own that Harper is a knight or David is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the claim of Sebastian that David is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the claim of Daniel that Sebastian is not a knave.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Sebastian is not a knave.", "Sebastian cannot be a knight, because this would contradict the false claim of Daniel that Sebastian is not a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that David is a knight.", "David cannot be a knight, because this would contradict the false claim of Sebastian that David is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Daniel is a knave if and only if Aurora is a knight.", "Aurora cannot be a knight, because this would contradict the false claim of David that Daniel is a knave if and only if Aurora is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Harper is a knight or David is a knight.", "Harper cannot be a knight, because this would contradict the false claim of Aurora that Harper is a knight or David is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Aurora is a knight or Jack is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Jack is a knight and Sebastian is a knave.", "Jacob cannot be a knight, because this would contradict the claim of their own that David is a knight and Aurora is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that David is a knight and Aurora is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Daniel is a knave or Jacob is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('telling-truth', 2), ('<=>', ('lying', 0), ('telling-truth', 6)), ('and', ('telling-truth', 2), ('telling-truth', 6)), ('or', ('telling-truth', 6), ('lying', 7)), ('or', ('lying', 0), ('telling-truth', 3)), ('or', ('telling-truth', 4), ('telling-truth', 2)), ('and', ('telling-truth', 7), ('lying', 1)))", "index": 594}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Samuel, Owen, William, Harper, Lucas, Logan, Jacob, and Sebastian. \"William is not a knight,\" Samuel declared. In Owen's words: \"Jacob is a knave if and only if Jacob is a knight\". William was heard saying, \"Jacob is a knave or Owen is a knave\". In a statement by Harper: \"Sebastian is a knave\". Lucas said, \"Jacob is not a knight.\" \"If Harper is a knight then Lucas is a knave,\" Logan declared. \"If Owen is a knave then Samuel is a knight,\" Jacob declared. In a statement by Sebastian: \"Logan is a knight or Owen is a knave\". So who is a knight and who is a knave?", "names": ["Samuel", "Owen", "William", "Harper", "Lucas", "Logan", "Jacob", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true, false, true], "solution_text": "Samuel is a knave, Owen is a knave, William is a knight, Harper is a knave, Lucas is a knight, Logan is a knight, Jacob is a knave, and Sebastian is a knight.", "solution_text_format": "(1) Samuel is a knave\n(2) Owen is a knave\n(3) William is a knight\n(4) Harper is a knave\n(5) Lucas is a knight\n(6) Logan is a knight\n(7) Jacob is a knave\n(8) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that William is not a knight.", "William cannot be a knight, because this would contradict the claim of Samuel that William is not a knight.", "Assume William is a knave. No contradiction is found in their false claim that Jacob is a knave or Owen is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that If Owen is a knave then Samuel is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Jacob is a knave if and only if Jacob is a knight.", "Owen cannot be a knave, because this would contradict the false claim of William that Jacob is a knave or Owen is a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the false claim of William that Jacob is a knave or Owen is a knave.", "We have exhausted all possibilities for Jacob and William, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that William is not a knight.", "Assume William is a knight. No contradiction is found in their claim that Jacob is a knave or Owen is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that If Owen is a knave then Samuel is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Jacob is a knave if and only if Jacob is a knight.", "Owen cannot be a knave, because this would contradict the claim of Jacob that If Owen is a knave then Samuel is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that If Owen is a knave then Samuel is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Jacob is a knave if and only if Jacob is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Jacob is a knave if and only if Jacob is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Harper that Sebastian is a knave.", "Sebastian cannot be a knave, because this would contradict the false claim of their own that Logan is a knight or Owen is a knave.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Sebastian is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Logan is a knight or Owen is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that If Harper is a knight then Lucas is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Jacob is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('<=>', ('lying', 6), ('telling-truth', 6)), ('or', ('lying', 6), ('lying', 1)), ('lying', 7), ('not', ('telling-truth', 6)), ('->', ('telling-truth', 3), ('lying', 4)), ('->', ('lying', 1), ('telling-truth', 0)), ('or', ('telling-truth', 5), ('lying', 1)))", "index": 595}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Scarlett, Logan, William, Aria, Zoey, Victoria, Samuel, and Noah. Scarlett said that If Noah is a knave then Noah is a knight. \"Scarlett is a knave or William is a knight\" - Logan. William expressed that Aria is a knight and Samuel is a knave. \"Scarlett is a knight,\" Aria mentioned. Zoey expressed that If Victoria is a knave then Scarlett is a knave. Victoria stated, \"If Aria is a knight then Samuel is a knight\". Samuel was heard saying, \"Aria is a knave and Noah is a knave\". \"Noah is a knight if and only if Zoey is a knight,\" Noah mentioned. So who is a knight and who is a knave?", "names": ["Scarlett", "Logan", "William", "Aria", "Zoey", "Victoria", "Samuel", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true, true, false], "solution_text": "Scarlett is a knave, Logan is a knight, William is a knave, Aria is a knave, Zoey is a knight, Victoria is a knight, Samuel is a knight, and Noah is a knave.", "solution_text_format": "(1) Scarlett is a knave\n(2) Logan is a knight\n(3) William is a knave\n(4) Aria is a knave\n(5) Zoey is a knight\n(6) Victoria is a knight\n(7) Samuel is a knight\n(8) Noah is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that If Noah is a knave then Noah is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Noah is a knight if and only if Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that If Victoria is a knave then Scarlett is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that If Aria is a knight then Samuel is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Scarlett is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Aria is a knave and Noah is a knave.", "Samuel cannot be a knave, because this would contradict the claim of Victoria that If Aria is a knight then Samuel is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Aria.", "Aria cannot be a knave, because this would contradict the false claim of their own that Scarlett is a knight.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Victoria.", "Victoria cannot be a knave, because this would contradict the claim of Zoey that If Victoria is a knave then Scarlett is a knave.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Zoey.", "Zoey cannot be a knave, because this would contradict the claim of Noah that Noah is a knight if and only if Zoey is a knight.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the claim of Scarlett that If Noah is a knave then Noah is a knight.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that If Noah is a knave then Noah is a knight.", "Noah cannot be a knight, because this would contradict the false claim of Scarlett that If Noah is a knave then Noah is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Noah is a knight if and only if Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that If Victoria is a knave then Scarlett is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that If Aria is a knight then Samuel is a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Scarlett is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Aria is a knave and Noah is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Scarlett is a knave or William is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Aria is a knight and Samuel is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Aria is a knight and Samuel is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 7), ('telling-truth', 7)), ('or', ('lying', 0), ('telling-truth', 2)), ('and', ('telling-truth', 3), ('lying', 6)), ('telling-truth', 0), ('->', ('lying', 5), ('lying', 0)), ('->', ('telling-truth', 3), ('telling-truth', 6)), ('and', ('lying', 3), ('lying', 7)), ('<=>', ('telling-truth', 7), ('telling-truth', 4)))", "index": 596}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Matthew, Daniel, Mason, Grace, Luke, Isabella, Sofia, and Sebastian. According to Matthew, \"Mason is a knight if and only if Sebastian is a knight\". As Daniel put it, \"If Mason is a knight then Matthew is a knight\". \"Sofia is a knave and Isabella is a knight,\" Mason mentioned. Grace was heard saying, \"Matthew is a knight and Sebastian is a knave\". Luke remarked, \"Mason is not a knight\". Isabella said, \"Isabella is a knight or Matthew is a knave.\" \"Matthew is a knave and Luke is a knave\" - Sofia. In Sebastian's words: \"Luke is a knight and Grace is a knave\". So who is a knight and who is a knave?", "names": ["Matthew", "Daniel", "Mason", "Grace", "Luke", "Isabella", "Sofia", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false, false, false], "solution_text": "Matthew is a knight, Daniel is a knight, Mason is a knave, Grace is a knight, Luke is a knight, Isabella is a knave, Sofia is a knave, and Sebastian is a knave.", "solution_text_format": "(1) Matthew is a knight\n(2) Daniel is a knight\n(3) Mason is a knave\n(4) Grace is a knight\n(5) Luke is a knight\n(6) Isabella is a knave\n(7) Sofia is a knave\n(8) Sebastian is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that Mason is a knight if and only if Sebastian is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Sofia is a knave and Isabella is a knight.", "Sofia cannot be a knight, because this would contradict the claim of Mason that Sofia is a knave and Isabella is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Matthew is a knave and Luke is a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that Mason is not a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Mason is not a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Isabella is a knight or Matthew is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Luke is a knight and Grace is a knave.", "Sebastian cannot be a knave, because this would contradict the claim of Matthew that Mason is a knight if and only if Sebastian is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the claim of Mason that Sofia is a knave and Isabella is a knight.", "We have exhausted all possibilities for Isabella, Luke, and Sofia, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Sofia is a knave and Isabella is a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that Matthew is a knave and Luke is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Matthew is a knave and Luke is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Mason is not a knight.", "Isabella cannot be a knight, because this would contradict the false claim of Mason that Sofia is a knave and Isabella is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Isabella is a knight or Matthew is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Matthew that Mason is a knight if and only if Sebastian is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Luke is a knight and Grace is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Matthew is a knight and Sebastian is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that If Mason is a knight then Matthew is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('telling-truth', 7)), ('->', ('telling-truth', 2), ('telling-truth', 0)), ('and', ('lying', 6), ('telling-truth', 5)), ('and', ('telling-truth', 0), ('lying', 7)), ('not', ('telling-truth', 2)), ('or', ('telling-truth', 5), ('lying', 0)), ('and', ('lying', 0), ('lying', 4)), ('and', ('telling-truth', 4), ('lying', 3)))", "index": 597}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Abigail, Daniel, James, Owen, Samuel, Logan, Victoria, and William. Abigail noted, \"Owen is a knight\". Daniel was heard saying, \"James is a knight or Abigail is a knave\". In a statement by James: \"If Abigail is a knight then James is a knight\". Owen expressed that William is not a knave. Samuel expressed that Logan is a knave if and only if Victoria is a knight. Logan expressed that Abigail is a knave. Victoria said that James is not a knave. William told you that Abigail is a knave if and only if Daniel is a knight. So who is a knight and who is a knave?", "names": ["Abigail", "Daniel", "James", "Owen", "Samuel", "Logan", "Victoria", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, false, false, true], "solution_text": "Abigail is a knight, Daniel is a knave, James is a knave, Owen is a knight, Samuel is a knave, Logan is a knave, Victoria is a knave, and William is a knight.", "solution_text_format": "(1) Abigail is a knight\n(2) Daniel is a knave\n(3) James is a knave\n(4) Owen is a knight\n(5) Samuel is a knave\n(6) Logan is a knave\n(7) Victoria is a knave\n(8) William is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Owen is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that William is not a knave.", "Assume William is a knight. No contradiction is found in their claim that Abigail is a knave if and only if Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the claim of William that Abigail is a knave if and only if Daniel is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that James is a knight or Abigail is a knave.", "James cannot be a knight, because this would contradict the false claim of Daniel that James is a knight or Abigail is a knave.", "Assume James is a knave. No contradiction is found in their false claim that If Abigail is a knight then James is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Logan is a knave if and only if Victoria is a knight.", "Logan cannot be a knight, because this would contradict the claim of their own that Abigail is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Abigail is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that James is not a knave.", "Victoria cannot be a knave, because this would contradict the claim of Samuel that Logan is a knave if and only if Victoria is a knight.", "We have exhausted all possibilities for Victoria and Logan, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Logan is a knave if and only if Victoria is a knight.", "Logan cannot be a knight, because this would contradict the claim of their own that Abigail is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Abigail is a knave.", "Victoria cannot be a knight, because this would contradict the false claim of Samuel that Logan is a knave if and only if Victoria is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that James is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 3), ('or', ('telling-truth', 2), ('lying', 0)), ('->', ('telling-truth', 0), ('telling-truth', 2)), ('not', ('lying', 7)), ('<=>', ('lying', 5), ('telling-truth', 6)), ('lying', 0), ('not', ('lying', 2)), ('<=>', ('lying', 0), ('telling-truth', 1)))", "index": 598}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: David, Aurora, Ethan, Avery, Emily, Penelope, James, and Henry. David told you that Emily is a knight or James is a knave. \"Penelope is not a knight,\" Aurora claimed. As Ethan put it, \"Aurora is a knight or Henry is a knight\". Avery noted, \"Ethan is a knave\". Emily stated, \"James is a knave if and only if Penelope is a knave\". Penelope noted, \"Ethan is a knight if and only if James is a knight\". James said that Henry is not a knave. \"James is a knave or Ethan is a knight\" - Henry. So who is a knight and who is a knave?", "names": ["David", "Aurora", "Ethan", "Avery", "Emily", "Penelope", "James", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true, true, true], "solution_text": "David is a knight, Aurora is a knave, Ethan is a knight, Avery is a knave, Emily is a knight, Penelope is a knight, James is a knight, and Henry is a knight.", "solution_text_format": "(1) David is a knight\n(2) Aurora is a knave\n(3) Ethan is a knight\n(4) Avery is a knave\n(5) Emily is a knight\n(6) Penelope is a knight\n(7) James is a knight\n(8) Henry is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Emily is a knight or James is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that James is a knave if and only if Penelope is a knave.", "Assume James is a knight. No contradiction is found in their claim that Henry is not a knave.", "Assume Henry is a knight. No contradiction is found in their claim that James is a knave or Ethan is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Aurora is a knight or Henry is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Penelope cannot be a knight, because this would contradict the claim of Aurora that Penelope is not a knight.", "Penelope cannot be a knave, because this would contradict the claim of Emily that James is a knave if and only if Penelope is a knave.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Penelope is not a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Ethan is a knight if and only if James is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Ethan is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Ethan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('lying', 6)), ('not', ('telling-truth', 5)), ('or', ('telling-truth', 1), ('telling-truth', 7)), ('lying', 2), ('<=>', ('lying', 6), ('lying', 5)), ('<=>', ('telling-truth', 2), ('telling-truth', 6)), ('not', ('lying', 7)), ('or', ('lying', 6), ('telling-truth', 2)))", "index": 599}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Grace, Harper, Abigail, Scarlett, Jack, Mia, Benjamin, and Matthew. Grace expressed that Harper is a knight if and only if Harper is a knave. Harper stated, \"Scarlett is not a knight\". Abigail expressed that Abigail is a knight. Scarlett asserted: \"Harper is a knight and Abigail is a knight\". In a statement by Jack: \"Scarlett is a knave if and only if Mia is a knight\". \"Abigail is a knight or Grace is a knave\" - Mia. Benjamin said that Abigail is a knave if and only if Jack is a knight. Matthew said, \"Jack is not a knight.\" So who is a knight and who is a knave?", "names": ["Grace", "Harper", "Abigail", "Scarlett", "Jack", "Mia", "Benjamin", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true, true, false], "solution_text": "Grace is a knave, Harper is a knight, Abigail is a knave, Scarlett is a knave, Jack is a knight, Mia is a knight, Benjamin is a knight, and Matthew is a knave.", "solution_text_format": "(1) Grace is a knave\n(2) Harper is a knight\n(3) Abigail is a knave\n(4) Scarlett is a knave\n(5) Jack is a knight\n(6) Mia is a knight\n(7) Benjamin is a knight\n(8) Matthew is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Grace cannot be a knight, because this would contradict the claim of their own that Harper is a knight if and only if Harper is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Harper is a knight if and only if Harper is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Scarlett is not a knight.", "Scarlett cannot be a knight, because this would contradict the claim of Harper that Scarlett is not a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Harper is a knight and Abigail is a knight.", "Abigail cannot be a knight, because this would contradict the false claim of Scarlett that Harper is a knight and Abigail is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Abigail is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Scarlett is a knave if and only if Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Abigail is a knight or Grace is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Abigail is a knave if and only if Jack is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Jack is not a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Jack is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('lying', 1)), ('not', ('telling-truth', 3)), ('telling-truth', 2), ('and', ('telling-truth', 1), ('telling-truth', 2)), ('<=>', ('lying', 3), ('telling-truth', 5)), ('or', ('telling-truth', 2), ('lying', 0)), ('<=>', ('lying', 2), ('telling-truth', 4)), ('not', ('telling-truth', 4)))", "index": 600}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Elizabeth, Emily, Isabella, Henry, Abigail, Emma, Alexander, and Mia. Elizabeth said, \"Abigail is a knight and Emma is a knave.\" Emily said, \"If Alexander is a knight then Mia is a knight.\" Isabella commented, \"Alexander is a knight and Abigail is a knight\". \"If Alexander is a knight then Mia is a knight,\" Henry declared. Abigail remarked, \"Isabella is a knight if and only if Henry is a knave\". Emma said that Emily is a knave or Emily is a knight. Alexander noted, \"Isabella is a knave if and only if Abigail is a knave\". Mia said that Emily is a knave or Henry is a knave. So who is a knight and who is a knave?", "names": ["Elizabeth", "Emily", "Isabella", "Henry", "Abigail", "Emma", "Alexander", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true, false, false], "solution_text": "Elizabeth is a knave, Emily is a knight, Isabella is a knave, Henry is a knight, Abigail is a knight, Emma is a knight, Alexander is a knave, and Mia is a knave.", "solution_text_format": "(1) Elizabeth is a knave\n(2) Emily is a knight\n(3) Isabella is a knave\n(4) Henry is a knight\n(5) Abigail is a knight\n(6) Emma is a knight\n(7) Alexander is a knave\n(8) Mia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Abigail is a knight and Emma is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Henry is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Alexander is a knight and Abigail is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Isabella is a knave if and only if Abigail is a knave.", "Henry cannot be a knight, because this would contradict the claim of Abigail that Isabella is a knight if and only if Henry is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that If Alexander is a knight then Mia is a knight.", "Mia cannot be a knight, because this would contradict the false claim of Henry that If Alexander is a knight then Mia is a knight.", "Mia cannot be a knave, because this would contradict the false claim of their own that Emily is a knave or Henry is a knave.", "We have exhausted all possibilities for Mia and Henry, so let us go back and reconsider Alexander.", "Alexander cannot be a knave, because this would contradict the claim of Isabella that Alexander is a knight and Abigail is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Alexander is a knight and Abigail is a knight.", "Alexander cannot be a knight, because this would contradict the false claim of Isabella that Alexander is a knight and Abigail is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Isabella is a knave if and only if Abigail is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Alexander is a knight then Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Emily is a knave or Henry is a knave.", "Emily cannot be a knight, because this would contradict the claim of Mia that Emily is a knave or Henry is a knave.", "Emily cannot be a knave, because this would contradict the false claim of their own that If Alexander is a knight then Mia is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Emily is a knave or Henry is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that If Alexander is a knight then Mia is a knight.", "Emma cannot be a knight, because this would contradict the claim of Elizabeth that Abigail is a knight and Emma is a knave.", "Emma cannot be a knave, because this would contradict the false claim of their own that Emily is a knave or Emily is a knight.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the false claim of their own that If Alexander is a knight then Mia is a knight.", "We have exhausted all possibilities for Emily and Mia, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the false claim of their own that If Alexander is a knight then Mia is a knight.", "We have exhausted all possibilities for Henry, Alexander, and Isabella, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the claim of Elizabeth that Abigail is a knight and Emma is a knave.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Abigail is a knight and Emma is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Henry is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Alexander is a knight and Abigail is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Isabella is a knave if and only if Abigail is a knave.", "Henry cannot be a knight, because this would contradict the claim of Abigail that Isabella is a knight if and only if Henry is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that If Alexander is a knight then Mia is a knight.", "Mia cannot be a knight, because this would contradict the false claim of Henry that If Alexander is a knight then Mia is a knight.", "Mia cannot be a knave, because this would contradict the false claim of their own that Emily is a knave or Henry is a knave.", "We have exhausted all possibilities for Mia and Henry, so let us go back and reconsider Alexander.", "Alexander cannot be a knave, because this would contradict the claim of Isabella that Alexander is a knight and Abigail is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Alexander is a knight and Abigail is a knight.", "Alexander cannot be a knight, because this would contradict the false claim of Isabella that Alexander is a knight and Abigail is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Isabella is a knave if and only if Abigail is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Alexander is a knight then Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Emily is a knave or Henry is a knave.", "Emily cannot be a knight, because this would contradict the claim of Mia that Emily is a knave or Henry is a knave.", "Emily cannot be a knave, because this would contradict the false claim of their own that If Alexander is a knight then Mia is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Emily is a knave or Henry is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that If Alexander is a knight then Mia is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Emily is a knave or Emily is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 4), ('lying', 5)), ('->', ('telling-truth', 6), ('telling-truth', 7)), ('and', ('telling-truth', 6), ('telling-truth', 4)), ('->', ('telling-truth', 6), ('telling-truth', 7)), ('<=>', ('telling-truth', 2), ('lying', 3)), ('or', ('lying', 1), ('telling-truth', 1)), ('<=>', ('lying', 2), ('lying', 4)), ('or', ('lying', 1), ('lying', 3)))", "index": 601}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Riley, James, Aiden, Emily, Ella, Jackson, Zoey, and Oliver. Riley commented, \"Emily is a knave and Ella is a knave\". James told you that Jackson is a knight and Jackson is a knave. Aiden told you that If Riley is a knave then James is a knight. Emily noted, \"Emily is a knight and James is a knight\". Ella stated, \"Emily is a knave\". \"Oliver is a knight if and only if Jackson is a knight,\" Jackson declared. Zoey said that James is not a knave. Oliver remarked, \"Emily is a knight or Jackson is a knight\". So who is a knight and who is a knave?", "names": ["Riley", "James", "Aiden", "Emily", "Ella", "Jackson", "Zoey", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, true, false, true], "solution_text": "Riley is a knave, James is a knave, Aiden is a knave, Emily is a knave, Ella is a knight, Jackson is a knight, Zoey is a knave, and Oliver is a knight.", "solution_text_format": "(1) Riley is a knave\n(2) James is a knave\n(3) Aiden is a knave\n(4) Emily is a knave\n(5) Ella is a knight\n(6) Jackson is a knight\n(7) Zoey is a knave\n(8) Oliver is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Emily is a knave and Ella is a knave.", "Emily cannot be a knight, because this would contradict the claim of Riley that Emily is a knave and Ella is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Emily is a knight and James is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Jackson is a knight and Jackson is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Jackson is a knight and Jackson is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Oliver is a knight if and only if Jackson is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Emily is a knight or Jackson is a knight.", "Ella cannot be a knight, because this would contradict the claim of Riley that Emily is a knave and Ella is a knave.", "Ella cannot be a knave, because this would contradict the false claim of their own that Emily is a knave.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the claim of Jackson that Oliver is a knight if and only if Jackson is a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Oliver is a knight if and only if Jackson is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Emily is a knight or Jackson is a knight.", "Oliver cannot be a knave, because this would contradict the false claim of Jackson that Oliver is a knight if and only if Jackson is a knight.", "We have exhausted all possibilities for Oliver, Jackson, James, and Emily, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Emily is a knave and Ella is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Emily is a knight and James is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Jackson is a knight and Jackson is a knave.", "James cannot be a knave, because this would contradict the claim of Emily that Emily is a knight and James is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Emily is a knight and James is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Jackson is a knight and Jackson is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Jackson is a knight and Jackson is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Oliver is a knight if and only if Jackson is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Emily is a knight or Jackson is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Emily is a knave.", "Aiden cannot be a knight, because this would contradict the claim of their own that If Riley is a knave then James is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that If Riley is a knave then James is a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that James is not a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that James is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('lying', 4)), ('and', ('telling-truth', 5), ('lying', 5)), ('->', ('lying', 0), ('telling-truth', 1)), ('and', ('telling-truth', 3), ('telling-truth', 1)), ('lying', 3), ('<=>', ('telling-truth', 7), ('telling-truth', 5)), ('not', ('lying', 1)), ('or', ('telling-truth', 3), ('telling-truth', 5)))", "index": 602}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aurora, Alexander, Samuel, Aria, Joseph, Charlotte, Mia, and Avery. Aurora expressed that Mia is a knight if and only if Charlotte is a knight. \"Mia is not a knave,\" Alexander declared. Samuel said, \"Joseph is a knave or Samuel is a knight.\" Aria stated, \"Aurora is a knave\". Joseph was heard saying, \"If Samuel is a knave then Aurora is a knave\". Charlotte commented, \"Avery is a knave and Joseph is a knight\". Mia was heard saying, \"Aria is not a knight\". Avery said, \"Samuel is a knave if and only if Avery is a knight.\" So who is a knight and who is a knave?", "names": ["Aurora", "Alexander", "Samuel", "Aria", "Joseph", "Charlotte", "Mia", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true, false, false], "solution_text": "Aurora is a knave, Alexander is a knave, Samuel is a knave, Aria is a knight, Joseph is a knight, Charlotte is a knight, Mia is a knave, and Avery is a knave.", "solution_text_format": "(1) Aurora is a knave\n(2) Alexander is a knave\n(3) Samuel is a knave\n(4) Aria is a knight\n(5) Joseph is a knight\n(6) Charlotte is a knight\n(7) Mia is a knave\n(8) Avery is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that Mia is a knight if and only if Charlotte is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Aria is not a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that Aurora is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Aurora is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Avery is a knave and Joseph is a knight.", "Avery cannot be a knight, because this would contradict the claim of Charlotte that Avery is a knave and Joseph is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Samuel is a knave if and only if Avery is a knight.", "Samuel cannot be a knight, because this would contradict the false claim of Avery that Samuel is a knave if and only if Avery is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Joseph is a knave or Samuel is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that If Samuel is a knave then Aurora is a knave.", "Joseph cannot be a knave, because this would contradict the false claim of Samuel that Joseph is a knave or Samuel is a knight.", "We have exhausted all possibilities for Joseph, Samuel, and Avery, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the claim of Aurora that Mia is a knight if and only if Charlotte is a knight.", "We have exhausted all possibilities for Charlotte and Aria, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Aria is not a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that Aurora is a knave.", "Aria cannot be a knave, because this would contradict the false claim of Mia that Aria is not a knight.", "We have exhausted all possibilities for Aria and Mia, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Mia is a knight if and only if Charlotte is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Aria is not a knight.", "Aria cannot be a knight, because this would contradict the claim of Mia that Aria is not a knight.", "Aria cannot be a knave, because this would contradict the false claim of their own that Aurora is a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Aria is not a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Aurora is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Avery is a knave and Joseph is a knight.", "Avery cannot be a knight, because this would contradict the claim of Charlotte that Avery is a knave and Joseph is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Samuel is a knave if and only if Avery is a knight.", "Samuel cannot be a knight, because this would contradict the false claim of Avery that Samuel is a knave if and only if Avery is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Joseph is a knave or Samuel is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Samuel is a knave then Aurora is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that Mia is not a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Mia is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 6), ('telling-truth', 5)), ('not', ('lying', 6)), ('or', ('lying', 4), ('telling-truth', 2)), ('lying', 0), ('->', ('lying', 2), ('lying', 0)), ('and', ('lying', 7), ('telling-truth', 4)), ('not', ('telling-truth', 3)), ('<=>', ('lying', 2), ('telling-truth', 7)))", "index": 603}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mason, Amelia, Ava, Riley, Lucas, Sofia, William, and Joseph. Mason noted, \"Ava is not a knight\". Amelia said, \"Joseph is a knight and Lucas is a knight.\" In a statement by Ava: \"Mason is a knight if and only if Mason is a knave\". Riley was heard saying, \"Joseph is a knave\". Lucas expressed that Amelia is a knight or William is a knight. \"Mason is not a knave,\" Sofia claimed. William told you that Riley is a knight if and only if Riley is a knave. Joseph remarked, \"Ava is a knight or William is a knight\". So who is a knight and who is a knave?", "names": ["Mason", "Amelia", "Ava", "Riley", "Lucas", "Sofia", "William", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, true, false, false], "solution_text": "Mason is a knight, Amelia is a knave, Ava is a knave, Riley is a knight, Lucas is a knave, Sofia is a knight, William is a knave, and Joseph is a knave.", "solution_text_format": "(1) Mason is a knight\n(2) Amelia is a knave\n(3) Ava is a knave\n(4) Riley is a knight\n(5) Lucas is a knave\n(6) Sofia is a knight\n(7) William is a knave\n(8) Joseph is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Ava is not a knight.", "Ava cannot be a knight, because this would contradict the claim of Mason that Ava is not a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Mason is a knight if and only if Mason is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Joseph is a knight and Lucas is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Ava is a knight or William is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Riley is a knight if and only if Riley is a knave.", "William cannot be a knave, because this would contradict the claim of Joseph that Ava is a knight or William is a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of Amelia that Joseph is a knight and Lucas is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Joseph is a knight and Lucas is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Ava is a knight or William is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Riley is a knight if and only if Riley is a knave.", "William cannot be a knave, because this would contradict the claim of Joseph that Ava is a knight or William is a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Ava is a knight or William is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Riley is a knight if and only if Riley is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Riley is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Joseph is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Amelia is a knight or William is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Amelia is a knight or William is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Mason is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('and', ('telling-truth', 7), ('telling-truth', 4)), ('<=>', ('telling-truth', 0), ('lying', 0)), ('lying', 7), ('or', ('telling-truth', 1), ('telling-truth', 6)), ('not', ('lying', 0)), ('<=>', ('telling-truth', 3), ('lying', 3)), ('or', ('telling-truth', 2), ('telling-truth', 6)))", "index": 604}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Luke, Scarlett, Henry, Joseph, James, Penelope, Abigail, and Avery. Luke stated, \"Scarlett is a knight or Penelope is a knave\". Scarlett noted, \"Avery is not a knight\". Henry expressed that If Penelope is a knave then Scarlett is a knight. Joseph stated, \"If James is a knight then Avery is a knave\". James said, \"Abigail is a knight.\" In Penelope's words: \"Joseph is a knave or James is a knight\". As Abigail put it, \"If Abigail is a knight then James is a knight\". Avery told you that James is not a knave. So who is a knight and who is a knave?", "names": ["Luke", "Scarlett", "Henry", "Joseph", "James", "Penelope", "Abigail", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true, true, true], "solution_text": "Luke is a knave, Scarlett is a knave, Henry is a knight, Joseph is a knave, James is a knight, Penelope is a knight, Abigail is a knight, and Avery is a knight.", "solution_text_format": "(1) Luke is a knave\n(2) Scarlett is a knave\n(3) Henry is a knight\n(4) Joseph is a knave\n(5) James is a knight\n(6) Penelope is a knight\n(7) Abigail is a knight\n(8) Avery is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Scarlett is a knight or Penelope is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Avery is not a knight.", "Avery cannot be a knight, because this would contradict the claim of Scarlett that Avery is not a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that James is not a knave.", "James cannot be a knight, because this would contradict the false claim of Avery that James is not a knave.", "Assume James is a knave. No contradiction is found in their false claim that Abigail is a knight.", "Abigail cannot be a knight, because this would contradict the false claim of James that Abigail is a knight.", "Abigail cannot be a knave, because this would contradict the false claim of their own that If Abigail is a knight then James is a knight.", "We have exhausted all possibilities for Abigail, James, and Avery, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Avery is not a knight.", "Assume Avery is a knight. No contradiction is found in their claim that James is not a knave.", "Assume James is a knight. No contradiction is found in their claim that Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If Abigail is a knight then James is a knight.", "Penelope cannot be a knight, because this would contradict the claim of Luke that Scarlett is a knight or Penelope is a knave.", "Penelope cannot be a knave, because this would contradict the false claim of their own that Joseph is a knave or James is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the claim of James that Abigail is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider James.", "James cannot be a knave, because this would contradict the claim of Avery that James is not a knave.", "We have exhausted all possibilities for James, so let us go back and reconsider Avery.", "Avery cannot be a knave, because this would contradict the false claim of Scarlett that Avery is not a knight.", "We have exhausted all possibilities for Avery and Scarlett, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Scarlett is a knight or Penelope is a knave.", "Scarlett cannot be a knight, because this would contradict the false claim of Luke that Scarlett is a knight or Penelope is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Avery is not a knight.", "Assume Avery is a knight. No contradiction is found in their claim that James is not a knave.", "Assume James is a knight. No contradiction is found in their claim that Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If Abigail is a knight then James is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Joseph is a knave or James is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that If James is a knight then Avery is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that If James is a knight then Avery is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Penelope is a knave then Scarlett is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('lying', 5)), ('not', ('telling-truth', 7)), ('->', ('lying', 5), ('telling-truth', 1)), ('->', ('telling-truth', 4), ('lying', 7)), ('telling-truth', 6), ('or', ('lying', 3), ('telling-truth', 4)), ('->', ('telling-truth', 6), ('telling-truth', 4)), ('not', ('lying', 4)))", "index": 605}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Avery, Lucas, Abigail, Evelyn, Aria, Riley, Michael, and Daniel. Avery told you that Lucas is a knight. Lucas asserted: \"Aria is not a knight\". Abigail told you that Lucas is not a knight. According to Evelyn, \"Daniel is a knave if and only if Aria is a knight\". Aria noted, \"If Evelyn is a knave then Lucas is a knight\". \"Abigail is a knave if and only if Michael is a knight,\" Riley declared. Michael asserted: \"Lucas is a knave\". Daniel commented, \"Avery is a knight and Evelyn is a knight\". So who is a knight and who is a knave?", "names": ["Avery", "Lucas", "Abigail", "Evelyn", "Aria", "Riley", "Michael", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false, true, false], "solution_text": "Avery is a knave, Lucas is a knave, Abigail is a knight, Evelyn is a knight, Aria is a knight, Riley is a knave, Michael is a knight, and Daniel is a knave.", "solution_text_format": "(1) Avery is a knave\n(2) Lucas is a knave\n(3) Abigail is a knight\n(4) Evelyn is a knight\n(5) Aria is a knight\n(6) Riley is a knave\n(7) Michael is a knight\n(8) Daniel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Aria is not a knight.", "Aria cannot be a knight, because this would contradict the claim of Lucas that Aria is not a knight.", "Aria cannot be a knave, because this would contradict the false claim of their own that If Evelyn is a knave then Lucas is a knight.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the claim of Avery that Lucas is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of Avery that Lucas is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Aria is not a knight.", "Assume Aria is a knight. No contradiction is found in their claim that If Evelyn is a knave then Lucas is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Daniel is a knave if and only if Aria is a knight.", "Daniel cannot be a knight, because this would contradict the claim of Evelyn that Daniel is a knave if and only if Aria is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Avery is a knight and Evelyn is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Lucas is not a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Abigail is a knave if and only if Michael is a knight.", "Michael cannot be a knight, because this would contradict the claim of Riley that Abigail is a knave if and only if Michael is a knight.", "Michael cannot be a knave, because this would contradict the false claim of their own that Lucas is a knave.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Abigail is a knave if and only if Michael is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Lucas is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('not', ('telling-truth', 4)), ('not', ('telling-truth', 1)), ('<=>', ('lying', 7), ('telling-truth', 4)), ('->', ('lying', 3), ('telling-truth', 1)), ('<=>', ('lying', 2), ('telling-truth', 6)), ('lying', 1), ('and', ('telling-truth', 0), ('telling-truth', 3)))", "index": 606}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emma, Avery, Daniel, Lucas, James, Olivia, Chloe, and Alexander. Emma stated, \"If James is a knave then Chloe is a knight\". Avery was heard saying, \"Olivia is not a knave\". Daniel said, \"Chloe is a knight and Alexander is a knave.\" \"Alexander is a knight and Daniel is a knave\" - Lucas. \"Alexander is not a knight,\" James declared. According to Olivia, \"Alexander is not a knight\". Chloe noted, \"If Avery is a knight then Olivia is a knight\". Alexander was heard saying, \"If Olivia is a knight then Avery is a knight\". So who is a knight and who is a knave?", "names": ["Emma", "Avery", "Daniel", "Lucas", "James", "Olivia", "Chloe", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, false, true, true], "solution_text": "Emma is a knight, Avery is a knave, Daniel is a knave, Lucas is a knight, James is a knave, Olivia is a knave, Chloe is a knight, and Alexander is a knight.", "solution_text_format": "(1) Emma is a knight\n(2) Avery is a knave\n(3) Daniel is a knave\n(4) Lucas is a knight\n(5) James is a knave\n(6) Olivia is a knave\n(7) Chloe is a knight\n(8) Alexander is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that If James is a knave then Chloe is a knight.", "Assume James is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of James that Alexander is not a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that If Olivia is a knight then Avery is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Avery cannot be a knight, because this would contradict the false claim of Alexander that If Olivia is a knight then Avery is a knight.", "Avery cannot be a knave, because this would contradict the false claim of their own that Olivia is not a knave.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the false claim of their own that Alexander is not a knight.", "We have exhausted all possibilities for Olivia and Alexander, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Alexander is not a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that If Olivia is a knight then Avery is a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that Alexander is not a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Alexander is not a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Olivia is not a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Olivia is not a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that If Avery is a knight then Olivia is a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that Chloe is a knight and Alexander is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Chloe is a knight and Alexander is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Alexander is a knight and Daniel is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 4), ('telling-truth', 6)), ('not', ('lying', 5)), ('and', ('telling-truth', 6), ('lying', 7)), ('and', ('telling-truth', 7), ('lying', 2)), ('not', ('telling-truth', 7)), ('not', ('telling-truth', 7)), ('->', ('telling-truth', 1), ('telling-truth', 5)), ('->', ('telling-truth', 5), ('telling-truth', 1)))", "index": 607}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aiden, Amelia, Emily, Avery, Liam, Matthew, James, and Grace. \"Amelia is a knave if and only if Matthew is a knight,\" Aiden claimed. Amelia expressed that Amelia is a knight if and only if Matthew is a knight. Emily said, \"Avery is a knave.\" Avery noted, \"Liam is a knight\". Liam told you that Amelia is not a knight. Matthew told you that Aiden is not a knight. James stated, \"Emily is a knave\". Grace noted, \"James is a knight if and only if Emily is a knight\". So who is a knight and who is a knave?", "names": ["Aiden", "Amelia", "Emily", "Avery", "Liam", "Matthew", "James", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true, false, false], "solution_text": "Aiden is a knave, Amelia is a knight, Emily is a knight, Avery is a knave, Liam is a knave, Matthew is a knight, James is a knave, and Grace is a knave.", "solution_text_format": "(1) Aiden is a knave\n(2) Amelia is a knight\n(3) Emily is a knight\n(4) Avery is a knave\n(5) Liam is a knave\n(6) Matthew is a knight\n(7) James is a knave\n(8) Grace is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Amelia is a knave if and only if Matthew is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Amelia is a knight if and only if Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the claim of Aiden that Amelia is a knave if and only if Matthew is a knight.", "Matthew cannot be a knave, because this would contradict the claim of Amelia that Amelia is a knight if and only if Matthew is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Amelia is a knight if and only if Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Aiden is not a knight.", "Matthew cannot be a knave, because this would contradict the claim of Aiden that Amelia is a knave if and only if Matthew is a knight.", "We have exhausted all possibilities for Matthew and Amelia, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Amelia is a knave if and only if Matthew is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Amelia is a knight if and only if Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Aiden is not a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Avery is a knave.", "Avery cannot be a knight, because this would contradict the claim of Emily that Avery is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Liam is a knight.", "Liam cannot be a knight, because this would contradict the false claim of Avery that Liam is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Amelia is not a knight.", "James cannot be a knight, because this would contradict the claim of their own that Emily is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Emily is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that James is a knight if and only if Emily is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that James is a knight if and only if Emily is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('telling-truth', 5)), ('<=>', ('telling-truth', 1), ('telling-truth', 5)), ('lying', 3), ('telling-truth', 4), ('not', ('telling-truth', 1)), ('not', ('telling-truth', 0)), ('lying', 2), ('<=>', ('telling-truth', 6), ('telling-truth', 2)))", "index": 608}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aria, Alexander, David, Jack, Daniel, Jackson, Charlotte, and Owen. \"Alexander is a knight if and only if David is a knight\" - Aria. In Alexander's words: \"Charlotte is a knave or Jack is a knave\". David told you that Owen is a knight if and only if Owen is a knave. Jack commented, \"Jackson is a knight and Jackson is a knave\". In Daniel's words: \"Jack is a knight or David is a knight\". Jackson told you that David is not a knave. \"Alexander is a knight if and only if Aria is a knight,\" Charlotte declared. Owen expressed that Daniel is not a knight. So who is a knight and who is a knave?", "names": ["Aria", "Alexander", "David", "Jack", "Daniel", "Jackson", "Charlotte", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, false, false, true], "solution_text": "Aria is a knave, Alexander is a knight, David is a knave, Jack is a knave, Daniel is a knave, Jackson is a knave, Charlotte is a knave, and Owen is a knight.", "solution_text_format": "(1) Aria is a knave\n(2) Alexander is a knight\n(3) David is a knave\n(4) Jack is a knave\n(5) Daniel is a knave\n(6) Jackson is a knave\n(7) Charlotte is a knave\n(8) Owen is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that Alexander is a knight if and only if David is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Charlotte is a knave or Jack is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Alexander is a knight if and only if Aria is a knight.", "Jack cannot be a knight, because this would contradict the claim of Alexander that Charlotte is a knave or Jack is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Jackson is a knight and Jackson is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that David is not a knave.", "David cannot be a knight, because this would contradict the claim of their own that Owen is a knight if and only if Owen is a knave.", "David cannot be a knave, because this would contradict the claim of Aria that Alexander is a knight if and only if David is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that David is not a knave.", "David cannot be a knight, because this would contradict the claim of their own that Owen is a knight if and only if Owen is a knave.", "David cannot be a knave, because this would contradict the claim of Aria that Alexander is a knight if and only if David is a knight.", "We have exhausted all possibilities for David, Jackson, and Jack, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that Alexander is a knight if and only if Aria is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Charlotte is a knave or Jack is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Alexander is a knight if and only if Aria is a knight.", "Charlotte cannot be a knave, because this would contradict the false claim of Alexander that Charlotte is a knave or Jack is a knave.", "We have exhausted all possibilities for Charlotte and Alexander, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Alexander is a knight if and only if David is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Charlotte is a knave or Jack is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Alexander is a knight if and only if Aria is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Alexander is a knight if and only if Aria is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Jackson is a knight and Jackson is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Jackson is a knight and Jackson is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that David is not a knave.", "David cannot be a knight, because this would contradict the false claim of Aria that Alexander is a knight if and only if David is a knight.", "David cannot be a knave, because this would contradict the claim of Jackson that David is not a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that David is not a knave.", "David cannot be a knight, because this would contradict the false claim of Aria that Alexander is a knight if and only if David is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Owen is a knight if and only if Owen is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Daniel is not a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that Jack is a knight or David is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Jack is a knight or David is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('telling-truth', 2)), ('or', ('lying', 6), ('lying', 3)), ('<=>', ('telling-truth', 7), ('lying', 7)), ('and', ('telling-truth', 5), ('lying', 5)), ('or', ('telling-truth', 3), ('telling-truth', 2)), ('not', ('lying', 2)), ('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('not', ('telling-truth', 4)))", "index": 609}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Joseph, Avery, Riley, Aurora, Aria, Zoey, David, and Emily. \"If Aria is a knave then Riley is a knave,\" Joseph mentioned. In a statement by Avery: \"Joseph is a knave or David is a knight\". \"Aria is a knight if and only if Emily is a knight,\" Riley declared. Aurora noted, \"Avery is a knight or David is a knave\". \"Zoey is a knight or Joseph is a knave\" - Aria. In a statement by Zoey: \"Zoey is a knight or Aurora is a knave\". In David's words: \"Emily is a knave if and only if Emily is a knight\". Emily commented, \"Zoey is a knight if and only if Zoey is a knave\". So who is a knight and who is a knave?", "names": ["Joseph", "Avery", "Riley", "Aurora", "Aria", "Zoey", "David", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true, false, false], "solution_text": "Joseph is a knight, Avery is a knave, Riley is a knave, Aurora is a knight, Aria is a knight, Zoey is a knight, David is a knave, and Emily is a knave.", "solution_text_format": "(1) Joseph is a knight\n(2) Avery is a knave\n(3) Riley is a knave\n(4) Aurora is a knight\n(5) Aria is a knight\n(6) Zoey is a knight\n(7) David is a knave\n(8) Emily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that If Aria is a knave then Riley is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Zoey is a knight or Joseph is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Zoey is a knight or Aurora is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Avery is a knight or David is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Joseph is a knave or David is a knight.", "David cannot be a knight, because this would contradict the claim of their own that Emily is a knave if and only if Emily is a knight.", "David cannot be a knave, because this would contradict the claim of Avery that Joseph is a knave or David is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Joseph is a knave or David is a knight.", "David cannot be a knight, because this would contradict the false claim of Avery that Joseph is a knave or David is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Emily is a knave if and only if Emily is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Zoey is a knight if and only if Zoey is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Zoey is a knight if and only if Zoey is a knave.", "Riley cannot be a knight, because this would contradict the claim of their own that Aria is a knight if and only if Emily is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Aria is a knight if and only if Emily is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 4), ('lying', 2)), ('or', ('lying', 0), ('telling-truth', 6)), ('<=>', ('telling-truth', 4), ('telling-truth', 7)), ('or', ('telling-truth', 1), ('lying', 6)), ('or', ('telling-truth', 5), ('lying', 0)), ('or', ('telling-truth', 5), ('lying', 3)), ('<=>', ('lying', 7), ('telling-truth', 7)), ('<=>', ('telling-truth', 5), ('lying', 5)))", "index": 610}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sebastian, David, Mason, Lily, Liam, William, Penelope, and Emily. Sebastian was heard saying, \"David is a knight and William is a knight\". \"Penelope is not a knight,\" David declared. Mason said, \"Emily is not a knave.\" Lily remarked, \"Penelope is a knight and William is a knave\". \"William is a knave and William is a knight,\" Liam mentioned. William said, \"Penelope is not a knave.\" As Penelope put it, \"Sebastian is not a knight\". In Emily's words: \"Sebastian is a knight and Lily is a knight\". So who is a knight and who is a knave?", "names": ["Sebastian", "David", "Mason", "Lily", "Liam", "William", "Penelope", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, true, true, false], "solution_text": "Sebastian is a knave, David is a knave, Mason is a knave, Lily is a knave, Liam is a knave, William is a knight, Penelope is a knight, and Emily is a knave.", "solution_text_format": "(1) Sebastian is a knave\n(2) David is a knave\n(3) Mason is a knave\n(4) Lily is a knave\n(5) Liam is a knave\n(6) William is a knight\n(7) Penelope is a knight\n(8) Emily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that David is a knight and William is a knight.", "Assume David is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Penelope cannot be a knight, because this would contradict the claim of David that Penelope is not a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Sebastian is not a knight.", "William cannot be a knight, because this would contradict the claim of their own that Penelope is not a knave.", "William cannot be a knave, because this would contradict the claim of Sebastian that David is a knight and William is a knight.", "We have exhausted all possibilities for William and Penelope, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the claim of Sebastian that David is a knight and William is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that David is a knight and William is a knight.", "Assume David is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Penelope cannot be a knight, because this would contradict the claim of David that Penelope is not a knight.", "Penelope cannot be a knave, because this would contradict the false claim of their own that Sebastian is not a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Penelope is not a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Sebastian is not a knight.", "Assume William is a knight. No contradiction is found in their claim that Penelope is not a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Emily is not a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight and Lily is a knight.", "Emily cannot be a knave, because this would contradict the claim of Mason that Emily is not a knave.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Emily is not a knave.", "Emily cannot be a knight, because this would contradict the false claim of Mason that Emily is not a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Sebastian is a knight and Lily is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Penelope is a knight and William is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Penelope is a knight and William is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that William is a knave and William is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that William is a knave and William is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('telling-truth', 5)), ('not', ('telling-truth', 6)), ('not', ('lying', 7)), ('and', ('telling-truth', 6), ('lying', 5)), ('and', ('lying', 5), ('telling-truth', 5)), ('not', ('lying', 6)), ('not', ('telling-truth', 0)), ('and', ('telling-truth', 0), ('telling-truth', 3)))", "index": 611}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Riley, Ava, Sofia, Avery, Aurora, Chloe, Oliver, and Samuel. \"Chloe is a knight or Sofia is a knave,\" Riley mentioned. In a statement by Ava: \"Sofia is a knight if and only if Samuel is a knight\". Sofia said, \"Riley is a knight.\" \"Riley is not a knight,\" Avery declared. Aurora remarked, \"Aurora is a knight and Avery is a knight\". Chloe expressed that Oliver is a knave if and only if Chloe is a knight. Oliver asserted: \"If Aurora is a knave then Ava is a knave\". According to Samuel, \"Sofia is a knave if and only if Oliver is a knight\". So who is a knight and who is a knave?", "names": ["Riley", "Ava", "Sofia", "Avery", "Aurora", "Chloe", "Oliver", "Samuel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true, false, true], "solution_text": "Riley is a knight, Ava is a knight, Sofia is a knight, Avery is a knave, Aurora is a knave, Chloe is a knight, Oliver is a knave, and Samuel is a knight.", "solution_text_format": "(1) Riley is a knight\n(2) Ava is a knight\n(3) Sofia is a knight\n(4) Avery is a knave\n(5) Aurora is a knave\n(6) Chloe is a knight\n(7) Oliver is a knave\n(8) Samuel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Chloe is a knight or Sofia is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Oliver is a knave if and only if Chloe is a knight.", "Oliver cannot be a knight, because this would contradict the claim of Chloe that Oliver is a knave if and only if Chloe is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that If Aurora is a knave then Ava is a knave.", "Aurora cannot be a knight, because this would contradict the false claim of Oliver that If Aurora is a knave then Ava is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Aurora is a knight and Avery is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Riley is not a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Riley is not a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Sofia is a knight if and only if Samuel is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Riley is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Sofia is a knave if and only if Oliver is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('lying', 2)), ('<=>', ('telling-truth', 2), ('telling-truth', 7)), ('telling-truth', 0), ('not', ('telling-truth', 0)), ('and', ('telling-truth', 4), ('telling-truth', 3)), ('<=>', ('lying', 6), ('telling-truth', 5)), ('->', ('lying', 4), ('lying', 1)), ('<=>', ('lying', 2), ('telling-truth', 6)))", "index": 612}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aurora, William, Logan, Victoria, Joseph, Jackson, Alexander, and Lucas. Aurora stated, \"Logan is not a knave\". In a statement by William: \"Aurora is a knight\". According to Logan, \"Joseph is a knight if and only if Alexander is a knight\". Victoria noted, \"Logan is a knight or Logan is a knave\". In a statement by Joseph: \"William is a knight and Aurora is a knave\". Jackson said that William is a knave or Alexander is a knight. Alexander told you that Jackson is a knave or Victoria is a knight. According to Lucas, \"Victoria is a knight if and only if Logan is a knight\". So who is a knight and who is a knave?", "names": ["Aurora", "William", "Logan", "Victoria", "Joseph", "Jackson", "Alexander", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, true, true, false], "solution_text": "Aurora is a knave, William is a knave, Logan is a knave, Victoria is a knight, Joseph is a knave, Jackson is a knight, Alexander is a knight, and Lucas is a knave.", "solution_text_format": "(1) Aurora is a knave\n(2) William is a knave\n(3) Logan is a knave\n(4) Victoria is a knight\n(5) Joseph is a knave\n(6) Jackson is a knight\n(7) Alexander is a knight\n(8) Lucas is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that Logan is not a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Joseph is a knight if and only if Alexander is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that William is a knight and Aurora is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that William is a knight and Aurora is a knave.", "Assume William is a knight. No contradiction is found in their claim that Aurora is a knight.", "Alexander cannot be a knight, because this would contradict the claim of Logan that Joseph is a knight if and only if Alexander is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Jackson is a knave or Victoria is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that William is a knave or Alexander is a knight.", "Jackson cannot be a knave, because this would contradict the false claim of Alexander that Jackson is a knave or Victoria is a knight.", "We have exhausted all possibilities for Jackson and Alexander, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the false claim of their own that Aurora is a knight.", "We have exhausted all possibilities for William and Joseph, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the claim of Aurora that Logan is not a knave.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Logan is not a knave.", "Logan cannot be a knight, because this would contradict the false claim of Aurora that Logan is not a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Joseph is a knight if and only if Alexander is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that William is a knight and Aurora is a knave.", "William cannot be a knight, because this would contradict the claim of their own that Aurora is a knight.", "William cannot be a knave, because this would contradict the claim of Joseph that William is a knight and Aurora is a knave.", "We have exhausted all possibilities for William, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that William is a knight and Aurora is a knave.", "William cannot be a knight, because this would contradict the claim of their own that Aurora is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Aurora is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Jackson is a knave or Victoria is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that William is a knave or Alexander is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Logan is a knight or Logan is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Victoria is a knight if and only if Logan is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Victoria is a knight if and only if Logan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('telling-truth', 0), ('<=>', ('telling-truth', 4), ('telling-truth', 6)), ('or', ('telling-truth', 2), ('lying', 2)), ('and', ('telling-truth', 1), ('lying', 0)), ('or', ('lying', 1), ('telling-truth', 6)), ('or', ('lying', 5), ('telling-truth', 3)), ('<=>', ('telling-truth', 3), ('telling-truth', 2)))", "index": 613}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aria, Sophia, Samuel, Amelia, Evelyn, Olivia, Logan, and Owen. In Aria's words: \"Logan is a knave or Olivia is a knave\". Sophia expressed that Olivia is a knave and Aria is a knave. Samuel said that If Logan is a knave then Owen is a knave. Amelia asserted: \"Olivia is a knave\". Evelyn said that Amelia is a knave. As Olivia put it, \"Owen is a knave or Owen is a knight\". Logan told you that Sophia is a knave. Owen remarked, \"Evelyn is not a knight\". So who is a knight and who is a knave?", "names": ["Aria", "Sophia", "Samuel", "Amelia", "Evelyn", "Olivia", "Logan", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true, true, false], "solution_text": "Aria is a knave, Sophia is a knave, Samuel is a knight, Amelia is a knave, Evelyn is a knight, Olivia is a knight, Logan is a knight, and Owen is a knave.", "solution_text_format": "(1) Aria is a knave\n(2) Sophia is a knave\n(3) Samuel is a knight\n(4) Amelia is a knave\n(5) Evelyn is a knight\n(6) Olivia is a knight\n(7) Logan is a knight\n(8) Owen is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that Logan is a knave or Olivia is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Sophia is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that Olivia is a knave and Aria is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Olivia is a knave and Aria is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Aria that Logan is a knave or Olivia is a knave.", "Olivia cannot be a knave, because this would contradict the false claim of their own that Owen is a knave or Owen is a knight.", "We have exhausted all possibilities for Olivia and Sophia, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Sophia is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that Olivia is a knave and Aria is a knave.", "Sophia cannot be a knave, because this would contradict the false claim of Logan that Sophia is a knave.", "We have exhausted all possibilities for Sophia and Logan, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Logan is a knave or Olivia is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Sophia is a knave.", "Sophia cannot be a knight, because this would contradict the claim of Logan that Sophia is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Olivia is a knave and Aria is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Owen is a knave or Owen is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Evelyn is not a knight.", "Evelyn cannot be a knight, because this would contradict the claim of Owen that Evelyn is not a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Olivia is a knave.", "Amelia cannot be a knave, because this would contradict the false claim of Evelyn that Amelia is a knave.", "We have exhausted all possibilities for Amelia and Evelyn, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Evelyn is not a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Olivia is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Olivia is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that If Logan is a knave then Owen is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 6), ('lying', 5)), ('and', ('lying', 5), ('lying', 0)), ('->', ('lying', 6), ('lying', 7)), ('lying', 5), ('lying', 3), ('or', ('lying', 7), ('telling-truth', 7)), ('lying', 1), ('not', ('telling-truth', 4)))", "index": 614}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Chloe, Joseph, Samuel, Luke, Daniel, William, Riley, and Sebastian. Chloe said, \"Daniel is a knight.\" \"Luke is a knave and William is a knave,\" Joseph declared. Samuel was heard saying, \"William is not a knight\". Luke remarked, \"William is a knave\". In Daniel's words: \"Samuel is not a knight\". William asserted: \"If Sebastian is a knave then Daniel is a knight\". According to Riley, \"If Samuel is a knight then Joseph is a knave\". Sebastian remarked, \"William is a knave\". So who is a knight and who is a knave?", "names": ["Chloe", "Joseph", "Samuel", "Luke", "Daniel", "William", "Riley", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true, true, false], "solution_text": "Chloe is a knight, Joseph is a knave, Samuel is a knave, Luke is a knave, Daniel is a knight, William is a knight, Riley is a knight, and Sebastian is a knave.", "solution_text_format": "(1) Chloe is a knight\n(2) Joseph is a knave\n(3) Samuel is a knave\n(4) Luke is a knave\n(5) Daniel is a knight\n(6) William is a knight\n(7) Riley is a knight\n(8) Sebastian is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Daniel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Samuel is not a knight.", "Samuel cannot be a knight, because this would contradict the claim of Daniel that Samuel is not a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that William is not a knight.", "Assume William is a knight. No contradiction is found in their claim that If Sebastian is a knave then Daniel is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that William is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that William is a knave.", "Joseph cannot be a knight, because this would contradict the claim of their own that Luke is a knave and William is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Luke is a knave and William is a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that William is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that William is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that If Samuel is a knight then Joseph is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('and', ('lying', 3), ('lying', 5)), ('not', ('telling-truth', 5)), ('lying', 5), ('not', ('telling-truth', 2)), ('->', ('lying', 7), ('telling-truth', 4)), ('->', ('telling-truth', 2), ('lying', 1)), ('lying', 5))", "index": 615}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Victoria, Riley, James, Mason, David, Aiden, Emily, and Owen. Victoria noted, \"James is a knave and Aiden is a knight\". Riley said that David is not a knight. As James put it, \"David is a knave or Riley is a knight\". According to Mason, \"James is a knight or Aiden is a knight\". \"Owen is a knight if and only if Mason is a knave\" - David. \"James is a knight or Riley is a knight,\" Aiden mentioned. In Emily's words: \"Owen is a knave or Mason is a knave\". Owen expressed that Victoria is a knight if and only if Emily is a knave. So who is a knight and who is a knave?", "names": ["Victoria", "Riley", "James", "Mason", "David", "Aiden", "Emily", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, false, true, true], "solution_text": "Victoria is a knave, Riley is a knave, James is a knave, Mason is a knave, David is a knight, Aiden is a knave, Emily is a knight, and Owen is a knight.", "solution_text_format": "(1) Victoria is a knave\n(2) Riley is a knave\n(3) James is a knave\n(4) Mason is a knave\n(5) David is a knight\n(6) Aiden is a knave\n(7) Emily is a knight\n(8) Owen is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that James is a knave and Aiden is a knight.", "James cannot be a knight, because this would contradict the claim of Victoria that James is a knave and Aiden is a knight.", "Assume James is a knave. No contradiction is found in their false claim that David is a knave or Riley is a knight.", "Assume David is a knight. No contradiction is found in their claim that Owen is a knight if and only if Mason is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of Owen that Victoria is a knight if and only if Emily is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Owen is a knave or Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of David that Owen is a knight if and only if Mason is a knave.", "Mason cannot be a knave, because this would contradict the false claim of Emily that Owen is a knave or Mason is a knave.", "We have exhausted all possibilities for Mason and Emily, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Victoria is a knight if and only if Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Owen is a knave or Mason is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that James is a knight or Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that James is a knight or Riley is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that David is not a knight.", "Riley cannot be a knave, because this would contradict the claim of Aiden that James is a knight or Riley is a knight.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the claim of Victoria that James is a knave and Aiden is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Mason.", "Mason cannot be a knave, because this would contradict the claim of David that Owen is a knight if and only if Mason is a knave.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the false claim of their own that Owen is a knave or Mason is a knave.", "We have exhausted all possibilities for Emily and Owen, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the false claim of James that David is a knave or Riley is a knight.", "We have exhausted all possibilities for David and James, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that James is a knave and Aiden is a knight.", "Assume James is a knight. No contradiction is found in their claim that David is a knave or Riley is a knight.", "Assume David is a knight. No contradiction is found in their claim that Owen is a knight if and only if Mason is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Owen is a knave or Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of David that Owen is a knight if and only if Mason is a knave.", "Mason cannot be a knave, because this would contradict the false claim of their own that James is a knight or Aiden is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the claim of Owen that Victoria is a knight if and only if Emily is a knave.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Victoria is a knight if and only if Emily is a knave.", "Emily cannot be a knight, because this would contradict the false claim of Owen that Victoria is a knight if and only if Emily is a knave.", "Emily cannot be a knave, because this would contradict the false claim of their own that Owen is a knave or Mason is a knave.", "We have exhausted all possibilities for Emily and Owen, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Owen is a knight if and only if Mason is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Owen is a knave or Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of Emily that Owen is a knave or Mason is a knave.", "Mason cannot be a knave, because this would contradict the false claim of their own that James is a knight or Aiden is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the claim of Owen that Victoria is a knight if and only if Emily is a knave.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Victoria is a knight if and only if Emily is a knave.", "Emily cannot be a knight, because this would contradict the false claim of Owen that Victoria is a knight if and only if Emily is a knave.", "Emily cannot be a knave, because this would contradict the false claim of their own that Owen is a knave or Mason is a knave.", "We have exhausted all possibilities for Emily, Owen, and David, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that David is a knave or Riley is a knight.", "Assume David is a knight. No contradiction is found in their claim that Owen is a knight if and only if Mason is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Owen is a knave or Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of David that Owen is a knight if and only if Mason is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that James is a knight or Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the false claim of Victoria that James is a knave and Aiden is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that James is a knight or Riley is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that David is not a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that David is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('telling-truth', 5)), ('not', ('telling-truth', 4)), ('or', ('lying', 4), ('telling-truth', 1)), ('or', ('telling-truth', 2), ('telling-truth', 5)), ('<=>', ('telling-truth', 7), ('lying', 3)), ('or', ('telling-truth', 2), ('telling-truth', 1)), ('or', ('lying', 7), ('lying', 3)), ('<=>', ('telling-truth', 0), ('lying', 6)))", "index": 616}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Penelope, Logan, Chloe, Joseph, Samuel, Emma, Ella, and Isabella. Penelope told you that Logan is a knave or Penelope is a knight. Logan expressed that Samuel is not a knave. Chloe commented, \"Isabella is not a knave\". Joseph said, \"Logan is a knight or Chloe is a knave.\" \"Penelope is a knight or Logan is a knave,\" Samuel mentioned. Emma noted, \"Joseph is a knave and Chloe is a knight\". Ella was heard saying, \"Samuel is a knight or Samuel is a knave\". In Isabella's words: \"Samuel is a knave and Ella is a knave\". So who is a knight and who is a knave?", "names": ["Penelope", "Logan", "Chloe", "Joseph", "Samuel", "Emma", "Ella", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false, true, false], "solution_text": "Penelope is a knight, Logan is a knight, Chloe is a knave, Joseph is a knight, Samuel is a knight, Emma is a knave, Ella is a knight, and Isabella is a knave.", "solution_text_format": "(1) Penelope is a knight\n(2) Logan is a knight\n(3) Chloe is a knave\n(4) Joseph is a knight\n(5) Samuel is a knight\n(6) Emma is a knave\n(7) Ella is a knight\n(8) Isabella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that Logan is a knave or Penelope is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Samuel is not a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Penelope is a knight or Logan is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Isabella is not a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that Samuel is a knave and Ella is a knave.", "Isabella cannot be a knave, because this would contradict the claim of Chloe that Isabella is not a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Isabella is not a knave.", "Isabella cannot be a knight, because this would contradict the false claim of Chloe that Isabella is not a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Samuel is a knave and Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Samuel is a knight or Samuel is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Logan is a knight or Chloe is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Joseph is a knave and Chloe is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Joseph is a knave and Chloe is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('telling-truth', 0)), ('not', ('lying', 4)), ('not', ('lying', 7)), ('or', ('telling-truth', 1), ('lying', 2)), ('or', ('telling-truth', 0), ('lying', 1)), ('and', ('lying', 3), ('telling-truth', 2)), ('or', ('telling-truth', 4), ('lying', 4)), ('and', ('lying', 4), ('lying', 6)))", "index": 617}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Riley, Isabella, Aria, Liam, Lucas, James, Penelope, and Harper. According to Riley, \"Aria is a knight or Liam is a knave\". In a statement by Isabella: \"Penelope is a knave and Riley is a knave\". \"Penelope is a knight or Harper is a knight,\" Aria declared. Liam expressed that If Aria is a knave then Lucas is a knave. In a statement by Lucas: \"Isabella is a knight if and only if Penelope is a knight\". James noted, \"Penelope is a knave if and only if Lucas is a knave\". \"Harper is not a knight,\" Penelope declared. In Harper's words: \"Aria is not a knave\". So who is a knight and who is a knave?", "names": ["Riley", "Isabella", "Aria", "Liam", "Lucas", "James", "Penelope", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false, false, true], "solution_text": "Riley is a knight, Isabella is a knave, Aria is a knight, Liam is a knight, Lucas is a knight, James is a knave, Penelope is a knave, and Harper is a knight.", "solution_text_format": "(1) Riley is a knight\n(2) Isabella is a knave\n(3) Aria is a knight\n(4) Liam is a knight\n(5) Lucas is a knight\n(6) James is a knave\n(7) Penelope is a knave\n(8) Harper is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Aria is a knight or Liam is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Penelope is a knight or Harper is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Harper is not a knight.", "Harper cannot be a knight, because this would contradict the claim of Penelope that Harper is not a knight.", "Harper cannot be a knave, because this would contradict the false claim of their own that Aria is not a knave.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Harper is not a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Aria is not a knave.", "Assume Liam is a knight. No contradiction is found in their claim that If Aria is a knave then Lucas is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Penelope is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Penelope is a knave and Riley is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Penelope is a knave and Riley is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Penelope is a knave if and only if Lucas is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Penelope is a knave if and only if Lucas is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('lying', 3)), ('and', ('lying', 6), ('lying', 0)), ('or', ('telling-truth', 6), ('telling-truth', 7)), ('->', ('lying', 2), ('lying', 4)), ('<=>', ('telling-truth', 1), ('telling-truth', 6)), ('<=>', ('lying', 6), ('lying', 4)), ('not', ('telling-truth', 7)), ('not', ('lying', 2)))", "index": 618}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: James, Daniel, Evelyn, Noah, Scarlett, Ethan, Samuel, and Jacob. James was heard saying, \"Daniel is a knight and Scarlett is a knight\". Daniel commented, \"Noah is a knave if and only if Evelyn is a knave\". Evelyn commented, \"Jacob is a knight\". Noah noted, \"Noah is a knight and Jacob is a knight\". \"Evelyn is a knave if and only if Samuel is a knight\" - Scarlett. \"If Scarlett is a knave then Evelyn is a knight,\" Ethan declared. \"Noah is a knight or Daniel is a knight,\" Samuel declared. Jacob remarked, \"Scarlett is a knight\". So who is a knight and who is a knave?", "names": ["James", "Daniel", "Evelyn", "Noah", "Scarlett", "Ethan", "Samuel", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true, false, true], "solution_text": "James is a knave, Daniel is a knave, Evelyn is a knight, Noah is a knave, Scarlett is a knight, Ethan is a knight, Samuel is a knave, and Jacob is a knight.", "solution_text_format": "(1) James is a knave\n(2) Daniel is a knave\n(3) Evelyn is a knight\n(4) Noah is a knave\n(5) Scarlett is a knight\n(6) Ethan is a knight\n(7) Samuel is a knave\n(8) Jacob is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Daniel is a knight and Scarlett is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Noah is a knave if and only if Evelyn is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Noah is a knight and Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Evelyn is a knave if and only if Samuel is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Jacob is a knight.", "Samuel cannot be a knight, because this would contradict the claim of Scarlett that Evelyn is a knave if and only if Samuel is a knight.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Noah is a knight or Daniel is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the claim of Daniel that Noah is a knave if and only if Evelyn is a knave.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the claim of James that Daniel is a knight and Scarlett is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the claim of Noah that Noah is a knight and Jacob is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Noah is a knight and Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Evelyn is a knave if and only if Samuel is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of Daniel that Noah is a knave if and only if Evelyn is a knave.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that Jacob is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the claim of James that Daniel is a knight and Scarlett is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the false claim of Jacob that Scarlett is a knight.", "Scarlett cannot be a knave, because this would contradict the claim of James that Daniel is a knight and Scarlett is a knight.", "We have exhausted all possibilities for Scarlett, Jacob, and Noah, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the claim of James that Daniel is a knight and Scarlett is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Daniel is a knight and Scarlett is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Noah is a knave if and only if Evelyn is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Noah is a knight and Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the false claim of James that Daniel is a knight and Scarlett is a knight.", "Scarlett cannot be a knave, because this would contradict the claim of Jacob that Scarlett is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the claim of Noah that Noah is a knight and Jacob is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Noah is a knight and Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the false claim of James that Daniel is a knight and Scarlett is a knight.", "Scarlett cannot be a knave, because this would contradict the claim of Jacob that Scarlett is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the false claim of James that Daniel is a knight and Scarlett is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Evelyn is a knave if and only if Samuel is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of Daniel that Noah is a knave if and only if Evelyn is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Jacob is a knight.", "Samuel cannot be a knight, because this would contradict the false claim of Scarlett that Evelyn is a knave if and only if Samuel is a knight.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Noah is a knight or Daniel is a knight.", "We have exhausted all possibilities for Samuel, Evelyn, Scarlett, Jacob, and Noah, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Noah is a knave if and only if Evelyn is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Noah is a knight and Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Evelyn is a knave if and only if Samuel is a knight.", "Evelyn cannot be a knight, because this would contradict the false claim of Daniel that Noah is a knave if and only if Evelyn is a knave.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that Jacob is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the claim of Jacob that Scarlett is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the claim of Noah that Noah is a knight and Jacob is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Noah is a knight and Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Evelyn is a knave if and only if Samuel is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Jacob is a knight.", "Samuel cannot be a knight, because this would contradict the claim of Scarlett that Evelyn is a knave if and only if Samuel is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Noah is a knight or Daniel is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If Scarlett is a knave then Evelyn is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('telling-truth', 4)), ('<=>', ('lying', 3), ('lying', 2)), ('telling-truth', 7), ('and', ('telling-truth', 3), ('telling-truth', 7)), ('<=>', ('lying', 2), ('telling-truth', 6)), ('->', ('lying', 4), ('telling-truth', 2)), ('or', ('telling-truth', 3), ('telling-truth', 1)), ('telling-truth', 4))", "index": 619}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Abigail, Matthew, Oliver, Aurora, Aiden, Victoria, Logan, and David. \"Matthew is a knight and Aiden is a knave,\" Abigail declared. Matthew noted, \"Abigail is a knight\". Oliver remarked, \"If Abigail is a knave then Aurora is a knight\". In a statement by Aurora: \"Logan is a knight and Aiden is a knave\". Aiden was heard saying, \"Aurora is a knave and Abigail is a knight\". \"David is a knight and Aiden is a knight,\" Victoria declared. In a statement by Logan: \"If David is a knave then Aurora is a knave\". David said, \"Matthew is a knave.\" So who is a knight and who is a knave?", "names": ["Abigail", "Matthew", "Oliver", "Aurora", "Aiden", "Victoria", "Logan", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false, true, true], "solution_text": "Abigail is a knave, Matthew is a knave, Oliver is a knight, Aurora is a knight, Aiden is a knave, Victoria is a knave, Logan is a knight, and David is a knight.", "solution_text_format": "(1) Abigail is a knave\n(2) Matthew is a knave\n(3) Oliver is a knight\n(4) Aurora is a knight\n(5) Aiden is a knave\n(6) Victoria is a knave\n(7) Logan is a knight\n(8) David is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Matthew is a knight and Aiden is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Abigail is a knight.", "Aiden cannot be a knight, because this would contradict the claim of Abigail that Matthew is a knight and Aiden is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Aurora is a knave and Abigail is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Logan is a knight and Aiden is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that If David is a knave then Aurora is a knave.", "David cannot be a knight, because this would contradict the claim of their own that Matthew is a knave.", "David cannot be a knave, because this would contradict the claim of Logan that If David is a knave then Aurora is a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the claim of Aurora that Logan is a knight and Aiden is a knave.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the false claim of Aiden that Aurora is a knave and Abigail is a knight.", "We have exhausted all possibilities for Aurora and Aiden, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the claim of Abigail that Matthew is a knight and Aiden is a knave.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Matthew is a knight and Aiden is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Abigail is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Abigail is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Aurora is a knave and Abigail is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Aurora is a knave and Abigail is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Logan is a knight and Aiden is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that If David is a knave then Aurora is a knave.", "Assume David is a knight. No contradiction is found in their claim that Matthew is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that If Abigail is a knave then Aurora is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that David is a knight and Aiden is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that David is a knight and Aiden is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('lying', 4)), ('telling-truth', 0), ('->', ('lying', 0), ('telling-truth', 3)), ('and', ('telling-truth', 6), ('lying', 4)), ('and', ('lying', 3), ('telling-truth', 0)), ('and', ('telling-truth', 7), ('telling-truth', 4)), ('->', ('lying', 7), ('lying', 3)), ('lying', 1))", "index": 620}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Grace, Evelyn, Alexander, Aria, David, Noah, Abigail, and Avery. Grace stated, \"Avery is not a knave\". In a statement by Evelyn: \"Aria is a knave\". As Alexander put it, \"Aria is a knave if and only if Grace is a knight\". Aria commented, \"Noah is a knight if and only if Evelyn is a knave\". David asserted: \"Avery is a knight\". Noah asserted: \"David is not a knave\". According to Abigail, \"Avery is a knight and Grace is a knight\". Avery said that Noah is a knave if and only if Alexander is a knight. So who is a knight and who is a knave?", "names": ["Grace", "Evelyn", "Alexander", "Aria", "David", "Noah", "Abigail", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true, true, true], "solution_text": "Grace is a knight, Evelyn is a knave, Alexander is a knave, Aria is a knight, David is a knight, Noah is a knight, Abigail is a knight, and Avery is a knight.", "solution_text_format": "(1) Grace is a knight\n(2) Evelyn is a knave\n(3) Alexander is a knave\n(4) Aria is a knight\n(5) David is a knight\n(6) Noah is a knight\n(7) Abigail is a knight\n(8) Avery is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Avery is not a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Noah is a knave if and only if Alexander is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that David is not a knave.", "Assume David is a knight. No contradiction is found in their claim that Avery is a knight.", "Alexander cannot be a knight, because this would contradict the claim of Avery that Noah is a knave if and only if Alexander is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Aria is a knave if and only if Grace is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Noah is a knight if and only if Evelyn is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Aria is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Aria is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Avery is a knight and Grace is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 7)), ('lying', 3), ('<=>', ('lying', 3), ('telling-truth', 0)), ('<=>', ('telling-truth', 5), ('lying', 1)), ('telling-truth', 7), ('not', ('lying', 4)), ('and', ('telling-truth', 7), ('telling-truth', 0)), ('<=>', ('lying', 5), ('telling-truth', 2)))", "index": 621}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aria, Henry, Chloe, Ethan, Penelope, Emily, Sofia, and Zoey. As Aria put it, \"Henry is a knight or Penelope is a knight\". Henry asserted: \"Emily is a knave\". Chloe remarked, \"Aria is not a knave\". Ethan commented, \"Emily is not a knave\". In a statement by Penelope: \"Aria is not a knave\". Emily said that Zoey is a knight and Henry is a knight. Sofia told you that Ethan is a knave and Chloe is a knave. In a statement by Zoey: \"Ethan is a knave if and only if Ethan is a knight\". So who is a knight and who is a knave?", "names": ["Aria", "Henry", "Chloe", "Ethan", "Penelope", "Emily", "Sofia", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false, false, false], "solution_text": "Aria is a knight, Henry is a knight, Chloe is a knight, Ethan is a knave, Penelope is a knight, Emily is a knave, Sofia is a knave, and Zoey is a knave.", "solution_text_format": "(1) Aria is a knight\n(2) Henry is a knight\n(3) Chloe is a knight\n(4) Ethan is a knave\n(5) Penelope is a knight\n(6) Emily is a knave\n(7) Sofia is a knave\n(8) Zoey is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that Henry is a knight or Penelope is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of Henry that Emily is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Zoey is a knight and Henry is a knight.", "Zoey cannot be a knight, because this would contradict the false claim of Emily that Zoey is a knight and Henry is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Ethan is a knave if and only if Ethan is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Emily is not a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Emily is not a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Aria is not a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Aria is not a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Ethan is a knave and Chloe is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Ethan is a knave and Chloe is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('telling-truth', 4)), ('lying', 5), ('not', ('lying', 0)), ('not', ('lying', 5)), ('not', ('lying', 0)), ('and', ('telling-truth', 7), ('telling-truth', 1)), ('and', ('lying', 3), ('lying', 2)), ('<=>', ('lying', 3), ('telling-truth', 3)))", "index": 622}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Henry, Sebastian, Samuel, David, Sofia, Benjamin, Elizabeth, and Alexander. According to Henry, \"David is a knight or Sofia is a knave\". As Sebastian put it, \"Henry is a knight if and only if Samuel is a knight\". Samuel said, \"Elizabeth is a knight.\" David said, \"Henry is not a knight.\" As Sofia put it, \"Benjamin is a knight and Henry is a knight\". Benjamin said that Sofia is not a knave. Elizabeth remarked, \"Alexander is not a knight\". Alexander expressed that If Sebastian is a knave then Benjamin is a knave. So who is a knight and who is a knave?", "names": ["Henry", "Sebastian", "Samuel", "David", "Sofia", "Benjamin", "Elizabeth", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, false, false, true], "solution_text": "Henry is a knight, Sebastian is a knave, Samuel is a knave, David is a knave, Sofia is a knave, Benjamin is a knave, Elizabeth is a knave, and Alexander is a knight.", "solution_text_format": "(1) Henry is a knight\n(2) Sebastian is a knave\n(3) Samuel is a knave\n(4) David is a knave\n(5) Sofia is a knave\n(6) Benjamin is a knave\n(7) Elizabeth is a knave\n(8) Alexander is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that David is a knight or Sofia is a knave.", "David cannot be a knight, because this would contradict the claim of their own that Henry is not a knight.", "Assume David is a knave. No contradiction is found in their false claim that Henry is not a knight.", "Sofia cannot be a knight, because this would contradict the claim of Henry that David is a knight or Sofia is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Benjamin is a knight and Henry is a knight.", "Benjamin cannot be a knight, because this would contradict the false claim of Sofia that Benjamin is a knight and Henry is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Sofia is not a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Henry is a knight if and only if Samuel is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of Elizabeth that Alexander is not a knight.", "Alexander cannot be a knave, because this would contradict the false claim of their own that If Sebastian is a knave then Benjamin is a knave.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Elizabeth.", "Elizabeth cannot be a knave, because this would contradict the claim of Samuel that Elizabeth is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Samuel.", "Samuel cannot be a knave, because this would contradict the claim of Sebastian that Henry is a knight if and only if Samuel is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Henry is a knight if and only if Samuel is a knight.", "Samuel cannot be a knight, because this would contradict the false claim of Sebastian that Henry is a knight if and only if Samuel is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the false claim of Samuel that Elizabeth is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Alexander is not a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that If Sebastian is a knave then Benjamin is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('lying', 4)), ('<=>', ('telling-truth', 0), ('telling-truth', 2)), ('telling-truth', 6), ('not', ('telling-truth', 0)), ('and', ('telling-truth', 5), ('telling-truth', 0)), ('not', ('lying', 4)), ('not', ('telling-truth', 7)), ('->', ('lying', 1), ('lying', 5)))", "index": 623}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Benjamin, Charlotte, Aria, Henry, Emily, Alexander, Owen, and Riley. Benjamin told you that Emily is a knight or Henry is a knave. Charlotte told you that Henry is a knave and Henry is a knight. Aria told you that Charlotte is a knight. Henry stated, \"Alexander is a knave\". As Emily put it, \"Owen is a knight if and only if Henry is a knave\". In a statement by Alexander: \"If Owen is a knave then Aria is a knight\". \"Emily is a knight,\" Owen claimed. As Riley put it, \"Owen is not a knave\". So who is a knight and who is a knave?", "names": ["Benjamin", "Charlotte", "Aria", "Henry", "Emily", "Alexander", "Owen", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true, true, true], "solution_text": "Benjamin is a knight, Charlotte is a knave, Aria is a knave, Henry is a knave, Emily is a knight, Alexander is a knight, Owen is a knight, and Riley is a knight.", "solution_text_format": "(1) Benjamin is a knight\n(2) Charlotte is a knave\n(3) Aria is a knave\n(4) Henry is a knave\n(5) Emily is a knight\n(6) Alexander is a knight\n(7) Owen is a knight\n(8) Riley is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Emily is a knight or Henry is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Owen is a knight if and only if Henry is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Emily is a knight.", "Henry cannot be a knight, because this would contradict the claim of Emily that Owen is a knight if and only if Henry is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Alexander is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that If Owen is a knave then Aria is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Henry is a knave and Henry is a knight.", "Charlotte cannot be a knave, because this would contradict the claim of Aria that Charlotte is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Henry is a knave and Henry is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Henry is a knave and Henry is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Owen is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('lying', 3)), ('and', ('lying', 3), ('telling-truth', 3)), ('telling-truth', 1), ('lying', 5), ('<=>', ('telling-truth', 6), ('lying', 3)), ('->', ('lying', 6), ('telling-truth', 2)), ('telling-truth', 4), ('not', ('lying', 6)))", "index": 624}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Riley, Grace, Benjamin, Isabella, Elizabeth, Michael, Abigail, and Oliver. \"Oliver is a knight if and only if Benjamin is a knave\" - Riley. Grace commented, \"Oliver is a knave if and only if Elizabeth is a knave\". Benjamin asserted: \"Abigail is a knight\". \"Benjamin is a knight and Riley is a knave\" - Isabella. In Elizabeth's words: \"Isabella is a knave or Benjamin is a knight\". \"Oliver is a knave,\" Michael declared. Abigail told you that Grace is not a knave. In a statement by Oliver: \"Isabella is a knight if and only if Michael is a knight\". So who is a knight and who is a knave?", "names": ["Riley", "Grace", "Benjamin", "Isabella", "Elizabeth", "Michael", "Abigail", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, true, false, false], "solution_text": "Riley is a knave, Grace is a knave, Benjamin is a knave, Isabella is a knave, Elizabeth is a knight, Michael is a knight, Abigail is a knave, and Oliver is a knave.", "solution_text_format": "(1) Riley is a knave\n(2) Grace is a knave\n(3) Benjamin is a knave\n(4) Isabella is a knave\n(5) Elizabeth is a knight\n(6) Michael is a knight\n(7) Abigail is a knave\n(8) Oliver is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Oliver is a knight if and only if Benjamin is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Michael is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight and Riley is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Benjamin is a knight and Riley is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Riley that Oliver is a knight if and only if Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Abigail is a knight.", "Abigail cannot be a knight, because this would contradict the false claim of Benjamin that Abigail is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Grace is not a knave.", "Grace cannot be a knight, because this would contradict the false claim of Abigail that Grace is not a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Oliver is a knave if and only if Elizabeth is a knave.", "Elizabeth cannot be a knight, because this would contradict the false claim of Grace that Oliver is a knave if and only if Elizabeth is a knave.", "Elizabeth cannot be a knave, because this would contradict the false claim of their own that Isabella is a knave or Benjamin is a knight.", "We have exhausted all possibilities for Elizabeth, Grace, Abigail, Benjamin, and Isabella, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Isabella is a knight if and only if Michael is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight and Riley is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Benjamin is a knight and Riley is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Grace is not a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Oliver is a knave if and only if Elizabeth is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of Grace that Oliver is a knave if and only if Elizabeth is a knave.", "Elizabeth cannot be a knave, because this would contradict the false claim of their own that Isabella is a knave or Benjamin is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Grace.", "Grace cannot be a knave, because this would contradict the claim of Abigail that Grace is not a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the claim of Benjamin that Abigail is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the claim of Riley that Oliver is a knight if and only if Benjamin is a knave.", "We have exhausted all possibilities for Benjamin, Isabella, and Oliver, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Oliver is a knight if and only if Benjamin is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Michael is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Benjamin is a knight and Riley is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Grace is not a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Oliver is a knave if and only if Elizabeth is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Isabella is a knave or Benjamin is a knight.", "Michael cannot be a knight, because this would contradict the claim of their own that Oliver is a knave.", "Michael cannot be a knave, because this would contradict the claim of Oliver that Isabella is a knight if and only if Michael is a knight.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Elizabeth.", "Elizabeth cannot be a knave, because this would contradict the claim of Grace that Oliver is a knave if and only if Elizabeth is a knave.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Grace.", "Grace cannot be a knave, because this would contradict the claim of Abigail that Grace is not a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the claim of Benjamin that Abigail is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the false claim of Riley that Oliver is a knight if and only if Benjamin is a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Benjamin is a knight and Riley is a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Isabella that Benjamin is a knight and Riley is a knave.", "Benjamin cannot be a knave, because this would contradict the false claim of Riley that Oliver is a knight if and only if Benjamin is a knave.", "We have exhausted all possibilities for Benjamin and Isabella, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Isabella is a knight if and only if Michael is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Benjamin is a knight and Riley is a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Riley that Oliver is a knight if and only if Benjamin is a knave.", "Benjamin cannot be a knave, because this would contradict the claim of Isabella that Benjamin is a knight and Riley is a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Benjamin is a knight and Riley is a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Riley that Oliver is a knight if and only if Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Abigail is a knight.", "Abigail cannot be a knight, because this would contradict the false claim of Benjamin that Abigail is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Grace is not a knave.", "Grace cannot be a knight, because this would contradict the false claim of Abigail that Grace is not a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Oliver is a knave if and only if Elizabeth is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Isabella is a knave or Benjamin is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Oliver is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 7), ('lying', 2)), ('<=>', ('lying', 7), ('lying', 4)), ('telling-truth', 6), ('and', ('telling-truth', 2), ('lying', 0)), ('or', ('lying', 3), ('telling-truth', 2)), ('lying', 7), ('not', ('lying', 1)), ('<=>', ('telling-truth', 3), ('telling-truth', 5)))", "index": 625}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mason, Victoria, Ava, Daniel, Grace, Zoey, Sebastian, and James. In a statement by Mason: \"If Ava is a knight then James is a knave\". Victoria expressed that Zoey is a knave and James is a knave. \"James is a knight if and only if Ava is a knight\" - Ava. \"Zoey is not a knave\" - Daniel. Grace commented, \"Sebastian is a knave or Mason is a knight\". Zoey remarked, \"Mason is a knave\". According to Sebastian, \"Ava is a knight or Zoey is a knave\". \"Victoria is a knave if and only if Ava is a knave,\" James claimed. So who is a knight and who is a knave?", "names": ["Mason", "Victoria", "Ava", "Daniel", "Grace", "Zoey", "Sebastian", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, false, true, true], "solution_text": "Mason is a knight, Victoria is a knave, Ava is a knave, Daniel is a knave, Grace is a knight, Zoey is a knave, Sebastian is a knight, and James is a knight.", "solution_text_format": "(1) Mason is a knight\n(2) Victoria is a knave\n(3) Ava is a knave\n(4) Daniel is a knave\n(5) Grace is a knight\n(6) Zoey is a knave\n(7) Sebastian is a knight\n(8) James is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that If Ava is a knight then James is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that James is a knight if and only if Ava is a knight.", "James cannot be a knight, because this would contradict the claim of Mason that If Ava is a knight then James is a knave.", "James cannot be a knave, because this would contradict the claim of Ava that James is a knight if and only if Ava is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that James is a knight if and only if Ava is a knight.", "Assume James is a knight. No contradiction is found in their claim that Victoria is a knave if and only if Ava is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that Zoey is a knave and James is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Zoey is a knave and James is a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that Mason is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Mason is a knave.", "Daniel cannot be a knight, because this would contradict the claim of their own that Zoey is not a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Zoey is not a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Sebastian is a knave or Mason is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Ava is a knight or Zoey is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('lying', 7)), ('and', ('lying', 5), ('lying', 7)), ('<=>', ('telling-truth', 7), ('telling-truth', 2)), ('not', ('lying', 5)), ('or', ('lying', 6), ('telling-truth', 0)), ('lying', 0), ('or', ('telling-truth', 2), ('lying', 5)), ('<=>', ('lying', 1), ('lying', 2)))", "index": 626}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sofia, Mason, Elizabeth, Scarlett, Charlotte, Daniel, Lucas, and Sebastian. Sofia noted, \"Scarlett is a knight\". \"If Lucas is a knave then Sofia is a knave\" - Mason. Elizabeth commented, \"Charlotte is a knight\". Scarlett commented, \"If Elizabeth is a knight then Sofia is a knave\". Charlotte remarked, \"Lucas is a knave if and only if Sofia is a knight\". \"Mason is a knight and Sofia is a knight,\" Daniel claimed. Lucas expressed that Lucas is a knight or Sebastian is a knight. Sebastian noted, \"If Mason is a knight then Daniel is a knight\". So who is a knight and who is a knave?", "names": ["Sofia", "Mason", "Elizabeth", "Scarlett", "Charlotte", "Daniel", "Lucas", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true, true, true], "solution_text": "Sofia is a knight, Mason is a knight, Elizabeth is a knave, Scarlett is a knight, Charlotte is a knave, Daniel is a knight, Lucas is a knight, and Sebastian is a knight.", "solution_text_format": "(1) Sofia is a knight\n(2) Mason is a knight\n(3) Elizabeth is a knave\n(4) Scarlett is a knight\n(5) Charlotte is a knave\n(6) Daniel is a knight\n(7) Lucas is a knight\n(8) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Elizabeth is a knight then Sofia is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of Scarlett that If Elizabeth is a knight then Sofia is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of Elizabeth that Charlotte is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Lucas is a knave if and only if Sofia is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Lucas is a knight or Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Mason is a knight then Daniel is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that If Lucas is a knave then Sofia is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Mason is a knight and Sofia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 3), ('->', ('lying', 6), ('lying', 0)), ('telling-truth', 4), ('->', ('telling-truth', 2), ('lying', 0)), ('<=>', ('lying', 6), ('telling-truth', 0)), ('and', ('telling-truth', 1), ('telling-truth', 0)), ('or', ('telling-truth', 6), ('telling-truth', 7)), ('->', ('telling-truth', 1), ('telling-truth', 5)))", "index": 627}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ethan, Olivia, Sofia, Samuel, Mason, Charlotte, Benjamin, and William. Ethan noted, \"If Mason is a knave then Benjamin is a knight\". \"Sofia is a knight if and only if Samuel is a knave,\" Olivia declared. In a statement by Sofia: \"Samuel is a knave if and only if Charlotte is a knave\". Samuel asserted: \"Benjamin is a knave if and only if Ethan is a knave\". Mason was heard saying, \"If Samuel is a knight then Olivia is a knight\". \"Samuel is a knight,\" Charlotte claimed. As Benjamin put it, \"Mason is a knight\". \"Ethan is not a knight,\" William declared. So who is a knight and who is a knave?", "names": ["Ethan", "Olivia", "Sofia", "Samuel", "Mason", "Charlotte", "Benjamin", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, true, false, true], "solution_text": "Ethan is a knave, Olivia is a knave, Sofia is a knight, Samuel is a knight, Mason is a knave, Charlotte is a knight, Benjamin is a knave, and William is a knight.", "solution_text_format": "(1) Ethan is a knave\n(2) Olivia is a knave\n(3) Sofia is a knight\n(4) Samuel is a knight\n(5) Mason is a knave\n(6) Charlotte is a knight\n(7) Benjamin is a knave\n(8) William is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that If Mason is a knave then Benjamin is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that If Samuel is a knight then Olivia is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Benjamin is a knave if and only if Ethan is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Mason is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Sofia is a knight if and only if Samuel is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Olivia that Sofia is a knight if and only if Samuel is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Samuel is a knave if and only if Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the false claim of Sofia that Samuel is a knave if and only if Charlotte is a knave.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that Samuel is a knight.", "We have exhausted all possibilities for Charlotte and Sofia, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the claim of Mason that If Samuel is a knight then Olivia is a knight.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the claim of Samuel that Benjamin is a knave if and only if Ethan is a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Benjamin is a knave if and only if Ethan is a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Samuel that Benjamin is a knave if and only if Ethan is a knave.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that Mason is a knight.", "We have exhausted all possibilities for Benjamin and Samuel, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that If Samuel is a knight then Olivia is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Benjamin is a knave if and only if Ethan is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Mason is a knight.", "Benjamin cannot be a knave, because this would contradict the claim of Ethan that If Mason is a knave then Benjamin is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Samuel.", "Samuel cannot be a knave, because this would contradict the false claim of Mason that If Samuel is a knight then Olivia is a knight.", "We have exhausted all possibilities for Samuel and Mason, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that If Mason is a knave then Benjamin is a knight.", "Mason cannot be a knight, because this would contradict the false claim of Ethan that If Mason is a knave then Benjamin is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that If Samuel is a knight then Olivia is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Benjamin is a knave if and only if Ethan is a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Ethan that If Mason is a knave then Benjamin is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Mason is a knight.", "Olivia cannot be a knight, because this would contradict the false claim of Mason that If Samuel is a knight then Olivia is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Sofia is a knight if and only if Samuel is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Charlotte is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Samuel is a knight.", "Assume William is a knight. No contradiction is found in their claim that Ethan is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 4), ('telling-truth', 6)), ('<=>', ('telling-truth', 2), ('lying', 3)), ('<=>', ('lying', 3), ('lying', 5)), ('<=>', ('lying', 6), ('lying', 0)), ('->', ('telling-truth', 3), ('telling-truth', 1)), ('telling-truth', 3), ('telling-truth', 4), ('not', ('telling-truth', 0)))", "index": 628}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Luke, Zoey, Grace, Alexander, Oliver, Evelyn, Riley, and Ava. Luke stated, \"Riley is a knight and Zoey is a knave\". \"Grace is a knight,\" Zoey mentioned. Grace told you that Luke is a knave if and only if Ava is a knight. In a statement by Alexander: \"Riley is a knave if and only if Grace is a knave\". In a statement by Oliver: \"Luke is a knight if and only if Ava is a knave\". According to Evelyn, \"If Grace is a knight then Zoey is a knave\". Riley noted, \"Zoey is a knave and Grace is a knave\". \"Oliver is not a knave,\" Ava claimed. So who is a knight and who is a knave?", "names": ["Luke", "Zoey", "Grace", "Alexander", "Oliver", "Evelyn", "Riley", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, false, false, true], "solution_text": "Luke is a knave, Zoey is a knight, Grace is a knight, Alexander is a knave, Oliver is a knight, Evelyn is a knave, Riley is a knave, and Ava is a knight.", "solution_text_format": "(1) Luke is a knave\n(2) Zoey is a knight\n(3) Grace is a knight\n(4) Alexander is a knave\n(5) Oliver is a knight\n(6) Evelyn is a knave\n(7) Riley is a knave\n(8) Ava is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Riley is a knight and Zoey is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Zoey is a knave and Grace is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Luke that Riley is a knight and Zoey is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Grace is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Zoey that Grace is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Luke is a knave if and only if Ava is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Oliver is not a knave.", "Oliver cannot be a knight, because this would contradict the claim of their own that Luke is a knight if and only if Ava is a knave.", "Oliver cannot be a knave, because this would contradict the claim of Ava that Oliver is not a knave.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the false claim of Grace that Luke is a knave if and only if Ava is a knight.", "We have exhausted all possibilities for Ava, Grace, and Zoey, so let us go back and reconsider Riley.", "Riley cannot be a knave, because this would contradict the claim of Luke that Riley is a knight and Zoey is a knave.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Riley is a knight and Zoey is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Zoey is a knave and Grace is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Riley that Zoey is a knave and Grace is a knave.", "Zoey cannot be a knave, because this would contradict the false claim of Luke that Riley is a knight and Zoey is a knave.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Zoey is a knave and Grace is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Luke is a knave if and only if Ava is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Oliver is not a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Luke is a knight if and only if Ava is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that Riley is a knave if and only if Grace is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Riley is a knave if and only if Grace is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that If Grace is a knight then Zoey is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that If Grace is a knight then Zoey is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 6), ('lying', 1)), ('telling-truth', 2), ('<=>', ('lying', 0), ('telling-truth', 7)), ('<=>', ('lying', 6), ('lying', 2)), ('<=>', ('telling-truth', 0), ('lying', 7)), ('->', ('telling-truth', 2), ('lying', 1)), ('and', ('lying', 1), ('lying', 2)), ('not', ('lying', 4)))", "index": 629}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sebastian, Sophia, Aria, Jackson, Grace, Matthew, Ethan, and Aiden. Sebastian remarked, \"Jackson is a knave if and only if Grace is a knave\". Sophia asserted: \"Aiden is a knave if and only if Sebastian is a knave\". \"Sophia is a knight if and only if Sophia is a knave,\" Aria mentioned. \"Grace is a knight or Aiden is a knave,\" Jackson declared. Grace expressed that Jackson is a knight and Grace is a knight. Matthew said that Aiden is not a knave. Ethan noted, \"Jackson is a knave if and only if Grace is a knight\". In Aiden's words: \"Sebastian is not a knight\". So who is a knight and who is a knave?", "names": ["Sebastian", "Sophia", "Aria", "Jackson", "Grace", "Matthew", "Ethan", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false, false, false], "solution_text": "Sebastian is a knight, Sophia is a knave, Aria is a knave, Jackson is a knight, Grace is a knight, Matthew is a knave, Ethan is a knave, and Aiden is a knave.", "solution_text_format": "(1) Sebastian is a knight\n(2) Sophia is a knave\n(3) Aria is a knave\n(4) Jackson is a knight\n(5) Grace is a knight\n(6) Matthew is a knave\n(7) Ethan is a knave\n(8) Aiden is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that Jackson is a knave if and only if Grace is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Grace is a knight or Aiden is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Jackson is a knight and Grace is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Sebastian is not a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Sebastian is not a knight.", "Sophia cannot be a knight, because this would contradict the claim of their own that Aiden is a knave if and only if Sebastian is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if Sebastian is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Sophia is a knight if and only if Sophia is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Sophia is a knight if and only if Sophia is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Aiden is not a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Aiden is not a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Jackson is a knave if and only if Grace is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Jackson is a knave if and only if Grace is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('lying', 4)), ('<=>', ('lying', 7), ('lying', 0)), ('<=>', ('telling-truth', 1), ('lying', 1)), ('or', ('telling-truth', 4), ('lying', 7)), ('and', ('telling-truth', 3), ('telling-truth', 4)), ('not', ('lying', 7)), ('<=>', ('lying', 3), ('telling-truth', 4)), ('not', ('telling-truth', 0)))", "index": 630}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aria, Aurora, Lucas, Joseph, Benjamin, James, Oliver, and Victoria. \"James is a knight and Benjamin is a knight,\" Aria declared. Aurora told you that Joseph is a knight. \"If Benjamin is a knave then Aria is a knight,\" Lucas claimed. Joseph commented, \"If Joseph is a knight then Aurora is a knight\". Benjamin said, \"If Aria is a knave then Victoria is a knight.\" \"Lucas is a knight and Benjamin is a knight,\" James claimed. Oliver told you that James is a knave or Benjamin is a knight. Victoria expressed that Aria is a knave. So who is a knight and who is a knave?", "names": ["Aria", "Aurora", "Lucas", "Joseph", "Benjamin", "James", "Oliver", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true, true, false], "solution_text": "Aria is a knight, Aurora is a knight, Lucas is a knight, Joseph is a knight, Benjamin is a knight, James is a knight, Oliver is a knight, and Victoria is a knave.", "solution_text_format": "(1) Aria is a knight\n(2) Aurora is a knight\n(3) Lucas is a knight\n(4) Joseph is a knight\n(5) Benjamin is a knight\n(6) James is a knight\n(7) Oliver is a knight\n(8) Victoria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that James is a knight and Benjamin is a knight.", "Assume James is a knight. No contradiction is found in their claim that Lucas is a knight and Benjamin is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that If Benjamin is a knave then Aria is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Aria is a knave then Victoria is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Aria is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Aria is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Joseph is a knight then Aurora is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that James is a knave or Benjamin is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('telling-truth', 4)), ('telling-truth', 3), ('->', ('lying', 4), ('telling-truth', 0)), ('->', ('telling-truth', 3), ('telling-truth', 1)), ('->', ('lying', 0), ('telling-truth', 7)), ('and', ('telling-truth', 2), ('telling-truth', 4)), ('or', ('lying', 5), ('telling-truth', 4)), ('lying', 0))", "index": 631}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Avery, Henry, Aiden, James, Luke, Jacob, Liam, and Chloe. Avery remarked, \"If Aiden is a knave then Liam is a knave\". According to Henry, \"James is not a knight\". Aiden asserted: \"James is a knave and Luke is a knave\". James asserted: \"Chloe is a knight if and only if Chloe is a knave\". Luke asserted: \"James is a knave\". Jacob expressed that Liam is not a knave. \"Chloe is a knave or James is a knave,\" Liam declared. Chloe remarked, \"Aiden is a knight and Luke is a knight\". So who is a knight and who is a knave?", "names": ["Avery", "Henry", "Aiden", "James", "Luke", "Jacob", "Liam", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true, true, false], "solution_text": "Avery is a knave, Henry is a knight, Aiden is a knave, James is a knave, Luke is a knight, Jacob is a knight, Liam is a knight, and Chloe is a knave.", "solution_text_format": "(1) Avery is a knave\n(2) Henry is a knight\n(3) Aiden is a knave\n(4) James is a knave\n(5) Luke is a knight\n(6) Jacob is a knight\n(7) Liam is a knight\n(8) Chloe is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that If Aiden is a knave then Liam is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that James is a knave and Luke is a knave.", "James cannot be a knight, because this would contradict the claim of Aiden that James is a knave and Luke is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Chloe is a knight if and only if Chloe is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Aiden is a knight and Luke is a knight.", "Luke cannot be a knight, because this would contradict the claim of Aiden that James is a knave and Luke is a knave.", "Luke cannot be a knave, because this would contradict the false claim of their own that James is a knave.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Aiden is a knight and Luke is a knight.", "Luke cannot be a knight, because this would contradict the claim of Aiden that James is a knave and Luke is a knave.", "Luke cannot be a knave, because this would contradict the false claim of their own that James is a knave.", "We have exhausted all possibilities for Luke, Chloe, and James, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that James is a knave and Luke is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Chloe is a knight if and only if Chloe is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Chloe is a knight if and only if Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Aiden is a knight and Luke is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Aiden is a knight and Luke is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that James is a knave.", "Liam cannot be a knight, because this would contradict the claim of Avery that If Aiden is a knave then Liam is a knave.", "Liam cannot be a knave, because this would contradict the false claim of their own that Chloe is a knave or James is a knave.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the false claim of Aiden that James is a knave and Luke is a knave.", "We have exhausted all possibilities for Luke, Chloe, James, and Aiden, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that If Aiden is a knave then Liam is a knave.", "Aiden cannot be a knight, because this would contradict the false claim of Avery that If Aiden is a knave then Liam is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that James is a knave and Luke is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Chloe is a knight if and only if Chloe is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Chloe is a knight if and only if Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Aiden is a knight and Luke is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Aiden is a knight and Luke is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that James is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Chloe is a knave or James is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that James is not a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Liam is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 2), ('lying', 6)), ('not', ('telling-truth', 3)), ('and', ('lying', 3), ('lying', 4)), ('<=>', ('telling-truth', 7), ('lying', 7)), ('lying', 3), ('not', ('lying', 6)), ('or', ('lying', 7), ('lying', 3)), ('and', ('telling-truth', 2), ('telling-truth', 4)))", "index": 632}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Oliver, Zoey, Aria, Henry, Liam, Ella, Victoria, and Scarlett. Oliver expressed that Zoey is a knight and Victoria is a knight. Zoey was heard saying, \"If Aria is a knave then Liam is a knight\". Aria expressed that Henry is a knave and Liam is a knight. Henry said that If Zoey is a knight then Henry is a knight. Liam remarked, \"Ella is a knave or Henry is a knight\". Ella was heard saying, \"Aria is a knight or Liam is a knave\". In Victoria's words: \"Zoey is a knight or Oliver is a knight\". Scarlett expressed that Victoria is a knave if and only if Henry is a knave. So who is a knight and who is a knave?", "names": ["Oliver", "Zoey", "Aria", "Henry", "Liam", "Ella", "Victoria", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false, true, true], "solution_text": "Oliver is a knight, Zoey is a knight, Aria is a knave, Henry is a knight, Liam is a knight, Ella is a knave, Victoria is a knight, and Scarlett is a knight.", "solution_text_format": "(1) Oliver is a knight\n(2) Zoey is a knight\n(3) Aria is a knave\n(4) Henry is a knight\n(5) Liam is a knight\n(6) Ella is a knave\n(7) Victoria is a knight\n(8) Scarlett is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Zoey is a knight and Victoria is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that If Aria is a knave then Liam is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Henry is a knave and Liam is a knight.", "Henry cannot be a knight, because this would contradict the claim of Aria that Henry is a knave and Liam is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that If Zoey is a knight then Henry is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Ella is a knave or Henry is a knight.", "Ella cannot be a knight, because this would contradict the claim of Liam that Ella is a knave or Henry is a knight.", "Ella cannot be a knave, because this would contradict the false claim of their own that Aria is a knight or Liam is a knave.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the claim of Aria that Henry is a knave and Liam is a knight.", "We have exhausted all possibilities for Liam and Henry, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Henry is a knave and Liam is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that If Zoey is a knight then Henry is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Ella is a knave or Henry is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Aria is a knight or Liam is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Aria is a knight or Liam is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Zoey is a knight or Oliver is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Victoria is a knave if and only if Henry is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('telling-truth', 6)), ('->', ('lying', 2), ('telling-truth', 4)), ('and', ('lying', 3), ('telling-truth', 4)), ('->', ('telling-truth', 1), ('telling-truth', 3)), ('or', ('lying', 5), ('telling-truth', 3)), ('or', ('telling-truth', 2), ('lying', 4)), ('or', ('telling-truth', 1), ('telling-truth', 0)), ('<=>', ('lying', 6), ('lying', 3)))", "index": 633}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Alexander, Jackson, Emily, Grace, Luke, Emma, Noah, and David. Alexander stated, \"Alexander is a knight or Emily is a knight\". \"If Alexander is a knave then Noah is a knight,\" Jackson claimed. Emily stated, \"If Jackson is a knight then Grace is a knight\". Grace said that Jackson is not a knave. \"Alexander is not a knight\" - Luke. Emma expressed that If Luke is a knave then Alexander is a knave. As Noah put it, \"Grace is a knave or Alexander is a knave\". David remarked, \"Grace is a knight\". So who is a knight and who is a knave?", "names": ["Alexander", "Jackson", "Emily", "Grace", "Luke", "Emma", "Noah", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false, false, true], "solution_text": "Alexander is a knight, Jackson is a knight, Emily is a knight, Grace is a knight, Luke is a knave, Emma is a knave, Noah is a knave, and David is a knight.", "solution_text_format": "(1) Alexander is a knight\n(2) Jackson is a knight\n(3) Emily is a knight\n(4) Grace is a knight\n(5) Luke is a knave\n(6) Emma is a knave\n(7) Noah is a knave\n(8) David is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that Alexander is a knight or Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that If Jackson is a knight then Grace is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that If Alexander is a knave then Noah is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Grace is a knave or Alexander is a knave.", "Grace cannot be a knight, because this would contradict the claim of Noah that Grace is a knave or Alexander is a knave.", "Grace cannot be a knave, because this would contradict the claim of Emily that If Jackson is a knight then Grace is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Grace is a knave or Alexander is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Jackson is not a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that Alexander is not a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Alexander is not a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that If Luke is a knave then Alexander is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that If Luke is a knave then Alexander is a knave.", "Assume David is a knight. No contradiction is found in their claim that Grace is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 0), ('telling-truth', 2)), ('->', ('lying', 0), ('telling-truth', 6)), ('->', ('telling-truth', 1), ('telling-truth', 3)), ('not', ('lying', 1)), ('not', ('telling-truth', 0)), ('->', ('lying', 4), ('lying', 0)), ('or', ('lying', 3), ('lying', 0)), ('telling-truth', 3))", "index": 634}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Luke, Lily, Lucas, Riley, Ethan, Jackson, Mason, and Emily. Luke commented, \"Lucas is a knight and Mason is a knight\". \"Mason is a knight or Jackson is a knave,\" Lily mentioned. According to Lucas, \"Jackson is not a knave\". \"Lily is a knight\" - Riley. In a statement by Ethan: \"Jackson is not a knight\". As Jackson put it, \"Jackson is a knight and Luke is a knight\". \"Riley is not a knight,\" Mason claimed. Emily expressed that Luke is a knave. So who is a knight and who is a knave?", "names": ["Luke", "Lily", "Lucas", "Riley", "Ethan", "Jackson", "Mason", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false, false, true], "solution_text": "Luke is a knave, Lily is a knight, Lucas is a knave, Riley is a knight, Ethan is a knight, Jackson is a knave, Mason is a knave, and Emily is a knight.", "solution_text_format": "(1) Luke is a knave\n(2) Lily is a knight\n(3) Lucas is a knave\n(4) Riley is a knight\n(5) Ethan is a knight\n(6) Jackson is a knave\n(7) Mason is a knave\n(8) Emily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Lucas is a knight and Mason is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Jackson is not a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Jackson is a knight and Luke is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Riley is not a knight.", "Riley cannot be a knight, because this would contradict the claim of Mason that Riley is not a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Lily is a knight.", "Lily cannot be a knight, because this would contradict the false claim of Riley that Lily is a knight.", "Lily cannot be a knave, because this would contradict the false claim of their own that Mason is a knight or Jackson is a knave.", "We have exhausted all possibilities for Lily and Riley, so let us go back and reconsider Mason.", "Mason cannot be a knave, because this would contradict the claim of Luke that Lucas is a knight and Mason is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Jackson.", "Jackson cannot be a knave, because this would contradict the claim of Lucas that Jackson is not a knave.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the claim of Luke that Lucas is a knight and Mason is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Lucas is a knight and Mason is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Jackson is not a knave.", "Jackson cannot be a knight, because this would contradict the claim of their own that Jackson is a knight and Luke is a knight.", "Jackson cannot be a knave, because this would contradict the claim of Lucas that Jackson is not a knave.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Jackson is not a knave.", "Jackson cannot be a knight, because this would contradict the false claim of Lucas that Jackson is not a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Jackson is a knight and Luke is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Riley is not a knight.", "Riley cannot be a knight, because this would contradict the claim of Mason that Riley is not a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Lily is a knight.", "Lily cannot be a knight, because this would contradict the false claim of Riley that Lily is a knight.", "Lily cannot be a knave, because this would contradict the false claim of their own that Mason is a knight or Jackson is a knave.", "We have exhausted all possibilities for Lily and Riley, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Riley is not a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Lily is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Mason is a knight or Jackson is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Jackson is not a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Luke is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 2), ('telling-truth', 6)), ('or', ('telling-truth', 6), ('lying', 5)), ('not', ('lying', 5)), ('telling-truth', 1), ('not', ('telling-truth', 5)), ('and', ('telling-truth', 5), ('telling-truth', 0)), ('not', ('telling-truth', 3)), ('lying', 0))", "index": 635}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sofia, Charlotte, William, Noah, Chloe, Avery, Henry, and Olivia. In a statement by Sofia: \"If Noah is a knight then Sofia is a knight\". Charlotte told you that Chloe is a knave. In William's words: \"Charlotte is a knave\". In Noah's words: \"Henry is a knight or Sofia is a knave\". Chloe stated, \"William is a knight if and only if Avery is a knave\". \"Sofia is a knight\" - Avery. Henry was heard saying, \"Sofia is a knight\". \"If Olivia is a knight then William is a knight,\" Olivia mentioned. So who is a knight and who is a knave?", "names": ["Sofia", "Charlotte", "William", "Noah", "Chloe", "Avery", "Henry", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false, false, true], "solution_text": "Sofia is a knave, Charlotte is a knave, William is a knight, Noah is a knight, Chloe is a knight, Avery is a knave, Henry is a knave, and Olivia is a knight.", "solution_text_format": "(1) Sofia is a knave\n(2) Charlotte is a knave\n(3) William is a knight\n(4) Noah is a knight\n(5) Chloe is a knight\n(6) Avery is a knave\n(7) Henry is a knave\n(8) Olivia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that If Noah is a knight then Sofia is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Henry is a knight or Sofia is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Sofia is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Charlotte that Chloe is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that William is a knight if and only if Avery is a knave.", "William cannot be a knight, because this would contradict the claim of their own that Charlotte is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Charlotte is a knave.", "Avery cannot be a knight, because this would contradict the false claim of Chloe that William is a knight if and only if Avery is a knave.", "Avery cannot be a knave, because this would contradict the false claim of their own that Sofia is a knight.", "We have exhausted all possibilities for Avery, William, and Chloe, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Chloe is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that William is a knight if and only if Avery is a knave.", "Assume William is a knight. No contradiction is found in their claim that Charlotte is a knave.", "Avery cannot be a knight, because this would contradict the claim of Chloe that William is a knight if and only if Avery is a knave.", "Avery cannot be a knave, because this would contradict the false claim of their own that Sofia is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the false claim of their own that Charlotte is a knave.", "We have exhausted all possibilities for William, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the false claim of Charlotte that Chloe is a knave.", "We have exhausted all possibilities for Chloe and Charlotte, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the claim of Noah that Henry is a knight or Sofia is a knave.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Henry is a knight or Sofia is a knave.", "Henry cannot be a knight, because this would contradict the false claim of Noah that Henry is a knight or Sofia is a knave.", "Henry cannot be a knave, because this would contradict the false claim of their own that Sofia is a knight.", "We have exhausted all possibilities for Henry and Noah, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that If Noah is a knight then Sofia is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Henry is a knight or Sofia is a knave.", "Henry cannot be a knight, because this would contradict the claim of their own that Sofia is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Sofia is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Charlotte that Chloe is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that William is a knight if and only if Avery is a knave.", "William cannot be a knight, because this would contradict the claim of their own that Charlotte is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Charlotte is a knave.", "Avery cannot be a knight, because this would contradict the false claim of Chloe that William is a knight if and only if Avery is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Sofia is a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that If Olivia is a knight then William is a knight.", "Olivia cannot be a knave, because this would contradict the false claim of their own that If Olivia is a knight then William is a knight.", "We have exhausted all possibilities for Olivia, Avery, William, and Chloe, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Chloe is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that William is a knight if and only if Avery is a knave.", "Assume William is a knight. No contradiction is found in their claim that Charlotte is a knave.", "Avery cannot be a knight, because this would contradict the claim of Chloe that William is a knight if and only if Avery is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Sofia is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that If Olivia is a knight then William is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('telling-truth', 0)), ('lying', 4), ('lying', 1), ('or', ('telling-truth', 6), ('lying', 0)), ('<=>', ('telling-truth', 2), ('lying', 5)), ('telling-truth', 0), ('telling-truth', 0), ('->', ('telling-truth', 7), ('telling-truth', 2)))", "index": 636}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Evelyn, James, Sophia, Matthew, Ethan, Luke, Scarlett, and Logan. As Evelyn put it, \"Logan is a knight if and only if Scarlett is a knight\". James expressed that Scarlett is a knight and James is a knight. Sophia commented, \"Evelyn is a knight\". Matthew remarked, \"Ethan is not a knight\". Ethan asserted: \"If Scarlett is a knight then Logan is a knave\". Luke expressed that If Matthew is a knave then Sophia is a knave. Scarlett stated, \"Sophia is a knave and James is a knight\". In Logan's words: \"Matthew is not a knight\". So who is a knight and who is a knave?", "names": ["Evelyn", "James", "Sophia", "Matthew", "Ethan", "Luke", "Scarlett", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, true, false, true], "solution_text": "Evelyn is a knave, James is a knave, Sophia is a knave, Matthew is a knave, Ethan is a knight, Luke is a knight, Scarlett is a knave, and Logan is a knight.", "solution_text_format": "(1) Evelyn is a knave\n(2) James is a knave\n(3) Sophia is a knave\n(4) Matthew is a knave\n(5) Ethan is a knight\n(6) Luke is a knight\n(7) Scarlett is a knave\n(8) Logan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Logan is a knight if and only if Scarlett is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Matthew is not a knight.", "Matthew cannot be a knight, because this would contradict the claim of Logan that Matthew is not a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Ethan is not a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If Scarlett is a knight then Logan is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Ethan that If Scarlett is a knight then Logan is a knave.", "Scarlett cannot be a knave, because this would contradict the claim of Evelyn that Logan is a knight if and only if Scarlett is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the false claim of Matthew that Ethan is not a knight.", "We have exhausted all possibilities for Ethan and Matthew, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Matthew is not a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Ethan is not a knight.", "Ethan cannot be a knight, because this would contradict the claim of Matthew that Ethan is not a knight.", "Ethan cannot be a knave, because this would contradict the false claim of their own that If Scarlett is a knight then Logan is a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the false claim of Logan that Matthew is not a knight.", "We have exhausted all possibilities for Matthew and Logan, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Logan is a knight if and only if Scarlett is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Matthew is not a knight.", "Matthew cannot be a knight, because this would contradict the claim of Logan that Matthew is not a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Ethan is not a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If Scarlett is a knight then Logan is a knave.", "Scarlett cannot be a knight, because this would contradict the false claim of Evelyn that Logan is a knight if and only if Scarlett is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Sophia is a knave and James is a knight.", "Sophia cannot be a knight, because this would contradict the claim of their own that Evelyn is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Evelyn is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight and James is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Scarlett is a knight and James is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that If Matthew is a knave then Sophia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 7), ('telling-truth', 6)), ('and', ('telling-truth', 6), ('telling-truth', 1)), ('telling-truth', 0), ('not', ('telling-truth', 4)), ('->', ('telling-truth', 6), ('lying', 7)), ('->', ('lying', 3), ('lying', 2)), ('and', ('lying', 2), ('telling-truth', 1)), ('not', ('telling-truth', 3)))", "index": 637}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jacob, Amelia, Samuel, Liam, Emily, Owen, Logan, and Scarlett. Jacob asserted: \"If Owen is a knight then Logan is a knave\". Amelia said that If Owen is a knight then Liam is a knight. Samuel asserted: \"Liam is a knight if and only if Owen is a knight\". As Liam put it, \"Logan is a knight and Samuel is a knight\". \"If Scarlett is a knave then Liam is a knave\" - Emily. Owen said that Logan is a knave if and only if Amelia is a knight. Logan told you that Liam is a knave. \"Jacob is a knave if and only if Logan is a knave\" - Scarlett. So who is a knight and who is a knave?", "names": ["Jacob", "Amelia", "Samuel", "Liam", "Emily", "Owen", "Logan", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, true, true, false], "solution_text": "Jacob is a knave, Amelia is a knave, Samuel is a knave, Liam is a knave, Emily is a knight, Owen is a knight, Logan is a knight, and Scarlett is a knave.", "solution_text_format": "(1) Jacob is a knave\n(2) Amelia is a knave\n(3) Samuel is a knave\n(4) Liam is a knave\n(5) Emily is a knight\n(6) Owen is a knight\n(7) Logan is a knight\n(8) Scarlett is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that If Owen is a knight then Logan is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Logan is a knave if and only if Amelia is a knight.", "Logan cannot be a knight, because this would contradict the claim of Jacob that If Owen is a knight then Logan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Logan is a knight and Samuel is a knight.", "Liam cannot be a knave, because this would contradict the false claim of Logan that Liam is a knave.", "We have exhausted all possibilities for Liam and Logan, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Logan is a knave if and only if Amelia is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of Logan that Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Logan is a knight and Samuel is a knight.", "Samuel cannot be a knight, because this would contradict the false claim of Liam that Logan is a knight and Samuel is a knight.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Liam is a knight if and only if Owen is a knight.", "We have exhausted all possibilities for Samuel and Liam, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Logan is a knight and Samuel is a knight.", "Liam cannot be a knave, because this would contradict the false claim of Logan that Liam is a knave.", "We have exhausted all possibilities for Liam, Logan, and Owen, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that If Owen is a knight then Logan is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Logan is a knave if and only if Amelia is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of Logan that Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Logan is a knight and Samuel is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Liam is a knight if and only if Owen is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Liam is a knight if and only if Owen is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that If Owen is a knight then Liam is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that If Owen is a knight then Liam is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that If Scarlett is a knave then Liam is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Jacob is a knave if and only if Logan is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Jacob is a knave if and only if Logan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 5), ('lying', 6)), ('->', ('telling-truth', 5), ('telling-truth', 3)), ('<=>', ('telling-truth', 3), ('telling-truth', 5)), ('and', ('telling-truth', 6), ('telling-truth', 2)), ('->', ('lying', 7), ('lying', 3)), ('<=>', ('lying', 6), ('telling-truth', 1)), ('lying', 3), ('<=>', ('lying', 0), ('lying', 6)))", "index": 638}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Daniel, Abigail, Ethan, Joseph, Jackson, William, Victoria, and Lily. Daniel said that Lily is a knave. In a statement by Abigail: \"If William is a knave then Daniel is a knave\". Ethan told you that Daniel is a knight. Joseph asserted: \"William is a knave if and only if Ethan is a knave\". \"William is a knave and William is a knight,\" Jackson claimed. William stated, \"Victoria is a knight\". Victoria remarked, \"If Jackson is a knight then Ethan is a knight\". \"Abigail is a knight or Ethan is a knight,\" Lily declared. So who is a knight and who is a knave?", "names": ["Daniel", "Abigail", "Ethan", "Joseph", "Jackson", "William", "Victoria", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, true, true, true], "solution_text": "Daniel is a knave, Abigail is a knight, Ethan is a knave, Joseph is a knave, Jackson is a knave, William is a knight, Victoria is a knight, and Lily is a knight.", "solution_text_format": "(1) Daniel is a knave\n(2) Abigail is a knight\n(3) Ethan is a knave\n(4) Joseph is a knave\n(5) Jackson is a knave\n(6) William is a knight\n(7) Victoria is a knight\n(8) Lily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of Daniel that Lily is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Abigail is a knight or Ethan is a knight.", "Abigail cannot be a knight, because this would contradict the false claim of Lily that Abigail is a knight or Ethan is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that If William is a knave then Daniel is a knave.", "William cannot be a knight, because this would contradict the false claim of Abigail that If William is a knave then Daniel is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Victoria is a knight.", "Victoria cannot be a knight, because this would contradict the false claim of William that Victoria is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that If Jackson is a knight then Ethan is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that William is a knave and William is a knight.", "Jackson cannot be a knave, because this would contradict the false claim of Victoria that If Jackson is a knight then Ethan is a knight.", "We have exhausted all possibilities for Jackson, Victoria, William, Abigail, and Lily, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Lily is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Abigail is a knight or Ethan is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If William is a knave then Daniel is a knave.", "Assume William is a knight. No contradiction is found in their claim that Victoria is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that If Jackson is a knight then Ethan is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that William is a knave and William is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that William is a knave and William is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Daniel is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Daniel is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that William is a knave if and only if Ethan is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that William is a knave if and only if Ethan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 7), ('->', ('lying', 5), ('lying', 0)), ('telling-truth', 0), ('<=>', ('lying', 5), ('lying', 2)), ('and', ('lying', 5), ('telling-truth', 5)), ('telling-truth', 6), ('->', ('telling-truth', 4), ('telling-truth', 2)), ('or', ('telling-truth', 1), ('telling-truth', 2)))", "index": 639}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Riley, Abigail, Ella, Evelyn, Aiden, Michael, Jackson, and Logan. In a statement by Riley: \"Riley is a knight or Logan is a knight\". \"If Ella is a knight then Jackson is a knave,\" Abigail mentioned. In a statement by Ella: \"Abigail is a knave or Abigail is a knight\". In a statement by Evelyn: \"Aiden is a knave if and only if Jackson is a knight\". In a statement by Aiden: \"Jackson is a knight if and only if Ella is a knight\". \"Evelyn is not a knight,\" Michael mentioned. Jackson expressed that Michael is a knight if and only if Riley is a knave. Logan remarked, \"If Logan is a knight then Evelyn is a knave\". So who is a knight and who is a knave?", "names": ["Riley", "Abigail", "Ella", "Evelyn", "Aiden", "Michael", "Jackson", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true, false, true], "solution_text": "Riley is a knight, Abigail is a knight, Ella is a knight, Evelyn is a knave, Aiden is a knave, Michael is a knight, Jackson is a knave, and Logan is a knight.", "solution_text_format": "(1) Riley is a knight\n(2) Abigail is a knight\n(3) Ella is a knight\n(4) Evelyn is a knave\n(5) Aiden is a knave\n(6) Michael is a knight\n(7) Jackson is a knave\n(8) Logan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Riley is a knight or Logan is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that If Logan is a knight then Evelyn is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of Logan that If Logan is a knight then Evelyn is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if Jackson is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Ella is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Michael is a knight if and only if Riley is a knave.", "Michael cannot be a knight, because this would contradict the claim of Jackson that Michael is a knight if and only if Riley is a knave.", "Michael cannot be a knave, because this would contradict the false claim of their own that Evelyn is not a knight.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Jackson.", "Jackson cannot be a knave, because this would contradict the false claim of Evelyn that Aiden is a knave if and only if Jackson is a knight.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Jackson is a knight if and only if Ella is a knight.", "Jackson cannot be a knight, because this would contradict the false claim of Evelyn that Aiden is a knave if and only if Jackson is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Michael is a knight if and only if Riley is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Evelyn is not a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Abigail is a knave or Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If Ella is a knight then Jackson is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 0), ('telling-truth', 7)), ('->', ('telling-truth', 2), ('lying', 6)), ('or', ('lying', 1), ('telling-truth', 1)), ('<=>', ('lying', 4), ('telling-truth', 6)), ('<=>', ('telling-truth', 6), ('telling-truth', 2)), ('not', ('telling-truth', 3)), ('<=>', ('telling-truth', 5), ('lying', 0)), ('->', ('telling-truth', 7), ('lying', 3)))", "index": 640}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Elizabeth, Liam, Owen, Zoey, Alexander, James, Emily, and Jacob. Elizabeth said that Jacob is a knight and Owen is a knave. Liam said, \"Emily is a knave.\" Owen said, \"Emily is a knight.\" \"Elizabeth is a knave,\" Zoey claimed. \"Elizabeth is a knight if and only if James is a knave,\" Alexander mentioned. James commented, \"Zoey is not a knight\". Emily expressed that Zoey is a knave or Alexander is a knight. Jacob commented, \"If Elizabeth is a knave then Owen is a knight\". So who is a knight and who is a knave?", "names": ["Elizabeth", "Liam", "Owen", "Zoey", "Alexander", "James", "Emily", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, false, false, false], "solution_text": "Elizabeth is a knave, Liam is a knight, Owen is a knave, Zoey is a knight, Alexander is a knave, James is a knave, Emily is a knave, and Jacob is a knave.", "solution_text_format": "(1) Elizabeth is a knave\n(2) Liam is a knight\n(3) Owen is a knave\n(4) Zoey is a knight\n(5) Alexander is a knave\n(6) James is a knave\n(7) Emily is a knave\n(8) Jacob is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Jacob is a knight and Owen is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Owen is a knight.", "Owen cannot be a knight, because this would contradict the claim of Elizabeth that Jacob is a knight and Owen is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Emily is a knight.", "Emily cannot be a knight, because this would contradict the false claim of Owen that Emily is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Zoey is a knave or Alexander is a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave.", "Zoey cannot be a knave, because this would contradict the false claim of Emily that Zoey is a knave or Alexander is a knight.", "We have exhausted all possibilities for Zoey, Emily, and Owen, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the claim of Elizabeth that Jacob is a knight and Owen is a knave.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Jacob is a knight and Owen is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Owen is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Zoey is a knave or Alexander is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Elizabeth is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Elizabeth is a knight if and only if James is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Zoey is not a knight.", "James cannot be a knave, because this would contradict the claim of Alexander that Elizabeth is a knight if and only if James is a knave.", "We have exhausted all possibilities for James, so let us go back and reconsider Alexander.", "Alexander cannot be a knave, because this would contradict the claim of Emily that Zoey is a knave or Alexander is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Zoey.", "Zoey cannot be a knave, because this would contradict the false claim of their own that Elizabeth is a knave.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the claim of Owen that Emily is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the false claim of Elizabeth that Jacob is a knight and Owen is a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that If Elizabeth is a knave then Owen is a knight.", "Owen cannot be a knight, because this would contradict the false claim of Jacob that If Elizabeth is a knave then Owen is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Emily is a knight.", "Emily cannot be a knight, because this would contradict the false claim of Owen that Emily is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Zoey is a knave or Alexander is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Elizabeth is a knave.", "Alexander cannot be a knight, because this would contradict the false claim of Emily that Zoey is a knave or Alexander is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Elizabeth is a knight if and only if James is a knave.", "James cannot be a knight, because this would contradict the false claim of Alexander that Elizabeth is a knight if and only if James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Zoey is not a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Emily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 7), ('lying', 2)), ('lying', 6), ('telling-truth', 6), ('lying', 0), ('<=>', ('telling-truth', 0), ('lying', 5)), ('not', ('telling-truth', 3)), ('or', ('lying', 3), ('telling-truth', 4)), ('->', ('lying', 0), ('telling-truth', 2)))", "index": 641}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Olivia, Aiden, Victoria, Ethan, Isabella, Mia, Zoey, and Avery. Olivia stated, \"Isabella is a knight if and only if Ethan is a knave\". Aiden commented, \"Avery is a knave or Avery is a knight\". Victoria said that Aiden is a knight and Ethan is a knight. Ethan expressed that Mia is a knave or Aiden is a knave. Isabella asserted: \"If Victoria is a knave then Victoria is a knight\". Mia asserted: \"Isabella is a knave and Aiden is a knave\". Zoey said that If Avery is a knave then Isabella is a knight. Avery told you that Zoey is not a knight. So who is a knight and who is a knave?", "names": ["Olivia", "Aiden", "Victoria", "Ethan", "Isabella", "Mia", "Zoey", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false, true, false], "solution_text": "Olivia is a knave, Aiden is a knight, Victoria is a knight, Ethan is a knight, Isabella is a knight, Mia is a knave, Zoey is a knight, and Avery is a knave.", "solution_text_format": "(1) Olivia is a knave\n(2) Aiden is a knight\n(3) Victoria is a knight\n(4) Ethan is a knight\n(5) Isabella is a knight\n(6) Mia is a knave\n(7) Zoey is a knight\n(8) Avery is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Ethan is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that If Victoria is a knave then Victoria is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Aiden is a knight and Ethan is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Avery is a knave or Avery is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Zoey is not a knight.", "Zoey cannot be a knight, because this would contradict the claim of Avery that Zoey is not a knight.", "Zoey cannot be a knave, because this would contradict the false claim of their own that If Avery is a knave then Isabella is a knight.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Zoey is not a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that If Avery is a knave then Isabella is a knight.", "Ethan cannot be a knight, because this would contradict the claim of Olivia that Isabella is a knight if and only if Ethan is a knave.", "Ethan cannot be a knave, because this would contradict the claim of Victoria that Aiden is a knight and Ethan is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Zoey.", "Zoey cannot be a knave, because this would contradict the false claim of their own that If Avery is a knave then Isabella is a knight.", "We have exhausted all possibilities for Zoey and Avery, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the false claim of their own that Avery is a knave or Avery is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Victoria.", "Victoria cannot be a knave, because this would contradict the claim of Isabella that If Victoria is a knave then Victoria is a knight.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that If Victoria is a knave then Victoria is a knight.", "Victoria cannot be a knight, because this would contradict the false claim of Isabella that If Victoria is a knave then Victoria is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Aiden is a knight and Ethan is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Avery is a knave or Avery is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Zoey is not a knight.", "Zoey cannot be a knight, because this would contradict the claim of Avery that Zoey is not a knight.", "Zoey cannot be a knave, because this would contradict the false claim of their own that If Avery is a knave then Isabella is a knight.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Zoey is not a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that If Avery is a knave then Isabella is a knight.", "Zoey cannot be a knave, because this would contradict the false claim of Avery that Zoey is not a knight.", "We have exhausted all possibilities for Zoey and Avery, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the false claim of their own that Avery is a knave or Avery is a knight.", "We have exhausted all possibilities for Aiden, Victoria, and Isabella, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Isabella is a knight if and only if Ethan is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that If Victoria is a knave then Victoria is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Aiden is a knight and Ethan is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Avery is a knave or Avery is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Zoey is not a knight.", "Zoey cannot be a knight, because this would contradict the claim of Avery that Zoey is not a knight.", "Zoey cannot be a knave, because this would contradict the false claim of their own that If Avery is a knave then Isabella is a knight.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Zoey is not a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that If Avery is a knave then Isabella is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Mia is a knave or Aiden is a knave.", "Mia cannot be a knight, because this would contradict the claim of Ethan that Mia is a knave or Aiden is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Isabella is a knave and Aiden is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 4), ('lying', 3)), ('or', ('lying', 7), ('telling-truth', 7)), ('and', ('telling-truth', 1), ('telling-truth', 3)), ('or', ('lying', 5), ('lying', 1)), ('->', ('lying', 2), ('telling-truth', 2)), ('and', ('lying', 4), ('lying', 1)), ('->', ('lying', 7), ('telling-truth', 4)), ('not', ('telling-truth', 6)))", "index": 642}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mason, Michael, Ethan, Abigail, Benjamin, Aria, Daniel, and Aurora. Mason noted, \"If Aurora is a knight then Ethan is a knave\". Michael said that Benjamin is a knave or Mason is a knave. \"If Abigail is a knave then Aurora is a knight,\" Ethan declared. Abigail asserted: \"Benjamin is not a knave\". \"Aurora is not a knight\" - Benjamin. As Aria put it, \"Daniel is not a knight\". Daniel told you that Abigail is a knight. \"If Aria is a knave then Daniel is a knight\" - Aurora. So who is a knight and who is a knave?", "names": ["Mason", "Michael", "Ethan", "Abigail", "Benjamin", "Aria", "Daniel", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true, false, true], "solution_text": "Mason is a knave, Michael is a knight, Ethan is a knight, Abigail is a knave, Benjamin is a knave, Aria is a knight, Daniel is a knave, and Aurora is a knight.", "solution_text_format": "(1) Mason is a knave\n(2) Michael is a knight\n(3) Ethan is a knight\n(4) Abigail is a knave\n(5) Benjamin is a knave\n(6) Aria is a knight\n(7) Daniel is a knave\n(8) Aurora is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that If Aurora is a knight then Ethan is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that If Aria is a knave then Daniel is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Daniel is not a knight.", "Daniel cannot be a knight, because this would contradict the claim of Aria that Daniel is not a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Abigail is a knight.", "Abigail cannot be a knight, because this would contradict the false claim of Daniel that Abigail is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Benjamin is not a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Abigail that Benjamin is not a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Aurora is not a knight.", "Ethan cannot be a knight, because this would contradict the claim of Mason that If Aurora is a knight then Ethan is a knave.", "Ethan cannot be a knave, because this would contradict the false claim of their own that If Abigail is a knave then Aurora is a knight.", "We have exhausted all possibilities for Ethan, Benjamin, Abigail, and Daniel, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Daniel is not a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Benjamin is not a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Aurora is not a knight.", "Benjamin cannot be a knave, because this would contradict the claim of Abigail that Benjamin is not a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the claim of Daniel that Abigail is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the false claim of Aria that Daniel is not a knight.", "We have exhausted all possibilities for Daniel and Aria, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that If Aria is a knave then Daniel is a knight.", "Aria cannot be a knight, because this would contradict the false claim of Aurora that If Aria is a knave then Daniel is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Daniel is not a knight.", "Daniel cannot be a knight, because this would contradict the false claim of Aurora that If Aria is a knave then Daniel is a knight.", "Daniel cannot be a knave, because this would contradict the false claim of Aria that Daniel is not a knight.", "We have exhausted all possibilities for Daniel, Aria, and Aurora, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that If Aurora is a knight then Ethan is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that If Aria is a knave then Daniel is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Daniel is not a knight.", "Daniel cannot be a knight, because this would contradict the claim of Aria that Daniel is not a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Abigail is a knight.", "Abigail cannot be a knight, because this would contradict the false claim of Daniel that Abigail is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Benjamin is not a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Abigail that Benjamin is not a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Aurora is not a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If Abigail is a knave then Aurora is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Benjamin is a knave or Mason is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 7), ('lying', 2)), ('or', ('lying', 4), ('lying', 0)), ('->', ('lying', 3), ('telling-truth', 7)), ('not', ('lying', 4)), ('not', ('telling-truth', 7)), ('not', ('telling-truth', 6)), ('telling-truth', 3), ('->', ('lying', 5), ('telling-truth', 6)))", "index": 643}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aria, Ella, Aurora, Jackson, Sofia, Sophia, Lily, and Matthew. In a statement by Aria: \"Sophia is a knave\". In Ella's words: \"If Matthew is a knight then Aurora is a knight\". Aurora told you that Jackson is not a knave. \"Sofia is a knight or Ella is a knight,\" Jackson declared. According to Sofia, \"Sophia is a knight if and only if Aria is a knave\". \"Matthew is a knight\" - Sophia. Lily told you that Matthew is a knave if and only if Ella is a knight. Matthew remarked, \"Ella is a knave and Ella is a knight\". So who is a knight and who is a knave?", "names": ["Aria", "Ella", "Aurora", "Jackson", "Sofia", "Sophia", "Lily", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false, true, false], "solution_text": "Aria is a knight, Ella is a knight, Aurora is a knight, Jackson is a knight, Sofia is a knight, Sophia is a knave, Lily is a knight, and Matthew is a knave.", "solution_text_format": "(1) Aria is a knight\n(2) Ella is a knight\n(3) Aurora is a knight\n(4) Jackson is a knight\n(5) Sofia is a knight\n(6) Sophia is a knave\n(7) Lily is a knight\n(8) Matthew is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that Sophia is a knave.", "Sophia cannot be a knight, because this would contradict the claim of Aria that Sophia is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the false claim of Sophia that Matthew is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Ella is a knave and Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that If Matthew is a knight then Aurora is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Jackson is not a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Sofia is a knight or Ella is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Sophia is a knight if and only if Aria is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Matthew is a knave if and only if Ella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 5), ('->', ('telling-truth', 7), ('telling-truth', 2)), ('not', ('lying', 3)), ('or', ('telling-truth', 4), ('telling-truth', 1)), ('<=>', ('telling-truth', 5), ('lying', 0)), ('telling-truth', 7), ('<=>', ('lying', 7), ('telling-truth', 1)), ('and', ('lying', 1), ('telling-truth', 1)))", "index": 644}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emma, Charlotte, Sophia, Sofia, Emily, Michael, Sebastian, and Evelyn. \"Sophia is a knave and Sofia is a knave,\" Emma declared. As Charlotte put it, \"Emma is not a knave\". Sophia said, \"Charlotte is a knave and Emma is a knight.\" In a statement by Sofia: \"Charlotte is a knight if and only if Sebastian is a knave\". Emily stated, \"Evelyn is a knight\". \"Sophia is a knave or Emma is a knave,\" Michael mentioned. \"Charlotte is a knight,\" Sebastian mentioned. Evelyn commented, \"Emma is a knight and Emma is a knave\". So who is a knight and who is a knave?", "names": ["Emma", "Charlotte", "Sophia", "Sofia", "Emily", "Michael", "Sebastian", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, true, true, false], "solution_text": "Emma is a knight, Charlotte is a knight, Sophia is a knave, Sofia is a knave, Emily is a knave, Michael is a knight, Sebastian is a knight, and Evelyn is a knave.", "solution_text_format": "(1) Emma is a knight\n(2) Charlotte is a knight\n(3) Sophia is a knave\n(4) Sofia is a knave\n(5) Emily is a knave\n(6) Michael is a knight\n(7) Sebastian is a knight\n(8) Evelyn is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Sophia is a knave and Sofia is a knave.", "Sophia cannot be a knight, because this would contradict the claim of Emma that Sophia is a knave and Sofia is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Charlotte is a knave and Emma is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Emma is not a knave.", "Sofia cannot be a knight, because this would contradict the claim of Emma that Sophia is a knave and Sofia is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Charlotte is a knight if and only if Sebastian is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Charlotte is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Evelyn is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Emma is a knight and Emma is a knave.", "Evelyn cannot be a knave, because this would contradict the claim of Emily that Evelyn is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Evelyn is a knight.", "Evelyn cannot be a knight, because this would contradict the false claim of Emily that Evelyn is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Emma is a knight and Emma is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Sophia is a knave or Emma is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('lying', 3)), ('not', ('lying', 0)), ('and', ('lying', 1), ('telling-truth', 0)), ('<=>', ('telling-truth', 1), ('lying', 6)), ('telling-truth', 7), ('or', ('lying', 2), ('lying', 0)), ('telling-truth', 1), ('and', ('telling-truth', 0), ('lying', 0)))", "index": 645}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Noah, Joseph, Charlotte, Ethan, Penelope, Sophia, Lucas, and Scarlett. Noah expressed that Ethan is a knight. Joseph said that Ethan is a knight and Lucas is a knight. Charlotte expressed that If Noah is a knave then Scarlett is a knight. As Ethan put it, \"Penelope is a knave and Scarlett is a knave\". Penelope said, \"Joseph is a knight or Charlotte is a knave.\" Sophia asserted: \"Noah is a knight or Scarlett is a knave\". Lucas expressed that Scarlett is a knave and Sophia is a knight. Scarlett stated, \"Lucas is a knight if and only if Sophia is a knave\". So who is a knight and who is a knave?", "names": ["Noah", "Joseph", "Charlotte", "Ethan", "Penelope", "Sophia", "Lucas", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, true, true, false], "solution_text": "Noah is a knave, Joseph is a knave, Charlotte is a knave, Ethan is a knave, Penelope is a knight, Sophia is a knight, Lucas is a knight, and Scarlett is a knave.", "solution_text_format": "(1) Noah is a knave\n(2) Joseph is a knave\n(3) Charlotte is a knave\n(4) Ethan is a knave\n(5) Penelope is a knight\n(6) Sophia is a knight\n(7) Lucas is a knight\n(8) Scarlett is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Noah is a knight. No contradiction is found in their claim that Ethan is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Penelope is a knave and Scarlett is a knave.", "Penelope cannot be a knight, because this would contradict the claim of Ethan that Penelope is a knave and Scarlett is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Joseph is a knight or Charlotte is a knave.", "Joseph cannot be a knight, because this would contradict the false claim of Penelope that Joseph is a knight or Charlotte is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Ethan is a knight and Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of Joseph that Ethan is a knight and Lucas is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Scarlett is a knave and Sophia is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of Ethan that Penelope is a knave and Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Lucas is a knight if and only if Sophia is a knave.", "Sophia cannot be a knight, because this would contradict the false claim of Lucas that Scarlett is a knave and Sophia is a knight.", "Sophia cannot be a knave, because this would contradict the false claim of their own that Noah is a knight or Scarlett is a knave.", "We have exhausted all possibilities for Sophia, Scarlett, Lucas, Joseph, and Penelope, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the claim of Noah that Ethan is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Ethan is a knight.", "Ethan cannot be a knight, because this would contradict the false claim of Noah that Ethan is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Penelope is a knave and Scarlett is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Joseph is a knight or Charlotte is a knave.", "Joseph cannot be a knight, because this would contradict the claim of their own that Ethan is a knight and Lucas is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Ethan is a knight and Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Scarlett is a knave and Sophia is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of Lucas that Scarlett is a knave and Sophia is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Lucas is a knight if and only if Sophia is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Noah is a knight or Scarlett is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that If Noah is a knave then Scarlett is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that If Noah is a knave then Scarlett is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 3), ('and', ('telling-truth', 3), ('telling-truth', 6)), ('->', ('lying', 0), ('telling-truth', 7)), ('and', ('lying', 4), ('lying', 7)), ('or', ('telling-truth', 1), ('lying', 2)), ('or', ('telling-truth', 0), ('lying', 7)), ('and', ('lying', 7), ('telling-truth', 5)), ('<=>', ('telling-truth', 6), ('lying', 5)))", "index": 646}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jack, Harper, Charlotte, Matthew, William, Samuel, David, and Emma. According to Jack, \"If Emma is a knight then Samuel is a knave\". Harper stated, \"Charlotte is a knave or Jack is a knight\". \"Emma is not a knight\" - Charlotte. According to Matthew, \"Jack is a knight if and only if Samuel is a knave\". William remarked, \"Harper is a knight\". As Samuel put it, \"Matthew is not a knight\". In David's words: \"Jack is not a knight\". Emma asserted: \"David is a knave if and only if William is a knight\". So who is a knight and who is a knave?", "names": ["Jack", "Harper", "Charlotte", "Matthew", "William", "Samuel", "David", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false, false, true], "solution_text": "Jack is a knight, Harper is a knight, Charlotte is a knave, Matthew is a knight, William is a knight, Samuel is a knave, David is a knave, and Emma is a knight.", "solution_text_format": "(1) Jack is a knight\n(2) Harper is a knight\n(3) Charlotte is a knave\n(4) Matthew is a knight\n(5) William is a knight\n(6) Samuel is a knave\n(7) David is a knave\n(8) Emma is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that If Emma is a knight then Samuel is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that David is a knave if and only if William is a knight.", "David cannot be a knight, because this would contradict the claim of their own that Jack is not a knight.", "Assume David is a knave. No contradiction is found in their false claim that Jack is not a knight.", "Assume William is a knight. No contradiction is found in their claim that Harper is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Charlotte is a knave or Jack is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Emma is not a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Emma is not a knight.", "Samuel cannot be a knight, because this would contradict the claim of Jack that If Emma is a knight then Samuel is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Matthew is not a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Jack is a knight if and only if Samuel is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 7), ('lying', 5)), ('or', ('lying', 2), ('telling-truth', 0)), ('not', ('telling-truth', 7)), ('<=>', ('telling-truth', 0), ('lying', 5)), ('telling-truth', 1), ('not', ('telling-truth', 3)), ('not', ('telling-truth', 0)), ('<=>', ('lying', 6), ('telling-truth', 4)))", "index": 647}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: William, Oliver, Henry, Mia, Chloe, Grace, Emily, and Scarlett. William told you that Henry is not a knave. Oliver asserted: \"Emily is not a knight\". \"Oliver is not a knave\" - Henry. \"If Henry is a knave then Oliver is a knave,\" Mia claimed. Chloe remarked, \"William is a knave if and only if Henry is a knight\". Grace said, \"Mia is a knight if and only if Henry is a knave.\" \"Mia is a knave and Grace is a knave,\" Emily claimed. Scarlett stated, \"Oliver is not a knight\". So who is a knight and who is a knave?", "names": ["William", "Oliver", "Henry", "Mia", "Chloe", "Grace", "Emily", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false, false, false], "solution_text": "William is a knight, Oliver is a knight, Henry is a knight, Mia is a knight, Chloe is a knave, Grace is a knave, Emily is a knave, and Scarlett is a knave.", "solution_text_format": "(1) William is a knight\n(2) Oliver is a knight\n(3) Henry is a knight\n(4) Mia is a knight\n(5) Chloe is a knave\n(6) Grace is a knave\n(7) Emily is a knave\n(8) Scarlett is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Henry is not a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Oliver is not a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Emily is not a knight.", "Emily cannot be a knight, because this would contradict the claim of Oliver that Emily is not a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Mia is a knave and Grace is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that If Henry is a knave then Oliver is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Mia is a knight if and only if Henry is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Mia is a knight if and only if Henry is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that William is a knave if and only if Henry is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that William is a knave if and only if Henry is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Oliver is not a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Oliver is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('not', ('telling-truth', 6)), ('not', ('lying', 1)), ('->', ('lying', 2), ('lying', 1)), ('<=>', ('lying', 0), ('telling-truth', 2)), ('<=>', ('telling-truth', 3), ('lying', 2)), ('and', ('lying', 3), ('lying', 5)), ('not', ('telling-truth', 1)))", "index": 648}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Isabella, Mason, Luke, Matthew, Joseph, Henry, Zoey, and Evelyn. In Isabella's words: \"Mason is a knight\". In Mason's words: \"Zoey is a knave or Isabella is a knave\". \"Matthew is not a knight,\" Luke claimed. \"Isabella is a knave\" - Matthew. \"Isabella is a knave if and only if Matthew is a knave,\" Joseph declared. Henry expressed that Luke is a knave if and only if Evelyn is a knight. \"If Evelyn is a knight then Matthew is a knight\" - Zoey. As Evelyn put it, \"Matthew is a knave if and only if Luke is a knight\". So who is a knight and who is a knave?", "names": ["Isabella", "Mason", "Luke", "Matthew", "Joseph", "Henry", "Zoey", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false, false, true], "solution_text": "Isabella is a knight, Mason is a knight, Luke is a knight, Matthew is a knave, Joseph is a knave, Henry is a knave, Zoey is a knave, and Evelyn is a knight.", "solution_text_format": "(1) Isabella is a knight\n(2) Mason is a knight\n(3) Luke is a knight\n(4) Matthew is a knave\n(5) Joseph is a knave\n(6) Henry is a knave\n(7) Zoey is a knave\n(8) Evelyn is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Mason is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Zoey is a knave or Isabella is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Mason that Zoey is a knave or Isabella is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that If Evelyn is a knight then Matthew is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Matthew is a knave if and only if Luke is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Isabella is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Isabella is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Matthew is not a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Isabella is a knave if and only if Matthew is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Isabella is a knave if and only if Matthew is a knave.", "Henry cannot be a knight, because this would contradict the claim of their own that Luke is a knave if and only if Evelyn is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Luke is a knave if and only if Evelyn is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('or', ('lying', 6), ('lying', 0)), ('not', ('telling-truth', 3)), ('lying', 0), ('<=>', ('lying', 0), ('lying', 3)), ('<=>', ('lying', 2), ('telling-truth', 7)), ('->', ('telling-truth', 7), ('telling-truth', 3)), ('<=>', ('lying', 3), ('telling-truth', 2)))", "index": 649}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Amelia, Owen, Mason, Aurora, Olivia, Isabella, Sophia, and Matthew. \"Matthew is a knight\" - Amelia. Owen asserted: \"Olivia is a knave\". In Mason's words: \"Sophia is not a knight\". In Aurora's words: \"Amelia is not a knight\". Olivia was heard saying, \"Mason is not a knave\". Isabella told you that Aurora is a knight and Sophia is a knight. Sophia stated, \"If Isabella is a knight then Isabella is a knave\". Matthew commented, \"If Aurora is a knight then Mason is a knight\". So who is a knight and who is a knave?", "names": ["Amelia", "Owen", "Mason", "Aurora", "Olivia", "Isabella", "Sophia", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, false, true, true], "solution_text": "Amelia is a knight, Owen is a knight, Mason is a knave, Aurora is a knave, Olivia is a knave, Isabella is a knave, Sophia is a knight, and Matthew is a knight.", "solution_text_format": "(1) Amelia is a knight\n(2) Owen is a knight\n(3) Mason is a knave\n(4) Aurora is a knave\n(5) Olivia is a knave\n(6) Isabella is a knave\n(7) Sophia is a knight\n(8) Matthew is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Amelia is a knight. No contradiction is found in their claim that Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that If Aurora is a knight then Mason is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Amelia is not a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Amelia is not a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Sophia is not a knight.", "Sophia cannot be a knight, because this would contradict the claim of Mason that Sophia is not a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that If Isabella is a knight then Isabella is a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that Aurora is a knight and Sophia is a knight.", "Isabella cannot be a knave, because this would contradict the false claim of Sophia that If Isabella is a knight then Isabella is a knave.", "We have exhausted all possibilities for Isabella and Sophia, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Sophia is not a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that If Isabella is a knight then Isabella is a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that Aurora is a knight and Sophia is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Aurora is a knight and Sophia is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Owen that Olivia is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Mason is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 7), ('lying', 4), ('not', ('telling-truth', 6)), ('not', ('telling-truth', 0)), ('not', ('lying', 2)), ('and', ('telling-truth', 3), ('telling-truth', 6)), ('->', ('telling-truth', 5), ('lying', 5)), ('->', ('telling-truth', 3), ('telling-truth', 2)))", "index": 650}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Luke, Elizabeth, Jackson, Chloe, Emily, Jacob, William, and Isabella. \"William is a knave or Jacob is a knight\" - Luke. Elizabeth stated, \"Chloe is a knight if and only if Jackson is a knave\". \"Emily is a knight if and only if Luke is a knight,\" Jackson mentioned. Chloe noted, \"Emily is a knight and Elizabeth is a knight\". In Emily's words: \"Elizabeth is a knave\". In Jacob's words: \"If Elizabeth is a knave then Luke is a knight\". William expressed that Isabella is a knave if and only if Emily is a knight. Isabella asserted: \"Emily is a knave\". So who is a knight and who is a knave?", "names": ["Luke", "Elizabeth", "Jackson", "Chloe", "Emily", "Jacob", "William", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, false, true, false], "solution_text": "Luke is a knave, Elizabeth is a knave, Jackson is a knave, Chloe is a knave, Emily is a knight, Jacob is a knave, William is a knight, and Isabella is a knave.", "solution_text_format": "(1) Luke is a knave\n(2) Elizabeth is a knave\n(3) Jackson is a knave\n(4) Chloe is a knave\n(5) Emily is a knight\n(6) Jacob is a knave\n(7) William is a knight\n(8) Isabella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that William is a knave or Jacob is a knight.", "Assume William is a knight. No contradiction is found in their claim that Isabella is a knave if and only if Emily is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of William that Isabella is a knave if and only if Emily is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Elizabeth is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Chloe is a knight if and only if Jackson is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Emily is a knight and Elizabeth is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Emily is a knight and Elizabeth is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Emily is a knight if and only if Luke is a knight.", "Jackson cannot be a knave, because this would contradict the claim of Elizabeth that Chloe is a knight if and only if Jackson is a knave.", "We have exhausted all possibilities for Jackson and Chloe, so let us go back and reconsider Elizabeth.", "Elizabeth cannot be a knave, because this would contradict the false claim of Emily that Elizabeth is a knave.", "We have exhausted all possibilities for Elizabeth and Emily, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Elizabeth is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of Emily that Elizabeth is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Chloe is a knight if and only if Jackson is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Emily is a knight and Elizabeth is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Emily is a knight and Elizabeth is a knight.", "Jackson cannot be a knight, because this would contradict the false claim of Elizabeth that Chloe is a knight if and only if Jackson is a knave.", "Jackson cannot be a knave, because this would contradict the false claim of their own that Emily is a knight if and only if Luke is a knight.", "We have exhausted all possibilities for Jackson, Chloe, and Elizabeth, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the claim of William that Isabella is a knave if and only if Emily is a knight.", "We have exhausted all possibilities for Emily and Isabella, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Isabella is a knave if and only if Emily is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of Isabella that Emily is a knave.", "Emily cannot be a knave, because this would contradict the false claim of William that Isabella is a knave if and only if Emily is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Emily is a knave.", "Emily cannot be a knight, because this would contradict the false claim of William that Isabella is a knave if and only if Emily is a knight.", "Emily cannot be a knave, because this would contradict the false claim of Isabella that Emily is a knave.", "We have exhausted all possibilities for Emily, Isabella, and William, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that William is a knave or Jacob is a knight.", "Assume William is a knight. No contradiction is found in their claim that Isabella is a knave if and only if Emily is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of William that Isabella is a knave if and only if Emily is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Elizabeth is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Chloe is a knight if and only if Jackson is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Emily is a knight and Elizabeth is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Emily is a knight and Elizabeth is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Emily is a knight if and only if Luke is a knight.", "Jacob cannot be a knight, because this would contradict the false claim of Luke that William is a knave or Jacob is a knight.", "Jacob cannot be a knave, because this would contradict the false claim of their own that If Elizabeth is a knave then Luke is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Jackson.", "Jackson cannot be a knave, because this would contradict the claim of Elizabeth that Chloe is a knight if and only if Jackson is a knave.", "We have exhausted all possibilities for Jackson and Chloe, so let us go back and reconsider Elizabeth.", "Elizabeth cannot be a knave, because this would contradict the false claim of Emily that Elizabeth is a knave.", "We have exhausted all possibilities for Elizabeth and Emily, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Elizabeth is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of Emily that Elizabeth is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Chloe is a knight if and only if Jackson is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Emily is a knight and Elizabeth is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Emily is a knight and Elizabeth is a knight.", "Jackson cannot be a knight, because this would contradict the false claim of Elizabeth that Chloe is a knight if and only if Jackson is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Emily is a knight if and only if Luke is a knight.", "Jacob cannot be a knight, because this would contradict the false claim of Luke that William is a knave or Jacob is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that If Elizabeth is a knave then Luke is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 6), ('telling-truth', 5)), ('<=>', ('telling-truth', 3), ('lying', 2)), ('<=>', ('telling-truth', 4), ('telling-truth', 0)), ('and', ('telling-truth', 4), ('telling-truth', 1)), ('lying', 1), ('->', ('lying', 1), ('telling-truth', 0)), ('<=>', ('lying', 7), ('telling-truth', 4)), ('lying', 4))", "index": 651}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Logan, Penelope, Sophia, Olivia, Emily, David, Lucas, and Oliver. Logan told you that Oliver is not a knave. \"If Logan is a knave then Lucas is a knight,\" Penelope mentioned. \"Oliver is a knave if and only if Olivia is a knight,\" Sophia claimed. In a statement by Olivia: \"Logan is a knave if and only if Penelope is a knave\". Emily told you that Olivia is a knight if and only if Emily is a knight. David remarked, \"Oliver is a knight and Penelope is a knight\". As Lucas put it, \"David is a knight or Emily is a knight\". In Oliver's words: \"Emily is not a knight\". So who is a knight and who is a knave?", "names": ["Logan", "Penelope", "Sophia", "Olivia", "Emily", "David", "Lucas", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true, true, true], "solution_text": "Logan is a knight, Penelope is a knight, Sophia is a knave, Olivia is a knight, Emily is a knave, David is a knight, Lucas is a knight, and Oliver is a knight.", "solution_text_format": "(1) Logan is a knight\n(2) Penelope is a knight\n(3) Sophia is a knave\n(4) Olivia is a knight\n(5) Emily is a knave\n(6) David is a knight\n(7) Lucas is a knight\n(8) Oliver is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that Oliver is not a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Emily is not a knight.", "Emily cannot be a knight, because this would contradict the claim of Oliver that Emily is not a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Olivia is a knight if and only if Emily is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Logan is a knave if and only if Penelope is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that If Logan is a knave then Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that David is a knight or Emily is a knight.", "Assume David is a knight. No contradiction is found in their claim that Oliver is a knight and Penelope is a knight.", "Sophia cannot be a knight, because this would contradict the claim of their own that Oliver is a knave if and only if Olivia is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Oliver is a knave if and only if Olivia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 7)), ('->', ('lying', 0), ('telling-truth', 6)), ('<=>', ('lying', 7), ('telling-truth', 3)), ('<=>', ('lying', 0), ('lying', 1)), ('<=>', ('telling-truth', 3), ('telling-truth', 4)), ('and', ('telling-truth', 7), ('telling-truth', 1)), ('or', ('telling-truth', 5), ('telling-truth', 4)), ('not', ('telling-truth', 4)))", "index": 652}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Scarlett, Mason, Mia, Grace, Aurora, Abigail, Ella, and Jack. Scarlett stated, \"Grace is a knave\". Mason expressed that Jack is a knave and Scarlett is a knight. \"Scarlett is a knave or Mia is a knight\" - Mia. Grace stated, \"Mia is a knight or Abigail is a knight\". Aurora expressed that Mia is a knave and Scarlett is a knight. In Abigail's words: \"Grace is a knight or Jack is a knave\". Ella stated, \"If Grace is a knave then Jack is a knight\". In a statement by Jack: \"If Jack is a knight then Abigail is a knight\". So who is a knight and who is a knave?", "names": ["Scarlett", "Mason", "Mia", "Grace", "Aurora", "Abigail", "Ella", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, true, true, true], "solution_text": "Scarlett is a knave, Mason is a knave, Mia is a knight, Grace is a knight, Aurora is a knave, Abigail is a knight, Ella is a knight, and Jack is a knight.", "solution_text_format": "(1) Scarlett is a knave\n(2) Mason is a knave\n(3) Mia is a knight\n(4) Grace is a knight\n(5) Aurora is a knave\n(6) Abigail is a knight\n(7) Ella is a knight\n(8) Jack is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Grace is a knave.", "Grace cannot be a knight, because this would contradict the claim of Scarlett that Grace is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Mia is a knight or Abigail is a knight.", "Mia cannot be a knight, because this would contradict the false claim of Grace that Mia is a knight or Abigail is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Scarlett is a knave or Mia is a knight.", "Abigail cannot be a knight, because this would contradict the false claim of Grace that Mia is a knight or Abigail is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Grace is a knight or Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that If Jack is a knight then Abigail is a knight.", "Jack cannot be a knave, because this would contradict the false claim of Abigail that Grace is a knight or Jack is a knave.", "We have exhausted all possibilities for Jack, Abigail, Mia, and Grace, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Grace is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Mia is a knight or Abigail is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Scarlett is a knave or Mia is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Grace is a knight or Jack is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that If Jack is a knight then Abigail is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Jack is a knave and Scarlett is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Jack is a knave and Scarlett is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Mia is a knave and Scarlett is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Mia is a knave and Scarlett is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that If Grace is a knave then Jack is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('and', ('lying', 7), ('telling-truth', 0)), ('or', ('lying', 0), ('telling-truth', 2)), ('or', ('telling-truth', 2), ('telling-truth', 5)), ('and', ('lying', 2), ('telling-truth', 0)), ('or', ('telling-truth', 3), ('lying', 7)), ('->', ('lying', 3), ('telling-truth', 7)), ('->', ('telling-truth', 7), ('telling-truth', 5)))", "index": 653}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emma, Emily, Amelia, Owen, Chloe, Mason, Sebastian, and Benjamin. In a statement by Emma: \"Chloe is a knight if and only if Mason is a knave\". Emily commented, \"Benjamin is a knight if and only if Emma is a knave\". Amelia told you that Emma is a knight. As Owen put it, \"Chloe is not a knave\". In Chloe's words: \"If Benjamin is a knight then Chloe is a knight\". \"Emma is a knave or Owen is a knave,\" Mason declared. \"Owen is a knight,\" Sebastian declared. Benjamin remarked, \"Emma is a knave or Emily is a knight\". So who is a knight and who is a knave?", "names": ["Emma", "Emily", "Amelia", "Owen", "Chloe", "Mason", "Sebastian", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true, true, true], "solution_text": "Emma is a knave, Emily is a knight, Amelia is a knave, Owen is a knight, Chloe is a knight, Mason is a knight, Sebastian is a knight, and Benjamin is a knight.", "solution_text_format": "(1) Emma is a knave\n(2) Emily is a knight\n(3) Amelia is a knave\n(4) Owen is a knight\n(5) Chloe is a knight\n(6) Mason is a knight\n(7) Sebastian is a knight\n(8) Benjamin is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Chloe is a knight if and only if Mason is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that If Benjamin is a knight then Chloe is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Emma is a knave or Emily is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight if and only if Emma is a knave.", "Emily cannot be a knave, because this would contradict the claim of Benjamin that Emma is a knave or Emily is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Emma is a knave or Emily is a knight.", "Emily cannot be a knight, because this would contradict the false claim of Benjamin that Emma is a knave or Emily is a knight.", "Emily cannot be a knave, because this would contradict the false claim of their own that Benjamin is a knight if and only if Emma is a knave.", "We have exhausted all possibilities for Emily and Benjamin, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that If Benjamin is a knight then Chloe is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Emma is a knave or Emily is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight if and only if Emma is a knave.", "Emily cannot be a knave, because this would contradict the claim of Benjamin that Emma is a knave or Emily is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the false claim of Chloe that If Benjamin is a knight then Chloe is a knight.", "We have exhausted all possibilities for Benjamin and Chloe, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Chloe is a knight if and only if Mason is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that If Benjamin is a knight then Chloe is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Emma is a knave or Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Benjamin is a knight if and only if Emma is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Emma is a knave or Owen is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Chloe is not a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Emma is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Emma is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Owen is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 4), ('lying', 5)), ('<=>', ('telling-truth', 7), ('lying', 0)), ('telling-truth', 0), ('not', ('lying', 4)), ('->', ('telling-truth', 7), ('telling-truth', 4)), ('or', ('lying', 0), ('lying', 3)), ('telling-truth', 3), ('or', ('lying', 0), ('telling-truth', 1)))", "index": 654}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: James, Owen, Sophia, Alexander, Scarlett, Victoria, Sebastian, and Mason. \"Mason is a knave and Owen is a knight,\" James mentioned. \"Scarlett is a knight and Scarlett is a knave,\" Owen declared. Sophia remarked, \"Owen is a knave\". Alexander commented, \"Owen is not a knight\". \"Alexander is a knave\" - Scarlett. Victoria stated, \"James is a knight and Alexander is a knave\". Sebastian noted, \"If Sophia is a knave then James is a knave\". In Mason's words: \"Victoria is not a knight\". So who is a knight and who is a knave?", "names": ["James", "Owen", "Sophia", "Alexander", "Scarlett", "Victoria", "Sebastian", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false, true, true], "solution_text": "James is a knave, Owen is a knave, Sophia is a knight, Alexander is a knight, Scarlett is a knave, Victoria is a knave, Sebastian is a knight, and Mason is a knight.", "solution_text_format": "(1) James is a knave\n(2) Owen is a knave\n(3) Sophia is a knight\n(4) Alexander is a knight\n(5) Scarlett is a knave\n(6) Victoria is a knave\n(7) Sebastian is a knight\n(8) Mason is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Mason is a knave and Owen is a knight.", "Mason cannot be a knight, because this would contradict the claim of James that Mason is a knave and Owen is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Victoria is not a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that James is a knight and Alexander is a knave.", "Alexander cannot be a knight, because this would contradict the claim of Victoria that James is a knight and Alexander is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Owen is not a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight and Scarlett is a knave.", "Owen cannot be a knave, because this would contradict the claim of James that Mason is a knave and Owen is a knight.", "We have exhausted all possibilities for Owen and Alexander, so let us go back and reconsider Victoria.", "Victoria cannot be a knave, because this would contradict the false claim of Mason that Victoria is not a knight.", "We have exhausted all possibilities for Victoria and Mason, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Mason is a knave and Owen is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Victoria is not a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that James is a knight and Alexander is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that James is a knight and Alexander is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Owen is not a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight and Scarlett is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Scarlett is a knight and Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Alexander is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Alexander is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Owen is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Sophia is a knave then James is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 7), ('telling-truth', 1)), ('and', ('telling-truth', 4), ('lying', 4)), ('lying', 1), ('not', ('telling-truth', 1)), ('lying', 3), ('and', ('telling-truth', 0), ('lying', 3)), ('->', ('lying', 2), ('lying', 0)), ('not', ('telling-truth', 5)))", "index": 655}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: David, Penelope, Aria, Avery, Oliver, Isabella, Emma, and Zoey. David expressed that Emma is a knave. Penelope told you that Aria is not a knight. \"David is a knight if and only if David is a knave\" - Aria. Avery noted, \"Aria is a knight and Zoey is a knight\". Oliver asserted: \"Isabella is a knave if and only if Avery is a knight\". Isabella commented, \"Aria is not a knave\". Emma said that If Penelope is a knave then Isabella is a knave. \"Penelope is not a knight,\" Zoey mentioned. So who is a knight and who is a knave?", "names": ["David", "Penelope", "Aria", "Avery", "Oliver", "Isabella", "Emma", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, false, true, false], "solution_text": "David is a knave, Penelope is a knight, Aria is a knave, Avery is a knave, Oliver is a knave, Isabella is a knave, Emma is a knight, and Zoey is a knave.", "solution_text_format": "(1) David is a knave\n(2) Penelope is a knight\n(3) Aria is a knave\n(4) Avery is a knave\n(5) Oliver is a knave\n(6) Isabella is a knave\n(7) Emma is a knight\n(8) Zoey is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of David that Emma is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that If Penelope is a knave then Isabella is a knave.", "Penelope cannot be a knight, because this would contradict the false claim of Emma that If Penelope is a knave then Isabella is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Aria is not a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that David is a knight if and only if David is a knave.", "Aria cannot be a knave, because this would contradict the false claim of Penelope that Aria is not a knight.", "We have exhausted all possibilities for Aria, Penelope, and Emma, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Emma is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that If Penelope is a knave then Isabella is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Aria is not a knight.", "Aria cannot be a knight, because this would contradict the claim of Penelope that Aria is not a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that David is a knight if and only if David is a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that Aria is not a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Aria is not a knave.", "Avery cannot be a knight, because this would contradict the claim of their own that Aria is a knight and Zoey is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Aria is a knight and Zoey is a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that Penelope is not a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Penelope is not a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Isabella is a knave if and only if Avery is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Isabella is a knave if and only if Avery is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 6), ('not', ('telling-truth', 2)), ('<=>', ('telling-truth', 0), ('lying', 0)), ('and', ('telling-truth', 2), ('telling-truth', 7)), ('<=>', ('lying', 5), ('telling-truth', 3)), ('not', ('lying', 2)), ('->', ('lying', 1), ('lying', 5)), ('not', ('telling-truth', 1)))", "index": 656}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Logan, Olivia, Owen, Noah, Lily, Lucas, Penelope, and Emma. In a statement by Logan: \"Logan is a knight if and only if Olivia is a knave\". Olivia remarked, \"If Owen is a knight then Penelope is a knight\". Owen asserted: \"Logan is a knave or Penelope is a knave\". \"Logan is a knave or Olivia is a knight,\" Noah mentioned. Lily said, \"Noah is not a knight.\" Lucas noted, \"Logan is a knight if and only if Noah is a knave\". \"Lily is a knight if and only if Olivia is a knight,\" Penelope declared. Emma remarked, \"If Owen is a knave then Olivia is a knave\". So who is a knight and who is a knave?", "names": ["Logan", "Olivia", "Owen", "Noah", "Lily", "Lucas", "Penelope", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true, false, true], "solution_text": "Logan is a knight, Olivia is a knave, Owen is a knight, Noah is a knave, Lily is a knight, Lucas is a knight, Penelope is a knave, and Emma is a knight.", "solution_text_format": "(1) Logan is a knight\n(2) Olivia is a knave\n(3) Owen is a knight\n(4) Noah is a knave\n(5) Lily is a knight\n(6) Lucas is a knight\n(7) Penelope is a knave\n(8) Emma is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that Logan is a knight if and only if Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Logan that Logan is a knight if and only if Olivia is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that If Owen is a knight then Penelope is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Logan is a knave or Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the false claim of Olivia that If Owen is a knight then Penelope is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Lily is a knight if and only if Olivia is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Noah is not a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that Logan is a knave or Olivia is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Logan is a knave or Olivia is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Logan is a knight if and only if Noah is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that If Owen is a knave then Olivia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 0), ('lying', 1)), ('->', ('telling-truth', 2), ('telling-truth', 6)), ('or', ('lying', 0), ('lying', 6)), ('or', ('lying', 0), ('telling-truth', 1)), ('not', ('telling-truth', 3)), ('<=>', ('telling-truth', 0), ('lying', 3)), ('<=>', ('telling-truth', 4), ('telling-truth', 1)), ('->', ('lying', 2), ('lying', 1)))", "index": 657}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Evelyn, James, Elizabeth, Avery, Lucas, Michael, Daniel, and Aurora. Evelyn was heard saying, \"Aurora is not a knave\". According to James, \"Elizabeth is a knight and Aurora is a knave\". Elizabeth said that Michael is a knave and Lucas is a knave. According to Avery, \"Avery is a knight if and only if Evelyn is a knight\". Lucas stated, \"Evelyn is not a knave\". Michael said that Evelyn is a knight if and only if Lucas is a knave. According to Daniel, \"Aurora is a knave and Evelyn is a knave\". Aurora was heard saying, \"Avery is a knight if and only if Elizabeth is a knave\". So who is a knight and who is a knave?", "names": ["Evelyn", "James", "Elizabeth", "Avery", "Lucas", "Michael", "Daniel", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false, false, true], "solution_text": "Evelyn is a knight, James is a knave, Elizabeth is a knave, Avery is a knight, Lucas is a knight, Michael is a knave, Daniel is a knave, and Aurora is a knight.", "solution_text_format": "(1) Evelyn is a knight\n(2) James is a knave\n(3) Elizabeth is a knave\n(4) Avery is a knight\n(5) Lucas is a knight\n(6) Michael is a knave\n(7) Daniel is a knave\n(8) Aurora is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Aurora is not a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Avery is a knight if and only if Elizabeth is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Avery is a knight if and only if Evelyn is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Aurora that Avery is a knight if and only if Elizabeth is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Michael is a knave and Lucas is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Evelyn is a knight if and only if Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the claim of Michael that Evelyn is a knight if and only if Lucas is a knave.", "Lucas cannot be a knave, because this would contradict the false claim of their own that Evelyn is not a knave.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Evelyn is a knight if and only if Lucas is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Evelyn is not a knave.", "James cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight and Aurora is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Elizabeth is a knight and Aurora is a knave.", "Daniel cannot be a knight, because this would contradict the claim of their own that Aurora is a knave and Evelyn is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Aurora is a knave and Evelyn is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 7)), ('and', ('telling-truth', 2), ('lying', 7)), ('and', ('lying', 5), ('lying', 4)), ('<=>', ('telling-truth', 3), ('telling-truth', 0)), ('not', ('lying', 0)), ('<=>', ('telling-truth', 0), ('lying', 4)), ('and', ('lying', 7), ('lying', 0)), ('<=>', ('telling-truth', 3), ('lying', 2)))", "index": 658}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jack, Logan, Oliver, Abigail, David, Victoria, Elizabeth, and Emma. Jack expressed that David is a knight if and only if Jack is a knight. Logan expressed that Emma is a knight. In Oliver's words: \"Abigail is a knight if and only if Elizabeth is a knight\". Abigail stated, \"Jack is a knave\". In a statement by David: \"Abigail is not a knave\". Victoria stated, \"Emma is a knave or David is a knave\". Elizabeth expressed that Logan is a knight or Emma is a knight. Emma was heard saying, \"Jack is a knave or David is a knight\". So who is a knight and who is a knave?", "names": ["Jack", "Logan", "Oliver", "Abigail", "David", "Victoria", "Elizabeth", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false, true, true], "solution_text": "Jack is a knave, Logan is a knight, Oliver is a knight, Abigail is a knight, David is a knight, Victoria is a knave, Elizabeth is a knight, and Emma is a knight.", "solution_text_format": "(1) Jack is a knave\n(2) Logan is a knight\n(3) Oliver is a knight\n(4) Abigail is a knight\n(5) David is a knight\n(6) Victoria is a knave\n(7) Elizabeth is a knight\n(8) Emma is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that David is a knight if and only if Jack is a knight.", "Assume David is a knight. No contradiction is found in their claim that Abigail is not a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Jack is a knave.", "Abigail cannot be a knave, because this would contradict the claim of David that Abigail is not a knave.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the claim of Jack that David is a knight if and only if Jack is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that David is a knight if and only if Jack is a knight.", "Assume David is a knight. No contradiction is found in their claim that Abigail is not a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Jack is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Emma is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Jack is a knave or David is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Abigail is a knight if and only if Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Logan is a knight or Emma is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Emma is a knave or David is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Emma is a knave or David is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 4), ('telling-truth', 0)), ('telling-truth', 7), ('<=>', ('telling-truth', 3), ('telling-truth', 6)), ('lying', 0), ('not', ('lying', 3)), ('or', ('lying', 7), ('lying', 4)), ('or', ('telling-truth', 1), ('telling-truth', 7)), ('or', ('lying', 0), ('telling-truth', 4)))", "index": 659}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sebastian, Emily, Zoey, Henry, Daniel, Oliver, Ava, and Scarlett. As Sebastian put it, \"Zoey is a knave if and only if Scarlett is a knave\". Emily stated, \"Ava is a knight or Scarlett is a knave\". In a statement by Zoey: \"Sebastian is a knight or Emily is a knight\". Henry commented, \"Ava is not a knight\". \"Ava is not a knave,\" Daniel declared. In Oliver's words: \"Scarlett is a knight if and only if Ava is a knight\". As Ava put it, \"If Sebastian is a knave then Oliver is a knave\". Scarlett commented, \"Emily is a knight and Daniel is a knave\". So who is a knight and who is a knave?", "names": ["Sebastian", "Emily", "Zoey", "Henry", "Daniel", "Oliver", "Ava", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, false, true, false], "solution_text": "Sebastian is a knave, Emily is a knight, Zoey is a knight, Henry is a knave, Daniel is a knight, Oliver is a knave, Ava is a knight, and Scarlett is a knave.", "solution_text_format": "(1) Sebastian is a knave\n(2) Emily is a knight\n(3) Zoey is a knight\n(4) Henry is a knave\n(5) Daniel is a knight\n(6) Oliver is a knave\n(7) Ava is a knight\n(8) Scarlett is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that Zoey is a knave if and only if Scarlett is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Sebastian is a knight or Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Ava is a knight or Scarlett is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that If Sebastian is a knave then Oliver is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Scarlett is a knight if and only if Ava is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Emily is a knight and Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of Scarlett that Emily is a knight and Daniel is a knave.", "Daniel cannot be a knave, because this would contradict the false claim of their own that Ava is not a knave.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the claim of Sebastian that Zoey is a knave if and only if Scarlett is a knave.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Scarlett is a knight if and only if Ava is a knight.", "Scarlett cannot be a knight, because this would contradict the false claim of Oliver that Scarlett is a knight if and only if Ava is a knight.", "Scarlett cannot be a knave, because this would contradict the claim of Sebastian that Zoey is a knave if and only if Scarlett is a knave.", "We have exhausted all possibilities for Scarlett and Oliver, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the false claim of their own that If Sebastian is a knave then Oliver is a knave.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Ava is a knight or Scarlett is a knave.", "Ava cannot be a knight, because this would contradict the false claim of Emily that Ava is a knight or Scarlett is a knave.", "Ava cannot be a knave, because this would contradict the false claim of their own that If Sebastian is a knave then Oliver is a knave.", "We have exhausted all possibilities for Ava and Emily, so let us go back and reconsider Zoey.", "Zoey cannot be a knave, because this would contradict the false claim of their own that Sebastian is a knight or Emily is a knight.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Zoey is a knave if and only if Scarlett is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Sebastian is a knight or Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Ava is a knight or Scarlett is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that If Sebastian is a knave then Oliver is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Ava that If Sebastian is a knave then Oliver is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Scarlett is a knight if and only if Ava is a knight.", "Scarlett cannot be a knight, because this would contradict the false claim of Sebastian that Zoey is a knave if and only if Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Emily is a knight and Daniel is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Ava is not a knave.", "Henry cannot be a knight, because this would contradict the claim of their own that Ava is not a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Ava is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('lying', 7)), ('or', ('telling-truth', 6), ('lying', 7)), ('or', ('telling-truth', 0), ('telling-truth', 1)), ('not', ('telling-truth', 6)), ('not', ('lying', 6)), ('<=>', ('telling-truth', 7), ('telling-truth', 6)), ('->', ('lying', 0), ('lying', 5)), ('and', ('telling-truth', 1), ('lying', 4)))", "index": 660}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sebastian, James, Lily, Elizabeth, Avery, Chloe, Lucas, and Benjamin. Sebastian commented, \"Avery is a knave\". In a statement by James: \"Sebastian is not a knight\". Lily was heard saying, \"Benjamin is not a knight\". Elizabeth asserted: \"Lily is a knight if and only if Chloe is a knave\". Avery commented, \"Lucas is a knight and Chloe is a knight\". Chloe said that Elizabeth is a knight if and only if Lucas is a knight. Lucas expressed that Lily is a knave. Benjamin expressed that James is not a knight. So who is a knight and who is a knave?", "names": ["Sebastian", "James", "Lily", "Elizabeth", "Avery", "Chloe", "Lucas", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, false, true, true], "solution_text": "Sebastian is a knight, James is a knave, Lily is a knave, Elizabeth is a knave, Avery is a knave, Chloe is a knave, Lucas is a knight, and Benjamin is a knight.", "solution_text_format": "(1) Sebastian is a knight\n(2) James is a knave\n(3) Lily is a knave\n(4) Elizabeth is a knave\n(5) Avery is a knave\n(6) Chloe is a knave\n(7) Lucas is a knight\n(8) Benjamin is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that Avery is a knave.", "Avery cannot be a knight, because this would contradict the claim of Sebastian that Avery is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Lucas is a knight and Chloe is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of Lucas that Lily is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Benjamin is not a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that James is not a knight.", "James cannot be a knight, because this would contradict the claim of their own that Sebastian is not a knight.", "Assume James is a knave. No contradiction is found in their false claim that Sebastian is not a knight.", "Chloe cannot be a knight, because this would contradict the false claim of Avery that Lucas is a knight and Chloe is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Elizabeth is a knight if and only if Lucas is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Lily is a knight if and only if Chloe is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Lily is a knight if and only if Chloe is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('not', ('telling-truth', 0)), ('not', ('telling-truth', 7)), ('<=>', ('telling-truth', 2), ('lying', 5)), ('and', ('telling-truth', 6), ('telling-truth', 5)), ('<=>', ('telling-truth', 3), ('telling-truth', 6)), ('lying', 2), ('not', ('telling-truth', 1)))", "index": 661}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jacob, Samuel, James, Victoria, Abigail, Sebastian, Ethan, and Alexander. Jacob said, \"James is not a knight.\" Samuel said, \"Jacob is not a knight.\" James said, \"If Victoria is a knight then Jacob is a knight.\" Victoria commented, \"Abigail is a knight and Samuel is a knave\". As Abigail put it, \"Ethan is a knave if and only if Samuel is a knight\". \"If Samuel is a knave then Victoria is a knight,\" Sebastian claimed. Ethan remarked, \"James is a knight\". \"Jacob is not a knight\" - Alexander. So who is a knight and who is a knave?", "names": ["Jacob", "Samuel", "James", "Victoria", "Abigail", "Sebastian", "Ethan", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true, true, true], "solution_text": "Jacob is a knave, Samuel is a knight, James is a knight, Victoria is a knave, Abigail is a knave, Sebastian is a knight, Ethan is a knight, and Alexander is a knight.", "solution_text_format": "(1) Jacob is a knave\n(2) Samuel is a knight\n(3) James is a knight\n(4) Victoria is a knave\n(5) Abigail is a knave\n(6) Sebastian is a knight\n(7) Ethan is a knight\n(8) Alexander is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that James is not a knight.", "James cannot be a knight, because this would contradict the claim of Jacob that James is not a knight.", "James cannot be a knave, because this would contradict the false claim of their own that If Victoria is a knight then Jacob is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that James is not a knight.", "Assume James is a knight. No contradiction is found in their claim that If Victoria is a knight then Jacob is a knight.", "Victoria cannot be a knight, because this would contradict the claim of James that If Victoria is a knight then Jacob is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Abigail is a knight and Samuel is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Ethan is a knave if and only if Samuel is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that James is a knight.", "Samuel cannot be a knight, because this would contradict the claim of Abigail that Ethan is a knave if and only if Samuel is a knight.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Jacob is not a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the false claim of their own that James is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Ethan is a knave if and only if Samuel is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that James is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Jacob is not a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Samuel is a knave then Victoria is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Jacob is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('not', ('telling-truth', 0)), ('->', ('telling-truth', 3), ('telling-truth', 0)), ('and', ('telling-truth', 4), ('lying', 1)), ('<=>', ('lying', 6), ('telling-truth', 1)), ('->', ('lying', 1), ('telling-truth', 3)), ('telling-truth', 2), ('not', ('telling-truth', 0)))", "index": 662}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ava, Riley, Matthew, Abigail, David, Ethan, Jackson, and Daniel. According to Ava, \"Jackson is a knight and David is a knight\". Riley was heard saying, \"Ava is not a knight\". As Matthew put it, \"Abigail is not a knight\". \"Abigail is a knight or Jackson is a knave\" - Abigail. David was heard saying, \"Daniel is a knight\". Ethan told you that Jackson is not a knave. \"Abigail is a knight,\" Jackson declared. In a statement by Daniel: \"Ava is a knight and Ethan is a knave\". So who is a knight and who is a knave?", "names": ["Ava", "Riley", "Matthew", "Abigail", "David", "Ethan", "Jackson", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, true, true, false], "solution_text": "Ava is a knave, Riley is a knight, Matthew is a knave, Abigail is a knight, David is a knave, Ethan is a knight, Jackson is a knight, and Daniel is a knave.", "solution_text_format": "(1) Ava is a knave\n(2) Riley is a knight\n(3) Matthew is a knave\n(4) Abigail is a knight\n(5) David is a knave\n(6) Ethan is a knight\n(7) Jackson is a knight\n(8) Daniel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Jackson is a knight and David is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Abigail is a knight or Jackson is a knave.", "Assume David is a knight. No contradiction is found in their claim that Daniel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Ava is a knight and Ethan is a knave.", "Ethan cannot be a knight, because this would contradict the claim of Daniel that Ava is a knight and Ethan is a knave.", "Ethan cannot be a knave, because this would contradict the false claim of their own that Jackson is not a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the claim of David that Daniel is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the claim of Ava that Jackson is a knight and David is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the claim of Jackson that Abigail is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Jackson.", "Jackson cannot be a knave, because this would contradict the claim of Ava that Jackson is a knight and David is a knight.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Jackson is a knight and David is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Abigail is a knight or Jackson is a knave.", "David cannot be a knight, because this would contradict the false claim of Ava that Jackson is a knight and David is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of David that Daniel is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Ava is a knight and Ethan is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Jackson is not a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Ava is not a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Abigail is not a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Abigail is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 6), ('telling-truth', 4)), ('not', ('telling-truth', 0)), ('not', ('telling-truth', 3)), ('or', ('telling-truth', 3), ('lying', 6)), ('telling-truth', 7), ('not', ('lying', 6)), ('telling-truth', 3), ('and', ('telling-truth', 0), ('lying', 5)))", "index": 663}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aiden, Sophia, Penelope, Ella, Matthew, Joseph, Charlotte, and Sofia. According to Aiden, \"If Penelope is a knight then Matthew is a knight\". Sophia told you that Sofia is not a knight. Penelope stated, \"Joseph is a knight or Sofia is a knight\". Ella noted, \"Matthew is a knight\". Matthew said, \"Aiden is a knave if and only if Sophia is a knave.\" In a statement by Joseph: \"If Charlotte is a knave then Charlotte is a knight\". Charlotte commented, \"Matthew is a knave or Matthew is a knight\". \"If Aiden is a knight then Ella is a knave\" - Sofia. So who is a knight and who is a knave?", "names": ["Aiden", "Sophia", "Penelope", "Ella", "Matthew", "Joseph", "Charlotte", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true, true, false], "solution_text": "Aiden is a knight, Sophia is a knight, Penelope is a knight, Ella is a knight, Matthew is a knight, Joseph is a knight, Charlotte is a knight, and Sofia is a knave.", "solution_text_format": "(1) Aiden is a knight\n(2) Sophia is a knight\n(3) Penelope is a knight\n(4) Ella is a knight\n(5) Matthew is a knight\n(6) Joseph is a knight\n(7) Charlotte is a knight\n(8) Sofia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that If Penelope is a knight then Matthew is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Joseph is a knight or Sofia is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Charlotte is a knave then Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Matthew is a knave or Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Aiden is a knave if and only if Sophia is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Sofia is not a knight.", "Sofia cannot be a knight, because this would contradict the claim of Sophia that Sofia is not a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that If Aiden is a knight then Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Matthew is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('telling-truth', 4)), ('not', ('telling-truth', 7)), ('or', ('telling-truth', 5), ('telling-truth', 7)), ('telling-truth', 4), ('<=>', ('lying', 0), ('lying', 1)), ('->', ('lying', 6), ('telling-truth', 6)), ('or', ('lying', 4), ('telling-truth', 4)), ('->', ('telling-truth', 0), ('lying', 3)))", "index": 664}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Henry, Amelia, Sophia, Harper, Chloe, Emily, Luke, and Matthew. Henry commented, \"Matthew is a knight if and only if Henry is a knight\". Amelia asserted: \"Harper is a knave and Harper is a knight\". Sophia was heard saying, \"Henry is a knight\". Harper remarked, \"Matthew is a knight\". Chloe commented, \"Matthew is a knave if and only if Emily is a knight\". In a statement by Emily: \"Henry is not a knave\". As Luke put it, \"Amelia is a knight or Harper is a knight\". Matthew said, \"Henry is a knight.\" So who is a knight and who is a knave?", "names": ["Henry", "Amelia", "Sophia", "Harper", "Chloe", "Emily", "Luke", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true, true, true], "solution_text": "Henry is a knight, Amelia is a knave, Sophia is a knight, Harper is a knight, Chloe is a knave, Emily is a knight, Luke is a knight, and Matthew is a knight.", "solution_text_format": "(1) Henry is a knight\n(2) Amelia is a knave\n(3) Sophia is a knight\n(4) Harper is a knight\n(5) Chloe is a knave\n(6) Emily is a knight\n(7) Luke is a knight\n(8) Matthew is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that Matthew is a knight if and only if Henry is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Henry is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Harper is a knave and Harper is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Harper is a knave and Harper is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Matthew is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Henry is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Matthew is a knave if and only if Emily is a knight.", "Emily cannot be a knight, because this would contradict the claim of Chloe that Matthew is a knave if and only if Emily is a knight.", "Emily cannot be a knave, because this would contradict the false claim of their own that Henry is not a knave.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Matthew is a knave if and only if Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Henry is not a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Amelia is a knight or Harper is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 7), ('telling-truth', 0)), ('and', ('lying', 3), ('telling-truth', 3)), ('telling-truth', 0), ('telling-truth', 7), ('<=>', ('lying', 7), ('telling-truth', 5)), ('not', ('lying', 0)), ('or', ('telling-truth', 1), ('telling-truth', 3)), ('telling-truth', 0))", "index": 665}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Scarlett, Jack, Zoey, Ella, Logan, Sophia, William, and Abigail. Scarlett noted, \"Sophia is a knight\". As Jack put it, \"Sophia is not a knave\". \"Logan is a knight\" - Zoey. Ella commented, \"Zoey is a knave or Jack is a knave\". Logan remarked, \"Scarlett is a knight and Jack is a knave\". \"Ella is a knight or Jack is a knight,\" Sophia mentioned. William noted, \"Sophia is a knight\". \"Zoey is a knave if and only if Logan is a knight\" - Abigail. So who is a knight and who is a knave?", "names": ["Scarlett", "Jack", "Zoey", "Ella", "Logan", "Sophia", "William", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true, true, false], "solution_text": "Scarlett is a knight, Jack is a knight, Zoey is a knave, Ella is a knight, Logan is a knave, Sophia is a knight, William is a knight, and Abigail is a knave.", "solution_text_format": "(1) Scarlett is a knight\n(2) Jack is a knight\n(3) Zoey is a knave\n(4) Ella is a knight\n(5) Logan is a knave\n(6) Sophia is a knight\n(7) William is a knight\n(8) Abigail is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Sophia is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Ella is a knight or Jack is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Zoey is a knave or Jack is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Logan is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Scarlett is a knight and Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of Ella that Zoey is a knave or Jack is a knave.", "Jack cannot be a knave, because this would contradict the false claim of their own that Sophia is not a knave.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the claim of Zoey that Logan is a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Logan is a knight.", "Logan cannot be a knight, because this would contradict the false claim of Zoey that Logan is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Scarlett is a knight and Jack is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Sophia is not a knave.", "Assume William is a knight. No contradiction is found in their claim that Sophia is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Zoey is a knave if and only if Logan is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Zoey is a knave if and only if Logan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 5), ('not', ('lying', 5)), ('telling-truth', 4), ('or', ('lying', 2), ('lying', 1)), ('and', ('telling-truth', 0), ('lying', 1)), ('or', ('telling-truth', 3), ('telling-truth', 1)), ('telling-truth', 5), ('<=>', ('lying', 2), ('telling-truth', 4)))", "index": 666}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Isabella, Mason, Luke, Scarlett, Daniel, Samuel, Ethan, and Lily. Isabella was heard saying, \"Ethan is not a knave\". Mason asserted: \"Luke is a knave or Samuel is a knight\". Luke commented, \"Daniel is a knight\". Scarlett said that Samuel is a knave or Daniel is a knave. According to Daniel, \"Samuel is a knight or Lily is a knight\". Samuel remarked, \"Mason is a knave if and only if Ethan is a knave\". \"Scarlett is not a knight\" - Ethan. \"Luke is a knave if and only if Lily is a knight,\" Lily claimed. So who is a knight and who is a knave?", "names": ["Isabella", "Mason", "Luke", "Scarlett", "Daniel", "Samuel", "Ethan", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, false, false, false], "solution_text": "Isabella is a knave, Mason is a knight, Luke is a knave, Scarlett is a knight, Daniel is a knave, Samuel is a knave, Ethan is a knave, and Lily is a knave.", "solution_text_format": "(1) Isabella is a knave\n(2) Mason is a knight\n(3) Luke is a knave\n(4) Scarlett is a knight\n(5) Daniel is a knave\n(6) Samuel is a knave\n(7) Ethan is a knave\n(8) Lily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Ethan is not a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Scarlett is not a knight.", "Scarlett cannot be a knight, because this would contradict the claim of Ethan that Scarlett is not a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Samuel is a knave or Daniel is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Mason is a knave if and only if Ethan is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Luke is a knave or Samuel is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Daniel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Samuel is a knight or Lily is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Luke is a knave if and only if Lily is a knight.", "Lily cannot be a knave, because this would contradict the false claim of their own that Luke is a knave if and only if Lily is a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the claim of Luke that Daniel is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of Luke that Daniel is a knight.", "Daniel cannot be a knave, because this would contradict the false claim of Scarlett that Samuel is a knave or Daniel is a knave.", "We have exhausted all possibilities for Daniel and Luke, so let us go back and reconsider Mason.", "Mason cannot be a knave, because this would contradict the false claim of their own that Luke is a knave or Samuel is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Samuel.", "Samuel cannot be a knave, because this would contradict the false claim of Scarlett that Samuel is a knave or Daniel is a knave.", "We have exhausted all possibilities for Samuel and Scarlett, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the claim of Isabella that Ethan is not a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Ethan is not a knave.", "Ethan cannot be a knight, because this would contradict the false claim of Isabella that Ethan is not a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Scarlett is not a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Samuel is a knave or Daniel is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Mason is a knave if and only if Ethan is a knave.", "Mason cannot be a knight, because this would contradict the claim of Samuel that Mason is a knave if and only if Ethan is a knave.", "Mason cannot be a knave, because this would contradict the false claim of their own that Luke is a knave or Samuel is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Mason is a knave if and only if Ethan is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Luke is a knave or Samuel is a knight.", "Luke cannot be a knight, because this would contradict the claim of Mason that Luke is a knave or Samuel is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of Luke that Daniel is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Samuel is a knight or Lily is a knight.", "Lily cannot be a knight, because this would contradict the false claim of Daniel that Samuel is a knight or Lily is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Luke is a knave if and only if Lily is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 6)), ('or', ('lying', 2), ('telling-truth', 5)), ('telling-truth', 4), ('or', ('lying', 5), ('lying', 4)), ('or', ('telling-truth', 5), ('telling-truth', 7)), ('<=>', ('lying', 1), ('lying', 6)), ('not', ('telling-truth', 3)), ('<=>', ('lying', 2), ('telling-truth', 7)))", "index": 667}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Amelia, Emily, Chloe, Owen, Jacob, Lucas, Harper, and Michael. Amelia was heard saying, \"Lucas is a knave or Chloe is a knave\". In Emily's words: \"Jacob is a knave and Amelia is a knight\". Chloe asserted: \"Harper is a knight if and only if Emily is a knave\". Owen expressed that If Jacob is a knave then Emily is a knight. Jacob told you that Owen is a knight if and only if Lucas is a knave. \"Michael is a knight or Chloe is a knave,\" Lucas declared. \"Chloe is not a knave,\" Harper declared. According to Michael, \"Owen is not a knight\". So who is a knight and who is a knave?", "names": ["Amelia", "Emily", "Chloe", "Owen", "Jacob", "Lucas", "Harper", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false, true, false], "solution_text": "Amelia is a knight, Emily is a knave, Chloe is a knight, Owen is a knight, Jacob is a knight, Lucas is a knave, Harper is a knight, and Michael is a knave.", "solution_text_format": "(1) Amelia is a knight\n(2) Emily is a knave\n(3) Chloe is a knight\n(4) Owen is a knight\n(5) Jacob is a knight\n(6) Lucas is a knave\n(7) Harper is a knight\n(8) Michael is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Amelia is a knight. No contradiction is found in their claim that Lucas is a knave or Chloe is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Michael is a knight or Chloe is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Owen is not a knight.", "Owen cannot be a knight, because this would contradict the claim of Michael that Owen is not a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that If Jacob is a knave then Emily is a knight.", "Jacob cannot be a knight, because this would contradict the false claim of Owen that If Jacob is a knave then Emily is a knight.", "Jacob cannot be a knave, because this would contradict the false claim of their own that Owen is a knight if and only if Lucas is a knave.", "We have exhausted all possibilities for Jacob and Owen, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Owen is not a knight.", "Assume Owen is a knight. No contradiction is found in their claim that If Jacob is a knave then Emily is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Owen is a knight if and only if Lucas is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Owen is a knight if and only if Lucas is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Jacob is a knave and Amelia is a knight.", "Chloe cannot be a knight, because this would contradict the claim of Amelia that Lucas is a knave or Chloe is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Harper is a knight if and only if Emily is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Chloe is not a knave.", "Harper cannot be a knave, because this would contradict the false claim of Chloe that Harper is a knight if and only if Emily is a knave.", "We have exhausted all possibilities for Harper and Chloe, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the false claim of their own that Jacob is a knave and Amelia is a knight.", "We have exhausted all possibilities for Emily and Jacob, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the false claim of Michael that Owen is not a knight.", "We have exhausted all possibilities for Owen and Michael, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Michael is a knight or Chloe is a knave.", "Michael cannot be a knight, because this would contradict the false claim of Lucas that Michael is a knight or Chloe is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Owen is not a knight.", "Assume Owen is a knight. No contradiction is found in their claim that If Jacob is a knave then Emily is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Owen is a knight if and only if Lucas is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Jacob is a knave and Amelia is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Jacob is a knave and Amelia is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Harper is a knight if and only if Emily is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Chloe is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 5), ('lying', 2)), ('and', ('lying', 4), ('telling-truth', 0)), ('<=>', ('telling-truth', 6), ('lying', 1)), ('->', ('lying', 4), ('telling-truth', 1)), ('<=>', ('telling-truth', 3), ('lying', 5)), ('or', ('telling-truth', 7), ('lying', 2)), ('not', ('lying', 2)), ('not', ('telling-truth', 3)))", "index": 668}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: William, Luke, Sophia, Aiden, Victoria, Daniel, Aria, and Ethan. \"Sophia is not a knight\" - William. Luke commented, \"William is a knight\". Sophia asserted: \"Luke is a knight or Ethan is a knave\". \"William is a knight,\" Aiden claimed. Victoria said, \"If Aiden is a knave then William is a knight.\" Daniel told you that Luke is a knave. \"If Daniel is a knight then William is a knave,\" Aria mentioned. \"Daniel is a knave and Aiden is a knave,\" Ethan mentioned. So who is a knight and who is a knave?", "names": ["William", "Luke", "Sophia", "Aiden", "Victoria", "Daniel", "Aria", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, true, true, false], "solution_text": "William is a knave, Luke is a knave, Sophia is a knight, Aiden is a knave, Victoria is a knave, Daniel is a knight, Aria is a knight, and Ethan is a knave.", "solution_text_format": "(1) William is a knave\n(2) Luke is a knave\n(3) Sophia is a knight\n(4) Aiden is a knave\n(5) Victoria is a knave\n(6) Daniel is a knight\n(7) Aria is a knight\n(8) Ethan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Sophia is not a knight.", "Sophia cannot be a knight, because this would contradict the claim of William that Sophia is not a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Luke is a knight or Ethan is a knave.", "Luke cannot be a knight, because this would contradict the false claim of Sophia that Luke is a knight or Ethan is a knave.", "Luke cannot be a knave, because this would contradict the false claim of their own that William is a knight.", "We have exhausted all possibilities for Luke and Sophia, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Sophia is not a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Luke is a knight or Ethan is a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that William is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that William is a knight.", "Ethan cannot be a knight, because this would contradict the claim of Sophia that Luke is a knight or Ethan is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Daniel is a knave and Aiden is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Luke is a knave.", "Aiden cannot be a knight, because this would contradict the claim of their own that William is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that William is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that If Aiden is a knave then William is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that If Aiden is a knave then William is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that If Daniel is a knight then William is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('telling-truth', 0), ('or', ('telling-truth', 1), ('lying', 7)), ('telling-truth', 0), ('->', ('lying', 3), ('telling-truth', 0)), ('lying', 1), ('->', ('telling-truth', 5), ('lying', 0)), ('and', ('lying', 5), ('lying', 3)))", "index": 669}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emma, Daniel, Ella, James, Jack, Emily, Lucas, and Liam. As Emma put it, \"If Lucas is a knight then Emily is a knight\". According to Daniel, \"James is a knight or Jack is a knave\". Ella asserted: \"James is not a knave\". James expressed that If Liam is a knight then Lucas is a knave. Jack expressed that Emily is not a knave. In a statement by Emily: \"Jack is a knave if and only if Emma is a knight\". Lucas noted, \"Liam is a knave if and only if Emma is a knave\". \"If Ella is a knight then Emma is a knight,\" Liam declared. So who is a knight and who is a knave?", "names": ["Emma", "Daniel", "Ella", "James", "Jack", "Emily", "Lucas", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false, true, false], "solution_text": "Emma is a knave, Daniel is a knight, Ella is a knight, James is a knight, Jack is a knave, Emily is a knave, Lucas is a knight, and Liam is a knave.", "solution_text_format": "(1) Emma is a knave\n(2) Daniel is a knight\n(3) Ella is a knight\n(4) James is a knight\n(5) Jack is a knave\n(6) Emily is a knave\n(7) Lucas is a knight\n(8) Liam is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that If Lucas is a knight then Emily is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Liam is a knave if and only if Emma is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that If Ella is a knight then Emma is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that James is not a knave.", "James cannot be a knight, because this would contradict the claim of their own that If Liam is a knight then Lucas is a knave.", "James cannot be a knave, because this would contradict the claim of Ella that James is not a knave.", "We have exhausted all possibilities for James, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that James is not a knave.", "James cannot be a knight, because this would contradict the false claim of Ella that James is not a knave.", "Assume James is a knave. No contradiction is found in their false claim that If Liam is a knight then Lucas is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Jack is a knave if and only if Emma is a knight.", "Jack cannot be a knight, because this would contradict the claim of Emily that Jack is a knave if and only if Emma is a knight.", "Jack cannot be a knave, because this would contradict the false claim of their own that Emily is not a knave.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the claim of Emma that If Lucas is a knight then Emily is a knight.", "We have exhausted all possibilities for Emily, James, and Ella, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the claim of Lucas that Liam is a knave if and only if Emma is a knave.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Liam is a knave if and only if Emma is a knave.", "Liam cannot be a knight, because this would contradict the false claim of Lucas that Liam is a knave if and only if Emma is a knave.", "Liam cannot be a knave, because this would contradict the false claim of their own that If Ella is a knight then Emma is a knight.", "We have exhausted all possibilities for Liam and Lucas, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that If Lucas is a knight then Emily is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Liam is a knave if and only if Emma is a knave.", "Liam cannot be a knight, because this would contradict the claim of Lucas that Liam is a knave if and only if Emma is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that If Ella is a knight then Emma is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that James is not a knave.", "Assume James is a knight. No contradiction is found in their claim that If Liam is a knight then Lucas is a knave.", "Emily cannot be a knight, because this would contradict the false claim of Emma that If Lucas is a knight then Emily is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Jack is a knave if and only if Emma is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Emily is not a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Emily is not a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that James is a knight or Jack is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 6), ('telling-truth', 5)), ('or', ('telling-truth', 3), ('lying', 4)), ('not', ('lying', 3)), ('->', ('telling-truth', 7), ('lying', 6)), ('not', ('lying', 5)), ('<=>', ('lying', 4), ('telling-truth', 0)), ('<=>', ('lying', 7), ('lying', 0)), ('->', ('telling-truth', 2), ('telling-truth', 0)))", "index": 670}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Noah, Logan, Lucas, Avery, Ava, Aurora, Ethan, and Aiden. In a statement by Noah: \"Ethan is a knight if and only if Logan is a knight\". Logan noted, \"Lucas is not a knight\". Lucas said that If Ethan is a knave then Ava is a knight. Avery noted, \"Noah is a knave or Noah is a knight\". \"If Lucas is a knave then Aurora is a knave,\" Ava claimed. Aurora noted, \"Avery is a knight or Noah is a knave\". Ethan asserted: \"Noah is a knave and Aiden is a knave\". Aiden was heard saying, \"Logan is a knave\". So who is a knight and who is a knave?", "names": ["Noah", "Logan", "Lucas", "Avery", "Ava", "Aurora", "Ethan", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true, false, true], "solution_text": "Noah is a knight, Logan is a knave, Lucas is a knight, Avery is a knight, Ava is a knight, Aurora is a knight, Ethan is a knave, and Aiden is a knight.", "solution_text_format": "(1) Noah is a knight\n(2) Logan is a knave\n(3) Lucas is a knight\n(4) Avery is a knight\n(5) Ava is a knight\n(6) Aurora is a knight\n(7) Ethan is a knave\n(8) Aiden is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Noah is a knight. No contradiction is found in their claim that Ethan is a knight if and only if Logan is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Noah is a knave and Aiden is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Noah is a knave and Aiden is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of Noah that Ethan is a knight if and only if Logan is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Lucas is not a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that If Ethan is a knave then Ava is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that If Lucas is a knave then Aurora is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Avery is a knight or Noah is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Noah is a knave or Noah is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 6), ('telling-truth', 1)), ('not', ('telling-truth', 2)), ('->', ('lying', 6), ('telling-truth', 4)), ('or', ('lying', 0), ('telling-truth', 0)), ('->', ('lying', 2), ('lying', 5)), ('or', ('telling-truth', 3), ('lying', 0)), ('and', ('lying', 0), ('lying', 7)), ('lying', 1))", "index": 671}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: David, Jack, Noah, Michael, Mason, Evelyn, Samuel, and Amelia. David stated, \"Noah is a knight and Amelia is a knight\". In Jack's words: \"Samuel is a knave and David is a knave\". Noah commented, \"If Evelyn is a knave then Samuel is a knave\". Michael remarked, \"If Noah is a knight then Mason is a knight\". As Mason put it, \"Evelyn is a knave if and only if Noah is a knave\". \"Jack is not a knave,\" Evelyn mentioned. Samuel noted, \"Evelyn is not a knave\". \"Michael is a knight or Jack is a knave,\" Amelia claimed. So who is a knight and who is a knave?", "names": ["David", "Jack", "Noah", "Michael", "Mason", "Evelyn", "Samuel", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, false, false, true], "solution_text": "David is a knight, Jack is a knave, Noah is a knight, Michael is a knave, Mason is a knave, Evelyn is a knave, Samuel is a knave, and Amelia is a knight.", "solution_text_format": "(1) David is a knight\n(2) Jack is a knave\n(3) Noah is a knight\n(4) Michael is a knave\n(5) Mason is a knave\n(6) Evelyn is a knave\n(7) Samuel is a knave\n(8) Amelia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Noah is a knight and Amelia is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that If Evelyn is a knave then Samuel is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Jack is not a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Samuel is a knave and David is a knave.", "Jack cannot be a knave, because this would contradict the claim of Evelyn that Jack is not a knave.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Jack is not a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Samuel is a knave and David is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Samuel is a knave and David is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Noah that If Evelyn is a knave then Samuel is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Evelyn is not a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Michael is a knight or Jack is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that If Noah is a knight then Mason is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave if and only if Noah is a knave.", "Mason cannot be a knave, because this would contradict the claim of Michael that If Noah is a knight then Mason is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that If Noah is a knight then Mason is a knight.", "Mason cannot be a knight, because this would contradict the false claim of Michael that If Noah is a knight then Mason is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Evelyn is a knave if and only if Noah is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 2), ('telling-truth', 7)), ('and', ('lying', 6), ('lying', 0)), ('->', ('lying', 5), ('lying', 6)), ('->', ('telling-truth', 2), ('telling-truth', 4)), ('<=>', ('lying', 5), ('lying', 2)), ('not', ('lying', 1)), ('not', ('lying', 5)), ('or', ('telling-truth', 3), ('lying', 1)))", "index": 672}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Owen, Mason, Grace, Penelope, Aurora, Liam, Noah, and Sebastian. \"Grace is a knight,\" Owen mentioned. Mason said that If Aurora is a knight then Noah is a knight. Grace was heard saying, \"Mason is not a knave\". \"Aurora is a knave and Noah is a knave,\" Penelope claimed. Aurora remarked, \"Liam is a knave if and only if Liam is a knight\". \"Owen is a knight and Penelope is a knight,\" Liam mentioned. Noah noted, \"Grace is a knave\". Sebastian remarked, \"Liam is a knave if and only if Penelope is a knave\". So who is a knight and who is a knave?", "names": ["Owen", "Mason", "Grace", "Penelope", "Aurora", "Liam", "Noah", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true, false, true], "solution_text": "Owen is a knight, Mason is a knight, Grace is a knight, Penelope is a knight, Aurora is a knave, Liam is a knight, Noah is a knave, and Sebastian is a knight.", "solution_text_format": "(1) Owen is a knight\n(2) Mason is a knight\n(3) Grace is a knight\n(4) Penelope is a knight\n(5) Aurora is a knave\n(6) Liam is a knight\n(7) Noah is a knave\n(8) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Mason is not a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Aurora is a knight then Noah is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Liam is a knave if and only if Liam is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Liam is a knave if and only if Liam is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Owen is a knight and Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Aurora is a knave and Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of Penelope that Aurora is a knave and Noah is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Grace is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Liam is a knave if and only if Penelope is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('->', ('telling-truth', 4), ('telling-truth', 6)), ('not', ('lying', 1)), ('and', ('lying', 4), ('lying', 6)), ('<=>', ('lying', 5), ('telling-truth', 5)), ('and', ('telling-truth', 0), ('telling-truth', 3)), ('lying', 2), ('<=>', ('lying', 5), ('lying', 3)))", "index": 673}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jack, Charlotte, Grace, Elizabeth, Ava, Noah, James, and Olivia. As Jack put it, \"Olivia is a knight and Ava is a knave\". According to Charlotte, \"Noah is a knight or Olivia is a knave\". Grace asserted: \"Grace is a knight and Elizabeth is a knave\". Elizabeth said that Grace is a knight if and only if Charlotte is a knave. Ava expressed that Olivia is a knight or Noah is a knave. Noah commented, \"Grace is not a knave\". James stated, \"If Charlotte is a knave then Grace is a knight\". Olivia stated, \"Ava is a knave\". So who is a knight and who is a knave?", "names": ["Jack", "Charlotte", "Grace", "Elizabeth", "Ava", "Noah", "James", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false, true, false], "solution_text": "Jack is a knave, Charlotte is a knight, Grace is a knave, Elizabeth is a knight, Ava is a knight, Noah is a knave, James is a knight, and Olivia is a knave.", "solution_text_format": "(1) Jack is a knave\n(2) Charlotte is a knight\n(3) Grace is a knave\n(4) Elizabeth is a knight\n(5) Ava is a knight\n(6) Noah is a knave\n(7) James is a knight\n(8) Olivia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Olivia is a knight and Ava is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of Jack that Olivia is a knight and Ava is a knave.", "Ava cannot be a knave, because this would contradict the false claim of their own that Olivia is a knight or Noah is a knave.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the claim of Jack that Olivia is a knight and Ava is a knave.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Olivia is a knight and Ava is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of Olivia that Ava is a knave.", "Ava cannot be a knave, because this would contradict the false claim of Jack that Olivia is a knight and Ava is a knave.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Ava is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Olivia is a knight or Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of Ava that Olivia is a knight or Noah is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Grace is not a knave.", "Grace cannot be a knight, because this would contradict the false claim of Noah that Grace is not a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Grace is a knight and Elizabeth is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Grace is a knight if and only if Charlotte is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Noah is a knight or Olivia is a knave.", "Assume James is a knight. No contradiction is found in their claim that If Charlotte is a knave then Grace is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 7), ('lying', 4)), ('or', ('telling-truth', 5), ('lying', 7)), ('and', ('telling-truth', 2), ('lying', 3)), ('<=>', ('telling-truth', 2), ('lying', 1)), ('or', ('telling-truth', 7), ('lying', 5)), ('not', ('lying', 2)), ('->', ('lying', 1), ('telling-truth', 2)), ('lying', 4))", "index": 674}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aiden, Harper, Abigail, Amelia, Luke, Sebastian, David, and Michael. As Aiden put it, \"If David is a knight then Michael is a knight\". Harper noted, \"Sebastian is a knave if and only if Abigail is a knave\". Abigail noted, \"If Luke is a knave then Harper is a knight\". Amelia asserted: \"David is a knight or Abigail is a knave\". As Luke put it, \"If Abigail is a knight then Michael is a knight\". As Sebastian put it, \"David is not a knave\". In David's words: \"Luke is a knave and Aiden is a knight\". Michael told you that Luke is a knight or Amelia is a knight. So who is a knight and who is a knave?", "names": ["Aiden", "Harper", "Abigail", "Amelia", "Luke", "Sebastian", "David", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, false, false, true], "solution_text": "Aiden is a knight, Harper is a knave, Abigail is a knight, Amelia is a knave, Luke is a knight, Sebastian is a knave, David is a knave, and Michael is a knight.", "solution_text_format": "(1) Aiden is a knight\n(2) Harper is a knave\n(3) Abigail is a knight\n(4) Amelia is a knave\n(5) Luke is a knight\n(6) Sebastian is a knave\n(7) David is a knave\n(8) Michael is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that If David is a knight then Michael is a knight.", "Assume David is a knight. No contradiction is found in their claim that Luke is a knave and Aiden is a knight.", "Luke cannot be a knight, because this would contradict the claim of David that Luke is a knave and Aiden is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that If Abigail is a knight then Michael is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If Luke is a knave then Harper is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Sebastian is a knave if and only if Abigail is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that David is not a knave.", "Michael cannot be a knight, because this would contradict the false claim of Luke that If Abigail is a knight then Michael is a knight.", "Michael cannot be a knave, because this would contradict the claim of Aiden that If David is a knight then Michael is a knight.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the claim of Harper that Sebastian is a knave if and only if Abigail is a knave.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the claim of Abigail that If Luke is a knave then Harper is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the false claim of Luke that If Abigail is a knight then Michael is a knight.", "We have exhausted all possibilities for Abigail and Luke, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Luke is a knave and Aiden is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that If Abigail is a knight then Michael is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If Luke is a knave then Harper is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Sebastian is a knave if and only if Abigail is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of their own that David is not a knave.", "Sebastian cannot be a knave, because this would contradict the claim of Harper that Sebastian is a knave if and only if Abigail is a knave.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Sebastian is a knave if and only if Abigail is a knave.", "Sebastian cannot be a knight, because this would contradict the false claim of Harper that Sebastian is a knave if and only if Abigail is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that David is not a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Luke is a knight or Amelia is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that David is a knight or Abigail is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that David is a knight or Abigail is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 6), ('telling-truth', 7)), ('<=>', ('lying', 5), ('lying', 2)), ('->', ('lying', 4), ('telling-truth', 1)), ('or', ('telling-truth', 6), ('lying', 2)), ('->', ('telling-truth', 2), ('telling-truth', 7)), ('not', ('lying', 6)), ('and', ('lying', 4), ('telling-truth', 0)), ('or', ('telling-truth', 4), ('telling-truth', 3)))", "index": 675}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Owen, Emily, James, Riley, Jack, Victoria, Harper, and Chloe. Owen told you that Chloe is a knight. Emily remarked, \"If Harper is a knight then Victoria is a knave\". James remarked, \"Chloe is a knave if and only if Owen is a knight\". Riley said, \"Chloe is a knight if and only if Harper is a knave.\" In a statement by Jack: \"Harper is a knight if and only if Emily is a knight\". Victoria remarked, \"Owen is a knight and Chloe is a knight\". \"Owen is not a knave,\" Harper claimed. \"Jack is a knave,\" Chloe claimed. So who is a knight and who is a knave?", "names": ["Owen", "Emily", "James", "Riley", "Jack", "Victoria", "Harper", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, true, true, true], "solution_text": "Owen is a knight, Emily is a knave, James is a knave, Riley is a knave, Jack is a knave, Victoria is a knight, Harper is a knight, and Chloe is a knight.", "solution_text_format": "(1) Owen is a knight\n(2) Emily is a knave\n(3) James is a knave\n(4) Riley is a knave\n(5) Jack is a knave\n(6) Victoria is a knight\n(7) Harper is a knight\n(8) Chloe is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Chloe is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of Chloe that Jack is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Harper is a knight if and only if Emily is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Owen is not a knave.", "Emily cannot be a knight, because this would contradict the false claim of Jack that Harper is a knight if and only if Emily is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that If Harper is a knight then Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Owen is a knight and Chloe is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Chloe is a knave if and only if Owen is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Chloe is a knave if and only if Owen is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Chloe is a knight if and only if Harper is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Chloe is a knight if and only if Harper is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 7), ('->', ('telling-truth', 6), ('lying', 5)), ('<=>', ('lying', 7), ('telling-truth', 0)), ('<=>', ('telling-truth', 7), ('lying', 6)), ('<=>', ('telling-truth', 6), ('telling-truth', 1)), ('and', ('telling-truth', 0), ('telling-truth', 7)), ('not', ('lying', 0)), ('lying', 4))", "index": 676}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Noah, Isabella, Joseph, Daniel, Jack, Sophia, William, and Harper. Noah said, \"Isabella is a knave if and only if Daniel is a knave.\" Isabella noted, \"Noah is a knave if and only if Daniel is a knave\". In a statement by Joseph: \"Harper is not a knave\". Daniel asserted: \"If Daniel is a knight then Harper is a knave\". In a statement by Jack: \"Isabella is a knave and Harper is a knave\". Sophia expressed that Noah is a knave and Isabella is a knave. In a statement by William: \"Jack is a knave\". \"Joseph is a knight if and only if Noah is a knight,\" Harper mentioned. So who is a knight and who is a knave?", "names": ["Noah", "Isabella", "Joseph", "Daniel", "Jack", "Sophia", "William", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false, true, false], "solution_text": "Noah is a knight, Isabella is a knight, Joseph is a knave, Daniel is a knight, Jack is a knave, Sophia is a knave, William is a knight, and Harper is a knave.", "solution_text_format": "(1) Noah is a knight\n(2) Isabella is a knight\n(3) Joseph is a knave\n(4) Daniel is a knight\n(5) Jack is a knave\n(6) Sophia is a knave\n(7) William is a knight\n(8) Harper is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Noah is a knight. No contradiction is found in their claim that Isabella is a knave if and only if Daniel is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Noah is a knave if and only if Daniel is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that If Daniel is a knight then Harper is a knave.", "Harper cannot be a knight, because this would contradict the claim of Daniel that If Daniel is a knight then Harper is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Joseph is a knight if and only if Noah is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Harper is not a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Harper is not a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Isabella is a knave and Harper is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Isabella is a knave and Harper is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that Noah is a knave and Isabella is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Noah is a knave and Isabella is a knave.", "Assume William is a knight. No contradiction is found in their claim that Jack is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('lying', 3)), ('<=>', ('lying', 0), ('lying', 3)), ('not', ('lying', 7)), ('->', ('telling-truth', 3), ('lying', 7)), ('and', ('lying', 1), ('lying', 7)), ('and', ('lying', 0), ('lying', 1)), ('lying', 4), ('<=>', ('telling-truth', 2), ('telling-truth', 0)))", "index": 677}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emma, Samuel, Aurora, Aria, James, Avery, Chloe, and Evelyn. Emma told you that Chloe is a knave and Chloe is a knight. Samuel told you that Chloe is a knave if and only if Emma is a knave. In Aurora's words: \"Evelyn is a knave and Chloe is a knave\". As Aria put it, \"Avery is not a knight\". James commented, \"If Avery is a knight then Aria is a knave\". \"James is a knight or Evelyn is a knight,\" Avery claimed. Chloe asserted: \"If Avery is a knave then Samuel is a knight\". \"Aria is a knave if and only if Aurora is a knave,\" Evelyn declared. So who is a knight and who is a knave?", "names": ["Emma", "Samuel", "Aurora", "Aria", "James", "Avery", "Chloe", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, true, true, true], "solution_text": "Emma is a knave, Samuel is a knave, Aurora is a knave, Aria is a knave, James is a knight, Avery is a knight, Chloe is a knight, and Evelyn is a knight.", "solution_text_format": "(1) Emma is a knave\n(2) Samuel is a knave\n(3) Aurora is a knave\n(4) Aria is a knave\n(5) James is a knight\n(6) Avery is a knight\n(7) Chloe is a knight\n(8) Evelyn is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Emma cannot be a knight, because this would contradict the claim of their own that Chloe is a knave and Chloe is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Chloe is a knave and Chloe is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that If Avery is a knave then Samuel is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that James is a knight or Evelyn is a knight.", "Assume James is a knight. No contradiction is found in their claim that If Avery is a knight then Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Avery is not a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Avery is not a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Aria is a knave if and only if Aurora is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave and Chloe is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Evelyn is a knave and Chloe is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that Chloe is a knave if and only if Emma is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Chloe is a knave if and only if Emma is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 6), ('telling-truth', 6)), ('<=>', ('lying', 6), ('lying', 0)), ('and', ('lying', 7), ('lying', 6)), ('not', ('telling-truth', 5)), ('->', ('telling-truth', 5), ('lying', 3)), ('or', ('telling-truth', 4), ('telling-truth', 7)), ('->', ('lying', 5), ('telling-truth', 1)), ('<=>', ('lying', 3), ('lying', 2)))", "index": 678}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Elizabeth, Chloe, Noah, James, Sofia, Riley, Penelope, and William. According to Elizabeth, \"If William is a knight then Sofia is a knight\". \"If Penelope is a knight then William is a knave,\" Chloe claimed. \"Chloe is a knight,\" Noah claimed. As James put it, \"Noah is a knave if and only if Sofia is a knight\". Sofia asserted: \"Sofia is a knight if and only if William is a knight\". \"Sofia is a knight and Sofia is a knave,\" Riley declared. Penelope was heard saying, \"James is a knight\". \"Noah is a knave,\" William mentioned. So who is a knight and who is a knave?", "names": ["Elizabeth", "Chloe", "Noah", "James", "Sofia", "Riley", "Penelope", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false, true, true], "solution_text": "Elizabeth is a knight, Chloe is a knave, Noah is a knave, James is a knight, Sofia is a knight, Riley is a knave, Penelope is a knight, and William is a knight.", "solution_text_format": "(1) Elizabeth is a knight\n(2) Chloe is a knave\n(3) Noah is a knave\n(4) James is a knight\n(5) Sofia is a knight\n(6) Riley is a knave\n(7) Penelope is a knight\n(8) William is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that If William is a knight then Sofia is a knight.", "Assume William is a knight. No contradiction is found in their claim that Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of William that Noah is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Chloe is a knight.", "Chloe cannot be a knight, because this would contradict the false claim of Noah that Chloe is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that If Penelope is a knight then William is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that James is a knight.", "Assume James is a knight. No contradiction is found in their claim that Noah is a knave if and only if Sofia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Sofia is a knight if and only if William is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Sofia is a knight and Sofia is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Sofia is a knight and Sofia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 7), ('telling-truth', 4)), ('->', ('telling-truth', 6), ('lying', 7)), ('telling-truth', 1), ('<=>', ('lying', 2), ('telling-truth', 4)), ('<=>', ('telling-truth', 4), ('telling-truth', 7)), ('and', ('telling-truth', 4), ('lying', 4)), ('telling-truth', 3), ('lying', 2))", "index": 679}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Grace, James, Chloe, Noah, Aiden, Olivia, Logan, and Luke. Grace was heard saying, \"Luke is a knave\". James commented, \"Luke is not a knave\". \"Luke is a knave if and only if James is a knave,\" Chloe declared. Noah said, \"James is a knight.\" As Aiden put it, \"James is a knave or Logan is a knight\". Olivia noted, \"Noah is a knave if and only if Luke is a knight\". Logan commented, \"Aiden is not a knight\". \"Chloe is a knave and Chloe is a knight\" - Luke. So who is a knight and who is a knave?", "names": ["Grace", "James", "Chloe", "Noah", "Aiden", "Olivia", "Logan", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, false, false, false], "solution_text": "Grace is a knight, James is a knave, Chloe is a knight, Noah is a knave, Aiden is a knight, Olivia is a knave, Logan is a knave, and Luke is a knave.", "solution_text_format": "(1) Grace is a knight\n(2) James is a knave\n(3) Chloe is a knight\n(4) Noah is a knave\n(5) Aiden is a knight\n(6) Olivia is a knave\n(7) Logan is a knave\n(8) Luke is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Luke is a knave.", "Luke cannot be a knight, because this would contradict the claim of Grace that Luke is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Chloe is a knave and Chloe is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Luke is a knave if and only if James is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Luke is not a knave.", "Assume James is a knave. No contradiction is found in their false claim that Luke is not a knave.", "Noah cannot be a knight, because this would contradict the claim of their own that James is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that James is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that James is a knave or Logan is a knight.", "Logan cannot be a knight, because this would contradict the claim of their own that Aiden is not a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Aiden is not a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that Noah is a knave if and only if Luke is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Noah is a knave if and only if Luke is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 7), ('not', ('lying', 7)), ('<=>', ('lying', 7), ('lying', 1)), ('telling-truth', 1), ('or', ('lying', 1), ('telling-truth', 6)), ('<=>', ('lying', 3), ('telling-truth', 7)), ('not', ('telling-truth', 4)), ('and', ('lying', 2), ('telling-truth', 2)))", "index": 680}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Matthew, Ava, William, Logan, Oliver, Aria, Abigail, and Noah. Matthew remarked, \"If Oliver is a knight then Abigail is a knave\". \"Noah is a knight and Matthew is a knight,\" Ava declared. William expressed that Matthew is a knight if and only if Matthew is a knave. In Logan's words: \"Oliver is a knight\". Oliver noted, \"Abigail is a knight if and only if William is a knave\". \"Abigail is a knave\" - Aria. Abigail expressed that If Ava is a knave then Aria is a knave. \"If Noah is a knight then Aria is a knave,\" Noah mentioned. So who is a knight and who is a knave?", "names": ["Matthew", "Ava", "William", "Logan", "Oliver", "Aria", "Abigail", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, false, true, true], "solution_text": "Matthew is a knave, Ava is a knave, William is a knave, Logan is a knight, Oliver is a knight, Aria is a knave, Abigail is a knight, and Noah is a knight.", "solution_text_format": "(1) Matthew is a knave\n(2) Ava is a knave\n(3) William is a knave\n(4) Logan is a knight\n(5) Oliver is a knight\n(6) Aria is a knave\n(7) Abigail is a knight\n(8) Noah is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that If Oliver is a knight then Abigail is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Abigail is a knight if and only if William is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Matthew that If Oliver is a knight then Abigail is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that If Ava is a knave then Aria is a knave.", "Ava cannot be a knight, because this would contradict the false claim of Abigail that If Ava is a knave then Aria is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Noah is a knight and Matthew is a knight.", "Noah cannot be a knight, because this would contradict the false claim of Ava that Noah is a knight and Matthew is a knight.", "Noah cannot be a knave, because this would contradict the false claim of their own that If Noah is a knight then Aria is a knave.", "We have exhausted all possibilities for Noah, Ava, and Abigail, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Abigail is a knight if and only if William is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that If Ava is a knave then Aria is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Noah is a knight and Matthew is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that If Noah is a knight then Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Abigail is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Abigail is a knave.", "William cannot be a knight, because this would contradict the claim of their own that Matthew is a knight if and only if Matthew is a knave.", "William cannot be a knave, because this would contradict the false claim of Oliver that Abigail is a knight if and only if William is a knave.", "We have exhausted all possibilities for William and Aria, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the claim of Ava that Noah is a knight and Matthew is a knight.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Noah is a knight and Matthew is a knight.", "Noah cannot be a knight, because this would contradict the false claim of Ava that Noah is a knight and Matthew is a knight.", "Noah cannot be a knave, because this would contradict the false claim of their own that If Noah is a knight then Aria is a knave.", "We have exhausted all possibilities for Noah and Ava, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that If Ava is a knave then Aria is a knave.", "Ava cannot be a knight, because this would contradict the false claim of Abigail that If Ava is a knave then Aria is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Noah is a knight and Matthew is a knight.", "Noah cannot be a knight, because this would contradict the false claim of Ava that Noah is a knight and Matthew is a knight.", "Noah cannot be a knave, because this would contradict the false claim of their own that If Noah is a knight then Aria is a knave.", "We have exhausted all possibilities for Noah, Ava, Abigail, and Oliver, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that If Oliver is a knight then Abigail is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Abigail is a knight if and only if William is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that If Ava is a knave then Aria is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Noah is a knight and Matthew is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Noah is a knight and Matthew is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that If Noah is a knight then Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Abigail is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Abigail is a knave.", "William cannot be a knight, because this would contradict the claim of their own that Matthew is a knight if and only if Matthew is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Matthew is a knight if and only if Matthew is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Oliver is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 4), ('lying', 6)), ('and', ('telling-truth', 7), ('telling-truth', 0)), ('<=>', ('telling-truth', 0), ('lying', 0)), ('telling-truth', 4), ('<=>', ('telling-truth', 6), ('lying', 2)), ('lying', 6), ('->', ('lying', 1), ('lying', 5)), ('->', ('telling-truth', 7), ('lying', 5)))", "index": 681}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Isabella, Daniel, Noah, Alexander, Jack, Jacob, James, and Sofia. Isabella commented, \"Noah is a knave and James is a knight\". According to Daniel, \"Jacob is a knight or Sofia is a knight\". In a statement by Noah: \"Alexander is not a knave\". Alexander stated, \"If Noah is a knight then James is a knight\". In a statement by Jack: \"Daniel is a knave or James is a knave\". Jacob commented, \"Jacob is a knight and Alexander is a knave\". James remarked, \"Daniel is not a knave\". Sofia remarked, \"Sofia is a knight if and only if Jacob is a knave\". So who is a knight and who is a knave?", "names": ["Isabella", "Daniel", "Noah", "Alexander", "Jack", "Jacob", "James", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false, true, true], "solution_text": "Isabella is a knave, Daniel is a knight, Noah is a knight, Alexander is a knight, Jack is a knave, Jacob is a knave, James is a knight, and Sofia is a knight.", "solution_text_format": "(1) Isabella is a knave\n(2) Daniel is a knight\n(3) Noah is a knight\n(4) Alexander is a knight\n(5) Jack is a knave\n(6) Jacob is a knave\n(7) James is a knight\n(8) Sofia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Noah is a knave and James is a knight.", "Noah cannot be a knight, because this would contradict the claim of Isabella that Noah is a knave and James is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Alexander is not a knave.", "Alexander cannot be a knight, because this would contradict the false claim of Noah that Alexander is not a knave.", "Alexander cannot be a knave, because this would contradict the false claim of their own that If Noah is a knight then James is a knight.", "We have exhausted all possibilities for Alexander and Noah, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Noah is a knave and James is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Alexander is not a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that If Noah is a knight then James is a knight.", "Assume James is a knight. No contradiction is found in their claim that Daniel is not a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Jacob is a knight or Sofia is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Jacob is a knight and Alexander is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Jacob is a knight and Alexander is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Sofia is a knight if and only if Jacob is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Daniel is a knave or James is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Daniel is a knave or James is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('telling-truth', 6)), ('or', ('telling-truth', 5), ('telling-truth', 7)), ('not', ('lying', 3)), ('->', ('telling-truth', 2), ('telling-truth', 6)), ('or', ('lying', 1), ('lying', 6)), ('and', ('telling-truth', 5), ('lying', 3)), ('not', ('lying', 1)), ('<=>', ('telling-truth', 7), ('lying', 5)))", "index": 682}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ella, Olivia, Sofia, Daniel, Sophia, Isabella, Scarlett, and Luke. According to Ella, \"Daniel is a knight or Luke is a knave\". Olivia was heard saying, \"Scarlett is a knight\". Sofia commented, \"If Ella is a knight then Luke is a knave\". Daniel expressed that Scarlett is a knave or Luke is a knight. Sophia commented, \"Scarlett is a knight\". Isabella told you that Sophia is a knave and Ella is a knave. According to Scarlett, \"Ella is not a knight\". In Luke's words: \"Olivia is a knight and Scarlett is a knight\". So who is a knight and who is a knave?", "names": ["Ella", "Olivia", "Sofia", "Daniel", "Sophia", "Isabella", "Scarlett", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, false, false, false], "solution_text": "Ella is a knight, Olivia is a knave, Sofia is a knight, Daniel is a knight, Sophia is a knave, Isabella is a knave, Scarlett is a knave, and Luke is a knave.", "solution_text_format": "(1) Ella is a knight\n(2) Olivia is a knave\n(3) Sofia is a knight\n(4) Daniel is a knight\n(5) Sophia is a knave\n(6) Isabella is a knave\n(7) Scarlett is a knave\n(8) Luke is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Daniel is a knight or Luke is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Scarlett is a knave or Luke is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Ella is not a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Ella is not a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Olivia is a knight and Scarlett is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Olivia is a knight and Scarlett is a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Scarlett is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that If Ella is a knight then Luke is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Scarlett is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Sophia is a knave and Ella is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Sophia is a knave and Ella is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('lying', 7)), ('telling-truth', 6), ('->', ('telling-truth', 0), ('lying', 7)), ('or', ('lying', 6), ('telling-truth', 7)), ('telling-truth', 6), ('and', ('lying', 4), ('lying', 0)), ('not', ('telling-truth', 0)), ('and', ('telling-truth', 1), ('telling-truth', 6)))", "index": 683}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Chloe, Luke, Liam, Sophia, Jacob, Mia, Lucas, and Jackson. Chloe stated, \"If Sophia is a knave then Jackson is a knave\". \"Lucas is a knight if and only if Sophia is a knight,\" Luke claimed. Liam stated, \"If Jackson is a knave then Mia is a knave\". \"Jacob is a knight and Chloe is a knave\" - Sophia. In a statement by Jacob: \"Liam is a knave or Mia is a knight\". In a statement by Mia: \"Liam is a knight or Chloe is a knight\". According to Lucas, \"Liam is a knight or Mia is a knight\". Jackson stated, \"Luke is a knight\". So who is a knight and who is a knave?", "names": ["Chloe", "Luke", "Liam", "Sophia", "Jacob", "Mia", "Lucas", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true, true, false], "solution_text": "Chloe is a knight, Luke is a knave, Liam is a knave, Sophia is a knave, Jacob is a knight, Mia is a knight, Lucas is a knight, and Jackson is a knave.", "solution_text_format": "(1) Chloe is a knight\n(2) Luke is a knave\n(3) Liam is a knave\n(4) Sophia is a knave\n(5) Jacob is a knight\n(6) Mia is a knight\n(7) Lucas is a knight\n(8) Jackson is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that If Sophia is a knave then Jackson is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that Jacob is a knight and Chloe is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Jacob is a knight and Chloe is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Liam is a knave or Mia is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that If Jackson is a knave then Mia is a knave.", "Jackson cannot be a knight, because this would contradict the claim of Chloe that If Sophia is a knave then Jackson is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Luke is a knight.", "Luke cannot be a knight, because this would contradict the false claim of Jackson that Luke is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Lucas is a knight if and only if Sophia is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Liam is a knight or Mia is a knight.", "Mia cannot be a knight, because this would contradict the claim of Liam that If Jackson is a knave then Mia is a knave.", "Mia cannot be a knave, because this would contradict the claim of Jacob that Liam is a knave or Mia is a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the false claim of Luke that Lucas is a knight if and only if Sophia is a knight.", "We have exhausted all possibilities for Lucas, Luke, and Jackson, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that If Jackson is a knave then Mia is a knave.", "Jackson cannot be a knight, because this would contradict the claim of Chloe that If Sophia is a knave then Jackson is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Luke is a knight.", "Luke cannot be a knight, because this would contradict the false claim of Jackson that Luke is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Lucas is a knight if and only if Sophia is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Liam is a knight or Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Liam is a knight or Chloe is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('lying', 7)), ('<=>', ('telling-truth', 6), ('telling-truth', 3)), ('->', ('lying', 7), ('lying', 5)), ('and', ('telling-truth', 4), ('lying', 0)), ('or', ('lying', 2), ('telling-truth', 5)), ('or', ('telling-truth', 2), ('telling-truth', 0)), ('or', ('telling-truth', 2), ('telling-truth', 5)), ('telling-truth', 1))", "index": 684}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: William, Abigail, Harper, Aria, Michael, Scarlett, Owen, and Alexander. \"Aria is a knave if and only if Abigail is a knight,\" William mentioned. As Abigail put it, \"Alexander is a knave\". \"William is a knight,\" Harper claimed. Aria stated, \"If William is a knight then William is a knave\". Michael told you that William is a knight if and only if Owen is a knave. \"If Aria is a knight then William is a knight,\" Scarlett declared. As Owen put it, \"William is a knight if and only if Abigail is a knight\". Alexander commented, \"Aria is a knave if and only if Alexander is a knight\". So who is a knight and who is a knave?", "names": ["William", "Abigail", "Harper", "Aria", "Michael", "Scarlett", "Owen", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true, true, false], "solution_text": "William is a knight, Abigail is a knight, Harper is a knight, Aria is a knave, Michael is a knave, Scarlett is a knight, Owen is a knight, and Alexander is a knave.", "solution_text_format": "(1) William is a knight\n(2) Abigail is a knight\n(3) Harper is a knight\n(4) Aria is a knave\n(5) Michael is a knave\n(6) Scarlett is a knight\n(7) Owen is a knight\n(8) Alexander is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Aria is a knave if and only if Abigail is a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that If William is a knight then William is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that If William is a knight then William is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Alexander is a knave.", "Alexander cannot be a knight, because this would contradict the claim of Abigail that Alexander is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Aria is a knave if and only if Alexander is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that William is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that William is a knight if and only if Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of Michael that William is a knight if and only if Owen is a knave.", "Owen cannot be a knave, because this would contradict the false claim of their own that William is a knight if and only if Abigail is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that William is a knight if and only if Owen is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that William is a knight if and only if Abigail is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Aria is a knight then William is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('telling-truth', 1)), ('lying', 7), ('telling-truth', 0), ('->', ('telling-truth', 0), ('lying', 0)), ('<=>', ('telling-truth', 0), ('lying', 6)), ('->', ('telling-truth', 3), ('telling-truth', 0)), ('<=>', ('telling-truth', 0), ('telling-truth', 1)), ('<=>', ('lying', 3), ('telling-truth', 7)))", "index": 685}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Daniel, Penelope, Lucas, Owen, Luke, Lily, Mason, and Jackson. As Daniel put it, \"Jackson is a knave if and only if Mason is a knave\". In Penelope's words: \"If Luke is a knave then Jackson is a knave\". Lucas noted, \"If Mason is a knave then Mason is a knight\". \"Lily is not a knight,\" Owen declared. Luke expressed that Daniel is a knave and Penelope is a knave. Lily remarked, \"Jackson is a knave\". \"Jackson is a knight if and only if Jackson is a knave,\" Mason claimed. \"Owen is a knight if and only if Mason is a knave\" - Jackson. So who is a knight and who is a knave?", "names": ["Daniel", "Penelope", "Lucas", "Owen", "Luke", "Lily", "Mason", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, true, false, false], "solution_text": "Daniel is a knight, Penelope is a knight, Lucas is a knave, Owen is a knave, Luke is a knave, Lily is a knight, Mason is a knave, and Jackson is a knave.", "solution_text_format": "(1) Daniel is a knight\n(2) Penelope is a knight\n(3) Lucas is a knave\n(4) Owen is a knave\n(5) Luke is a knave\n(6) Lily is a knight\n(7) Mason is a knave\n(8) Jackson is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that Jackson is a knave if and only if Mason is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Owen is a knight if and only if Mason is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Lily is not a knight.", "Lily cannot be a knight, because this would contradict the claim of Owen that Lily is not a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Jackson is a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Jackson is a knight if and only if Jackson is a knave.", "Mason cannot be a knave, because this would contradict the claim of Daniel that Jackson is a knave if and only if Mason is a knave.", "We have exhausted all possibilities for Mason and Lily, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Lily is not a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Jackson is a knave.", "Lily cannot be a knave, because this would contradict the false claim of Owen that Lily is not a knight.", "We have exhausted all possibilities for Lily and Owen, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Owen is a knight if and only if Mason is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Lily is not a knight.", "Lily cannot be a knight, because this would contradict the claim of Owen that Lily is not a knight.", "Lily cannot be a knave, because this would contradict the false claim of their own that Jackson is a knave.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Lily is not a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Jackson is a knave.", "Mason cannot be a knight, because this would contradict the claim of Daniel that Jackson is a knave if and only if Mason is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Jackson is a knight if and only if Jackson is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that If Luke is a knave then Jackson is a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that Daniel is a knave and Penelope is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Daniel is a knave and Penelope is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that If Mason is a knave then Mason is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that If Mason is a knave then Mason is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 7), ('lying', 6)), ('->', ('lying', 4), ('lying', 7)), ('->', ('lying', 6), ('telling-truth', 6)), ('not', ('telling-truth', 5)), ('and', ('lying', 0), ('lying', 1)), ('lying', 7), ('<=>', ('telling-truth', 7), ('lying', 7)), ('<=>', ('telling-truth', 3), ('lying', 6)))", "index": 686}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Olivia, Samuel, Aiden, Michael, Aurora, Elizabeth, Liam, and Mia. Olivia asserted: \"Michael is a knight or Aiden is a knight\". In a statement by Samuel: \"Mia is a knight\". Aiden stated, \"Samuel is not a knight\". Michael was heard saying, \"Samuel is a knave or Michael is a knight\". Aurora expressed that Michael is a knave. Elizabeth was heard saying, \"Olivia is a knight and Michael is a knave\". Liam told you that Samuel is not a knight. Mia asserted: \"Aurora is a knave if and only if Samuel is a knave\". So who is a knight and who is a knave?", "names": ["Olivia", "Samuel", "Aiden", "Michael", "Aurora", "Elizabeth", "Liam", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, false, false, true], "solution_text": "Olivia is a knave, Samuel is a knight, Aiden is a knave, Michael is a knave, Aurora is a knight, Elizabeth is a knave, Liam is a knave, and Mia is a knight.", "solution_text_format": "(1) Olivia is a knave\n(2) Samuel is a knight\n(3) Aiden is a knave\n(4) Michael is a knave\n(5) Aurora is a knight\n(6) Elizabeth is a knave\n(7) Liam is a knave\n(8) Mia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Michael is a knight or Aiden is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Samuel is a knave or Michael is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Aurora is a knave if and only if Samuel is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Michael is a knave.", "Aurora cannot be a knave, because this would contradict the claim of Mia that Aurora is a knave if and only if Samuel is a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the claim of Samuel that Mia is a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Mia is a knight.", "Mia cannot be a knight, because this would contradict the false claim of Samuel that Mia is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Aurora is a knave if and only if Samuel is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Michael is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of Mia that Aurora is a knave if and only if Samuel is a knave.", "We have exhausted all possibilities for Aurora, Mia, and Samuel, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Samuel is a knave or Michael is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Aurora is a knave if and only if Samuel is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Michael is a knave.", "Aiden cannot be a knight, because this would contradict the claim of their own that Samuel is not a knight.", "Aiden cannot be a knave, because this would contradict the claim of Olivia that Michael is a knight or Aiden is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the false claim of their own that Michael is a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the claim of Samuel that Mia is a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Samuel.", "Samuel cannot be a knave, because this would contradict the false claim of Michael that Samuel is a knave or Michael is a knight.", "We have exhausted all possibilities for Samuel and Michael, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Michael is a knight or Aiden is a knight.", "Michael cannot be a knight, because this would contradict the false claim of Olivia that Michael is a knight or Aiden is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Samuel is a knave or Michael is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Aurora is a knave if and only if Samuel is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Michael is a knave.", "Aiden cannot be a knight, because this would contradict the false claim of Olivia that Michael is a knight or Aiden is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Samuel is not a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Olivia is a knight and Michael is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Olivia is a knight and Michael is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Samuel is not a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Samuel is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('telling-truth', 2)), ('telling-truth', 7), ('not', ('telling-truth', 1)), ('or', ('lying', 1), ('telling-truth', 3)), ('lying', 3), ('and', ('telling-truth', 0), ('lying', 3)), ('not', ('telling-truth', 1)), ('<=>', ('lying', 4), ('lying', 1)))", "index": 687}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ava, Logan, Sebastian, Sophia, Harper, Sofia, Noah, and Mia. According to Ava, \"Sebastian is a knave if and only if Sofia is a knight\". Logan said that Sofia is a knave. In a statement by Sebastian: \"If Noah is a knight then Sofia is a knave\". \"Noah is not a knight,\" Sophia claimed. Harper said that Logan is a knave and Sebastian is a knight. Sofia was heard saying, \"Ava is a knave\". Noah asserted: \"Harper is not a knave\". \"If Ava is a knave then Sofia is a knight,\" Mia claimed. So who is a knight and who is a knave?", "names": ["Ava", "Logan", "Sebastian", "Sophia", "Harper", "Sofia", "Noah", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false, false, true], "solution_text": "Ava is a knight, Logan is a knight, Sebastian is a knight, Sophia is a knight, Harper is a knave, Sofia is a knave, Noah is a knave, and Mia is a knight.", "solution_text_format": "(1) Ava is a knight\n(2) Logan is a knight\n(3) Sebastian is a knight\n(4) Sophia is a knight\n(5) Harper is a knave\n(6) Sofia is a knave\n(7) Noah is a knave\n(8) Mia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Sebastian is a knave if and only if Sofia is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Noah is a knight then Sofia is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Harper is not a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Logan is a knave and Sebastian is a knight.", "Logan cannot be a knight, because this would contradict the claim of Harper that Logan is a knave and Sebastian is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Ava that Sebastian is a knave if and only if Sofia is a knight.", "Sofia cannot be a knave, because this would contradict the false claim of Logan that Sofia is a knave.", "We have exhausted all possibilities for Sofia and Logan, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the claim of Noah that Harper is not a knave.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Harper is not a knave.", "Harper cannot be a knight, because this would contradict the false claim of Noah that Harper is not a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Logan is a knave and Sebastian is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Ava that Sebastian is a knave if and only if Sofia is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Ava is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Noah is not a knight.", "Assume Mia is a knight. No contradiction is found in their claim that If Ava is a knave then Sofia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('telling-truth', 5)), ('lying', 5), ('->', ('telling-truth', 6), ('lying', 5)), ('not', ('telling-truth', 6)), ('and', ('lying', 1), ('telling-truth', 2)), ('lying', 0), ('not', ('lying', 4)), ('->', ('lying', 0), ('telling-truth', 5)))", "index": 688}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: David, Aiden, Elizabeth, Joseph, Victoria, Chloe, Matthew, and Harper. David expressed that Harper is a knight or Elizabeth is a knave. In a statement by Aiden: \"If Elizabeth is a knave then Aiden is a knight\". Elizabeth stated, \"Chloe is a knave or Joseph is a knave\". \"Victoria is a knight and Matthew is a knave,\" Joseph claimed. As Victoria put it, \"Joseph is a knave\". In Chloe's words: \"Joseph is a knight or Harper is a knight\". Matthew said that If Harper is a knight then Victoria is a knight. According to Harper, \"If Aiden is a knight then Victoria is a knave\". So who is a knight and who is a knave?", "names": ["David", "Aiden", "Elizabeth", "Joseph", "Victoria", "Chloe", "Matthew", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, false, true, false], "solution_text": "David is a knave, Aiden is a knight, Elizabeth is a knight, Joseph is a knave, Victoria is a knight, Chloe is a knave, Matthew is a knight, and Harper is a knave.", "solution_text_format": "(1) David is a knave\n(2) Aiden is a knight\n(3) Elizabeth is a knight\n(4) Joseph is a knave\n(5) Victoria is a knight\n(6) Chloe is a knave\n(7) Matthew is a knight\n(8) Harper is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Harper is a knight or Elizabeth is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that If Aiden is a knight then Victoria is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Aiden is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Chloe is a knave or Joseph is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Joseph is a knight or Harper is a knight.", "Joseph cannot be a knight, because this would contradict the claim of Elizabeth that Chloe is a knave or Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Victoria is a knight and Matthew is a knave.", "Victoria cannot be a knight, because this would contradict the claim of Harper that If Aiden is a knight then Victoria is a knave.", "Victoria cannot be a knave, because this would contradict the false claim of their own that Joseph is a knave.", "We have exhausted all possibilities for Victoria and Joseph, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the false claim of their own that Joseph is a knight or Harper is a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Chloe is a knave or Joseph is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Joseph is a knight or Harper is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Victoria is a knight and Matthew is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that Joseph is a knave.", "Victoria cannot be a knave, because this would contradict the claim of Joseph that Victoria is a knight and Matthew is a knave.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the false claim of Elizabeth that Chloe is a knave or Joseph is a knave.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the false claim of Elizabeth that Chloe is a knave or Joseph is a knave.", "We have exhausted all possibilities for Chloe and Elizabeth, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that If Elizabeth is a knave then Aiden is a knight.", "Elizabeth cannot be a knight, because this would contradict the false claim of Aiden that If Elizabeth is a knave then Aiden is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Chloe is a knave or Joseph is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Joseph is a knight or Harper is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Victoria is a knight and Matthew is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that Joseph is a knave.", "Victoria cannot be a knave, because this would contradict the claim of Joseph that Victoria is a knight and Matthew is a knave.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the false claim of Elizabeth that Chloe is a knave or Joseph is a knave.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the false claim of Elizabeth that Chloe is a knave or Joseph is a knave.", "We have exhausted all possibilities for Chloe, Elizabeth, and Aiden, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that If Aiden is a knight then Victoria is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Aiden is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of David that Harper is a knight or Elizabeth is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Chloe is a knave or Joseph is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Joseph is a knight or Harper is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Victoria is a knight and Matthew is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that Joseph is a knave.", "Victoria cannot be a knave, because this would contradict the claim of Joseph that Victoria is a knight and Matthew is a knave.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the false claim of Elizabeth that Chloe is a knave or Joseph is a knave.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the false claim of Elizabeth that Chloe is a knave or Joseph is a knave.", "We have exhausted all possibilities for Chloe and Elizabeth, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the false claim of Harper that If Aiden is a knight then Victoria is a knave.", "We have exhausted all possibilities for Aiden and Harper, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Harper is a knight or Elizabeth is a knave.", "Harper cannot be a knight, because this would contradict the false claim of David that Harper is a knight or Elizabeth is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that If Aiden is a knight then Victoria is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Aiden is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Chloe is a knave or Joseph is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Joseph is a knight or Harper is a knight.", "Joseph cannot be a knight, because this would contradict the claim of Elizabeth that Chloe is a knave or Joseph is a knave.", "Joseph cannot be a knave, because this would contradict the claim of Chloe that Joseph is a knight or Harper is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Joseph is a knight or Harper is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of Chloe that Joseph is a knight or Harper is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Victoria is a knight and Matthew is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Joseph is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that If Harper is a knight then Victoria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 7), ('lying', 2)), ('->', ('lying', 2), ('telling-truth', 1)), ('or', ('lying', 5), ('lying', 3)), ('and', ('telling-truth', 4), ('lying', 6)), ('lying', 3), ('or', ('telling-truth', 3), ('telling-truth', 7)), ('->', ('telling-truth', 7), ('telling-truth', 4)), ('->', ('telling-truth', 1), ('lying', 4)))", "index": 689}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Benjamin, Elizabeth, Aiden, Evelyn, Michael, Ella, Joseph, and Olivia. In a statement by Benjamin: \"Aiden is a knight or Benjamin is a knight\". Elizabeth stated, \"If Benjamin is a knave then Ella is a knight\". Aiden told you that Evelyn is a knight. In a statement by Evelyn: \"Elizabeth is not a knight\". As Michael put it, \"Benjamin is a knight if and only if Evelyn is a knight\". Ella expressed that Olivia is a knight and Elizabeth is a knave. In a statement by Joseph: \"Elizabeth is a knight or Benjamin is a knight\". Olivia told you that Evelyn is a knave and Benjamin is a knave. So who is a knight and who is a knave?", "names": ["Benjamin", "Elizabeth", "Aiden", "Evelyn", "Michael", "Ella", "Joseph", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, false, true, false], "solution_text": "Benjamin is a knight, Elizabeth is a knight, Aiden is a knave, Evelyn is a knave, Michael is a knave, Ella is a knave, Joseph is a knight, and Olivia is a knave.", "solution_text_format": "(1) Benjamin is a knight\n(2) Elizabeth is a knight\n(3) Aiden is a knave\n(4) Evelyn is a knave\n(5) Michael is a knave\n(6) Ella is a knave\n(7) Joseph is a knight\n(8) Olivia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Aiden is a knight or Benjamin is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Evelyn is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Elizabeth is not a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Evelyn that Elizabeth is not a knight.", "Elizabeth cannot be a knave, because this would contradict the false claim of their own that If Benjamin is a knave then Ella is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the claim of Aiden that Evelyn is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Evelyn is a knight.", "Evelyn cannot be a knight, because this would contradict the false claim of Aiden that Evelyn is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Elizabeth is not a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Benjamin is a knave then Ella is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Olivia is a knight and Elizabeth is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Olivia is a knight and Elizabeth is a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave and Benjamin is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Evelyn is a knave and Benjamin is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight if and only if Evelyn is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Benjamin is a knight if and only if Evelyn is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Elizabeth is a knight or Benjamin is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('telling-truth', 0)), ('->', ('lying', 0), ('telling-truth', 5)), ('telling-truth', 3), ('not', ('telling-truth', 1)), ('<=>', ('telling-truth', 0), ('telling-truth', 3)), ('and', ('telling-truth', 7), ('lying', 1)), ('or', ('telling-truth', 1), ('telling-truth', 0)), ('and', ('lying', 3), ('lying', 0)))", "index": 690}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: William, Penelope, Sebastian, Jacob, Sophia, Charlotte, Amelia, and Harper. According to William, \"If Amelia is a knave then Sophia is a knave\". Penelope commented, \"Amelia is a knight\". Sebastian told you that Jacob is a knave and Charlotte is a knight. According to Jacob, \"If Jacob is a knight then Penelope is a knave\". \"If Charlotte is a knight then Jacob is a knight,\" Sophia mentioned. In Charlotte's words: \"Harper is a knight or William is a knave\". Amelia expressed that William is a knight. Harper was heard saying, \"If Sebastian is a knave then Amelia is a knight\". So who is a knight and who is a knave?", "names": ["William", "Penelope", "Sebastian", "Jacob", "Sophia", "Charlotte", "Amelia", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true, false, false], "solution_text": "William is a knave, Penelope is a knave, Sebastian is a knave, Jacob is a knight, Sophia is a knight, Charlotte is a knight, Amelia is a knave, and Harper is a knave.", "solution_text_format": "(1) William is a knave\n(2) Penelope is a knave\n(3) Sebastian is a knave\n(4) Jacob is a knight\n(5) Sophia is a knight\n(6) Charlotte is a knight\n(7) Amelia is a knave\n(8) Harper is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that If Amelia is a knave then Sophia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that William is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that If Charlotte is a knight then Jacob is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Harper is a knight or William is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that If Sebastian is a knave then Amelia is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Jacob is a knave and Charlotte is a knight.", "Jacob cannot be a knight, because this would contradict the claim of Sebastian that Jacob is a knave and Charlotte is a knight.", "Jacob cannot be a knave, because this would contradict the false claim of their own that If Jacob is a knight then Penelope is a knave.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Jacob is a knave and Charlotte is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that If Jacob is a knight then Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the claim of Jacob that If Jacob is a knight then Penelope is a knave.", "Penelope cannot be a knave, because this would contradict the false claim of their own that Amelia is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the false claim of Sebastian that Jacob is a knave and Charlotte is a knight.", "We have exhausted all possibilities for Jacob and Sebastian, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the claim of Charlotte that Harper is a knight or William is a knave.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Harper is a knight or William is a knave.", "Harper cannot be a knight, because this would contradict the false claim of Charlotte that Harper is a knight or William is a knave.", "Harper cannot be a knave, because this would contradict the false claim of their own that If Sebastian is a knave then Amelia is a knight.", "We have exhausted all possibilities for Harper and Charlotte, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that If Charlotte is a knight then Jacob is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Harper is a knight or William is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that If Sebastian is a knave then Amelia is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Jacob is a knave and Charlotte is a knight.", "Jacob cannot be a knight, because this would contradict the claim of Sebastian that Jacob is a knave and Charlotte is a knight.", "Jacob cannot be a knave, because this would contradict the false claim of their own that If Jacob is a knight then Penelope is a knave.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Jacob is a knave and Charlotte is a knight.", "Jacob cannot be a knight, because this would contradict the false claim of Sophia that If Charlotte is a knight then Jacob is a knight.", "Jacob cannot be a knave, because this would contradict the false claim of Sebastian that Jacob is a knave and Charlotte is a knight.", "We have exhausted all possibilities for Jacob and Sebastian, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the claim of Charlotte that Harper is a knight or William is a knave.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the false claim of Sophia that If Charlotte is a knight then Jacob is a knight.", "We have exhausted all possibilities for Charlotte and Sophia, so let us go back and reconsider Amelia.", "Amelia cannot be a knave, because this would contradict the false claim of their own that William is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that If Amelia is a knave then Sophia is a knave.", "Amelia cannot be a knight, because this would contradict the false claim of William that If Amelia is a knave then Sophia is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that William is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that If Charlotte is a knight then Jacob is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Harper is a knight or William is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that If Sebastian is a knave then Amelia is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Jacob is a knave and Charlotte is a knight.", "Jacob cannot be a knight, because this would contradict the claim of Sebastian that Jacob is a knave and Charlotte is a knight.", "Jacob cannot be a knave, because this would contradict the false claim of their own that If Jacob is a knight then Penelope is a knave.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the claim of Harper that If Sebastian is a knave then Amelia is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that If Sebastian is a knave then Amelia is a knight.", "Sebastian cannot be a knight, because this would contradict the false claim of Harper that If Sebastian is a knave then Amelia is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Jacob is a knave and Charlotte is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that If Jacob is a knight then Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Amelia is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Amelia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 6), ('lying', 4)), ('telling-truth', 6), ('and', ('lying', 3), ('telling-truth', 5)), ('->', ('telling-truth', 3), ('lying', 1)), ('->', ('telling-truth', 5), ('telling-truth', 3)), ('or', ('telling-truth', 7), ('lying', 0)), ('telling-truth', 0), ('->', ('lying', 2), ('telling-truth', 6)))", "index": 691}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Daniel, Ethan, Riley, Michael, Oliver, Penelope, Victoria, and Liam. \"Penelope is a knight or Riley is a knave,\" Daniel claimed. Ethan remarked, \"If Liam is a knight then Victoria is a knight\". Riley asserted: \"Penelope is not a knave\". Michael remarked, \"Daniel is a knight and Riley is a knave\". Oliver was heard saying, \"Penelope is a knave if and only if Liam is a knave\". Penelope commented, \"Ethan is a knight\". \"Daniel is a knight\" - Victoria. As Liam put it, \"Daniel is a knave\". So who is a knight and who is a knave?", "names": ["Daniel", "Ethan", "Riley", "Michael", "Oliver", "Penelope", "Victoria", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true, true, false], "solution_text": "Daniel is a knight, Ethan is a knight, Riley is a knight, Michael is a knave, Oliver is a knave, Penelope is a knight, Victoria is a knight, and Liam is a knave.", "solution_text_format": "(1) Daniel is a knight\n(2) Ethan is a knight\n(3) Riley is a knight\n(4) Michael is a knave\n(5) Oliver is a knave\n(6) Penelope is a knight\n(7) Victoria is a knight\n(8) Liam is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that Penelope is a knight or Riley is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Ethan is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If Liam is a knight then Victoria is a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that Daniel is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Daniel is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Daniel is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Penelope is not a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Daniel is a knight and Riley is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Daniel is a knight and Riley is a knave.", "Oliver cannot be a knight, because this would contradict the claim of their own that Penelope is a knave if and only if Liam is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Penelope is a knave if and only if Liam is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('lying', 2)), ('->', ('telling-truth', 7), ('telling-truth', 6)), ('not', ('lying', 5)), ('and', ('telling-truth', 0), ('lying', 2)), ('<=>', ('lying', 5), ('lying', 7)), ('telling-truth', 1), ('telling-truth', 0), ('lying', 0))", "index": 692}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Elizabeth, Evelyn, Lily, Joseph, Sofia, Mason, Ethan, and William. \"Mason is a knave if and only if Evelyn is a knave,\" Elizabeth mentioned. \"Joseph is not a knave\" - Evelyn. According to Lily, \"Ethan is a knight\". Joseph said that Mason is a knave or Evelyn is a knight. Sofia noted, \"Joseph is a knave\". Mason asserted: \"Sofia is a knave or Evelyn is a knight\". Ethan stated, \"Sofia is a knight or William is a knave\". William expressed that Mason is not a knight. So who is a knight and who is a knave?", "names": ["Elizabeth", "Evelyn", "Lily", "Joseph", "Sofia", "Mason", "Ethan", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true, true, false], "solution_text": "Elizabeth is a knight, Evelyn is a knight, Lily is a knight, Joseph is a knight, Sofia is a knave, Mason is a knight, Ethan is a knight, and William is a knave.", "solution_text_format": "(1) Elizabeth is a knight\n(2) Evelyn is a knight\n(3) Lily is a knight\n(4) Joseph is a knight\n(5) Sofia is a knave\n(6) Mason is a knight\n(7) Ethan is a knight\n(8) William is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Mason is a knave if and only if Evelyn is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Sofia is a knave or Evelyn is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Sofia that Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Mason is a knave or Evelyn is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Joseph is not a knave.", "Evelyn cannot be a knave, because this would contradict the claim of Elizabeth that Mason is a knave if and only if Evelyn is a knave.", "We have exhausted all possibilities for Evelyn and Joseph, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Joseph is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Mason is a knave or Evelyn is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Joseph is not a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Ethan is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Sofia is a knight or William is a knave.", "William cannot be a knight, because this would contradict the claim of Ethan that Sofia is a knight or William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Mason is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 5), ('lying', 1)), ('not', ('lying', 3)), ('telling-truth', 6), ('or', ('lying', 5), ('telling-truth', 1)), ('lying', 3), ('or', ('lying', 4), ('telling-truth', 1)), ('or', ('telling-truth', 4), ('lying', 7)), ('not', ('telling-truth', 5)))", "index": 693}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Owen, Logan, Matthew, Grace, David, Sebastian, Mia, and Isabella. Owen commented, \"Sebastian is a knave\". In a statement by Logan: \"David is a knight and Isabella is a knave\". In a statement by Matthew: \"Grace is a knight if and only if Isabella is a knight\". \"Mia is a knight if and only if Logan is a knight,\" Grace declared. In David's words: \"Grace is a knave\". \"Owen is a knight if and only if Matthew is a knave,\" Sebastian mentioned. Mia remarked, \"Logan is a knave if and only if Sebastian is a knight\". \"If Isabella is a knight then Grace is a knight,\" Isabella mentioned. So who is a knight and who is a knave?", "names": ["Owen", "Logan", "Matthew", "Grace", "David", "Sebastian", "Mia", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, false, false, true], "solution_text": "Owen is a knight, Logan is a knave, Matthew is a knight, Grace is a knight, David is a knave, Sebastian is a knave, Mia is a knave, and Isabella is a knight.", "solution_text_format": "(1) Owen is a knight\n(2) Logan is a knave\n(3) Matthew is a knight\n(4) Grace is a knight\n(5) David is a knave\n(6) Sebastian is a knave\n(7) Mia is a knave\n(8) Isabella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Owen that Sebastian is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Owen is a knight if and only if Matthew is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Grace is a knight if and only if Isabella is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Mia is a knight if and only if Logan is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Logan is a knave if and only if Sebastian is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that David is a knight and Isabella is a knave.", "David cannot be a knight, because this would contradict the claim of their own that Grace is a knave.", "David cannot be a knave, because this would contradict the claim of Logan that David is a knight and Isabella is a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the claim of Grace that Mia is a knight if and only if Logan is a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Logan is a knave if and only if Sebastian is a knight.", "Logan cannot be a knight, because this would contradict the claim of Grace that Mia is a knight if and only if Logan is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that David is a knight and Isabella is a knave.", "David cannot be a knight, because this would contradict the claim of their own that Grace is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Grace is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that If Isabella is a knight then Grace is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 5), ('and', ('telling-truth', 4), ('lying', 7)), ('<=>', ('telling-truth', 3), ('telling-truth', 7)), ('<=>', ('telling-truth', 6), ('telling-truth', 1)), ('lying', 3), ('<=>', ('telling-truth', 0), ('lying', 2)), ('<=>', ('lying', 1), ('telling-truth', 5)), ('->', ('telling-truth', 7), ('telling-truth', 3)))", "index": 694}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sebastian, Abigail, Ava, Jackson, Liam, Charlotte, Luke, and Logan. Sebastian asserted: \"Luke is a knave or Abigail is a knave\". Abigail remarked, \"If Logan is a knave then Jackson is a knave\". Ava remarked, \"Sebastian is a knight if and only if Jackson is a knave\". In Jackson's words: \"Liam is a knave\". Liam noted, \"If Charlotte is a knave then Logan is a knave\". \"If Sebastian is a knight then Liam is a knave,\" Charlotte declared. In Luke's words: \"Jackson is not a knight\". Logan said that Liam is a knight if and only if Abigail is a knight. So who is a knight and who is a knave?", "names": ["Sebastian", "Abigail", "Ava", "Jackson", "Liam", "Charlotte", "Luke", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true, true, true], "solution_text": "Sebastian is a knave, Abigail is a knight, Ava is a knave, Jackson is a knave, Liam is a knight, Charlotte is a knight, Luke is a knight, and Logan is a knight.", "solution_text_format": "(1) Sebastian is a knave\n(2) Abigail is a knight\n(3) Ava is a knave\n(4) Jackson is a knave\n(5) Liam is a knight\n(6) Charlotte is a knight\n(7) Luke is a knight\n(8) Logan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that Luke is a knave or Abigail is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Jackson is not a knight.", "Jackson cannot be a knight, because this would contradict the claim of Luke that Jackson is not a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Liam is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that If Charlotte is a knave then Logan is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that If Sebastian is a knight then Liam is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that If Sebastian is a knight then Liam is a knave.", "Logan cannot be a knight, because this would contradict the claim of Liam that If Charlotte is a knave then Logan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Liam is a knight if and only if Abigail is a knight.", "Abigail cannot be a knight, because this would contradict the claim of Sebastian that Luke is a knave or Abigail is a knave.", "Abigail cannot be a knave, because this would contradict the false claim of their own that If Logan is a knave then Jackson is a knave.", "We have exhausted all possibilities for Abigail, Logan, and Charlotte, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the false claim of Jackson that Liam is a knave.", "We have exhausted all possibilities for Liam and Jackson, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Jackson is not a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of Jackson that Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that If Charlotte is a knave then Logan is a knave.", "Charlotte cannot be a knight, because this would contradict the false claim of Liam that If Charlotte is a knave then Logan is a knave.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that If Sebastian is a knight then Liam is a knave.", "We have exhausted all possibilities for Charlotte and Liam, so let us go back and reconsider Jackson.", "Jackson cannot be a knave, because this would contradict the false claim of Luke that Jackson is not a knight.", "We have exhausted all possibilities for Jackson and Luke, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Luke is a knave or Abigail is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Jackson is not a knight.", "Jackson cannot be a knight, because this would contradict the claim of Luke that Jackson is not a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Liam is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that If Charlotte is a knave then Logan is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Sebastian is a knight then Liam is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Liam is a knight if and only if Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If Logan is a knave then Jackson is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight if and only if Jackson is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Sebastian is a knight if and only if Jackson is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 6), ('lying', 1)), ('->', ('lying', 7), ('lying', 3)), ('<=>', ('telling-truth', 0), ('lying', 3)), ('lying', 4), ('->', ('lying', 5), ('lying', 7)), ('->', ('telling-truth', 0), ('lying', 4)), ('not', ('telling-truth', 3)), ('<=>', ('telling-truth', 4), ('telling-truth', 1)))", "index": 695}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: James, Samuel, Olivia, Charlotte, Grace, Benjamin, Logan, and Avery. \"Avery is not a knight\" - James. \"Logan is a knight,\" Samuel declared. In Olivia's words: \"If Grace is a knight then Avery is a knight\". As Charlotte put it, \"If Benjamin is a knight then Avery is a knave\". \"Avery is a knave or Samuel is a knight,\" Grace claimed. Benjamin told you that James is not a knave. \"Grace is not a knight,\" Logan declared. In a statement by Avery: \"James is a knave or Logan is a knight\". So who is a knight and who is a knave?", "names": ["James", "Samuel", "Olivia", "Charlotte", "Grace", "Benjamin", "Logan", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true, false, false], "solution_text": "James is a knight, Samuel is a knave, Olivia is a knave, Charlotte is a knight, Grace is a knight, Benjamin is a knight, Logan is a knave, and Avery is a knave.", "solution_text_format": "(1) James is a knight\n(2) Samuel is a knave\n(3) Olivia is a knave\n(4) Charlotte is a knight\n(5) Grace is a knight\n(6) Benjamin is a knight\n(7) Logan is a knave\n(8) Avery is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Avery is not a knight.", "Avery cannot be a knight, because this would contradict the claim of James that Avery is not a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that James is a knave or Logan is a knight.", "Logan cannot be a knight, because this would contradict the false claim of Avery that James is a knave or Logan is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Grace is not a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Avery is a knave or Samuel is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Logan is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Logan is a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that If Grace is a knight then Avery is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that If Grace is a knight then Avery is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Benjamin is a knight then Avery is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that James is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 7)), ('telling-truth', 6), ('->', ('telling-truth', 4), ('telling-truth', 7)), ('->', ('telling-truth', 5), ('lying', 7)), ('or', ('lying', 7), ('telling-truth', 1)), ('not', ('lying', 0)), ('not', ('telling-truth', 4)), ('or', ('lying', 0), ('telling-truth', 6)))", "index": 696}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Scarlett, Sebastian, Joseph, Mason, Aurora, Henry, Olivia, and Aria. In a statement by Scarlett: \"Aria is not a knave\". \"If Henry is a knight then Mason is a knight,\" Sebastian claimed. \"Mason is not a knave,\" Joseph claimed. In a statement by Mason: \"If Olivia is a knave then Henry is a knave\". \"Joseph is not a knave,\" Aurora mentioned. \"Scarlett is not a knave,\" Henry mentioned. \"Aurora is a knight,\" Olivia declared. \"Scarlett is a knave if and only if Olivia is a knight,\" Aria claimed. So who is a knight and who is a knave?", "names": ["Scarlett", "Sebastian", "Joseph", "Mason", "Aurora", "Henry", "Olivia", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, true, false, true], "solution_text": "Scarlett is a knight, Sebastian is a knave, Joseph is a knave, Mason is a knave, Aurora is a knave, Henry is a knight, Olivia is a knave, and Aria is a knight.", "solution_text_format": "(1) Scarlett is a knight\n(2) Sebastian is a knave\n(3) Joseph is a knave\n(4) Mason is a knave\n(5) Aurora is a knave\n(6) Henry is a knight\n(7) Olivia is a knave\n(8) Aria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Aria is not a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Scarlett is a knave if and only if Olivia is a knight.", "Olivia cannot be a knight, because this would contradict the claim of Aria that Scarlett is a knave if and only if Olivia is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Aurora is a knight.", "Aurora cannot be a knight, because this would contradict the false claim of Olivia that Aurora is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Joseph is not a knave.", "Joseph cannot be a knight, because this would contradict the false claim of Aurora that Joseph is not a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Mason is not a knave.", "Mason cannot be a knight, because this would contradict the false claim of Joseph that Mason is not a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that If Olivia is a knave then Henry is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Sebastian cannot be a knight, because this would contradict the claim of their own that If Henry is a knight then Mason is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that If Henry is a knight then Mason is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 7)), ('->', ('telling-truth', 5), ('telling-truth', 3)), ('not', ('lying', 3)), ('->', ('lying', 6), ('lying', 5)), ('not', ('lying', 2)), ('not', ('lying', 0)), ('telling-truth', 4), ('<=>', ('lying', 0), ('telling-truth', 6)))", "index": 697}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Oliver, Lily, William, Aurora, Abigail, Isabella, Lucas, and Chloe. Oliver told you that Isabella is not a knave. \"Chloe is a knave,\" Lily claimed. William commented, \"Aurora is a knight\". Aurora remarked, \"Isabella is not a knight\". Abigail stated, \"Isabella is a knave if and only if Lucas is a knave\". In Isabella's words: \"William is a knight and Oliver is a knight\". Lucas said that Lily is not a knave. Chloe said that Oliver is a knave and Isabella is a knight. So who is a knight and who is a knave?", "names": ["Oliver", "Lily", "William", "Aurora", "Abigail", "Isabella", "Lucas", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false, true, false], "solution_text": "Oliver is a knave, Lily is a knight, William is a knight, Aurora is a knight, Abigail is a knave, Isabella is a knave, Lucas is a knight, and Chloe is a knave.", "solution_text_format": "(1) Oliver is a knave\n(2) Lily is a knight\n(3) William is a knight\n(4) Aurora is a knight\n(5) Abigail is a knave\n(6) Isabella is a knave\n(7) Lucas is a knight\n(8) Chloe is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Isabella is not a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that William is a knight and Oliver is a knight.", "Assume William is a knight. No contradiction is found in their claim that Aurora is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Isabella is not a knight.", "Aurora cannot be a knave, because this would contradict the claim of William that Aurora is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the claim of Isabella that William is a knight and Oliver is a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the claim of Oliver that Isabella is not a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Isabella is not a knave.", "Isabella cannot be a knight, because this would contradict the false claim of Oliver that Isabella is not a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that William is a knight and Oliver is a knight.", "Assume William is a knight. No contradiction is found in their claim that Aurora is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Isabella is not a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Lily that Chloe is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Oliver is a knave and Isabella is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Isabella is a knave if and only if Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the claim of Abigail that Isabella is a knave if and only if Lucas is a knave.", "Lucas cannot be a knave, because this would contradict the false claim of their own that Lily is not a knave.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Isabella is a knave if and only if Lucas is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Lily is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 5)), ('lying', 7), ('telling-truth', 3), ('not', ('telling-truth', 5)), ('<=>', ('lying', 5), ('lying', 6)), ('and', ('telling-truth', 2), ('telling-truth', 0)), ('not', ('lying', 1)), ('and', ('lying', 0), ('telling-truth', 5)))", "index": 698}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sophia, Zoey, Aria, David, Matthew, Alexander, Ella, and Mia. As Sophia put it, \"Sophia is a knight or Mia is a knave\". In a statement by Zoey: \"If David is a knight then Ella is a knave\". According to Aria, \"Alexander is a knave if and only if Ella is a knight\". David expressed that Matthew is a knight. Matthew asserted: \"Sophia is a knave\". In a statement by Alexander: \"David is a knight and Mia is a knave\". Ella noted, \"Sophia is not a knave\". Mia stated, \"David is not a knight\". So who is a knight and who is a knave?", "names": ["Sophia", "Zoey", "Aria", "David", "Matthew", "Alexander", "Ella", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false, true, true], "solution_text": "Sophia is a knight, Zoey is a knight, Aria is a knight, David is a knave, Matthew is a knave, Alexander is a knave, Ella is a knight, and Mia is a knight.", "solution_text_format": "(1) Sophia is a knight\n(2) Zoey is a knight\n(3) Aria is a knight\n(4) David is a knave\n(5) Matthew is a knave\n(6) Alexander is a knave\n(7) Ella is a knight\n(8) Mia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Sophia is a knight or Mia is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that David is not a knight.", "David cannot be a knight, because this would contradict the claim of Mia that David is not a knight.", "Assume David is a knave. No contradiction is found in their false claim that Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the false claim of David that Matthew is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Sophia is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that If David is a knight then Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Sophia is not a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Alexander is a knave if and only if Ella is a knight.", "Alexander cannot be a knight, because this would contradict the claim of Aria that Alexander is a knave if and only if Ella is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that David is a knight and Mia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 0), ('lying', 7)), ('->', ('telling-truth', 3), ('lying', 6)), ('<=>', ('lying', 5), ('telling-truth', 6)), ('telling-truth', 4), ('lying', 0), ('and', ('telling-truth', 3), ('lying', 7)), ('not', ('lying', 0)), ('not', ('telling-truth', 3)))", "index": 699}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Joseph, Mia, Emily, Lily, Mason, Ava, Victoria, and Chloe. Joseph said, \"Emily is a knave and Mia is a knave.\" According to Mia, \"Victoria is a knave\". \"Lily is a knave or Chloe is a knave,\" Emily mentioned. According to Lily, \"Mason is a knight or Joseph is a knave\". In Mason's words: \"Ava is a knave or Mason is a knight\". Ava was heard saying, \"Mason is a knave and Mason is a knight\". \"Lily is a knave,\" Victoria claimed. As Chloe put it, \"Joseph is a knave or Mason is a knave\". So who is a knight and who is a knave?", "names": ["Joseph", "Mia", "Emily", "Lily", "Mason", "Ava", "Victoria", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false, false, true], "solution_text": "Joseph is a knave, Mia is a knight, Emily is a knave, Lily is a knight, Mason is a knight, Ava is a knave, Victoria is a knave, and Chloe is a knight.", "solution_text_format": "(1) Joseph is a knave\n(2) Mia is a knight\n(3) Emily is a knave\n(4) Lily is a knight\n(5) Mason is a knight\n(6) Ava is a knave\n(7) Victoria is a knave\n(8) Chloe is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that Emily is a knave and Mia is a knave.", "Emily cannot be a knight, because this would contradict the claim of Joseph that Emily is a knave and Mia is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Lily is a knave or Chloe is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Mason is a knight or Joseph is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Ava is a knave or Mason is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Mason is a knave and Mason is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Mason is a knave and Mason is a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Joseph is a knave or Mason is a knave.", "Chloe cannot be a knave, because this would contradict the false claim of Emily that Lily is a knave or Chloe is a knave.", "We have exhausted all possibilities for Chloe and Ava, so let us go back and reconsider Mason.", "Mason cannot be a knave, because this would contradict the claim of Lily that Mason is a knight or Joseph is a knave.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the false claim of Emily that Lily is a knave or Chloe is a knave.", "We have exhausted all possibilities for Lily and Emily, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Emily is a knave and Mia is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Lily is a knave or Chloe is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Mason is a knight or Joseph is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Ava is a knave or Mason is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Mason is a knave and Mason is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Mason is a knave and Mason is a knight.", "Chloe cannot be a knight, because this would contradict the claim of Emily that Lily is a knave or Chloe is a knave.", "Chloe cannot be a knave, because this would contradict the false claim of their own that Joseph is a knave or Mason is a knave.", "We have exhausted all possibilities for Chloe and Ava, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Ava is a knave or Mason is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Mason is a knave and Mason is a knight.", "Ava cannot be a knave, because this would contradict the false claim of Mason that Ava is a knave or Mason is a knight.", "We have exhausted all possibilities for Ava and Mason, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the false claim of their own that Mason is a knight or Joseph is a knave.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Lily is a knave or Chloe is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Mason is a knight or Joseph is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Ava is a knave or Mason is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Mason is a knave and Mason is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Mason is a knave and Mason is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Joseph is a knave or Mason is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Victoria is a knave.", "Victoria cannot be a knight, because this would contradict the claim of Mia that Victoria is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Lily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('lying', 1)), ('lying', 6), ('or', ('lying', 3), ('lying', 7)), ('or', ('telling-truth', 4), ('lying', 0)), ('or', ('lying', 5), ('telling-truth', 4)), ('and', ('lying', 4), ('telling-truth', 4)), ('lying', 3), ('or', ('lying', 0), ('lying', 4)))", "index": 700}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: William, Charlotte, Alexander, Penelope, Sebastian, Owen, Samuel, and Logan. William was heard saying, \"Sebastian is a knight\". \"William is a knight if and only if William is a knave,\" Charlotte declared. Alexander remarked, \"If Penelope is a knight then William is a knight\". In Penelope's words: \"Samuel is a knave if and only if Charlotte is a knave\". In Sebastian's words: \"If Owen is a knave then Penelope is a knave\". Owen stated, \"Owen is a knight and Logan is a knave\". Samuel said that Logan is not a knight. According to Logan, \"Charlotte is not a knight\". So who is a knight and who is a knave?", "names": ["William", "Charlotte", "Alexander", "Penelope", "Sebastian", "Owen", "Samuel", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, false, false, true], "solution_text": "William is a knave, Charlotte is a knave, Alexander is a knave, Penelope is a knight, Sebastian is a knave, Owen is a knave, Samuel is a knave, and Logan is a knight.", "solution_text_format": "(1) William is a knave\n(2) Charlotte is a knave\n(3) Alexander is a knave\n(4) Penelope is a knight\n(5) Sebastian is a knave\n(6) Owen is a knave\n(7) Samuel is a knave\n(8) Logan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Owen is a knave then Penelope is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Owen is a knight and Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of Owen that Owen is a knight and Logan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Charlotte is not a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that William is a knight if and only if William is a knave.", "Charlotte cannot be a knave, because this would contradict the false claim of Logan that Charlotte is not a knight.", "We have exhausted all possibilities for Charlotte and Logan, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Owen is a knight and Logan is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Charlotte is not a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that William is a knight if and only if William is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that William is a knight if and only if William is a knave.", "Penelope cannot be a knight, because this would contradict the claim of Sebastian that If Owen is a knave then Penelope is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Samuel is a knave if and only if Charlotte is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that Logan is not a knight.", "Samuel cannot be a knave, because this would contradict the false claim of Penelope that Samuel is a knave if and only if Charlotte is a knave.", "We have exhausted all possibilities for Samuel, Penelope, and Charlotte, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Charlotte is not a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that William is a knight if and only if William is a knave.", "Charlotte cannot be a knave, because this would contradict the false claim of Logan that Charlotte is not a knight.", "We have exhausted all possibilities for Charlotte, Logan, and Owen, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the claim of William that Sebastian is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Sebastian is a knight.", "Sebastian cannot be a knight, because this would contradict the false claim of William that Sebastian is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that If Owen is a knave then Penelope is a knave.", "Owen cannot be a knight, because this would contradict the false claim of Sebastian that If Owen is a knave then Penelope is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Owen is a knight and Logan is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Charlotte is not a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that William is a knight if and only if William is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that William is a knight if and only if William is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Charlotte is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Penelope that Samuel is a knave if and only if Charlotte is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Logan is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that If Penelope is a knight then William is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that If Penelope is a knight then William is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('<=>', ('telling-truth', 0), ('lying', 0)), ('->', ('telling-truth', 3), ('telling-truth', 0)), ('<=>', ('lying', 6), ('lying', 1)), ('->', ('lying', 5), ('lying', 3)), ('and', ('telling-truth', 5), ('lying', 7)), ('not', ('telling-truth', 7)), ('not', ('telling-truth', 1)))", "index": 701}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Isabella, Emma, Sofia, Mia, Ethan, Joseph, Lucas, and Sophia. Isabella commented, \"If Sofia is a knight then Sofia is a knave\". According to Emma, \"Joseph is not a knight\". Sofia noted, \"If Mia is a knight then Sophia is a knight\". In Mia's words: \"Emma is a knave if and only if Joseph is a knave\". Ethan commented, \"Sophia is not a knave\". \"Isabella is a knight if and only if Mia is a knight\" - Joseph. In Lucas's words: \"If Ethan is a knight then Emma is a knave\". Sophia stated, \"Sofia is a knight\". So who is a knight and who is a knave?", "names": ["Isabella", "Emma", "Sofia", "Mia", "Ethan", "Joseph", "Lucas", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true, true, true], "solution_text": "Isabella is a knave, Emma is a knave, Sofia is a knight, Mia is a knave, Ethan is a knight, Joseph is a knight, Lucas is a knight, and Sophia is a knight.", "solution_text_format": "(1) Isabella is a knave\n(2) Emma is a knave\n(3) Sofia is a knight\n(4) Mia is a knave\n(5) Ethan is a knight\n(6) Joseph is a knight\n(7) Lucas is a knight\n(8) Sophia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that If Sofia is a knight then Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Isabella that If Sofia is a knight then Sofia is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that If Mia is a knight then Sophia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Emma is a knave if and only if Joseph is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Joseph is not a knight.", "Joseph cannot be a knight, because this would contradict the claim of Emma that Joseph is not a knight.", "Joseph cannot be a knave, because this would contradict the claim of Mia that Emma is a knave if and only if Joseph is a knave.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Joseph is not a knight.", "Joseph cannot be a knight, because this would contradict the claim of Mia that Emma is a knave if and only if Joseph is a knave.", "Joseph cannot be a knave, because this would contradict the false claim of Emma that Joseph is not a knight.", "We have exhausted all possibilities for Joseph and Emma, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the false claim of Sofia that If Mia is a knight then Sophia is a knight.", "We have exhausted all possibilities for Mia and Sofia, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that If Sofia is a knight then Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that If Mia is a knight then Sophia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Emma is a knave if and only if Joseph is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Joseph is not a knight.", "Joseph cannot be a knight, because this would contradict the claim of Emma that Joseph is not a knight.", "Joseph cannot be a knave, because this would contradict the claim of Mia that Emma is a knave if and only if Joseph is a knave.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Joseph is not a knight.", "Joseph cannot be a knight, because this would contradict the claim of Mia that Emma is a knave if and only if Joseph is a knave.", "Joseph cannot be a knave, because this would contradict the false claim of Emma that Joseph is not a knight.", "We have exhausted all possibilities for Joseph and Emma, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Emma is a knave if and only if Joseph is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Joseph is not a knight.", "Joseph cannot be a knight, because this would contradict the claim of Emma that Joseph is not a knight.", "Joseph cannot be a knave, because this would contradict the false claim of their own that Isabella is a knight if and only if Mia is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Joseph is not a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Mia is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Sofia is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Sophia is not a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that If Ethan is a knight then Emma is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('lying', 2)), ('not', ('telling-truth', 5)), ('->', ('telling-truth', 3), ('telling-truth', 7)), ('<=>', ('lying', 1), ('lying', 5)), ('not', ('lying', 7)), ('<=>', ('telling-truth', 0), ('telling-truth', 3)), ('->', ('telling-truth', 4), ('lying', 1)), ('telling-truth', 2))", "index": 702}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lily, James, Scarlett, Liam, Ethan, Aiden, Mia, and Sofia. In Lily's words: \"Ethan is a knave and Lily is a knight\". James told you that Sofia is a knave or Liam is a knight. Scarlett told you that If Mia is a knight then Liam is a knight. As Liam put it, \"Mia is not a knight\". In a statement by Ethan: \"Mia is a knave and Aiden is a knave\". Aiden stated, \"Ethan is a knight if and only if Mia is a knight\". Mia expressed that Aiden is not a knave. Sofia was heard saying, \"Mia is a knight if and only if Scarlett is a knave\". So who is a knight and who is a knave?", "names": ["Lily", "James", "Scarlett", "Liam", "Ethan", "Aiden", "Mia", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false, false, true], "solution_text": "Lily is a knave, James is a knight, Scarlett is a knight, Liam is a knight, Ethan is a knight, Aiden is a knave, Mia is a knave, and Sofia is a knight.", "solution_text_format": "(1) Lily is a knave\n(2) James is a knight\n(3) Scarlett is a knight\n(4) Liam is a knight\n(5) Ethan is a knight\n(6) Aiden is a knave\n(7) Mia is a knave\n(8) Sofia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that Ethan is a knave and Lily is a knight.", "Ethan cannot be a knight, because this would contradict the claim of Lily that Ethan is a knave and Lily is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Mia is a knave and Aiden is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Aiden is not a knave.", "Aiden cannot be a knight, because this would contradict the claim of their own that Ethan is a knight if and only if Mia is a knight.", "Aiden cannot be a knave, because this would contradict the claim of Mia that Aiden is not a knave.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Aiden is not a knave.", "Aiden cannot be a knight, because this would contradict the false claim of Mia that Aiden is not a knave.", "Aiden cannot be a knave, because this would contradict the false claim of Ethan that Mia is a knave and Aiden is a knave.", "We have exhausted all possibilities for Aiden, Mia, and Ethan, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Ethan is a knave and Lily is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Mia is a knave and Aiden is a knave.", "Mia cannot be a knight, because this would contradict the claim of Ethan that Mia is a knave and Aiden is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Aiden is not a knave.", "Aiden cannot be a knight, because this would contradict the claim of Ethan that Mia is a knave and Aiden is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Ethan is a knight if and only if Mia is a knight.", "Assume James is a knight. No contradiction is found in their claim that Sofia is a knave or Liam is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Mia is a knight if and only if Scarlett is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Mia is a knight then Liam is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Mia is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('telling-truth', 0)), ('or', ('lying', 7), ('telling-truth', 3)), ('->', ('telling-truth', 6), ('telling-truth', 3)), ('not', ('telling-truth', 6)), ('and', ('lying', 6), ('lying', 5)), ('<=>', ('telling-truth', 4), ('telling-truth', 6)), ('not', ('lying', 5)), ('<=>', ('telling-truth', 6), ('lying', 2)))", "index": 703}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Grace, Riley, Chloe, Emma, Logan, Owen, Penelope, and Aurora. Grace remarked, \"Emma is a knight if and only if Chloe is a knave\". Riley stated, \"Logan is a knight if and only if Grace is a knave\". Chloe was heard saying, \"Logan is a knight\". \"If Grace is a knight then Grace is a knave,\" Emma claimed. Logan told you that Aurora is a knave if and only if Emma is a knight. In a statement by Owen: \"Grace is not a knave\". As Penelope put it, \"Owen is a knave if and only if Chloe is a knight\". \"Aurora is a knight if and only if Emma is a knight,\" Aurora mentioned. So who is a knight and who is a knave?", "names": ["Grace", "Riley", "Chloe", "Emma", "Logan", "Owen", "Penelope", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false, true, false], "solution_text": "Grace is a knave, Riley is a knight, Chloe is a knight, Emma is a knight, Logan is a knight, Owen is a knave, Penelope is a knight, and Aurora is a knave.", "solution_text_format": "(1) Grace is a knave\n(2) Riley is a knight\n(3) Chloe is a knight\n(4) Emma is a knight\n(5) Logan is a knight\n(6) Owen is a knave\n(7) Penelope is a knight\n(8) Aurora is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Emma is a knight if and only if Chloe is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that If Grace is a knight then Grace is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that If Grace is a knight then Grace is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Logan is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Aurora is a knave if and only if Emma is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Aurora is a knight if and only if Emma is a knight.", "Aurora cannot be a knave, because this would contradict the claim of Logan that Aurora is a knave if and only if Emma is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the claim of Chloe that Logan is a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the claim of Grace that Emma is a knight if and only if Chloe is a knave.", "We have exhausted all possibilities for Chloe and Emma, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Emma is a knight if and only if Chloe is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that If Grace is a knight then Grace is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Logan is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Aurora is a knave if and only if Emma is a knight.", "Aurora cannot be a knight, because this would contradict the claim of Logan that Aurora is a knave if and only if Emma is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Aurora is a knight if and only if Emma is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Logan is a knight if and only if Grace is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Grace is not a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Grace is not a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Owen is a knave if and only if Chloe is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 3), ('lying', 2)), ('<=>', ('telling-truth', 4), ('lying', 0)), ('telling-truth', 4), ('->', ('telling-truth', 0), ('lying', 0)), ('<=>', ('lying', 7), ('telling-truth', 3)), ('not', ('lying', 0)), ('<=>', ('lying', 5), ('telling-truth', 2)), ('<=>', ('telling-truth', 7), ('telling-truth', 3)))", "index": 704}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Liam, Alexander, Aiden, Jackson, Victoria, Evelyn, Chloe, and Sophia. As Liam put it, \"Alexander is a knight and Liam is a knight\". Alexander expressed that Jackson is a knight if and only if Aiden is a knight. Aiden said that If Jackson is a knave then Liam is a knave. Jackson commented, \"Liam is a knave if and only if Victoria is a knight\". \"If Aiden is a knave then Liam is a knave\" - Victoria. Evelyn told you that Evelyn is a knight or Alexander is a knight. In Chloe's words: \"Jackson is a knave and Alexander is a knave\". Sophia stated, \"If Victoria is a knave then Jackson is a knight\". So who is a knight and who is a knave?", "names": ["Liam", "Alexander", "Aiden", "Jackson", "Victoria", "Evelyn", "Chloe", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true, false, true], "solution_text": "Liam is a knave, Alexander is a knight, Aiden is a knight, Jackson is a knight, Victoria is a knight, Evelyn is a knight, Chloe is a knave, and Sophia is a knight.", "solution_text_format": "(1) Liam is a knave\n(2) Alexander is a knight\n(3) Aiden is a knight\n(4) Jackson is a knight\n(5) Victoria is a knight\n(6) Evelyn is a knight\n(7) Chloe is a knave\n(8) Sophia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Alexander is a knight and Liam is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Aiden is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Liam is a knave if and only if Victoria is a knight.", "Victoria cannot be a knight, because this would contradict the claim of Jackson that Liam is a knave if and only if Victoria is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that If Aiden is a knave then Liam is a knave.", "Aiden cannot be a knight, because this would contradict the false claim of Victoria that If Aiden is a knave then Liam is a knave.", "Aiden cannot be a knave, because this would contradict the claim of Alexander that Jackson is a knight if and only if Aiden is a knight.", "We have exhausted all possibilities for Aiden and Victoria, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Liam is a knave if and only if Victoria is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that If Aiden is a knave then Liam is a knave.", "Aiden cannot be a knight, because this would contradict the claim of Alexander that Jackson is a knight if and only if Aiden is a knight.", "Aiden cannot be a knave, because this would contradict the claim of Victoria that If Aiden is a knave then Liam is a knave.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Victoria.", "Victoria cannot be a knave, because this would contradict the false claim of Jackson that Liam is a knave if and only if Victoria is a knight.", "We have exhausted all possibilities for Victoria and Jackson, so let us go back and reconsider Alexander.", "Alexander cannot be a knave, because this would contradict the claim of Liam that Alexander is a knight and Liam is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Alexander is a knight and Liam is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Aiden is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Liam is a knave if and only if Victoria is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that If Aiden is a knave then Liam is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Jackson is a knave then Liam is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Evelyn is a knight or Alexander is a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Jackson is a knave and Alexander is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Jackson is a knave and Alexander is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that If Victoria is a knave then Jackson is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('telling-truth', 0)), ('<=>', ('telling-truth', 3), ('telling-truth', 2)), ('->', ('lying', 3), ('lying', 0)), ('<=>', ('lying', 0), ('telling-truth', 4)), ('->', ('lying', 2), ('lying', 0)), ('or', ('telling-truth', 5), ('telling-truth', 1)), ('and', ('lying', 3), ('lying', 1)), ('->', ('lying', 4), ('telling-truth', 3)))", "index": 705}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Chloe, Elizabeth, Matthew, Sofia, William, Victoria, Jackson, and Abigail. Chloe asserted: \"Abigail is not a knave\". \"Matthew is not a knave,\" Elizabeth mentioned. \"Abigail is a knight,\" Matthew claimed. Sofia remarked, \"Victoria is a knight and Abigail is a knight\". William said, \"Sofia is not a knight.\" Victoria told you that Abigail is a knight and Jackson is a knight. \"Matthew is a knave and Victoria is a knight,\" Jackson claimed. Abigail stated, \"Jackson is a knight\". So who is a knight and who is a knave?", "names": ["Chloe", "Elizabeth", "Matthew", "Sofia", "William", "Victoria", "Jackson", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, false, false, false], "solution_text": "Chloe is a knave, Elizabeth is a knave, Matthew is a knave, Sofia is a knave, William is a knight, Victoria is a knave, Jackson is a knave, and Abigail is a knave.", "solution_text_format": "(1) Chloe is a knave\n(2) Elizabeth is a knave\n(3) Matthew is a knave\n(4) Sofia is a knave\n(5) William is a knight\n(6) Victoria is a knave\n(7) Jackson is a knave\n(8) Abigail is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Abigail is not a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Jackson is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Matthew is a knave and Victoria is a knight.", "Matthew cannot be a knight, because this would contradict the claim of Jackson that Matthew is a knave and Victoria is a knight.", "Matthew cannot be a knave, because this would contradict the false claim of their own that Abigail is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Jackson.", "Jackson cannot be a knave, because this would contradict the claim of Abigail that Jackson is a knight.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the claim of Chloe that Abigail is not a knave.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Abigail is not a knave.", "Abigail cannot be a knight, because this would contradict the false claim of Chloe that Abigail is not a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Jackson is a knight.", "Jackson cannot be a knight, because this would contradict the false claim of Abigail that Jackson is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Matthew is a knave and Victoria is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Abigail is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Abigail is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Abigail is a knight and Jackson is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Abigail is a knight and Jackson is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Matthew is not a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Matthew is not a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Victoria is a knight and Abigail is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Victoria is a knight and Abigail is a knight.", "Assume William is a knight. No contradiction is found in their claim that Sofia is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 7)), ('not', ('lying', 2)), ('telling-truth', 7), ('and', ('telling-truth', 5), ('telling-truth', 7)), ('not', ('telling-truth', 3)), ('and', ('telling-truth', 7), ('telling-truth', 6)), ('and', ('lying', 2), ('telling-truth', 5)), ('telling-truth', 6))", "index": 706}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Owen, Emily, Noah, Jacob, Zoey, Grace, Jackson, and Aurora. \"If Jacob is a knave then Grace is a knight,\" Owen mentioned. As Emily put it, \"Grace is a knight\". Noah asserted: \"Emily is not a knave\". Jacob remarked, \"Owen is not a knight\". Zoey commented, \"Jacob is a knave and Zoey is a knight\". Grace asserted: \"Zoey is a knave\". Jackson told you that Owen is a knight. \"Jacob is a knave or Owen is a knave,\" Aurora declared. So who is a knight and who is a knave?", "names": ["Owen", "Emily", "Noah", "Jacob", "Zoey", "Grace", "Jackson", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true, true, true], "solution_text": "Owen is a knight, Emily is a knight, Noah is a knight, Jacob is a knave, Zoey is a knave, Grace is a knight, Jackson is a knight, and Aurora is a knight.", "solution_text_format": "(1) Owen is a knight\n(2) Emily is a knight\n(3) Noah is a knight\n(4) Jacob is a knave\n(5) Zoey is a knave\n(6) Grace is a knight\n(7) Jackson is a knight\n(8) Aurora is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that If Jacob is a knave then Grace is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Owen is not a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Owen is not a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Grace that Zoey is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Jacob is a knave and Zoey is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Grace is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Emily is not a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Owen is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Jacob is a knave or Owen is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('telling-truth', 5)), ('telling-truth', 5), ('not', ('lying', 1)), ('not', ('telling-truth', 0)), ('and', ('lying', 3), ('telling-truth', 4)), ('lying', 4), ('telling-truth', 0), ('or', ('lying', 3), ('lying', 0)))", "index": 707}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Liam, Alexander, Lucas, Lily, Victoria, Aria, Abigail, and Charlotte. Liam commented, \"Charlotte is not a knave\". According to Alexander, \"If Victoria is a knave then Lily is a knave\". \"Abigail is a knave and Victoria is a knight,\" Lucas mentioned. Lily said, \"If Lucas is a knight then Aria is a knight.\" \"Charlotte is a knight,\" Victoria declared. \"Victoria is a knight if and only if Charlotte is a knight,\" Aria mentioned. Abigail stated, \"Lily is a knight or Liam is a knave\". Charlotte said that Lucas is a knight. So who is a knight and who is a knave?", "names": ["Liam", "Alexander", "Lucas", "Lily", "Victoria", "Aria", "Abigail", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, true, true, false], "solution_text": "Liam is a knave, Alexander is a knave, Lucas is a knave, Lily is a knight, Victoria is a knave, Aria is a knight, Abigail is a knight, and Charlotte is a knave.", "solution_text_format": "(1) Liam is a knave\n(2) Alexander is a knave\n(3) Lucas is a knave\n(4) Lily is a knight\n(5) Victoria is a knave\n(6) Aria is a knight\n(7) Abigail is a knight\n(8) Charlotte is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Charlotte is not a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Abigail is a knave and Victoria is a knight.", "Abigail cannot be a knight, because this would contradict the claim of Lucas that Abigail is a knave and Victoria is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Lily is a knight or Liam is a knave.", "Lily cannot be a knight, because this would contradict the false claim of Abigail that Lily is a knight or Liam is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that If Lucas is a knight then Aria is a knight.", "Aria cannot be a knight, because this would contradict the false claim of Lily that If Lucas is a knight then Aria is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Victoria is a knight if and only if Charlotte is a knight.", "Victoria cannot be a knight, because this would contradict the false claim of Aria that Victoria is a knight if and only if Charlotte is a knight.", "Victoria cannot be a knave, because this would contradict the claim of Lucas that Abigail is a knave and Victoria is a knight.", "We have exhausted all possibilities for Victoria, Aria, Lily, and Abigail, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the claim of Charlotte that Lucas is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the claim of Liam that Charlotte is not a knave.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Charlotte is not a knave.", "Charlotte cannot be a knight, because this would contradict the false claim of Liam that Charlotte is not a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of Charlotte that Lucas is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Abigail is a knave and Victoria is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Lily is a knight or Liam is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that If Lucas is a knight then Aria is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Charlotte is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Charlotte is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Charlotte is a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that If Victoria is a knave then Lily is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that If Victoria is a knave then Lily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 7)), ('->', ('lying', 4), ('lying', 3)), ('and', ('lying', 6), ('telling-truth', 4)), ('->', ('telling-truth', 2), ('telling-truth', 5)), ('telling-truth', 7), ('<=>', ('telling-truth', 4), ('telling-truth', 7)), ('or', ('telling-truth', 3), ('lying', 0)), ('telling-truth', 2))", "index": 708}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Harper, Scarlett, James, Emma, Lucas, Noah, Jack, and Penelope. \"Noah is a knight,\" Harper mentioned. Scarlett expressed that If Harper is a knight then Jack is a knave. James said that Scarlett is a knight. Emma said, \"James is a knight and Lucas is a knave.\" Lucas said that James is a knight and Jack is a knight. According to Noah, \"Penelope is a knave\". Jack commented, \"If Noah is a knave then Penelope is a knight\". \"James is a knave if and only if Scarlett is a knave,\" Penelope claimed. So who is a knight and who is a knave?", "names": ["Harper", "Scarlett", "James", "Emma", "Lucas", "Noah", "Jack", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, false, true, true], "solution_text": "Harper is a knave, Scarlett is a knight, James is a knight, Emma is a knave, Lucas is a knight, Noah is a knave, Jack is a knight, and Penelope is a knight.", "solution_text_format": "(1) Harper is a knave\n(2) Scarlett is a knight\n(3) James is a knight\n(4) Emma is a knave\n(5) Lucas is a knight\n(6) Noah is a knave\n(7) Jack is a knight\n(8) Penelope is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that Noah is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the claim of Noah that Penelope is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that James is a knave if and only if Scarlett is a knave.", "Assume James is a knight. No contradiction is found in their claim that Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the false claim of Penelope that James is a knave if and only if Scarlett is a knave.", "Scarlett cannot be a knave, because this would contradict the claim of James that Scarlett is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the false claim of James that Scarlett is a knight.", "Scarlett cannot be a knave, because this would contradict the false claim of Penelope that James is a knave if and only if Scarlett is a knave.", "We have exhausted all possibilities for Scarlett, James, and Penelope, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the claim of Harper that Noah is a knight.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Noah is a knight.", "Noah cannot be a knight, because this would contradict the false claim of Harper that Noah is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Penelope is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that James is a knave if and only if Scarlett is a knave.", "Assume James is a knight. No contradiction is found in their claim that Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Harper is a knight then Jack is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that If Noah is a knave then Penelope is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that James is a knight and Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the claim of Emma that James is a knight and Lucas is a knave.", "Lucas cannot be a knave, because this would contradict the false claim of their own that James is a knight and Jack is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that James is a knight and Lucas is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that James is a knight and Jack is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 5), ('->', ('telling-truth', 0), ('lying', 6)), ('telling-truth', 1), ('and', ('telling-truth', 2), ('lying', 4)), ('and', ('telling-truth', 2), ('telling-truth', 6)), ('lying', 7), ('->', ('lying', 5), ('telling-truth', 7)), ('<=>', ('lying', 2), ('lying', 1)))", "index": 709}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jackson, Victoria, Ella, Luke, Olivia, Benjamin, Amelia, and Isabella. \"Ella is a knight or Amelia is a knave,\" Jackson declared. \"Benjamin is a knave and Amelia is a knight,\" Victoria claimed. Ella said, \"Jackson is a knight.\" Luke noted, \"Olivia is a knave if and only if Amelia is a knight\". Olivia said, \"Benjamin is not a knight.\" Benjamin stated, \"Amelia is a knave and Isabella is a knave\". In a statement by Amelia: \"Ella is a knave or Olivia is a knave\". \"Luke is a knight if and only if Victoria is a knight,\" Isabella mentioned. So who is a knight and who is a knave?", "names": ["Jackson", "Victoria", "Ella", "Luke", "Olivia", "Benjamin", "Amelia", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, false, true, false], "solution_text": "Jackson is a knave, Victoria is a knight, Ella is a knave, Luke is a knave, Olivia is a knight, Benjamin is a knave, Amelia is a knight, and Isabella is a knave.", "solution_text_format": "(1) Jackson is a knave\n(2) Victoria is a knight\n(3) Ella is a knave\n(4) Luke is a knave\n(5) Olivia is a knight\n(6) Benjamin is a knave\n(7) Amelia is a knight\n(8) Isabella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Ella is a knight or Amelia is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Jackson is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Ella is a knave or Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Amelia that Ella is a knave or Olivia is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Benjamin is not a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Amelia is a knave and Isabella is a knave.", "Benjamin cannot be a knave, because this would contradict the false claim of Olivia that Benjamin is not a knight.", "We have exhausted all possibilities for Benjamin and Olivia, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Ella is a knave or Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Benjamin is not a knight.", "Benjamin cannot be a knight, because this would contradict the claim of Olivia that Benjamin is not a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Amelia is a knave and Isabella is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Luke is a knight if and only if Victoria is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Olivia is a knave if and only if Amelia is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave and Amelia is a knight.", "Victoria cannot be a knave, because this would contradict the claim of Isabella that Luke is a knight if and only if Victoria is a knight.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the false claim of their own that Olivia is a knave if and only if Amelia is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the false claim of Benjamin that Amelia is a knave and Isabella is a knave.", "We have exhausted all possibilities for Isabella and Benjamin, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the false claim of Amelia that Ella is a knave or Olivia is a knave.", "We have exhausted all possibilities for Olivia and Amelia, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the false claim of their own that Jackson is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Ella is a knight or Amelia is a knave.", "Ella cannot be a knight, because this would contradict the false claim of Jackson that Ella is a knight or Amelia is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Jackson is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Ella is a knave or Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Benjamin is not a knight.", "Benjamin cannot be a knight, because this would contradict the claim of Olivia that Benjamin is not a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Amelia is a knave and Isabella is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Luke is a knight if and only if Victoria is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Olivia is a knave if and only if Amelia is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Olivia is a knave if and only if Amelia is a knight.", "Victoria cannot be a knight, because this would contradict the claim of Isabella that Luke is a knight if and only if Victoria is a knight.", "Victoria cannot be a knave, because this would contradict the false claim of their own that Benjamin is a knave and Amelia is a knight.", "We have exhausted all possibilities for Victoria and Luke, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Luke is a knight if and only if Victoria is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Olivia is a knave if and only if Amelia is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Olivia is a knave if and only if Amelia is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Benjamin is a knave and Amelia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('lying', 6)), ('and', ('lying', 5), ('telling-truth', 6)), ('telling-truth', 0), ('<=>', ('lying', 4), ('telling-truth', 6)), ('not', ('telling-truth', 5)), ('and', ('lying', 6), ('lying', 7)), ('or', ('lying', 2), ('lying', 4)), ('<=>', ('telling-truth', 3), ('telling-truth', 1)))", "index": 710}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Samuel, Jacob, Riley, Abigail, Emma, Grace, Zoey, and Sebastian. Samuel told you that Zoey is not a knave. \"Riley is a knight or Jacob is a knight,\" Jacob mentioned. Riley said that Grace is a knave if and only if Abigail is a knight. \"Jacob is a knight\" - Abigail. In Emma's words: \"Sebastian is a knight if and only if Samuel is a knave\". Grace commented, \"Samuel is a knight or Samuel is a knave\". According to Zoey, \"Riley is a knave if and only if Grace is a knave\". \"Abigail is not a knight,\" Sebastian claimed. So who is a knight and who is a knave?", "names": ["Samuel", "Jacob", "Riley", "Abigail", "Emma", "Grace", "Zoey", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, true, false, false], "solution_text": "Samuel is a knave, Jacob is a knight, Riley is a knave, Abigail is a knight, Emma is a knave, Grace is a knight, Zoey is a knave, and Sebastian is a knave.", "solution_text_format": "(1) Samuel is a knave\n(2) Jacob is a knight\n(3) Riley is a knave\n(4) Abigail is a knight\n(5) Emma is a knave\n(6) Grace is a knight\n(7) Zoey is a knave\n(8) Sebastian is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that Zoey is not a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Riley is a knave if and only if Grace is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Grace is a knave if and only if Abigail is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Samuel is a knight or Samuel is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Riley that Grace is a knave if and only if Abigail is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Jacob is a knight.", "Jacob cannot be a knight, because this would contradict the false claim of Abigail that Jacob is a knight.", "Jacob cannot be a knave, because this would contradict the false claim of their own that Riley is a knight or Jacob is a knight.", "We have exhausted all possibilities for Jacob and Abigail, so let us go back and reconsider Grace.", "Grace cannot be a knave, because this would contradict the false claim of their own that Samuel is a knight or Samuel is a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Grace is a knave if and only if Abigail is a knight.", "Grace cannot be a knight, because this would contradict the claim of Zoey that Riley is a knave if and only if Grace is a knave.", "Grace cannot be a knave, because this would contradict the false claim of their own that Samuel is a knight or Samuel is a knave.", "We have exhausted all possibilities for Grace and Riley, so let us go back and reconsider Zoey.", "Zoey cannot be a knave, because this would contradict the claim of Samuel that Zoey is not a knave.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Zoey is not a knave.", "Zoey cannot be a knight, because this would contradict the false claim of Samuel that Zoey is not a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Riley is a knave if and only if Grace is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Grace is a knave if and only if Abigail is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Zoey that Riley is a knave if and only if Grace is a knave.", "Grace cannot be a knave, because this would contradict the false claim of their own that Samuel is a knight or Samuel is a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Grace is a knave if and only if Abigail is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Samuel is a knight or Samuel is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Riley is a knight or Jacob is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Sebastian is a knight if and only if Samuel is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Abigail is not a knight.", "Sebastian cannot be a knave, because this would contradict the claim of Emma that Sebastian is a knight if and only if Samuel is a knave.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Sebastian is a knight if and only if Samuel is a knave.", "Sebastian cannot be a knight, because this would contradict the false claim of Emma that Sebastian is a knight if and only if Samuel is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Abigail is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 6)), ('or', ('telling-truth', 2), ('telling-truth', 1)), ('<=>', ('lying', 5), ('telling-truth', 3)), ('telling-truth', 1), ('<=>', ('telling-truth', 7), ('lying', 0)), ('or', ('telling-truth', 0), ('lying', 0)), ('<=>', ('lying', 2), ('lying', 5)), ('not', ('telling-truth', 3)))", "index": 711}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Scarlett, Amelia, Riley, Matthew, Michael, Elizabeth, Sebastian, and Harper. Scarlett commented, \"Scarlett is a knight and Matthew is a knight\". According to Amelia, \"If Amelia is a knight then Sebastian is a knave\". Riley noted, \"If Scarlett is a knight then Elizabeth is a knave\". Matthew expressed that Scarlett is a knave if and only if Scarlett is a knight. In Michael's words: \"Scarlett is a knave if and only if Riley is a knight\". Elizabeth remarked, \"Harper is a knave\". In Sebastian's words: \"Riley is a knave if and only if Riley is a knight\". According to Harper, \"Michael is a knave\". So who is a knight and who is a knave?", "names": ["Scarlett", "Amelia", "Riley", "Matthew", "Michael", "Elizabeth", "Sebastian", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true, false, false], "solution_text": "Scarlett is a knave, Amelia is a knight, Riley is a knight, Matthew is a knave, Michael is a knight, Elizabeth is a knight, Sebastian is a knave, and Harper is a knave.", "solution_text_format": "(1) Scarlett is a knave\n(2) Amelia is a knight\n(3) Riley is a knight\n(4) Matthew is a knave\n(5) Michael is a knight\n(6) Elizabeth is a knight\n(7) Sebastian is a knave\n(8) Harper is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Scarlett is a knight and Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Scarlett is a knave if and only if Scarlett is a knight.", "Matthew cannot be a knave, because this would contradict the claim of Scarlett that Scarlett is a knight and Matthew is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Scarlett is a knight and Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Scarlett is a knave if and only if Scarlett is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Scarlett is a knave if and only if Scarlett is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that If Amelia is a knight then Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Amelia that If Amelia is a knight then Sebastian is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Riley is a knave if and only if Riley is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that If Scarlett is a knight then Elizabeth is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Harper is a knave.", "Harper cannot be a knight, because this would contradict the claim of Elizabeth that Harper is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Michael is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Scarlett is a knave if and only if Riley is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 0), ('telling-truth', 3)), ('->', ('telling-truth', 1), ('lying', 6)), ('->', ('telling-truth', 0), ('lying', 5)), ('<=>', ('lying', 0), ('telling-truth', 0)), ('<=>', ('lying', 0), ('telling-truth', 2)), ('lying', 7), ('<=>', ('lying', 2), ('telling-truth', 2)), ('lying', 4))", "index": 712}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Scarlett, Daniel, Benjamin, Sebastian, Luke, Riley, Grace, and Emily. Scarlett said that Riley is not a knave. Daniel said that If Scarlett is a knave then Grace is a knave. Benjamin expressed that Riley is not a knave. Sebastian asserted: \"Daniel is a knave and Riley is a knave\". In a statement by Luke: \"Sebastian is not a knave\". Riley asserted: \"Daniel is not a knight\". Grace told you that Luke is a knight or Sebastian is a knight. Emily was heard saying, \"Sebastian is a knight or Sebastian is a knave\". So who is a knight and who is a knave?", "names": ["Scarlett", "Daniel", "Benjamin", "Sebastian", "Luke", "Riley", "Grace", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, false, false, true], "solution_text": "Scarlett is a knave, Daniel is a knight, Benjamin is a knave, Sebastian is a knave, Luke is a knave, Riley is a knave, Grace is a knave, and Emily is a knight.", "solution_text_format": "(1) Scarlett is a knave\n(2) Daniel is a knight\n(3) Benjamin is a knave\n(4) Sebastian is a knave\n(5) Luke is a knave\n(6) Riley is a knave\n(7) Grace is a knave\n(8) Emily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Riley is not a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Daniel is not a knight.", "Daniel cannot be a knight, because this would contradict the claim of Riley that Daniel is not a knight.", "Daniel cannot be a knave, because this would contradict the false claim of their own that If Scarlett is a knave then Grace is a knave.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Riley.", "Riley cannot be a knave, because this would contradict the claim of Scarlett that Riley is not a knave.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Riley is not a knave.", "Riley cannot be a knight, because this would contradict the false claim of Scarlett that Riley is not a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Daniel is not a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that If Scarlett is a knave then Grace is a knave.", "Grace cannot be a knight, because this would contradict the claim of Daniel that If Scarlett is a knave then Grace is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Luke is a knight or Sebastian is a knight.", "Luke cannot be a knight, because this would contradict the false claim of Grace that Luke is a knight or Sebastian is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Sebastian is not a knave.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Daniel is a knave and Riley is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Daniel is a knave and Riley is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Riley is not a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Riley is not a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Sebastian is a knight or Sebastian is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 5)), ('->', ('lying', 0), ('lying', 6)), ('not', ('lying', 5)), ('and', ('lying', 1), ('lying', 5)), ('not', ('lying', 3)), ('not', ('telling-truth', 1)), ('or', ('telling-truth', 4), ('telling-truth', 3)), ('or', ('telling-truth', 3), ('lying', 3)))", "index": 713}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lily, Aiden, Sebastian, Sophia, Liam, Sofia, Joseph, and Oliver. According to Lily, \"Sofia is a knight and Sofia is a knave\". \"Joseph is a knight and Sophia is a knight,\" Aiden claimed. \"Sofia is a knave,\" Sebastian mentioned. Sophia told you that If Liam is a knave then Sofia is a knight. Liam commented, \"Sebastian is a knave\". \"Aiden is not a knave\" - Sofia. Joseph commented, \"If Sebastian is a knave then Sebastian is a knight\". Oliver asserted: \"Liam is a knight\". So who is a knight and who is a knave?", "names": ["Lily", "Aiden", "Sebastian", "Sophia", "Liam", "Sofia", "Joseph", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, false, true, false], "solution_text": "Lily is a knave, Aiden is a knave, Sebastian is a knight, Sophia is a knave, Liam is a knave, Sofia is a knave, Joseph is a knight, and Oliver is a knave.", "solution_text_format": "(1) Lily is a knave\n(2) Aiden is a knave\n(3) Sebastian is a knight\n(4) Sophia is a knave\n(5) Liam is a knave\n(6) Sofia is a knave\n(7) Joseph is a knight\n(8) Oliver is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Lily cannot be a knight, because this would contradict the claim of their own that Sofia is a knight and Sofia is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Sofia is a knight and Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Aiden is not a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Joseph is a knight and Sophia is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Sebastian is a knave then Sebastian is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Sofia is a knave.", "Sebastian cannot be a knave, because this would contradict the claim of Joseph that If Sebastian is a knave then Sebastian is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of Aiden that Joseph is a knight and Sophia is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the claim of Sofia that Aiden is not a knave.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Aiden is not a knave.", "Aiden cannot be a knight, because this would contradict the false claim of Sofia that Aiden is not a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Joseph is a knight and Sophia is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Sebastian is a knave then Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Sofia is a knave.", "Sophia cannot be a knight, because this would contradict the false claim of Aiden that Joseph is a knight and Sophia is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that If Liam is a knave then Sofia is a knight.", "Liam cannot be a knight, because this would contradict the false claim of Sophia that If Liam is a knave then Sofia is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Sebastian is a knave.", "Oliver cannot be a knight, because this would contradict the claim of their own that Liam is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Liam is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('lying', 5)), ('and', ('telling-truth', 6), ('telling-truth', 3)), ('lying', 5), ('->', ('lying', 4), ('telling-truth', 5)), ('lying', 2), ('not', ('lying', 1)), ('->', ('lying', 2), ('telling-truth', 2)), ('telling-truth', 4))", "index": 714}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mason, Samuel, Ethan, Scarlett, Oliver, Jack, Joseph, and Owen. Mason said that Ethan is a knave if and only if Scarlett is a knave. In Samuel's words: \"Oliver is a knave if and only if Jack is a knave\". Ethan said, \"Oliver is a knight if and only if Owen is a knave.\" Scarlett remarked, \"Owen is a knight\". \"Owen is not a knave,\" Oliver declared. \"Samuel is a knave,\" Jack mentioned. As Joseph put it, \"Mason is a knave\". Owen said that Jack is not a knight. So who is a knight and who is a knave?", "names": ["Mason", "Samuel", "Ethan", "Scarlett", "Oliver", "Jack", "Joseph", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, true, false, false], "solution_text": "Mason is a knight, Samuel is a knave, Ethan is a knave, Scarlett is a knave, Oliver is a knave, Jack is a knight, Joseph is a knave, and Owen is a knave.", "solution_text_format": "(1) Mason is a knight\n(2) Samuel is a knave\n(3) Ethan is a knave\n(4) Scarlett is a knave\n(5) Oliver is a knave\n(6) Jack is a knight\n(7) Joseph is a knave\n(8) Owen is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Ethan is a knave if and only if Scarlett is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Oliver is a knight if and only if Owen is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Owen is not a knave.", "Owen cannot be a knight, because this would contradict the claim of Ethan that Oliver is a knight if and only if Owen is a knave.", "Owen cannot be a knave, because this would contradict the claim of Oliver that Owen is not a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Owen is not a knave.", "Owen cannot be a knight, because this would contradict the false claim of Oliver that Owen is not a knave.", "Owen cannot be a knave, because this would contradict the claim of Ethan that Oliver is a knight if and only if Owen is a knave.", "We have exhausted all possibilities for Owen and Oliver, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Oliver is a knight if and only if Owen is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Owen is not a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Jack is not a knight.", "Jack cannot be a knight, because this would contradict the claim of Owen that Jack is not a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that Oliver is a knave if and only if Jack is a knave.", "Samuel cannot be a knave, because this would contradict the false claim of Jack that Samuel is a knave.", "We have exhausted all possibilities for Samuel and Jack, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the false claim of Ethan that Oliver is a knight if and only if Owen is a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Owen is not a knave.", "Owen cannot be a knight, because this would contradict the false claim of Ethan that Oliver is a knight if and only if Owen is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Jack is not a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that Oliver is a knave if and only if Jack is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Oliver is a knave if and only if Jack is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Mason that Ethan is a knave if and only if Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Owen is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Mason is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Mason is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('lying', 3)), ('<=>', ('lying', 4), ('lying', 5)), ('<=>', ('telling-truth', 4), ('lying', 7)), ('telling-truth', 7), ('not', ('lying', 7)), ('lying', 1), ('lying', 0), ('not', ('telling-truth', 5)))", "index": 715}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Oliver, Luke, Lucas, Mia, Alexander, Emma, Jack, and Ella. \"If Alexander is a knave then Lucas is a knave,\" Oliver claimed. According to Luke, \"If Lucas is a knave then Alexander is a knight\". Lucas was heard saying, \"Jack is a knight and Ella is a knight\". \"Jack is a knight if and only if Luke is a knight,\" Mia mentioned. In Alexander's words: \"Alexander is a knight if and only if Ella is a knave\". Emma expressed that Luke is a knight. According to Jack, \"Emma is a knave and Ella is a knight\". Ella said that If Alexander is a knight then Emma is a knave. So who is a knight and who is a knave?", "names": ["Oliver", "Luke", "Lucas", "Mia", "Alexander", "Emma", "Jack", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true, false, false], "solution_text": "Oliver is a knight, Luke is a knight, Lucas is a knave, Mia is a knave, Alexander is a knight, Emma is a knight, Jack is a knave, and Ella is a knave.", "solution_text_format": "(1) Oliver is a knight\n(2) Luke is a knight\n(3) Lucas is a knave\n(4) Mia is a knave\n(5) Alexander is a knight\n(6) Emma is a knight\n(7) Jack is a knave\n(8) Ella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that If Alexander is a knave then Lucas is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Alexander is a knight if and only if Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of Alexander that Alexander is a knight if and only if Ella is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that If Alexander is a knight then Emma is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Luke is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that If Lucas is a knave then Alexander is a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Jack is a knight and Ella is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Jack is a knight and Ella is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Emma is a knave and Ella is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Emma is a knave and Ella is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that Jack is a knight if and only if Luke is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Jack is a knight if and only if Luke is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 4), ('lying', 2)), ('->', ('lying', 2), ('telling-truth', 4)), ('and', ('telling-truth', 6), ('telling-truth', 7)), ('<=>', ('telling-truth', 6), ('telling-truth', 1)), ('<=>', ('telling-truth', 4), ('lying', 7)), ('telling-truth', 1), ('and', ('lying', 5), ('telling-truth', 7)), ('->', ('telling-truth', 4), ('lying', 5)))", "index": 716}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Luke, Avery, Oliver, Riley, Henry, Michael, Samuel, and Matthew. In Luke's words: \"Henry is a knave\". Avery asserted: \"Henry is not a knight\". As Oliver put it, \"Samuel is a knave if and only if Riley is a knight\". \"Oliver is a knave,\" Riley mentioned. As Henry put it, \"Matthew is a knight and Samuel is a knave\". According to Michael, \"Avery is not a knave\". Samuel asserted: \"Riley is not a knave\". Matthew expressed that If Avery is a knave then Matthew is a knight. So who is a knight and who is a knave?", "names": ["Luke", "Avery", "Oliver", "Riley", "Henry", "Michael", "Samuel", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true, true, true], "solution_text": "Luke is a knight, Avery is a knight, Oliver is a knave, Riley is a knight, Henry is a knave, Michael is a knight, Samuel is a knight, and Matthew is a knight.", "solution_text_format": "(1) Luke is a knight\n(2) Avery is a knight\n(3) Oliver is a knave\n(4) Riley is a knight\n(5) Henry is a knave\n(6) Michael is a knight\n(7) Samuel is a knight\n(8) Matthew is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of Luke that Henry is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Matthew is a knight and Samuel is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that If Avery is a knave then Matthew is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Henry is not a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Riley is not a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Oliver is a knave.", "Oliver cannot be a knight, because this would contradict the claim of their own that Samuel is a knave if and only if Riley is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Samuel is a knave if and only if Riley is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Avery is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('not', ('telling-truth', 4)), ('<=>', ('lying', 6), ('telling-truth', 3)), ('lying', 2), ('and', ('telling-truth', 7), ('lying', 6)), ('not', ('lying', 1)), ('not', ('lying', 3)), ('->', ('lying', 1), ('telling-truth', 7)))", "index": 717}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ella, Samuel, Jackson, Grace, William, Ava, Aria, and James. Ella remarked, \"Grace is a knight or William is a knight\". \"If William is a knave then Jackson is a knight,\" Samuel declared. Jackson remarked, \"If James is a knight then Samuel is a knave\". \"James is not a knight,\" Grace mentioned. According to William, \"James is a knave or Ella is a knight\". Ava told you that James is a knight. Aria said, \"Jackson is a knight if and only if Ella is a knight.\" \"Aria is a knight if and only if James is a knight,\" James claimed. So who is a knight and who is a knave?", "names": ["Ella", "Samuel", "Jackson", "Grace", "William", "Ava", "Aria", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false, true, false], "solution_text": "Ella is a knight, Samuel is a knight, Jackson is a knight, Grace is a knight, William is a knight, Ava is a knave, Aria is a knight, and James is a knave.", "solution_text_format": "(1) Ella is a knight\n(2) Samuel is a knight\n(3) Jackson is a knight\n(4) Grace is a knight\n(5) William is a knight\n(6) Ava is a knave\n(7) Aria is a knight\n(8) James is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Grace is a knight or William is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that James is not a knight.", "James cannot be a knight, because this would contradict the claim of Grace that James is not a knight.", "Assume James is a knave. No contradiction is found in their false claim that Aria is a knight if and only if James is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Ella is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that If James is a knight then Samuel is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that If William is a knave then Jackson is a knight.", "Assume William is a knight. No contradiction is found in their claim that James is a knave or Ella is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that James is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that James is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('telling-truth', 4)), ('->', ('lying', 4), ('telling-truth', 2)), ('->', ('telling-truth', 7), ('lying', 1)), ('not', ('telling-truth', 7)), ('or', ('lying', 7), ('telling-truth', 0)), ('telling-truth', 7), ('<=>', ('telling-truth', 2), ('telling-truth', 0)), ('<=>', ('telling-truth', 6), ('telling-truth', 7)))", "index": 718}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Chloe, Penelope, Mason, Logan, Oliver, Victoria, Mia, and Sebastian. Chloe said, \"Mia is a knight or Sebastian is a knave.\" \"Victoria is a knave or Chloe is a knave,\" Penelope mentioned. In Mason's words: \"Sebastian is not a knight\". \"Chloe is a knave and Oliver is a knight\" - Logan. Oliver told you that Penelope is a knight if and only if Mason is a knave. Victoria remarked, \"Mia is a knight if and only if Penelope is a knave\". Mia noted, \"If Penelope is a knave then Logan is a knight\". Sebastian told you that If Mia is a knave then Mia is a knight. So who is a knight and who is a knave?", "names": ["Chloe", "Penelope", "Mason", "Logan", "Oliver", "Victoria", "Mia", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, false, true, true], "solution_text": "Chloe is a knight, Penelope is a knight, Mason is a knave, Logan is a knave, Oliver is a knight, Victoria is a knave, Mia is a knight, and Sebastian is a knight.", "solution_text_format": "(1) Chloe is a knight\n(2) Penelope is a knight\n(3) Mason is a knave\n(4) Logan is a knave\n(5) Oliver is a knight\n(6) Victoria is a knave\n(7) Mia is a knight\n(8) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Mia is a knight or Sebastian is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that If Penelope is a knave then Logan is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Victoria is a knave or Chloe is a knave.", "Victoria cannot be a knight, because this would contradict the claim of Penelope that Victoria is a knave or Chloe is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Mia is a knight if and only if Penelope is a knave.", "Logan cannot be a knight, because this would contradict the claim of their own that Chloe is a knave and Oliver is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Chloe is a knave and Oliver is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Penelope is a knight if and only if Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of Oliver that Penelope is a knight if and only if Mason is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Sebastian is not a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Mia is a knave then Mia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 6), ('lying', 7)), ('or', ('lying', 5), ('lying', 0)), ('not', ('telling-truth', 7)), ('and', ('lying', 0), ('telling-truth', 4)), ('<=>', ('telling-truth', 1), ('lying', 2)), ('<=>', ('telling-truth', 6), ('lying', 1)), ('->', ('lying', 1), ('telling-truth', 3)), ('->', ('lying', 6), ('telling-truth', 6)))", "index": 719}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Grace, Alexander, Lily, Riley, Ethan, Aurora, Emily, and Samuel. Grace expressed that Samuel is not a knave. Alexander commented, \"If Lily is a knave then Aurora is a knave\". Lily commented, \"Grace is a knight\". In Riley's words: \"Emily is a knave\". \"If Riley is a knight then Emily is a knight\" - Ethan. \"Alexander is a knave or Lily is a knave\" - Aurora. As Emily put it, \"Lily is a knave if and only if Riley is a knave\". Samuel said that If Lily is a knave then Emily is a knight. So who is a knight and who is a knave?", "names": ["Grace", "Alexander", "Lily", "Riley", "Ethan", "Aurora", "Emily", "Samuel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, true, false, false], "solution_text": "Grace is a knave, Alexander is a knave, Lily is a knave, Riley is a knight, Ethan is a knave, Aurora is a knight, Emily is a knave, and Samuel is a knave.", "solution_text_format": "(1) Grace is a knave\n(2) Alexander is a knave\n(3) Lily is a knave\n(4) Riley is a knight\n(5) Ethan is a knave\n(6) Aurora is a knight\n(7) Emily is a knave\n(8) Samuel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Samuel is not a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that If Lily is a knave then Emily is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Grace is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Lily is a knave if and only if Riley is a knave.", "Riley cannot be a knight, because this would contradict the claim of their own that Emily is a knave.", "Riley cannot be a knave, because this would contradict the claim of Emily that Lily is a knave if and only if Riley is a knave.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Lily is a knave if and only if Riley is a knave.", "Riley cannot be a knight, because this would contradict the false claim of Emily that Lily is a knave if and only if Riley is a knave.", "Riley cannot be a knave, because this would contradict the false claim of their own that Emily is a knave.", "We have exhausted all possibilities for Riley and Emily, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the false claim of their own that Grace is a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Samuel.", "Samuel cannot be a knave, because this would contradict the claim of Grace that Samuel is not a knave.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Samuel is not a knave.", "Samuel cannot be a knight, because this would contradict the false claim of Grace that Samuel is not a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that If Lily is a knave then Emily is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Grace is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Grace is a knight.", "Emily cannot be a knight, because this would contradict the false claim of Samuel that If Lily is a knave then Emily is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Lily is a knave if and only if Riley is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Emily is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that If Lily is a knave then Aurora is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Alexander that If Lily is a knave then Aurora is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of their own that Alexander is a knave or Lily is a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that If Lily is a knave then Aurora is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Alexander is a knave or Lily is a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that If Riley is a knight then Emily is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that If Riley is a knight then Emily is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 7)), ('->', ('lying', 2), ('lying', 5)), ('telling-truth', 0), ('lying', 6), ('->', ('telling-truth', 3), ('telling-truth', 6)), ('or', ('lying', 1), ('lying', 2)), ('<=>', ('lying', 2), ('lying', 3)), ('->', ('lying', 2), ('telling-truth', 6)))", "index": 720}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mason, Ethan, Riley, Chloe, Lucas, Jacob, Aria, and Oliver. \"Aria is not a knave,\" Mason declared. In Ethan's words: \"Oliver is not a knight\". \"Ethan is a knight and Lucas is a knight\" - Riley. \"Ethan is a knight,\" Chloe declared. As Lucas put it, \"Riley is a knave or Aria is a knight\". Jacob remarked, \"Oliver is a knight if and only if Lucas is a knight\". Aria was heard saying, \"Jacob is a knave if and only if Mason is a knave\". Oliver said that Riley is a knight if and only if Aria is a knight. So who is a knight and who is a knave?", "names": ["Mason", "Ethan", "Riley", "Chloe", "Lucas", "Jacob", "Aria", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, true, false, true], "solution_text": "Mason is a knave, Ethan is a knave, Riley is a knave, Chloe is a knave, Lucas is a knight, Jacob is a knight, Aria is a knave, and Oliver is a knight.", "solution_text_format": "(1) Mason is a knave\n(2) Ethan is a knave\n(3) Riley is a knave\n(4) Chloe is a knave\n(5) Lucas is a knight\n(6) Jacob is a knight\n(7) Aria is a knave\n(8) Oliver is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Aria is not a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Jacob is a knave if and only if Mason is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Oliver is a knight if and only if Lucas is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Riley is a knight if and only if Aria is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Ethan is a knight and Lucas is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Oliver is not a knight.", "Ethan cannot be a knave, because this would contradict the claim of Riley that Ethan is a knight and Lucas is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Riley.", "Riley cannot be a knave, because this would contradict the claim of Oliver that Riley is a knight if and only if Aria is a knight.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Aria is a knight.", "Riley cannot be a knight, because this would contradict the false claim of Oliver that Riley is a knight if and only if Aria is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Ethan is a knight and Lucas is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Oliver is not a knight.", "Lucas cannot be a knight, because this would contradict the false claim of Riley that Ethan is a knight and Lucas is a knight.", "Lucas cannot be a knave, because this would contradict the false claim of their own that Riley is a knave or Aria is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the false claim of their own that Oliver is not a knight.", "We have exhausted all possibilities for Ethan, Riley, and Oliver, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the claim of Aria that Jacob is a knave if and only if Mason is a knave.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Aria.", "Aria cannot be a knave, because this would contradict the claim of Mason that Aria is not a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Aria is not a knave.", "Aria cannot be a knight, because this would contradict the false claim of Mason that Aria is not a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Jacob is a knave if and only if Mason is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Oliver is a knight if and only if Lucas is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Riley is a knight if and only if Aria is a knight.", "Riley cannot be a knight, because this would contradict the claim of Oliver that Riley is a knight if and only if Aria is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Ethan is a knight and Lucas is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Oliver is not a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Oliver is not a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Riley is a knave or Aria is a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Ethan is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Ethan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 6)), ('not', ('telling-truth', 7)), ('and', ('telling-truth', 1), ('telling-truth', 4)), ('telling-truth', 1), ('or', ('lying', 2), ('telling-truth', 6)), ('<=>', ('telling-truth', 7), ('telling-truth', 4)), ('<=>', ('lying', 5), ('lying', 0)), ('<=>', ('telling-truth', 2), ('telling-truth', 6)))", "index": 721}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ava, Joseph, Penelope, Zoey, Ella, Evelyn, Mia, and Aurora. \"Zoey is a knave,\" Ava declared. \"Ella is a knave and Evelyn is a knave\" - Joseph. Penelope remarked, \"Aurora is not a knight\". According to Zoey, \"Ella is not a knave\". \"Aurora is a knave or Zoey is a knave,\" Ella claimed. \"Ava is a knave or Aurora is a knight,\" Evelyn claimed. Mia expressed that Aurora is not a knight. \"Aurora is a knight,\" Aurora declared. So who is a knight and who is a knave?", "names": ["Ava", "Joseph", "Penelope", "Zoey", "Ella", "Evelyn", "Mia", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true, true, false], "solution_text": "Ava is a knave, Joseph is a knave, Penelope is a knight, Zoey is a knight, Ella is a knight, Evelyn is a knight, Mia is a knight, and Aurora is a knave.", "solution_text_format": "(1) Ava is a knave\n(2) Joseph is a knave\n(3) Penelope is a knight\n(4) Zoey is a knight\n(5) Ella is a knight\n(6) Evelyn is a knight\n(7) Mia is a knight\n(8) Aurora is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Ava that Zoey is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Ella is not a knave.", "Ella cannot be a knight, because this would contradict the false claim of Zoey that Ella is not a knave.", "Ella cannot be a knave, because this would contradict the false claim of their own that Aurora is a knave or Zoey is a knave.", "We have exhausted all possibilities for Ella and Zoey, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Zoey is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Ella is not a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Aurora is a knave or Zoey is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Ella that Aurora is a knave or Zoey is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Aurora is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Ella is a knave and Evelyn is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Ella is a knave and Evelyn is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Ava is a knave or Aurora is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Aurora is not a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Aurora is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('and', ('lying', 4), ('lying', 5)), ('not', ('telling-truth', 7)), ('not', ('lying', 4)), ('or', ('lying', 7), ('lying', 3)), ('or', ('lying', 0), ('telling-truth', 7)), ('not', ('telling-truth', 7)), ('telling-truth', 7))", "index": 722}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aria, Noah, Owen, Jackson, Lily, Emma, Liam, and Scarlett. \"Lily is a knave,\" Aria declared. Noah noted, \"Liam is a knave or Liam is a knight\". According to Owen, \"Lily is a knight or Jackson is a knave\". Jackson remarked, \"If Owen is a knight then Noah is a knave\". In Lily's words: \"Owen is a knave or Scarlett is a knave\". According to Emma, \"Scarlett is a knave or Aria is a knight\". Liam said that Scarlett is not a knave. As Scarlett put it, \"Owen is a knave if and only if Noah is a knight\". So who is a knight and who is a knave?", "names": ["Aria", "Noah", "Owen", "Jackson", "Lily", "Emma", "Liam", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true, false, false], "solution_text": "Aria is a knave, Noah is a knight, Owen is a knight, Jackson is a knave, Lily is a knight, Emma is a knight, Liam is a knave, and Scarlett is a knave.", "solution_text_format": "(1) Aria is a knave\n(2) Noah is a knight\n(3) Owen is a knight\n(4) Jackson is a knave\n(5) Lily is a knight\n(6) Emma is a knight\n(7) Liam is a knave\n(8) Scarlett is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of Aria that Lily is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Owen is a knave or Scarlett is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Lily is a knight or Jackson is a knave.", "Jackson cannot be a knight, because this would contradict the claim of Owen that Lily is a knight or Jackson is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that If Owen is a knight then Noah is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Liam is a knave or Liam is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Owen is a knave if and only if Noah is a knight.", "Scarlett cannot be a knave, because this would contradict the false claim of Lily that Owen is a knave or Scarlett is a knave.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Scarlett is not a knave.", "Scarlett cannot be a knight, because this would contradict the false claim of Liam that Scarlett is not a knave.", "Scarlett cannot be a knave, because this would contradict the false claim of Lily that Owen is a knave or Scarlett is a knave.", "We have exhausted all possibilities for Scarlett and Liam, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the false claim of their own that Liam is a knave or Liam is a knight.", "We have exhausted all possibilities for Noah and Jackson, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the false claim of Lily that Owen is a knave or Scarlett is a knave.", "We have exhausted all possibilities for Owen and Lily, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Lily is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Owen is a knave or Scarlett is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Lily is a knight or Jackson is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that If Owen is a knight then Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of Jackson that If Owen is a knight then Noah is a knave.", "Noah cannot be a knave, because this would contradict the false claim of their own that Liam is a knave or Liam is a knight.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that If Owen is a knight then Noah is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Liam is a knave or Liam is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Lily that Owen is a knave or Scarlett is a knave.", "Scarlett cannot be a knave, because this would contradict the claim of Liam that Scarlett is not a knave.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Scarlett is not a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Lily that Owen is a knave or Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Owen is a knave if and only if Noah is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Scarlett is a knave or Aria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('or', ('lying', 6), ('telling-truth', 6)), ('or', ('telling-truth', 4), ('lying', 3)), ('->', ('telling-truth', 2), ('lying', 1)), ('or', ('lying', 2), ('lying', 7)), ('or', ('lying', 7), ('telling-truth', 0)), ('not', ('lying', 7)), ('<=>', ('lying', 2), ('telling-truth', 1)))", "index": 723}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sofia, Liam, Aria, Zoey, Aurora, Jack, Samuel, and Noah. Sofia said that If Zoey is a knave then Jack is a knave. \"If Jack is a knave then Aurora is a knave\" - Liam. \"Jack is a knave and Sofia is a knight\" - Aria. Zoey was heard saying, \"Aria is a knight and Sofia is a knight\". \"Sofia is not a knight,\" Aurora declared. Jack commented, \"Aurora is a knight or Zoey is a knight\". Samuel expressed that Zoey is a knave and Noah is a knave. According to Noah, \"Jack is a knave if and only if Aurora is a knave\". So who is a knight and who is a knave?", "names": ["Sofia", "Liam", "Aria", "Zoey", "Aurora", "Jack", "Samuel", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true, false, true], "solution_text": "Sofia is a knave, Liam is a knight, Aria is a knave, Zoey is a knave, Aurora is a knight, Jack is a knight, Samuel is a knave, and Noah is a knight.", "solution_text_format": "(1) Sofia is a knave\n(2) Liam is a knight\n(3) Aria is a knave\n(4) Zoey is a knave\n(5) Aurora is a knight\n(6) Jack is a knight\n(7) Samuel is a knave\n(8) Noah is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that If Zoey is a knave then Jack is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Aria is a knight and Sofia is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Jack is a knave and Sofia is a knight.", "Jack cannot be a knight, because this would contradict the claim of Aria that Jack is a knave and Sofia is a knight.", "Jack cannot be a knave, because this would contradict the false claim of their own that Aurora is a knight or Zoey is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Aria.", "Aria cannot be a knave, because this would contradict the claim of Zoey that Aria is a knight and Sofia is a knight.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Aria is a knight and Sofia is a knight.", "Aria cannot be a knight, because this would contradict the false claim of Zoey that Aria is a knight and Sofia is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Jack is a knave and Sofia is a knight.", "Jack cannot be a knight, because this would contradict the claim of Sofia that If Zoey is a knave then Jack is a knave.", "Jack cannot be a knave, because this would contradict the false claim of Aria that Jack is a knave and Sofia is a knight.", "We have exhausted all possibilities for Jack, Aria, and Zoey, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that If Zoey is a knave then Jack is a knave.", "Zoey cannot be a knight, because this would contradict the false claim of Sofia that If Zoey is a knave then Jack is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Aria is a knight and Sofia is a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that Jack is a knave and Sofia is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Jack is a knave and Sofia is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Aurora is a knight or Zoey is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Sofia is not a knight.", "Assume Liam is a knight. No contradiction is found in their claim that If Jack is a knave then Aurora is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Zoey is a knave and Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of Samuel that Zoey is a knave and Noah is a knave.", "Noah cannot be a knave, because this would contradict the false claim of their own that Jack is a knave if and only if Aurora is a knave.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Zoey is a knave and Noah is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Jack is a knave if and only if Aurora is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('lying', 5)), ('->', ('lying', 5), ('lying', 4)), ('and', ('lying', 5), ('telling-truth', 0)), ('and', ('telling-truth', 2), ('telling-truth', 0)), ('not', ('telling-truth', 0)), ('or', ('telling-truth', 4), ('telling-truth', 3)), ('and', ('lying', 3), ('lying', 7)), ('<=>', ('lying', 5), ('lying', 4)))", "index": 724}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Benjamin, Jacob, Evelyn, Amelia, Abigail, Elizabeth, Lucas, and Joseph. Benjamin said that Abigail is a knave if and only if Lucas is a knave. Jacob told you that Evelyn is a knave if and only if Joseph is a knight. Evelyn remarked, \"Lucas is a knave or Lucas is a knight\". \"Jacob is not a knave,\" Amelia claimed. Abigail said that Lucas is a knight and Elizabeth is a knight. \"Amelia is not a knave,\" Elizabeth mentioned. Lucas said that Jacob is a knave if and only if Joseph is a knave. Joseph was heard saying, \"Benjamin is not a knight\". So who is a knight and who is a knave?", "names": ["Benjamin", "Jacob", "Evelyn", "Amelia", "Abigail", "Elizabeth", "Lucas", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true, false, false], "solution_text": "Benjamin is a knight, Jacob is a knight, Evelyn is a knight, Amelia is a knight, Abigail is a knave, Elizabeth is a knight, Lucas is a knave, and Joseph is a knave.", "solution_text_format": "(1) Benjamin is a knight\n(2) Jacob is a knight\n(3) Evelyn is a knight\n(4) Amelia is a knight\n(5) Abigail is a knave\n(6) Elizabeth is a knight\n(7) Lucas is a knave\n(8) Joseph is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Abigail is a knave if and only if Lucas is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Lucas is a knight and Elizabeth is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Jacob is a knave if and only if Joseph is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Evelyn is a knave if and only if Joseph is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Lucas is a knave or Lucas is a knight.", "Joseph cannot be a knight, because this would contradict the claim of Jacob that Evelyn is a knave if and only if Joseph is a knight.", "Joseph cannot be a knave, because this would contradict the claim of Lucas that Jacob is a knave if and only if Joseph is a knave.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that Lucas is a knave or Lucas is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Evelyn is a knave if and only if Joseph is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Lucas is a knave or Lucas is a knight.", "Joseph cannot be a knight, because this would contradict the claim of Lucas that Jacob is a knave if and only if Joseph is a knave.", "Joseph cannot be a knave, because this would contradict the false claim of Jacob that Evelyn is a knave if and only if Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that Lucas is a knave or Lucas is a knight.", "We have exhausted all possibilities for Evelyn and Jacob, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the claim of Benjamin that Abigail is a knave if and only if Lucas is a knave.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Lucas is a knight and Elizabeth is a knight.", "Lucas cannot be a knight, because this would contradict the claim of Benjamin that Abigail is a knave if and only if Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Jacob is a knave if and only if Joseph is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Evelyn is a knave if and only if Joseph is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Lucas is a knave or Lucas is a knight.", "Joseph cannot be a knight, because this would contradict the claim of Jacob that Evelyn is a knave if and only if Joseph is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Benjamin is not a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Amelia is not a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Jacob is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 4), ('lying', 6)), ('<=>', ('lying', 2), ('telling-truth', 7)), ('or', ('lying', 6), ('telling-truth', 6)), ('not', ('lying', 1)), ('and', ('telling-truth', 6), ('telling-truth', 5)), ('not', ('lying', 3)), ('<=>', ('lying', 1), ('lying', 7)), ('not', ('telling-truth', 0)))", "index": 725}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: David, Mia, Grace, Luke, Daniel, Riley, Benjamin, and Harper. David expressed that Riley is a knight or David is a knight. Mia asserted: \"David is a knight and Benjamin is a knight\". Grace remarked, \"If Harper is a knight then Luke is a knave\". Luke was heard saying, \"Daniel is a knight and Benjamin is a knave\". Daniel said that Mia is not a knave. Riley remarked, \"Daniel is a knave if and only if Grace is a knight\". \"David is not a knight,\" Benjamin claimed. \"David is a knave and Luke is a knight\" - Harper. So who is a knight and who is a knave?", "names": ["David", "Mia", "Grace", "Luke", "Daniel", "Riley", "Benjamin", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true, false, false], "solution_text": "David is a knight, Mia is a knave, Grace is a knight, Luke is a knave, Daniel is a knave, Riley is a knight, Benjamin is a knave, and Harper is a knave.", "solution_text_format": "(1) David is a knight\n(2) Mia is a knave\n(3) Grace is a knight\n(4) Luke is a knave\n(5) Daniel is a knave\n(6) Riley is a knight\n(7) Benjamin is a knave\n(8) Harper is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Riley is a knight or David is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Daniel is a knave if and only if Grace is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Mia is not a knave.", "Assume Mia is a knight. No contradiction is found in their claim that David is a knight and Benjamin is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that David is not a knight.", "Benjamin cannot be a knave, because this would contradict the claim of Mia that David is a knight and Benjamin is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the claim of Daniel that Mia is not a knave.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Mia is not a knave.", "Mia cannot be a knight, because this would contradict the false claim of Daniel that Mia is not a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that David is a knight and Benjamin is a knight.", "Benjamin cannot be a knight, because this would contradict the false claim of Mia that David is a knight and Benjamin is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that David is not a knight.", "Assume Grace is a knight. No contradiction is found in their claim that If Harper is a knight then Luke is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that David is a knave and Luke is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that David is a knave and Luke is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Daniel is a knight and Benjamin is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Daniel is a knight and Benjamin is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('telling-truth', 0)), ('and', ('telling-truth', 0), ('telling-truth', 6)), ('->', ('telling-truth', 7), ('lying', 3)), ('and', ('telling-truth', 4), ('lying', 6)), ('not', ('lying', 1)), ('<=>', ('lying', 4), ('telling-truth', 2)), ('not', ('telling-truth', 0)), ('and', ('lying', 0), ('telling-truth', 3)))", "index": 726}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aiden, Emma, Alexander, Chloe, Oliver, Sofia, Ethan, and Sebastian. According to Aiden, \"Aiden is a knight if and only if Alexander is a knave\". Emma said that Alexander is a knave or Aiden is a knight. Alexander was heard saying, \"Aiden is not a knight\". Chloe told you that If Sebastian is a knave then Emma is a knight. In Oliver's words: \"Alexander is a knave if and only if Sofia is a knight\". \"Alexander is not a knight,\" Sofia claimed. Ethan told you that Oliver is a knight or Ethan is a knight. Sebastian asserted: \"Alexander is a knight if and only if Emma is a knave\". So who is a knight and who is a knave?", "names": ["Aiden", "Emma", "Alexander", "Chloe", "Oliver", "Sofia", "Ethan", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true, true, true], "solution_text": "Aiden is a knight, Emma is a knight, Alexander is a knave, Chloe is a knight, Oliver is a knight, Sofia is a knight, Ethan is a knight, and Sebastian is a knight.", "solution_text_format": "(1) Aiden is a knight\n(2) Emma is a knight\n(3) Alexander is a knave\n(4) Chloe is a knight\n(5) Oliver is a knight\n(6) Sofia is a knight\n(7) Ethan is a knight\n(8) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Aiden is a knight if and only if Alexander is a knave.", "Alexander cannot be a knight, because this would contradict the claim of Aiden that Aiden is a knight if and only if Alexander is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Aiden is not a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Alexander is a knave or Aiden is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that If Sebastian is a knave then Emma is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Alexander is a knight if and only if Emma is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Alexander is a knave if and only if Sofia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Oliver is a knight or Ethan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 0), ('lying', 2)), ('or', ('lying', 2), ('telling-truth', 0)), ('not', ('telling-truth', 0)), ('->', ('lying', 7), ('telling-truth', 1)), ('<=>', ('lying', 2), ('telling-truth', 5)), ('not', ('telling-truth', 2)), ('or', ('telling-truth', 4), ('telling-truth', 6)), ('<=>', ('telling-truth', 2), ('lying', 1)))", "index": 727}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emily, William, Amelia, Abigail, Aurora, Sofia, Sophia, and Charlotte. Emily told you that Charlotte is not a knight. William remarked, \"Charlotte is a knight and Aurora is a knight\". Amelia told you that Abigail is not a knave. Abigail remarked, \"Sofia is not a knave\". According to Aurora, \"Sophia is a knave and William is a knight\". \"Aurora is a knight or Emily is a knave,\" Sofia mentioned. \"Sophia is a knight and William is a knight,\" Sophia mentioned. Charlotte remarked, \"Amelia is a knave if and only if William is a knave\". So who is a knight and who is a knave?", "names": ["Emily", "William", "Amelia", "Abigail", "Aurora", "Sofia", "Sophia", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true, false, true], "solution_text": "Emily is a knave, William is a knight, Amelia is a knight, Abigail is a knight, Aurora is a knight, Sofia is a knight, Sophia is a knave, and Charlotte is a knight.", "solution_text_format": "(1) Emily is a knave\n(2) William is a knight\n(3) Amelia is a knight\n(4) Abigail is a knight\n(5) Aurora is a knight\n(6) Sofia is a knight\n(7) Sophia is a knave\n(8) Charlotte is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Charlotte is not a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Emily that Charlotte is not a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Amelia is a knave if and only if William is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Abigail is not a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Sofia is not a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Aurora is a knight or Emily is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Sophia is a knave and William is a knight.", "Sophia cannot be a knight, because this would contradict the claim of Aurora that Sophia is a knave and William is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Sophia is a knight and William is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Charlotte is a knight and Aurora is a knight.", "William cannot be a knave, because this would contradict the claim of Aurora that Sophia is a knave and William is a knight.", "We have exhausted all possibilities for William and Sophia, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the claim of Sofia that Aurora is a knight or Emily is a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Sofia.", "Sofia cannot be a knave, because this would contradict the claim of Abigail that Sofia is not a knave.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the claim of Amelia that Abigail is not a knave.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Abigail is not a knave.", "Abigail cannot be a knight, because this would contradict the false claim of Amelia that Abigail is not a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Sofia is not a knave.", "Sofia cannot be a knight, because this would contradict the false claim of Abigail that Sofia is not a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Aurora is a knight or Emily is a knave.", "Aurora cannot be a knight, because this would contradict the false claim of Sofia that Aurora is a knight or Emily is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Sophia is a knave and William is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Sophia is a knight and William is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Charlotte is a knight and Aurora is a knight.", "William cannot be a knave, because this would contradict the claim of Sophia that Sophia is a knight and William is a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Sophia is a knight and William is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Charlotte is a knight and Aurora is a knight.", "William cannot be a knave, because this would contradict the false claim of Charlotte that Amelia is a knave if and only if William is a knave.", "We have exhausted all possibilities for William, Sophia, Aurora, Sofia, Abigail, Amelia, and Charlotte, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Charlotte is not a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Amelia is a knave if and only if William is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Abigail is not a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Sofia is not a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Aurora is a knight or Emily is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Sophia is a knave and William is a knight.", "Sophia cannot be a knight, because this would contradict the claim of Aurora that Sophia is a knave and William is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Sophia is a knight and William is a knight.", "Assume William is a knight. No contradiction is found in their claim that Charlotte is a knight and Aurora is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 7)), ('and', ('telling-truth', 7), ('telling-truth', 4)), ('not', ('lying', 3)), ('not', ('lying', 5)), ('and', ('lying', 6), ('telling-truth', 1)), ('or', ('telling-truth', 4), ('lying', 0)), ('and', ('telling-truth', 6), ('telling-truth', 1)), ('<=>', ('lying', 2), ('lying', 1)))", "index": 728}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Liam, Michael, Ethan, Logan, Jack, Riley, Isabella, and Henry. \"Ethan is a knight or Riley is a knave,\" Liam declared. Michael told you that Jack is a knight. As Ethan put it, \"Logan is not a knave\". Logan commented, \"Henry is a knight if and only if Jack is a knight\". Jack expressed that Henry is a knight or Ethan is a knight. \"Michael is a knave,\" Riley declared. \"Ethan is a knight or Henry is a knave,\" Isabella mentioned. \"Logan is a knave if and only if Michael is a knave\" - Henry. So who is a knight and who is a knave?", "names": ["Liam", "Michael", "Ethan", "Logan", "Jack", "Riley", "Isabella", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false, true, true], "solution_text": "Liam is a knight, Michael is a knight, Ethan is a knight, Logan is a knight, Jack is a knight, Riley is a knave, Isabella is a knight, and Henry is a knight.", "solution_text_format": "(1) Liam is a knight\n(2) Michael is a knight\n(3) Ethan is a knight\n(4) Logan is a knight\n(5) Jack is a knight\n(6) Riley is a knave\n(7) Isabella is a knight\n(8) Henry is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Ethan is a knight or Riley is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Logan is not a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Henry is a knight if and only if Jack is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Logan is a knave if and only if Michael is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Henry is a knight or Ethan is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Michael is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Michael is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Ethan is a knight or Henry is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('lying', 5)), ('telling-truth', 4), ('not', ('lying', 3)), ('<=>', ('telling-truth', 7), ('telling-truth', 4)), ('or', ('telling-truth', 7), ('telling-truth', 2)), ('lying', 1), ('or', ('telling-truth', 2), ('lying', 7)), ('<=>', ('lying', 3), ('lying', 1)))", "index": 729}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Logan, Ava, Liam, Luke, Lily, Elizabeth, Jack, and Ella. Logan stated, \"Ella is a knight\". Ava told you that If Lily is a knave then Ella is a knave. Liam was heard saying, \"Logan is not a knight\". According to Luke, \"Jack is a knave or Logan is a knight\". Lily expressed that Logan is a knight. Elizabeth stated, \"Ava is a knave\". Jack expressed that Ava is a knight. Ella told you that Jack is not a knave. So who is a knight and who is a knave?", "names": ["Logan", "Ava", "Liam", "Luke", "Lily", "Elizabeth", "Jack", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false, true, true], "solution_text": "Logan is a knight, Ava is a knight, Liam is a knave, Luke is a knight, Lily is a knight, Elizabeth is a knave, Jack is a knight, and Ella is a knight.", "solution_text_format": "(1) Logan is a knight\n(2) Ava is a knight\n(3) Liam is a knave\n(4) Luke is a knight\n(5) Lily is a knight\n(6) Elizabeth is a knave\n(7) Jack is a knight\n(8) Ella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Jack is not a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Ava is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that If Lily is a knave then Ella is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Logan is a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that Logan is not a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Logan is not a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Jack is a knave or Logan is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Ava is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Ava is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 7), ('->', ('lying', 4), ('lying', 7)), ('not', ('telling-truth', 0)), ('or', ('lying', 6), ('telling-truth', 0)), ('telling-truth', 0), ('lying', 1), ('telling-truth', 1), ('not', ('lying', 6)))", "index": 730}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Riley, Oliver, Evelyn, Emily, Chloe, Sophia, Liam, and Sofia. Riley was heard saying, \"If Oliver is a knave then Sophia is a knave\". \"Sofia is a knave if and only if Emily is a knight,\" Oliver claimed. In a statement by Evelyn: \"Riley is a knight or Sophia is a knight\". \"Evelyn is a knave if and only if Oliver is a knave,\" Emily declared. \"Emily is a knave if and only if Evelyn is a knave\" - Chloe. In Sophia's words: \"Oliver is a knave\". Liam commented, \"Chloe is a knave\". Sofia said, \"Riley is a knave or Liam is a knight.\" So who is a knight and who is a knave?", "names": ["Riley", "Oliver", "Evelyn", "Emily", "Chloe", "Sophia", "Liam", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false, false, false], "solution_text": "Riley is a knight, Oliver is a knight, Evelyn is a knight, Emily is a knight, Chloe is a knight, Sophia is a knave, Liam is a knave, and Sofia is a knave.", "solution_text_format": "(1) Riley is a knight\n(2) Oliver is a knight\n(3) Evelyn is a knight\n(4) Emily is a knight\n(5) Chloe is a knight\n(6) Sophia is a knave\n(7) Liam is a knave\n(8) Sofia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that If Oliver is a knave then Sophia is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Sofia is a knave if and only if Emily is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Riley is a knave or Liam is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Liam that Chloe is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Emily is a knave if and only if Evelyn is a knave.", "Emily cannot be a knight, because this would contradict the claim of Oliver that Sofia is a knave if and only if Emily is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Evelyn is a knave if and only if Oliver is a knave.", "Evelyn cannot be a knight, because this would contradict the false claim of Emily that Evelyn is a knave if and only if Oliver is a knave.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that Riley is a knight or Sophia is a knight.", "We have exhausted all possibilities for Evelyn, Emily, and Chloe, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the claim of Sofia that Riley is a knave or Liam is a knight.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Riley is a knave or Liam is a knight.", "Liam cannot be a knight, because this would contradict the false claim of Sofia that Riley is a knave or Liam is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Chloe is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Emily is a knave if and only if Evelyn is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Evelyn is a knave if and only if Oliver is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Riley is a knight or Sophia is a knight.", "Sophia cannot be a knight, because this would contradict the claim of their own that Oliver is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Oliver is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 1), ('lying', 5)), ('<=>', ('lying', 7), ('telling-truth', 3)), ('or', ('telling-truth', 0), ('telling-truth', 5)), ('<=>', ('lying', 2), ('lying', 1)), ('<=>', ('lying', 3), ('lying', 2)), ('lying', 1), ('lying', 4), ('or', ('lying', 0), ('telling-truth', 6)))", "index": 731}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Daniel, Owen, Evelyn, Aria, Sofia, Noah, Grace, and Elizabeth. Daniel said, \"Evelyn is a knight or Elizabeth is a knight.\" As Owen put it, \"If Sofia is a knight then Daniel is a knave\". Evelyn said, \"Evelyn is a knight if and only if Aria is a knave.\" Aria noted, \"If Evelyn is a knight then Aria is a knight\". Sofia was heard saying, \"If Elizabeth is a knight then Aria is a knave\". Noah commented, \"Daniel is a knight\". As Grace put it, \"Daniel is not a knight\". \"Daniel is a knave and Evelyn is a knight,\" Elizabeth mentioned. So who is a knight and who is a knave?", "names": ["Daniel", "Owen", "Evelyn", "Aria", "Sofia", "Noah", "Grace", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true, false, false], "solution_text": "Daniel is a knight, Owen is a knave, Evelyn is a knight, Aria is a knave, Sofia is a knight, Noah is a knight, Grace is a knave, and Elizabeth is a knave.", "solution_text_format": "(1) Daniel is a knight\n(2) Owen is a knave\n(3) Evelyn is a knight\n(4) Aria is a knave\n(5) Sofia is a knight\n(6) Noah is a knight\n(7) Grace is a knave\n(8) Elizabeth is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that Evelyn is a knight or Elizabeth is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Evelyn is a knight if and only if Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of Evelyn that Evelyn is a knight if and only if Aria is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that If Evelyn is a knight then Aria is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Daniel is a knave and Evelyn is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Daniel is a knave and Evelyn is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that If Sofia is a knight then Daniel is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Owen that If Sofia is a knight then Daniel is a knave.", "Sofia cannot be a knave, because this would contradict the false claim of their own that If Elizabeth is a knight then Aria is a knave.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that If Sofia is a knight then Daniel is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that If Elizabeth is a knight then Aria is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Daniel is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Daniel is not a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Daniel is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('telling-truth', 7)), ('->', ('telling-truth', 4), ('lying', 0)), ('<=>', ('telling-truth', 2), ('lying', 3)), ('->', ('telling-truth', 2), ('telling-truth', 3)), ('->', ('telling-truth', 7), ('lying', 3)), ('telling-truth', 0), ('not', ('telling-truth', 0)), ('and', ('lying', 0), ('telling-truth', 2)))", "index": 732}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Michael, Jack, Lily, James, Emily, Alexander, Jackson, and Aiden. Michael remarked, \"If Jackson is a knave then James is a knave\". \"Michael is a knave and Jackson is a knight,\" Jack mentioned. Lily told you that Emily is a knight or Jackson is a knave. James expressed that Emily is a knight and Lily is a knight. Emily commented, \"Lily is a knave and Emily is a knight\". As Alexander put it, \"Jack is a knave\". In Jackson's words: \"If James is a knight then James is a knave\". Aiden noted, \"Alexander is a knave if and only if Jack is a knight\". So who is a knight and who is a knave?", "names": ["Michael", "Jack", "Lily", "James", "Emily", "Alexander", "Jackson", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, true, true, true], "solution_text": "Michael is a knight, Jack is a knave, Lily is a knave, James is a knave, Emily is a knave, Alexander is a knight, Jackson is a knight, and Aiden is a knight.", "solution_text_format": "(1) Michael is a knight\n(2) Jack is a knave\n(3) Lily is a knave\n(4) James is a knave\n(5) Emily is a knave\n(6) Alexander is a knight\n(7) Jackson is a knight\n(8) Aiden is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that If Jackson is a knave then James is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that If James is a knight then James is a knave.", "James cannot be a knight, because this would contradict the claim of Jackson that If James is a knight then James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Emily is a knight and Lily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Lily is a knave and Emily is a knight.", "Lily cannot be a knight, because this would contradict the false claim of James that Emily is a knight and Lily is a knight.", "Lily cannot be a knave, because this would contradict the false claim of their own that Emily is a knight or Jackson is a knave.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Lily is a knave and Emily is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Emily is a knight or Jackson is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Emily is a knight or Jackson is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Jackson is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Michael is a knave and Jackson is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Jack is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Alexander is a knave if and only if Jack is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 6), ('lying', 3)), ('and', ('lying', 0), ('telling-truth', 6)), ('or', ('telling-truth', 4), ('lying', 6)), ('and', ('telling-truth', 4), ('telling-truth', 2)), ('and', ('lying', 2), ('telling-truth', 4)), ('lying', 1), ('->', ('telling-truth', 3), ('lying', 3)), ('<=>', ('lying', 5), ('telling-truth', 1)))", "index": 733}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lucas, Samuel, Ethan, Emma, Oliver, Victoria, Sofia, and Chloe. Lucas stated, \"Chloe is a knight or Ethan is a knight\". Samuel told you that If Lucas is a knight then Victoria is a knave. Ethan remarked, \"Emma is a knave if and only if Emma is a knight\". As Emma put it, \"Lucas is not a knave\". Oliver asserted: \"Ethan is a knight\". Victoria asserted: \"Oliver is a knave if and only if Samuel is a knight\". Sofia commented, \"Chloe is not a knight\". \"Lucas is not a knave,\" Chloe claimed. So who is a knight and who is a knave?", "names": ["Lucas", "Samuel", "Ethan", "Emma", "Oliver", "Victoria", "Sofia", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, true, true, false], "solution_text": "Lucas is a knave, Samuel is a knight, Ethan is a knave, Emma is a knave, Oliver is a knave, Victoria is a knight, Sofia is a knight, and Chloe is a knave.", "solution_text_format": "(1) Lucas is a knave\n(2) Samuel is a knight\n(3) Ethan is a knave\n(4) Emma is a knave\n(5) Oliver is a knave\n(6) Victoria is a knight\n(7) Sofia is a knight\n(8) Chloe is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that Chloe is a knight or Ethan is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Lucas is not a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Emma is a knave if and only if Emma is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Emma is a knave if and only if Emma is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Lucas is not a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that If Lucas is a knight then Victoria is a knave.", "Victoria cannot be a knight, because this would contradict the claim of Samuel that If Lucas is a knight then Victoria is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Oliver is a knave if and only if Samuel is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Ethan is a knight.", "Oliver cannot be a knave, because this would contradict the false claim of Victoria that Oliver is a knave if and only if Samuel is a knight.", "We have exhausted all possibilities for Oliver and Victoria, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that If Lucas is a knight then Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Oliver is a knave if and only if Samuel is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Ethan is a knight.", "Oliver cannot be a knave, because this would contradict the claim of Victoria that Oliver is a knave if and only if Samuel is a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Victoria.", "Victoria cannot be a knave, because this would contradict the false claim of Samuel that If Lucas is a knight then Victoria is a knave.", "We have exhausted all possibilities for Victoria and Samuel, so let us go back and reconsider Emma.", "Emma cannot be a knave, because this would contradict the false claim of their own that Lucas is not a knave.", "We have exhausted all possibilities for Emma and Ethan, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the false claim of their own that Lucas is not a knave.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Chloe is a knight or Ethan is a knight.", "Chloe cannot be a knight, because this would contradict the false claim of Lucas that Chloe is a knight or Ethan is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Lucas is not a knave.", "Ethan cannot be a knight, because this would contradict the false claim of Lucas that Chloe is a knight or Ethan is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Emma is a knave if and only if Emma is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Lucas is not a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Lucas is not a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that If Lucas is a knight then Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Oliver is a knave if and only if Samuel is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Ethan is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Ethan is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Chloe is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 7), ('telling-truth', 2)), ('->', ('telling-truth', 0), ('lying', 5)), ('<=>', ('lying', 3), ('telling-truth', 3)), ('not', ('lying', 0)), ('telling-truth', 2), ('<=>', ('lying', 4), ('telling-truth', 1)), ('not', ('telling-truth', 7)), ('not', ('lying', 0)))", "index": 734}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Zoey, Victoria, Olivia, Oliver, Harper, Liam, Michael, and Avery. Zoey said that Avery is a knave and Harper is a knave. Victoria said that Victoria is a knight if and only if Liam is a knight. Olivia told you that Oliver is a knave and Michael is a knave. Oliver noted, \"Victoria is a knave or Avery is a knave\". According to Harper, \"If Avery is a knight then Victoria is a knave\". \"Harper is a knight and Victoria is a knave,\" Liam claimed. Michael remarked, \"Liam is a knight or Harper is a knave\". Avery expressed that Michael is not a knight. So who is a knight and who is a knave?", "names": ["Zoey", "Victoria", "Olivia", "Oliver", "Harper", "Liam", "Michael", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true, true, false], "solution_text": "Zoey is a knave, Victoria is a knave, Olivia is a knave, Oliver is a knight, Harper is a knight, Liam is a knight, Michael is a knight, and Avery is a knave.", "solution_text_format": "(1) Zoey is a knave\n(2) Victoria is a knave\n(3) Olivia is a knave\n(4) Oliver is a knight\n(5) Harper is a knight\n(6) Liam is a knight\n(7) Michael is a knight\n(8) Avery is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Zoey is a knight. No contradiction is found in their claim that Avery is a knave and Harper is a knave.", "Avery cannot be a knight, because this would contradict the claim of Zoey that Avery is a knave and Harper is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Michael is not a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Liam is a knight or Harper is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Harper is a knight and Victoria is a knave.", "Harper cannot be a knight, because this would contradict the claim of Zoey that Avery is a knave and Harper is a knave.", "Harper cannot be a knave, because this would contradict the false claim of their own that If Avery is a knight then Victoria is a knave.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Harper is a knight and Victoria is a knave.", "Harper cannot be a knight, because this would contradict the claim of Zoey that Avery is a knave and Harper is a knave.", "Harper cannot be a knave, because this would contradict the false claim of their own that If Avery is a knight then Victoria is a knave.", "We have exhausted all possibilities for Harper and Liam, so let us go back and reconsider Michael.", "Michael cannot be a knave, because this would contradict the false claim of Avery that Michael is not a knight.", "We have exhausted all possibilities for Michael and Avery, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Avery is a knave and Harper is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Michael is not a knight.", "Michael cannot be a knight, because this would contradict the claim of Avery that Michael is not a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Liam is a knight or Harper is a knave.", "Liam cannot be a knight, because this would contradict the false claim of Michael that Liam is a knight or Harper is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Harper is a knight and Victoria is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that If Avery is a knight then Victoria is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that Victoria is a knight if and only if Liam is a knight.", "Victoria cannot be a knave, because this would contradict the false claim of their own that Victoria is a knight if and only if Liam is a knight.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the false claim of Michael that Liam is a knight or Harper is a knave.", "We have exhausted all possibilities for Harper, Liam, and Michael, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Michael is not a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Liam is a knight or Harper is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Harper is a knight and Victoria is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that If Avery is a knight then Victoria is a knave.", "Victoria cannot be a knight, because this would contradict the claim of Liam that Harper is a knight and Victoria is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Victoria is a knight if and only if Liam is a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that Oliver is a knave and Michael is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Oliver is a knave and Michael is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Victoria is a knave or Avery is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 7), ('lying', 4)), ('<=>', ('telling-truth', 1), ('telling-truth', 5)), ('and', ('lying', 3), ('lying', 6)), ('or', ('lying', 1), ('lying', 7)), ('->', ('telling-truth', 7), ('lying', 1)), ('and', ('telling-truth', 4), ('lying', 1)), ('or', ('telling-truth', 5), ('lying', 4)), ('not', ('telling-truth', 6)))", "index": 735}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Avery, Henry, William, Charlotte, Victoria, Jacob, Mason, and Daniel. As Avery put it, \"Charlotte is a knight or Victoria is a knave\". In a statement by Henry: \"Jacob is not a knight\". William asserted: \"Avery is a knight or Avery is a knave\". Charlotte asserted: \"William is not a knave\". Victoria stated, \"If Victoria is a knight then Jacob is a knight\". Jacob said that Avery is a knave if and only if Mason is a knave. Mason was heard saying, \"Daniel is a knight or Avery is a knight\". As Daniel put it, \"Jacob is a knave\". So who is a knight and who is a knave?", "names": ["Avery", "Henry", "William", "Charlotte", "Victoria", "Jacob", "Mason", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true, true, false], "solution_text": "Avery is a knight, Henry is a knave, William is a knight, Charlotte is a knight, Victoria is a knight, Jacob is a knight, Mason is a knight, and Daniel is a knave.", "solution_text_format": "(1) Avery is a knight\n(2) Henry is a knave\n(3) William is a knight\n(4) Charlotte is a knight\n(5) Victoria is a knight\n(6) Jacob is a knight\n(7) Mason is a knight\n(8) Daniel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Charlotte is a knight or Victoria is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that William is not a knave.", "Assume William is a knight. No contradiction is found in their claim that Avery is a knight or Avery is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that If Victoria is a knight then Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Avery is a knave if and only if Mason is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Daniel is a knight or Avery is a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that Jacob is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Jacob is a knave.", "Henry cannot be a knight, because this would contradict the claim of their own that Jacob is not a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Jacob is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('lying', 4)), ('not', ('telling-truth', 5)), ('or', ('telling-truth', 0), ('lying', 0)), ('not', ('lying', 2)), ('->', ('telling-truth', 4), ('telling-truth', 5)), ('<=>', ('lying', 0), ('lying', 6)), ('or', ('telling-truth', 7), ('telling-truth', 0)), ('lying', 5))", "index": 736}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: William, Jackson, Aria, Michael, Matthew, Jacob, Zoey, and Owen. William remarked, \"Michael is a knave and Zoey is a knave\". As Jackson put it, \"Jacob is a knight or Matthew is a knave\". In a statement by Aria: \"Owen is a knight and Owen is a knave\". Michael asserted: \"Zoey is not a knave\". Matthew said, \"William is a knight and Aria is a knight.\" In a statement by Jacob: \"Zoey is a knight if and only if Aria is a knight\". According to Zoey, \"Matthew is a knight or Matthew is a knave\". Owen expressed that Matthew is a knave. So who is a knight and who is a knave?", "names": ["William", "Jackson", "Aria", "Michael", "Matthew", "Jacob", "Zoey", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, false, true, true], "solution_text": "William is a knave, Jackson is a knight, Aria is a knave, Michael is a knight, Matthew is a knave, Jacob is a knave, Zoey is a knight, and Owen is a knight.", "solution_text_format": "(1) William is a knave\n(2) Jackson is a knight\n(3) Aria is a knave\n(4) Michael is a knight\n(5) Matthew is a knave\n(6) Jacob is a knave\n(7) Zoey is a knight\n(8) Owen is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Michael is a knave and Zoey is a knave.", "Michael cannot be a knight, because this would contradict the claim of William that Michael is a knave and Zoey is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Zoey is not a knave.", "Zoey cannot be a knight, because this would contradict the claim of William that Michael is a knave and Zoey is a knave.", "Zoey cannot be a knave, because this would contradict the false claim of their own that Matthew is a knight or Matthew is a knave.", "We have exhausted all possibilities for Zoey and Michael, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Michael is a knave and Zoey is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Zoey is not a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Matthew is a knight or Matthew is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that William is a knight and Aria is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that William is a knight and Aria is a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that Owen is a knight and Owen is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Owen is a knight and Owen is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Matthew is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Jacob is a knight or Matthew is a knave.", "Jacob cannot be a knight, because this would contradict the claim of their own that Zoey is a knight if and only if Aria is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Zoey is a knight if and only if Aria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('lying', 6)), ('or', ('telling-truth', 5), ('lying', 4)), ('and', ('telling-truth', 7), ('lying', 7)), ('not', ('lying', 6)), ('and', ('telling-truth', 0), ('telling-truth', 2)), ('<=>', ('telling-truth', 6), ('telling-truth', 2)), ('or', ('telling-truth', 4), ('lying', 4)), ('lying', 4))", "index": 737}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Olivia, Zoey, Matthew, David, Grace, Victoria, James, and Aiden. Olivia asserted: \"Zoey is not a knave\". Zoey commented, \"Aiden is a knave if and only if Grace is a knave\". \"Olivia is a knave,\" Matthew mentioned. David stated, \"Matthew is a knave or Matthew is a knight\". Grace expressed that Aiden is not a knight. Victoria expressed that Aiden is a knave or David is a knight. James stated, \"Matthew is a knight and Aiden is a knight\". As Aiden put it, \"If David is a knave then Matthew is a knave\". So who is a knight and who is a knave?", "names": ["Olivia", "Zoey", "Matthew", "David", "Grace", "Victoria", "James", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, true, true, true], "solution_text": "Olivia is a knave, Zoey is a knave, Matthew is a knight, David is a knight, Grace is a knave, Victoria is a knight, James is a knight, and Aiden is a knight.", "solution_text_format": "(1) Olivia is a knave\n(2) Zoey is a knave\n(3) Matthew is a knight\n(4) David is a knight\n(5) Grace is a knave\n(6) Victoria is a knight\n(7) James is a knight\n(8) Aiden is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Zoey is not a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Aiden is a knave if and only if Grace is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If David is a knave then Matthew is a knave.", "Assume David is a knight. No contradiction is found in their claim that Matthew is a knave or Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Olivia is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Olivia is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Aiden is not a knight.", "Grace cannot be a knave, because this would contradict the claim of Zoey that Aiden is a knave if and only if Grace is a knave.", "We have exhausted all possibilities for Grace and Matthew, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the false claim of their own that Matthew is a knave or Matthew is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that If David is a knave then Matthew is a knave.", "David cannot be a knight, because this would contradict the false claim of Aiden that If David is a knave then Matthew is a knave.", "David cannot be a knave, because this would contradict the false claim of their own that Matthew is a knave or Matthew is a knight.", "We have exhausted all possibilities for David and Aiden, so let us go back and reconsider Zoey.", "Zoey cannot be a knave, because this would contradict the claim of Olivia that Zoey is not a knave.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Zoey is not a knave.", "Zoey cannot be a knight, because this would contradict the false claim of Olivia that Zoey is not a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if Grace is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If David is a knave then Matthew is a knave.", "Assume David is a knight. No contradiction is found in their claim that Matthew is a knave or Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Olivia is a knave.", "Grace cannot be a knight, because this would contradict the false claim of Zoey that Aiden is a knave if and only if Grace is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Aiden is not a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Aiden is a knave or David is a knight.", "Assume James is a knight. No contradiction is found in their claim that Matthew is a knight and Aiden is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('<=>', ('lying', 7), ('lying', 4)), ('lying', 0), ('or', ('lying', 2), ('telling-truth', 2)), ('not', ('telling-truth', 7)), ('or', ('lying', 7), ('telling-truth', 3)), ('and', ('telling-truth', 2), ('telling-truth', 7)), ('->', ('lying', 3), ('lying', 2)))", "index": 738}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Michael, Avery, Elizabeth, Penelope, Alexander, Daniel, William, and James. According to Michael, \"Elizabeth is a knight or William is a knight\". Avery noted, \"Penelope is not a knave\". Elizabeth said, \"James is a knight if and only if Avery is a knave.\" According to Penelope, \"William is a knave or Michael is a knave\". \"Penelope is a knave or James is a knight,\" Alexander declared. Daniel stated, \"If Avery is a knight then Alexander is a knight\". According to William, \"Alexander is a knight\". \"If Alexander is a knight then Avery is a knight,\" James claimed. So who is a knight and who is a knave?", "names": ["Michael", "Avery", "Elizabeth", "Penelope", "Alexander", "Daniel", "William", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true, true, false], "solution_text": "Michael is a knight, Avery is a knave, Elizabeth is a knave, Penelope is a knave, Alexander is a knight, Daniel is a knight, William is a knight, and James is a knave.", "solution_text_format": "(1) Michael is a knight\n(2) Avery is a knave\n(3) Elizabeth is a knave\n(4) Penelope is a knave\n(5) Alexander is a knight\n(6) Daniel is a knight\n(7) William is a knight\n(8) James is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Elizabeth is a knight or William is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that James is a knight if and only if Avery is a knave.", "Assume James is a knight. No contradiction is found in their claim that If Alexander is a knight then Avery is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Penelope is a knave or James is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that William is a knave or Michael is a knave.", "William cannot be a knight, because this would contradict the claim of Penelope that William is a knave or Michael is a knave.", "William cannot be a knave, because this would contradict the false claim of their own that Alexander is a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that William is a knave or Michael is a knave.", "Assume William is a knight. No contradiction is found in their claim that Alexander is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Penelope is not a knave.", "Avery cannot be a knave, because this would contradict the claim of James that If Alexander is a knight then Avery is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the false claim of Penelope that William is a knave or Michael is a knave.", "We have exhausted all possibilities for William and Penelope, so let us go back and reconsider Alexander.", "Alexander cannot be a knave, because this would contradict the false claim of their own that Penelope is a knave or James is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that If Alexander is a knight then Avery is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Penelope is a knave or James is a knight.", "Penelope cannot be a knight, because this would contradict the claim of Alexander that Penelope is a knave or James is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that William is a knave or Michael is a knave.", "Assume William is a knight. No contradiction is found in their claim that Alexander is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Penelope is not a knave.", "Avery cannot be a knave, because this would contradict the claim of Elizabeth that James is a knight if and only if Avery is a knave.", "We have exhausted all possibilities for Avery, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the false claim of Penelope that William is a knave or Michael is a knave.", "We have exhausted all possibilities for William and Penelope, so let us go back and reconsider Alexander.", "Alexander cannot be a knave, because this would contradict the false claim of James that If Alexander is a knight then Avery is a knight.", "We have exhausted all possibilities for Alexander and James, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that James is a knight if and only if Avery is a knave.", "Assume James is a knight. No contradiction is found in their claim that If Alexander is a knight then Avery is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Penelope is a knave or James is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that William is a knave or Michael is a knave.", "William cannot be a knight, because this would contradict the claim of Penelope that William is a knave or Michael is a knave.", "William cannot be a knave, because this would contradict the claim of Michael that Elizabeth is a knight or William is a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that William is a knave or Michael is a knave.", "Assume William is a knight. No contradiction is found in their claim that Alexander is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Penelope is not a knave.", "Avery cannot be a knave, because this would contradict the false claim of Elizabeth that James is a knight if and only if Avery is a knave.", "We have exhausted all possibilities for Avery, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the claim of Michael that Elizabeth is a knight or William is a knight.", "We have exhausted all possibilities for William and Penelope, so let us go back and reconsider Alexander.", "Alexander cannot be a knave, because this would contradict the false claim of their own that Penelope is a knave or James is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that If Alexander is a knight then Avery is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Penelope is a knave or James is a knight.", "Penelope cannot be a knight, because this would contradict the claim of Alexander that Penelope is a knave or James is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that William is a knave or Michael is a knave.", "Assume William is a knight. No contradiction is found in their claim that Alexander is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Penelope is not a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Penelope is not a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that If Avery is a knight then Alexander is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('telling-truth', 6)), ('not', ('lying', 3)), ('<=>', ('telling-truth', 7), ('lying', 1)), ('or', ('lying', 6), ('lying', 0)), ('or', ('lying', 3), ('telling-truth', 7)), ('->', ('telling-truth', 1), ('telling-truth', 4)), ('telling-truth', 4), ('->', ('telling-truth', 4), ('telling-truth', 1)))", "index": 739}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mia, Matthew, Owen, Ella, William, Scarlett, Elizabeth, and Joseph. Mia told you that Joseph is not a knave. \"If Joseph is a knave then Ella is a knight\" - Matthew. Owen expressed that William is a knight. Ella was heard saying, \"If Matthew is a knight then Joseph is a knave\". \"Scarlett is a knave or Mia is a knight,\" William claimed. Scarlett said that William is a knight or Joseph is a knight. Elizabeth noted, \"Matthew is a knight and Joseph is a knave\". Joseph said, \"Ella is a knight or Scarlett is a knight.\" So who is a knight and who is a knave?", "names": ["Mia", "Matthew", "Owen", "Ella", "William", "Scarlett", "Elizabeth", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true, false, true], "solution_text": "Mia is a knight, Matthew is a knight, Owen is a knight, Ella is a knave, William is a knight, Scarlett is a knight, Elizabeth is a knave, and Joseph is a knight.", "solution_text_format": "(1) Mia is a knight\n(2) Matthew is a knight\n(3) Owen is a knight\n(4) Ella is a knave\n(5) William is a knight\n(6) Scarlett is a knight\n(7) Elizabeth is a knave\n(8) Joseph is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Joseph is not a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Ella is a knight or Scarlett is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that If Matthew is a knight then Joseph is a knave.", "Matthew cannot be a knight, because this would contradict the claim of Ella that If Matthew is a knight then Joseph is a knave.", "Matthew cannot be a knave, because this would contradict the false claim of their own that If Joseph is a knave then Ella is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that If Matthew is a knight then Joseph is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that If Joseph is a knave then Ella is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that William is a knight or Joseph is a knight.", "Assume William is a knight. No contradiction is found in their claim that Scarlett is a knave or Mia is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that William is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Matthew is a knight and Joseph is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Matthew is a knight and Joseph is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 7)), ('->', ('lying', 7), ('telling-truth', 3)), ('telling-truth', 4), ('->', ('telling-truth', 1), ('lying', 7)), ('or', ('lying', 5), ('telling-truth', 0)), ('or', ('telling-truth', 4), ('telling-truth', 7)), ('and', ('telling-truth', 1), ('lying', 7)), ('or', ('telling-truth', 3), ('telling-truth', 5)))", "index": 740}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aria, Ella, Scarlett, Jackson, Charlotte, Isabella, Emma, and Matthew. Aria stated, \"If Matthew is a knight then Scarlett is a knight\". In a statement by Ella: \"Emma is not a knave\". \"Jackson is a knave and Scarlett is a knight,\" Scarlett mentioned. Jackson commented, \"If Matthew is a knave then Matthew is a knight\". Charlotte was heard saying, \"Jackson is a knave\". In a statement by Isabella: \"Jackson is a knave if and only if Emma is a knight\". In a statement by Emma: \"If Aria is a knave then Jackson is a knight\". Matthew was heard saying, \"Scarlett is not a knave\". So who is a knight and who is a knave?", "names": ["Aria", "Ella", "Scarlett", "Jackson", "Charlotte", "Isabella", "Emma", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true, true, false], "solution_text": "Aria is a knight, Ella is a knight, Scarlett is a knave, Jackson is a knave, Charlotte is a knight, Isabella is a knight, Emma is a knight, and Matthew is a knave.", "solution_text_format": "(1) Aria is a knight\n(2) Ella is a knight\n(3) Scarlett is a knave\n(4) Jackson is a knave\n(5) Charlotte is a knight\n(6) Isabella is a knight\n(7) Emma is a knight\n(8) Matthew is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that If Matthew is a knight then Scarlett is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Jackson is a knave and Scarlett is a knight.", "Jackson cannot be a knight, because this would contradict the claim of Scarlett that Jackson is a knave and Scarlett is a knight.", "Jackson cannot be a knave, because this would contradict the false claim of their own that If Matthew is a knave then Matthew is a knight.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the claim of Aria that If Matthew is a knight then Scarlett is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Scarlett is not a knave.", "Scarlett cannot be a knight, because this would contradict the false claim of Matthew that Scarlett is not a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Jackson is a knave and Scarlett is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that If Matthew is a knave then Matthew is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that If Matthew is a knave then Matthew is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Emma is not a knave.", "Assume Emma is a knight. No contradiction is found in their claim that If Aria is a knave then Jackson is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Jackson is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Jackson is a knave if and only if Emma is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 7), ('telling-truth', 2)), ('not', ('lying', 6)), ('and', ('lying', 3), ('telling-truth', 2)), ('->', ('lying', 7), ('telling-truth', 7)), ('lying', 3), ('<=>', ('lying', 3), ('telling-truth', 6)), ('->', ('lying', 0), ('telling-truth', 3)), ('not', ('lying', 2)))", "index": 741}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Zoey, Scarlett, Logan, Aria, Chloe, Emily, Jacob, and Noah. In Zoey's words: \"If Zoey is a knight then Scarlett is a knight\". Scarlett told you that Logan is a knight or Chloe is a knight. \"If Emily is a knave then Jacob is a knave,\" Logan mentioned. Aria commented, \"Jacob is a knight if and only if Noah is a knight\". \"Scarlett is not a knight,\" Chloe declared. Emily noted, \"Noah is a knight\". Jacob asserted: \"Zoey is a knave and Scarlett is a knave\". Noah asserted: \"Logan is a knave and Scarlett is a knight\". So who is a knight and who is a knave?", "names": ["Zoey", "Scarlett", "Logan", "Aria", "Chloe", "Emily", "Jacob", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false, false, false], "solution_text": "Zoey is a knight, Scarlett is a knight, Logan is a knight, Aria is a knight, Chloe is a knave, Emily is a knave, Jacob is a knave, and Noah is a knave.", "solution_text_format": "(1) Zoey is a knight\n(2) Scarlett is a knight\n(3) Logan is a knight\n(4) Aria is a knight\n(5) Chloe is a knave\n(6) Emily is a knave\n(7) Jacob is a knave\n(8) Noah is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Zoey is a knight. No contradiction is found in their claim that If Zoey is a knight then Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Logan is a knight or Chloe is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that If Emily is a knave then Jacob is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Noah is a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that Logan is a knave and Scarlett is a knight.", "Noah cannot be a knave, because this would contradict the claim of Emily that Noah is a knight.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Noah is a knight.", "Noah cannot be a knight, because this would contradict the false claim of Emily that Noah is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Logan is a knave and Scarlett is a knight.", "Jacob cannot be a knight, because this would contradict the claim of Logan that If Emily is a knave then Jacob is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Zoey is a knave and Scarlett is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Scarlett is not a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Scarlett is not a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Jacob is a knight if and only if Noah is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 0), ('telling-truth', 1)), ('or', ('telling-truth', 2), ('telling-truth', 4)), ('->', ('lying', 5), ('lying', 6)), ('<=>', ('telling-truth', 6), ('telling-truth', 7)), ('not', ('telling-truth', 1)), ('telling-truth', 7), ('and', ('lying', 0), ('lying', 1)), ('and', ('lying', 2), ('telling-truth', 1)))", "index": 742}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sophia, Victoria, Ava, Benjamin, Grace, Emma, Elizabeth, and Scarlett. According to Sophia, \"Emma is a knave or Benjamin is a knight\". In Victoria's words: \"Elizabeth is a knight and Sophia is a knave\". Ava noted, \"Victoria is a knave and Emma is a knave\". In a statement by Benjamin: \"Scarlett is a knave\". According to Grace, \"Sophia is not a knave\". \"If Benjamin is a knave then Sophia is a knight\" - Emma. \"Emma is not a knave\" - Elizabeth. Scarlett said, \"Grace is not a knight.\" So who is a knight and who is a knave?", "names": ["Sophia", "Victoria", "Ava", "Benjamin", "Grace", "Emma", "Elizabeth", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true, true, false], "solution_text": "Sophia is a knight, Victoria is a knave, Ava is a knave, Benjamin is a knight, Grace is a knight, Emma is a knight, Elizabeth is a knight, and Scarlett is a knave.", "solution_text_format": "(1) Sophia is a knight\n(2) Victoria is a knave\n(3) Ava is a knave\n(4) Benjamin is a knight\n(5) Grace is a knight\n(6) Emma is a knight\n(7) Elizabeth is a knight\n(8) Scarlett is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Emma is a knave or Benjamin is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If Benjamin is a knave then Sophia is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Benjamin that Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Grace is not a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Sophia is not a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight and Sophia is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Elizabeth is a knight and Sophia is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Emma is not a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Victoria is a knave and Emma is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Victoria is a knave and Emma is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 5), ('telling-truth', 3)), ('and', ('telling-truth', 6), ('lying', 0)), ('and', ('lying', 1), ('lying', 5)), ('lying', 7), ('not', ('lying', 0)), ('->', ('lying', 3), ('telling-truth', 0)), ('not', ('lying', 5)), ('not', ('telling-truth', 4)))", "index": 743}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Penelope, Matthew, Aiden, Scarlett, Aurora, Olivia, Lucas, and Grace. Penelope told you that Scarlett is a knave or Scarlett is a knight. Matthew said, \"Grace is a knight.\" Aiden asserted: \"Olivia is a knave\". In Scarlett's words: \"If Grace is a knave then Lucas is a knight\". In Aurora's words: \"Scarlett is a knight or Scarlett is a knave\". In a statement by Olivia: \"Lucas is a knight and Aurora is a knave\". Lucas stated, \"Lucas is a knight or Aiden is a knight\". \"Aurora is a knight or Matthew is a knave,\" Grace declared. So who is a knight and who is a knave?", "names": ["Penelope", "Matthew", "Aiden", "Scarlett", "Aurora", "Olivia", "Lucas", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false, true, true], "solution_text": "Penelope is a knight, Matthew is a knight, Aiden is a knight, Scarlett is a knight, Aurora is a knight, Olivia is a knave, Lucas is a knight, and Grace is a knight.", "solution_text_format": "(1) Penelope is a knight\n(2) Matthew is a knight\n(3) Aiden is a knight\n(4) Scarlett is a knight\n(5) Aurora is a knight\n(6) Olivia is a knave\n(7) Lucas is a knight\n(8) Grace is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that Scarlett is a knave or Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Grace is a knave then Lucas is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Aurora is a knight or Matthew is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Scarlett is a knight or Scarlett is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Grace is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Lucas is a knight or Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Aiden that Olivia is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Lucas is a knight and Aurora is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('telling-truth', 3)), ('telling-truth', 7), ('lying', 5), ('->', ('lying', 7), ('telling-truth', 6)), ('or', ('telling-truth', 3), ('lying', 3)), ('and', ('telling-truth', 6), ('lying', 4)), ('or', ('telling-truth', 6), ('telling-truth', 2)), ('or', ('telling-truth', 4), ('lying', 1)))", "index": 744}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emma, Olivia, Ava, Matthew, Aiden, Sophia, Jackson, and Sofia. In a statement by Emma: \"Sophia is a knight or Matthew is a knave\". \"Jackson is a knight if and only if Matthew is a knave,\" Olivia claimed. As Ava put it, \"Jackson is a knave\". \"If Matthew is a knight then Ava is a knave,\" Matthew claimed. Aiden stated, \"If Matthew is a knave then Sophia is a knight\". According to Sophia, \"Ava is a knave if and only if Matthew is a knight\". \"Ava is not a knight\" - Jackson. According to Sofia, \"Emma is not a knight\". So who is a knight and who is a knave?", "names": ["Emma", "Olivia", "Ava", "Matthew", "Aiden", "Sophia", "Jackson", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true, true, false], "solution_text": "Emma is a knight, Olivia is a knave, Ava is a knave, Matthew is a knight, Aiden is a knight, Sophia is a knight, Jackson is a knight, and Sofia is a knave.", "solution_text_format": "(1) Emma is a knight\n(2) Olivia is a knave\n(3) Ava is a knave\n(4) Matthew is a knight\n(5) Aiden is a knight\n(6) Sophia is a knight\n(7) Jackson is a knight\n(8) Sofia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Sophia is a knight or Matthew is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Ava is a knave if and only if Matthew is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Jackson is a knave.", "Jackson cannot be a knight, because this would contradict the claim of Ava that Jackson is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Ava is not a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that If Matthew is a knight then Ava is a knave.", "Matthew cannot be a knave, because this would contradict the false claim of their own that If Matthew is a knight then Ava is a knave.", "We have exhausted all possibilities for Matthew and Jackson, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Jackson is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Ava is not a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that If Matthew is a knight then Ava is a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that Jackson is a knight if and only if Matthew is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Jackson is a knight if and only if Matthew is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Matthew is a knave then Sophia is a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that Emma is not a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Emma is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('lying', 3)), ('<=>', ('telling-truth', 6), ('lying', 3)), ('lying', 6), ('->', ('telling-truth', 3), ('lying', 2)), ('->', ('lying', 3), ('telling-truth', 5)), ('<=>', ('lying', 2), ('telling-truth', 3)), ('not', ('telling-truth', 2)), ('not', ('telling-truth', 0)))", "index": 745}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Amelia, Sofia, Charlotte, Ethan, Zoey, Sophia, Samuel, and Benjamin. Amelia commented, \"Ethan is not a knight\". In a statement by Sofia: \"Ethan is a knave\". Charlotte commented, \"Benjamin is not a knight\". \"Sophia is a knave and Zoey is a knight,\" Ethan claimed. In Zoey's words: \"Sofia is a knave if and only if Ethan is a knight\". Sophia asserted: \"If Benjamin is a knave then Zoey is a knight\". As Samuel put it, \"Ethan is not a knight\". Benjamin remarked, \"Samuel is not a knight\". So who is a knight and who is a knave?", "names": ["Amelia", "Sofia", "Charlotte", "Ethan", "Zoey", "Sophia", "Samuel", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true, true, false], "solution_text": "Amelia is a knight, Sofia is a knight, Charlotte is a knight, Ethan is a knave, Zoey is a knight, Sophia is a knight, Samuel is a knight, and Benjamin is a knave.", "solution_text_format": "(1) Amelia is a knight\n(2) Sofia is a knight\n(3) Charlotte is a knight\n(4) Ethan is a knave\n(5) Zoey is a knight\n(6) Sophia is a knight\n(7) Samuel is a knight\n(8) Benjamin is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Amelia is a knight. No contradiction is found in their claim that Ethan is not a knight.", "Ethan cannot be a knight, because this would contradict the claim of Amelia that Ethan is not a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Sophia is a knave and Zoey is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that If Benjamin is a knave then Zoey is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Samuel is not a knight.", "Samuel cannot be a knight, because this would contradict the claim of Benjamin that Samuel is not a knight.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Ethan is not a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Samuel is not a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Ethan is not a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Sofia is a knave if and only if Ethan is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Ethan is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Benjamin is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 3)), ('lying', 3), ('not', ('telling-truth', 7)), ('and', ('lying', 5), ('telling-truth', 4)), ('<=>', ('lying', 1), ('telling-truth', 3)), ('->', ('lying', 7), ('telling-truth', 4)), ('not', ('telling-truth', 3)), ('not', ('telling-truth', 6)))", "index": 746}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Michael, Sophia, Zoey, Oliver, Scarlett, Charlotte, Noah, and Harper. Michael was heard saying, \"Zoey is a knight\". According to Sophia, \"If Michael is a knave then Harper is a knave\". Zoey stated, \"Oliver is a knight or Sophia is a knight\". \"Zoey is a knave\" - Oliver. Scarlett expressed that Michael is a knave or Charlotte is a knave. Charlotte said, \"Oliver is a knight or Harper is a knave.\" Noah asserted: \"Michael is a knight if and only if Sophia is a knight\". \"Zoey is a knight and Oliver is a knave,\" Harper declared. So who is a knight and who is a knave?", "names": ["Michael", "Sophia", "Zoey", "Oliver", "Scarlett", "Charlotte", "Noah", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false, true, true], "solution_text": "Michael is a knight, Sophia is a knight, Zoey is a knight, Oliver is a knave, Scarlett is a knight, Charlotte is a knave, Noah is a knight, and Harper is a knight.", "solution_text_format": "(1) Michael is a knight\n(2) Sophia is a knight\n(3) Zoey is a knight\n(4) Oliver is a knave\n(5) Scarlett is a knight\n(6) Charlotte is a knave\n(7) Noah is a knight\n(8) Harper is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Oliver is a knight or Sophia is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Zoey is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Zoey is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that If Michael is a knave then Harper is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Zoey is a knight and Oliver is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Michael is a knave or Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Scarlett that Michael is a knave or Charlotte is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Oliver is a knight or Harper is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Michael is a knight if and only if Sophia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('->', ('lying', 0), ('lying', 7)), ('or', ('telling-truth', 3), ('telling-truth', 1)), ('lying', 2), ('or', ('lying', 0), ('lying', 5)), ('or', ('telling-truth', 3), ('lying', 7)), ('<=>', ('telling-truth', 0), ('telling-truth', 1)), ('and', ('telling-truth', 2), ('lying', 3)))", "index": 747}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jack, Chloe, Ethan, Isabella, Liam, Sophia, Victoria, and Michael. \"Michael is a knave if and only if Chloe is a knight,\" Jack mentioned. According to Chloe, \"If Victoria is a knight then Ethan is a knight\". \"Sophia is a knight and Liam is a knave\" - Ethan. \"Liam is a knight or Victoria is a knave,\" Isabella declared. \"Isabella is not a knight,\" Liam claimed. Sophia stated, \"Victoria is not a knight\". \"Isabella is a knave\" - Victoria. \"Chloe is a knave and Sophia is a knave,\" Michael declared. So who is a knight and who is a knave?", "names": ["Jack", "Chloe", "Ethan", "Isabella", "Liam", "Sophia", "Victoria", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true, false, false], "solution_text": "Jack is a knight, Chloe is a knight, Ethan is a knight, Isabella is a knight, Liam is a knave, Sophia is a knight, Victoria is a knave, and Michael is a knave.", "solution_text_format": "(1) Jack is a knight\n(2) Chloe is a knight\n(3) Ethan is a knight\n(4) Isabella is a knight\n(5) Liam is a knave\n(6) Sophia is a knight\n(7) Victoria is a knave\n(8) Michael is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Michael is a knave if and only if Chloe is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Chloe is a knave and Sophia is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Jack that Michael is a knave if and only if Chloe is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that If Victoria is a knight then Ethan is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Isabella is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Victoria that Isabella is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Liam is a knight or Victoria is a knave.", "Liam cannot be a knight, because this would contradict the false claim of Isabella that Liam is a knight or Victoria is a knave.", "Liam cannot be a knave, because this would contradict the false claim of their own that Isabella is not a knight.", "We have exhausted all possibilities for Liam and Isabella, so let us go back and reconsider Victoria.", "Victoria cannot be a knave, because this would contradict the false claim of Chloe that If Victoria is a knight then Ethan is a knight.", "We have exhausted all possibilities for Victoria and Chloe, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Chloe is a knave and Sophia is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that If Victoria is a knight then Ethan is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Isabella is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Victoria that Isabella is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Liam is a knight or Victoria is a knave.", "Liam cannot be a knight, because this would contradict the false claim of Isabella that Liam is a knight or Victoria is a knave.", "Liam cannot be a knave, because this would contradict the false claim of their own that Isabella is not a knight.", "We have exhausted all possibilities for Liam and Isabella, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Isabella is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Liam is a knight or Victoria is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Isabella is not a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Isabella is not a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Sophia is a knight and Liam is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Victoria is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 7), ('telling-truth', 1)), ('->', ('telling-truth', 6), ('telling-truth', 2)), ('and', ('telling-truth', 5), ('lying', 4)), ('or', ('telling-truth', 4), ('lying', 6)), ('not', ('telling-truth', 3)), ('not', ('telling-truth', 6)), ('lying', 3), ('and', ('lying', 1), ('lying', 5)))", "index": 748}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Penelope, Lucas, Oliver, Mia, Jackson, William, Noah, and Michael. Penelope was heard saying, \"William is a knight or Lucas is a knave\". Lucas said that William is a knight and Oliver is a knave. Oliver remarked, \"If Penelope is a knave then Jackson is a knight\". \"Jackson is not a knight,\" Mia mentioned. Jackson said, \"If Penelope is a knight then Lucas is a knave.\" \"Noah is not a knave,\" William claimed. Noah said that Penelope is not a knave. \"Mia is a knave if and only if Lucas is a knight,\" Michael mentioned. So who is a knight and who is a knave?", "names": ["Penelope", "Lucas", "Oliver", "Mia", "Jackson", "William", "Noah", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true, true, false], "solution_text": "Penelope is a knight, Lucas is a knave, Oliver is a knight, Mia is a knave, Jackson is a knight, William is a knight, Noah is a knight, and Michael is a knave.", "solution_text_format": "(1) Penelope is a knight\n(2) Lucas is a knave\n(3) Oliver is a knight\n(4) Mia is a knave\n(5) Jackson is a knight\n(6) William is a knight\n(7) Noah is a knight\n(8) Michael is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that William is a knight or Lucas is a knave.", "Assume William is a knight. No contradiction is found in their claim that Noah is not a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Penelope is not a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that William is a knight and Oliver is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Lucas that William is a knight and Oliver is a knave.", "Oliver cannot be a knave, because this would contradict the false claim of their own that If Penelope is a knave then Jackson is a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that William is a knight and Oliver is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that If Penelope is a knave then Jackson is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that If Penelope is a knight then Lucas is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Jackson is not a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Jackson is not a knight.", "Michael cannot be a knight, because this would contradict the claim of their own that Mia is a knave if and only if Lucas is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Mia is a knave if and only if Lucas is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('lying', 1)), ('and', ('telling-truth', 5), ('lying', 2)), ('->', ('lying', 0), ('telling-truth', 4)), ('not', ('telling-truth', 4)), ('->', ('telling-truth', 0), ('lying', 1)), ('not', ('lying', 6)), ('not', ('lying', 0)), ('<=>', ('lying', 3), ('telling-truth', 1)))", "index": 749}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Isabella, Mia, Olivia, Owen, Aiden, Victoria, Ava, and Emma. Isabella stated, \"Aiden is a knave and Mia is a knave\". Mia told you that If Isabella is a knave then Owen is a knight. Olivia said, \"Isabella is a knight or Owen is a knave.\" Owen commented, \"If Aiden is a knave then Isabella is a knave\". As Aiden put it, \"Ava is a knight\". Victoria remarked, \"If Isabella is a knight then Mia is a knight\". Ava said, \"If Isabella is a knight then Emma is a knight.\" Emma asserted: \"Victoria is a knave\". So who is a knight and who is a knave?", "names": ["Isabella", "Mia", "Olivia", "Owen", "Aiden", "Victoria", "Ava", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true, true, false], "solution_text": "Isabella is a knave, Mia is a knight, Olivia is a knave, Owen is a knight, Aiden is a knight, Victoria is a knight, Ava is a knight, and Emma is a knave.", "solution_text_format": "(1) Isabella is a knave\n(2) Mia is a knight\n(3) Olivia is a knave\n(4) Owen is a knight\n(5) Aiden is a knight\n(6) Victoria is a knight\n(7) Ava is a knight\n(8) Emma is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Aiden is a knave and Mia is a knave.", "Aiden cannot be a knight, because this would contradict the claim of Isabella that Aiden is a knave and Mia is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Ava is a knight.", "Ava cannot be a knight, because this would contradict the false claim of Aiden that Ava is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that If Isabella is a knight then Emma is a knight.", "Emma cannot be a knight, because this would contradict the false claim of Ava that If Isabella is a knight then Emma is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that If Isabella is a knight then Mia is a knight.", "Mia cannot be a knight, because this would contradict the claim of Isabella that Aiden is a knave and Mia is a knave.", "Mia cannot be a knave, because this would contradict the false claim of their own that If Isabella is a knave then Owen is a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Victoria.", "Victoria cannot be a knave, because this would contradict the false claim of Emma that Victoria is a knave.", "We have exhausted all possibilities for Victoria, Emma, Ava, and Aiden, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Aiden is a knave and Mia is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Ava is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that If Isabella is a knight then Emma is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Victoria is a knave.", "Victoria cannot be a knight, because this would contradict the claim of Emma that Victoria is a knave.", "Victoria cannot be a knave, because this would contradict the false claim of their own that If Isabella is a knight then Mia is a knight.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that If Isabella is a knight then Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that If Isabella is a knave then Owen is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that If Aiden is a knave then Isabella is a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that Isabella is a knight or Owen is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Isabella is a knight or Owen is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('lying', 1)), ('->', ('lying', 0), ('telling-truth', 3)), ('or', ('telling-truth', 0), ('lying', 3)), ('->', ('lying', 4), ('lying', 0)), ('telling-truth', 6), ('->', ('telling-truth', 0), ('telling-truth', 1)), ('->', ('telling-truth', 0), ('telling-truth', 7)), ('lying', 5))", "index": 750}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emma, Michael, Avery, Aurora, William, Harper, Sophia, and Emily. Emma expressed that Aurora is not a knight. Michael asserted: \"If Avery is a knight then Sophia is a knight\". Avery was heard saying, \"Michael is a knave and Emily is a knight\". Aurora said that Harper is a knight. In a statement by William: \"Avery is a knave\". Harper asserted: \"Emily is not a knave\". Sophia noted, \"If Aurora is a knave then Emma is a knight\". In a statement by Emily: \"Avery is not a knight\". So who is a knight and who is a knave?", "names": ["Emma", "Michael", "Avery", "Aurora", "William", "Harper", "Sophia", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true, true, true], "solution_text": "Emma is a knave, Michael is a knight, Avery is a knave, Aurora is a knight, William is a knight, Harper is a knight, Sophia is a knight, and Emily is a knight.", "solution_text_format": "(1) Emma is a knave\n(2) Michael is a knight\n(3) Avery is a knave\n(4) Aurora is a knight\n(5) William is a knight\n(6) Harper is a knight\n(7) Sophia is a knight\n(8) Emily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Aurora is not a knight.", "Aurora cannot be a knight, because this would contradict the claim of Emma that Aurora is not a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Harper is a knight.", "Harper cannot be a knight, because this would contradict the false claim of Aurora that Harper is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Emily is not a knave.", "Emily cannot be a knight, because this would contradict the false claim of Harper that Emily is not a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Avery is not a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Emily is a knight.", "Avery cannot be a knave, because this would contradict the false claim of Emily that Avery is not a knight.", "We have exhausted all possibilities for Avery, Emily, Harper, and Aurora, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Aurora is not a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Harper is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Emily is not a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Avery is not a knight.", "Avery cannot be a knight, because this would contradict the claim of Emily that Avery is not a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Michael is a knave and Emily is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that If Avery is a knight then Sophia is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that If Aurora is a knave then Emma is a knight.", "Assume William is a knight. No contradiction is found in their claim that Avery is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 3)), ('->', ('telling-truth', 2), ('telling-truth', 6)), ('and', ('lying', 1), ('telling-truth', 7)), ('telling-truth', 5), ('lying', 2), ('not', ('lying', 7)), ('->', ('lying', 3), ('telling-truth', 0)), ('not', ('telling-truth', 2)))", "index": 751}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Evelyn, Chloe, Charlotte, Samuel, Mason, Sofia, Jack, and Noah. According to Evelyn, \"If Noah is a knave then Charlotte is a knight\". \"Charlotte is a knave if and only if Jack is a knight,\" Chloe mentioned. Charlotte told you that Mason is a knight and Noah is a knight. Samuel stated, \"If Chloe is a knight then Mason is a knight\". In a statement by Mason: \"Evelyn is a knave\". \"Mason is a knave if and only if Jack is a knave,\" Sofia declared. Jack remarked, \"Charlotte is not a knave\". Noah was heard saying, \"Charlotte is a knave\". So who is a knight and who is a knave?", "names": ["Evelyn", "Chloe", "Charlotte", "Samuel", "Mason", "Sofia", "Jack", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, true, false, true], "solution_text": "Evelyn is a knight, Chloe is a knave, Charlotte is a knave, Samuel is a knight, Mason is a knave, Sofia is a knight, Jack is a knave, and Noah is a knight.", "solution_text_format": "(1) Evelyn is a knight\n(2) Chloe is a knave\n(3) Charlotte is a knave\n(4) Samuel is a knight\n(5) Mason is a knave\n(6) Sofia is a knight\n(7) Jack is a knave\n(8) Noah is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that If Noah is a knave then Charlotte is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Noah that Charlotte is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Mason is a knight and Noah is a knight.", "Mason cannot be a knight, because this would contradict the false claim of Charlotte that Mason is a knight and Noah is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Evelyn is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Charlotte is a knave if and only if Jack is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Charlotte is not a knave.", "Jack cannot be a knave, because this would contradict the claim of Chloe that Charlotte is a knave if and only if Jack is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Charlotte is a knave if and only if Jack is a knight.", "Jack cannot be a knight, because this would contradict the false claim of Chloe that Charlotte is a knave if and only if Jack is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Charlotte is not a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that If Chloe is a knight then Mason is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Mason is a knave if and only if Jack is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 7), ('telling-truth', 2)), ('<=>', ('lying', 2), ('telling-truth', 6)), ('and', ('telling-truth', 4), ('telling-truth', 7)), ('->', ('telling-truth', 1), ('telling-truth', 4)), ('lying', 0), ('<=>', ('lying', 4), ('lying', 6)), ('not', ('lying', 2)), ('lying', 2))", "index": 752}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ella, Charlotte, Sofia, Harper, Amelia, Samuel, Matthew, and Jack. Ella said, \"Jack is a knave if and only if Matthew is a knave.\" \"Amelia is not a knight,\" Charlotte declared. Sofia stated, \"Jack is a knight if and only if Matthew is a knave\". As Harper put it, \"Matthew is a knave\". In Amelia's words: \"If Amelia is a knight then Sofia is a knave\". Samuel was heard saying, \"Harper is a knave and Sofia is a knight\". Matthew was heard saying, \"Jack is a knave if and only if Sofia is a knight\". Jack told you that Samuel is a knight if and only if Charlotte is a knight. So who is a knight and who is a knave?", "names": ["Ella", "Charlotte", "Sofia", "Harper", "Amelia", "Samuel", "Matthew", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, false, true, true], "solution_text": "Ella is a knight, Charlotte is a knave, Sofia is a knave, Harper is a knave, Amelia is a knight, Samuel is a knave, Matthew is a knight, and Jack is a knight.", "solution_text_format": "(1) Ella is a knight\n(2) Charlotte is a knave\n(3) Sofia is a knave\n(4) Harper is a knave\n(5) Amelia is a knight\n(6) Samuel is a knave\n(7) Matthew is a knight\n(8) Jack is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Jack is a knave if and only if Matthew is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Samuel is a knight if and only if Charlotte is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Harper is a knave and Sofia is a knight.", "Harper cannot be a knight, because this would contradict the claim of Samuel that Harper is a knave and Sofia is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Matthew is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Jack is a knave if and only if Sofia is a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that Jack is a knight if and only if Matthew is a knave.", "Sofia cannot be a knave, because this would contradict the claim of Samuel that Harper is a knave and Sofia is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the claim of Ella that Jack is a knave if and only if Matthew is a knave.", "We have exhausted all possibilities for Matthew and Harper, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Harper is a knave and Sofia is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Matthew is a knave.", "Matthew cannot be a knight, because this would contradict the claim of Harper that Matthew is a knave.", "Matthew cannot be a knave, because this would contradict the claim of Ella that Jack is a knave if and only if Matthew is a knave.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Matthew is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Jack is a knave if and only if Sofia is a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that Jack is a knight if and only if Matthew is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Jack is a knight if and only if Matthew is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Jack that Samuel is a knight if and only if Charlotte is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Amelia is not a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that If Amelia is a knight then Sofia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 7), ('lying', 6)), ('not', ('telling-truth', 4)), ('<=>', ('telling-truth', 7), ('lying', 6)), ('lying', 6), ('->', ('telling-truth', 4), ('lying', 2)), ('and', ('lying', 3), ('telling-truth', 2)), ('<=>', ('lying', 7), ('telling-truth', 2)), ('<=>', ('telling-truth', 5), ('telling-truth', 1)))", "index": 753}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emma, Alexander, Benjamin, Ella, Lucas, David, Riley, and Sebastian. Emma said, \"Lucas is a knave or Riley is a knight.\" Alexander commented, \"Benjamin is a knave if and only if Benjamin is a knight\". Benjamin said that Emma is a knight. Ella said that Benjamin is a knave if and only if Alexander is a knave. Lucas asserted: \"Ella is a knave and Sebastian is a knave\". As David put it, \"If Emma is a knight then Benjamin is a knight\". Riley was heard saying, \"Ella is not a knight\". According to Sebastian, \"Riley is a knave and Lucas is a knave\". So who is a knight and who is a knave?", "names": ["Emma", "Alexander", "Benjamin", "Ella", "Lucas", "David", "Riley", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true, true, false], "solution_text": "Emma is a knight, Alexander is a knave, Benjamin is a knight, Ella is a knave, Lucas is a knight, David is a knight, Riley is a knight, and Sebastian is a knave.", "solution_text_format": "(1) Emma is a knight\n(2) Alexander is a knave\n(3) Benjamin is a knight\n(4) Ella is a knave\n(5) Lucas is a knight\n(6) David is a knight\n(7) Riley is a knight\n(8) Sebastian is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Lucas is a knave or Riley is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Ella is a knave and Sebastian is a knave.", "Ella cannot be a knight, because this would contradict the claim of Lucas that Ella is a knave and Sebastian is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Benjamin is a knave if and only if Alexander is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Emma is a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave if and only if Benjamin is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Benjamin is a knave if and only if Benjamin is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of Lucas that Ella is a knave and Sebastian is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Riley is a knave and Lucas is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Ella is not a knight.", "Assume David is a knight. No contradiction is found in their claim that If Emma is a knight then Benjamin is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 4), ('telling-truth', 6)), ('<=>', ('lying', 2), ('telling-truth', 2)), ('telling-truth', 0), ('<=>', ('lying', 2), ('lying', 1)), ('and', ('lying', 3), ('lying', 7)), ('->', ('telling-truth', 0), ('telling-truth', 2)), ('not', ('telling-truth', 3)), ('and', ('lying', 6), ('lying', 4)))", "index": 754}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Grace, Riley, Ella, Zoey, Noah, Victoria, Scarlett, and Ethan. Grace was heard saying, \"Scarlett is a knave\". In a statement by Riley: \"Zoey is a knight if and only if Victoria is a knight\". \"Grace is a knave,\" Ella mentioned. Zoey was heard saying, \"Victoria is a knave or Riley is a knave\". Noah stated, \"Zoey is a knight or Grace is a knave\". Victoria noted, \"Zoey is a knave and Ella is a knave\". As Scarlett put it, \"Victoria is not a knave\". Ethan told you that Noah is a knave. So who is a knight and who is a knave?", "names": ["Grace", "Riley", "Ella", "Zoey", "Noah", "Victoria", "Scarlett", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false, false, false], "solution_text": "Grace is a knight, Riley is a knave, Ella is a knave, Zoey is a knight, Noah is a knight, Victoria is a knave, Scarlett is a knave, and Ethan is a knave.", "solution_text_format": "(1) Grace is a knight\n(2) Riley is a knave\n(3) Ella is a knave\n(4) Zoey is a knight\n(5) Noah is a knight\n(6) Victoria is a knave\n(7) Scarlett is a knave\n(8) Ethan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Grace that Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Victoria is not a knave.", "Victoria cannot be a knight, because this would contradict the false claim of Scarlett that Victoria is not a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Zoey is a knave and Ella is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Victoria is a knave or Riley is a knave.", "Riley cannot be a knight, because this would contradict the claim of their own that Zoey is a knight if and only if Victoria is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Zoey is a knight if and only if Victoria is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Grace is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Grace is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Zoey is a knight or Grace is a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Noah is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Noah is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 6), ('<=>', ('telling-truth', 3), ('telling-truth', 5)), ('lying', 0), ('or', ('lying', 5), ('lying', 1)), ('or', ('telling-truth', 3), ('lying', 0)), ('and', ('lying', 3), ('lying', 2)), ('not', ('lying', 5)), ('lying', 4))", "index": 755}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sofia, Elizabeth, Emma, Michael, Grace, Ella, Emily, and Avery. In a statement by Sofia: \"Grace is a knave or Avery is a knave\". Elizabeth noted, \"Emily is a knight or Avery is a knave\". According to Emma, \"If Grace is a knave then Michael is a knight\". \"Ella is a knave,\" Michael claimed. Grace was heard saying, \"Sofia is not a knight\". According to Ella, \"Grace is a knave\". Emily expressed that Avery is a knave and Elizabeth is a knight. Avery noted, \"Michael is a knave\". So who is a knight and who is a knave?", "names": ["Sofia", "Elizabeth", "Emma", "Michael", "Grace", "Ella", "Emily", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, true, false, true], "solution_text": "Sofia is a knight, Elizabeth is a knave, Emma is a knave, Michael is a knave, Grace is a knave, Ella is a knight, Emily is a knave, and Avery is a knight.", "solution_text_format": "(1) Sofia is a knight\n(2) Elizabeth is a knave\n(3) Emma is a knave\n(4) Michael is a knave\n(5) Grace is a knave\n(6) Ella is a knight\n(7) Emily is a knave\n(8) Avery is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Grace is a knave or Avery is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Sofia is not a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Sofia is not a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of Avery that Michael is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Grace is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Emily is a knight or Avery is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Avery is a knave and Elizabeth is a knight.", "Emily cannot be a knave, because this would contradict the claim of Elizabeth that Emily is a knight or Avery is a knave.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Emily is a knight or Avery is a knave.", "Emily cannot be a knight, because this would contradict the false claim of Elizabeth that Emily is a knight or Avery is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Avery is a knave and Elizabeth is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that If Grace is a knave then Michael is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that If Grace is a knave then Michael is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 4), ('lying', 7)), ('or', ('telling-truth', 6), ('lying', 7)), ('->', ('lying', 4), ('telling-truth', 3)), ('lying', 5), ('not', ('telling-truth', 0)), ('lying', 4), ('and', ('lying', 7), ('telling-truth', 1)), ('lying', 3))", "index": 756}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jackson, David, Chloe, Michael, Lily, Mason, Riley, and Penelope. \"Chloe is a knight,\" Jackson declared. David said, \"If Jackson is a knight then Riley is a knight.\" Chloe asserted: \"Mason is a knight\". \"Riley is a knave or Mason is a knight,\" Michael declared. Lily commented, \"Chloe is a knave and Mason is a knight\". In a statement by Mason: \"If Penelope is a knave then Chloe is a knight\". Riley was heard saying, \"If David is a knight then Michael is a knight\". \"Michael is not a knave\" - Penelope. So who is a knight and who is a knave?", "names": ["Jackson", "David", "Chloe", "Michael", "Lily", "Mason", "Riley", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true, true, true], "solution_text": "Jackson is a knight, David is a knight, Chloe is a knight, Michael is a knight, Lily is a knave, Mason is a knight, Riley is a knight, and Penelope is a knight.", "solution_text_format": "(1) Jackson is a knight\n(2) David is a knight\n(3) Chloe is a knight\n(4) Michael is a knight\n(5) Lily is a knave\n(6) Mason is a knight\n(7) Riley is a knight\n(8) Penelope is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Chloe is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Mason is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that If Penelope is a knave then Chloe is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Michael is not a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Riley is a knave or Mason is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that If David is a knight then Michael is a knight.", "Assume David is a knight. No contradiction is found in their claim that If Jackson is a knight then Riley is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Chloe is a knave and Mason is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Chloe is a knave and Mason is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('->', ('telling-truth', 0), ('telling-truth', 6)), ('telling-truth', 5), ('or', ('lying', 6), ('telling-truth', 5)), ('and', ('lying', 2), ('telling-truth', 5)), ('->', ('lying', 7), ('telling-truth', 2)), ('->', ('telling-truth', 1), ('telling-truth', 3)), ('not', ('lying', 3)))", "index": 757}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Elizabeth, Luke, William, Oliver, Olivia, Noah, Jacob, and Sophia. In Elizabeth's words: \"Noah is a knave if and only if Luke is a knight\". Luke stated, \"Oliver is a knight\". William remarked, \"If Oliver is a knave then Luke is a knave\". \"Jacob is not a knight\" - Oliver. Olivia was heard saying, \"William is a knave\". \"Elizabeth is a knight and Sophia is a knave,\" Noah declared. Jacob told you that Olivia is a knave if and only if Luke is a knave. Sophia said that Jacob is not a knave. So who is a knight and who is a knave?", "names": ["Elizabeth", "Luke", "William", "Oliver", "Olivia", "Noah", "Jacob", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, false, true, true], "solution_text": "Elizabeth is a knave, Luke is a knave, William is a knight, Oliver is a knave, Olivia is a knave, Noah is a knave, Jacob is a knight, and Sophia is a knight.", "solution_text_format": "(1) Elizabeth is a knave\n(2) Luke is a knave\n(3) William is a knight\n(4) Oliver is a knave\n(5) Olivia is a knave\n(6) Noah is a knave\n(7) Jacob is a knight\n(8) Sophia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Noah is a knave if and only if Luke is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Elizabeth is a knight and Sophia is a knave.", "Sophia cannot be a knight, because this would contradict the claim of Noah that Elizabeth is a knight and Sophia is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Jacob is not a knave.", "Jacob cannot be a knight, because this would contradict the false claim of Sophia that Jacob is not a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Olivia is a knave if and only if Luke is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that William is a knave.", "William cannot be a knight, because this would contradict the claim of Olivia that William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that If Oliver is a knave then Luke is a knave.", "Oliver cannot be a knight, because this would contradict the false claim of William that If Oliver is a knave then Luke is a knave.", "Oliver cannot be a knave, because this would contradict the false claim of their own that Jacob is not a knight.", "We have exhausted all possibilities for Oliver and William, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that William is a knave.", "Assume William is a knight. No contradiction is found in their claim that If Oliver is a knave then Luke is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Jacob is not a knight.", "Luke cannot be a knight, because this would contradict the claim of Elizabeth that Noah is a knave if and only if Luke is a knight.", "Luke cannot be a knave, because this would contradict the false claim of their own that Oliver is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the false claim of their own that Jacob is not a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the false claim of Olivia that William is a knave.", "We have exhausted all possibilities for William, Olivia, Jacob, and Sophia, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Elizabeth is a knight and Sophia is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Jacob is not a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Olivia is a knave if and only if Luke is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that William is a knave.", "William cannot be a knight, because this would contradict the claim of Olivia that William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that If Oliver is a knave then Luke is a knave.", "Oliver cannot be a knight, because this would contradict the false claim of William that If Oliver is a knave then Luke is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Jacob is not a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Oliver is a knight.", "Luke cannot be a knave, because this would contradict the claim of Elizabeth that Noah is a knave if and only if Luke is a knight.", "We have exhausted all possibilities for Luke, Oliver, and William, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that William is a knave.", "Assume William is a knight. No contradiction is found in their claim that If Oliver is a knave then Luke is a knave.", "Oliver cannot be a knight, because this would contradict the claim of their own that Jacob is not a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Jacob is not a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Oliver is a knight.", "Luke cannot be a knave, because this would contradict the claim of Elizabeth that Noah is a knave if and only if Luke is a knight.", "We have exhausted all possibilities for Luke and Oliver, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the false claim of Olivia that William is a knave.", "We have exhausted all possibilities for William and Olivia, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the claim of Sophia that Jacob is not a knave.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the false claim of Noah that Elizabeth is a knight and Sophia is a knave.", "We have exhausted all possibilities for Sophia and Noah, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Noah is a knave if and only if Luke is a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight and Sophia is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Elizabeth is a knight and Sophia is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Jacob is not a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Olivia is a knave if and only if Luke is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that William is a knave.", "William cannot be a knight, because this would contradict the claim of Olivia that William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that If Oliver is a knave then Luke is a knave.", "Oliver cannot be a knight, because this would contradict the false claim of William that If Oliver is a knave then Luke is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Jacob is not a knight.", "Luke cannot be a knight, because this would contradict the false claim of Elizabeth that Noah is a knave if and only if Luke is a knight.", "Luke cannot be a knave, because this would contradict the false claim of William that If Oliver is a knave then Luke is a knave.", "We have exhausted all possibilities for Luke, Oliver, and William, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that William is a knave.", "Assume William is a knight. No contradiction is found in their claim that If Oliver is a knave then Luke is a knave.", "Oliver cannot be a knight, because this would contradict the claim of their own that Jacob is not a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Jacob is not a knight.", "Luke cannot be a knight, because this would contradict the false claim of Elizabeth that Noah is a knave if and only if Luke is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Oliver is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 5), ('telling-truth', 1)), ('telling-truth', 3), ('->', ('lying', 3), ('lying', 1)), ('not', ('telling-truth', 6)), ('lying', 2), ('and', ('telling-truth', 0), ('lying', 7)), ('<=>', ('lying', 4), ('lying', 1)), ('not', ('lying', 6)))", "index": 758}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jackson, Amelia, Noah, Lucas, Isabella, Charlotte, Emily, and Emma. Jackson commented, \"Emily is a knight\". Amelia was heard saying, \"Emily is a knight\". \"Isabella is not a knight,\" Noah mentioned. Lucas expressed that Isabella is a knight or Jackson is a knight. Isabella said that If Emily is a knight then Jackson is a knight. As Charlotte put it, \"Noah is not a knight\". As Emily put it, \"Charlotte is a knave\". In a statement by Emma: \"Charlotte is not a knave\". So who is a knight and who is a knave?", "names": ["Jackson", "Amelia", "Noah", "Lucas", "Isabella", "Charlotte", "Emily", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true, false, true], "solution_text": "Jackson is a knave, Amelia is a knave, Noah is a knave, Lucas is a knight, Isabella is a knight, Charlotte is a knight, Emily is a knave, and Emma is a knight.", "solution_text_format": "(1) Jackson is a knave\n(2) Amelia is a knave\n(3) Noah is a knave\n(4) Lucas is a knight\n(5) Isabella is a knight\n(6) Charlotte is a knight\n(7) Emily is a knave\n(8) Emma is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Emily that Charlotte is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Noah is not a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Isabella is not a knight.", "Isabella cannot be a knight, because this would contradict the claim of Noah that Isabella is not a knight.", "Isabella cannot be a knave, because this would contradict the false claim of their own that If Emily is a knight then Jackson is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the false claim of Charlotte that Noah is not a knight.", "We have exhausted all possibilities for Noah and Charlotte, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the claim of Jackson that Emily is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Emily is a knight.", "Emily cannot be a knight, because this would contradict the false claim of Jackson that Emily is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Charlotte is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Noah is not a knight.", "Noah cannot be a knight, because this would contradict the claim of Charlotte that Noah is not a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Isabella is not a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that If Emily is a knight then Jackson is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Emily is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Emily is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Isabella is a knight or Jackson is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Charlotte is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 6), ('telling-truth', 6), ('not', ('telling-truth', 4)), ('or', ('telling-truth', 4), ('telling-truth', 0)), ('->', ('telling-truth', 6), ('telling-truth', 0)), ('not', ('telling-truth', 2)), ('lying', 5), ('not', ('lying', 5)))", "index": 759}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Chloe, Victoria, Avery, Evelyn, Zoey, Emma, Jackson, and Aurora. Chloe expressed that Aurora is a knave if and only if Avery is a knight. In a statement by Victoria: \"Avery is a knave\". Avery expressed that Evelyn is not a knight. In Evelyn's words: \"Emma is a knight\". \"Jackson is a knight if and only if Evelyn is a knave,\" Zoey mentioned. Emma expressed that Avery is a knight and Chloe is a knight. Jackson expressed that If Emma is a knight then Evelyn is a knight. Aurora noted, \"Chloe is not a knight\". So who is a knight and who is a knave?", "names": ["Chloe", "Victoria", "Avery", "Evelyn", "Zoey", "Emma", "Jackson", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, false, true, true], "solution_text": "Chloe is a knave, Victoria is a knave, Avery is a knight, Evelyn is a knave, Zoey is a knight, Emma is a knave, Jackson is a knight, and Aurora is a knight.", "solution_text_format": "(1) Chloe is a knave\n(2) Victoria is a knave\n(3) Avery is a knight\n(4) Evelyn is a knave\n(5) Zoey is a knight\n(6) Emma is a knave\n(7) Jackson is a knight\n(8) Aurora is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Aurora is a knave if and only if Avery is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Chloe is not a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Chloe is not a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Evelyn is not a knight.", "Evelyn cannot be a knight, because this would contradict the claim of Avery that Evelyn is not a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Emma is a knight.", "Emma cannot be a knight, because this would contradict the false claim of Evelyn that Emma is a knight.", "Emma cannot be a knave, because this would contradict the false claim of their own that Avery is a knight and Chloe is a knight.", "We have exhausted all possibilities for Emma and Evelyn, so let us go back and reconsider Avery.", "Avery cannot be a knave, because this would contradict the claim of Chloe that Aurora is a knave if and only if Avery is a knight.", "We have exhausted all possibilities for Avery and Aurora, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Aurora is a knave if and only if Avery is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Chloe is not a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Evelyn is not a knight.", "Evelyn cannot be a knight, because this would contradict the claim of Avery that Evelyn is not a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Emma is a knight.", "Emma cannot be a knight, because this would contradict the false claim of Evelyn that Emma is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Avery is a knight and Chloe is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Avery is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Avery is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Evelyn is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that If Emma is a knight then Evelyn is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 7), ('telling-truth', 2)), ('lying', 2), ('not', ('telling-truth', 3)), ('telling-truth', 5), ('<=>', ('telling-truth', 6), ('lying', 3)), ('and', ('telling-truth', 2), ('telling-truth', 0)), ('->', ('telling-truth', 5), ('telling-truth', 3)), ('not', ('telling-truth', 0)))", "index": 760}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ethan, Emily, Jacob, Elizabeth, William, Matthew, Jack, and Sophia. Ethan noted, \"Matthew is a knave if and only if Jacob is a knave\". Emily told you that Sophia is a knight or Matthew is a knight. \"Matthew is a knave,\" Jacob claimed. Elizabeth expressed that Emily is not a knave. William commented, \"Emily is a knight\". Matthew said, \"Sophia is a knave or William is a knight.\" In a statement by Jack: \"Sophia is not a knave\". Sophia expressed that Emily is not a knave. So who is a knight and who is a knave?", "names": ["Ethan", "Emily", "Jacob", "Elizabeth", "William", "Matthew", "Jack", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true, true, true], "solution_text": "Ethan is a knave, Emily is a knight, Jacob is a knave, Elizabeth is a knight, William is a knight, Matthew is a knight, Jack is a knight, and Sophia is a knight.", "solution_text_format": "(1) Ethan is a knave\n(2) Emily is a knight\n(3) Jacob is a knave\n(4) Elizabeth is a knight\n(5) William is a knight\n(6) Matthew is a knight\n(7) Jack is a knight\n(8) Sophia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Matthew is a knave if and only if Jacob is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Sophia is a knave or William is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Emily is not a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Sophia is a knight or Matthew is a knight.", "Assume William is a knight. No contradiction is found in their claim that Emily is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Matthew is a knave.", "Jacob cannot be a knave, because this would contradict the claim of Ethan that Matthew is a knave if and only if Jacob is a knave.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the false claim of their own that Emily is a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the false claim of their own that Sophia is a knight or Matthew is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Emily is not a knave.", "Emily cannot be a knight, because this would contradict the false claim of Sophia that Emily is not a knave.", "Emily cannot be a knave, because this would contradict the false claim of their own that Sophia is a knight or Matthew is a knight.", "We have exhausted all possibilities for Emily and Sophia, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Sophia is a knave or William is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Emily is not a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Sophia is a knight or Matthew is a knight.", "William cannot be a knight, because this would contradict the false claim of Matthew that Sophia is a knave or William is a knight.", "William cannot be a knave, because this would contradict the false claim of their own that Emily is a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the false claim of their own that Sophia is a knight or Matthew is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the false claim of Matthew that Sophia is a knave or William is a knight.", "We have exhausted all possibilities for Sophia and Matthew, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Matthew is a knave if and only if Jacob is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Sophia is a knave or William is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Emily is not a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Sophia is a knight or Matthew is a knight.", "Assume William is a knight. No contradiction is found in their claim that Emily is a knight.", "Jacob cannot be a knight, because this would contradict the false claim of Ethan that Matthew is a knave if and only if Jacob is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Matthew is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Emily is not a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Sophia is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 5), ('lying', 2)), ('or', ('telling-truth', 7), ('telling-truth', 5)), ('lying', 5), ('not', ('lying', 1)), ('telling-truth', 1), ('or', ('lying', 7), ('telling-truth', 4)), ('not', ('lying', 7)), ('not', ('lying', 1)))", "index": 761}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emily, Riley, Joseph, Oliver, Mia, Luke, Owen, and Jack. Emily stated, \"Joseph is a knave and Riley is a knave\". Riley said that Luke is not a knight. \"If Riley is a knight then Owen is a knave,\" Joseph claimed. Oliver asserted: \"Riley is a knight or Owen is a knave\". Mia remarked, \"Luke is a knave\". Luke noted, \"Owen is a knave if and only if Jack is a knight\". Owen was heard saying, \"Joseph is a knave or Luke is a knight\". According to Jack, \"Luke is a knight\". So who is a knight and who is a knave?", "names": ["Emily", "Riley", "Joseph", "Oliver", "Mia", "Luke", "Owen", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false, false, false], "solution_text": "Emily is a knave, Riley is a knight, Joseph is a knight, Oliver is a knight, Mia is a knight, Luke is a knave, Owen is a knave, and Jack is a knave.", "solution_text_format": "(1) Emily is a knave\n(2) Riley is a knight\n(3) Joseph is a knight\n(4) Oliver is a knight\n(5) Mia is a knight\n(6) Luke is a knave\n(7) Owen is a knave\n(8) Jack is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Joseph is a knave and Riley is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Emily that Joseph is a knave and Riley is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that If Riley is a knight then Owen is a knave.", "Riley cannot be a knight, because this would contradict the claim of Emily that Joseph is a knave and Riley is a knave.", "Riley cannot be a knave, because this would contradict the false claim of Joseph that If Riley is a knight then Owen is a knave.", "We have exhausted all possibilities for Riley and Joseph, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Joseph is a knave and Riley is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that If Riley is a knight then Owen is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Luke is not a knight.", "Luke cannot be a knight, because this would contradict the claim of Riley that Luke is not a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Owen is a knave if and only if Jack is a knight.", "Owen cannot be a knight, because this would contradict the claim of Joseph that If Riley is a knight then Owen is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Joseph is a knave or Luke is a knight.", "Jack cannot be a knight, because this would contradict the false claim of Luke that Owen is a knave if and only if Jack is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Luke is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Riley is a knight or Owen is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Luke is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('lying', 1)), ('not', ('telling-truth', 5)), ('->', ('telling-truth', 1), ('lying', 6)), ('or', ('telling-truth', 1), ('lying', 6)), ('lying', 5), ('<=>', ('lying', 6), ('telling-truth', 7)), ('or', ('lying', 2), ('telling-truth', 5)), ('telling-truth', 5))", "index": 762}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Evelyn, Grace, Zoey, Liam, Charlotte, Lucas, Ella, and Alexander. \"Alexander is not a knave,\" Evelyn declared. According to Grace, \"Lucas is a knight if and only if Evelyn is a knave\". In Zoey's words: \"Liam is not a knight\". Liam stated, \"Evelyn is a knave if and only if Zoey is a knight\". \"Evelyn is a knave,\" Charlotte declared. \"Liam is not a knight,\" Lucas claimed. Ella said, \"Evelyn is a knave.\" In Alexander's words: \"Lucas is a knight if and only if Charlotte is a knight\". So who is a knight and who is a knave?", "names": ["Evelyn", "Grace", "Zoey", "Liam", "Charlotte", "Lucas", "Ella", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false, false, true], "solution_text": "Evelyn is a knight, Grace is a knight, Zoey is a knave, Liam is a knight, Charlotte is a knave, Lucas is a knave, Ella is a knave, and Alexander is a knight.", "solution_text_format": "(1) Evelyn is a knight\n(2) Grace is a knight\n(3) Zoey is a knave\n(4) Liam is a knight\n(5) Charlotte is a knave\n(6) Lucas is a knave\n(7) Ella is a knave\n(8) Alexander is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Alexander is not a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Lucas is a knight if and only if Charlotte is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Liam is not a knight.", "Liam cannot be a knight, because this would contradict the claim of Lucas that Liam is not a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Evelyn is a knave if and only if Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Liam is not a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave.", "Charlotte cannot be a knave, because this would contradict the claim of Alexander that Lucas is a knight if and only if Charlotte is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Zoey.", "Zoey cannot be a knave, because this would contradict the false claim of their own that Liam is not a knight.", "We have exhausted all possibilities for Zoey and Liam, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Liam is not a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Evelyn is a knave if and only if Zoey is a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that Liam is not a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Liam is not a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Evelyn is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Lucas is a knight if and only if Evelyn is a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Evelyn is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 7)), ('<=>', ('telling-truth', 5), ('lying', 0)), ('not', ('telling-truth', 3)), ('<=>', ('lying', 0), ('telling-truth', 2)), ('lying', 0), ('not', ('telling-truth', 3)), ('lying', 0), ('<=>', ('telling-truth', 5), ('telling-truth', 4)))", "index": 763}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Riley, Michael, Sophia, Chloe, Benjamin, Charlotte, Daniel, and Elizabeth. Riley stated, \"Charlotte is a knight or Benjamin is a knight\". \"If Sophia is a knight then Riley is a knave,\" Michael declared. Sophia expressed that If Riley is a knave then Daniel is a knight. Chloe said, \"Riley is a knave and Riley is a knight.\" Benjamin commented, \"Michael is a knight if and only if Riley is a knave\". Charlotte told you that Elizabeth is not a knight. Daniel told you that Charlotte is a knave or Benjamin is a knight. Elizabeth told you that Michael is a knight and Daniel is a knight. So who is a knight and who is a knave?", "names": ["Riley", "Michael", "Sophia", "Chloe", "Benjamin", "Charlotte", "Daniel", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true, true, false], "solution_text": "Riley is a knight, Michael is a knave, Sophia is a knight, Chloe is a knave, Benjamin is a knight, Charlotte is a knight, Daniel is a knight, and Elizabeth is a knave.", "solution_text_format": "(1) Riley is a knight\n(2) Michael is a knave\n(3) Sophia is a knight\n(4) Chloe is a knave\n(5) Benjamin is a knight\n(6) Charlotte is a knight\n(7) Daniel is a knight\n(8) Elizabeth is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Charlotte is a knight or Benjamin is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Elizabeth is not a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Charlotte that Elizabeth is not a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Michael is a knight and Daniel is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that If Sophia is a knight then Riley is a knave.", "Sophia cannot be a knight, because this would contradict the claim of Michael that If Sophia is a knight then Riley is a knave.", "Sophia cannot be a knave, because this would contradict the false claim of their own that If Riley is a knave then Daniel is a knight.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that If Sophia is a knight then Riley is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that If Riley is a knave then Daniel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Charlotte is a knave or Benjamin is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Michael is a knight if and only if Riley is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Riley is a knave and Riley is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Riley is a knave and Riley is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('telling-truth', 4)), ('->', ('telling-truth', 2), ('lying', 0)), ('->', ('lying', 0), ('telling-truth', 6)), ('and', ('lying', 0), ('telling-truth', 0)), ('<=>', ('telling-truth', 1), ('lying', 0)), ('not', ('telling-truth', 7)), ('or', ('lying', 5), ('telling-truth', 4)), ('and', ('telling-truth', 1), ('telling-truth', 6)))", "index": 764}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Penelope, Scarlett, Lily, Logan, Sofia, Abigail, Emily, and Alexander. Penelope commented, \"Scarlett is a knave\". In Scarlett's words: \"Alexander is not a knight\". Lily commented, \"Penelope is a knight and Abigail is a knave\". \"If Scarlett is a knight then Sofia is a knave,\" Logan claimed. Sofia asserted: \"Abigail is not a knight\". Abigail expressed that Lily is a knight if and only if Sofia is a knave. Emily asserted: \"Logan is a knight if and only if Logan is a knave\". \"Abigail is a knave if and only if Alexander is a knight,\" Alexander claimed. So who is a knight and who is a knave?", "names": ["Penelope", "Scarlett", "Lily", "Logan", "Sofia", "Abigail", "Emily", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false, false, true], "solution_text": "Penelope is a knight, Scarlett is a knave, Lily is a knight, Logan is a knight, Sofia is a knight, Abigail is a knave, Emily is a knave, and Alexander is a knight.", "solution_text_format": "(1) Penelope is a knight\n(2) Scarlett is a knave\n(3) Lily is a knight\n(4) Logan is a knight\n(5) Sofia is a knight\n(6) Abigail is a knave\n(7) Emily is a knave\n(8) Alexander is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Penelope that Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Alexander is not a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Abigail is a knave if and only if Alexander is a knight.", "Abigail cannot be a knight, because this would contradict the claim of Alexander that Abigail is a knave if and only if Alexander is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Lily is a knight if and only if Sofia is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Penelope is a knight and Abigail is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Abigail is not a knight.", "Assume Logan is a knight. No contradiction is found in their claim that If Scarlett is a knight then Sofia is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Logan is a knight if and only if Logan is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Logan is a knight if and only if Logan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 1), ('not', ('telling-truth', 7)), ('and', ('telling-truth', 0), ('lying', 5)), ('->', ('telling-truth', 1), ('lying', 4)), ('not', ('telling-truth', 5)), ('<=>', ('telling-truth', 2), ('lying', 4)), ('<=>', ('telling-truth', 3), ('lying', 3)), ('<=>', ('lying', 5), ('telling-truth', 7)))", "index": 765}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mia, Liam, William, Daniel, Jacob, Penelope, Isabella, and Ella. \"Jacob is not a knave,\" Mia declared. Liam stated, \"William is a knave and Penelope is a knave\". William expressed that Isabella is a knave and Penelope is a knight. \"Penelope is a knave or Isabella is a knight,\" Daniel claimed. Jacob told you that If Isabella is a knave then Penelope is a knight. Penelope told you that Ella is a knave if and only if William is a knight. Isabella told you that Daniel is a knight if and only if Liam is a knave. According to Ella, \"Jacob is not a knight\". So who is a knight and who is a knave?", "names": ["Mia", "Liam", "William", "Daniel", "Jacob", "Penelope", "Isabella", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true, false, false], "solution_text": "Mia is a knight, Liam is a knave, William is a knight, Daniel is a knave, Jacob is a knight, Penelope is a knight, Isabella is a knave, and Ella is a knave.", "solution_text_format": "(1) Mia is a knight\n(2) Liam is a knave\n(3) William is a knight\n(4) Daniel is a knave\n(5) Jacob is a knight\n(6) Penelope is a knight\n(7) Isabella is a knave\n(8) Ella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Jacob is not a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that If Isabella is a knave then Penelope is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Daniel is a knight if and only if Liam is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Penelope is a knave or Isabella is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Ella is a knave if and only if William is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Jacob is not a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Jacob is not a knight.", "William cannot be a knight, because this would contradict the claim of their own that Isabella is a knave and Penelope is a knight.", "William cannot be a knave, because this would contradict the claim of Penelope that Ella is a knave if and only if William is a knight.", "We have exhausted all possibilities for William and Ella, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Ella is a knave if and only if William is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Jacob is not a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Jacob is not a knight.", "William cannot be a knight, because this would contradict the claim of their own that Isabella is a knave and Penelope is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Isabella is a knave and Penelope is a knight.", "Liam cannot be a knight, because this would contradict the claim of Isabella that Daniel is a knight if and only if Liam is a knave.", "Liam cannot be a knave, because this would contradict the false claim of their own that William is a knave and Penelope is a knave.", "We have exhausted all possibilities for Liam, William, Ella, and Penelope, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the false claim of their own that Penelope is a knave or Isabella is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Daniel is a knight if and only if Liam is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Penelope is a knave or Isabella is a knight.", "Penelope cannot be a knight, because this would contradict the claim of Daniel that Penelope is a knave or Isabella is a knight.", "Penelope cannot be a knave, because this would contradict the claim of Jacob that If Isabella is a knave then Penelope is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Penelope is a knave or Isabella is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Ella is a knave if and only if William is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Jacob is not a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Jacob is not a knight.", "Assume William is a knight. No contradiction is found in their claim that Isabella is a knave and Penelope is a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that William is a knave and Penelope is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that William is a knave and Penelope is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('and', ('lying', 2), ('lying', 5)), ('and', ('lying', 6), ('telling-truth', 5)), ('or', ('lying', 5), ('telling-truth', 6)), ('->', ('lying', 6), ('telling-truth', 5)), ('<=>', ('lying', 7), ('telling-truth', 2)), ('<=>', ('telling-truth', 3), ('lying', 1)), ('not', ('telling-truth', 4)))", "index": 766}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Daniel, Zoey, Liam, Oliver, Alexander, Emma, William, and Mia. Daniel commented, \"William is a knight if and only if Mia is a knave\". \"Daniel is a knight or Oliver is a knight,\" Zoey declared. Liam stated, \"Oliver is a knight\". \"Zoey is a knight if and only if Alexander is a knave,\" Oliver mentioned. \"Emma is not a knave\" - Alexander. Emma said, \"William is a knight.\" \"Liam is a knave and Oliver is a knave,\" William claimed. Mia expressed that Daniel is not a knight. So who is a knight and who is a knave?", "names": ["Daniel", "Zoey", "Liam", "Oliver", "Alexander", "Emma", "William", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true, true, false], "solution_text": "Daniel is a knight, Zoey is a knight, Liam is a knave, Oliver is a knave, Alexander is a knight, Emma is a knight, William is a knight, and Mia is a knave.", "solution_text_format": "(1) Daniel is a knight\n(2) Zoey is a knight\n(3) Liam is a knave\n(4) Oliver is a knave\n(5) Alexander is a knight\n(6) Emma is a knight\n(7) William is a knight\n(8) Mia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that William is a knight if and only if Mia is a knave.", "Assume William is a knight. No contradiction is found in their claim that Liam is a knave and Oliver is a knave.", "Liam cannot be a knight, because this would contradict the claim of William that Liam is a knave and Oliver is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Oliver is a knight.", "Oliver cannot be a knight, because this would contradict the false claim of Liam that Oliver is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Zoey is a knight if and only if Alexander is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Daniel is a knight or Oliver is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Emma is not a knave.", "Assume Emma is a knight. No contradiction is found in their claim that William is a knight.", "Mia cannot be a knight, because this would contradict the claim of Daniel that William is a knight if and only if Mia is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Daniel is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 6), ('lying', 7)), ('or', ('telling-truth', 0), ('telling-truth', 3)), ('telling-truth', 3), ('<=>', ('telling-truth', 1), ('lying', 4)), ('not', ('lying', 5)), ('telling-truth', 6), ('and', ('lying', 2), ('lying', 3)), ('not', ('telling-truth', 0)))", "index": 767}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sophia, Samuel, Luke, Lucas, Scarlett, Owen, Mason, and Lily. Sophia stated, \"Luke is a knave if and only if Sophia is a knight\". Samuel noted, \"If Mason is a knight then Lily is a knight\". Luke noted, \"Sophia is a knave\". \"Mason is not a knight\" - Lucas. Scarlett remarked, \"If Samuel is a knave then Owen is a knave\". In a statement by Owen: \"If Luke is a knave then Scarlett is a knight\". Mason noted, \"Scarlett is not a knave\". Lily expressed that Owen is a knight and Scarlett is a knight. So who is a knight and who is a knave?", "names": ["Sophia", "Samuel", "Luke", "Lucas", "Scarlett", "Owen", "Mason", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true, true, true], "solution_text": "Sophia is a knight, Samuel is a knight, Luke is a knave, Lucas is a knave, Scarlett is a knight, Owen is a knight, Mason is a knight, and Lily is a knight.", "solution_text_format": "(1) Sophia is a knight\n(2) Samuel is a knight\n(3) Luke is a knave\n(4) Lucas is a knave\n(5) Scarlett is a knight\n(6) Owen is a knight\n(7) Mason is a knight\n(8) Lily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Luke is a knave if and only if Sophia is a knight.", "Luke cannot be a knight, because this would contradict the claim of Sophia that Luke is a knave if and only if Sophia is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Sophia is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that If Mason is a knight then Lily is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Samuel is a knave then Owen is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that If Luke is a knave then Scarlett is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Owen is a knight and Scarlett is a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Mason is not a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Mason is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('telling-truth', 0)), ('->', ('telling-truth', 6), ('telling-truth', 7)), ('lying', 0), ('not', ('telling-truth', 6)), ('->', ('lying', 1), ('lying', 5)), ('->', ('lying', 2), ('telling-truth', 4)), ('not', ('lying', 4)), ('and', ('telling-truth', 5), ('telling-truth', 4)))", "index": 768}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Penelope, Matthew, Logan, Benjamin, Aiden, Sebastian, Avery, and Joseph. According to Penelope, \"Matthew is a knave if and only if Avery is a knight\". \"Penelope is a knight or Penelope is a knave\" - Matthew. According to Logan, \"Logan is a knight\". According to Benjamin, \"Aiden is a knave\". Aiden asserted: \"Logan is a knave and Matthew is a knight\". Sebastian asserted: \"Avery is a knight or Aiden is a knave\". Avery said that Sebastian is a knave and Aiden is a knight. Joseph remarked, \"Logan is a knight\". So who is a knight and who is a knave?", "names": ["Penelope", "Matthew", "Logan", "Benjamin", "Aiden", "Sebastian", "Avery", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true, false, true], "solution_text": "Penelope is a knight, Matthew is a knight, Logan is a knight, Benjamin is a knight, Aiden is a knave, Sebastian is a knight, Avery is a knave, and Joseph is a knight.", "solution_text_format": "(1) Penelope is a knight\n(2) Matthew is a knight\n(3) Logan is a knight\n(4) Benjamin is a knight\n(5) Aiden is a knave\n(6) Sebastian is a knight\n(7) Avery is a knave\n(8) Joseph is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that Matthew is a knave if and only if Avery is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Penelope is a knight or Penelope is a knave.", "Avery cannot be a knight, because this would contradict the claim of Penelope that Matthew is a knave if and only if Avery is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Sebastian is a knave and Aiden is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Avery is a knight or Aiden is a knave.", "Aiden cannot be a knight, because this would contradict the claim of Sebastian that Avery is a knight or Aiden is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Logan is a knave and Matthew is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Logan is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Aiden is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Logan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('telling-truth', 6)), ('or', ('telling-truth', 0), ('lying', 0)), ('telling-truth', 2), ('lying', 4), ('and', ('lying', 2), ('telling-truth', 1)), ('or', ('telling-truth', 6), ('lying', 4)), ('and', ('lying', 5), ('telling-truth', 4)), ('telling-truth', 2))", "index": 769}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Zoey, Emily, Avery, Chloe, Jack, Sebastian, Benjamin, and Lily. Zoey expressed that Chloe is a knave or Avery is a knave. Emily told you that Lily is not a knight. Avery stated, \"Chloe is a knave\". Chloe said that Lily is a knight. Jack was heard saying, \"Zoey is a knave\". Sebastian told you that Benjamin is a knight. As Benjamin put it, \"Jack is not a knave\". Lily asserted: \"Jack is a knight or Zoey is a knave\". So who is a knight and who is a knave?", "names": ["Zoey", "Emily", "Avery", "Chloe", "Jack", "Sebastian", "Benjamin", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false, false, false], "solution_text": "Zoey is a knight, Emily is a knight, Avery is a knight, Chloe is a knave, Jack is a knave, Sebastian is a knave, Benjamin is a knave, and Lily is a knave.", "solution_text_format": "(1) Zoey is a knight\n(2) Emily is a knight\n(3) Avery is a knight\n(4) Chloe is a knave\n(5) Jack is a knave\n(6) Sebastian is a knave\n(7) Benjamin is a knave\n(8) Lily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Zoey is a knight. No contradiction is found in their claim that Chloe is a knave or Avery is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Lily is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Jack is a knight or Zoey is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Zoey is a knave.", "Jack cannot be a knave, because this would contradict the claim of Lily that Jack is a knight or Zoey is a knave.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the claim of Chloe that Lily is a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Lily is a knight.", "Lily cannot be a knight, because this would contradict the false claim of Chloe that Lily is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Jack is a knight or Zoey is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Zoey is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Zoey is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Chloe is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Lily is not a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Benjamin is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Jack is not a knave.", "Benjamin cannot be a knave, because this would contradict the claim of Sebastian that Benjamin is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Benjamin is a knight.", "Benjamin cannot be a knight, because this would contradict the false claim of Sebastian that Benjamin is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Jack is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('lying', 2)), ('not', ('telling-truth', 7)), ('lying', 3), ('telling-truth', 7), ('lying', 0), ('telling-truth', 6), ('not', ('lying', 4)), ('or', ('telling-truth', 4), ('lying', 0)))", "index": 770}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aurora, Emily, Scarlett, Samuel, Luke, Oliver, Benjamin, and Jacob. Aurora asserted: \"Benjamin is a knave\". Emily stated, \"Aurora is a knight or Jacob is a knight\". Scarlett said that Emily is a knight. Samuel noted, \"Luke is a knight\". Luke remarked, \"Oliver is not a knight\". In a statement by Oliver: \"If Luke is a knight then Scarlett is a knave\". \"If Oliver is a knight then Aurora is a knight,\" Benjamin mentioned. Jacob said that If Luke is a knight then Samuel is a knight. So who is a knight and who is a knave?", "names": ["Aurora", "Emily", "Scarlett", "Samuel", "Luke", "Oliver", "Benjamin", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false, true, true], "solution_text": "Aurora is a knave, Emily is a knight, Scarlett is a knight, Samuel is a knight, Luke is a knight, Oliver is a knave, Benjamin is a knight, and Jacob is a knight.", "solution_text_format": "(1) Aurora is a knave\n(2) Emily is a knight\n(3) Scarlett is a knight\n(4) Samuel is a knight\n(5) Luke is a knight\n(6) Oliver is a knave\n(7) Benjamin is a knight\n(8) Jacob is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Aurora that Benjamin is a knave.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that If Oliver is a knight then Aurora is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Benjamin is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Oliver is a knight then Aurora is a knight.", "Oliver cannot be a knight, because this would contradict the claim of Benjamin that If Oliver is a knight then Aurora is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that If Luke is a knight then Scarlett is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Oliver is not a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Aurora is a knight or Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that If Luke is a knight then Samuel is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Luke is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 6), ('or', ('telling-truth', 0), ('telling-truth', 7)), ('telling-truth', 1), ('telling-truth', 4), ('not', ('telling-truth', 5)), ('->', ('telling-truth', 4), ('lying', 2)), ('->', ('telling-truth', 5), ('telling-truth', 0)), ('->', ('telling-truth', 4), ('telling-truth', 3)))", "index": 771}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Henry, Samuel, Sofia, Sophia, Amelia, Ava, Jackson, and Evelyn. \"Evelyn is a knight if and only if Evelyn is a knave,\" Henry declared. Samuel asserted: \"If Samuel is a knight then Henry is a knave\". \"Amelia is a knave if and only if Sofia is a knight,\" Sofia claimed. Sophia stated, \"Ava is a knave and Sofia is a knight\". In a statement by Amelia: \"Sofia is a knave\". \"Sofia is not a knave\" - Ava. Jackson was heard saying, \"Sophia is a knight and Jackson is a knight\". Evelyn commented, \"Sofia is a knave if and only if Sophia is a knave\". So who is a knight and who is a knave?", "names": ["Henry", "Samuel", "Sofia", "Sophia", "Amelia", "Ava", "Jackson", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true, false, false], "solution_text": "Henry is a knave, Samuel is a knight, Sofia is a knight, Sophia is a knave, Amelia is a knave, Ava is a knight, Jackson is a knave, and Evelyn is a knave.", "solution_text_format": "(1) Henry is a knave\n(2) Samuel is a knight\n(3) Sofia is a knight\n(4) Sophia is a knave\n(5) Amelia is a knave\n(6) Ava is a knight\n(7) Jackson is a knave\n(8) Evelyn is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Henry cannot be a knight, because this would contradict the claim of their own that Evelyn is a knight if and only if Evelyn is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Evelyn is a knight if and only if Evelyn is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Sofia is a knave if and only if Sophia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Amelia is a knave if and only if Sofia is a knight.", "Amelia cannot be a knight, because this would contradict the claim of Sofia that Amelia is a knave if and only if Sofia is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Sofia is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Ava is a knave and Sofia is a knight.", "Ava cannot be a knight, because this would contradict the claim of Sophia that Ava is a knave and Sofia is a knight.", "Ava cannot be a knave, because this would contradict the false claim of their own that Sofia is not a knave.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the claim of Evelyn that Sofia is a knave if and only if Sophia is a knave.", "We have exhausted all possibilities for Sophia and Amelia, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Amelia is a knave if and only if Sofia is a knight.", "Amelia cannot be a knight, because this would contradict the false claim of Sofia that Amelia is a knave if and only if Sofia is a knight.", "Amelia cannot be a knave, because this would contradict the false claim of their own that Sofia is a knave.", "We have exhausted all possibilities for Amelia and Sofia, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Sofia is a knave if and only if Sophia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Amelia is a knave if and only if Sofia is a knight.", "Amelia cannot be a knight, because this would contradict the claim of Sofia that Amelia is a knave if and only if Sofia is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Sofia is a knave.", "Sophia cannot be a knight, because this would contradict the false claim of Evelyn that Sofia is a knave if and only if Sophia is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Ava is a knave and Sofia is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Sofia is not a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that If Samuel is a knight then Henry is a knave.", "Jackson cannot be a knight, because this would contradict the claim of their own that Sophia is a knight and Jackson is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Sophia is a knight and Jackson is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 7), ('lying', 7)), ('->', ('telling-truth', 1), ('lying', 0)), ('<=>', ('lying', 4), ('telling-truth', 2)), ('and', ('lying', 5), ('telling-truth', 2)), ('lying', 2), ('not', ('lying', 2)), ('and', ('telling-truth', 3), ('telling-truth', 6)), ('<=>', ('lying', 2), ('lying', 3)))", "index": 772}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mia, Henry, Benjamin, Matthew, Emily, Grace, Jack, and Emma. Mia told you that Jack is not a knave. Henry expressed that Grace is a knave. Benjamin asserted: \"Henry is a knave if and only if Emma is a knave\". Matthew remarked, \"Grace is not a knave\". According to Emily, \"Grace is a knight if and only if Henry is a knave\". Grace said, \"If Henry is a knave then Mia is a knight.\" Jack asserted: \"Matthew is not a knave\". \"Emily is a knight and Grace is a knight,\" Emma declared. So who is a knight and who is a knave?", "names": ["Mia", "Henry", "Benjamin", "Matthew", "Emily", "Grace", "Jack", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true, true, true], "solution_text": "Mia is a knight, Henry is a knave, Benjamin is a knave, Matthew is a knight, Emily is a knight, Grace is a knight, Jack is a knight, and Emma is a knight.", "solution_text_format": "(1) Mia is a knight\n(2) Henry is a knave\n(3) Benjamin is a knave\n(4) Matthew is a knight\n(5) Emily is a knight\n(6) Grace is a knight\n(7) Jack is a knight\n(8) Emma is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Jack is not a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Matthew is not a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Grace is not a knave.", "Assume Grace is a knight. No contradiction is found in their claim that If Henry is a knave then Mia is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Grace is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Grace is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Henry is a knave if and only if Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of Benjamin that Henry is a knave if and only if Emma is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Emily is a knight and Grace is a knight.", "Emily cannot be a knight, because this would contradict the false claim of Emma that Emily is a knight and Grace is a knight.", "Emily cannot be a knave, because this would contradict the false claim of their own that Grace is a knight if and only if Henry is a knave.", "We have exhausted all possibilities for Emily and Emma, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Henry is a knave if and only if Emma is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Emily is a knight and Grace is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Grace is a knight if and only if Henry is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 6)), ('lying', 5), ('<=>', ('lying', 1), ('lying', 7)), ('not', ('lying', 5)), ('<=>', ('telling-truth', 5), ('lying', 1)), ('->', ('lying', 1), ('telling-truth', 0)), ('not', ('lying', 3)), ('and', ('telling-truth', 4), ('telling-truth', 5)))", "index": 773}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Alexander, Emma, Matthew, Grace, Scarlett, Olivia, Riley, and Jackson. Alexander noted, \"Scarlett is not a knave\". Emma remarked, \"Alexander is a knight and Alexander is a knave\". Matthew told you that Scarlett is not a knight. \"If Matthew is a knave then Emma is a knight,\" Grace mentioned. \"If Jackson is a knave then Matthew is a knave\" - Scarlett. Olivia commented, \"Riley is a knight and Scarlett is a knave\". In a statement by Riley: \"If Olivia is a knight then Alexander is a knight\". Jackson noted, \"If Matthew is a knight then Olivia is a knave\". So who is a knight and who is a knave?", "names": ["Alexander", "Emma", "Matthew", "Grace", "Scarlett", "Olivia", "Riley", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, false, true, true], "solution_text": "Alexander is a knight, Emma is a knave, Matthew is a knave, Grace is a knave, Scarlett is a knight, Olivia is a knave, Riley is a knight, and Jackson is a knight.", "solution_text_format": "(1) Alexander is a knight\n(2) Emma is a knave\n(3) Matthew is a knave\n(4) Grace is a knave\n(5) Scarlett is a knight\n(6) Olivia is a knave\n(7) Riley is a knight\n(8) Jackson is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Jackson is a knave then Matthew is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that If Matthew is a knight then Olivia is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Scarlett is not a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Scarlett is not a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that Riley is a knight and Scarlett is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Riley is a knight and Scarlett is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that If Olivia is a knight then Alexander is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Alexander is a knight and Alexander is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Alexander is a knight and Alexander is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that If Matthew is a knave then Emma is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that If Matthew is a knave then Emma is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('and', ('telling-truth', 0), ('lying', 0)), ('not', ('telling-truth', 4)), ('->', ('lying', 2), ('telling-truth', 1)), ('->', ('lying', 7), ('lying', 2)), ('and', ('telling-truth', 6), ('lying', 4)), ('->', ('telling-truth', 5), ('telling-truth', 0)), ('->', ('telling-truth', 2), ('lying', 5)))", "index": 774}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Owen, William, Avery, Ava, Zoey, Michael, Henry, and Samuel. In Owen's words: \"Samuel is a knight and Ava is a knight\". William stated, \"Samuel is not a knave\". \"Michael is a knave,\" Avery mentioned. \"Zoey is a knave if and only if Michael is a knave,\" Ava mentioned. Zoey told you that If Owen is a knave then Michael is a knave. Michael noted, \"If William is a knight then Owen is a knave\". Henry was heard saying, \"Zoey is a knight or William is a knight\". Samuel said that Avery is not a knave. So who is a knight and who is a knave?", "names": ["Owen", "William", "Avery", "Ava", "Zoey", "Michael", "Henry", "Samuel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, true, false, false], "solution_text": "Owen is a knave, William is a knave, Avery is a knave, Ava is a knave, Zoey is a knave, Michael is a knight, Henry is a knave, and Samuel is a knave.", "solution_text_format": "(1) Owen is a knave\n(2) William is a knave\n(3) Avery is a knave\n(4) Ava is a knave\n(5) Zoey is a knave\n(6) Michael is a knight\n(7) Henry is a knave\n(8) Samuel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Samuel is a knight and Ava is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Avery is not a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of Avery that Michael is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that If William is a knight then Owen is a knave.", "Assume William is a knight. No contradiction is found in their claim that Samuel is not a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Zoey is a knave if and only if Michael is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Ava that Zoey is a knave if and only if Michael is a knave.", "Zoey cannot be a knave, because this would contradict the false claim of their own that If Owen is a knave then Michael is a knave.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the claim of Owen that Samuel is a knight and Ava is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the false claim of their own that Samuel is not a knave.", "We have exhausted all possibilities for William and Michael, so let us go back and reconsider Avery.", "Avery cannot be a knave, because this would contradict the claim of Samuel that Avery is not a knave.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Samuel.", "Samuel cannot be a knave, because this would contradict the claim of Owen that Samuel is a knight and Ava is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Samuel is a knight and Ava is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Avery is not a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of Avery that Michael is a knave.", "Michael cannot be a knave, because this would contradict the false claim of their own that If William is a knight then Owen is a knave.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Avery.", "Avery cannot be a knave, because this would contradict the claim of Samuel that Avery is not a knave.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Avery is not a knave.", "Avery cannot be a knight, because this would contradict the false claim of Samuel that Avery is not a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Michael is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that If William is a knight then Owen is a knave.", "William cannot be a knight, because this would contradict the claim of their own that Samuel is not a knave.", "Assume William is a knave. No contradiction is found in their false claim that Samuel is not a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Zoey is a knave if and only if Michael is a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that If Owen is a knave then Michael is a knave.", "Zoey cannot be a knave, because this would contradict the claim of Ava that Zoey is a knave if and only if Michael is a knave.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Zoey is a knave if and only if Michael is a knave.", "Zoey cannot be a knight, because this would contradict the false claim of Ava that Zoey is a knave if and only if Michael is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that If Owen is a knave then Michael is a knave.", "Henry cannot be a knight, because this would contradict the claim of their own that Zoey is a knight or William is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Zoey is a knight or William is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 7), ('telling-truth', 3)), ('not', ('lying', 7)), ('lying', 5), ('<=>', ('lying', 4), ('lying', 5)), ('->', ('lying', 0), ('lying', 5)), ('->', ('telling-truth', 1), ('lying', 0)), ('or', ('telling-truth', 4), ('telling-truth', 1)), ('not', ('lying', 2)))", "index": 775}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mia, Jack, Charlotte, Matthew, Lucas, Grace, Aurora, and Logan. In a statement by Mia: \"Logan is not a knight\". Jack asserted: \"Aurora is a knight if and only if Lucas is a knight\". Charlotte stated, \"Mia is a knight if and only if Aurora is a knave\". Matthew was heard saying, \"Logan is a knight if and only if Grace is a knight\". According to Lucas, \"Aurora is a knave\". Grace said, \"Matthew is not a knave.\" Aurora remarked, \"Grace is a knave\". As Logan put it, \"Grace is a knight\". So who is a knight and who is a knave?", "names": ["Mia", "Jack", "Charlotte", "Matthew", "Lucas", "Grace", "Aurora", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true, false, true], "solution_text": "Mia is a knave, Jack is a knave, Charlotte is a knave, Matthew is a knight, Lucas is a knight, Grace is a knight, Aurora is a knave, and Logan is a knight.", "solution_text_format": "(1) Mia is a knave\n(2) Jack is a knave\n(3) Charlotte is a knave\n(4) Matthew is a knight\n(5) Lucas is a knight\n(6) Grace is a knight\n(7) Aurora is a knave\n(8) Logan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Logan is not a knight.", "Logan cannot be a knight, because this would contradict the claim of Mia that Logan is not a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Grace is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Logan that Grace is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Matthew is not a knave.", "Matthew cannot be a knight, because this would contradict the false claim of Grace that Matthew is not a knave.", "Matthew cannot be a knave, because this would contradict the false claim of their own that Logan is a knight if and only if Grace is a knight.", "We have exhausted all possibilities for Matthew, Grace, and Logan, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Logan is not a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Matthew is not a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Logan is a knight if and only if Grace is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Aurora is a knight if and only if Lucas is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Grace is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Grace is a knave.", "Lucas cannot be a knight, because this would contradict the claim of Jack that Aurora is a knight if and only if Lucas is a knight.", "Lucas cannot be a knave, because this would contradict the false claim of their own that Aurora is a knave.", "We have exhausted all possibilities for Lucas and Aurora, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Aurora is a knight if and only if Lucas is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Grace is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Grace is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Aurora is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Mia is a knight if and only if Aurora is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Mia is a knight if and only if Aurora is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 7)), ('<=>', ('telling-truth', 6), ('telling-truth', 4)), ('<=>', ('telling-truth', 0), ('lying', 6)), ('<=>', ('telling-truth', 7), ('telling-truth', 5)), ('lying', 6), ('not', ('lying', 3)), ('lying', 5), ('telling-truth', 5))", "index": 776}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: James, Sebastian, Charlotte, Zoey, Jack, Aria, Matthew, and Avery. James noted, \"Charlotte is a knight and Zoey is a knave\". Sebastian said that Charlotte is a knight. Charlotte said that If James is a knight then Aria is a knave. Zoey told you that Avery is a knave or Charlotte is a knight. Jack was heard saying, \"Zoey is a knight if and only if Zoey is a knave\". According to Aria, \"Avery is a knight if and only if Matthew is a knave\". According to Matthew, \"Avery is a knight\". Avery remarked, \"Sebastian is a knight if and only if James is a knight\". So who is a knight and who is a knave?", "names": ["James", "Sebastian", "Charlotte", "Zoey", "Jack", "Aria", "Matthew", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false, false, false], "solution_text": "James is a knave, Sebastian is a knight, Charlotte is a knight, Zoey is a knight, Jack is a knave, Aria is a knave, Matthew is a knave, and Avery is a knave.", "solution_text_format": "(1) James is a knave\n(2) Sebastian is a knight\n(3) Charlotte is a knight\n(4) Zoey is a knight\n(5) Jack is a knave\n(6) Aria is a knave\n(7) Matthew is a knave\n(8) Avery is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Charlotte is a knight and Zoey is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that If James is a knight then Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of Charlotte that If James is a knight then Aria is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Avery is a knight if and only if Matthew is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Sebastian is a knight if and only if James is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Charlotte is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Avery is a knight.", "Zoey cannot be a knight, because this would contradict the claim of James that Charlotte is a knight and Zoey is a knave.", "Zoey cannot be a knave, because this would contradict the false claim of their own that Avery is a knave or Charlotte is a knight.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the false claim of Aria that Avery is a knight if and only if Matthew is a knave.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the false claim of their own that Charlotte is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Sebastian is a knight if and only if James is a knight.", "Sebastian cannot be a knight, because this would contradict the false claim of Avery that Sebastian is a knight if and only if James is a knight.", "Sebastian cannot be a knave, because this would contradict the false claim of their own that Charlotte is a knight.", "We have exhausted all possibilities for Sebastian, Avery, and Aria, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the claim of James that Charlotte is a knight and Zoey is a knave.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Charlotte is a knight and Zoey is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that If James is a knight then Aria is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Avery is a knight if and only if Matthew is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Sebastian is a knight if and only if James is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of Avery that Sebastian is a knight if and only if James is a knight.", "Sebastian cannot be a knave, because this would contradict the false claim of their own that Charlotte is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Sebastian is a knight if and only if James is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Charlotte is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Avery is a knight.", "Matthew cannot be a knave, because this would contradict the claim of Aria that Avery is a knight if and only if Matthew is a knave.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the false claim of their own that Charlotte is a knight.", "We have exhausted all possibilities for Sebastian and Avery, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Avery is a knight if and only if Matthew is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Sebastian is a knight if and only if James is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of Avery that Sebastian is a knight if and only if James is a knight.", "Sebastian cannot be a knave, because this would contradict the false claim of their own that Charlotte is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Sebastian is a knight if and only if James is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Charlotte is a knight.", "Matthew cannot be a knight, because this would contradict the false claim of Aria that Avery is a knight if and only if Matthew is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Avery is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Avery is a knave or Charlotte is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Zoey is a knight if and only if Zoey is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Zoey is a knight if and only if Zoey is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 2), ('lying', 3)), ('telling-truth', 2), ('->', ('telling-truth', 0), ('lying', 5)), ('or', ('lying', 7), ('telling-truth', 2)), ('<=>', ('telling-truth', 3), ('lying', 3)), ('<=>', ('telling-truth', 7), ('lying', 6)), ('telling-truth', 7), ('<=>', ('telling-truth', 1), ('telling-truth', 0)))", "index": 777}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Victoria, Abigail, Mia, Emily, Amelia, Ethan, Henry, and Noah. \"If Mia is a knave then Ethan is a knight,\" Victoria declared. Abigail noted, \"If Victoria is a knight then Henry is a knave\". Mia told you that Amelia is a knave. In a statement by Emily: \"Henry is a knight or Amelia is a knight\". Amelia asserted: \"If Mia is a knave then Noah is a knight\". \"Mia is not a knight,\" Ethan mentioned. According to Henry, \"Victoria is a knight\". As Noah put it, \"Amelia is a knave or Noah is a knight\". So who is a knight and who is a knave?", "names": ["Victoria", "Abigail", "Mia", "Emily", "Amelia", "Ethan", "Henry", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true, true, true], "solution_text": "Victoria is a knight, Abigail is a knave, Mia is a knave, Emily is a knight, Amelia is a knight, Ethan is a knight, Henry is a knight, and Noah is a knight.", "solution_text_format": "(1) Victoria is a knight\n(2) Abigail is a knave\n(3) Mia is a knave\n(4) Emily is a knight\n(5) Amelia is a knight\n(6) Ethan is a knight\n(7) Henry is a knight\n(8) Noah is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that If Mia is a knave then Ethan is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Mia that Amelia is a knave.", "Amelia cannot be a knave, because this would contradict the false claim of their own that If Mia is a knave then Noah is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Amelia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that If Mia is a knave then Noah is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Amelia is a knave or Noah is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Mia is not a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If Victoria is a knight then Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of Abigail that If Victoria is a knight then Henry is a knave.", "Henry cannot be a knave, because this would contradict the false claim of their own that Victoria is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that If Victoria is a knight then Henry is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Victoria is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Henry is a knight or Amelia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 2), ('telling-truth', 5)), ('->', ('telling-truth', 0), ('lying', 6)), ('lying', 4), ('or', ('telling-truth', 6), ('telling-truth', 4)), ('->', ('lying', 2), ('telling-truth', 7)), ('not', ('telling-truth', 2)), ('telling-truth', 0), ('or', ('lying', 4), ('telling-truth', 7)))", "index": 778}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Abigail, Aurora, Penelope, David, Jackson, Sofia, William, and Charlotte. \"If Charlotte is a knight then David is a knave,\" Abigail claimed. As Aurora put it, \"Jackson is a knight or William is a knight\". Penelope noted, \"Jackson is not a knight\". \"Aurora is not a knave,\" David declared. \"Charlotte is a knight and Abigail is a knight,\" Jackson declared. \"William is a knight if and only if Sofia is a knight,\" Sofia mentioned. William stated, \"If Sofia is a knave then Penelope is a knave\". Charlotte said that Sofia is a knight and Penelope is a knight. So who is a knight and who is a knave?", "names": ["Abigail", "Aurora", "Penelope", "David", "Jackson", "Sofia", "William", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true, true, true], "solution_text": "Abigail is a knave, Aurora is a knight, Penelope is a knight, David is a knight, Jackson is a knave, Sofia is a knight, William is a knight, and Charlotte is a knight.", "solution_text_format": "(1) Abigail is a knave\n(2) Aurora is a knight\n(3) Penelope is a knight\n(4) David is a knight\n(5) Jackson is a knave\n(6) Sofia is a knight\n(7) William is a knight\n(8) Charlotte is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that If Charlotte is a knight then David is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Sofia is a knight and Penelope is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that William is a knight if and only if Sofia is a knight.", "Assume William is a knight. No contradiction is found in their claim that If Sofia is a knave then Penelope is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Jackson is not a knight.", "Jackson cannot be a knight, because this would contradict the claim of Penelope that Jackson is not a knight.", "Jackson cannot be a knave, because this would contradict the false claim of their own that Charlotte is a knight and Abigail is a knight.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the claim of Charlotte that Sofia is a knight and Penelope is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the claim of Sofia that William is a knight if and only if Sofia is a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider Sofia.", "Sofia cannot be a knave, because this would contradict the claim of Charlotte that Sofia is a knight and Penelope is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Sofia is a knight and Penelope is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that William is a knight if and only if Sofia is a knight.", "Assume William is a knight. No contradiction is found in their claim that If Sofia is a knave then Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the false claim of Charlotte that Sofia is a knight and Penelope is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Jackson is not a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Charlotte is a knight and Abigail is a knight.", "Jackson cannot be a knave, because this would contradict the false claim of Penelope that Jackson is not a knight.", "We have exhausted all possibilities for Jackson and Penelope, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the claim of Sofia that William is a knight if and only if Sofia is a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that William is a knight if and only if Sofia is a knight.", "Assume William is a knight. No contradiction is found in their claim that If Sofia is a knave then Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the claim of William that If Sofia is a knave then Penelope is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Jackson is not a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Charlotte is a knight and Abigail is a knight.", "Jackson cannot be a knave, because this would contradict the false claim of Penelope that Jackson is not a knight.", "We have exhausted all possibilities for Jackson and Penelope, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the false claim of Sofia that William is a knight if and only if Sofia is a knight.", "We have exhausted all possibilities for William, Sofia, and Charlotte, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that If Charlotte is a knight then David is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Sofia is a knight and Penelope is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that William is a knight if and only if Sofia is a knight.", "Assume William is a knight. No contradiction is found in their claim that If Sofia is a knave then Penelope is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Jackson is not a knight.", "Jackson cannot be a knight, because this would contradict the claim of Penelope that Jackson is not a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Charlotte is a knight and Abigail is a knight.", "Assume David is a knight. No contradiction is found in their claim that Aurora is not a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Jackson is a knight or William is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 7), ('lying', 3)), ('or', ('telling-truth', 4), ('telling-truth', 6)), ('not', ('telling-truth', 4)), ('not', ('lying', 1)), ('and', ('telling-truth', 7), ('telling-truth', 0)), ('<=>', ('telling-truth', 6), ('telling-truth', 5)), ('->', ('lying', 5), ('lying', 2)), ('and', ('telling-truth', 5), ('telling-truth', 2)))", "index": 779}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Grace, Jack, Matthew, Harper, Daniel, Sofia, Benjamin, and Ella. \"Daniel is a knave if and only if Harper is a knight,\" Grace mentioned. Jack told you that Grace is not a knave. Matthew asserted: \"If Harper is a knight then Benjamin is a knight\". According to Harper, \"Daniel is a knight\". Daniel noted, \"Harper is a knight and Benjamin is a knave\". \"If Matthew is a knave then Sofia is a knight,\" Sofia mentioned. Benjamin stated, \"Harper is not a knave\". \"Matthew is a knave or Daniel is a knave,\" Ella mentioned. So who is a knight and who is a knave?", "names": ["Grace", "Jack", "Matthew", "Harper", "Daniel", "Sofia", "Benjamin", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, true, false, true], "solution_text": "Grace is a knave, Jack is a knave, Matthew is a knight, Harper is a knave, Daniel is a knave, Sofia is a knight, Benjamin is a knave, and Ella is a knight.", "solution_text_format": "(1) Grace is a knave\n(2) Jack is a knave\n(3) Matthew is a knight\n(4) Harper is a knave\n(5) Daniel is a knave\n(6) Sofia is a knight\n(7) Benjamin is a knave\n(8) Ella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Daniel is a knave if and only if Harper is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Harper is a knight and Benjamin is a knave.", "Harper cannot be a knight, because this would contradict the claim of Grace that Daniel is a knave if and only if Harper is a knight.", "Harper cannot be a knave, because this would contradict the false claim of their own that Daniel is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Harper is a knight and Benjamin is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Daniel is a knight.", "Harper cannot be a knave, because this would contradict the claim of Grace that Daniel is a knave if and only if Harper is a knight.", "We have exhausted all possibilities for Harper and Daniel, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Daniel is a knave if and only if Harper is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Harper is a knight and Benjamin is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Daniel is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of Daniel that Harper is a knight and Benjamin is a knave.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that Harper is not a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the false claim of Grace that Daniel is a knave if and only if Harper is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Harper is a knight and Benjamin is a knave.", "Harper cannot be a knight, because this would contradict the false claim of Grace that Daniel is a knave if and only if Harper is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Daniel is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Harper is not a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Harper is not a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Grace is not a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Grace is not a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that If Harper is a knight then Benjamin is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that If Matthew is a knave then Sofia is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Matthew is a knave or Daniel is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 4), ('telling-truth', 3)), ('not', ('lying', 0)), ('->', ('telling-truth', 3), ('telling-truth', 6)), ('telling-truth', 4), ('and', ('telling-truth', 3), ('lying', 6)), ('->', ('lying', 2), ('telling-truth', 5)), ('not', ('lying', 3)), ('or', ('lying', 2), ('lying', 4)))", "index": 780}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Oliver, Abigail, Aurora, Amelia, Owen, Grace, Emily, and Mia. In a statement by Oliver: \"If Owen is a knave then Abigail is a knave\". Abigail remarked, \"Grace is a knight and Emily is a knight\". In Aurora's words: \"If Oliver is a knight then Oliver is a knave\". In Amelia's words: \"Emily is a knave or Oliver is a knave\". \"If Aurora is a knave then Mia is a knave,\" Owen claimed. Grace noted, \"Emily is a knave or Abigail is a knight\". Emily commented, \"Owen is a knight\". Mia remarked, \"Grace is not a knight\". So who is a knight and who is a knave?", "names": ["Oliver", "Abigail", "Aurora", "Amelia", "Owen", "Grace", "Emily", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true, true, false], "solution_text": "Oliver is a knight, Abigail is a knight, Aurora is a knave, Amelia is a knave, Owen is a knight, Grace is a knight, Emily is a knight, and Mia is a knave.", "solution_text_format": "(1) Oliver is a knight\n(2) Abigail is a knight\n(3) Aurora is a knave\n(4) Amelia is a knave\n(5) Owen is a knight\n(6) Grace is a knight\n(7) Emily is a knight\n(8) Mia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that If Owen is a knave then Abigail is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that If Aurora is a knave then Mia is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that If Oliver is a knight then Oliver is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that If Oliver is a knight then Oliver is a knave.", "Mia cannot be a knight, because this would contradict the claim of Owen that If Aurora is a knave then Mia is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Grace is not a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Emily is a knave or Abigail is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Owen is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Grace is a knight and Emily is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Emily is a knave or Oliver is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Emily is a knave or Oliver is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 4), ('lying', 1)), ('and', ('telling-truth', 5), ('telling-truth', 6)), ('->', ('telling-truth', 0), ('lying', 0)), ('or', ('lying', 6), ('lying', 0)), ('->', ('lying', 2), ('lying', 7)), ('or', ('lying', 6), ('telling-truth', 1)), ('telling-truth', 4), ('not', ('telling-truth', 5)))", "index": 781}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: William, Joseph, Ella, Lucas, James, Abigail, Jackson, and Charlotte. William expressed that Abigail is a knave or James is a knight. Joseph said, \"Lucas is a knight.\" Ella remarked, \"Jackson is a knave\". \"Ella is a knight if and only if Joseph is a knight\" - Lucas. In James's words: \"Ella is a knight if and only if Jackson is a knave\". Abigail remarked, \"William is a knave if and only if Joseph is a knave\". Jackson was heard saying, \"Joseph is a knight and Ella is a knight\". Charlotte commented, \"Joseph is a knight and Abigail is a knight\". So who is a knight and who is a knave?", "names": ["William", "Joseph", "Ella", "Lucas", "James", "Abigail", "Jackson", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, false, false, false], "solution_text": "William is a knight, Joseph is a knave, Ella is a knight, Lucas is a knave, James is a knight, Abigail is a knave, Jackson is a knave, and Charlotte is a knave.", "solution_text_format": "(1) William is a knight\n(2) Joseph is a knave\n(3) Ella is a knight\n(4) Lucas is a knave\n(5) James is a knight\n(6) Abigail is a knave\n(7) Jackson is a knave\n(8) Charlotte is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Abigail is a knave or James is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that William is a knave if and only if Joseph is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Ella is a knight if and only if Joseph is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Jackson is a knave.", "Jackson cannot be a knight, because this would contradict the claim of Ella that Jackson is a knave.", "Jackson cannot be a knave, because this would contradict the false claim of their own that Joseph is a knight and Ella is a knight.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the claim of Lucas that Ella is a knight if and only if Joseph is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the claim of Joseph that Lucas is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of Abigail that William is a knave if and only if Joseph is a knave.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that William is a knave if and only if Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the false claim of Abigail that William is a knave if and only if Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of Joseph that Lucas is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Ella is a knight if and only if Joseph is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Jackson is a knave.", "Jackson cannot be a knight, because this would contradict the claim of Ella that Jackson is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Joseph is a knight and Ella is a knight.", "Assume James is a knight. No contradiction is found in their claim that Ella is a knight if and only if Jackson is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Joseph is a knight and Abigail is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Joseph is a knight and Abigail is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 5), ('telling-truth', 4)), ('telling-truth', 3), ('lying', 6), ('<=>', ('telling-truth', 2), ('telling-truth', 1)), ('<=>', ('telling-truth', 2), ('lying', 6)), ('<=>', ('lying', 0), ('lying', 1)), ('and', ('telling-truth', 1), ('telling-truth', 2)), ('and', ('telling-truth', 1), ('telling-truth', 5)))", "index": 782}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Henry, Noah, Aria, Oliver, Samuel, Jacob, Evelyn, and Daniel. In Henry's words: \"Daniel is a knave\". Noah said, \"Oliver is a knave.\" Aria stated, \"Samuel is a knave or Jacob is a knight\". Oliver asserted: \"Henry is a knave if and only if Jacob is a knight\". \"If Daniel is a knave then Henry is a knight\" - Samuel. Jacob remarked, \"Samuel is a knight or Evelyn is a knave\". Evelyn asserted: \"If Henry is a knave then Aria is a knave\". Daniel told you that Jacob is a knave. So who is a knight and who is a knave?", "names": ["Henry", "Noah", "Aria", "Oliver", "Samuel", "Jacob", "Evelyn", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true, true, false], "solution_text": "Henry is a knight, Noah is a knight, Aria is a knight, Oliver is a knave, Samuel is a knight, Jacob is a knight, Evelyn is a knight, and Daniel is a knave.", "solution_text_format": "(1) Henry is a knight\n(2) Noah is a knight\n(3) Aria is a knight\n(4) Oliver is a knave\n(5) Samuel is a knight\n(6) Jacob is a knight\n(7) Evelyn is a knight\n(8) Daniel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of Henry that Daniel is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Jacob is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Samuel is a knight or Evelyn is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that If Daniel is a knave then Henry is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Henry is a knave then Aria is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Samuel is a knave or Jacob is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Oliver is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Noah that Oliver is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Henry is a knave if and only if Jacob is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 7), ('lying', 3), ('or', ('lying', 4), ('telling-truth', 5)), ('<=>', ('lying', 0), ('telling-truth', 5)), ('->', ('lying', 7), ('telling-truth', 0)), ('or', ('telling-truth', 4), ('lying', 6)), ('->', ('lying', 0), ('lying', 2)), ('lying', 5))", "index": 783}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lily, Ava, Sophia, Penelope, Charlotte, Isabella, Benjamin, and Michael. As Lily put it, \"Sophia is a knight if and only if Benjamin is a knave\". Ava expressed that Lily is a knave and Sophia is a knave. According to Sophia, \"If Michael is a knave then Benjamin is a knight\". In a statement by Penelope: \"Charlotte is a knight\". Charlotte commented, \"Benjamin is a knave or Michael is a knight\". Isabella noted, \"If Lily is a knave then Penelope is a knight\". Benjamin asserted: \"Charlotte is a knave\". Michael told you that If Benjamin is a knave then Benjamin is a knight. So who is a knight and who is a knave?", "names": ["Lily", "Ava", "Sophia", "Penelope", "Charlotte", "Isabella", "Benjamin", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true, false, false], "solution_text": "Lily is a knave, Ava is a knight, Sophia is a knave, Penelope is a knight, Charlotte is a knight, Isabella is a knight, Benjamin is a knave, and Michael is a knave.", "solution_text_format": "(1) Lily is a knave\n(2) Ava is a knight\n(3) Sophia is a knave\n(4) Penelope is a knight\n(5) Charlotte is a knight\n(6) Isabella is a knight\n(7) Benjamin is a knave\n(8) Michael is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that Sophia is a knight if and only if Benjamin is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that If Michael is a knave then Benjamin is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that If Benjamin is a knave then Benjamin is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of Lily that Sophia is a knight if and only if Benjamin is a knave.", "Benjamin cannot be a knave, because this would contradict the claim of Michael that If Benjamin is a knave then Benjamin is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that If Benjamin is a knave then Benjamin is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of Lily that Sophia is a knight if and only if Benjamin is a knave.", "Benjamin cannot be a knave, because this would contradict the claim of Sophia that If Michael is a knave then Benjamin is a knight.", "We have exhausted all possibilities for Benjamin and Michael, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that If Michael is a knave then Benjamin is a knight.", "Michael cannot be a knight, because this would contradict the false claim of Sophia that If Michael is a knave then Benjamin is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that If Benjamin is a knave then Benjamin is a knight.", "Benjamin cannot be a knight, because this would contradict the false claim of Sophia that If Michael is a knave then Benjamin is a knight.", "Benjamin cannot be a knave, because this would contradict the claim of Lily that Sophia is a knight if and only if Benjamin is a knave.", "We have exhausted all possibilities for Benjamin, Michael, and Sophia, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Sophia is a knight if and only if Benjamin is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that If Michael is a knave then Benjamin is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that If Benjamin is a knave then Benjamin is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Benjamin that Charlotte is a knave.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that Benjamin is a knave or Michael is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the false claim of Lily that Sophia is a knight if and only if Benjamin is a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that If Benjamin is a knave then Benjamin is a knight.", "Benjamin cannot be a knight, because this would contradict the false claim of Michael that If Benjamin is a knave then Benjamin is a knight.", "Benjamin cannot be a knave, because this would contradict the false claim of Lily that Sophia is a knight if and only if Benjamin is a knave.", "We have exhausted all possibilities for Benjamin and Michael, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that If Michael is a knave then Benjamin is a knight.", "Michael cannot be a knight, because this would contradict the false claim of Sophia that If Michael is a knave then Benjamin is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that If Benjamin is a knave then Benjamin is a knight.", "Benjamin cannot be a knight, because this would contradict the false claim of Lily that Sophia is a knight if and only if Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Charlotte is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Benjamin is a knave or Michael is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Lily is a knave and Sophia is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Charlotte is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that If Lily is a knave then Penelope is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('lying', 6)), ('and', ('lying', 0), ('lying', 2)), ('->', ('lying', 7), ('telling-truth', 6)), ('telling-truth', 4), ('or', ('lying', 6), ('telling-truth', 7)), ('->', ('lying', 0), ('telling-truth', 3)), ('lying', 4), ('->', ('lying', 6), ('telling-truth', 6)))", "index": 784}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Abigail, Elizabeth, Penelope, Benjamin, Henry, Oliver, Sophia, and Harper. As Abigail put it, \"Abigail is a knight or Penelope is a knight\". Elizabeth was heard saying, \"Oliver is a knight if and only if Sophia is a knight\". Penelope asserted: \"Penelope is a knight or Henry is a knight\". \"Oliver is not a knight,\" Benjamin mentioned. Henry expressed that Sophia is a knave or Oliver is a knave. Oliver noted, \"Sophia is a knave or Oliver is a knight\". In a statement by Sophia: \"Harper is a knight and Henry is a knight\". Harper stated, \"Henry is not a knight\". So who is a knight and who is a knave?", "names": ["Abigail", "Elizabeth", "Penelope", "Benjamin", "Henry", "Oliver", "Sophia", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true, false, false], "solution_text": "Abigail is a knight, Elizabeth is a knave, Penelope is a knight, Benjamin is a knave, Henry is a knight, Oliver is a knight, Sophia is a knave, and Harper is a knave.", "solution_text_format": "(1) Abigail is a knight\n(2) Elizabeth is a knave\n(3) Penelope is a knight\n(4) Benjamin is a knave\n(5) Henry is a knight\n(6) Oliver is a knight\n(7) Sophia is a knave\n(8) Harper is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Abigail is a knight or Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Penelope is a knight or Henry is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Sophia is a knave or Oliver is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Harper is a knight and Henry is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that Henry is not a knight.", "Harper cannot be a knave, because this would contradict the claim of Sophia that Harper is a knight and Henry is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Harper is a knight and Henry is a knight.", "Harper cannot be a knight, because this would contradict the false claim of Sophia that Harper is a knight and Henry is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Henry is not a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Sophia is a knave or Oliver is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Oliver is a knight if and only if Sophia is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Oliver is a knight if and only if Sophia is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Oliver is not a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Oliver is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 0), ('telling-truth', 2)), ('<=>', ('telling-truth', 5), ('telling-truth', 6)), ('or', ('telling-truth', 2), ('telling-truth', 4)), ('not', ('telling-truth', 5)), ('or', ('lying', 6), ('lying', 5)), ('or', ('lying', 6), ('telling-truth', 5)), ('and', ('telling-truth', 7), ('telling-truth', 4)), ('not', ('telling-truth', 4)))", "index": 785}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Liam, Chloe, Michael, Aria, Scarlett, Mason, Jack, and Elizabeth. Liam expressed that If Michael is a knave then Scarlett is a knight. Chloe noted, \"If Aria is a knight then Jack is a knave\". \"Scarlett is a knight,\" Michael mentioned. In a statement by Aria: \"Michael is a knight\". Scarlett was heard saying, \"Aria is a knight if and only if Michael is a knight\". Mason commented, \"If Michael is a knight then Aria is a knave\". In a statement by Jack: \"Scarlett is not a knave\". Elizabeth said that Michael is a knight and Chloe is a knave. So who is a knight and who is a knave?", "names": ["Liam", "Chloe", "Michael", "Aria", "Scarlett", "Mason", "Jack", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false, true, true], "solution_text": "Liam is a knight, Chloe is a knave, Michael is a knight, Aria is a knight, Scarlett is a knight, Mason is a knave, Jack is a knight, and Elizabeth is a knight.", "solution_text_format": "(1) Liam is a knight\n(2) Chloe is a knave\n(3) Michael is a knight\n(4) Aria is a knight\n(5) Scarlett is a knight\n(6) Mason is a knave\n(7) Jack is a knight\n(8) Elizabeth is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that If Michael is a knave then Scarlett is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Aria is a knight if and only if Michael is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Michael is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that If Aria is a knight then Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of Chloe that If Aria is a knight then Jack is a knave.", "Jack cannot be a knave, because this would contradict the false claim of their own that Scarlett is not a knave.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that If Aria is a knight then Jack is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that If Michael is a knight then Aria is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that If Michael is a knight then Aria is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Michael is a knight and Chloe is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 2), ('telling-truth', 4)), ('->', ('telling-truth', 3), ('lying', 6)), ('telling-truth', 4), ('telling-truth', 2), ('<=>', ('telling-truth', 3), ('telling-truth', 2)), ('->', ('telling-truth', 2), ('lying', 3)), ('not', ('lying', 4)), ('and', ('telling-truth', 2), ('lying', 1)))", "index": 786}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emily, Jackson, Sofia, Grace, Jack, Lily, Harper, and Sebastian. Emily was heard saying, \"Lily is not a knight\". Jackson told you that Jack is a knave if and only if Jack is a knight. In Sofia's words: \"Jackson is a knave or Jack is a knave\". \"If Sofia is a knave then Jackson is a knave,\" Grace claimed. Jack asserted: \"Jackson is a knave if and only if Lily is a knave\". In Lily's words: \"If Grace is a knave then Lily is a knight\". Harper noted, \"Grace is a knave or Sofia is a knight\". Sebastian stated, \"Jack is a knight\". So who is a knight and who is a knave?", "names": ["Emily", "Jackson", "Sofia", "Grace", "Jack", "Lily", "Harper", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, true, true, false], "solution_text": "Emily is a knave, Jackson is a knave, Sofia is a knight, Grace is a knight, Jack is a knave, Lily is a knight, Harper is a knight, and Sebastian is a knave.", "solution_text_format": "(1) Emily is a knave\n(2) Jackson is a knave\n(3) Sofia is a knight\n(4) Grace is a knight\n(5) Jack is a knave\n(6) Lily is a knight\n(7) Harper is a knight\n(8) Sebastian is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Lily is not a knight.", "Lily cannot be a knight, because this would contradict the claim of Emily that Lily is not a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that If Grace is a knave then Lily is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Lily that If Grace is a knave then Lily is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that If Sofia is a knave then Jackson is a knave.", "Sofia cannot be a knight, because this would contradict the false claim of Grace that If Sofia is a knave then Jackson is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Jackson is a knave or Jack is a knave.", "Jackson cannot be a knight, because this would contradict the claim of their own that Jack is a knave if and only if Jack is a knight.", "Jackson cannot be a knave, because this would contradict the false claim of Sofia that Jackson is a knave or Jack is a knave.", "We have exhausted all possibilities for Jackson, Sofia, Grace, and Lily, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Lily is not a knight.", "Assume Lily is a knight. No contradiction is found in their claim that If Grace is a knave then Lily is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that If Sofia is a knave then Jackson is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Jackson is a knave or Jack is a knave.", "Jackson cannot be a knight, because this would contradict the claim of their own that Jack is a knave if and only if Jack is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Jack is a knave if and only if Jack is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Jackson is a knave if and only if Lily is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Jackson is a knave if and only if Lily is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Grace is a knave or Sofia is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Jack is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Jack is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 5)), ('<=>', ('lying', 4), ('telling-truth', 4)), ('or', ('lying', 1), ('lying', 4)), ('->', ('lying', 2), ('lying', 1)), ('<=>', ('lying', 1), ('lying', 5)), ('->', ('lying', 3), ('telling-truth', 5)), ('or', ('lying', 3), ('telling-truth', 2)), ('telling-truth', 4))", "index": 787}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Grace, James, Noah, Aurora, Ava, Jackson, William, and Sebastian. Grace said that If James is a knight then Aurora is a knight. James told you that Ava is a knight. \"Ava is a knave,\" Noah declared. In a statement by Aurora: \"Noah is a knight if and only if Jackson is a knight\". \"If Grace is a knight then Noah is a knight,\" Ava claimed. Jackson remarked, \"Jackson is a knight\". \"If Grace is a knave then Noah is a knight,\" William claimed. Sebastian said that Jackson is not a knight. So who is a knight and who is a knave?", "names": ["Grace", "James", "Noah", "Aurora", "Ava", "Jackson", "William", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true, false, false], "solution_text": "Grace is a knave, James is a knight, Noah is a knave, Aurora is a knave, Ava is a knight, Jackson is a knight, William is a knave, and Sebastian is a knave.", "solution_text_format": "(1) Grace is a knave\n(2) James is a knight\n(3) Noah is a knave\n(4) Aurora is a knave\n(5) Ava is a knight\n(6) Jackson is a knight\n(7) William is a knave\n(8) Sebastian is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that If James is a knight then Aurora is a knight.", "Assume James is a knight. No contradiction is found in their claim that Ava is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that If Grace is a knight then Noah is a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that Ava is a knave.", "Noah cannot be a knave, because this would contradict the claim of Ava that If Grace is a knight then Noah is a knight.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the claim of James that Ava is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Ava is a knight.", "Ava cannot be a knight, because this would contradict the false claim of James that Ava is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that If Grace is a knight then Noah is a knight.", "Noah cannot be a knight, because this would contradict the false claim of Ava that If Grace is a knight then Noah is a knight.", "Noah cannot be a knave, because this would contradict the false claim of their own that Ava is a knave.", "We have exhausted all possibilities for Noah, Ava, and James, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that If James is a knight then Aurora is a knight.", "Assume James is a knight. No contradiction is found in their claim that Ava is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that If Grace is a knight then Noah is a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that Ava is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Ava is a knave.", "Aurora cannot be a knight, because this would contradict the false claim of Grace that If James is a knight then Aurora is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Noah is a knight if and only if Jackson is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Jackson is a knight.", "William cannot be a knight, because this would contradict the claim of their own that If Grace is a knave then Noah is a knight.", "Assume William is a knave. No contradiction is found in their false claim that If Grace is a knave then Noah is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Jackson is not a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Jackson is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 1), ('telling-truth', 3)), ('telling-truth', 4), ('lying', 4), ('<=>', ('telling-truth', 2), ('telling-truth', 5)), ('->', ('telling-truth', 0), ('telling-truth', 2)), ('telling-truth', 5), ('->', ('lying', 0), ('telling-truth', 2)), ('not', ('telling-truth', 5)))", "index": 788}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mia, Ethan, Jackson, Noah, Emily, Abigail, Amelia, and Mason. \"Abigail is not a knight\" - Mia. \"Emily is not a knave,\" Ethan declared. Jackson noted, \"If Mia is a knight then Jackson is a knight\". Noah said, \"Ethan is not a knight.\" Emily said, \"Mia is a knight and Mason is a knight.\" Abigail stated, \"If Noah is a knave then Amelia is a knave\". Amelia expressed that Mia is a knave and Mia is a knight. In Mason's words: \"If Mia is a knight then Emily is a knight\". So who is a knight and who is a knave?", "names": ["Mia", "Ethan", "Jackson", "Noah", "Emily", "Abigail", "Amelia", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, true, false, true], "solution_text": "Mia is a knave, Ethan is a knave, Jackson is a knight, Noah is a knight, Emily is a knave, Abigail is a knight, Amelia is a knave, and Mason is a knight.", "solution_text_format": "(1) Mia is a knave\n(2) Ethan is a knave\n(3) Jackson is a knight\n(4) Noah is a knight\n(5) Emily is a knave\n(6) Abigail is a knight\n(7) Amelia is a knave\n(8) Mason is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Abigail is not a knight.", "Abigail cannot be a knight, because this would contradict the claim of Mia that Abigail is not a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that If Noah is a knave then Amelia is a knave.", "Noah cannot be a knight, because this would contradict the false claim of Abigail that If Noah is a knave then Amelia is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Ethan is not a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Emily is not a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Mia is a knight and Mason is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that If Mia is a knight then Emily is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Mia is a knave and Mia is a knight.", "Amelia cannot be a knave, because this would contradict the false claim of Abigail that If Noah is a knave then Amelia is a knave.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Mason.", "Mason cannot be a knave, because this would contradict the claim of Emily that Mia is a knight and Mason is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the claim of Ethan that Emily is not a knave.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the false claim of Noah that Ethan is not a knight.", "We have exhausted all possibilities for Ethan, Noah, and Abigail, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Abigail is not a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If Noah is a knave then Amelia is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Ethan is not a knight.", "Ethan cannot be a knight, because this would contradict the claim of Noah that Ethan is not a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Emily is not a knave.", "Emily cannot be a knight, because this would contradict the false claim of Ethan that Emily is not a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Mia is a knight and Mason is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that If Mia is a knight then Emily is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Mia is a knave and Mia is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Mia is a knave and Mia is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that If Mia is a knight then Jackson is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 5)), ('not', ('lying', 4)), ('->', ('telling-truth', 0), ('telling-truth', 2)), ('not', ('telling-truth', 1)), ('and', ('telling-truth', 0), ('telling-truth', 7)), ('->', ('lying', 3), ('lying', 6)), ('and', ('lying', 0), ('telling-truth', 0)), ('->', ('telling-truth', 0), ('telling-truth', 4)))", "index": 789}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ella, Ava, Lucas, Aurora, Zoey, Mia, Luke, and Riley. Ella stated, \"If Lucas is a knight then Luke is a knight\". Ava noted, \"Lucas is not a knave\". Lucas remarked, \"Mia is a knight if and only if Zoey is a knight\". According to Aurora, \"Lucas is a knave and Riley is a knave\". Zoey stated, \"Ella is a knave or Lucas is a knight\". Mia was heard saying, \"If Ella is a knave then Zoey is a knight\". \"If Mia is a knave then Aurora is a knave\" - Luke. Riley commented, \"Aurora is not a knave\". So who is a knight and who is a knave?", "names": ["Ella", "Ava", "Lucas", "Aurora", "Zoey", "Mia", "Luke", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true, true, false], "solution_text": "Ella is a knight, Ava is a knight, Lucas is a knight, Aurora is a knave, Zoey is a knight, Mia is a knight, Luke is a knight, and Riley is a knave.", "solution_text_format": "(1) Ella is a knight\n(2) Ava is a knight\n(3) Lucas is a knight\n(4) Aurora is a knave\n(5) Zoey is a knight\n(6) Mia is a knight\n(7) Luke is a knight\n(8) Riley is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that If Lucas is a knight then Luke is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Mia is a knight if and only if Zoey is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that If Ella is a knave then Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Ella is a knave or Lucas is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that If Mia is a knave then Aurora is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Lucas is a knave and Riley is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Lucas is a knave and Riley is a knave.", "Riley cannot be a knight, because this would contradict the claim of their own that Aurora is not a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Aurora is not a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Lucas is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('telling-truth', 6)), ('not', ('lying', 2)), ('<=>', ('telling-truth', 5), ('telling-truth', 4)), ('and', ('lying', 2), ('lying', 7)), ('or', ('lying', 0), ('telling-truth', 2)), ('->', ('lying', 0), ('telling-truth', 4)), ('->', ('lying', 5), ('lying', 3)), ('not', ('lying', 3)))", "index": 790}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Henry, Riley, David, Lily, Alexander, Luke, Aria, and Sebastian. Henry noted, \"Sebastian is a knight and Aria is a knight\". \"David is a knight and Aria is a knight,\" Riley claimed. David asserted: \"Lily is not a knight\". As Lily put it, \"Henry is a knave and Aria is a knight\". In Alexander's words: \"Riley is a knight if and only if Lily is a knight\". Luke said that David is a knave. \"If Lily is a knave then Luke is a knave,\" Aria declared. Sebastian was heard saying, \"If Lily is a knave then Alexander is a knave\". So who is a knight and who is a knave?", "names": ["Henry", "Riley", "David", "Lily", "Alexander", "Luke", "Aria", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false, true, true], "solution_text": "Henry is a knight, Riley is a knight, David is a knight, Lily is a knave, Alexander is a knave, Luke is a knave, Aria is a knight, and Sebastian is a knight.", "solution_text_format": "(1) Henry is a knight\n(2) Riley is a knight\n(3) David is a knight\n(4) Lily is a knave\n(5) Alexander is a knave\n(6) Luke is a knave\n(7) Aria is a knight\n(8) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that Sebastian is a knight and Aria is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Lily is a knave then Alexander is a knave.", "Lily cannot be a knight, because this would contradict the claim of their own that Henry is a knave and Aria is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Henry is a knave and Aria is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that If Lily is a knave then Luke is a knave.", "Luke cannot be a knight, because this would contradict the claim of Aria that If Lily is a knave then Luke is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that David is a knave.", "Assume David is a knight. No contradiction is found in their claim that Lily is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of Sebastian that If Lily is a knave then Alexander is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Lily is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that David is a knight and Aria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 7), ('telling-truth', 6)), ('and', ('telling-truth', 2), ('telling-truth', 6)), ('not', ('telling-truth', 3)), ('and', ('lying', 0), ('telling-truth', 6)), ('<=>', ('telling-truth', 1), ('telling-truth', 3)), ('lying', 2), ('->', ('lying', 3), ('lying', 5)), ('->', ('lying', 3), ('lying', 4)))", "index": 791}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Owen, Isabella, Evelyn, Noah, Ella, Henry, Liam, and Emily. Owen stated, \"Evelyn is a knight or Emily is a knave\". In a statement by Isabella: \"Noah is not a knight\". As Evelyn put it, \"Emily is a knave if and only if Henry is a knight\". Noah told you that Henry is not a knight. In Ella's words: \"Evelyn is a knave or Emily is a knight\". Henry said, \"Henry is a knight or Evelyn is a knight.\" \"Owen is a knave,\" Liam claimed. \"Noah is a knave or Ella is a knight,\" Emily mentioned. So who is a knight and who is a knave?", "names": ["Owen", "Isabella", "Evelyn", "Noah", "Ella", "Henry", "Liam", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true, true, true], "solution_text": "Owen is a knave, Isabella is a knight, Evelyn is a knave, Noah is a knave, Ella is a knight, Henry is a knight, Liam is a knight, and Emily is a knight.", "solution_text_format": "(1) Owen is a knave\n(2) Isabella is a knight\n(3) Evelyn is a knave\n(4) Noah is a knave\n(5) Ella is a knight\n(6) Henry is a knight\n(7) Liam is a knight\n(8) Emily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Evelyn is a knight or Emily is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Emily is a knave if and only if Henry is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Noah is a knave or Ella is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Henry is not a knight.", "Henry cannot be a knight, because this would contradict the claim of Evelyn that Emily is a knave if and only if Henry is a knight.", "Henry cannot be a knave, because this would contradict the false claim of their own that Henry is a knight or Evelyn is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Henry is not a knight.", "Henry cannot be a knight, because this would contradict the claim of Evelyn that Emily is a knave if and only if Henry is a knight.", "Henry cannot be a knave, because this would contradict the false claim of Noah that Henry is not a knight.", "We have exhausted all possibilities for Henry and Noah, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Noah is a knave or Ella is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Henry is not a knight.", "Henry cannot be a knight, because this would contradict the claim of Noah that Henry is not a knight.", "Henry cannot be a knave, because this would contradict the claim of Evelyn that Emily is a knave if and only if Henry is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the false claim of Emily that Noah is a knave or Ella is a knight.", "We have exhausted all possibilities for Noah and Emily, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Emily is a knave if and only if Henry is a knight.", "Emily cannot be a knight, because this would contradict the claim of Owen that Evelyn is a knight or Emily is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Noah is a knave or Ella is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Henry is not a knight.", "Henry cannot be a knight, because this would contradict the false claim of Evelyn that Emily is a knave if and only if Henry is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Henry is a knight or Evelyn is a knight.", "Ella cannot be a knight, because this would contradict the false claim of Emily that Noah is a knave or Ella is a knight.", "Ella cannot be a knave, because this would contradict the false claim of their own that Evelyn is a knave or Emily is a knight.", "We have exhausted all possibilities for Ella and Henry, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the false claim of Emily that Noah is a knave or Ella is a knight.", "We have exhausted all possibilities for Noah, Emily, and Evelyn, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Evelyn is a knight or Emily is a knave.", "Evelyn cannot be a knight, because this would contradict the false claim of Owen that Evelyn is a knight or Emily is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Emily is a knave if and only if Henry is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Noah is a knave or Ella is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Henry is not a knight.", "Henry cannot be a knight, because this would contradict the claim of Noah that Henry is not a knight.", "Henry cannot be a knave, because this would contradict the false claim of Evelyn that Emily is a knave if and only if Henry is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Henry is not a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Henry is a knight or Evelyn is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Evelyn is a knave or Emily is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Noah is not a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Owen is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('lying', 7)), ('not', ('telling-truth', 3)), ('<=>', ('lying', 7), ('telling-truth', 5)), ('not', ('telling-truth', 5)), ('or', ('lying', 2), ('telling-truth', 7)), ('or', ('telling-truth', 5), ('telling-truth', 2)), ('lying', 0), ('or', ('lying', 3), ('telling-truth', 4)))", "index": 792}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emma, Ava, Logan, Sophia, Daniel, Benjamin, Evelyn, and Jacob. As Emma put it, \"Sophia is a knave and Benjamin is a knight\". Ava expressed that If Ava is a knight then Daniel is a knight. \"If Ava is a knave then Emma is a knave\" - Logan. Sophia told you that Benjamin is a knight. Daniel told you that Sophia is a knight and Ava is a knight. \"Daniel is not a knave,\" Benjamin mentioned. Evelyn said that Sophia is a knight or Emma is a knight. Jacob expressed that Emma is a knight or Logan is a knight. So who is a knight and who is a knave?", "names": ["Emma", "Ava", "Logan", "Sophia", "Daniel", "Benjamin", "Evelyn", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true, true, true], "solution_text": "Emma is a knave, Ava is a knight, Logan is a knight, Sophia is a knight, Daniel is a knight, Benjamin is a knight, Evelyn is a knight, and Jacob is a knight.", "solution_text_format": "(1) Emma is a knave\n(2) Ava is a knight\n(3) Logan is a knight\n(4) Sophia is a knight\n(5) Daniel is a knight\n(6) Benjamin is a knight\n(7) Evelyn is a knight\n(8) Jacob is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Sophia is a knave and Benjamin is a knight.", "Sophia cannot be a knight, because this would contradict the claim of Emma that Sophia is a knave and Benjamin is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Benjamin is a knight.", "Benjamin cannot be a knight, because this would contradict the false claim of Sophia that Benjamin is a knight.", "Benjamin cannot be a knave, because this would contradict the claim of Emma that Sophia is a knave and Benjamin is a knight.", "We have exhausted all possibilities for Benjamin and Sophia, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Sophia is a knave and Benjamin is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Benjamin is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Daniel is not a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Sophia is a knight and Ava is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that If Ava is a knight then Daniel is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that If Ava is a knave then Emma is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Sophia is a knight or Emma is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Emma is a knight or Logan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('telling-truth', 5)), ('->', ('telling-truth', 1), ('telling-truth', 4)), ('->', ('lying', 1), ('lying', 0)), ('telling-truth', 5), ('and', ('telling-truth', 3), ('telling-truth', 1)), ('not', ('lying', 4)), ('or', ('telling-truth', 3), ('telling-truth', 0)), ('or', ('telling-truth', 0), ('telling-truth', 2)))", "index": 793}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Elizabeth, Logan, Harper, James, Oliver, Henry, Chloe, and Penelope. Elizabeth was heard saying, \"Logan is a knave\". \"Elizabeth is a knave if and only if Oliver is a knight,\" Logan claimed. \"Chloe is a knave,\" Harper declared. According to James, \"Chloe is a knave if and only if James is a knight\". Oliver told you that Penelope is a knave and Henry is a knave. Henry remarked, \"James is a knave or Chloe is a knight\". Chloe said that Elizabeth is a knight. Penelope asserted: \"James is a knave\". So who is a knight and who is a knave?", "names": ["Elizabeth", "Logan", "Harper", "James", "Oliver", "Henry", "Chloe", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false, false, false], "solution_text": "Elizabeth is a knave, Logan is a knight, Harper is a knight, James is a knight, Oliver is a knight, Henry is a knave, Chloe is a knave, and Penelope is a knave.", "solution_text_format": "(1) Elizabeth is a knave\n(2) Logan is a knight\n(3) Harper is a knight\n(4) James is a knight\n(5) Oliver is a knight\n(6) Henry is a knave\n(7) Chloe is a knave\n(8) Penelope is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of Elizabeth that Logan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Elizabeth is a knave if and only if Oliver is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Penelope is a knave and Henry is a knave.", "Penelope cannot be a knight, because this would contradict the claim of Oliver that Penelope is a knave and Henry is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that James is a knave.", "Assume James is a knight. No contradiction is found in their claim that Chloe is a knave if and only if James is a knight.", "Chloe cannot be a knight, because this would contradict the claim of James that Chloe is a knave if and only if James is a knight.", "Chloe cannot be a knave, because this would contradict the false claim of their own that Elizabeth is a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider James.", "James cannot be a knave, because this would contradict the false claim of Penelope that James is a knave.", "We have exhausted all possibilities for James and Penelope, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the false claim of Logan that Elizabeth is a knave if and only if Oliver is a knight.", "We have exhausted all possibilities for Oliver and Logan, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Logan is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Elizabeth is a knave if and only if Oliver is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Penelope is a knave and Henry is a knave.", "Penelope cannot be a knight, because this would contradict the claim of Oliver that Penelope is a knave and Henry is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that James is a knave.", "Assume James is a knight. No contradiction is found in their claim that Chloe is a knave if and only if James is a knight.", "Chloe cannot be a knight, because this would contradict the claim of James that Chloe is a knave if and only if James is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Elizabeth is a knight.", "Henry cannot be a knight, because this would contradict the claim of Oliver that Penelope is a knave and Henry is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that James is a knave or Chloe is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Chloe is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 1), ('<=>', ('lying', 0), ('telling-truth', 4)), ('lying', 6), ('<=>', ('lying', 6), ('telling-truth', 3)), ('and', ('lying', 7), ('lying', 5)), ('or', ('lying', 3), ('telling-truth', 6)), ('telling-truth', 0), ('lying', 3))", "index": 794}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Abigail, Charlotte, David, Luke, Victoria, Sophia, Liam, and Aiden. According to Abigail, \"David is a knave if and only if Luke is a knave\". \"If Charlotte is a knight then Sophia is a knave,\" Charlotte declared. David expressed that Sophia is a knight. Luke commented, \"Victoria is a knave\". \"Abigail is a knave and Aiden is a knave,\" Victoria declared. Sophia told you that Abigail is a knave if and only if Aiden is a knave. Liam told you that Charlotte is not a knight. Aiden commented, \"Liam is not a knight\". So who is a knight and who is a knave?", "names": ["Abigail", "Charlotte", "David", "Luke", "Victoria", "Sophia", "Liam", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, false, false, true], "solution_text": "Abigail is a knave, Charlotte is a knight, David is a knave, Luke is a knight, Victoria is a knave, Sophia is a knave, Liam is a knave, and Aiden is a knight.", "solution_text_format": "(1) Abigail is a knave\n(2) Charlotte is a knight\n(3) David is a knave\n(4) Luke is a knight\n(5) Victoria is a knave\n(6) Sophia is a knave\n(7) Liam is a knave\n(8) Aiden is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that David is a knave if and only if Luke is a knave.", "Assume David is a knight. No contradiction is found in their claim that Sophia is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Abigail is a knave if and only if Aiden is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Liam is not a knight.", "Liam cannot be a knight, because this would contradict the claim of Aiden that Liam is not a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Charlotte is not a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that If Charlotte is a knight then Sophia is a knave.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that If Charlotte is a knight then Sophia is a knave.", "We have exhausted all possibilities for Charlotte and Liam, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the claim of Sophia that Abigail is a knave if and only if Aiden is a knave.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the claim of David that Sophia is a knight.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Sophia is a knight.", "Sophia cannot be a knight, because this would contradict the false claim of David that Sophia is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Abigail is a knave if and only if Aiden is a knave.", "Aiden cannot be a knight, because this would contradict the false claim of Sophia that Abigail is a knave if and only if Aiden is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Liam is not a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Charlotte is not a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Liam that Charlotte is not a knight.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that If Charlotte is a knight then Sophia is a knave.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the false claim of Aiden that Liam is not a knight.", "We have exhausted all possibilities for Liam, Aiden, Sophia, and David, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that David is a knave if and only if Luke is a knave.", "Assume David is a knight. No contradiction is found in their claim that Sophia is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Abigail is a knave if and only if Aiden is a knave.", "Aiden cannot be a knight, because this would contradict the claim of Sophia that Abigail is a knave if and only if Aiden is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Liam is not a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Charlotte is not a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that If Charlotte is a knight then Sophia is a knave.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that If Charlotte is a knight then Sophia is a knave.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the false claim of Aiden that Liam is not a knight.", "We have exhausted all possibilities for Liam and Aiden, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the claim of David that Sophia is a knight.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Sophia is a knight.", "Sophia cannot be a knight, because this would contradict the false claim of David that Sophia is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Abigail is a knave if and only if Aiden is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Liam is not a knight.", "Liam cannot be a knight, because this would contradict the claim of Aiden that Liam is not a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Charlotte is not a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Charlotte is a knight then Sophia is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Victoria is a knave.", "Victoria cannot be a knight, because this would contradict the claim of Luke that Victoria is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Abigail is a knave and Aiden is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('lying', 3)), ('->', ('telling-truth', 1), ('lying', 5)), ('telling-truth', 5), ('lying', 4), ('and', ('lying', 0), ('lying', 7)), ('<=>', ('lying', 0), ('lying', 7)), ('not', ('telling-truth', 1)), ('not', ('telling-truth', 6)))", "index": 795}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Avery, Riley, Alexander, Olivia, Luke, Liam, Henry, and Owen. Avery said that Owen is a knight or Henry is a knight. Riley stated, \"Owen is a knave or Olivia is a knave\". Alexander asserted: \"Luke is not a knight\". In a statement by Olivia: \"Riley is a knight if and only if Avery is a knight\". In Luke's words: \"Olivia is a knight or Henry is a knave\". Liam asserted: \"Olivia is not a knight\". In a statement by Henry: \"Riley is a knight and Riley is a knave\". Owen said, \"Riley is a knight if and only if Liam is a knave.\" So who is a knight and who is a knave?", "names": ["Avery", "Riley", "Alexander", "Olivia", "Luke", "Liam", "Henry", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true, false, false], "solution_text": "Avery is a knave, Riley is a knight, Alexander is a knave, Olivia is a knave, Luke is a knight, Liam is a knight, Henry is a knave, and Owen is a knave.", "solution_text_format": "(1) Avery is a knave\n(2) Riley is a knight\n(3) Alexander is a knave\n(4) Olivia is a knave\n(5) Luke is a knight\n(6) Liam is a knight\n(7) Henry is a knave\n(8) Owen is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Owen is a knight or Henry is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Riley is a knight if and only if Liam is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Owen is a knave or Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Riley that Owen is a knave or Olivia is a knave.", "Olivia cannot be a knave, because this would contradict the false claim of their own that Riley is a knight if and only if Avery is a knight.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Owen is a knave or Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that Riley is a knight if and only if Avery is a knight.", "Olivia cannot be a knave, because this would contradict the false claim of Riley that Owen is a knave or Olivia is a knave.", "We have exhausted all possibilities for Olivia and Riley, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Liam is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Owen is a knave or Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Riley is a knight if and only if Avery is a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that Olivia is not a knight.", "Liam cannot be a knave, because this would contradict the false claim of Owen that Riley is a knight if and only if Liam is a knave.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the false claim of their own that Riley is a knight if and only if Avery is a knight.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Riley.", "Riley cannot be a knave, because this would contradict the false claim of their own that Owen is a knave or Olivia is a knave.", "We have exhausted all possibilities for Riley and Owen, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Owen is a knight or Henry is a knight.", "Owen cannot be a knight, because this would contradict the false claim of Avery that Owen is a knight or Henry is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Liam is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Owen is a knave or Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that Riley is a knight if and only if Avery is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Avery is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Olivia is not a knight.", "Henry cannot be a knight, because this would contradict the false claim of Avery that Owen is a knight or Henry is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Riley is a knight and Riley is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Luke is not a knight.", "Luke cannot be a knight, because this would contradict the claim of Alexander that Luke is not a knight.", "Luke cannot be a knave, because this would contradict the false claim of their own that Olivia is a knight or Henry is a knave.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Luke is not a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Olivia is a knight or Henry is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 7), ('telling-truth', 6)), ('or', ('lying', 7), ('lying', 3)), ('not', ('telling-truth', 4)), ('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('or', ('telling-truth', 3), ('lying', 6)), ('not', ('telling-truth', 3)), ('and', ('telling-truth', 1), ('lying', 1)), ('<=>', ('telling-truth', 1), ('lying', 5)))", "index": 796}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sofia, Henry, Amelia, Chloe, Jack, Emma, Elizabeth, and Luke. Sofia asserted: \"Henry is not a knave\". \"Chloe is a knave or Emma is a knave,\" Henry claimed. Amelia remarked, \"If Luke is a knave then Chloe is a knave\". Chloe commented, \"Luke is a knave and Elizabeth is a knight\". According to Jack, \"If Elizabeth is a knave then Amelia is a knave\". \"Sofia is a knight if and only if Chloe is a knight,\" Emma mentioned. Elizabeth commented, \"Henry is a knight and Henry is a knave\". In a statement by Luke: \"Sofia is a knave if and only if Emma is a knave\". So who is a knight and who is a knave?", "names": ["Sofia", "Henry", "Amelia", "Chloe", "Jack", "Emma", "Elizabeth", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false, false, false], "solution_text": "Sofia is a knight, Henry is a knight, Amelia is a knight, Chloe is a knave, Jack is a knave, Emma is a knave, Elizabeth is a knave, and Luke is a knave.", "solution_text_format": "(1) Sofia is a knight\n(2) Henry is a knight\n(3) Amelia is a knight\n(4) Chloe is a knave\n(5) Jack is a knave\n(6) Emma is a knave\n(7) Elizabeth is a knave\n(8) Luke is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Henry is not a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Chloe is a knave or Emma is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Luke is a knave and Elizabeth is a knight.", "Luke cannot be a knight, because this would contradict the claim of Chloe that Luke is a knave and Elizabeth is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Sofia is a knave if and only if Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of Henry that Chloe is a knave or Emma is a knave.", "Emma cannot be a knave, because this would contradict the false claim of their own that Sofia is a knight if and only if Chloe is a knight.", "We have exhausted all possibilities for Emma and Luke, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Luke is a knave and Elizabeth is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Sofia is a knave if and only if Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Sofia is a knight if and only if Chloe is a knight.", "Emma cannot be a knave, because this would contradict the claim of Luke that Sofia is a knave if and only if Emma is a knave.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Sofia is a knave if and only if Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Sofia is a knight if and only if Chloe is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Sofia is a knight if and only if Chloe is a knight.", "Elizabeth cannot be a knight, because this would contradict the false claim of Chloe that Luke is a knave and Elizabeth is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Henry is a knight and Henry is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that If Luke is a knave then Chloe is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that If Elizabeth is a knave then Amelia is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that If Elizabeth is a knave then Amelia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('or', ('lying', 3), ('lying', 5)), ('->', ('lying', 7), ('lying', 3)), ('and', ('lying', 7), ('telling-truth', 6)), ('->', ('lying', 6), ('lying', 2)), ('<=>', ('telling-truth', 0), ('telling-truth', 3)), ('and', ('telling-truth', 1), ('lying', 1)), ('<=>', ('lying', 0), ('lying', 5)))", "index": 797}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Abigail, Amelia, Scarlett, Lily, Penelope, Avery, Harper, and Daniel. Abigail asserted: \"Lily is a knight or Avery is a knight\". \"If Harper is a knight then Scarlett is a knave,\" Amelia mentioned. Scarlett told you that Amelia is not a knave. In Lily's words: \"Daniel is a knave\". Penelope commented, \"Lily is a knave or Amelia is a knight\". Avery said, \"Daniel is a knave.\" Harper commented, \"Daniel is not a knight\". Daniel stated, \"Amelia is not a knave\". So who is a knight and who is a knave?", "names": ["Abigail", "Amelia", "Scarlett", "Lily", "Penelope", "Avery", "Harper", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, false, false, true], "solution_text": "Abigail is a knave, Amelia is a knight, Scarlett is a knight, Lily is a knave, Penelope is a knight, Avery is a knave, Harper is a knave, and Daniel is a knight.", "solution_text_format": "(1) Abigail is a knave\n(2) Amelia is a knight\n(3) Scarlett is a knight\n(4) Lily is a knave\n(5) Penelope is a knight\n(6) Avery is a knave\n(7) Harper is a knave\n(8) Daniel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Lily is a knight or Avery is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of Lily that Daniel is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Amelia is not a knave.", "Amelia cannot be a knight, because this would contradict the false claim of Daniel that Amelia is not a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that If Harper is a knight then Scarlett is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Daniel is not a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Amelia is not a knave.", "Scarlett cannot be a knave, because this would contradict the false claim of Amelia that If Harper is a knight then Scarlett is a knave.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the false claim of Amelia that If Harper is a knight then Scarlett is a knave.", "We have exhausted all possibilities for Harper, Amelia, and Daniel, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Daniel is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Amelia is not a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that If Harper is a knight then Scarlett is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Daniel is not a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Daniel is not a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Amelia is not a knave.", "Avery cannot be a knight, because this would contradict the claim of their own that Daniel is a knave.", "Avery cannot be a knave, because this would contradict the claim of Abigail that Lily is a knight or Avery is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the false claim of their own that Amelia is not a knave.", "We have exhausted all possibilities for Scarlett and Harper, so let us go back and reconsider Amelia.", "Amelia cannot be a knave, because this would contradict the claim of Daniel that Amelia is not a knave.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the false claim of Lily that Daniel is a knave.", "We have exhausted all possibilities for Daniel and Lily, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Lily is a knight or Avery is a knight.", "Lily cannot be a knight, because this would contradict the false claim of Abigail that Lily is a knight or Avery is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Daniel is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Amelia is not a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that If Harper is a knight then Scarlett is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Daniel is not a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Daniel is not a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Amelia is not a knave.", "Avery cannot be a knight, because this would contradict the false claim of Abigail that Lily is a knight or Avery is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Daniel is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Lily is a knave or Amelia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('telling-truth', 5)), ('->', ('telling-truth', 6), ('lying', 2)), ('not', ('lying', 1)), ('lying', 7), ('or', ('lying', 3), ('telling-truth', 1)), ('lying', 7), ('not', ('telling-truth', 7)), ('not', ('lying', 1)))", "index": 798}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ava, Sebastian, Sophia, Zoey, Samuel, Penelope, Avery, and Noah. Ava stated, \"Noah is a knight or Zoey is a knave\". Sebastian expressed that Zoey is a knight and Samuel is a knave. According to Sophia, \"Penelope is a knave or Sophia is a knight\". \"Avery is not a knave,\" Zoey claimed. Samuel stated, \"If Samuel is a knight then Ava is a knave\". As Penelope put it, \"Noah is a knight\". \"Sophia is a knight and Zoey is a knight,\" Avery claimed. Noah remarked, \"Sebastian is a knight\". So who is a knight and who is a knave?", "names": ["Ava", "Sebastian", "Sophia", "Zoey", "Samuel", "Penelope", "Avery", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false, true, false], "solution_text": "Ava is a knave, Sebastian is a knave, Sophia is a knight, Zoey is a knight, Samuel is a knight, Penelope is a knave, Avery is a knight, and Noah is a knave.", "solution_text_format": "(1) Ava is a knave\n(2) Sebastian is a knave\n(3) Sophia is a knight\n(4) Zoey is a knight\n(5) Samuel is a knight\n(6) Penelope is a knave\n(7) Avery is a knight\n(8) Noah is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Noah is a knight or Zoey is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Zoey is a knight and Samuel is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Avery is not a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Sophia is a knight and Zoey is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Penelope is a knave or Sophia is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Noah is a knight.", "Samuel cannot be a knight, because this would contradict the claim of Sebastian that Zoey is a knight and Samuel is a knave.", "Samuel cannot be a knave, because this would contradict the false claim of their own that If Samuel is a knight then Ava is a knave.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the false claim of their own that Noah is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the claim of Avery that Sophia is a knight and Zoey is a knight.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Avery.", "Avery cannot be a knave, because this would contradict the claim of Zoey that Avery is not a knave.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Zoey.", "Zoey cannot be a knave, because this would contradict the claim of Sebastian that Zoey is a knight and Samuel is a knave.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the claim of Noah that Sebastian is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Sebastian is a knight.", "Sebastian cannot be a knight, because this would contradict the false claim of Noah that Sebastian is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Zoey is a knight and Samuel is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Ava that Noah is a knight or Zoey is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Avery is not a knave.", "Avery cannot be a knight, because this would contradict the false claim of Zoey that Avery is not a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Sophia is a knight and Zoey is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Penelope is a knave or Sophia is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Noah is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Noah is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that If Samuel is a knight then Ava is a knave.", "Samuel cannot be a knave, because this would contradict the false claim of their own that If Samuel is a knight then Ava is a knave.", "We have exhausted all possibilities for Samuel and Penelope, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Penelope is a knave or Sophia is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Noah is a knight.", "Penelope cannot be a knave, because this would contradict the false claim of Sophia that Penelope is a knave or Sophia is a knight.", "We have exhausted all possibilities for Penelope, Sophia, Avery, Zoey, Sebastian, and Noah, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Noah is a knight or Zoey is a knave.", "Noah cannot be a knight, because this would contradict the false claim of Ava that Noah is a knight or Zoey is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Sebastian is a knight.", "Sebastian cannot be a knight, because this would contradict the false claim of Noah that Sebastian is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Zoey is a knight and Samuel is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Avery is not a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Sophia is a knight and Zoey is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Penelope is a knave or Sophia is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Noah is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Noah is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that If Samuel is a knight then Ava is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 7), ('lying', 3)), ('and', ('telling-truth', 3), ('lying', 4)), ('or', ('lying', 5), ('telling-truth', 2)), ('not', ('lying', 6)), ('->', ('telling-truth', 4), ('lying', 0)), ('telling-truth', 7), ('and', ('telling-truth', 2), ('telling-truth', 3)), ('telling-truth', 1))", "index": 799}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Henry, Olivia, Aiden, Amelia, Emma, Victoria, Abigail, and Owen. Henry remarked, \"Amelia is a knave\". Olivia said that Victoria is a knave or Victoria is a knight. \"Henry is not a knave,\" Aiden declared. Amelia stated, \"Olivia is a knave and Aiden is a knave\". \"Amelia is a knave and Olivia is a knight\" - Emma. According to Victoria, \"If Aiden is a knight then Olivia is a knave\". As Abigail put it, \"Olivia is a knave if and only if Emma is a knave\". Owen asserted: \"Emma is a knave if and only if Amelia is a knave\". So who is a knight and who is a knave?", "names": ["Henry", "Olivia", "Aiden", "Amelia", "Emma", "Victoria", "Abigail", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false, true, false], "solution_text": "Henry is a knight, Olivia is a knight, Aiden is a knight, Amelia is a knave, Emma is a knight, Victoria is a knave, Abigail is a knight, and Owen is a knave.", "solution_text_format": "(1) Henry is a knight\n(2) Olivia is a knight\n(3) Aiden is a knight\n(4) Amelia is a knave\n(5) Emma is a knight\n(6) Victoria is a knave\n(7) Abigail is a knight\n(8) Owen is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Henry that Amelia is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Olivia is a knave and Aiden is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Victoria is a knave or Victoria is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that If Aiden is a knight then Olivia is a knave.", "Aiden cannot be a knight, because this would contradict the claim of Victoria that If Aiden is a knight then Olivia is a knave.", "Aiden cannot be a knave, because this would contradict the false claim of their own that Henry is not a knave.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that If Aiden is a knight then Olivia is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Henry is not a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Amelia is a knave and Olivia is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Olivia is a knave if and only if Emma is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Emma is a knave if and only if Amelia is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Emma is a knave if and only if Amelia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('or', ('lying', 5), ('telling-truth', 5)), ('not', ('lying', 0)), ('and', ('lying', 1), ('lying', 2)), ('and', ('lying', 3), ('telling-truth', 1)), ('->', ('telling-truth', 2), ('lying', 1)), ('<=>', ('lying', 1), ('lying', 4)), ('<=>', ('lying', 4), ('lying', 3)))", "index": 800}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Olivia, Victoria, Mason, Benjamin, Amelia, Daniel, David, and Grace. Olivia expressed that Benjamin is a knight and Mason is a knight. According to Victoria, \"Daniel is a knave if and only if Grace is a knight\". Mason stated, \"Amelia is a knave if and only if Olivia is a knave\". \"Mason is not a knight,\" Benjamin declared. In a statement by Amelia: \"David is a knave if and only if Benjamin is a knave\". \"Amelia is a knight or Victoria is a knight,\" Daniel claimed. David expressed that Daniel is a knight and Victoria is a knight. \"Mason is a knave if and only if Victoria is a knave,\" Grace declared. So who is a knight and who is a knave?", "names": ["Olivia", "Victoria", "Mason", "Benjamin", "Amelia", "Daniel", "David", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true, true, false], "solution_text": "Olivia is a knave, Victoria is a knight, Mason is a knave, Benjamin is a knight, Amelia is a knight, Daniel is a knight, David is a knight, and Grace is a knave.", "solution_text_format": "(1) Olivia is a knave\n(2) Victoria is a knight\n(3) Mason is a knave\n(4) Benjamin is a knight\n(5) Amelia is a knight\n(6) Daniel is a knight\n(7) David is a knight\n(8) Grace is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Benjamin is a knight and Mason is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Mason is not a knight.", "Mason cannot be a knight, because this would contradict the claim of Benjamin that Mason is not a knight.", "Mason cannot be a knave, because this would contradict the claim of Olivia that Benjamin is a knight and Mason is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the claim of Olivia that Benjamin is a knight and Mason is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Benjamin is a knight and Mason is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Mason is not a knight.", "Mason cannot be a knight, because this would contradict the false claim of Olivia that Benjamin is a knight and Mason is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Amelia is a knave if and only if Olivia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that David is a knave if and only if Benjamin is a knave.", "Assume David is a knight. No contradiction is found in their claim that Daniel is a knight and Victoria is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Amelia is a knight or Victoria is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Daniel is a knave if and only if Grace is a knight.", "Grace cannot be a knight, because this would contradict the claim of Victoria that Daniel is a knave if and only if Grace is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Mason is a knave if and only if Victoria is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('telling-truth', 2)), ('<=>', ('lying', 5), ('telling-truth', 7)), ('<=>', ('lying', 4), ('lying', 0)), ('not', ('telling-truth', 2)), ('<=>', ('lying', 6), ('lying', 3)), ('or', ('telling-truth', 4), ('telling-truth', 1)), ('and', ('telling-truth', 5), ('telling-truth', 1)), ('<=>', ('lying', 2), ('lying', 1)))", "index": 801}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Elizabeth, Joseph, Mason, Grace, Harper, Benjamin, Evelyn, and Abigail. As Elizabeth put it, \"Joseph is a knight\". Joseph asserted: \"Benjamin is a knight if and only if Grace is a knave\". Mason remarked, \"Evelyn is a knight if and only if Abigail is a knight\". According to Grace, \"Mason is a knave and Joseph is a knight\". \"Grace is a knave and Harper is a knight,\" Harper declared. In a statement by Benjamin: \"Joseph is a knave or Evelyn is a knave\". Evelyn remarked, \"If Evelyn is a knight then Grace is a knight\". Abigail said that Benjamin is a knight. So who is a knight and who is a knave?", "names": ["Elizabeth", "Joseph", "Mason", "Grace", "Harper", "Benjamin", "Evelyn", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false, true, false], "solution_text": "Elizabeth is a knight, Joseph is a knight, Mason is a knave, Grace is a knight, Harper is a knave, Benjamin is a knave, Evelyn is a knight, and Abigail is a knave.", "solution_text_format": "(1) Elizabeth is a knight\n(2) Joseph is a knight\n(3) Mason is a knave\n(4) Grace is a knight\n(5) Harper is a knave\n(6) Benjamin is a knave\n(7) Evelyn is a knight\n(8) Abigail is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Benjamin is a knight if and only if Grace is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Joseph is a knave or Evelyn is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of Benjamin that Joseph is a knave or Evelyn is a knave.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that If Evelyn is a knight then Grace is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Joseph is a knave or Evelyn is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Evelyn is a knight then Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Mason is a knave and Joseph is a knight.", "Mason cannot be a knight, because this would contradict the claim of Grace that Mason is a knave and Joseph is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Evelyn is a knight if and only if Abigail is a knight.", "Abigail cannot be a knight, because this would contradict the false claim of Mason that Evelyn is a knight if and only if Abigail is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Benjamin is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that Grace is a knave and Harper is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Grace is a knave and Harper is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('<=>', ('telling-truth', 5), ('lying', 3)), ('<=>', ('telling-truth', 6), ('telling-truth', 7)), ('and', ('lying', 2), ('telling-truth', 1)), ('and', ('lying', 3), ('telling-truth', 4)), ('or', ('lying', 1), ('lying', 6)), ('->', ('telling-truth', 6), ('telling-truth', 3)), ('telling-truth', 5))", "index": 802}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Grace, James, Lily, Riley, Chloe, Amelia, Sophia, and Mason. \"Lily is a knave,\" Grace mentioned. James said, \"Sophia is a knave or Chloe is a knave.\" \"Riley is a knight if and only if Mason is a knight\" - Lily. Riley asserted: \"If Lily is a knight then Lily is a knave\". According to Chloe, \"Lily is a knight if and only if Mason is a knight\". Amelia expressed that Mason is a knave if and only if Lily is a knave. \"Grace is a knight and Lily is a knave\" - Sophia. \"Chloe is a knave,\" Mason mentioned. So who is a knight and who is a knave?", "names": ["Grace", "James", "Lily", "Riley", "Chloe", "Amelia", "Sophia", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true, true, false], "solution_text": "Grace is a knight, James is a knave, Lily is a knave, Riley is a knight, Chloe is a knight, Amelia is a knight, Sophia is a knight, and Mason is a knave.", "solution_text_format": "(1) Grace is a knight\n(2) James is a knave\n(3) Lily is a knave\n(4) Riley is a knight\n(5) Chloe is a knight\n(6) Amelia is a knight\n(7) Sophia is a knight\n(8) Mason is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of Grace that Lily is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Mason is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that If Lily is a knight then Lily is a knave.", "Mason cannot be a knight, because this would contradict the false claim of Lily that Riley is a knight if and only if Mason is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Chloe is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Lily is a knight if and only if Mason is a knight.", "Assume James is a knight. No contradiction is found in their claim that Sophia is a knave or Chloe is a knave.", "Sophia cannot be a knight, because this would contradict the claim of James that Sophia is a knave or Chloe is a knave.", "Sophia cannot be a knave, because this would contradict the false claim of their own that Grace is a knight and Lily is a knave.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Sophia is a knave or Chloe is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Grace is a knight and Lily is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Mason is a knave if and only if Lily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('or', ('lying', 6), ('lying', 4)), ('<=>', ('telling-truth', 3), ('telling-truth', 7)), ('->', ('telling-truth', 2), ('lying', 2)), ('<=>', ('telling-truth', 2), ('telling-truth', 7)), ('<=>', ('lying', 7), ('lying', 2)), ('and', ('telling-truth', 0), ('lying', 2)), ('lying', 4))", "index": 803}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aurora, Aiden, James, Matthew, Amelia, Jackson, Sophia, and Emma. According to Aurora, \"James is a knave if and only if Aiden is a knight\". According to Aiden, \"Sophia is a knave\". James said, \"Aiden is a knave or Sophia is a knight.\" Matthew asserted: \"Matthew is a knight or James is a knave\". Amelia said that Matthew is a knight. \"Matthew is a knave if and only if Aurora is a knave,\" Jackson claimed. In Sophia's words: \"Amelia is a knight\". Emma noted, \"If Aiden is a knave then Jackson is a knight\". So who is a knight and who is a knave?", "names": ["Aurora", "Aiden", "James", "Matthew", "Amelia", "Jackson", "Sophia", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true, true, true], "solution_text": "Aurora is a knight, Aiden is a knave, James is a knight, Matthew is a knight, Amelia is a knight, Jackson is a knight, Sophia is a knight, and Emma is a knight.", "solution_text_format": "(1) Aurora is a knight\n(2) Aiden is a knave\n(3) James is a knight\n(4) Matthew is a knight\n(5) Amelia is a knight\n(6) Jackson is a knight\n(7) Sophia is a knight\n(8) Emma is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that James is a knave if and only if Aiden is a knight.", "Assume James is a knight. No contradiction is found in their claim that Aiden is a knave or Sophia is a knight.", "Aiden cannot be a knight, because this would contradict the claim of Aurora that James is a knave if and only if Aiden is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Sophia is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Amelia is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Matthew is a knight or James is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Matthew is a knave if and only if Aurora is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that If Aiden is a knave then Jackson is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('telling-truth', 1)), ('lying', 6), ('or', ('lying', 1), ('telling-truth', 6)), ('or', ('telling-truth', 3), ('lying', 2)), ('telling-truth', 3), ('<=>', ('lying', 3), ('lying', 0)), ('telling-truth', 4), ('->', ('lying', 1), ('telling-truth', 5)))", "index": 804}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aria, Alexander, Riley, Logan, Matthew, Victoria, William, and Emily. \"Riley is not a knight,\" Aria declared. \"Victoria is not a knight,\" Alexander mentioned. Riley asserted: \"Alexander is a knight or William is a knave\". Logan commented, \"Victoria is a knave and Matthew is a knight\". \"Alexander is a knave,\" Matthew declared. Victoria was heard saying, \"Riley is a knight and Aria is a knave\". William said, \"Riley is a knight and Logan is a knight.\" Emily commented, \"Logan is a knave and Alexander is a knight\". So who is a knight and who is a knave?", "names": ["Aria", "Alexander", "Riley", "Logan", "Matthew", "Victoria", "William", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true, false, false], "solution_text": "Aria is a knave, Alexander is a knave, Riley is a knight, Logan is a knave, Matthew is a knight, Victoria is a knight, William is a knave, and Emily is a knave.", "solution_text_format": "(1) Aria is a knave\n(2) Alexander is a knave\n(3) Riley is a knight\n(4) Logan is a knave\n(5) Matthew is a knight\n(6) Victoria is a knight\n(7) William is a knave\n(8) Emily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that Riley is not a knight.", "Riley cannot be a knight, because this would contradict the claim of Aria that Riley is not a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Alexander is a knight or William is a knave.", "Alexander cannot be a knight, because this would contradict the false claim of Riley that Alexander is a knight or William is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Victoria is not a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Riley is a knight and Aria is a knave.", "Victoria cannot be a knave, because this would contradict the false claim of Alexander that Victoria is not a knight.", "We have exhausted all possibilities for Victoria, Alexander, and Riley, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Riley is not a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Alexander is a knight or William is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Victoria is not a knight.", "Victoria cannot be a knight, because this would contradict the claim of Alexander that Victoria is not a knight.", "Victoria cannot be a knave, because this would contradict the false claim of their own that Riley is a knight and Aria is a knave.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Victoria is not a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Riley is a knight and Aria is a knave.", "William cannot be a knight, because this would contradict the claim of Riley that Alexander is a knight or William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Riley is a knight and Logan is a knight.", "Logan cannot be a knight, because this would contradict the claim of their own that Victoria is a knave and Matthew is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Victoria is a knave and Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Alexander is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Logan is a knave and Alexander is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Logan is a knave and Alexander is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('not', ('telling-truth', 5)), ('or', ('telling-truth', 1), ('lying', 6)), ('and', ('lying', 5), ('telling-truth', 4)), ('lying', 1), ('and', ('telling-truth', 2), ('lying', 0)), ('and', ('telling-truth', 2), ('telling-truth', 3)), ('and', ('lying', 3), ('telling-truth', 1)))", "index": 805}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sebastian, Olivia, Ella, James, Joseph, David, Ethan, and Logan. Sebastian noted, \"James is a knight\". Olivia asserted: \"David is not a knave\". Ella was heard saying, \"Olivia is a knight\". James commented, \"If Ethan is a knave then David is a knave\". \"Logan is a knight if and only if Olivia is a knave,\" Joseph claimed. As David put it, \"James is a knight if and only if Joseph is a knave\". Ethan was heard saying, \"Olivia is not a knave\". In a statement by Logan: \"Logan is a knight if and only if Joseph is a knave\". So who is a knight and who is a knave?", "names": ["Sebastian", "Olivia", "Ella", "James", "Joseph", "David", "Ethan", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true, true, true], "solution_text": "Sebastian is a knight, Olivia is a knight, Ella is a knight, James is a knight, Joseph is a knave, David is a knight, Ethan is a knight, and Logan is a knight.", "solution_text_format": "(1) Sebastian is a knight\n(2) Olivia is a knight\n(3) Ella is a knight\n(4) James is a knight\n(5) Joseph is a knave\n(6) David is a knight\n(7) Ethan is a knight\n(8) Logan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that James is a knight.", "Assume James is a knight. No contradiction is found in their claim that If Ethan is a knave then David is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Olivia is not a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that David is not a knave.", "Assume David is a knight. No contradiction is found in their claim that James is a knight if and only if Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of David that James is a knight if and only if Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Logan is a knight if and only if Olivia is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Logan is a knight if and only if Joseph is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Olivia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 3), ('not', ('lying', 5)), ('telling-truth', 1), ('->', ('lying', 6), ('lying', 5)), ('<=>', ('telling-truth', 7), ('lying', 1)), ('<=>', ('telling-truth', 3), ('lying', 4)), ('not', ('lying', 1)), ('<=>', ('telling-truth', 7), ('lying', 4)))", "index": 806}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Chloe, Emily, Samuel, Sofia, Oliver, Sebastian, Sophia, and Ethan. Chloe asserted: \"Sofia is a knight if and only if Samuel is a knight\". \"Sophia is a knave if and only if Sebastian is a knight,\" Emily declared. Samuel expressed that Oliver is a knave. In a statement by Sofia: \"Emily is a knight\". Oliver told you that Chloe is a knight if and only if Emily is a knave. \"If Oliver is a knight then Chloe is a knight\" - Sebastian. \"Ethan is a knight and Oliver is a knave,\" Sophia claimed. \"Sofia is a knave or Sebastian is a knight,\" Ethan claimed. So who is a knight and who is a knave?", "names": ["Chloe", "Emily", "Samuel", "Sofia", "Oliver", "Sebastian", "Sophia", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, true, true, true], "solution_text": "Chloe is a knave, Emily is a knave, Samuel is a knight, Sofia is a knave, Oliver is a knave, Sebastian is a knight, Sophia is a knight, and Ethan is a knight.", "solution_text_format": "(1) Chloe is a knave\n(2) Emily is a knave\n(3) Samuel is a knight\n(4) Sofia is a knave\n(5) Oliver is a knave\n(6) Sebastian is a knight\n(7) Sophia is a knight\n(8) Ethan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Sofia is a knight if and only if Samuel is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Sophia is a knave if and only if Sebastian is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Ethan is a knight and Oliver is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Sofia is a knave or Sebastian is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of Emily that Sophia is a knave if and only if Sebastian is a knight.", "Sebastian cannot be a knave, because this would contradict the false claim of their own that If Oliver is a knight then Chloe is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the claim of Sophia that Ethan is a knight and Oliver is a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Ethan is a knight and Oliver is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Sofia is a knave or Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Oliver is a knight then Chloe is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Chloe is a knight if and only if Emily is a knave.", "Oliver cannot be a knave, because this would contradict the false claim of Sophia that Ethan is a knight and Oliver is a knave.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the claim of Emily that Sophia is a knave if and only if Sebastian is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Sofia is a knave or Sebastian is a knight.", "Sebastian cannot be a knight, because this would contradict the false claim of Ethan that Sofia is a knave or Sebastian is a knight.", "Sebastian cannot be a knave, because this would contradict the claim of Emily that Sophia is a knave if and only if Sebastian is a knight.", "We have exhausted all possibilities for Sebastian, Ethan, and Sophia, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the claim of Sofia that Emily is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Emily is a knight.", "Emily cannot be a knight, because this would contradict the false claim of Sofia that Emily is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Sophia is a knave if and only if Sebastian is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Ethan is a knight and Oliver is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Sofia is a knave or Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Oliver is a knight then Chloe is a knight.", "Oliver cannot be a knight, because this would contradict the claim of Sophia that Ethan is a knight and Oliver is a knave.", "Oliver cannot be a knave, because this would contradict the false claim of their own that Chloe is a knight if and only if Emily is a knave.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the false claim of Emily that Sophia is a knave if and only if Sebastian is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the claim of Sophia that Ethan is a knight and Oliver is a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Ethan is a knight and Oliver is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Sofia is a knave or Sebastian is a knight.", "Sebastian cannot be a knight, because this would contradict the false claim of Emily that Sophia is a knave if and only if Sebastian is a knight.", "Sebastian cannot be a knave, because this would contradict the false claim of their own that If Oliver is a knight then Chloe is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the false claim of their own that Sofia is a knave or Sebastian is a knight.", "We have exhausted all possibilities for Ethan, Sophia, Emily, and Sofia, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Sofia is a knight if and only if Samuel is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Sophia is a knave if and only if Sebastian is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Ethan is a knight and Oliver is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Sofia is a knave or Sebastian is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of Emily that Sophia is a knave if and only if Sebastian is a knight.", "Sebastian cannot be a knave, because this would contradict the claim of Ethan that Sofia is a knave or Sebastian is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the claim of Sophia that Ethan is a knight and Oliver is a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Ethan is a knight and Oliver is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Sofia is a knave or Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Oliver is a knight then Chloe is a knight.", "Oliver cannot be a knight, because this would contradict the claim of Sebastian that If Oliver is a knight then Chloe is a knight.", "Oliver cannot be a knave, because this would contradict the false claim of their own that Chloe is a knight if and only if Emily is a knave.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the claim of Emily that Sophia is a knave if and only if Sebastian is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Sofia is a knave or Sebastian is a knight.", "Sebastian cannot be a knight, because this would contradict the false claim of Ethan that Sofia is a knave or Sebastian is a knight.", "Sebastian cannot be a knave, because this would contradict the claim of Emily that Sophia is a knave if and only if Sebastian is a knight.", "We have exhausted all possibilities for Sebastian, Ethan, and Sophia, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the claim of Sofia that Emily is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Emily is a knight.", "Emily cannot be a knight, because this would contradict the false claim of Sofia that Emily is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Sophia is a knave if and only if Sebastian is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Ethan is a knight and Oliver is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Sofia is a knave or Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Oliver is a knight then Chloe is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Chloe is a knight if and only if Emily is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Chloe is a knight if and only if Emily is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Oliver is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 3), ('telling-truth', 2)), ('<=>', ('lying', 6), ('telling-truth', 5)), ('lying', 4), ('telling-truth', 1), ('<=>', ('telling-truth', 0), ('lying', 1)), ('->', ('telling-truth', 4), ('telling-truth', 0)), ('and', ('telling-truth', 7), ('lying', 4)), ('or', ('lying', 3), ('telling-truth', 5)))", "index": 807}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sebastian, Victoria, Benjamin, Lucas, David, Scarlett, Olivia, and Elizabeth. Sebastian told you that If Elizabeth is a knight then David is a knight. \"Benjamin is a knave or Elizabeth is a knave\" - Victoria. Benjamin was heard saying, \"David is a knave or Lucas is a knave\". Lucas expressed that David is a knight and Scarlett is a knave. David asserted: \"Victoria is a knave\". As Scarlett put it, \"Benjamin is a knave\". Olivia was heard saying, \"Scarlett is a knave if and only if Elizabeth is a knave\". \"Elizabeth is a knight and David is a knave,\" Elizabeth mentioned. So who is a knight and who is a knave?", "names": ["Sebastian", "Victoria", "Benjamin", "Lucas", "David", "Scarlett", "Olivia", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false, true, false], "solution_text": "Sebastian is a knight, Victoria is a knight, Benjamin is a knight, Lucas is a knave, David is a knave, Scarlett is a knave, Olivia is a knight, and Elizabeth is a knave.", "solution_text_format": "(1) Sebastian is a knight\n(2) Victoria is a knight\n(3) Benjamin is a knight\n(4) Lucas is a knave\n(5) David is a knave\n(6) Scarlett is a knave\n(7) Olivia is a knight\n(8) Elizabeth is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that If Elizabeth is a knight then David is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Elizabeth is a knight and David is a knave.", "David cannot be a knight, because this would contradict the claim of Elizabeth that Elizabeth is a knight and David is a knave.", "David cannot be a knave, because this would contradict the claim of Sebastian that If Elizabeth is a knight then David is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Elizabeth is a knight and David is a knave.", "Assume David is a knight. No contradiction is found in their claim that Victoria is a knave.", "Victoria cannot be a knight, because this would contradict the claim of David that Victoria is a knave.", "Victoria cannot be a knave, because this would contradict the false claim of their own that Benjamin is a knave or Elizabeth is a knave.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Benjamin is a knave or Elizabeth is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that David is a knave or Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that David is a knight and Scarlett is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that David is a knight and Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Benjamin is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Scarlett is a knave if and only if Elizabeth is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 7), ('telling-truth', 4)), ('or', ('lying', 2), ('lying', 7)), ('or', ('lying', 4), ('lying', 3)), ('and', ('telling-truth', 4), ('lying', 5)), ('lying', 1), ('lying', 2), ('<=>', ('lying', 5), ('lying', 7)), ('and', ('telling-truth', 7), ('lying', 4)))", "index": 808}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Owen, Evelyn, Aurora, Lucas, Abigail, Elizabeth, Lily, and Sebastian. Owen commented, \"Lily is a knight or Lucas is a knight\". \"Lily is a knave if and only if Sebastian is a knight\" - Evelyn. Aurora said that Owen is a knight or Lucas is a knave. Lucas said, \"Evelyn is not a knave.\" According to Abigail, \"Lucas is a knave\". Elizabeth said that Aurora is a knight or Evelyn is a knave. Lily noted, \"Lucas is not a knight\". Sebastian remarked, \"Abigail is a knight\". So who is a knight and who is a knave?", "names": ["Owen", "Evelyn", "Aurora", "Lucas", "Abigail", "Elizabeth", "Lily", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true, true, true], "solution_text": "Owen is a knight, Evelyn is a knave, Aurora is a knight, Lucas is a knave, Abigail is a knight, Elizabeth is a knight, Lily is a knight, and Sebastian is a knight.", "solution_text_format": "(1) Owen is a knight\n(2) Evelyn is a knave\n(3) Aurora is a knight\n(4) Lucas is a knave\n(5) Abigail is a knight\n(6) Elizabeth is a knight\n(7) Lily is a knight\n(8) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Lily is a knight or Lucas is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Lucas is not a knight.", "Lucas cannot be a knight, because this would contradict the claim of Lily that Lucas is not a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Evelyn is not a knave.", "Evelyn cannot be a knight, because this would contradict the false claim of Lucas that Evelyn is not a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Lily is a knave if and only if Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Lucas is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Owen is a knight or Lucas is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Aurora is a knight or Evelyn is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 6), ('telling-truth', 3)), ('<=>', ('lying', 6), ('telling-truth', 7)), ('or', ('telling-truth', 0), ('lying', 3)), ('not', ('lying', 1)), ('lying', 3), ('or', ('telling-truth', 2), ('lying', 1)), ('not', ('telling-truth', 3)), ('telling-truth', 4))", "index": 809}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Abigail, Isabella, Lily, Joseph, Matthew, Evelyn, Logan, and Ella. Abigail told you that Ella is a knight if and only if Matthew is a knight. \"Lily is not a knave\" - Isabella. Lily commented, \"Isabella is a knave or Evelyn is a knight\". In a statement by Joseph: \"Abigail is a knave\". Matthew asserted: \"Joseph is not a knave\". \"Evelyn is a knight\" - Evelyn. Logan remarked, \"If Evelyn is a knight then Evelyn is a knave\". \"Abigail is not a knave,\" Ella claimed. So who is a knight and who is a knave?", "names": ["Abigail", "Isabella", "Lily", "Joseph", "Matthew", "Evelyn", "Logan", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true, false, false], "solution_text": "Abigail is a knave, Isabella is a knight, Lily is a knight, Joseph is a knight, Matthew is a knight, Evelyn is a knight, Logan is a knave, and Ella is a knave.", "solution_text_format": "(1) Abigail is a knave\n(2) Isabella is a knight\n(3) Lily is a knight\n(4) Joseph is a knight\n(5) Matthew is a knight\n(6) Evelyn is a knight\n(7) Logan is a knave\n(8) Ella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Ella is a knight if and only if Matthew is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Abigail is not a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Joseph is not a knave.", "Joseph cannot be a knight, because this would contradict the claim of their own that Abigail is a knave.", "Joseph cannot be a knave, because this would contradict the claim of Matthew that Joseph is not a knave.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the claim of Abigail that Ella is a knight if and only if Matthew is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the false claim of their own that Abigail is not a knave.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Ella is a knight if and only if Matthew is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Abigail is not a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Abigail is not a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Joseph is not a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Abigail is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Lily is not a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Isabella is a knave or Evelyn is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Evelyn is a knight.", "Logan cannot be a knight, because this would contradict the claim of their own that If Evelyn is a knight then Evelyn is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that If Evelyn is a knight then Evelyn is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 7), ('telling-truth', 4)), ('not', ('lying', 2)), ('or', ('lying', 1), ('telling-truth', 5)), ('lying', 0), ('not', ('lying', 3)), ('telling-truth', 5), ('->', ('telling-truth', 5), ('lying', 5)), ('not', ('lying', 0)))", "index": 810}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emily, Matthew, Ella, Logan, Jackson, Liam, Chloe, and Sebastian. In a statement by Emily: \"Matthew is a knight\". As Matthew put it, \"Liam is a knight\". Ella was heard saying, \"Jackson is a knight if and only if Matthew is a knave\". As Logan put it, \"Ella is a knave and Matthew is a knight\". As Jackson put it, \"If Logan is a knave then Liam is a knave\". Liam was heard saying, \"Sebastian is a knave if and only if Jackson is a knight\". \"Jackson is a knight\" - Chloe. Sebastian remarked, \"Emily is a knight\". So who is a knight and who is a knave?", "names": ["Emily", "Matthew", "Ella", "Logan", "Jackson", "Liam", "Chloe", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true, false, true], "solution_text": "Emily is a knight, Matthew is a knight, Ella is a knight, Logan is a knave, Jackson is a knave, Liam is a knight, Chloe is a knave, and Sebastian is a knight.", "solution_text_format": "(1) Emily is a knight\n(2) Matthew is a knight\n(3) Ella is a knight\n(4) Logan is a knave\n(5) Jackson is a knave\n(6) Liam is a knight\n(7) Chloe is a knave\n(8) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Liam is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Sebastian is a knave if and only if Jackson is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Emily is a knight.", "Jackson cannot be a knight, because this would contradict the claim of Liam that Sebastian is a knave if and only if Jackson is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that If Logan is a knave then Liam is a knave.", "Logan cannot be a knight, because this would contradict the false claim of Jackson that If Logan is a knave then Liam is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Ella is a knave and Matthew is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Matthew is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Jackson is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Jackson is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('telling-truth', 5), ('<=>', ('telling-truth', 4), ('lying', 1)), ('and', ('lying', 2), ('telling-truth', 1)), ('->', ('lying', 3), ('lying', 5)), ('<=>', ('lying', 7), ('telling-truth', 4)), ('telling-truth', 4), ('telling-truth', 0))", "index": 811}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Elizabeth, Lucas, Charlotte, Lily, James, Liam, Henry, and Alexander. Elizabeth said, \"Charlotte is a knight.\" Lucas said, \"James is a knight.\" Charlotte was heard saying, \"Lucas is a knave\". Lily stated, \"Elizabeth is a knight or Liam is a knight\". According to James, \"Alexander is a knight or Lily is a knight\". Liam said, \"Charlotte is a knight and Alexander is a knave.\" Henry commented, \"James is a knight and Lucas is a knight\". Alexander said, \"Lucas is not a knave.\" So who is a knight and who is a knave?", "names": ["Elizabeth", "Lucas", "Charlotte", "Lily", "James", "Liam", "Henry", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, false, true, true], "solution_text": "Elizabeth is a knave, Lucas is a knight, Charlotte is a knave, Lily is a knave, James is a knight, Liam is a knave, Henry is a knight, and Alexander is a knight.", "solution_text_format": "(1) Elizabeth is a knave\n(2) Lucas is a knight\n(3) Charlotte is a knave\n(4) Lily is a knave\n(5) James is a knight\n(6) Liam is a knave\n(7) Henry is a knight\n(8) Alexander is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the claim of Charlotte that Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that James is a knight.", "James cannot be a knight, because this would contradict the false claim of Lucas that James is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Alexander is a knight or Lily is a knight.", "Alexander cannot be a knight, because this would contradict the false claim of James that Alexander is a knight or Lily is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Lucas is not a knave.", "Lily cannot be a knight, because this would contradict the false claim of James that Alexander is a knight or Lily is a knight.", "Lily cannot be a knave, because this would contradict the false claim of their own that Elizabeth is a knight or Liam is a knight.", "We have exhausted all possibilities for Lily, Alexander, James, and Lucas, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the claim of Elizabeth that Charlotte is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of Elizabeth that Charlotte is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Lucas is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that James is a knight.", "Assume James is a knight. No contradiction is found in their claim that Alexander is a knight or Lily is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Lucas is not a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Elizabeth is a knight or Liam is a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that Charlotte is a knight and Alexander is a knave.", "Liam cannot be a knave, because this would contradict the claim of Lily that Elizabeth is a knight or Liam is a knight.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Elizabeth is a knight or Liam is a knight.", "Liam cannot be a knight, because this would contradict the false claim of Lily that Elizabeth is a knight or Liam is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Charlotte is a knight and Alexander is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that James is a knight and Lucas is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('telling-truth', 4), ('lying', 1), ('or', ('telling-truth', 0), ('telling-truth', 5)), ('or', ('telling-truth', 7), ('telling-truth', 3)), ('and', ('telling-truth', 2), ('lying', 7)), ('and', ('telling-truth', 4), ('telling-truth', 1)), ('not', ('lying', 1)))", "index": 812}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Penelope, Chloe, Mia, Amelia, Jackson, Aria, Jacob, and Michael. \"Jackson is a knight and Jackson is a knave\" - Penelope. According to Chloe, \"Amelia is a knave and Mia is a knight\". Mia expressed that Jackson is a knight if and only if Chloe is a knave. \"Chloe is a knight,\" Amelia claimed. Jackson remarked, \"Aria is a knight or Jackson is a knight\". \"Penelope is a knight or Chloe is a knight,\" Aria claimed. In Jacob's words: \"If Chloe is a knight then Amelia is a knave\". \"Penelope is a knave or Mia is a knight,\" Michael mentioned. So who is a knight and who is a knave?", "names": ["Penelope", "Chloe", "Mia", "Amelia", "Jackson", "Aria", "Jacob", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, false, true, true], "solution_text": "Penelope is a knave, Chloe is a knave, Mia is a knave, Amelia is a knave, Jackson is a knave, Aria is a knave, Jacob is a knight, and Michael is a knight.", "solution_text_format": "(1) Penelope is a knave\n(2) Chloe is a knave\n(3) Mia is a knave\n(4) Amelia is a knave\n(5) Jackson is a knave\n(6) Aria is a knave\n(7) Jacob is a knight\n(8) Michael is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Penelope cannot be a knight, because this would contradict the claim of their own that Jackson is a knight and Jackson is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Jackson is a knight and Jackson is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Aria is a knight or Jackson is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Penelope is a knight or Chloe is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Amelia is a knave and Mia is a knight.", "Amelia cannot be a knight, because this would contradict the claim of Chloe that Amelia is a knave and Mia is a knight.", "Amelia cannot be a knave, because this would contradict the false claim of their own that Chloe is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the claim of Aria that Penelope is a knight or Chloe is a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Penelope is a knight or Chloe is a knight.", "Chloe cannot be a knight, because this would contradict the false claim of Aria that Penelope is a knight or Chloe is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Amelia is a knave and Mia is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Chloe is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Chloe is a knight.", "Mia cannot be a knight, because this would contradict the false claim of Chloe that Amelia is a knave and Mia is a knight.", "Mia cannot be a knave, because this would contradict the false claim of their own that Jackson is a knight if and only if Chloe is a knave.", "We have exhausted all possibilities for Mia, Amelia, Chloe, and Aria, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Aria is a knight or Jackson is a knight.", "Aria cannot be a knight, because this would contradict the false claim of Jackson that Aria is a knight or Jackson is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Penelope is a knight or Chloe is a knight.", "Chloe cannot be a knight, because this would contradict the false claim of Aria that Penelope is a knight or Chloe is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Amelia is a knave and Mia is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Chloe is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Chloe is a knight.", "Mia cannot be a knight, because this would contradict the false claim of Chloe that Amelia is a knave and Mia is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Jackson is a knight if and only if Chloe is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that If Chloe is a knight then Amelia is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Penelope is a knave or Mia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 4), ('lying', 4)), ('and', ('lying', 3), ('telling-truth', 2)), ('<=>', ('telling-truth', 4), ('lying', 1)), ('telling-truth', 1), ('or', ('telling-truth', 5), ('telling-truth', 4)), ('or', ('telling-truth', 0), ('telling-truth', 1)), ('->', ('telling-truth', 1), ('lying', 3)), ('or', ('lying', 0), ('telling-truth', 2)))", "index": 813}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Benjamin, Oliver, Matthew, Mia, Riley, Aiden, Ella, and Owen. \"Mia is a knight or Oliver is a knight,\" Benjamin claimed. \"Mia is a knight,\" Oliver mentioned. As Matthew put it, \"If Ella is a knight then Riley is a knave\". Mia said that If Owen is a knight then Matthew is a knight. According to Riley, \"Ella is a knave and Ella is a knight\". Aiden remarked, \"Owen is a knight or Matthew is a knight\". Ella said that Oliver is a knight and Riley is a knave. Owen noted, \"Benjamin is a knave if and only if Mia is a knight\". So who is a knight and who is a knave?", "names": ["Benjamin", "Oliver", "Matthew", "Mia", "Riley", "Aiden", "Ella", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true, true, false], "solution_text": "Benjamin is a knight, Oliver is a knight, Matthew is a knight, Mia is a knight, Riley is a knave, Aiden is a knight, Ella is a knight, and Owen is a knave.", "solution_text_format": "(1) Benjamin is a knight\n(2) Oliver is a knight\n(3) Matthew is a knight\n(4) Mia is a knight\n(5) Riley is a knave\n(6) Aiden is a knight\n(7) Ella is a knight\n(8) Owen is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Mia is a knight or Oliver is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that If Owen is a knight then Matthew is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave if and only if Mia is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Benjamin is a knave if and only if Mia is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that If Ella is a knight then Riley is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Oliver is a knight and Riley is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Mia is a knight.", "Riley cannot be a knight, because this would contradict the claim of Matthew that If Ella is a knight then Riley is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Ella is a knave and Ella is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Owen is a knight or Matthew is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('telling-truth', 1)), ('telling-truth', 3), ('->', ('telling-truth', 6), ('lying', 4)), ('->', ('telling-truth', 7), ('telling-truth', 2)), ('and', ('lying', 6), ('telling-truth', 6)), ('or', ('telling-truth', 7), ('telling-truth', 2)), ('and', ('telling-truth', 1), ('lying', 4)), ('<=>', ('lying', 0), ('telling-truth', 3)))", "index": 814}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ava, Luke, Emma, Lucas, David, Abigail, Evelyn, and Elizabeth. \"Emma is a knave\" - Ava. Luke told you that Abigail is not a knave. \"Evelyn is a knight and Lucas is a knight,\" Emma claimed. Lucas remarked, \"Evelyn is not a knight\". David said, \"Lucas is a knight or Emma is a knight.\" Abigail expressed that Elizabeth is a knight. Evelyn told you that David is a knight or Abigail is a knight. Elizabeth noted, \"Abigail is a knight and Evelyn is a knight\". So who is a knight and who is a knave?", "names": ["Ava", "Luke", "Emma", "Lucas", "David", "Abigail", "Evelyn", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, true, true, true], "solution_text": "Ava is a knight, Luke is a knight, Emma is a knave, Lucas is a knave, David is a knave, Abigail is a knight, Evelyn is a knight, and Elizabeth is a knight.", "solution_text_format": "(1) Ava is a knight\n(2) Luke is a knight\n(3) Emma is a knave\n(4) Lucas is a knave\n(5) David is a knave\n(6) Abigail is a knight\n(7) Evelyn is a knight\n(8) Elizabeth is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of Ava that Emma is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Evelyn is a knight and Lucas is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that David is a knight or Abigail is a knight.", "Assume David is a knight. No contradiction is found in their claim that Lucas is a knight or Emma is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of Emma that Evelyn is a knight and Lucas is a knight.", "Lucas cannot be a knave, because this would contradict the claim of David that Lucas is a knight or Emma is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Lucas is a knight or Emma is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of Emma that Evelyn is a knight and Lucas is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Evelyn is not a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Abigail is a knight and Evelyn is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Abigail is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('not', ('lying', 5)), ('and', ('telling-truth', 6), ('telling-truth', 3)), ('not', ('telling-truth', 6)), ('or', ('telling-truth', 3), ('telling-truth', 2)), ('telling-truth', 7), ('or', ('telling-truth', 4), ('telling-truth', 5)), ('and', ('telling-truth', 5), ('telling-truth', 6)))", "index": 815}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Grace, Victoria, Liam, Olivia, James, Lucas, Scarlett, and Joseph. Grace stated, \"Liam is a knave\". Victoria stated, \"Olivia is a knight\". In a statement by Liam: \"Joseph is a knight or Grace is a knave\". Olivia stated, \"James is a knave or Victoria is a knight\". James said, \"Lucas is a knave if and only if Grace is a knave.\" In a statement by Lucas: \"Lucas is a knight if and only if Liam is a knave\". Scarlett asserted: \"If Lucas is a knight then James is a knave\". Joseph asserted: \"Liam is a knight if and only if James is a knave\". So who is a knight and who is a knave?", "names": ["Grace", "Victoria", "Liam", "Olivia", "James", "Lucas", "Scarlett", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false, true, false], "solution_text": "Grace is a knight, Victoria is a knight, Liam is a knave, Olivia is a knight, James is a knave, Lucas is a knave, Scarlett is a knight, and Joseph is a knave.", "solution_text_format": "(1) Grace is a knight\n(2) Victoria is a knight\n(3) Liam is a knave\n(4) Olivia is a knight\n(5) James is a knave\n(6) Lucas is a knave\n(7) Scarlett is a knight\n(8) Joseph is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of Grace that Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Joseph is a knight or Grace is a knave.", "Joseph cannot be a knight, because this would contradict the false claim of Liam that Joseph is a knight or Grace is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Liam is a knight if and only if James is a knave.", "James cannot be a knight, because this would contradict the false claim of Joseph that Liam is a knight if and only if James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Lucas is a knave if and only if Grace is a knave.", "Lucas cannot be a knight, because this would contradict the false claim of James that Lucas is a knave if and only if Grace is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Lucas is a knight if and only if Liam is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Olivia is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that James is a knave or Victoria is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Lucas is a knight then James is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('telling-truth', 3), ('or', ('telling-truth', 7), ('lying', 0)), ('or', ('lying', 4), ('telling-truth', 1)), ('<=>', ('lying', 5), ('lying', 0)), ('<=>', ('telling-truth', 5), ('lying', 2)), ('->', ('telling-truth', 5), ('lying', 4)), ('<=>', ('telling-truth', 2), ('lying', 4)))", "index": 816}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lucas, Benjamin, Amelia, Jacob, Jack, Penelope, Daniel, and Emily. Lucas said that If Lucas is a knight then Jack is a knight. Benjamin commented, \"Penelope is a knave\". Amelia asserted: \"Jack is a knave if and only if Jack is a knight\". Jacob told you that Lucas is not a knave. \"If Daniel is a knave then Benjamin is a knave,\" Jack mentioned. Penelope said that Lucas is a knight or Penelope is a knight. Daniel said, \"Amelia is a knight if and only if Jack is a knight.\" Emily noted, \"Daniel is a knight if and only if Penelope is a knave\". So who is a knight and who is a knave?", "names": ["Lucas", "Benjamin", "Amelia", "Jacob", "Jack", "Penelope", "Daniel", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true, false, true], "solution_text": "Lucas is a knight, Benjamin is a knave, Amelia is a knave, Jacob is a knight, Jack is a knight, Penelope is a knight, Daniel is a knave, and Emily is a knight.", "solution_text_format": "(1) Lucas is a knight\n(2) Benjamin is a knave\n(3) Amelia is a knave\n(4) Jacob is a knight\n(5) Jack is a knight\n(6) Penelope is a knight\n(7) Daniel is a knave\n(8) Emily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that If Lucas is a knight then Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that If Daniel is a knave then Benjamin is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Amelia is a knight if and only if Jack is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Jack is a knave if and only if Jack is a knight.", "Amelia cannot be a knave, because this would contradict the claim of Daniel that Amelia is a knight if and only if Jack is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Amelia is a knight if and only if Jack is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Jack is a knave if and only if Jack is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Jack is a knave if and only if Jack is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of Jack that If Daniel is a knave then Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Penelope is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Lucas is a knight or Penelope is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Lucas is not a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Daniel is a knight if and only if Penelope is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 0), ('telling-truth', 4)), ('lying', 5), ('<=>', ('lying', 4), ('telling-truth', 4)), ('not', ('lying', 0)), ('->', ('lying', 6), ('lying', 1)), ('or', ('telling-truth', 0), ('telling-truth', 5)), ('<=>', ('telling-truth', 2), ('telling-truth', 4)), ('<=>', ('telling-truth', 6), ('lying', 5)))", "index": 817}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Harper, Mason, Emily, Scarlett, William, Samuel, Alexander, and Olivia. Harper told you that William is a knight or Emily is a knave. Mason remarked, \"If Olivia is a knight then Scarlett is a knave\". As Emily put it, \"Olivia is a knight if and only if Mason is a knave\". As Scarlett put it, \"Emily is a knight if and only if Harper is a knave\". William said, \"Alexander is not a knave.\" As Samuel put it, \"William is not a knight\". Alexander commented, \"Olivia is a knave\". Olivia said that Alexander is a knight if and only if Samuel is a knight. So who is a knight and who is a knave?", "names": ["Harper", "Mason", "Emily", "Scarlett", "William", "Samuel", "Alexander", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false, true, false], "solution_text": "Harper is a knight, Mason is a knight, Emily is a knight, Scarlett is a knave, William is a knight, Samuel is a knave, Alexander is a knight, and Olivia is a knave.", "solution_text_format": "(1) Harper is a knight\n(2) Mason is a knight\n(3) Emily is a knight\n(4) Scarlett is a knave\n(5) William is a knight\n(6) Samuel is a knave\n(7) Alexander is a knight\n(8) Olivia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that William is a knight or Emily is a knave.", "Assume William is a knight. No contradiction is found in their claim that Alexander is not a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Alexander that Olivia is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Alexander is a knight if and only if Samuel is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that William is not a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that William is not a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Mason is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Olivia is a knight then Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Emily is a knight if and only if Harper is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Emily is a knight if and only if Harper is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('lying', 2)), ('->', ('telling-truth', 7), ('lying', 3)), ('<=>', ('telling-truth', 7), ('lying', 1)), ('<=>', ('telling-truth', 2), ('lying', 0)), ('not', ('lying', 6)), ('not', ('telling-truth', 4)), ('lying', 7), ('<=>', ('telling-truth', 6), ('telling-truth', 5)))", "index": 818}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Harper, Sebastian, Luke, Lily, Scarlett, Oliver, Grace, and Liam. In a statement by Harper: \"Luke is a knave if and only if Lily is a knight\". Sebastian expressed that Liam is a knave if and only if Oliver is a knight. Luke commented, \"Harper is not a knave\". Lily told you that If Grace is a knave then Grace is a knight. \"Grace is a knight and Harper is a knave\" - Scarlett. According to Oliver, \"Lily is a knight and Harper is a knight\". Grace said that Liam is a knight or Sebastian is a knight. As Liam put it, \"Scarlett is a knight or Harper is a knave\". So who is a knight and who is a knave?", "names": ["Harper", "Sebastian", "Luke", "Lily", "Scarlett", "Oliver", "Grace", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, false, false, false], "solution_text": "Harper is a knight, Sebastian is a knave, Luke is a knight, Lily is a knave, Scarlett is a knave, Oliver is a knave, Grace is a knave, and Liam is a knave.", "solution_text_format": "(1) Harper is a knight\n(2) Sebastian is a knave\n(3) Luke is a knight\n(4) Lily is a knave\n(5) Scarlett is a knave\n(6) Oliver is a knave\n(7) Grace is a knave\n(8) Liam is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that Luke is a knave if and only if Lily is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Harper is not a knave.", "Lily cannot be a knight, because this would contradict the claim of Harper that Luke is a knave if and only if Lily is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that If Grace is a knave then Grace is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Lily that If Grace is a knave then Grace is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Liam is a knight or Sebastian is a knight.", "Liam cannot be a knight, because this would contradict the false claim of Grace that Liam is a knight or Sebastian is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Scarlett is a knight or Harper is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Grace is a knight and Harper is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Grace is a knight and Harper is a knave.", "Sebastian cannot be a knight, because this would contradict the false claim of Grace that Liam is a knight or Sebastian is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Liam is a knave if and only if Oliver is a knight.", "Oliver cannot be a knight, because this would contradict the false claim of Sebastian that Liam is a knave if and only if Oliver is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Lily is a knight and Harper is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('telling-truth', 3)), ('<=>', ('lying', 7), ('telling-truth', 5)), ('not', ('lying', 0)), ('->', ('lying', 6), ('telling-truth', 6)), ('and', ('telling-truth', 6), ('lying', 0)), ('and', ('telling-truth', 3), ('telling-truth', 0)), ('or', ('telling-truth', 7), ('telling-truth', 1)), ('or', ('telling-truth', 4), ('lying', 0)))", "index": 819}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ella, Evelyn, Grace, Matthew, Aiden, Amelia, Aurora, and Emily. Ella said that If Aurora is a knave then Matthew is a knight. Evelyn remarked, \"Ella is not a knight\". According to Grace, \"Grace is a knight if and only if Ella is a knave\". Matthew noted, \"Emily is a knight\". \"Aurora is a knight or Amelia is a knave,\" Aiden declared. As Amelia put it, \"Matthew is a knave and Emily is a knave\". Aurora noted, \"Emily is a knight\". Emily expressed that Grace is a knave if and only if Amelia is a knight. So who is a knight and who is a knave?", "names": ["Ella", "Evelyn", "Grace", "Matthew", "Aiden", "Amelia", "Aurora", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true, false, false], "solution_text": "Ella is a knave, Evelyn is a knight, Grace is a knight, Matthew is a knave, Aiden is a knave, Amelia is a knight, Aurora is a knave, and Emily is a knave.", "solution_text_format": "(1) Ella is a knave\n(2) Evelyn is a knight\n(3) Grace is a knight\n(4) Matthew is a knave\n(5) Aiden is a knave\n(6) Amelia is a knight\n(7) Aurora is a knave\n(8) Emily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that If Aurora is a knave then Matthew is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Grace is a knave if and only if Amelia is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Grace is a knight if and only if Ella is a knave.", "Grace cannot be a knave, because this would contradict the false claim of their own that Grace is a knight if and only if Ella is a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the claim of Aurora that Emily is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Emily is a knight.", "Emily cannot be a knight, because this would contradict the false claim of Aurora that Emily is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Grace is a knave if and only if Amelia is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Grace is a knight if and only if Ella is a knave.", "Grace cannot be a knave, because this would contradict the false claim of their own that Grace is a knight if and only if Ella is a knave.", "We have exhausted all possibilities for Grace, Emily, and Aurora, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that If Aurora is a knave then Matthew is a knight.", "Aurora cannot be a knight, because this would contradict the false claim of Ella that If Aurora is a knave then Matthew is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Emily is a knight.", "Emily cannot be a knight, because this would contradict the false claim of Aurora that Emily is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Grace is a knave if and only if Amelia is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Grace is a knight if and only if Ella is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Matthew is a knave and Emily is a knave.", "Matthew cannot be a knight, because this would contradict the false claim of Ella that If Aurora is a knave then Matthew is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Emily is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Ella is not a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Aurora is a knight or Amelia is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Aurora is a knight or Amelia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 6), ('telling-truth', 3)), ('not', ('telling-truth', 0)), ('<=>', ('telling-truth', 2), ('lying', 0)), ('telling-truth', 7), ('or', ('telling-truth', 6), ('lying', 5)), ('and', ('lying', 3), ('lying', 7)), ('telling-truth', 7), ('<=>', ('lying', 2), ('telling-truth', 5)))", "index": 820}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emily, Aurora, Samuel, Sophia, Jack, Ethan, Liam, and Riley. \"If Sophia is a knight then Aurora is a knave,\" Emily declared. Aurora expressed that Jack is not a knight. As Samuel put it, \"Ethan is a knight and Jack is a knave\". Sophia stated, \"If Sophia is a knight then Emily is a knave\". \"Aurora is a knave or Ethan is a knave,\" Jack claimed. Ethan said that If Riley is a knave then Samuel is a knight. Liam was heard saying, \"Sophia is a knave if and only if Jack is a knave\". As Riley put it, \"Ethan is a knight or Samuel is a knight\". So who is a knight and who is a knave?", "names": ["Emily", "Aurora", "Samuel", "Sophia", "Jack", "Ethan", "Liam", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true, false, true], "solution_text": "Emily is a knave, Aurora is a knight, Samuel is a knight, Sophia is a knight, Jack is a knave, Ethan is a knight, Liam is a knave, and Riley is a knight.", "solution_text_format": "(1) Emily is a knave\n(2) Aurora is a knight\n(3) Samuel is a knight\n(4) Sophia is a knight\n(5) Jack is a knave\n(6) Ethan is a knight\n(7) Liam is a knave\n(8) Riley is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that If Sophia is a knight then Aurora is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that If Sophia is a knight then Emily is a knave.", "Sophia cannot be a knave, because this would contradict the false claim of their own that If Sophia is a knight then Emily is a knave.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that If Sophia is a knight then Aurora is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that If Sophia is a knight then Emily is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Jack is not a knight.", "Jack cannot be a knight, because this would contradict the claim of Aurora that Jack is not a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Aurora is a knave or Ethan is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that If Riley is a knave then Samuel is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Ethan is a knight or Samuel is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Ethan is a knight and Jack is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Sophia is a knave if and only if Jack is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Sophia is a knave if and only if Jack is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('lying', 1)), ('not', ('telling-truth', 4)), ('and', ('telling-truth', 5), ('lying', 4)), ('->', ('telling-truth', 3), ('lying', 0)), ('or', ('lying', 1), ('lying', 5)), ('->', ('lying', 7), ('telling-truth', 2)), ('<=>', ('lying', 3), ('lying', 4)), ('or', ('telling-truth', 5), ('telling-truth', 2)))", "index": 821}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Benjamin, Lily, Emma, Victoria, Emily, Lucas, Daniel, and Alexander. \"Victoria is a knight if and only if Daniel is a knight,\" Benjamin mentioned. Lily noted, \"Lucas is a knight if and only if Emma is a knight\". According to Emma, \"Emily is a knave and Lucas is a knight\". Victoria told you that Emily is a knave. \"Lucas is a knight\" - Emily. Lucas asserted: \"Lily is a knight and Emma is a knight\". Daniel said, \"Lily is a knight.\" Alexander commented, \"Lily is a knave or Benjamin is a knight\". So who is a knight and who is a knave?", "names": ["Benjamin", "Lily", "Emma", "Victoria", "Emily", "Lucas", "Daniel", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false, true, true], "solution_text": "Benjamin is a knight, Lily is a knight, Emma is a knave, Victoria is a knight, Emily is a knave, Lucas is a knave, Daniel is a knight, and Alexander is a knight.", "solution_text_format": "(1) Benjamin is a knight\n(2) Lily is a knight\n(3) Emma is a knave\n(4) Victoria is a knight\n(5) Emily is a knave\n(6) Lucas is a knave\n(7) Daniel is a knight\n(8) Alexander is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Daniel is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of Victoria that Emily is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of Emily that Lucas is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Lily is a knight and Emma is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Lucas is a knight if and only if Emma is a knight.", "Emma cannot be a knight, because this would contradict the claim of Lily that Lucas is a knight if and only if Emma is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Emily is a knave and Lucas is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Lily is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Lily is a knave or Benjamin is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 3), ('telling-truth', 6)), ('<=>', ('telling-truth', 5), ('telling-truth', 2)), ('and', ('lying', 4), ('telling-truth', 5)), ('lying', 4), ('telling-truth', 5), ('and', ('telling-truth', 1), ('telling-truth', 2)), ('telling-truth', 1), ('or', ('lying', 1), ('telling-truth', 0)))", "index": 822}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sebastian, Aria, Harper, Avery, Lucas, Daniel, James, and Logan. Sebastian was heard saying, \"Lucas is a knave and Lucas is a knight\". Aria was heard saying, \"James is a knave if and only if Aria is a knight\". \"Daniel is a knave if and only if Harper is a knight\" - Harper. Avery said that Daniel is a knight if and only if Sebastian is a knave. Lucas asserted: \"Avery is a knight if and only if Aria is a knave\". Daniel noted, \"Sebastian is a knight and Daniel is a knight\". As James put it, \"If Harper is a knight then Aria is a knight\". Logan commented, \"Lucas is a knight and James is a knight\". So who is a knight and who is a knave?", "names": ["Sebastian", "Aria", "Harper", "Avery", "Lucas", "Daniel", "James", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, false, false, false], "solution_text": "Sebastian is a knave, Aria is a knave, Harper is a knight, Avery is a knave, Lucas is a knave, Daniel is a knave, James is a knave, and Logan is a knave.", "solution_text_format": "(1) Sebastian is a knave\n(2) Aria is a knave\n(3) Harper is a knight\n(4) Avery is a knave\n(5) Lucas is a knave\n(6) Daniel is a knave\n(7) James is a knave\n(8) Logan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Sebastian cannot be a knight, because this would contradict the claim of their own that Lucas is a knave and Lucas is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Lucas is a knave and Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Avery is a knight if and only if Aria is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Daniel is a knight if and only if Sebastian is a knave.", "Daniel cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight and Daniel is a knight.", "Daniel cannot be a knave, because this would contradict the claim of Avery that Daniel is a knight if and only if Sebastian is a knave.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Daniel is a knight if and only if Sebastian is a knave.", "Daniel cannot be a knight, because this would contradict the false claim of Avery that Daniel is a knight if and only if Sebastian is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Sebastian is a knight and Daniel is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that James is a knave if and only if Aria is a knight.", "James cannot be a knight, because this would contradict the claim of Aria that James is a knave if and only if Aria is a knight.", "James cannot be a knave, because this would contradict the false claim of their own that If Harper is a knight then Aria is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Aria.", "Aria cannot be a knave, because this would contradict the claim of Lucas that Avery is a knight if and only if Aria is a knave.", "We have exhausted all possibilities for Aria, Daniel, and Avery, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Avery is a knight if and only if Aria is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Daniel is a knight if and only if Sebastian is a knave.", "Daniel cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight and Daniel is a knight.", "Daniel cannot be a knave, because this would contradict the claim of Avery that Daniel is a knight if and only if Sebastian is a knave.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Daniel is a knight if and only if Sebastian is a knave.", "Daniel cannot be a knight, because this would contradict the false claim of Avery that Daniel is a knight if and only if Sebastian is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Sebastian is a knight and Daniel is a knight.", "Aria cannot be a knight, because this would contradict the false claim of Lucas that Avery is a knight if and only if Aria is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that James is a knave if and only if Aria is a knight.", "James cannot be a knight, because this would contradict the false claim of Aria that James is a knave if and only if Aria is a knight.", "Assume James is a knave. No contradiction is found in their false claim that If Harper is a knight then Aria is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Daniel is a knave if and only if Harper is a knight.", "Logan cannot be a knight, because this would contradict the claim of their own that Lucas is a knight and James is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Lucas is a knight and James is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('telling-truth', 4)), ('<=>', ('lying', 6), ('telling-truth', 1)), ('<=>', ('lying', 5), ('telling-truth', 2)), ('<=>', ('telling-truth', 5), ('lying', 0)), ('<=>', ('telling-truth', 3), ('lying', 1)), ('and', ('telling-truth', 0), ('telling-truth', 5)), ('->', ('telling-truth', 2), ('telling-truth', 1)), ('and', ('telling-truth', 4), ('telling-truth', 6)))", "index": 823}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: David, Alexander, Benjamin, Mason, Sofia, Emily, Elizabeth, and Harper. David was heard saying, \"Benjamin is not a knave\". Alexander said that Alexander is a knight or David is a knave. \"Mason is not a knave,\" Benjamin claimed. Mason commented, \"Harper is a knave\". Sofia remarked, \"Elizabeth is a knight and Alexander is a knave\". Emily said that Mason is a knight and David is a knave. \"Alexander is not a knave,\" Elizabeth declared. \"Sofia is a knave or Benjamin is a knave\" - Harper. So who is a knight and who is a knave?", "names": ["David", "Alexander", "Benjamin", "Mason", "Sofia", "Emily", "Elizabeth", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, false, true, true], "solution_text": "David is a knave, Alexander is a knight, Benjamin is a knave, Mason is a knave, Sofia is a knave, Emily is a knave, Elizabeth is a knight, and Harper is a knight.", "solution_text_format": "(1) David is a knave\n(2) Alexander is a knight\n(3) Benjamin is a knave\n(4) Mason is a knave\n(5) Sofia is a knave\n(6) Emily is a knave\n(7) Elizabeth is a knight\n(8) Harper is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Benjamin is not a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Mason is not a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Harper is a knave.", "Harper cannot be a knight, because this would contradict the claim of Mason that Harper is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Sofia is a knave or Benjamin is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Elizabeth is a knight and Alexander is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Alexander is not a knave.", "Alexander cannot be a knight, because this would contradict the claim of Sofia that Elizabeth is a knight and Alexander is a knave.", "Alexander cannot be a knave, because this would contradict the claim of Elizabeth that Alexander is not a knave.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Elizabeth.", "Elizabeth cannot be a knave, because this would contradict the claim of Sofia that Elizabeth is a knight and Alexander is a knave.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Sofia.", "Sofia cannot be a knave, because this would contradict the false claim of Harper that Sofia is a knave or Benjamin is a knave.", "We have exhausted all possibilities for Sofia and Harper, so let us go back and reconsider Mason.", "Mason cannot be a knave, because this would contradict the claim of Benjamin that Mason is not a knave.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the claim of David that Benjamin is not a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Benjamin is not a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of David that Benjamin is not a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Mason is not a knave.", "Mason cannot be a knight, because this would contradict the false claim of Benjamin that Mason is not a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Harper is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Sofia is a knave or Benjamin is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Elizabeth is a knight and Alexander is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Alexander is not a knave.", "Alexander cannot be a knight, because this would contradict the claim of Sofia that Elizabeth is a knight and Alexander is a knave.", "Alexander cannot be a knave, because this would contradict the false claim of their own that Alexander is a knight or David is a knave.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Elizabeth.", "Elizabeth cannot be a knave, because this would contradict the claim of Sofia that Elizabeth is a knight and Alexander is a knave.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Elizabeth is a knight and Alexander is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Alexander is not a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Alexander is a knight or David is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Mason is a knight and David is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Mason is a knight and David is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('or', ('telling-truth', 1), ('lying', 0)), ('not', ('lying', 3)), ('lying', 7), ('and', ('telling-truth', 6), ('lying', 1)), ('and', ('telling-truth', 3), ('lying', 0)), ('not', ('lying', 1)), ('or', ('lying', 4), ('lying', 2)))", "index": 824}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Charlotte, Ava, Henry, Matthew, Mia, Riley, Emma, and Luke. Charlotte expressed that If Luke is a knight then Mia is a knave. Ava expressed that Charlotte is a knight if and only if Henry is a knave. As Henry put it, \"Luke is not a knave\". \"Henry is a knight and Luke is a knave,\" Matthew claimed. Mia said, \"Emma is not a knave.\" Riley told you that Matthew is not a knight. According to Emma, \"Matthew is a knave\". \"Riley is a knave or Emma is a knight,\" Luke mentioned. So who is a knight and who is a knave?", "names": ["Charlotte", "Ava", "Henry", "Matthew", "Mia", "Riley", "Emma", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true, true, true], "solution_text": "Charlotte is a knave, Ava is a knight, Henry is a knight, Matthew is a knave, Mia is a knight, Riley is a knight, Emma is a knight, and Luke is a knight.", "solution_text_format": "(1) Charlotte is a knave\n(2) Ava is a knight\n(3) Henry is a knight\n(4) Matthew is a knave\n(5) Mia is a knight\n(6) Riley is a knight\n(7) Emma is a knight\n(8) Luke is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that If Luke is a knight then Mia is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Riley is a knave or Emma is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Matthew is not a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Henry is a knight and Luke is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Henry is a knight and Luke is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Luke is not a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Matthew is a knave.", "Mia cannot be a knight, because this would contradict the claim of Charlotte that If Luke is a knight then Mia is a knave.", "Mia cannot be a knave, because this would contradict the false claim of their own that Emma is not a knave.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Emma.", "Emma cannot be a knave, because this would contradict the false claim of their own that Matthew is a knave.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the false claim of their own that Luke is not a knave.", "We have exhausted all possibilities for Henry and Matthew, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Matthew is not a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Henry is a knight and Luke is a knave.", "Matthew cannot be a knave, because this would contradict the false claim of Riley that Matthew is not a knight.", "We have exhausted all possibilities for Matthew and Riley, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Riley is a knave or Emma is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Matthew is not a knight.", "Matthew cannot be a knight, because this would contradict the claim of Riley that Matthew is not a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Henry is a knight and Luke is a knave.", "Henry cannot be a knight, because this would contradict the claim of their own that Luke is not a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Luke is not a knave.", "Emma cannot be a knight, because this would contradict the false claim of Luke that Riley is a knave or Emma is a knight.", "Emma cannot be a knave, because this would contradict the false claim of their own that Matthew is a knave.", "We have exhausted all possibilities for Emma, Henry, and Matthew, so let us go back and reconsider Riley.", "Riley cannot be a knave, because this would contradict the false claim of Luke that Riley is a knave or Emma is a knight.", "We have exhausted all possibilities for Riley and Luke, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that If Luke is a knight then Mia is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Riley is a knave or Emma is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Matthew is not a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Henry is a knight and Luke is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Henry is a knight and Luke is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Luke is not a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Matthew is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Emma is not a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Charlotte is a knight if and only if Henry is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 7), ('lying', 4)), ('<=>', ('telling-truth', 0), ('lying', 2)), ('not', ('lying', 7)), ('and', ('telling-truth', 2), ('lying', 7)), ('not', ('lying', 6)), ('not', ('telling-truth', 3)), ('lying', 3), ('or', ('lying', 5), ('telling-truth', 6)))", "index": 825}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Elizabeth, Lily, Owen, Lucas, Jack, David, Mason, and Isabella. Elizabeth commented, \"David is a knave or Lily is a knave\". In a statement by Lily: \"If Owen is a knight then David is a knave\". Owen said that David is a knave and Jack is a knave. Lucas remarked, \"Lily is a knave or Elizabeth is a knave\". \"Mason is not a knave,\" Jack mentioned. David asserted: \"Owen is a knave\". Mason remarked, \"If Isabella is a knight then Isabella is a knave\". As Isabella put it, \"Lily is a knight and Lily is a knave\". So who is a knight and who is a knave?", "names": ["Elizabeth", "Lily", "Owen", "Lucas", "Jack", "David", "Mason", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true, true, false], "solution_text": "Elizabeth is a knave, Lily is a knight, Owen is a knave, Lucas is a knight, Jack is a knight, David is a knight, Mason is a knight, and Isabella is a knave.", "solution_text_format": "(1) Elizabeth is a knave\n(2) Lily is a knight\n(3) Owen is a knave\n(4) Lucas is a knight\n(5) Jack is a knight\n(6) David is a knight\n(7) Mason is a knight\n(8) Isabella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that David is a knave or Lily is a knave.", "Assume David is a knight. No contradiction is found in their claim that Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that David is a knave and Jack is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that David is a knave and Jack is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Mason is not a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Isabella is a knight then Isabella is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Mason that If Isabella is a knight then Isabella is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Lily is a knight and Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of Elizabeth that David is a knave or Lily is a knave.", "Lily cannot be a knave, because this would contradict the false claim of their own that If Owen is a knight then David is a knave.", "We have exhausted all possibilities for Lily and Isabella, so let us go back and reconsider Mason.", "Mason cannot be a knave, because this would contradict the claim of Jack that Mason is not a knave.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Mason is not a knave.", "Mason cannot be a knight, because this would contradict the false claim of Jack that Mason is not a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that If Isabella is a knight then Isabella is a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that Lily is a knight and Lily is a knave.", "Isabella cannot be a knave, because this would contradict the false claim of Mason that If Isabella is a knight then Isabella is a knave.", "We have exhausted all possibilities for Isabella, Mason, Jack, and Owen, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Owen is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that David is a knave and Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of Owen that David is a knave and Jack is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Mason is not a knave.", "Mason cannot be a knight, because this would contradict the false claim of Jack that Mason is not a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that If Isabella is a knight then Isabella is a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that Lily is a knight and Lily is a knave.", "Isabella cannot be a knave, because this would contradict the false claim of Mason that If Isabella is a knight then Isabella is a knave.", "We have exhausted all possibilities for Isabella, Mason, and Jack, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the false claim of David that Owen is a knave.", "We have exhausted all possibilities for Owen and David, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that David is a knave or Lily is a knave.", "Assume David is a knight. No contradiction is found in their claim that Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that David is a knave and Jack is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that David is a knave and Jack is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Mason is not a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Isabella is a knight then Isabella is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Mason that If Isabella is a knight then Isabella is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Lily is a knight and Lily is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that If Owen is a knight then David is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Lily is a knave or Elizabeth is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 5), ('lying', 1)), ('->', ('telling-truth', 2), ('lying', 5)), ('and', ('lying', 5), ('lying', 4)), ('or', ('lying', 1), ('lying', 0)), ('not', ('lying', 6)), ('lying', 2), ('->', ('telling-truth', 7), ('lying', 7)), ('and', ('telling-truth', 1), ('lying', 1)))", "index": 826}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Michael, Sophia, William, Avery, Penelope, Logan, Jack, and Daniel. Michael commented, \"William is a knave or Avery is a knight\". Sophia remarked, \"If Jack is a knight then William is a knight\". William said, \"Logan is a knave and Avery is a knave.\" Avery commented, \"Michael is a knight\". As Penelope put it, \"Sophia is a knave and Logan is a knight\". Logan commented, \"William is a knave or Sophia is a knave\". \"Michael is a knave or Penelope is a knave\" - Jack. Daniel noted, \"Logan is a knight and Michael is a knight\". So who is a knight and who is a knave?", "names": ["Michael", "Sophia", "William", "Avery", "Penelope", "Logan", "Jack", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false, true, false], "solution_text": "Michael is a knave, Sophia is a knight, William is a knight, Avery is a knave, Penelope is a knave, Logan is a knave, Jack is a knight, and Daniel is a knave.", "solution_text_format": "(1) Michael is a knave\n(2) Sophia is a knight\n(3) William is a knight\n(4) Avery is a knave\n(5) Penelope is a knave\n(6) Logan is a knave\n(7) Jack is a knight\n(8) Daniel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that William is a knave or Avery is a knight.", "Assume William is a knight. No contradiction is found in their claim that Logan is a knave and Avery is a knave.", "Logan cannot be a knight, because this would contradict the claim of William that Logan is a knave and Avery is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that William is a knave or Sophia is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that If Jack is a knight then William is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Michael is a knave or Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Sophia is a knave and Logan is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Sophia is a knave and Logan is a knight.", "Avery cannot be a knight, because this would contradict the claim of William that Logan is a knave and Avery is a knave.", "Avery cannot be a knave, because this would contradict the claim of Michael that William is a knave or Avery is a knight.", "We have exhausted all possibilities for Avery and Penelope, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Michael is a knave or Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Sophia is a knave and Logan is a knight.", "Penelope cannot be a knave, because this would contradict the false claim of Jack that Michael is a knave or Penelope is a knave.", "We have exhausted all possibilities for Penelope and Jack, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the false claim of their own that If Jack is a knight then William is a knight.", "We have exhausted all possibilities for Sophia and Logan, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Logan is a knave and Avery is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that William is a knave or Sophia is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that If Jack is a knight then William is a knight.", "Jack cannot be a knight, because this would contradict the claim of Sophia that If Jack is a knight then William is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Michael is a knave or Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Sophia is a knave and Logan is a knight.", "Penelope cannot be a knave, because this would contradict the false claim of Jack that Michael is a knave or Penelope is a knave.", "We have exhausted all possibilities for Penelope and Jack, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that If Jack is a knight then William is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Michael is a knave or Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the claim of Jack that Michael is a knave or Penelope is a knave.", "Penelope cannot be a knave, because this would contradict the false claim of their own that Sophia is a knave and Logan is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the false claim of Sophia that If Jack is a knight then William is a knight.", "We have exhausted all possibilities for Jack and Sophia, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the false claim of their own that William is a knave or Sophia is a knave.", "We have exhausted all possibilities for Logan and William, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that William is a knave or Avery is a knight.", "Assume William is a knight. No contradiction is found in their claim that Logan is a knave and Avery is a knave.", "Logan cannot be a knight, because this would contradict the claim of William that Logan is a knave and Avery is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that William is a knave or Sophia is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that If Jack is a knight then William is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Michael is a knave or Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Sophia is a knave and Logan is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Sophia is a knave and Logan is a knight.", "Avery cannot be a knight, because this would contradict the false claim of Michael that William is a knave or Avery is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Michael is a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that Logan is a knight and Michael is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Logan is a knight and Michael is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('telling-truth', 3)), ('->', ('telling-truth', 6), ('telling-truth', 2)), ('and', ('lying', 5), ('lying', 3)), ('telling-truth', 0), ('and', ('lying', 1), ('telling-truth', 5)), ('or', ('lying', 2), ('lying', 1)), ('or', ('lying', 0), ('lying', 4)), ('and', ('telling-truth', 5), ('telling-truth', 0)))", "index": 827}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mia, Samuel, Elizabeth, Jackson, Lily, Scarlett, Victoria, and Sophia. Mia stated, \"Elizabeth is a knave\". Samuel noted, \"Sophia is a knight\". Elizabeth told you that Victoria is not a knave. In a statement by Jackson: \"Lily is a knight or Mia is a knave\". Lily expressed that Elizabeth is a knave or Jackson is a knave. Scarlett asserted: \"Jackson is not a knight\". \"Scarlett is a knight if and only if Jackson is a knight,\" Victoria mentioned. Sophia asserted: \"Jackson is a knave or Scarlett is a knight\". So who is a knight and who is a knave?", "names": ["Mia", "Samuel", "Elizabeth", "Jackson", "Lily", "Scarlett", "Victoria", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false, false, false], "solution_text": "Mia is a knight, Samuel is a knave, Elizabeth is a knave, Jackson is a knight, Lily is a knight, Scarlett is a knave, Victoria is a knave, and Sophia is a knave.", "solution_text_format": "(1) Mia is a knight\n(2) Samuel is a knave\n(3) Elizabeth is a knave\n(4) Jackson is a knight\n(5) Lily is a knight\n(6) Scarlett is a knave\n(7) Victoria is a knave\n(8) Sophia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Elizabeth is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of Mia that Elizabeth is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Victoria is not a knave.", "Victoria cannot be a knight, because this would contradict the false claim of Elizabeth that Victoria is not a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Scarlett is a knight if and only if Jackson is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Jackson is not a knight.", "Jackson cannot be a knight, because this would contradict the claim of Scarlett that Jackson is not a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Lily is a knight or Mia is a knave.", "Lily cannot be a knight, because this would contradict the false claim of Jackson that Lily is a knight or Mia is a knave.", "Lily cannot be a knave, because this would contradict the false claim of their own that Elizabeth is a knave or Jackson is a knave.", "We have exhausted all possibilities for Lily and Jackson, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Jackson is not a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Lily is a knight or Mia is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Elizabeth is a knave or Jackson is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Sophia is a knight.", "Sophia cannot be a knight, because this would contradict the claim of their own that Jackson is a knave or Scarlett is a knight.", "Sophia cannot be a knave, because this would contradict the claim of Samuel that Sophia is a knight.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Sophia is a knight.", "Sophia cannot be a knight, because this would contradict the false claim of Samuel that Sophia is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Jackson is a knave or Scarlett is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('telling-truth', 7), ('not', ('lying', 6)), ('or', ('telling-truth', 4), ('lying', 0)), ('or', ('lying', 2), ('lying', 3)), ('not', ('telling-truth', 3)), ('<=>', ('telling-truth', 5), ('telling-truth', 3)), ('or', ('lying', 3), ('telling-truth', 5)))", "index": 828}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ava, Amelia, Isabella, Lily, Ella, Owen, Logan, and Olivia. Ava told you that Amelia is a knave and Owen is a knight. Amelia commented, \"Ella is a knave or Logan is a knave\". As Isabella put it, \"Olivia is a knave if and only if Owen is a knight\". In a statement by Lily: \"If Ava is a knave then Olivia is a knave\". Ella said that Logan is a knave or Amelia is a knave. Owen asserted: \"Ella is a knave and Ava is a knave\". Logan remarked, \"Amelia is a knight or Isabella is a knave\". \"Logan is a knight if and only if Ella is a knight\" - Olivia. So who is a knight and who is a knave?", "names": ["Ava", "Amelia", "Isabella", "Lily", "Ella", "Owen", "Logan", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true, true, false], "solution_text": "Ava is a knave, Amelia is a knight, Isabella is a knight, Lily is a knight, Ella is a knave, Owen is a knight, Logan is a knight, and Olivia is a knave.", "solution_text_format": "(1) Ava is a knave\n(2) Amelia is a knight\n(3) Isabella is a knight\n(4) Lily is a knight\n(5) Ella is a knave\n(6) Owen is a knight\n(7) Logan is a knight\n(8) Olivia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Amelia is a knave and Owen is a knight.", "Amelia cannot be a knight, because this would contradict the claim of Ava that Amelia is a knave and Owen is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Ella is a knave or Logan is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Logan is a knave or Amelia is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Amelia is a knight or Isabella is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Logan that Amelia is a knight or Isabella is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Olivia is a knave if and only if Owen is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Logan is a knight if and only if Ella is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Ella is a knave and Ava is a knave.", "Owen cannot be a knave, because this would contradict the claim of Ava that Amelia is a knave and Owen is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the false claim of their own that Logan is a knight if and only if Ella is a knight.", "We have exhausted all possibilities for Olivia and Isabella, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the false claim of Amelia that Ella is a knave or Logan is a knave.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the false claim of Amelia that Ella is a knave or Logan is a knave.", "We have exhausted all possibilities for Ella and Amelia, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Amelia is a knave and Owen is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Ella is a knave or Logan is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Logan is a knave or Amelia is a knave.", "Logan cannot be a knight, because this would contradict the claim of Amelia that Ella is a knave or Logan is a knave.", "Logan cannot be a knave, because this would contradict the false claim of their own that Amelia is a knight or Isabella is a knave.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Logan is a knave or Amelia is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Amelia is a knight or Isabella is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Olivia is a knave if and only if Owen is a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that Logan is a knight if and only if Ella is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Logan is a knight if and only if Ella is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Ella is a knave and Ava is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that If Ava is a knave then Olivia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 1), ('telling-truth', 5)), ('or', ('lying', 4), ('lying', 6)), ('<=>', ('lying', 7), ('telling-truth', 5)), ('->', ('lying', 0), ('lying', 7)), ('or', ('lying', 6), ('lying', 1)), ('and', ('lying', 4), ('lying', 0)), ('or', ('telling-truth', 1), ('lying', 2)), ('<=>', ('telling-truth', 6), ('telling-truth', 4)))", "index": 829}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jacob, Sebastian, Matthew, Zoey, Jackson, Olivia, Alexander, and David. Jacob asserted: \"If Olivia is a knight then David is a knave\". Sebastian noted, \"Matthew is a knight\". Matthew was heard saying, \"Alexander is a knave\". Zoey asserted: \"Jackson is a knave or Matthew is a knave\". Jackson told you that If Jacob is a knave then Jackson is a knight. Olivia was heard saying, \"If Olivia is a knight then Sebastian is a knave\". \"Zoey is a knave if and only if David is a knight,\" Alexander claimed. David said that If Zoey is a knight then Sebastian is a knight. So who is a knight and who is a knave?", "names": ["Jacob", "Sebastian", "Matthew", "Zoey", "Jackson", "Olivia", "Alexander", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true, true, false], "solution_text": "Jacob is a knight, Sebastian is a knave, Matthew is a knave, Zoey is a knight, Jackson is a knight, Olivia is a knight, Alexander is a knight, and David is a knave.", "solution_text_format": "(1) Jacob is a knight\n(2) Sebastian is a knave\n(3) Matthew is a knave\n(4) Zoey is a knight\n(5) Jackson is a knight\n(6) Olivia is a knight\n(7) Alexander is a knight\n(8) David is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that If Olivia is a knight then David is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that If Olivia is a knight then Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Olivia that If Olivia is a knight then Sebastian is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the false claim of Sebastian that Matthew is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Alexander is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Zoey is a knave if and only if David is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Jackson is a knave or Matthew is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that If Jacob is a knave then Jackson is a knight.", "David cannot be a knight, because this would contradict the claim of Jacob that If Olivia is a knight then David is a knave.", "Assume David is a knave. No contradiction is found in their false claim that If Zoey is a knight then Sebastian is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 5), ('lying', 7)), ('telling-truth', 2), ('lying', 6), ('or', ('lying', 4), ('lying', 2)), ('->', ('lying', 0), ('telling-truth', 4)), ('->', ('telling-truth', 5), ('lying', 1)), ('<=>', ('lying', 3), ('telling-truth', 7)), ('->', ('telling-truth', 3), ('telling-truth', 1)))", "index": 830}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jack, Daniel, Grace, Oliver, Mason, Charlotte, Jacob, and Avery. Jack noted, \"Jacob is not a knave\". \"Charlotte is a knight and Jack is a knave,\" Daniel declared. As Grace put it, \"If Oliver is a knave then Daniel is a knave\". \"Jacob is a knight and Jacob is a knave,\" Oliver declared. \"If Jacob is a knave then Oliver is a knight,\" Mason declared. Charlotte remarked, \"Avery is a knave or Avery is a knight\". In a statement by Jacob: \"Oliver is not a knave\". In Avery's words: \"Daniel is not a knave\". So who is a knight and who is a knave?", "names": ["Jack", "Daniel", "Grace", "Oliver", "Mason", "Charlotte", "Jacob", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, true, false, true], "solution_text": "Jack is a knave, Daniel is a knight, Grace is a knave, Oliver is a knave, Mason is a knave, Charlotte is a knight, Jacob is a knave, and Avery is a knight.", "solution_text_format": "(1) Jack is a knave\n(2) Daniel is a knight\n(3) Grace is a knave\n(4) Oliver is a knave\n(5) Mason is a knave\n(6) Charlotte is a knight\n(7) Jacob is a knave\n(8) Avery is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Jacob is not a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Oliver is not a knave.", "Oliver cannot be a knight, because this would contradict the claim of their own that Jacob is a knight and Jacob is a knave.", "Oliver cannot be a knave, because this would contradict the claim of Jacob that Oliver is not a knave.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the claim of Jack that Jacob is not a knave.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Jacob is not a knave.", "Jacob cannot be a knight, because this would contradict the false claim of Jack that Jacob is not a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Oliver is not a knave.", "Oliver cannot be a knight, because this would contradict the claim of their own that Jacob is a knight and Jacob is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Jacob is a knight and Jacob is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Charlotte is a knight and Jack is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Avery is a knave or Avery is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Daniel is not a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that If Oliver is a knave then Daniel is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that If Oliver is a knave then Daniel is a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that If Jacob is a knave then Oliver is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that If Jacob is a knave then Oliver is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 6)), ('and', ('telling-truth', 5), ('lying', 0)), ('->', ('lying', 3), ('lying', 1)), ('and', ('telling-truth', 6), ('lying', 6)), ('->', ('lying', 6), ('telling-truth', 3)), ('or', ('lying', 7), ('telling-truth', 7)), ('not', ('lying', 3)), ('not', ('lying', 1)))", "index": 831}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Owen, Riley, Emma, Sebastian, Joseph, Amelia, Aurora, and Benjamin. Owen expressed that If Amelia is a knave then Riley is a knave. \"If Joseph is a knight then Aurora is a knight\" - Riley. \"Amelia is not a knave\" - Emma. Sebastian said that Joseph is a knight or Owen is a knight. \"If Aurora is a knight then Amelia is a knave,\" Joseph declared. Amelia said that Riley is a knight if and only if Riley is a knave. Aurora commented, \"Emma is a knave\". Benjamin told you that Riley is a knight. So who is a knight and who is a knave?", "names": ["Owen", "Riley", "Emma", "Sebastian", "Joseph", "Amelia", "Aurora", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false, true, true], "solution_text": "Owen is a knave, Riley is a knight, Emma is a knave, Sebastian is a knight, Joseph is a knight, Amelia is a knave, Aurora is a knight, and Benjamin is a knight.", "solution_text_format": "(1) Owen is a knave\n(2) Riley is a knight\n(3) Emma is a knave\n(4) Sebastian is a knight\n(5) Joseph is a knight\n(6) Amelia is a knave\n(7) Aurora is a knight\n(8) Benjamin is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that If Amelia is a knave then Riley is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Riley is a knight if and only if Riley is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Riley is a knave.", "Riley cannot be a knight, because this would contradict the claim of Owen that If Amelia is a knave then Riley is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that If Joseph is a knight then Aurora is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Aurora is a knight then Amelia is a knave.", "Aurora cannot be a knight, because this would contradict the false claim of Riley that If Joseph is a knight then Aurora is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Amelia is not a knave.", "Emma cannot be a knave, because this would contradict the false claim of Aurora that Emma is a knave.", "We have exhausted all possibilities for Emma and Aurora, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the false claim of Riley that If Joseph is a knight then Aurora is a knight.", "We have exhausted all possibilities for Joseph, Riley, and Amelia, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that If Amelia is a knave then Riley is a knave.", "Amelia cannot be a knight, because this would contradict the false claim of Owen that If Amelia is a knave then Riley is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Riley is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that If Joseph is a knight then Aurora is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Aurora is a knight then Amelia is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Amelia is not a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Amelia is not a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Joseph is a knight or Owen is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Riley is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('lying', 1)), ('->', ('telling-truth', 4), ('telling-truth', 6)), ('not', ('lying', 5)), ('or', ('telling-truth', 4), ('telling-truth', 0)), ('->', ('telling-truth', 6), ('lying', 5)), ('<=>', ('telling-truth', 1), ('lying', 1)), ('lying', 2), ('telling-truth', 1))", "index": 832}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sofia, Daniel, Elizabeth, Noah, Jackson, Michael, Owen, and Riley. Sofia expressed that Noah is a knight and Elizabeth is a knave. Daniel stated, \"Daniel is a knight if and only if Owen is a knight\". According to Elizabeth, \"Noah is a knave and Daniel is a knight\". Noah was heard saying, \"Riley is a knave or Jackson is a knave\". Jackson asserted: \"Owen is not a knight\". According to Michael, \"Daniel is not a knave\". \"Jackson is a knave if and only if Michael is a knight\" - Owen. \"Noah is a knight or Jackson is a knight,\" Riley declared. So who is a knight and who is a knave?", "names": ["Sofia", "Daniel", "Elizabeth", "Noah", "Jackson", "Michael", "Owen", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true, true, true], "solution_text": "Sofia is a knight, Daniel is a knight, Elizabeth is a knave, Noah is a knight, Jackson is a knave, Michael is a knight, Owen is a knight, and Riley is a knight.", "solution_text_format": "(1) Sofia is a knight\n(2) Daniel is a knight\n(3) Elizabeth is a knave\n(4) Noah is a knight\n(5) Jackson is a knave\n(6) Michael is a knight\n(7) Owen is a knight\n(8) Riley is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Noah is a knight and Elizabeth is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Riley is a knave or Jackson is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Noah is a knight or Jackson is a knight.", "Jackson cannot be a knight, because this would contradict the claim of Noah that Riley is a knave or Jackson is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Owen is not a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Jackson is a knave if and only if Michael is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Daniel is not a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Daniel is a knight if and only if Owen is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Sofia that Noah is a knight and Elizabeth is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Noah is a knave and Daniel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('lying', 2)), ('<=>', ('telling-truth', 1), ('telling-truth', 6)), ('and', ('lying', 3), ('telling-truth', 1)), ('or', ('lying', 7), ('lying', 4)), ('not', ('telling-truth', 6)), ('not', ('lying', 1)), ('<=>', ('lying', 4), ('telling-truth', 5)), ('or', ('telling-truth', 3), ('telling-truth', 4)))", "index": 833}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Michael, Aria, Samuel, Liam, Ella, Daniel, Aiden, and Ethan. Michael expressed that If Daniel is a knight then Ethan is a knight. \"Ethan is not a knave\" - Aria. According to Samuel, \"Liam is a knave and Aria is a knight\". Liam stated, \"If Ella is a knight then Michael is a knave\". Ella remarked, \"Michael is a knave\". Daniel noted, \"Liam is a knight if and only if Daniel is a knight\". Aiden commented, \"Aiden is a knight and Samuel is a knight\". \"Aiden is a knave if and only if Ella is a knight\" - Ethan. So who is a knight and who is a knave?", "names": ["Michael", "Aria", "Samuel", "Liam", "Ella", "Daniel", "Aiden", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, false, false, false], "solution_text": "Michael is a knight, Aria is a knave, Samuel is a knave, Liam is a knight, Ella is a knave, Daniel is a knave, Aiden is a knave, and Ethan is a knave.", "solution_text_format": "(1) Michael is a knight\n(2) Aria is a knave\n(3) Samuel is a knave\n(4) Liam is a knight\n(5) Ella is a knave\n(6) Daniel is a knave\n(7) Aiden is a knave\n(8) Ethan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that If Daniel is a knight then Ethan is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Liam is a knight if and only if Daniel is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that If Ella is a knight then Michael is a knave.", "Ella cannot be a knight, because this would contradict the claim of Liam that If Ella is a knight then Michael is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Michael is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Aiden is a knave if and only if Ella is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Aiden is a knight and Samuel is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Liam is a knave and Aria is a knight.", "Samuel cannot be a knave, because this would contradict the claim of Aiden that Aiden is a knight and Samuel is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the claim of Ethan that Aiden is a knave if and only if Ella is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the claim of Michael that If Daniel is a knight then Ethan is a knight.", "We have exhausted all possibilities for Ethan and Ella, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the claim of Daniel that Liam is a knight if and only if Daniel is a knight.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Liam is a knight if and only if Daniel is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that If Ella is a knight then Michael is a knave.", "Ella cannot be a knight, because this would contradict the claim of Liam that If Ella is a knight then Michael is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Michael is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Aiden is a knave if and only if Ella is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Aiden is a knight and Samuel is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Liam is a knave and Aria is a knight.", "Samuel cannot be a knave, because this would contradict the claim of Aiden that Aiden is a knight and Samuel is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the claim of Ethan that Aiden is a knave if and only if Ella is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if Ella is a knight.", "Aiden cannot be a knight, because this would contradict the false claim of Ethan that Aiden is a knave if and only if Ella is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Aiden is a knight and Samuel is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Liam is a knave and Aria is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Liam is a knave and Aria is a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that Ethan is not a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Ethan is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 5), ('telling-truth', 7)), ('not', ('lying', 7)), ('and', ('lying', 3), ('telling-truth', 1)), ('->', ('telling-truth', 4), ('lying', 0)), ('lying', 0), ('<=>', ('telling-truth', 3), ('telling-truth', 5)), ('and', ('telling-truth', 6), ('telling-truth', 2)), ('<=>', ('lying', 6), ('telling-truth', 4)))", "index": 834}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Henry, Lucas, Amelia, Sofia, Sebastian, Daniel, Elizabeth, and Victoria. Henry noted, \"If Victoria is a knight then Elizabeth is a knight\". Lucas said that Daniel is a knave. In a statement by Amelia: \"Lucas is a knave\". Sofia commented, \"If Daniel is a knave then Lucas is a knight\". \"Victoria is not a knight,\" Sebastian mentioned. Daniel remarked, \"Lucas is not a knight\". In a statement by Elizabeth: \"Sebastian is a knave if and only if Henry is a knave\". In a statement by Victoria: \"Elizabeth is a knave or Amelia is a knight\". So who is a knight and who is a knave?", "names": ["Henry", "Lucas", "Amelia", "Sofia", "Sebastian", "Daniel", "Elizabeth", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false, true, false], "solution_text": "Henry is a knight, Lucas is a knight, Amelia is a knave, Sofia is a knight, Sebastian is a knight, Daniel is a knave, Elizabeth is a knight, and Victoria is a knave.", "solution_text_format": "(1) Henry is a knight\n(2) Lucas is a knight\n(3) Amelia is a knave\n(4) Sofia is a knight\n(5) Sebastian is a knight\n(6) Daniel is a knave\n(7) Elizabeth is a knight\n(8) Victoria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that If Victoria is a knight then Elizabeth is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Elizabeth is a knave or Amelia is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Sebastian is a knave if and only if Henry is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Victoria is not a knight.", "Sebastian cannot be a knave, because this would contradict the claim of Elizabeth that Sebastian is a knave if and only if Henry is a knave.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Elizabeth.", "Elizabeth cannot be a knave, because this would contradict the claim of Henry that If Victoria is a knight then Elizabeth is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Elizabeth is a knave or Amelia is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Sebastian is a knave if and only if Henry is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Victoria is not a knight.", "Amelia cannot be a knight, because this would contradict the false claim of Victoria that Elizabeth is a knave or Amelia is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Lucas is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of Lucas that Daniel is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Lucas is not a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that If Daniel is a knave then Lucas is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 7), ('telling-truth', 6)), ('lying', 5), ('lying', 1), ('->', ('lying', 5), ('telling-truth', 1)), ('not', ('telling-truth', 7)), ('not', ('telling-truth', 1)), ('<=>', ('lying', 4), ('lying', 0)), ('or', ('lying', 6), ('telling-truth', 2)))", "index": 835}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jacob, Jackson, Jack, Sofia, Daniel, James, Aiden, and Noah. According to Jacob, \"Noah is a knave or Daniel is a knave\". Jackson was heard saying, \"Sofia is a knight and Noah is a knave\". \"Daniel is not a knave\" - Jack. As Sofia put it, \"James is a knight if and only if Jackson is a knight\". \"Jacob is a knave\" - Daniel. \"Jack is a knight or Sofia is a knight,\" James claimed. Aiden said, \"Jack is a knight and James is a knight.\" Noah said that Jackson is a knave if and only if Jacob is a knave. So who is a knight and who is a knave?", "names": ["Jacob", "Jackson", "Jack", "Sofia", "Daniel", "James", "Aiden", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true, true, true], "solution_text": "Jacob is a knave, Jackson is a knave, Jack is a knight, Sofia is a knave, Daniel is a knight, James is a knight, Aiden is a knight, and Noah is a knight.", "solution_text_format": "(1) Jacob is a knave\n(2) Jackson is a knave\n(3) Jack is a knight\n(4) Sofia is a knave\n(5) Daniel is a knight\n(6) James is a knight\n(7) Aiden is a knight\n(8) Noah is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that Noah is a knave or Daniel is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Jackson is a knave if and only if Jacob is a knave.", "Jackson cannot be a knight, because this would contradict the claim of their own that Sofia is a knight and Noah is a knave.", "Jackson cannot be a knave, because this would contradict the claim of Noah that Jackson is a knave if and only if Jacob is a knave.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Jackson is a knave if and only if Jacob is a knave.", "Jackson cannot be a knight, because this would contradict the false claim of Noah that Jackson is a knave if and only if Jacob is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Sofia is a knight and Noah is a knave.", "Sofia cannot be a knight, because this would contradict the false claim of Jackson that Sofia is a knight and Noah is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that James is a knight if and only if Jackson is a knight.", "Assume James is a knight. No contradiction is found in their claim that Jack is a knight or Sofia is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Daniel is not a knave.", "Daniel cannot be a knight, because this would contradict the claim of their own that Jacob is a knave.", "Daniel cannot be a knave, because this would contradict the claim of Jack that Daniel is not a knave.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the claim of James that Jack is a knight or Sofia is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider James.", "James cannot be a knave, because this would contradict the false claim of Sofia that James is a knight if and only if Jackson is a knight.", "We have exhausted all possibilities for James, Sofia, Jackson, and Noah, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Noah is a knave or Daniel is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Jackson is a knave if and only if Jacob is a knave.", "Jackson cannot be a knight, because this would contradict the claim of their own that Sofia is a knight and Noah is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Sofia is a knight and Noah is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that James is a knight if and only if Jackson is a knight.", "James cannot be a knight, because this would contradict the claim of Sofia that James is a knight if and only if Jackson is a knight.", "James cannot be a knave, because this would contradict the false claim of their own that Jack is a knight or Sofia is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that James is a knight if and only if Jackson is a knight.", "Assume James is a knight. No contradiction is found in their claim that Jack is a knight or Sofia is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Daniel is not a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Jacob is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Jack is a knight and James is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 7), ('lying', 4)), ('and', ('telling-truth', 3), ('lying', 7)), ('not', ('lying', 4)), ('<=>', ('telling-truth', 5), ('telling-truth', 1)), ('lying', 0), ('or', ('telling-truth', 2), ('telling-truth', 3)), ('and', ('telling-truth', 2), ('telling-truth', 5)), ('<=>', ('lying', 1), ('lying', 0)))", "index": 836}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Matthew, Samuel, Daniel, Evelyn, Charlotte, Jacob, Emily, and Amelia. Matthew was heard saying, \"Jacob is a knight or Emily is a knight\". Samuel expressed that Jacob is a knight or Samuel is a knight. Daniel commented, \"Evelyn is a knight and Samuel is a knave\". In Evelyn's words: \"Emily is not a knave\". According to Charlotte, \"Daniel is a knight if and only if Evelyn is a knight\". Jacob commented, \"Evelyn is a knave or Amelia is a knight\". Emily said that Daniel is not a knight. Amelia told you that Matthew is a knight and Charlotte is a knight. So who is a knight and who is a knave?", "names": ["Matthew", "Samuel", "Daniel", "Evelyn", "Charlotte", "Jacob", "Emily", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false, true, false], "solution_text": "Matthew is a knight, Samuel is a knight, Daniel is a knave, Evelyn is a knight, Charlotte is a knave, Jacob is a knave, Emily is a knight, and Amelia is a knave.", "solution_text_format": "(1) Matthew is a knight\n(2) Samuel is a knight\n(3) Daniel is a knave\n(4) Evelyn is a knight\n(5) Charlotte is a knave\n(6) Jacob is a knave\n(7) Emily is a knight\n(8) Amelia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that Jacob is a knight or Emily is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Evelyn is a knave or Amelia is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Emily is not a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Daniel is not a knight.", "Daniel cannot be a knight, because this would contradict the claim of Emily that Daniel is not a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Evelyn is a knight and Samuel is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Jacob is a knight or Samuel is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Matthew is a knight and Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Daniel is a knight if and only if Evelyn is a knight.", "Charlotte cannot be a knave, because this would contradict the claim of Amelia that Matthew is a knight and Charlotte is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Amelia.", "Amelia cannot be a knave, because this would contradict the claim of Jacob that Evelyn is a knave or Amelia is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Samuel.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Jacob is a knight or Samuel is a knight.", "We have exhausted all possibilities for Samuel and Daniel, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the claim of Evelyn that Emily is not a knave.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Emily is not a knave.", "Emily cannot be a knight, because this would contradict the false claim of Evelyn that Emily is not a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Daniel is not a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that Evelyn is a knight and Samuel is a knave.", "Daniel cannot be a knave, because this would contradict the false claim of Emily that Daniel is not a knight.", "We have exhausted all possibilities for Daniel, Emily, and Evelyn, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Evelyn is a knave or Amelia is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Emily is not a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Daniel is not a knight.", "Daniel cannot be a knight, because this would contradict the claim of Emily that Daniel is not a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Evelyn is a knight and Samuel is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Jacob is a knight or Samuel is a knight.", "Amelia cannot be a knight, because this would contradict the false claim of Jacob that Evelyn is a knave or Amelia is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Matthew is a knight and Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Daniel is a knight if and only if Evelyn is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Daniel is a knight if and only if Evelyn is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('telling-truth', 6)), ('or', ('telling-truth', 5), ('telling-truth', 1)), ('and', ('telling-truth', 3), ('lying', 1)), ('not', ('lying', 6)), ('<=>', ('telling-truth', 2), ('telling-truth', 3)), ('or', ('lying', 3), ('telling-truth', 7)), ('not', ('telling-truth', 2)), ('and', ('telling-truth', 0), ('telling-truth', 4)))", "index": 837}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jackson, Sebastian, Oliver, Charlotte, Olivia, Zoey, Evelyn, and Ella. \"If Oliver is a knight then Olivia is a knave,\" Jackson claimed. Sebastian noted, \"Olivia is a knight\". \"Zoey is a knight\" - Oliver. Charlotte noted, \"Zoey is not a knight\". Olivia said, \"Ella is a knave.\" According to Zoey, \"Oliver is a knave if and only if Jackson is a knave\". \"If Oliver is a knave then Charlotte is a knave\" - Evelyn. Ella noted, \"Oliver is not a knight\". So who is a knight and who is a knave?", "names": ["Jackson", "Sebastian", "Oliver", "Charlotte", "Olivia", "Zoey", "Evelyn", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, false, false, true], "solution_text": "Jackson is a knight, Sebastian is a knave, Oliver is a knave, Charlotte is a knight, Olivia is a knave, Zoey is a knave, Evelyn is a knave, and Ella is a knight.", "solution_text_format": "(1) Jackson is a knight\n(2) Sebastian is a knave\n(3) Oliver is a knave\n(4) Charlotte is a knight\n(5) Olivia is a knave\n(6) Zoey is a knave\n(7) Evelyn is a knave\n(8) Ella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that If Oliver is a knight then Olivia is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Oliver is a knave if and only if Jackson is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Jackson that If Oliver is a knight then Olivia is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Oliver is not a knight.", "Ella cannot be a knave, because this would contradict the false claim of Olivia that Ella is a knave.", "We have exhausted all possibilities for Ella and Olivia, so let us go back and reconsider Zoey.", "Zoey cannot be a knave, because this would contradict the claim of Oliver that Zoey is a knight.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Zoey is a knight.", "Zoey cannot be a knight, because this would contradict the false claim of Oliver that Zoey is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Oliver is a knave if and only if Jackson is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of Olivia that Ella is a knave.", "Ella cannot be a knave, because this would contradict the false claim of their own that Oliver is not a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Oliver is not a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Olivia is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Olivia is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Zoey is not a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that If Oliver is a knave then Charlotte is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that If Oliver is a knave then Charlotte is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('lying', 4)), ('telling-truth', 4), ('telling-truth', 5), ('not', ('telling-truth', 5)), ('lying', 7), ('<=>', ('lying', 2), ('lying', 0)), ('->', ('lying', 2), ('lying', 3)), ('not', ('telling-truth', 2)))", "index": 838}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Samuel, Emma, Chloe, James, Amelia, Elizabeth, Lily, and Abigail. Samuel stated, \"James is a knight and Chloe is a knight\". Emma noted, \"Lily is not a knight\". Chloe was heard saying, \"Samuel is a knight\". \"Abigail is a knave and Emma is a knight\" - James. Amelia commented, \"Emma is a knight\". \"Lily is not a knave,\" Elizabeth claimed. According to Lily, \"Chloe is a knave or Elizabeth is a knave\". Abigail asserted: \"Elizabeth is a knight\". So who is a knight and who is a knave?", "names": ["Samuel", "Emma", "Chloe", "James", "Amelia", "Elizabeth", "Lily", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, true, true, true], "solution_text": "Samuel is a knave, Emma is a knave, Chloe is a knave, James is a knave, Amelia is a knave, Elizabeth is a knight, Lily is a knight, and Abigail is a knight.", "solution_text_format": "(1) Samuel is a knave\n(2) Emma is a knave\n(3) Chloe is a knave\n(4) James is a knave\n(5) Amelia is a knave\n(6) Elizabeth is a knight\n(7) Lily is a knight\n(8) Abigail is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that James is a knight and Chloe is a knight.", "Assume James is a knight. No contradiction is found in their claim that Abigail is a knave and Emma is a knight.", "Abigail cannot be a knight, because this would contradict the claim of James that Abigail is a knave and Emma is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the false claim of Abigail that Elizabeth is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Lily is not a knave.", "Lily cannot be a knight, because this would contradict the false claim of Elizabeth that Lily is not a knave.", "Lily cannot be a knave, because this would contradict the false claim of their own that Chloe is a knave or Elizabeth is a knave.", "We have exhausted all possibilities for Lily, Elizabeth, and Abigail, so let us go back and reconsider James.", "James cannot be a knave, because this would contradict the claim of Samuel that James is a knight and Chloe is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that James is a knight and Chloe is a knight.", "Assume James is a knight. No contradiction is found in their claim that Abigail is a knave and Emma is a knight.", "Abigail cannot be a knight, because this would contradict the claim of James that Abigail is a knave and Emma is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the false claim of Abigail that Elizabeth is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Lily is not a knave.", "Lily cannot be a knight, because this would contradict the false claim of Elizabeth that Lily is not a knave.", "Lily cannot be a knave, because this would contradict the false claim of their own that Chloe is a knave or Elizabeth is a knave.", "We have exhausted all possibilities for Lily, Elizabeth, and Abigail, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Abigail is a knave and Emma is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Lily is not a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Chloe is a knave or Elizabeth is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Samuel is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Samuel is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Lily is not a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Lily is not a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Emma is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Emma is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('telling-truth', 2)), ('not', ('telling-truth', 6)), ('telling-truth', 0), ('and', ('lying', 7), ('telling-truth', 1)), ('telling-truth', 1), ('not', ('lying', 6)), ('or', ('lying', 2), ('lying', 5)), ('telling-truth', 5))", "index": 839}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Oliver, Mia, Riley, William, Mason, Michael, Harper, and Owen. In Oliver's words: \"William is a knight\". According to Mia, \"Riley is not a knave\". \"Michael is a knight or Mason is a knave,\" Riley mentioned. According to William, \"Owen is not a knave\". Mason commented, \"Mia is a knave if and only if Harper is a knight\". Michael was heard saying, \"Owen is a knave and Riley is a knight\". Harper expressed that William is a knave. Owen remarked, \"Mia is a knave and Harper is a knight\". So who is a knight and who is a knave?", "names": ["Oliver", "Mia", "Riley", "William", "Mason", "Michael", "Harper", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true, true, false], "solution_text": "Oliver is a knave, Mia is a knight, Riley is a knight, William is a knave, Mason is a knave, Michael is a knight, Harper is a knight, and Owen is a knave.", "solution_text_format": "(1) Oliver is a knave\n(2) Mia is a knight\n(3) Riley is a knight\n(4) William is a knave\n(5) Mason is a knave\n(6) Michael is a knight\n(7) Harper is a knight\n(8) Owen is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that William is a knight.", "Assume William is a knight. No contradiction is found in their claim that Owen is not a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Mia is a knave and Harper is a knight.", "Mia cannot be a knight, because this would contradict the claim of Owen that Mia is a knave and Harper is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Riley is not a knave.", "Riley cannot be a knight, because this would contradict the false claim of Mia that Riley is not a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Michael is a knight or Mason is a knave.", "Michael cannot be a knight, because this would contradict the false claim of Riley that Michael is a knight or Mason is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Owen is a knave and Riley is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Mia is a knave if and only if Harper is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that William is a knave.", "Harper cannot be a knave, because this would contradict the claim of Mason that Mia is a knave if and only if Harper is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Mason.", "Mason cannot be a knave, because this would contradict the false claim of Riley that Michael is a knight or Mason is a knave.", "We have exhausted all possibilities for Mason, Michael, Riley, and Mia, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the claim of William that Owen is not a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the claim of Oliver that William is a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that William is a knight.", "William cannot be a knight, because this would contradict the false claim of Oliver that William is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Owen is not a knave.", "Owen cannot be a knight, because this would contradict the false claim of William that Owen is not a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Mia is a knave and Harper is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Riley is not a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Michael is a knight or Mason is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Owen is a knave and Riley is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Mia is a knave if and only if Harper is a knight.", "Harper cannot be a knight, because this would contradict the claim of Mason that Mia is a knave if and only if Harper is a knight.", "Harper cannot be a knave, because this would contradict the false claim of their own that William is a knave.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Mia is a knave if and only if Harper is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that William is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 3), ('not', ('lying', 2)), ('or', ('telling-truth', 5), ('lying', 4)), ('not', ('lying', 7)), ('<=>', ('lying', 1), ('telling-truth', 6)), ('and', ('lying', 7), ('telling-truth', 2)), ('lying', 3), ('and', ('lying', 1), ('telling-truth', 6)))", "index": 840}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jacob, Lily, Sofia, Henry, Avery, Elizabeth, Charlotte, and Emma. In a statement by Jacob: \"Sofia is a knave if and only if Lily is a knave\". Lily said that Avery is a knave or Elizabeth is a knave. Sofia said, \"Jacob is a knight and Avery is a knight.\" Henry said, \"Jacob is not a knight.\" Avery commented, \"Lily is a knave or Emma is a knave\". According to Elizabeth, \"Sofia is a knight if and only if Avery is a knight\". Charlotte noted, \"If Jacob is a knight then Elizabeth is a knight\". Emma noted, \"Sofia is a knight and Sofia is a knave\". So who is a knight and who is a knave?", "names": ["Jacob", "Lily", "Sofia", "Henry", "Avery", "Elizabeth", "Charlotte", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false, true, false], "solution_text": "Jacob is a knave, Lily is a knight, Sofia is a knave, Henry is a knight, Avery is a knight, Elizabeth is a knave, Charlotte is a knight, and Emma is a knave.", "solution_text_format": "(1) Jacob is a knave\n(2) Lily is a knight\n(3) Sofia is a knave\n(4) Henry is a knight\n(5) Avery is a knight\n(6) Elizabeth is a knave\n(7) Charlotte is a knight\n(8) Emma is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that Sofia is a knave if and only if Lily is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Jacob is a knight and Avery is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Lily is a knave or Emma is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Avery is a knave or Elizabeth is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of Lily that Avery is a knave or Elizabeth is a knave.", "Elizabeth cannot be a knave, because this would contradict the false claim of their own that Sofia is a knight if and only if Avery is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the claim of Jacob that Sofia is a knave if and only if Lily is a knave.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Avery.", "Avery cannot be a knave, because this would contradict the claim of Sofia that Jacob is a knight and Avery is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Jacob is a knight and Avery is a knight.", "Avery cannot be a knight, because this would contradict the false claim of Sofia that Jacob is a knight and Avery is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Lily is a knave or Emma is a knave.", "Lily cannot be a knight, because this would contradict the claim of Jacob that Sofia is a knave if and only if Lily is a knave.", "Lily cannot be a knave, because this would contradict the false claim of their own that Avery is a knave or Elizabeth is a knave.", "We have exhausted all possibilities for Lily, Avery, and Sofia, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Sofia is a knave if and only if Lily is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Jacob is a knight and Avery is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Jacob is a knight and Avery is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Lily is a knave or Emma is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Avery is a knave or Elizabeth is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of Lily that Avery is a knave or Elizabeth is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Sofia is a knight if and only if Avery is a knight.", "Emma cannot be a knight, because this would contradict the claim of Avery that Lily is a knave or Emma is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Sofia is a knight and Sofia is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Jacob is not a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Jacob is a knight then Elizabeth is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('lying', 1)), ('or', ('lying', 4), ('lying', 5)), ('and', ('telling-truth', 0), ('telling-truth', 4)), ('not', ('telling-truth', 0)), ('or', ('lying', 1), ('lying', 7)), ('<=>', ('telling-truth', 2), ('telling-truth', 4)), ('->', ('telling-truth', 0), ('telling-truth', 5)), ('and', ('telling-truth', 2), ('lying', 2)))", "index": 841}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: David, Scarlett, Joseph, Sophia, Daniel, Benjamin, Penelope, and Lucas. David said, \"Lucas is not a knight.\" Scarlett stated, \"Sophia is not a knave\". Joseph told you that Daniel is not a knave. Sophia asserted: \"Daniel is a knight if and only if Scarlett is a knave\". Daniel said, \"Lucas is a knight.\" Benjamin commented, \"Lucas is a knave and Sophia is a knight\". \"If Sophia is a knight then Daniel is a knight\" - Penelope. In Lucas's words: \"If Scarlett is a knave then Daniel is a knight\". So who is a knight and who is a knave?", "names": ["David", "Scarlett", "Joseph", "Sophia", "Daniel", "Benjamin", "Penelope", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, false, true, false], "solution_text": "David is a knight, Scarlett is a knave, Joseph is a knave, Sophia is a knave, Daniel is a knave, Benjamin is a knave, Penelope is a knight, and Lucas is a knave.", "solution_text_format": "(1) David is a knight\n(2) Scarlett is a knave\n(3) Joseph is a knave\n(4) Sophia is a knave\n(5) Daniel is a knave\n(6) Benjamin is a knave\n(7) Penelope is a knight\n(8) Lucas is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Lucas is not a knight.", "Lucas cannot be a knight, because this would contradict the claim of David that Lucas is not a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that If Scarlett is a knave then Daniel is a knight.", "Scarlett cannot be a knight, because this would contradict the false claim of Lucas that If Scarlett is a knave then Daniel is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Sophia is not a knave.", "Sophia cannot be a knight, because this would contradict the false claim of Scarlett that Sophia is not a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Daniel is a knight if and only if Scarlett is a knave.", "Daniel cannot be a knight, because this would contradict the false claim of Sophia that Daniel is a knight if and only if Scarlett is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Lucas is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Daniel is not a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Daniel is not a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Lucas is a knave and Sophia is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Lucas is a knave and Sophia is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that If Sophia is a knight then Daniel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 7)), ('not', ('lying', 3)), ('not', ('lying', 4)), ('<=>', ('telling-truth', 4), ('lying', 1)), ('telling-truth', 7), ('and', ('lying', 7), ('telling-truth', 3)), ('->', ('telling-truth', 3), ('telling-truth', 4)), ('->', ('lying', 1), ('telling-truth', 4)))", "index": 842}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Riley, Mia, Joseph, Oliver, James, Logan, Jack, and Sebastian. Riley said, \"Logan is a knave and James is a knight.\" Mia commented, \"Oliver is a knight if and only if Riley is a knave\". Joseph said that Mia is not a knight. Oliver expressed that Jack is not a knight. James stated, \"Sebastian is a knight or Sebastian is a knave\". Logan stated, \"Joseph is not a knave\". In a statement by Jack: \"Riley is a knave\". In a statement by Sebastian: \"Jack is not a knave\". So who is a knight and who is a knave?", "names": ["Riley", "Mia", "Joseph", "Oliver", "James", "Logan", "Jack", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true, true, true], "solution_text": "Riley is a knave, Mia is a knave, Joseph is a knight, Oliver is a knave, James is a knight, Logan is a knight, Jack is a knight, and Sebastian is a knight.", "solution_text_format": "(1) Riley is a knave\n(2) Mia is a knave\n(3) Joseph is a knight\n(4) Oliver is a knave\n(5) James is a knight\n(6) Logan is a knight\n(7) Jack is a knight\n(8) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Logan is a knave and James is a knight.", "Logan cannot be a knight, because this would contradict the claim of Riley that Logan is a knave and James is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Joseph is not a knave.", "Joseph cannot be a knight, because this would contradict the false claim of Logan that Joseph is not a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Mia is not a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Oliver is a knight if and only if Riley is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Mia that Oliver is a knight if and only if Riley is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Jack is not a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Riley is a knave.", "Jack cannot be a knave, because this would contradict the false claim of Oliver that Jack is not a knight.", "We have exhausted all possibilities for Jack and Oliver, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the false claim of Joseph that Mia is not a knight.", "We have exhausted all possibilities for Mia, Joseph, and Logan, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Logan is a knave and James is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Joseph is not a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Mia is not a knight.", "Mia cannot be a knight, because this would contradict the claim of Joseph that Mia is not a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Oliver is a knight if and only if Riley is a knave.", "Oliver cannot be a knight, because this would contradict the false claim of Mia that Oliver is a knight if and only if Riley is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Jack is not a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Riley is a knave.", "Assume James is a knight. No contradiction is found in their claim that Sebastian is a knight or Sebastian is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Jack is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 5), ('telling-truth', 4)), ('<=>', ('telling-truth', 3), ('lying', 0)), ('not', ('telling-truth', 1)), ('not', ('telling-truth', 6)), ('or', ('telling-truth', 7), ('lying', 7)), ('not', ('lying', 2)), ('lying', 0), ('not', ('lying', 6)))", "index": 843}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emily, Zoey, Amelia, Oliver, Aiden, Sofia, Jackson, and Isabella. In Emily's words: \"Sofia is not a knave\". Zoey commented, \"Isabella is a knight and Emily is a knave\". \"Aiden is a knight if and only if Oliver is a knave,\" Amelia claimed. \"Amelia is a knight if and only if Emily is a knave,\" Oliver claimed. Aiden noted, \"Amelia is a knight if and only if Isabella is a knight\". Sofia said, \"If Emily is a knight then Oliver is a knave.\" Jackson expressed that Zoey is a knight if and only if Emily is a knave. Isabella commented, \"Jackson is a knight\". So who is a knight and who is a knave?", "names": ["Emily", "Zoey", "Amelia", "Oliver", "Aiden", "Sofia", "Jackson", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true, true, true], "solution_text": "Emily is a knight, Zoey is a knave, Amelia is a knight, Oliver is a knave, Aiden is a knight, Sofia is a knight, Jackson is a knight, and Isabella is a knight.", "solution_text_format": "(1) Emily is a knight\n(2) Zoey is a knave\n(3) Amelia is a knight\n(4) Oliver is a knave\n(5) Aiden is a knight\n(6) Sofia is a knight\n(7) Jackson is a knight\n(8) Isabella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Sofia is not a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that If Emily is a knight then Oliver is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Sofia that If Emily is a knight then Oliver is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Amelia is a knight if and only if Emily is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Aiden is a knight if and only if Oliver is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Amelia is a knight if and only if Isabella is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Jackson is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Zoey is a knight if and only if Emily is a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that Isabella is a knight and Emily is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Isabella is a knight and Emily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 5)), ('and', ('telling-truth', 7), ('lying', 0)), ('<=>', ('telling-truth', 4), ('lying', 3)), ('<=>', ('telling-truth', 2), ('lying', 0)), ('<=>', ('telling-truth', 2), ('telling-truth', 7)), ('->', ('telling-truth', 0), ('lying', 3)), ('<=>', ('telling-truth', 1), ('lying', 0)), ('telling-truth', 6))", "index": 844}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emma, Jacob, Logan, Victoria, Daniel, Ethan, Emily, and Matthew. \"If Ethan is a knave then Ethan is a knight,\" Emma claimed. Jacob noted, \"Matthew is a knave and Emma is a knight\". \"Ethan is a knave,\" Logan declared. Victoria stated, \"Daniel is a knight or Jacob is a knave\". \"Victoria is a knight,\" Daniel mentioned. \"Victoria is a knight if and only if Jacob is a knave,\" Ethan claimed. Emily commented, \"Matthew is a knave\". Matthew told you that Daniel is a knight and Victoria is a knave. So who is a knight and who is a knave?", "names": ["Emma", "Jacob", "Logan", "Victoria", "Daniel", "Ethan", "Emily", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, true, true, false], "solution_text": "Emma is a knight, Jacob is a knight, Logan is a knave, Victoria is a knave, Daniel is a knave, Ethan is a knight, Emily is a knight, and Matthew is a knave.", "solution_text_format": "(1) Emma is a knight\n(2) Jacob is a knight\n(3) Logan is a knave\n(4) Victoria is a knave\n(5) Daniel is a knave\n(6) Ethan is a knight\n(7) Emily is a knight\n(8) Matthew is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that If Ethan is a knave then Ethan is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Jacob is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Daniel is a knight or Jacob is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Victoria is a knight.", "Jacob cannot be a knight, because this would contradict the claim of Ethan that Victoria is a knight if and only if Jacob is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Matthew is a knave and Emma is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Daniel is a knight and Victoria is a knave.", "Matthew cannot be a knave, because this would contradict the false claim of Jacob that Matthew is a knave and Emma is a knight.", "We have exhausted all possibilities for Matthew and Jacob, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the false claim of their own that Victoria is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Daniel is a knight or Jacob is a knave.", "Daniel cannot be a knight, because this would contradict the false claim of Victoria that Daniel is a knight or Jacob is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Victoria is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Matthew is a knave and Emma is a knight.", "Matthew cannot be a knight, because this would contradict the claim of Jacob that Matthew is a knave and Emma is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Daniel is a knight and Victoria is a knave.", "Logan cannot be a knight, because this would contradict the claim of their own that Ethan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Ethan is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Matthew is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('telling-truth', 5)), ('and', ('lying', 7), ('telling-truth', 0)), ('lying', 5), ('or', ('telling-truth', 4), ('lying', 1)), ('telling-truth', 3), ('<=>', ('telling-truth', 3), ('lying', 1)), ('lying', 7), ('and', ('telling-truth', 4), ('lying', 3)))", "index": 845}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Scarlett, Michael, Oliver, Ava, Olivia, Aria, Owen, and Elizabeth. Scarlett noted, \"Aria is a knight\". Michael expressed that Olivia is not a knight. \"Aria is a knave or Michael is a knave,\" Oliver mentioned. In Ava's words: \"If Aria is a knight then Owen is a knight\". \"Owen is not a knight,\" Olivia claimed. Aria stated, \"If Michael is a knave then Scarlett is a knave\". Owen said that Ava is a knave if and only if Michael is a knave. Elizabeth asserted: \"If Aria is a knight then Owen is a knave\". So who is a knight and who is a knave?", "names": ["Scarlett", "Michael", "Oliver", "Ava", "Olivia", "Aria", "Owen", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true, true, false], "solution_text": "Scarlett is a knight, Michael is a knight, Oliver is a knave, Ava is a knight, Olivia is a knave, Aria is a knight, Owen is a knight, and Elizabeth is a knave.", "solution_text_format": "(1) Scarlett is a knight\n(2) Michael is a knight\n(3) Oliver is a knave\n(4) Ava is a knight\n(5) Olivia is a knave\n(6) Aria is a knight\n(7) Owen is a knight\n(8) Elizabeth is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Aria is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that If Michael is a knave then Scarlett is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Olivia is not a knight.", "Olivia cannot be a knight, because this would contradict the claim of Michael that Olivia is not a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Owen is not a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Ava is a knave if and only if Michael is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that If Aria is a knight then Owen is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Aria is a knave or Michael is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Aria is a knave or Michael is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that If Aria is a knight then Owen is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that If Aria is a knight then Owen is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 5), ('not', ('telling-truth', 4)), ('or', ('lying', 5), ('lying', 1)), ('->', ('telling-truth', 5), ('telling-truth', 6)), ('not', ('telling-truth', 6)), ('->', ('lying', 1), ('lying', 0)), ('<=>', ('lying', 3), ('lying', 1)), ('->', ('telling-truth', 5), ('lying', 6)))", "index": 846}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: James, Elizabeth, Lucas, Sofia, Abigail, Alexander, Zoey, and Sebastian. James said that Elizabeth is a knight or Zoey is a knight. \"If Abigail is a knave then James is a knave\" - Elizabeth. Lucas remarked, \"If Sebastian is a knave then Alexander is a knight\". Sofia told you that Alexander is not a knave. Abigail remarked, \"Abigail is a knight or Lucas is a knight\". Alexander commented, \"Zoey is a knave or James is a knight\". Zoey told you that Lucas is a knave and Sofia is a knave. Sebastian said that Alexander is a knave or Zoey is a knight. So who is a knight and who is a knave?", "names": ["James", "Elizabeth", "Lucas", "Sofia", "Abigail", "Alexander", "Zoey", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true, false, false], "solution_text": "James is a knight, Elizabeth is a knight, Lucas is a knight, Sofia is a knight, Abigail is a knight, Alexander is a knight, Zoey is a knave, and Sebastian is a knave.", "solution_text_format": "(1) James is a knight\n(2) Elizabeth is a knight\n(3) Lucas is a knight\n(4) Sofia is a knight\n(5) Abigail is a knight\n(6) Alexander is a knight\n(7) Zoey is a knave\n(8) Sebastian is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Elizabeth is a knight or Zoey is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Abigail is a knave then James is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Abigail is a knight or Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that If Sebastian is a knave then Alexander is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Alexander is a knave or Zoey is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Zoey is a knave or James is a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that Lucas is a knave and Sofia is a knave.", "Zoey cannot be a knave, because this would contradict the claim of Sebastian that Alexander is a knave or Zoey is a knight.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Alexander.", "Alexander cannot be a knave, because this would contradict the false claim of their own that Zoey is a knave or James is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Alexander is a knave or Zoey is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Zoey is a knave or James is a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that Lucas is a knave and Sofia is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Lucas is a knave and Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Alexander is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('telling-truth', 6)), ('->', ('lying', 4), ('lying', 0)), ('->', ('lying', 7), ('telling-truth', 5)), ('not', ('lying', 5)), ('or', ('telling-truth', 4), ('telling-truth', 2)), ('or', ('lying', 6), ('telling-truth', 0)), ('and', ('lying', 2), ('lying', 3)), ('or', ('lying', 5), ('telling-truth', 6)))", "index": 847}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Abigail, Emma, Zoey, Sofia, Olivia, Mia, Elizabeth, and Amelia. As Abigail put it, \"Elizabeth is a knave\". Emma noted, \"If Amelia is a knave then Abigail is a knave\". \"Abigail is not a knight,\" Zoey declared. \"If Elizabeth is a knave then Sofia is a knight\" - Sofia. Olivia asserted: \"Amelia is a knave\". \"Olivia is a knight if and only if Emma is a knave,\" Mia declared. \"Sofia is a knave\" - Elizabeth. According to Amelia, \"If Mia is a knave then Emma is a knave\". So who is a knight and who is a knave?", "names": ["Abigail", "Emma", "Zoey", "Sofia", "Olivia", "Mia", "Elizabeth", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true, false, true], "solution_text": "Abigail is a knight, Emma is a knight, Zoey is a knave, Sofia is a knight, Olivia is a knave, Mia is a knight, Elizabeth is a knave, and Amelia is a knight.", "solution_text_format": "(1) Abigail is a knight\n(2) Emma is a knight\n(3) Zoey is a knave\n(4) Sofia is a knight\n(5) Olivia is a knave\n(6) Mia is a knight\n(7) Elizabeth is a knave\n(8) Amelia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Elizabeth is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of Abigail that Elizabeth is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Sofia is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If Amelia is a knave then Abigail is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that If Mia is a knave then Emma is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Emma is a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that Amelia is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Amelia is a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that Abigail is not a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Abigail is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 6), ('->', ('lying', 7), ('lying', 0)), ('not', ('telling-truth', 0)), ('->', ('lying', 6), ('telling-truth', 3)), ('lying', 7), ('<=>', ('telling-truth', 4), ('lying', 1)), ('lying', 3), ('->', ('lying', 5), ('lying', 1)))", "index": 848}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: David, Lucas, Emily, Evelyn, Harper, Henry, Joseph, and Jackson. \"Henry is a knave and Evelyn is a knight,\" David mentioned. Lucas stated, \"Joseph is a knight\". Emily stated, \"If Evelyn is a knight then Lucas is a knight\". In Evelyn's words: \"Jackson is not a knight\". Harper asserted: \"Jackson is a knight and Joseph is a knight\". Henry commented, \"Harper is not a knight\". Joseph said that If Evelyn is a knight then David is a knave. According to Jackson, \"Lucas is a knave or Joseph is a knight\". So who is a knight and who is a knave?", "names": ["David", "Lucas", "Emily", "Evelyn", "Harper", "Henry", "Joseph", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, false, true, true], "solution_text": "David is a knave, Lucas is a knight, Emily is a knight, Evelyn is a knave, Harper is a knight, Henry is a knave, Joseph is a knight, and Jackson is a knight.", "solution_text_format": "(1) David is a knave\n(2) Lucas is a knight\n(3) Emily is a knight\n(4) Evelyn is a knave\n(5) Harper is a knight\n(6) Henry is a knave\n(7) Joseph is a knight\n(8) Jackson is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Henry is a knave and Evelyn is a knight.", "Henry cannot be a knight, because this would contradict the claim of David that Henry is a knave and Evelyn is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Harper is not a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Jackson is a knight and Joseph is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Lucas is a knave or Joseph is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Evelyn is a knight then David is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Jackson is not a knight.", "Evelyn cannot be a knave, because this would contradict the claim of David that Henry is a knave and Evelyn is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of Lucas that Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of Lucas that Joseph is a knight.", "Joseph cannot be a knave, because this would contradict the claim of Harper that Jackson is a knight and Joseph is a knight.", "We have exhausted all possibilities for Joseph and Lucas, so let us go back and reconsider Jackson.", "Jackson cannot be a knave, because this would contradict the claim of Harper that Jackson is a knight and Joseph is a knight.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the false claim of Henry that Harper is not a knight.", "We have exhausted all possibilities for Harper and Henry, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Henry is a knave and Evelyn is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Harper is not a knight.", "Harper cannot be a knight, because this would contradict the claim of Henry that Harper is not a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Jackson is a knight and Joseph is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Lucas is a knave or Joseph is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of Harper that Jackson is a knight and Joseph is a knight.", "Joseph cannot be a knave, because this would contradict the claim of Lucas that Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of Lucas that Joseph is a knight.", "Joseph cannot be a knave, because this would contradict the false claim of their own that If Evelyn is a knight then David is a knave.", "We have exhausted all possibilities for Joseph and Lucas, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Lucas is a knave or Joseph is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of Jackson that Lucas is a knave or Joseph is a knight.", "Joseph cannot be a knave, because this would contradict the claim of Lucas that Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the false claim of Jackson that Lucas is a knave or Joseph is a knight.", "We have exhausted all possibilities for Lucas, Jackson, and Harper, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Harper is not a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Jackson is a knight and Joseph is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Lucas is a knave or Joseph is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Evelyn is a knight then David is a knave.", "Evelyn cannot be a knight, because this would contradict the false claim of David that Henry is a knave and Evelyn is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Jackson is not a knight.", "Assume Emily is a knight. No contradiction is found in their claim that If Evelyn is a knight then Lucas is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 5), ('telling-truth', 3)), ('telling-truth', 6), ('->', ('telling-truth', 3), ('telling-truth', 1)), ('not', ('telling-truth', 7)), ('and', ('telling-truth', 7), ('telling-truth', 6)), ('not', ('telling-truth', 4)), ('->', ('telling-truth', 3), ('lying', 0)), ('or', ('lying', 1), ('telling-truth', 6)))", "index": 849}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Victoria, Sophia, Jackson, Sebastian, Sofia, Joseph, William, and Oliver. Victoria asserted: \"Oliver is a knight\". Sophia remarked, \"If Jackson is a knave then Sebastian is a knave\". \"If Victoria is a knave then Jackson is a knight\" - Jackson. In Sebastian's words: \"Victoria is a knave if and only if Sophia is a knight\". Sofia commented, \"Sebastian is a knave and Joseph is a knave\". Joseph expressed that Sophia is a knight. \"Sebastian is a knight,\" William claimed. In a statement by Oliver: \"William is a knave and William is a knight\". So who is a knight and who is a knave?", "names": ["Victoria", "Sophia", "Jackson", "Sebastian", "Sofia", "Joseph", "William", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true, true, false], "solution_text": "Victoria is a knave, Sophia is a knight, Jackson is a knight, Sebastian is a knight, Sofia is a knave, Joseph is a knight, William is a knight, and Oliver is a knave.", "solution_text_format": "(1) Victoria is a knave\n(2) Sophia is a knight\n(3) Jackson is a knight\n(4) Sebastian is a knight\n(5) Sofia is a knave\n(6) Joseph is a knight\n(7) William is a knight\n(8) Oliver is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that Oliver is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that William is a knave and William is a knight.", "Oliver cannot be a knave, because this would contradict the claim of Victoria that Oliver is a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Oliver is a knight.", "Oliver cannot be a knight, because this would contradict the false claim of Victoria that Oliver is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that William is a knave and William is a knight.", "Assume William is a knight. No contradiction is found in their claim that Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Victoria is a knave if and only if Sophia is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that If Jackson is a knave then Sebastian is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that If Victoria is a knave then Jackson is a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave and Joseph is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Sebastian is a knave and Joseph is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Sophia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 7), ('->', ('lying', 2), ('lying', 3)), ('->', ('lying', 0), ('telling-truth', 2)), ('<=>', ('lying', 0), ('telling-truth', 1)), ('and', ('lying', 3), ('lying', 5)), ('telling-truth', 1), ('telling-truth', 3), ('and', ('lying', 6), ('telling-truth', 6)))", "index": 850}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Charlotte, Joseph, Alexander, Lily, Logan, Mia, Penelope, and Ethan. \"Logan is not a knave,\" Charlotte declared. Joseph stated, \"Penelope is not a knave\". Alexander told you that If Mia is a knight then Lily is a knave. \"Joseph is a knave if and only if Charlotte is a knight,\" Lily mentioned. \"If Lily is a knave then Charlotte is a knave\" - Logan. \"Lily is a knave,\" Mia declared. In a statement by Penelope: \"If Alexander is a knight then Charlotte is a knave\". Ethan was heard saying, \"Joseph is a knight\". So who is a knight and who is a knave?", "names": ["Charlotte", "Joseph", "Alexander", "Lily", "Logan", "Mia", "Penelope", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false, false, false], "solution_text": "Charlotte is a knight, Joseph is a knave, Alexander is a knight, Lily is a knight, Logan is a knight, Mia is a knave, Penelope is a knave, and Ethan is a knave.", "solution_text_format": "(1) Charlotte is a knight\n(2) Joseph is a knave\n(3) Alexander is a knight\n(4) Lily is a knight\n(5) Logan is a knight\n(6) Mia is a knave\n(7) Penelope is a knave\n(8) Ethan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that Logan is not a knave.", "Assume Logan is a knight. No contradiction is found in their claim that If Lily is a knave then Charlotte is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Joseph is a knave if and only if Charlotte is a knight.", "Joseph cannot be a knight, because this would contradict the claim of Lily that Joseph is a knave if and only if Charlotte is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Penelope is not a knave.", "Penelope cannot be a knight, because this would contradict the false claim of Joseph that Penelope is not a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that If Alexander is a knight then Charlotte is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that If Mia is a knight then Lily is a knave.", "Mia cannot be a knight, because this would contradict the claim of Alexander that If Mia is a knight then Lily is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Lily is a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Joseph is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Joseph is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('not', ('lying', 6)), ('->', ('telling-truth', 5), ('lying', 3)), ('<=>', ('lying', 1), ('telling-truth', 0)), ('->', ('lying', 3), ('lying', 0)), ('lying', 3), ('->', ('telling-truth', 2), ('lying', 0)), ('telling-truth', 1))", "index": 851}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Joseph, Ava, Olivia, Jack, Grace, Harper, Noah, and Jackson. Joseph expressed that Jackson is a knave if and only if Joseph is a knight. Ava noted, \"Jackson is not a knave\". Olivia commented, \"Jackson is a knight\". \"Harper is a knight or Joseph is a knight,\" Jack declared. Grace stated, \"Joseph is a knave if and only if Joseph is a knight\". Harper asserted: \"Ava is a knight and Jack is a knight\". \"Harper is a knave and Harper is a knight,\" Noah claimed. As Jackson put it, \"If Ava is a knave then Jack is a knight\". So who is a knight and who is a knave?", "names": ["Joseph", "Ava", "Olivia", "Jack", "Grace", "Harper", "Noah", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, false, false, false], "solution_text": "Joseph is a knave, Ava is a knave, Olivia is a knave, Jack is a knave, Grace is a knave, Harper is a knave, Noah is a knave, and Jackson is a knave.", "solution_text_format": "(1) Joseph is a knave\n(2) Ava is a knave\n(3) Olivia is a knave\n(4) Jack is a knave\n(5) Grace is a knave\n(6) Harper is a knave\n(7) Noah is a knave\n(8) Jackson is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that Jackson is a knave if and only if Joseph is a knight.", "Jackson cannot be a knight, because this would contradict the claim of Joseph that Jackson is a knave if and only if Joseph is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that If Ava is a knave then Jack is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Jackson is not a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Jackson is not a knave.", "Jack cannot be a knight, because this would contradict the false claim of Jackson that If Ava is a knave then Jack is a knight.", "Jack cannot be a knave, because this would contradict the false claim of their own that Harper is a knight or Joseph is a knight.", "We have exhausted all possibilities for Jack, Ava, and Jackson, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Jackson is a knave if and only if Joseph is a knight.", "Jackson cannot be a knight, because this would contradict the false claim of Joseph that Jackson is a knave if and only if Joseph is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that If Ava is a knave then Jack is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Jackson is not a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Jackson is not a knave.", "Jack cannot be a knight, because this would contradict the false claim of Jackson that If Ava is a knave then Jack is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Harper is a knight or Joseph is a knight.", "Harper cannot be a knight, because this would contradict the false claim of Jack that Harper is a knight or Joseph is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Ava is a knight and Jack is a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that Jackson is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Jackson is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Joseph is a knave if and only if Joseph is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Joseph is a knave if and only if Joseph is a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that Harper is a knave and Harper is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Harper is a knave and Harper is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 7), ('telling-truth', 0)), ('not', ('lying', 7)), ('telling-truth', 7), ('or', ('telling-truth', 5), ('telling-truth', 0)), ('<=>', ('lying', 0), ('telling-truth', 0)), ('and', ('telling-truth', 1), ('telling-truth', 3)), ('and', ('lying', 5), ('telling-truth', 5)), ('->', ('lying', 1), ('telling-truth', 3)))", "index": 852}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Evelyn, Aiden, Ella, Benjamin, Emma, Logan, Chloe, and Joseph. Evelyn said that Chloe is a knight if and only if Logan is a knave. In Aiden's words: \"Chloe is not a knight\". \"Evelyn is a knave if and only if Benjamin is a knave\" - Ella. As Benjamin put it, \"Joseph is a knight or Evelyn is a knave\". Emma asserted: \"Ella is not a knave\". Logan said that Joseph is a knave if and only if Ella is a knave. Chloe was heard saying, \"Joseph is a knight\". \"Aiden is a knight if and only if Joseph is a knight\" - Joseph. So who is a knight and who is a knave?", "names": ["Evelyn", "Aiden", "Ella", "Benjamin", "Emma", "Logan", "Chloe", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, true, false, false], "solution_text": "Evelyn is a knight, Aiden is a knight, Ella is a knave, Benjamin is a knave, Emma is a knave, Logan is a knight, Chloe is a knave, and Joseph is a knave.", "solution_text_format": "(1) Evelyn is a knight\n(2) Aiden is a knight\n(3) Ella is a knave\n(4) Benjamin is a knave\n(5) Emma is a knave\n(6) Logan is a knight\n(7) Chloe is a knave\n(8) Joseph is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Chloe is a knight if and only if Logan is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Aiden is a knight if and only if Joseph is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Chloe is not a knight.", "Aiden cannot be a knave, because this would contradict the claim of Joseph that Aiden is a knight if and only if Joseph is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of Chloe that Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of Chloe that Joseph is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Aiden is a knight if and only if Joseph is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Chloe is not a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Joseph is a knave if and only if Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of Logan that Joseph is a knave if and only if Ella is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Evelyn is a knave if and only if Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Ella that Evelyn is a knave if and only if Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Joseph is a knight or Evelyn is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Ella is not a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Ella is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 6), ('lying', 5)), ('not', ('telling-truth', 6)), ('<=>', ('lying', 0), ('lying', 3)), ('or', ('telling-truth', 7), ('lying', 0)), ('not', ('lying', 2)), ('<=>', ('lying', 7), ('lying', 2)), ('telling-truth', 7), ('<=>', ('telling-truth', 1), ('telling-truth', 7)))", "index": 853}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Amelia, Zoey, Olivia, Isabella, Victoria, Benjamin, Aiden, and Chloe. \"Amelia is a knight or Aiden is a knight,\" Amelia mentioned. According to Zoey, \"Isabella is a knight or Olivia is a knave\". \"Isabella is a knight,\" Olivia claimed. As Isabella put it, \"Amelia is a knight if and only if Zoey is a knave\". Victoria remarked, \"Chloe is a knave or Amelia is a knave\". Benjamin said that If Chloe is a knave then Isabella is a knave. Aiden told you that Benjamin is not a knight. Chloe commented, \"Olivia is a knave or Victoria is a knave\". So who is a knight and who is a knave?", "names": ["Amelia", "Zoey", "Olivia", "Isabella", "Victoria", "Benjamin", "Aiden", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, true, false, true], "solution_text": "Amelia is a knight, Zoey is a knight, Olivia is a knave, Isabella is a knave, Victoria is a knave, Benjamin is a knight, Aiden is a knave, and Chloe is a knight.", "solution_text_format": "(1) Amelia is a knight\n(2) Zoey is a knight\n(3) Olivia is a knave\n(4) Isabella is a knave\n(5) Victoria is a knave\n(6) Benjamin is a knight\n(7) Aiden is a knave\n(8) Chloe is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Amelia is a knight. No contradiction is found in their claim that Amelia is a knight or Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Benjamin is not a knight.", "Benjamin cannot be a knight, because this would contradict the claim of Aiden that Benjamin is not a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that If Chloe is a knave then Isabella is a knave.", "Chloe cannot be a knight, because this would contradict the false claim of Benjamin that If Chloe is a knave then Isabella is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Olivia is a knave or Victoria is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Isabella is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Amelia is a knight if and only if Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Isabella that Amelia is a knight if and only if Zoey is a knave.", "Zoey cannot be a knave, because this would contradict the false claim of their own that Isabella is a knight or Olivia is a knave.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the claim of Olivia that Isabella is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the false claim of Chloe that Olivia is a knave or Victoria is a knave.", "We have exhausted all possibilities for Olivia, Chloe, and Benjamin, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Benjamin is not a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Chloe is a knave then Isabella is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Olivia is a knave or Victoria is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Isabella is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Amelia is a knight if and only if Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Isabella that Amelia is a knight if and only if Zoey is a knave.", "Zoey cannot be a knave, because this would contradict the false claim of their own that Isabella is a knight or Olivia is a knave.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the claim of Olivia that Isabella is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Isabella is a knight.", "Isabella cannot be a knight, because this would contradict the false claim of Olivia that Isabella is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Amelia is a knight if and only if Zoey is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Isabella is a knight or Olivia is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that Chloe is a knave or Amelia is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Chloe is a knave or Amelia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 0), ('telling-truth', 6)), ('or', ('telling-truth', 3), ('lying', 2)), ('telling-truth', 3), ('<=>', ('telling-truth', 0), ('lying', 1)), ('or', ('lying', 7), ('lying', 0)), ('->', ('lying', 7), ('lying', 3)), ('not', ('telling-truth', 5)), ('or', ('lying', 2), ('lying', 4)))", "index": 854}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ava, Riley, Evelyn, Sophia, Zoey, Mia, Alexander, and Charlotte. Ava was heard saying, \"Alexander is a knave if and only if Charlotte is a knight\". Riley said, \"Charlotte is a knight and Riley is a knight.\" \"If Sophia is a knight then Charlotte is a knave,\" Evelyn declared. In Sophia's words: \"Evelyn is a knight and Riley is a knight\". \"Charlotte is a knave,\" Zoey declared. \"Evelyn is a knight and Riley is a knight,\" Mia mentioned. Alexander was heard saying, \"Sophia is a knight or Riley is a knave\". According to Charlotte, \"Mia is not a knave\". So who is a knight and who is a knave?", "names": ["Ava", "Riley", "Evelyn", "Sophia", "Zoey", "Mia", "Alexander", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, false, true, false], "solution_text": "Ava is a knight, Riley is a knave, Evelyn is a knight, Sophia is a knave, Zoey is a knight, Mia is a knave, Alexander is a knight, and Charlotte is a knave.", "solution_text_format": "(1) Ava is a knight\n(2) Riley is a knave\n(3) Evelyn is a knight\n(4) Sophia is a knave\n(5) Zoey is a knight\n(6) Mia is a knave\n(7) Alexander is a knight\n(8) Charlotte is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Alexander is a knave if and only if Charlotte is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Sophia is a knight or Riley is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Evelyn is a knight and Riley is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Sophia is a knight then Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Ava that Alexander is a knave if and only if Charlotte is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Mia is not a knave.", "Mia cannot be a knight, because this would contradict the false claim of Charlotte that Mia is not a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Evelyn is a knight and Riley is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Charlotte is a knight and Riley is a knight.", "Riley cannot be a knave, because this would contradict the claim of Sophia that Evelyn is a knight and Riley is a knight.", "We have exhausted all possibilities for Riley, Mia, and Charlotte, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the claim of Sophia that Evelyn is a knight and Riley is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Evelyn is a knight and Riley is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Sophia is a knight then Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Ava that Alexander is a knave if and only if Charlotte is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Mia is not a knave.", "Mia cannot be a knight, because this would contradict the false claim of Charlotte that Mia is not a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Evelyn is a knight and Riley is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Charlotte is a knight and Riley is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Charlotte is a knight and Riley is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Charlotte is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 6), ('telling-truth', 7)), ('and', ('telling-truth', 7), ('telling-truth', 1)), ('->', ('telling-truth', 3), ('lying', 7)), ('and', ('telling-truth', 2), ('telling-truth', 1)), ('lying', 7), ('and', ('telling-truth', 2), ('telling-truth', 1)), ('or', ('telling-truth', 3), ('lying', 1)), ('not', ('lying', 5)))", "index": 855}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Benjamin, William, Lily, Jackson, Penelope, Emily, Harper, and Chloe. Benjamin asserted: \"Harper is a knight\". William asserted: \"Penelope is not a knave\". Lily commented, \"If Benjamin is a knight then Penelope is a knight\". \"Emily is a knave and Penelope is a knave,\" Jackson declared. As Penelope put it, \"If Chloe is a knight then Benjamin is a knave\". Emily stated, \"Benjamin is a knight and Lily is a knight\". Harper said, \"Emily is a knave.\" \"If Lily is a knight then Harper is a knave,\" Chloe declared. So who is a knight and who is a knave?", "names": ["Benjamin", "William", "Lily", "Jackson", "Penelope", "Emily", "Harper", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, false, true, true], "solution_text": "Benjamin is a knight, William is a knave, Lily is a knave, Jackson is a knight, Penelope is a knave, Emily is a knave, Harper is a knight, and Chloe is a knight.", "solution_text_format": "(1) Benjamin is a knight\n(2) William is a knave\n(3) Lily is a knave\n(4) Jackson is a knight\n(5) Penelope is a knave\n(6) Emily is a knave\n(7) Harper is a knight\n(8) Chloe is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Harper is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of Harper that Emily is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Benjamin is a knight and Lily is a knight.", "Lily cannot be a knight, because this would contradict the false claim of Emily that Benjamin is a knight and Lily is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that If Benjamin is a knight then Penelope is a knight.", "Penelope cannot be a knight, because this would contradict the false claim of Lily that If Benjamin is a knight then Penelope is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that If Chloe is a knight then Benjamin is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that If Lily is a knight then Harper is a knave.", "William cannot be a knight, because this would contradict the claim of their own that Penelope is not a knave.", "Assume William is a knave. No contradiction is found in their false claim that Penelope is not a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Emily is a knave and Penelope is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 6), ('not', ('lying', 4)), ('->', ('telling-truth', 0), ('telling-truth', 4)), ('and', ('lying', 5), ('lying', 4)), ('->', ('telling-truth', 7), ('lying', 0)), ('and', ('telling-truth', 0), ('telling-truth', 2)), ('lying', 5), ('->', ('telling-truth', 2), ('lying', 6)))", "index": 856}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Victoria, Abigail, Jacob, Ethan, Mason, Ava, Emma, and Matthew. In Victoria's words: \"Ava is not a knave\". Abigail said that Mason is a knave or Mason is a knight. In a statement by Jacob: \"Victoria is a knave or Abigail is a knave\". Ethan commented, \"Jacob is a knight\". As Mason put it, \"Victoria is a knight\". Ava asserted: \"Victoria is a knight if and only if Ethan is a knight\". Emma noted, \"Matthew is not a knight\". Matthew expressed that Jacob is a knave. So who is a knight and who is a knave?", "names": ["Victoria", "Abigail", "Jacob", "Ethan", "Mason", "Ava", "Emma", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false, true, false], "solution_text": "Victoria is a knave, Abigail is a knight, Jacob is a knight, Ethan is a knight, Mason is a knave, Ava is a knave, Emma is a knight, and Matthew is a knave.", "solution_text_format": "(1) Victoria is a knave\n(2) Abigail is a knight\n(3) Jacob is a knight\n(4) Ethan is a knight\n(5) Mason is a knave\n(6) Ava is a knave\n(7) Emma is a knight\n(8) Matthew is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that Ava is not a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Ethan is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Victoria is a knave or Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Jacob that Victoria is a knave or Abigail is a knave.", "Abigail cannot be a knave, because this would contradict the false claim of their own that Mason is a knave or Mason is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the claim of Ethan that Jacob is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the claim of Ava that Victoria is a knight if and only if Ethan is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the claim of Victoria that Ava is not a knave.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Ava is not a knave.", "Ava cannot be a knight, because this would contradict the false claim of Victoria that Ava is not a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Victoria is a knight if and only if Ethan is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Victoria is a knave or Abigail is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Mason is a knave or Mason is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Victoria is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Victoria is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Matthew is not a knight.", "Matthew cannot be a knight, because this would contradict the claim of Emma that Matthew is not a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Jacob is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 5)), ('or', ('lying', 4), ('telling-truth', 4)), ('or', ('lying', 0), ('lying', 1)), ('telling-truth', 2), ('telling-truth', 0), ('<=>', ('telling-truth', 0), ('telling-truth', 3)), ('not', ('telling-truth', 7)), ('lying', 2))", "index": 857}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jackson, Riley, Matthew, Zoey, Alexander, Isabella, Abigail, and Jack. In Jackson's words: \"Matthew is a knave or Jack is a knight\". Riley commented, \"Isabella is a knave\". \"Isabella is a knight and Isabella is a knave,\" Matthew mentioned. Zoey told you that Matthew is a knight or Riley is a knight. According to Alexander, \"If Zoey is a knight then Abigail is a knave\". \"Zoey is a knight or Jackson is a knight,\" Isabella mentioned. Abigail expressed that Zoey is not a knave. Jack commented, \"Zoey is a knave if and only if Matthew is a knave\". So who is a knight and who is a knave?", "names": ["Jackson", "Riley", "Matthew", "Zoey", "Alexander", "Isabella", "Abigail", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true, false, true], "solution_text": "Jackson is a knight, Riley is a knave, Matthew is a knave, Zoey is a knave, Alexander is a knight, Isabella is a knight, Abigail is a knave, and Jack is a knight.", "solution_text_format": "(1) Jackson is a knight\n(2) Riley is a knave\n(3) Matthew is a knave\n(4) Zoey is a knave\n(5) Alexander is a knight\n(6) Isabella is a knight\n(7) Abigail is a knave\n(8) Jack is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Matthew is a knave or Jack is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Isabella is a knight and Isabella is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Isabella is a knight and Isabella is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Zoey is a knight or Jackson is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Matthew is a knight or Riley is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Isabella is a knave.", "Riley cannot be a knave, because this would contradict the claim of Zoey that Matthew is a knight or Riley is a knight.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Matthew is a knight or Riley is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Isabella is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Isabella is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Zoey is a knave if and only if Matthew is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that If Zoey is a knight then Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Zoey is not a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Zoey is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('telling-truth', 7)), ('lying', 5), ('and', ('telling-truth', 5), ('lying', 5)), ('or', ('telling-truth', 2), ('telling-truth', 1)), ('->', ('telling-truth', 3), ('lying', 6)), ('or', ('telling-truth', 3), ('telling-truth', 0)), ('not', ('lying', 3)), ('<=>', ('lying', 3), ('lying', 2)))", "index": 858}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Joseph, Liam, James, Grace, Lily, David, Amelia, and Riley. \"James is not a knight,\" Joseph mentioned. As Liam put it, \"Riley is a knight or Joseph is a knight\". James said that David is a knight and Amelia is a knight. Grace noted, \"Riley is a knight if and only if Joseph is a knave\". According to Lily, \"James is a knave\". David remarked, \"Grace is a knight and Joseph is a knave\". Amelia was heard saying, \"Lily is not a knight\". According to Riley, \"Amelia is a knave or Lily is a knight\". So who is a knight and who is a knave?", "names": ["Joseph", "Liam", "James", "Grace", "Lily", "David", "Amelia", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, false, false, true], "solution_text": "Joseph is a knight, Liam is a knight, James is a knave, Grace is a knave, Lily is a knight, David is a knave, Amelia is a knave, and Riley is a knight.", "solution_text_format": "(1) Joseph is a knight\n(2) Liam is a knight\n(3) James is a knave\n(4) Grace is a knave\n(5) Lily is a knight\n(6) David is a knave\n(7) Amelia is a knave\n(8) Riley is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that James is not a knight.", "James cannot be a knight, because this would contradict the claim of Joseph that James is not a knight.", "Assume James is a knave. No contradiction is found in their false claim that David is a knight and Amelia is a knight.", "David cannot be a knight, because this would contradict the claim of their own that Grace is a knight and Joseph is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Grace is a knight and Joseph is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Riley is a knight if and only if Joseph is a knave.", "Riley cannot be a knight, because this would contradict the claim of Grace that Riley is a knight if and only if Joseph is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Amelia is a knave or Lily is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Lily is not a knight.", "Lily cannot be a knight, because this would contradict the claim of Amelia that Lily is not a knight.", "Lily cannot be a knave, because this would contradict the false claim of their own that James is a knave.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Amelia.", "Amelia cannot be a knave, because this would contradict the false claim of Riley that Amelia is a knave or Lily is a knight.", "We have exhausted all possibilities for Amelia and Riley, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Joseph is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Amelia is a knave or Lily is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Lily is not a knight.", "Lily cannot be a knight, because this would contradict the claim of Amelia that Lily is not a knight.", "Lily cannot be a knave, because this would contradict the false claim of their own that James is a knave.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Lily is not a knight.", "Assume Lily is a knight. No contradiction is found in their claim that James is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Riley is a knight or Joseph is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('or', ('telling-truth', 7), ('telling-truth', 0)), ('and', ('telling-truth', 5), ('telling-truth', 6)), ('<=>', ('telling-truth', 7), ('lying', 0)), ('lying', 2), ('and', ('telling-truth', 3), ('lying', 0)), ('not', ('telling-truth', 4)), ('or', ('lying', 6), ('telling-truth', 4)))", "index": 859}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Liam, Jacob, Grace, Benjamin, Charlotte, Daniel, Ava, and Alexander. In a statement by Liam: \"If Ava is a knight then Ava is a knave\". Jacob commented, \"Charlotte is not a knave\". Grace told you that Ava is a knave or Alexander is a knave. In Benjamin's words: \"Daniel is a knight or Grace is a knave\". Charlotte noted, \"Ava is not a knight\". Daniel stated, \"If Jacob is a knave then Alexander is a knave\". In Ava's words: \"Ava is a knight and Jacob is a knight\". Alexander was heard saying, \"If Ava is a knave then Grace is a knave\". So who is a knight and who is a knave?", "names": ["Liam", "Jacob", "Grace", "Benjamin", "Charlotte", "Daniel", "Ava", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true, false, false], "solution_text": "Liam is a knight, Jacob is a knight, Grace is a knight, Benjamin is a knight, Charlotte is a knight, Daniel is a knight, Ava is a knave, and Alexander is a knave.", "solution_text_format": "(1) Liam is a knight\n(2) Jacob is a knight\n(3) Grace is a knight\n(4) Benjamin is a knight\n(5) Charlotte is a knight\n(6) Daniel is a knight\n(7) Ava is a knave\n(8) Alexander is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that If Ava is a knight then Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of Liam that If Ava is a knight then Ava is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Ava is a knight and Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Charlotte is not a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Ava is not a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Ava is a knave or Alexander is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that If Ava is a knave then Grace is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that If Ava is a knave then Grace is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Daniel is a knight or Grace is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that If Jacob is a knave then Alexander is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 6), ('lying', 6)), ('not', ('lying', 4)), ('or', ('lying', 6), ('lying', 7)), ('or', ('telling-truth', 5), ('lying', 2)), ('not', ('telling-truth', 6)), ('->', ('lying', 1), ('lying', 7)), ('and', ('telling-truth', 6), ('telling-truth', 1)), ('->', ('lying', 6), ('lying', 2)))", "index": 860}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: David, Scarlett, Aiden, Isabella, Luke, Aurora, Sofia, and Riley. David said, \"Isabella is a knave.\" As Scarlett put it, \"David is a knave or Sofia is a knave\". Aiden asserted: \"If Aurora is a knight then Luke is a knight\". Isabella asserted: \"Riley is a knight\". Luke stated, \"Scarlett is a knave if and only if Aiden is a knave\". Aurora remarked, \"Luke is not a knave\". \"If Isabella is a knave then Scarlett is a knave,\" Sofia claimed. Riley stated, \"Aiden is not a knave\". So who is a knight and who is a knave?", "names": ["David", "Scarlett", "Aiden", "Isabella", "Luke", "Aurora", "Sofia", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true, true, true], "solution_text": "David is a knave, Scarlett is a knight, Aiden is a knight, Isabella is a knight, Luke is a knight, Aurora is a knight, Sofia is a knight, and Riley is a knight.", "solution_text_format": "(1) David is a knave\n(2) Scarlett is a knight\n(3) Aiden is a knight\n(4) Isabella is a knight\n(5) Luke is a knight\n(6) Aurora is a knight\n(7) Sofia is a knight\n(8) Riley is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Isabella is a knave.", "Isabella cannot be a knight, because this would contradict the claim of David that Isabella is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Riley is a knight.", "Riley cannot be a knight, because this would contradict the false claim of Isabella that Riley is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Aiden is not a knave.", "Aiden cannot be a knight, because this would contradict the false claim of Riley that Aiden is not a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that If Aurora is a knight then Luke is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Luke is not a knave.", "Luke cannot be a knight, because this would contradict the false claim of Aiden that If Aurora is a knight then Luke is a knight.", "Luke cannot be a knave, because this would contradict the claim of Aurora that Luke is not a knave.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the false claim of Aiden that If Aurora is a knight then Luke is a knight.", "We have exhausted all possibilities for Aurora, Aiden, Riley, and Isabella, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Isabella is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Riley is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Aiden is not a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Aurora is a knight then Luke is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Luke is not a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Scarlett is a knave if and only if Aiden is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that David is a knave or Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that If Isabella is a knave then Scarlett is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('or', ('lying', 0), ('lying', 6)), ('->', ('telling-truth', 5), ('telling-truth', 4)), ('telling-truth', 7), ('<=>', ('lying', 1), ('lying', 2)), ('not', ('lying', 4)), ('->', ('lying', 3), ('lying', 1)), ('not', ('lying', 2)))", "index": 861}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emma, Luke, Michael, Evelyn, Lily, Sophia, Joseph, and Henry. Emma told you that Michael is a knight or Henry is a knight. Luke stated, \"Henry is a knave\". \"Joseph is a knave and Evelyn is a knight,\" Michael declared. Evelyn remarked, \"Luke is a knight and Lily is a knight\". Lily told you that Luke is a knight and Evelyn is a knave. Sophia said that Luke is a knave. Joseph said that Emma is not a knight. \"Henry is a knight or Joseph is a knave\" - Henry. So who is a knight and who is a knave?", "names": ["Emma", "Luke", "Michael", "Evelyn", "Lily", "Sophia", "Joseph", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, true, false, true], "solution_text": "Emma is a knight, Luke is a knave, Michael is a knave, Evelyn is a knave, Lily is a knave, Sophia is a knight, Joseph is a knave, and Henry is a knight.", "solution_text_format": "(1) Emma is a knight\n(2) Luke is a knave\n(3) Michael is a knave\n(4) Evelyn is a knave\n(5) Lily is a knave\n(6) Sophia is a knight\n(7) Joseph is a knave\n(8) Henry is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Michael is a knight or Henry is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Joseph is a knave and Evelyn is a knight.", "Joseph cannot be a knight, because this would contradict the claim of Michael that Joseph is a knave and Evelyn is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Emma is not a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Luke is a knight and Lily is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of Luke that Henry is a knave.", "Henry cannot be a knave, because this would contradict the false claim of their own that Henry is a knight or Joseph is a knave.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the claim of Evelyn that Luke is a knight and Lily is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the claim of Michael that Joseph is a knave and Evelyn is a knight.", "We have exhausted all possibilities for Evelyn and Joseph, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Joseph is a knave and Evelyn is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Emma is not a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Emma is not a knight.", "Evelyn cannot be a knight, because this would contradict the false claim of Michael that Joseph is a knave and Evelyn is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Luke is a knight and Lily is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of Luke that Henry is a knave.", "Henry cannot be a knave, because this would contradict the claim of Emma that Michael is a knight or Henry is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Henry is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Henry is a knight or Joseph is a knave.", "Lily cannot be a knight, because this would contradict the claim of their own that Luke is a knight and Evelyn is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Luke is a knight and Evelyn is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Luke is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('telling-truth', 7)), ('lying', 7), ('and', ('lying', 6), ('telling-truth', 3)), ('and', ('telling-truth', 1), ('telling-truth', 4)), ('and', ('telling-truth', 1), ('lying', 3)), ('lying', 1), ('not', ('telling-truth', 0)), ('or', ('telling-truth', 7), ('lying', 6)))", "index": 862}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sophia, Lily, Penelope, Ava, Owen, Jackson, Jack, and James. Sophia was heard saying, \"Jackson is a knave if and only if Jackson is a knight\". Lily remarked, \"Owen is a knave\". Penelope remarked, \"Jack is a knight or James is a knave\". Ava was heard saying, \"Sophia is a knight or James is a knave\". Owen stated, \"Sophia is a knight if and only if James is a knight\". Jackson noted, \"If Penelope is a knave then Sophia is a knight\". Jack expressed that Penelope is a knave and Sophia is a knight. In James's words: \"Sophia is not a knight\". So who is a knight and who is a knave?", "names": ["Sophia", "Lily", "Penelope", "Ava", "Owen", "Jackson", "Jack", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, false, false, true], "solution_text": "Sophia is a knave, Lily is a knight, Penelope is a knave, Ava is a knave, Owen is a knave, Jackson is a knave, Jack is a knave, and James is a knight.", "solution_text_format": "(1) Sophia is a knave\n(2) Lily is a knight\n(3) Penelope is a knave\n(4) Ava is a knave\n(5) Owen is a knave\n(6) Jackson is a knave\n(7) Jack is a knave\n(8) James is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Sophia cannot be a knight, because this would contradict the claim of their own that Jackson is a knave if and only if Jackson is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Jackson is a knave if and only if Jackson is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that If Penelope is a knave then Sophia is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Jack is a knight or James is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Penelope is a knave and Sophia is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Penelope is a knave and Sophia is a knight.", "James cannot be a knight, because this would contradict the claim of Penelope that Jack is a knight or James is a knave.", "James cannot be a knave, because this would contradict the false claim of their own that Sophia is not a knight.", "We have exhausted all possibilities for James and Jack, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the claim of Jackson that If Penelope is a knave then Sophia is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that If Penelope is a knave then Sophia is a knight.", "Penelope cannot be a knight, because this would contradict the false claim of Jackson that If Penelope is a knave then Sophia is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Jack is a knight or James is a knave.", "Jack cannot be a knight, because this would contradict the false claim of Penelope that Jack is a knight or James is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Penelope is a knave and Sophia is a knight.", "Assume James is a knight. No contradiction is found in their claim that Sophia is not a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of Lily that Owen is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Sophia is a knight if and only if James is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Sophia is a knight or James is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Sophia is a knight or James is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 5), ('telling-truth', 5)), ('lying', 4), ('or', ('telling-truth', 6), ('lying', 7)), ('or', ('telling-truth', 0), ('lying', 7)), ('<=>', ('telling-truth', 0), ('telling-truth', 7)), ('->', ('lying', 2), ('telling-truth', 0)), ('and', ('lying', 2), ('telling-truth', 0)), ('not', ('telling-truth', 0)))", "index": 863}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: James, Sophia, Ethan, Liam, Samuel, Lily, Daniel, and Alexander. \"Alexander is a knight if and only if Samuel is a knight,\" James mentioned. Sophia noted, \"James is a knight\". In Ethan's words: \"If Sophia is a knight then Daniel is a knave\". In a statement by Liam: \"Sophia is a knight\". \"Alexander is a knave,\" Samuel mentioned. Lily told you that Sophia is not a knight. According to Daniel, \"Alexander is a knight if and only if James is a knave\". In Alexander's words: \"Alexander is a knight or Daniel is a knave\". So who is a knight and who is a knave?", "names": ["James", "Sophia", "Ethan", "Liam", "Samuel", "Lily", "Daniel", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, true, true, true], "solution_text": "James is a knave, Sophia is a knave, Ethan is a knight, Liam is a knave, Samuel is a knave, Lily is a knight, Daniel is a knight, and Alexander is a knight.", "solution_text_format": "(1) James is a knave\n(2) Sophia is a knave\n(3) Ethan is a knight\n(4) Liam is a knave\n(5) Samuel is a knave\n(6) Lily is a knight\n(7) Daniel is a knight\n(8) Alexander is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Alexander is a knight if and only if Samuel is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Alexander is a knight or Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of their own that Alexander is a knight if and only if James is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Alexander is a knight if and only if James is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that Alexander is a knave.", "Samuel cannot be a knave, because this would contradict the claim of James that Alexander is a knight if and only if Samuel is a knight.", "We have exhausted all possibilities for Samuel and Daniel, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Alexander is a knight or Daniel is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Alexander is a knight if and only if James is a knave.", "Samuel cannot be a knight, because this would contradict the claim of James that Alexander is a knight if and only if Samuel is a knight.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Alexander is a knave.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the false claim of their own that Alexander is a knight if and only if James is a knave.", "We have exhausted all possibilities for Daniel and Alexander, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Alexander is a knight if and only if Samuel is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Alexander is a knight or Daniel is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Alexander is a knight if and only if James is a knave.", "Samuel cannot be a knight, because this would contradict the false claim of James that Alexander is a knight if and only if Samuel is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Alexander is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that James is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that James is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If Sophia is a knight then Daniel is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Sophia is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Sophia is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Sophia is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 7), ('telling-truth', 4)), ('telling-truth', 0), ('->', ('telling-truth', 1), ('lying', 6)), ('telling-truth', 1), ('lying', 7), ('not', ('telling-truth', 1)), ('<=>', ('telling-truth', 7), ('lying', 0)), ('or', ('telling-truth', 7), ('lying', 6)))", "index": 864}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Oliver, Owen, Michael, William, Jacob, Elizabeth, Ella, and Logan. Oliver stated, \"Jacob is a knave if and only if Michael is a knight\". \"Logan is a knight\" - Owen. \"Oliver is not a knight,\" Michael mentioned. \"Logan is a knight and Michael is a knave,\" William claimed. Jacob expressed that Oliver is not a knave. In a statement by Elizabeth: \"Oliver is a knave or Owen is a knight\". \"Logan is a knight or Elizabeth is a knave,\" Ella declared. Logan asserted: \"Michael is a knave if and only if Ella is a knight\". So who is a knight and who is a knave?", "names": ["Oliver", "Owen", "Michael", "William", "Jacob", "Elizabeth", "Ella", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true, true, true], "solution_text": "Oliver is a knight, Owen is a knight, Michael is a knave, William is a knight, Jacob is a knight, Elizabeth is a knight, Ella is a knight, and Logan is a knight.", "solution_text_format": "(1) Oliver is a knight\n(2) Owen is a knight\n(3) Michael is a knave\n(4) William is a knight\n(5) Jacob is a knight\n(6) Elizabeth is a knight\n(7) Ella is a knight\n(8) Logan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Jacob is a knave if and only if Michael is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Oliver is not a knave.", "Michael cannot be a knight, because this would contradict the claim of Oliver that Jacob is a knave if and only if Michael is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Oliver is not a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Logan is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Michael is a knave if and only if Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Logan is a knight or Elizabeth is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Oliver is a knave or Owen is a knight.", "Assume William is a knight. No contradiction is found in their claim that Logan is a knight and Michael is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 4), ('telling-truth', 2)), ('telling-truth', 7), ('not', ('telling-truth', 0)), ('and', ('telling-truth', 7), ('lying', 2)), ('not', ('lying', 0)), ('or', ('lying', 0), ('telling-truth', 1)), ('or', ('telling-truth', 7), ('lying', 5)), ('<=>', ('lying', 2), ('telling-truth', 6)))", "index": 865}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Zoey, Avery, Ethan, Ella, Benjamin, Lily, Joseph, and Owen. Zoey said that Lily is a knave or Zoey is a knight. Avery remarked, \"If Lily is a knave then Owen is a knight\". According to Ethan, \"If Joseph is a knave then Benjamin is a knave\". \"If Ethan is a knave then Joseph is a knight,\" Ella mentioned. Benjamin was heard saying, \"Avery is a knight and Ethan is a knave\". \"Avery is a knave and Joseph is a knight,\" Lily mentioned. Joseph expressed that Benjamin is a knight if and only if Owen is a knight. \"Owen is a knight\" - Owen. So who is a knight and who is a knave?", "names": ["Zoey", "Avery", "Ethan", "Ella", "Benjamin", "Lily", "Joseph", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false, false, true], "solution_text": "Zoey is a knight, Avery is a knight, Ethan is a knight, Ella is a knight, Benjamin is a knave, Lily is a knave, Joseph is a knave, and Owen is a knight.", "solution_text_format": "(1) Zoey is a knight\n(2) Avery is a knight\n(3) Ethan is a knight\n(4) Ella is a knight\n(5) Benjamin is a knave\n(6) Lily is a knave\n(7) Joseph is a knave\n(8) Owen is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Zoey is a knight. No contradiction is found in their claim that Lily is a knave or Zoey is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Avery is a knave and Joseph is a knight.", "Avery cannot be a knight, because this would contradict the claim of Lily that Avery is a knave and Joseph is a knight.", "Avery cannot be a knave, because this would contradict the false claim of their own that If Lily is a knave then Owen is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Avery is a knave and Joseph is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that If Lily is a knave then Owen is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Owen is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Benjamin is a knight if and only if Owen is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Avery is a knight and Ethan is a knave.", "Ethan cannot be a knight, because this would contradict the claim of Benjamin that Avery is a knight and Ethan is a knave.", "Ethan cannot be a knave, because this would contradict the false claim of their own that If Joseph is a knave then Benjamin is a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the claim of Joseph that Benjamin is a knight if and only if Owen is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Benjamin is a knight if and only if Owen is a knight.", "Benjamin cannot be a knight, because this would contradict the false claim of Joseph that Benjamin is a knight if and only if Owen is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Avery is a knight and Ethan is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that If Joseph is a knave then Benjamin is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that If Ethan is a knave then Joseph is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 5), ('telling-truth', 0)), ('->', ('lying', 5), ('telling-truth', 7)), ('->', ('lying', 6), ('lying', 4)), ('->', ('lying', 2), ('telling-truth', 6)), ('and', ('telling-truth', 1), ('lying', 2)), ('and', ('lying', 1), ('telling-truth', 6)), ('<=>', ('telling-truth', 4), ('telling-truth', 7)), ('telling-truth', 7))", "index": 866}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jacob, Ava, Evelyn, Noah, Charlotte, David, Aria, and Michael. Jacob expressed that Michael is a knight if and only if Evelyn is a knave. Ava said, \"Michael is not a knight.\" Evelyn commented, \"Jacob is a knight if and only if Charlotte is a knight\". Noah said, \"If Evelyn is a knight then Aria is a knight.\" \"Evelyn is a knight and Aria is a knight,\" Charlotte declared. David said, \"Jacob is a knight and David is a knight.\" \"If Michael is a knight then Michael is a knave\" - Aria. Michael stated, \"If Evelyn is a knave then Ava is a knight\". So who is a knight and who is a knave?", "names": ["Jacob", "Ava", "Evelyn", "Noah", "Charlotte", "David", "Aria", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, false, false, true], "solution_text": "Jacob is a knave, Ava is a knave, Evelyn is a knight, Noah is a knave, Charlotte is a knave, David is a knave, Aria is a knave, and Michael is a knight.", "solution_text_format": "(1) Jacob is a knave\n(2) Ava is a knave\n(3) Evelyn is a knight\n(4) Noah is a knave\n(5) Charlotte is a knave\n(6) David is a knave\n(7) Aria is a knave\n(8) Michael is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that Michael is a knight if and only if Evelyn is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that If Evelyn is a knave then Ava is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of Jacob that Michael is a knight if and only if Evelyn is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Jacob is a knight if and only if Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of Evelyn that Jacob is a knight if and only if Charlotte is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Evelyn is a knight and Aria is a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that If Michael is a knight then Michael is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that If Michael is a knight then Michael is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Michael is not a knight.", "Ava cannot be a knave, because this would contradict the claim of Michael that If Evelyn is a knave then Ava is a knight.", "We have exhausted all possibilities for Ava, Aria, Charlotte, and Evelyn, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that If Evelyn is a knave then Ava is a knight.", "Evelyn cannot be a knight, because this would contradict the false claim of Michael that If Evelyn is a knave then Ava is a knight.", "Evelyn cannot be a knave, because this would contradict the claim of Jacob that Michael is a knight if and only if Evelyn is a knave.", "We have exhausted all possibilities for Evelyn and Michael, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Michael is a knight if and only if Evelyn is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that If Evelyn is a knave then Ava is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Jacob is a knight if and only if Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Evelyn that Jacob is a knight if and only if Charlotte is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Evelyn is a knight and Aria is a knight.", "Aria cannot be a knight, because this would contradict the false claim of Charlotte that Evelyn is a knight and Aria is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that If Michael is a knight then Michael is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Michael is not a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Michael is not a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that If Evelyn is a knight then Aria is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that If Evelyn is a knight then Aria is a knight.", "David cannot be a knight, because this would contradict the claim of their own that Jacob is a knight and David is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Jacob is a knight and David is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 7), ('lying', 2)), ('not', ('telling-truth', 7)), ('<=>', ('telling-truth', 0), ('telling-truth', 4)), ('->', ('telling-truth', 2), ('telling-truth', 6)), ('and', ('telling-truth', 2), ('telling-truth', 6)), ('and', ('telling-truth', 0), ('telling-truth', 5)), ('->', ('telling-truth', 7), ('lying', 7)), ('->', ('lying', 2), ('telling-truth', 1)))", "index": 867}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sophia, Oliver, Liam, Emma, Matthew, Amelia, Daniel, and Chloe. \"Chloe is a knave or Oliver is a knave,\" Sophia mentioned. In a statement by Oliver: \"If Liam is a knight then Chloe is a knave\". \"If Daniel is a knight then Oliver is a knave,\" Liam declared. \"Amelia is a knave,\" Emma claimed. \"Matthew is a knight or Daniel is a knave,\" Matthew declared. \"Emma is a knave and Matthew is a knight,\" Amelia mentioned. As Daniel put it, \"Oliver is a knave or Emma is a knave\". Chloe said, \"Matthew is a knight and Oliver is a knight.\" So who is a knight and who is a knave?", "names": ["Sophia", "Oliver", "Liam", "Emma", "Matthew", "Amelia", "Daniel", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true, true, true], "solution_text": "Sophia is a knave, Oliver is a knight, Liam is a knave, Emma is a knave, Matthew is a knight, Amelia is a knight, Daniel is a knight, and Chloe is a knight.", "solution_text_format": "(1) Sophia is a knave\n(2) Oliver is a knight\n(3) Liam is a knave\n(4) Emma is a knave\n(5) Matthew is a knight\n(6) Amelia is a knight\n(7) Daniel is a knight\n(8) Chloe is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Chloe is a knave or Oliver is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Matthew is a knight and Oliver is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Matthew is a knight or Daniel is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Oliver is a knave or Emma is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Sophia that Chloe is a knave or Oliver is a knave.", "Oliver cannot be a knave, because this would contradict the claim of Chloe that Matthew is a knight and Oliver is a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Oliver is a knave or Emma is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Sophia that Chloe is a knave or Oliver is a knave.", "Oliver cannot be a knave, because this would contradict the false claim of Daniel that Oliver is a knave or Emma is a knave.", "We have exhausted all possibilities for Oliver and Daniel, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the claim of Chloe that Matthew is a knight and Oliver is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Matthew is a knight and Oliver is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Matthew is a knight or Daniel is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Oliver is a knave or Emma is a knave.", "Oliver cannot be a knight, because this would contradict the false claim of Chloe that Matthew is a knight and Oliver is a knight.", "Oliver cannot be a knave, because this would contradict the false claim of their own that If Liam is a knight then Chloe is a knave.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Oliver is a knave or Emma is a knave.", "Oliver cannot be a knight, because this would contradict the false claim of Chloe that Matthew is a knight and Oliver is a knight.", "Oliver cannot be a knave, because this would contradict the false claim of their own that If Liam is a knight then Chloe is a knave.", "We have exhausted all possibilities for Oliver and Daniel, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Matthew is a knight or Daniel is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Oliver is a knave or Emma is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that If Liam is a knight then Chloe is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that If Daniel is a knight then Oliver is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that If Daniel is a knight then Oliver is a knave.", "Emma cannot be a knight, because this would contradict the claim of Daniel that Oliver is a knave or Emma is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Emma is a knave and Matthew is a knight.", "Amelia cannot be a knave, because this would contradict the false claim of Emma that Amelia is a knave.", "We have exhausted all possibilities for Amelia, Emma, and Liam, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the false claim of their own that If Liam is a knight then Chloe is a knave.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the false claim of Matthew that Matthew is a knight or Daniel is a knave.", "We have exhausted all possibilities for Daniel, Matthew, and Chloe, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Chloe is a knave or Oliver is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Matthew is a knight and Oliver is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Matthew is a knight or Daniel is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Oliver is a knave or Emma is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that If Liam is a knight then Chloe is a knave.", "Liam cannot be a knight, because this would contradict the claim of Oliver that If Liam is a knight then Chloe is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that If Daniel is a knight then Oliver is a knave.", "Emma cannot be a knight, because this would contradict the claim of Daniel that Oliver is a knave or Emma is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Amelia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Emma is a knave and Matthew is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 7), ('lying', 1)), ('->', ('telling-truth', 2), ('lying', 7)), ('->', ('telling-truth', 6), ('lying', 1)), ('lying', 5), ('or', ('telling-truth', 4), ('lying', 6)), ('and', ('lying', 3), ('telling-truth', 4)), ('or', ('lying', 1), ('lying', 3)), ('and', ('telling-truth', 4), ('telling-truth', 1)))", "index": 868}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Penelope, Matthew, Michael, Emma, Jackson, Aria, Logan, and Oliver. Penelope said that Michael is a knight and Michael is a knave. Matthew said, \"Penelope is not a knight.\" In a statement by Michael: \"Penelope is a knave if and only if Matthew is a knave\". Emma commented, \"Penelope is a knave\". Jackson stated, \"Matthew is a knight or Emma is a knight\". As Aria put it, \"Emma is a knight or Logan is a knave\". \"Jackson is a knight,\" Logan mentioned. As Oliver put it, \"Michael is a knave\". So who is a knight and who is a knave?", "names": ["Penelope", "Matthew", "Michael", "Emma", "Jackson", "Aria", "Logan", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true, true, true], "solution_text": "Penelope is a knave, Matthew is a knight, Michael is a knave, Emma is a knight, Jackson is a knight, Aria is a knight, Logan is a knight, and Oliver is a knight.", "solution_text_format": "(1) Penelope is a knave\n(2) Matthew is a knight\n(3) Michael is a knave\n(4) Emma is a knight\n(5) Jackson is a knight\n(6) Aria is a knight\n(7) Logan is a knight\n(8) Oliver is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Penelope cannot be a knight, because this would contradict the claim of their own that Michael is a knight and Michael is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Michael is a knight and Michael is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Penelope is a knave if and only if Matthew is a knave.", "Matthew cannot be a knight, because this would contradict the claim of Michael that Penelope is a knave if and only if Matthew is a knave.", "Matthew cannot be a knave, because this would contradict the false claim of their own that Penelope is not a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Penelope is a knave if and only if Matthew is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Penelope is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Matthew is a knight or Emma is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Emma is a knight or Logan is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Jackson is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Michael is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 2), ('lying', 2)), ('not', ('telling-truth', 0)), ('<=>', ('lying', 0), ('lying', 1)), ('lying', 0), ('or', ('telling-truth', 1), ('telling-truth', 3)), ('or', ('telling-truth', 3), ('lying', 6)), ('telling-truth', 4), ('lying', 2))", "index": 869}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: David, Grace, Sebastian, Penelope, Jackson, Ava, Ella, and Ethan. David was heard saying, \"Penelope is a knight\". Grace stated, \"Ethan is a knight and Sebastian is a knight\". As Sebastian put it, \"Jackson is a knight and Ethan is a knave\". Penelope said that Ethan is not a knight. In Jackson's words: \"Ava is a knave if and only if Jackson is a knight\". According to Ava, \"Jackson is not a knight\". Ella said, \"Grace is not a knave.\" According to Ethan, \"If Ava is a knight then Jackson is a knight\". So who is a knight and who is a knave?", "names": ["David", "Grace", "Sebastian", "Penelope", "Jackson", "Ava", "Ella", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, false, false, true], "solution_text": "David is a knave, Grace is a knave, Sebastian is a knave, Penelope is a knave, Jackson is a knight, Ava is a knave, Ella is a knave, and Ethan is a knight.", "solution_text_format": "(1) David is a knave\n(2) Grace is a knave\n(3) Sebastian is a knave\n(4) Penelope is a knave\n(5) Jackson is a knight\n(6) Ava is a knave\n(7) Ella is a knave\n(8) Ethan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Ethan is not a knight.", "Ethan cannot be a knight, because this would contradict the claim of Penelope that Ethan is not a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that If Ava is a knight then Jackson is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Jackson is not a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Ava is a knave if and only if Jackson is a knight.", "Jackson cannot be a knave, because this would contradict the false claim of their own that Ava is a knave if and only if Jackson is a knight.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the false claim of Ethan that If Ava is a knight then Jackson is a knight.", "We have exhausted all possibilities for Ava and Ethan, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the claim of David that Penelope is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Penelope is a knight.", "Penelope cannot be a knight, because this would contradict the false claim of David that Penelope is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Ethan is not a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If Ava is a knight then Jackson is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Jackson is not a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Ava is a knave if and only if Jackson is a knight.", "Jackson cannot be a knave, because this would contradict the false claim of their own that Ava is a knave if and only if Jackson is a knight.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Jackson is not a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Ava is a knave if and only if Jackson is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Ethan is a knight and Sebastian is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Jackson is a knight and Ethan is a knave.", "Sebastian cannot be a knave, because this would contradict the claim of Grace that Ethan is a knight and Sebastian is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Ethan is a knight and Sebastian is a knight.", "Sebastian cannot be a knight, because this would contradict the false claim of Grace that Ethan is a knight and Sebastian is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Jackson is a knight and Ethan is a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Grace is not a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Grace is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 3), ('and', ('telling-truth', 7), ('telling-truth', 2)), ('and', ('telling-truth', 4), ('lying', 7)), ('not', ('telling-truth', 7)), ('<=>', ('lying', 5), ('telling-truth', 4)), ('not', ('telling-truth', 4)), ('not', ('lying', 1)), ('->', ('telling-truth', 5), ('telling-truth', 4)))", "index": 870}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mia, Isabella, Elizabeth, Emily, Matthew, Owen, Sophia, and Scarlett. Mia asserted: \"If Owen is a knave then Isabella is a knave\". In a statement by Isabella: \"Sophia is a knight if and only if Owen is a knight\". In a statement by Elizabeth: \"If Sophia is a knight then Scarlett is a knave\". Emily said, \"Scarlett is a knight if and only if Elizabeth is a knight.\" In Matthew's words: \"If Isabella is a knave then Emily is a knave\". \"Mia is a knave and Matthew is a knight,\" Owen declared. Sophia stated, \"Emily is a knave\". \"Isabella is a knave,\" Scarlett mentioned. So who is a knight and who is a knave?", "names": ["Mia", "Isabella", "Elizabeth", "Emily", "Matthew", "Owen", "Sophia", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, false, true, true], "solution_text": "Mia is a knight, Isabella is a knave, Elizabeth is a knave, Emily is a knave, Matthew is a knight, Owen is a knave, Sophia is a knight, and Scarlett is a knight.", "solution_text_format": "(1) Mia is a knight\n(2) Isabella is a knave\n(3) Elizabeth is a knave\n(4) Emily is a knave\n(5) Matthew is a knight\n(6) Owen is a knave\n(7) Sophia is a knight\n(8) Scarlett is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that If Owen is a knave then Isabella is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Mia is a knave and Matthew is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Mia is a knave and Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that If Isabella is a knave then Emily is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Mia that If Owen is a knave then Isabella is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Sophia is a knight if and only if Owen is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of Matthew that If Isabella is a knave then Emily is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Scarlett is a knight if and only if Elizabeth is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Isabella is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that If Sophia is a knight then Scarlett is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that If Sophia is a knight then Scarlett is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('lying', 1)), ('<=>', ('telling-truth', 6), ('telling-truth', 5)), ('->', ('telling-truth', 6), ('lying', 7)), ('<=>', ('telling-truth', 7), ('telling-truth', 2)), ('->', ('lying', 1), ('lying', 3)), ('and', ('lying', 0), ('telling-truth', 4)), ('lying', 3), ('lying', 1))", "index": 871}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sophia, Michael, Grace, Abigail, Ava, Harper, Charlotte, and Logan. Sophia commented, \"Abigail is a knave or Grace is a knight\". Michael commented, \"Grace is a knight\". \"Charlotte is a knave and Harper is a knight,\" Grace mentioned. \"Charlotte is a knave,\" Abigail declared. Ava stated, \"Sophia is not a knight\". Harper stated, \"Sophia is a knight or Charlotte is a knave\". Charlotte said, \"If Ava is a knight then Michael is a knave.\" In Logan's words: \"Grace is a knave or Charlotte is a knight\". So who is a knight and who is a knave?", "names": ["Sophia", "Michael", "Grace", "Abigail", "Ava", "Harper", "Charlotte", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, true, true, true], "solution_text": "Sophia is a knight, Michael is a knave, Grace is a knave, Abigail is a knave, Ava is a knave, Harper is a knight, Charlotte is a knight, and Logan is a knight.", "solution_text_format": "(1) Sophia is a knight\n(2) Michael is a knave\n(3) Grace is a knave\n(4) Abigail is a knave\n(5) Ava is a knave\n(6) Harper is a knight\n(7) Charlotte is a knight\n(8) Logan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Abigail is a knave or Grace is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Abigail that Charlotte is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that If Ava is a knight then Michael is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Sophia is not a knight.", "Ava cannot be a knave, because this would contradict the false claim of Charlotte that If Ava is a knight then Michael is a knave.", "We have exhausted all possibilities for Ava and Charlotte, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Charlotte is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Ava is a knight then Michael is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Sophia is not a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Sophia is not a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Grace is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Charlotte is a knave and Harper is a knight.", "Grace cannot be a knave, because this would contradict the claim of Michael that Grace is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Grace is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Michael that Grace is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Charlotte is a knave and Harper is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Sophia is a knight or Charlotte is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Grace is a knave or Charlotte is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('telling-truth', 2)), ('telling-truth', 2), ('and', ('lying', 6), ('telling-truth', 5)), ('lying', 6), ('not', ('telling-truth', 0)), ('or', ('telling-truth', 0), ('lying', 6)), ('->', ('telling-truth', 4), ('lying', 1)), ('or', ('lying', 2), ('telling-truth', 6)))", "index": 872}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lucas, William, Amelia, Sofia, Joseph, Elizabeth, Isabella, and Ella. Lucas stated, \"If Amelia is a knight then William is a knave\". William asserted: \"If Joseph is a knave then William is a knight\". In Amelia's words: \"If Elizabeth is a knight then Lucas is a knave\". \"Elizabeth is not a knight,\" Sofia claimed. Joseph said that Ella is a knave. \"Joseph is not a knight,\" Elizabeth claimed. In Isabella's words: \"William is a knave if and only if Joseph is a knight\". According to Ella, \"Amelia is not a knave\". So who is a knight and who is a knave?", "names": ["Lucas", "William", "Amelia", "Sofia", "Joseph", "Elizabeth", "Isabella", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true, true, true], "solution_text": "Lucas is a knave, William is a knight, Amelia is a knight, Sofia is a knave, Joseph is a knave, Elizabeth is a knight, Isabella is a knight, and Ella is a knight.", "solution_text_format": "(1) Lucas is a knave\n(2) William is a knight\n(3) Amelia is a knight\n(4) Sofia is a knave\n(5) Joseph is a knave\n(6) Elizabeth is a knight\n(7) Isabella is a knight\n(8) Ella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that If Amelia is a knight then William is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that If Elizabeth is a knight then Lucas is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of Amelia that If Elizabeth is a knight then Lucas is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Joseph is not a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of Joseph that Ella is a knave.", "Ella cannot be a knave, because this would contradict the false claim of their own that Amelia is not a knave.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the false claim of Elizabeth that Joseph is not a knight.", "We have exhausted all possibilities for Joseph and Elizabeth, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that If Elizabeth is a knight then Lucas is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Joseph is not a knight.", "Joseph cannot be a knight, because this would contradict the claim of Elizabeth that Joseph is not a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Amelia is not a knave.", "Ella cannot be a knave, because this would contradict the false claim of Joseph that Ella is a knave.", "We have exhausted all possibilities for Ella and Joseph, so let us go back and reconsider Elizabeth.", "Elizabeth cannot be a knave, because this would contradict the false claim of Amelia that If Elizabeth is a knight then Lucas is a knave.", "We have exhausted all possibilities for Elizabeth and Amelia, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that If Amelia is a knight then William is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that If Elizabeth is a knight then Lucas is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Joseph is not a knight.", "Joseph cannot be a knight, because this would contradict the claim of Elizabeth that Joseph is not a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Amelia is not a knave.", "Assume William is a knight. No contradiction is found in their claim that If Joseph is a knave then William is a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that Elizabeth is not a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Elizabeth is not a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that William is a knave if and only if Joseph is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('lying', 1)), ('->', ('lying', 4), ('telling-truth', 1)), ('->', ('telling-truth', 5), ('lying', 0)), ('not', ('telling-truth', 5)), ('lying', 7), ('not', ('telling-truth', 4)), ('<=>', ('lying', 1), ('telling-truth', 4)), ('not', ('lying', 2)))", "index": 873}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Avery, Daniel, Aria, Jacob, William, Chloe, Grace, and Abigail. Avery said, \"Jacob is not a knave.\" According to Daniel, \"Jacob is a knave or Abigail is a knight\". In a statement by Aria: \"Grace is a knight\". Jacob told you that Jacob is a knight if and only if Daniel is a knave. \"Avery is not a knave,\" William mentioned. Chloe said that Grace is a knave and Grace is a knight. Grace stated, \"William is a knave and Chloe is a knave\". Abigail noted, \"Daniel is not a knave\". So who is a knight and who is a knave?", "names": ["Avery", "Daniel", "Aria", "Jacob", "William", "Chloe", "Grace", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false, false, false], "solution_text": "Avery is a knight, Daniel is a knave, Aria is a knave, Jacob is a knight, William is a knight, Chloe is a knave, Grace is a knave, and Abigail is a knave.", "solution_text_format": "(1) Avery is a knight\n(2) Daniel is a knave\n(3) Aria is a knave\n(4) Jacob is a knight\n(5) William is a knight\n(6) Chloe is a knave\n(7) Grace is a knave\n(8) Abigail is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Jacob is not a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Jacob is a knight if and only if Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of Jacob that Jacob is a knight if and only if Daniel is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Jacob is a knave or Abigail is a knight.", "Abigail cannot be a knight, because this would contradict the false claim of Daniel that Jacob is a knave or Abigail is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Daniel is not a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that William is a knave and Chloe is a knave.", "William cannot be a knight, because this would contradict the claim of Grace that William is a knave and Chloe is a knave.", "William cannot be a knave, because this would contradict the false claim of their own that Avery is not a knave.", "We have exhausted all possibilities for William, so let us go back and reconsider Grace.", "Grace cannot be a knave, because this would contradict the claim of Aria that Grace is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Grace is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Aria that Grace is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that William is a knave and Chloe is a knave.", "Assume William is a knight. No contradiction is found in their claim that Avery is not a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Grace is a knave and Grace is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Grace is a knave and Grace is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 3)), ('or', ('lying', 3), ('telling-truth', 7)), ('telling-truth', 6), ('<=>', ('telling-truth', 3), ('lying', 1)), ('not', ('lying', 0)), ('and', ('lying', 6), ('telling-truth', 6)), ('and', ('lying', 4), ('lying', 5)), ('not', ('lying', 1)))", "index": 874}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Abigail, Isabella, Amelia, William, Luke, Mia, Henry, and Lucas. In a statement by Abigail: \"Lucas is a knave and Luke is a knave\". \"Luke is not a knight,\" Isabella claimed. Amelia expressed that William is a knight if and only if Lucas is a knave. In William's words: \"Mia is a knight or Isabella is a knight\". Luke expressed that Henry is a knight if and only if Luke is a knight. Mia was heard saying, \"Henry is a knave if and only if Abigail is a knave\". In a statement by Henry: \"If Lucas is a knight then Luke is a knave\". As Lucas put it, \"If Henry is a knave then Mia is a knave\". So who is a knight and who is a knave?", "names": ["Abigail", "Isabella", "Amelia", "William", "Luke", "Mia", "Henry", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, false, true, true], "solution_text": "Abigail is a knave, Isabella is a knight, Amelia is a knave, William is a knight, Luke is a knave, Mia is a knave, Henry is a knight, and Lucas is a knight.", "solution_text_format": "(1) Abigail is a knave\n(2) Isabella is a knight\n(3) Amelia is a knave\n(4) William is a knight\n(5) Luke is a knave\n(6) Mia is a knave\n(7) Henry is a knight\n(8) Lucas is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Lucas is a knave and Luke is a knave.", "Lucas cannot be a knight, because this would contradict the claim of Abigail that Lucas is a knave and Luke is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that If Henry is a knave then Mia is a knave.", "Henry cannot be a knight, because this would contradict the false claim of Lucas that If Henry is a knave then Mia is a knave.", "Henry cannot be a knave, because this would contradict the false claim of their own that If Lucas is a knight then Luke is a knave.", "We have exhausted all possibilities for Henry and Lucas, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Lucas is a knave and Luke is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that If Henry is a knave then Mia is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Lucas is a knight then Luke is a knave.", "Luke cannot be a knight, because this would contradict the claim of Henry that If Lucas is a knight then Luke is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Henry is a knight if and only if Luke is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that Henry is a knave if and only if Abigail is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Henry is a knave if and only if Abigail is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Luke is not a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that William is a knight if and only if Lucas is a knave.", "William cannot be a knight, because this would contradict the claim of Amelia that William is a knight if and only if Lucas is a knave.", "William cannot be a knave, because this would contradict the false claim of their own that Mia is a knight or Isabella is a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that William is a knight if and only if Lucas is a knave.", "Assume William is a knight. No contradiction is found in their claim that Mia is a knight or Isabella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 7), ('lying', 4)), ('not', ('telling-truth', 4)), ('<=>', ('telling-truth', 3), ('lying', 7)), ('or', ('telling-truth', 5), ('telling-truth', 1)), ('<=>', ('telling-truth', 6), ('telling-truth', 4)), ('<=>', ('lying', 6), ('lying', 0)), ('->', ('telling-truth', 7), ('lying', 4)), ('->', ('lying', 6), ('lying', 5)))", "index": 875}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Liam, Joseph, Sophia, Abigail, James, Aria, Jack, and Emma. Liam stated, \"Joseph is a knight if and only if Abigail is a knave\". Joseph noted, \"James is a knave or Jack is a knight\". Sophia said, \"Abigail is not a knave.\" Abigail commented, \"Emma is a knave if and only if Aria is a knave\". \"Abigail is a knight,\" James declared. Aria expressed that James is not a knave. Jack told you that James is a knight and Abigail is a knave. \"If Aria is a knave then Sophia is a knight,\" Emma claimed. So who is a knight and who is a knave?", "names": ["Liam", "Joseph", "Sophia", "Abigail", "James", "Aria", "Jack", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true, false, true], "solution_text": "Liam is a knight, Joseph is a knave, Sophia is a knight, Abigail is a knight, James is a knight, Aria is a knight, Jack is a knave, and Emma is a knight.", "solution_text_format": "(1) Liam is a knight\n(2) Joseph is a knave\n(3) Sophia is a knight\n(4) Abigail is a knight\n(5) James is a knight\n(6) Aria is a knight\n(7) Jack is a knave\n(8) Emma is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Joseph is a knight if and only if Abigail is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that James is a knave or Jack is a knight.", "Assume James is a knight. No contradiction is found in their claim that Abigail is a knight.", "Abigail cannot be a knight, because this would contradict the claim of Liam that Joseph is a knight if and only if Abigail is a knave.", "Abigail cannot be a knave, because this would contradict the claim of James that Abigail is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Abigail is a knight.", "Abigail cannot be a knight, because this would contradict the claim of Liam that Joseph is a knight if and only if Abigail is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Emma is a knave if and only if Aria is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that If Aria is a knave then Sophia is a knight.", "Aria cannot be a knight, because this would contradict the false claim of Abigail that Emma is a knave if and only if Aria is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that James is not a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that Abigail is not a knave.", "Sophia cannot be a knave, because this would contradict the claim of Emma that If Aria is a knave then Sophia is a knight.", "We have exhausted all possibilities for Sophia and Aria, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that If Aria is a knave then Sophia is a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that James is not a knave.", "Aria cannot be a knave, because this would contradict the false claim of Abigail that Emma is a knave if and only if Aria is a knave.", "We have exhausted all possibilities for Aria, Emma, Abigail, and James, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that James is a knave or Jack is a knight.", "Assume James is a knight. No contradiction is found in their claim that Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Emma is a knave if and only if Aria is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that If Aria is a knave then Sophia is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that James is not a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Abigail is not a knave.", "Jack cannot be a knight, because this would contradict the false claim of Joseph that James is a knave or Jack is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that James is a knight and Abigail is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('lying', 3)), ('or', ('lying', 4), ('telling-truth', 6)), ('not', ('lying', 3)), ('<=>', ('lying', 7), ('lying', 5)), ('telling-truth', 3), ('not', ('lying', 4)), ('and', ('telling-truth', 4), ('lying', 3)), ('->', ('lying', 5), ('telling-truth', 2)))", "index": 876}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Charlotte, Samuel, Michael, Aiden, Harper, Henry, Elizabeth, and Ella. Charlotte remarked, \"Henry is a knight and Ella is a knave\". Samuel was heard saying, \"Henry is not a knave\". Michael noted, \"Elizabeth is a knight and Harper is a knight\". \"Ella is a knave and Henry is a knave,\" Aiden declared. In a statement by Harper: \"Ella is not a knave\". Henry told you that If Harper is a knave then Michael is a knight. Elizabeth expressed that Charlotte is a knight or Harper is a knave. As Ella put it, \"Samuel is a knave and Michael is a knight\". So who is a knight and who is a knave?", "names": ["Charlotte", "Samuel", "Michael", "Aiden", "Harper", "Henry", "Elizabeth", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, false, true, false], "solution_text": "Charlotte is a knave, Samuel is a knave, Michael is a knave, Aiden is a knight, Harper is a knave, Henry is a knave, Elizabeth is a knight, and Ella is a knave.", "solution_text_format": "(1) Charlotte is a knave\n(2) Samuel is a knave\n(3) Michael is a knave\n(4) Aiden is a knight\n(5) Harper is a knave\n(6) Henry is a knave\n(7) Elizabeth is a knight\n(8) Ella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that Henry is a knight and Ella is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Harper is a knave then Michael is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Ella is not a knave.", "Ella cannot be a knight, because this would contradict the claim of Charlotte that Henry is a knight and Ella is a knave.", "Ella cannot be a knave, because this would contradict the claim of Harper that Ella is not a knave.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Ella is not a knave.", "Ella cannot be a knight, because this would contradict the claim of Charlotte that Henry is a knight and Ella is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Samuel is a knave and Michael is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Henry is not a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight and Harper is a knight.", "Michael cannot be a knave, because this would contradict the claim of Henry that If Harper is a knave then Michael is a knight.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Samuel.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Henry is not a knave.", "We have exhausted all possibilities for Samuel, Ella, and Harper, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the claim of Charlotte that Henry is a knight and Ella is a knave.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Henry is a knight and Ella is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Harper is a knave then Michael is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Ella is not a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Samuel is a knave and Michael is a knight.", "Samuel cannot be a knight, because this would contradict the claim of Ella that Samuel is a knave and Michael is a knight.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Henry is not a knave.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the false claim of Charlotte that Henry is a knight and Ella is a knave.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Ella is not a knave.", "Ella cannot be a knight, because this would contradict the false claim of Harper that Ella is not a knave.", "Ella cannot be a knave, because this would contradict the false claim of Charlotte that Henry is a knight and Ella is a knave.", "We have exhausted all possibilities for Ella and Harper, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that If Harper is a knave then Michael is a knight.", "Harper cannot be a knight, because this would contradict the false claim of Henry that If Harper is a knave then Michael is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Ella is not a knave.", "Ella cannot be a knight, because this would contradict the false claim of Harper that Ella is not a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Samuel is a knave and Michael is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Henry is not a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Henry is not a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight and Harper is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Elizabeth is a knight and Harper is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Charlotte is a knight or Harper is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Ella is a knave and Henry is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('lying', 7)), ('not', ('lying', 5)), ('and', ('telling-truth', 6), ('telling-truth', 4)), ('and', ('lying', 7), ('lying', 5)), ('not', ('lying', 7)), ('->', ('lying', 4), ('telling-truth', 2)), ('or', ('telling-truth', 0), ('lying', 4)), ('and', ('lying', 1), ('telling-truth', 2)))", "index": 877}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Zoey, Samuel, Aiden, Mason, Noah, Jackson, Grace, and Alexander. \"If Samuel is a knave then Samuel is a knight\" - Zoey. In Samuel's words: \"Mason is a knight\". Aiden stated, \"If Zoey is a knave then Aiden is a knight\". Mason commented, \"Alexander is a knight and Jackson is a knight\". In a statement by Noah: \"Mason is a knave if and only if Zoey is a knave\". Jackson asserted: \"Alexander is a knight\". \"If Jackson is a knave then Samuel is a knight,\" Grace claimed. Alexander expressed that If Zoey is a knave then Noah is a knight. So who is a knight and who is a knave?", "names": ["Zoey", "Samuel", "Aiden", "Mason", "Noah", "Jackson", "Grace", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true, true, true], "solution_text": "Zoey is a knight, Samuel is a knight, Aiden is a knight, Mason is a knight, Noah is a knight, Jackson is a knight, Grace is a knight, and Alexander is a knight.", "solution_text_format": "(1) Zoey is a knight\n(2) Samuel is a knight\n(3) Aiden is a knight\n(4) Mason is a knight\n(5) Noah is a knight\n(6) Jackson is a knight\n(7) Grace is a knight\n(8) Alexander is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Zoey is a knight. No contradiction is found in their claim that If Samuel is a knave then Samuel is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Mason is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Alexander is a knight and Jackson is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that If Zoey is a knave then Noah is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Mason is a knave if and only if Zoey is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Alexander is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that If Zoey is a knave then Aiden is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that If Jackson is a knave then Samuel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 1), ('telling-truth', 1)), ('telling-truth', 3), ('->', ('lying', 0), ('telling-truth', 2)), ('and', ('telling-truth', 7), ('telling-truth', 5)), ('<=>', ('lying', 3), ('lying', 0)), ('telling-truth', 7), ('->', ('lying', 5), ('telling-truth', 1)), ('->', ('lying', 0), ('telling-truth', 4)))", "index": 878}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Evelyn, Abigail, Samuel, Alexander, Henry, Noah, Owen, and Zoey. Evelyn said, \"Henry is a knight and Henry is a knave.\" Abigail told you that If Owen is a knave then Abigail is a knight. \"If Noah is a knight then Evelyn is a knight,\" Samuel mentioned. Alexander remarked, \"Samuel is not a knight\". Henry expressed that Samuel is a knave. Noah noted, \"Zoey is a knave and Alexander is a knight\". \"Zoey is a knave or Zoey is a knight,\" Owen claimed. \"Samuel is a knave or Samuel is a knight,\" Zoey declared. So who is a knight and who is a knave?", "names": ["Evelyn", "Abigail", "Samuel", "Alexander", "Henry", "Noah", "Owen", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false, true, true], "solution_text": "Evelyn is a knave, Abigail is a knight, Samuel is a knight, Alexander is a knave, Henry is a knave, Noah is a knave, Owen is a knight, and Zoey is a knight.", "solution_text_format": "(1) Evelyn is a knave\n(2) Abigail is a knight\n(3) Samuel is a knight\n(4) Alexander is a knave\n(5) Henry is a knave\n(6) Noah is a knave\n(7) Owen is a knight\n(8) Zoey is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Evelyn cannot be a knight, because this would contradict the claim of their own that Henry is a knight and Henry is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Henry is a knight and Henry is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Henry that Samuel is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that If Noah is a knight then Evelyn is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Zoey is a knave and Alexander is a knight.", "Zoey cannot be a knight, because this would contradict the claim of Noah that Zoey is a knave and Alexander is a knight.", "Zoey cannot be a knave, because this would contradict the false claim of their own that Samuel is a knave or Samuel is a knight.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the false claim of Samuel that If Noah is a knight then Evelyn is a knight.", "We have exhausted all possibilities for Noah and Samuel, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Samuel is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that If Noah is a knight then Evelyn is a knight.", "Noah cannot be a knight, because this would contradict the claim of Samuel that If Noah is a knight then Evelyn is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Zoey is a knave and Alexander is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Samuel is a knave or Samuel is a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that Samuel is not a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Samuel is not a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If Owen is a knave then Abigail is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Zoey is a knave or Zoey is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 4), ('lying', 4)), ('->', ('lying', 6), ('telling-truth', 1)), ('->', ('telling-truth', 5), ('telling-truth', 0)), ('not', ('telling-truth', 2)), ('lying', 2), ('and', ('lying', 7), ('telling-truth', 3)), ('or', ('lying', 7), ('telling-truth', 7)), ('or', ('lying', 2), ('telling-truth', 2)))", "index": 879}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Oliver, Isabella, Luke, Amelia, Lily, Mia, Aiden, and Charlotte. Oliver said, \"Isabella is a knight if and only if Mia is a knight.\" Isabella noted, \"Oliver is not a knight\". In Luke's words: \"Amelia is a knight or Oliver is a knave\". Amelia expressed that Luke is a knight and Aiden is a knave. \"Lily is a knight or Luke is a knight,\" Lily declared. Mia noted, \"If Lily is a knave then Amelia is a knight\". Aiden said that Mia is a knight and Amelia is a knight. Charlotte expressed that If Isabella is a knight then Aiden is a knight. So who is a knight and who is a knave?", "names": ["Oliver", "Isabella", "Luke", "Amelia", "Lily", "Mia", "Aiden", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, false, false, true], "solution_text": "Oliver is a knight, Isabella is a knave, Luke is a knave, Amelia is a knave, Lily is a knave, Mia is a knave, Aiden is a knave, and Charlotte is a knight.", "solution_text_format": "(1) Oliver is a knight\n(2) Isabella is a knave\n(3) Luke is a knave\n(4) Amelia is a knave\n(5) Lily is a knave\n(6) Mia is a knave\n(7) Aiden is a knave\n(8) Charlotte is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Mia is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Oliver is not a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Oliver is not a knight.", "Mia cannot be a knight, because this would contradict the claim of Oliver that Isabella is a knight if and only if Mia is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that If Lily is a knave then Amelia is a knight.", "Lily cannot be a knight, because this would contradict the false claim of Mia that If Lily is a knave then Amelia is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Lily is a knight or Luke is a knight.", "Luke cannot be a knight, because this would contradict the false claim of Lily that Lily is a knight or Luke is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Amelia is a knight or Oliver is a knave.", "Amelia cannot be a knight, because this would contradict the false claim of Luke that Amelia is a knight or Oliver is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Luke is a knight and Aiden is a knave.", "Aiden cannot be a knight, because this would contradict the claim of their own that Mia is a knight and Amelia is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Mia is a knight and Amelia is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Isabella is a knight then Aiden is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('telling-truth', 5)), ('not', ('telling-truth', 0)), ('or', ('telling-truth', 3), ('lying', 0)), ('and', ('telling-truth', 2), ('lying', 6)), ('or', ('telling-truth', 4), ('telling-truth', 2)), ('->', ('lying', 4), ('telling-truth', 3)), ('and', ('telling-truth', 5), ('telling-truth', 3)), ('->', ('telling-truth', 1), ('telling-truth', 6)))", "index": 880}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: William, Abigail, Mason, Sophia, Chloe, Zoey, Alexander, and Emily. \"Chloe is a knave or Abigail is a knave\" - William. Abigail told you that Zoey is a knight and William is a knave. In a statement by Mason: \"Emily is a knight or Emily is a knave\". In Sophia's words: \"Alexander is a knave or William is a knave\". In Chloe's words: \"Mason is not a knave\". \"Sophia is a knave or Alexander is a knight,\" Zoey mentioned. As Alexander put it, \"Mason is a knave and Abigail is a knave\". Emily said, \"Abigail is a knave and William is a knight.\" So who is a knight and who is a knave?", "names": ["William", "Abigail", "Mason", "Sophia", "Chloe", "Zoey", "Alexander", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false, false, true], "solution_text": "William is a knight, Abigail is a knave, Mason is a knight, Sophia is a knight, Chloe is a knight, Zoey is a knave, Alexander is a knave, and Emily is a knight.", "solution_text_format": "(1) William is a knight\n(2) Abigail is a knave\n(3) Mason is a knight\n(4) Sophia is a knight\n(5) Chloe is a knight\n(6) Zoey is a knave\n(7) Alexander is a knave\n(8) Emily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Chloe is a knave or Abigail is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Mason is not a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Emily is a knight or Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Abigail is a knave and William is a knight.", "Abigail cannot be a knight, because this would contradict the claim of William that Chloe is a knave or Abigail is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Zoey is a knight and William is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Sophia is a knave or Alexander is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Alexander is a knave or William is a knave.", "Alexander cannot be a knight, because this would contradict the claim of Sophia that Alexander is a knave or William is a knave.", "Alexander cannot be a knave, because this would contradict the claim of Zoey that Sophia is a knave or Alexander is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Alexander is a knave or William is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that Mason is a knave and Abigail is a knave.", "Alexander cannot be a knave, because this would contradict the false claim of Sophia that Alexander is a knave or William is a knave.", "We have exhausted all possibilities for Alexander and Sophia, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Sophia is a knave or Alexander is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Alexander is a knave or William is a knave.", "Alexander cannot be a knight, because this would contradict the claim of Sophia that Alexander is a knave or William is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Mason is a knave and Abigail is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 4), ('lying', 1)), ('and', ('telling-truth', 5), ('lying', 0)), ('or', ('telling-truth', 7), ('lying', 7)), ('or', ('lying', 6), ('lying', 0)), ('not', ('lying', 2)), ('or', ('lying', 3), ('telling-truth', 6)), ('and', ('lying', 2), ('lying', 1)), ('and', ('lying', 1), ('telling-truth', 0)))", "index": 881}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Michael, Emma, Chloe, Aria, Noah, Lily, Ava, and Amelia. Michael commented, \"Chloe is not a knave\". Emma noted, \"Ava is a knave and Noah is a knave\". \"Amelia is a knave,\" Chloe mentioned. \"Ava is a knave and Amelia is a knight,\" Aria claimed. Noah was heard saying, \"Emma is a knave\". Lily commented, \"If Chloe is a knight then Noah is a knave\". \"Lily is not a knave,\" Ava declared. \"Noah is not a knight\" - Amelia. So who is a knight and who is a knave?", "names": ["Michael", "Emma", "Chloe", "Aria", "Noah", "Lily", "Ava", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, false, false, false], "solution_text": "Michael is a knight, Emma is a knave, Chloe is a knight, Aria is a knave, Noah is a knight, Lily is a knave, Ava is a knave, and Amelia is a knave.", "solution_text_format": "(1) Michael is a knight\n(2) Emma is a knave\n(3) Chloe is a knight\n(4) Aria is a knave\n(5) Noah is a knight\n(6) Lily is a knave\n(7) Ava is a knave\n(8) Amelia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Chloe is not a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Chloe that Amelia is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Noah is not a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Ava is a knave and Noah is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Ava is a knave and Noah is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Lily is not a knave.", "Lily cannot be a knight, because this would contradict the claim of their own that If Chloe is a knight then Noah is a knave.", "Lily cannot be a knave, because this would contradict the claim of Ava that Lily is not a knave.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Lily is not a knave.", "Lily cannot be a knight, because this would contradict the claim of their own that If Chloe is a knight then Noah is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that If Chloe is a knight then Noah is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Ava is a knave and Amelia is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Ava is a knave and Amelia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('and', ('lying', 6), ('lying', 4)), ('lying', 7), ('and', ('lying', 6), ('telling-truth', 7)), ('lying', 1), ('->', ('telling-truth', 2), ('lying', 4)), ('not', ('lying', 5)), ('not', ('telling-truth', 4)))", "index": 882}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Samuel, Elizabeth, Evelyn, Logan, Sofia, Mason, Ava, and Lucas. In a statement by Samuel: \"Sofia is a knave or Ava is a knight\". According to Elizabeth, \"Samuel is a knight\". Evelyn expressed that Lucas is not a knave. \"Elizabeth is not a knave,\" Logan claimed. Sofia remarked, \"Mason is a knight\". \"Logan is a knight or Sofia is a knave,\" Mason declared. Ava said, \"If Lucas is a knight then Lucas is a knave.\" Lucas remarked, \"Ava is not a knight\". So who is a knight and who is a knave?", "names": ["Samuel", "Elizabeth", "Evelyn", "Logan", "Sofia", "Mason", "Ava", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true, true, false], "solution_text": "Samuel is a knight, Elizabeth is a knight, Evelyn is a knave, Logan is a knight, Sofia is a knight, Mason is a knight, Ava is a knight, and Lucas is a knave.", "solution_text_format": "(1) Samuel is a knight\n(2) Elizabeth is a knight\n(3) Evelyn is a knave\n(4) Logan is a knight\n(5) Sofia is a knight\n(6) Mason is a knight\n(7) Ava is a knight\n(8) Lucas is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that Sofia is a knave or Ava is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Mason is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Logan is a knight or Sofia is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Elizabeth is not a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Samuel is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that If Lucas is a knight then Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the claim of Ava that If Lucas is a knight then Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Ava is not a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Lucas is not a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Lucas is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 4), ('telling-truth', 6)), ('telling-truth', 0), ('not', ('lying', 7)), ('not', ('lying', 1)), ('telling-truth', 5), ('or', ('telling-truth', 3), ('lying', 4)), ('->', ('telling-truth', 7), ('lying', 7)), ('not', ('telling-truth', 6)))", "index": 883}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sebastian, David, Alexander, Mason, Ethan, Ella, Riley, and Amelia. Sebastian expressed that Ethan is a knave if and only if David is a knight. David told you that Sebastian is not a knight. Alexander was heard saying, \"Sebastian is not a knight\". Mason was heard saying, \"Riley is a knight\". Ethan remarked, \"Sebastian is a knight or Riley is a knave\". Ella remarked, \"David is a knave and Alexander is a knight\". \"Ethan is a knight or Mason is a knight\" - Riley. Amelia stated, \"Amelia is a knight or Mason is a knight\". So who is a knight and who is a knave?", "names": ["Sebastian", "David", "Alexander", "Mason", "Ethan", "Ella", "Riley", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false, true, true], "solution_text": "Sebastian is a knight, David is a knave, Alexander is a knave, Mason is a knight, Ethan is a knight, Ella is a knave, Riley is a knight, and Amelia is a knight.", "solution_text_format": "(1) Sebastian is a knight\n(2) David is a knave\n(3) Alexander is a knave\n(4) Mason is a knight\n(5) Ethan is a knight\n(6) Ella is a knave\n(7) Riley is a knight\n(8) Amelia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that Ethan is a knave if and only if David is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Sebastian is a knight or Riley is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Ethan is a knight or Mason is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Riley is a knight.", "David cannot be a knight, because this would contradict the claim of Sebastian that Ethan is a knave if and only if David is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Sebastian is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that Sebastian is not a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Sebastian is not a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that David is a knave and Alexander is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that David is a knave and Alexander is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Amelia is a knight or Mason is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 4), ('telling-truth', 1)), ('not', ('telling-truth', 0)), ('not', ('telling-truth', 0)), ('telling-truth', 6), ('or', ('telling-truth', 0), ('lying', 6)), ('and', ('lying', 1), ('telling-truth', 2)), ('or', ('telling-truth', 4), ('telling-truth', 3)), ('or', ('telling-truth', 7), ('telling-truth', 3)))", "index": 884}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Isabella, James, Lucas, Ella, Ava, Oliver, Victoria, and Ethan. \"Oliver is a knave or Ava is a knight\" - Isabella. As James put it, \"Oliver is a knight and Isabella is a knight\". \"Oliver is a knave if and only if Isabella is a knave,\" Lucas claimed. As Ella put it, \"Isabella is a knight and James is a knave\". Ava was heard saying, \"Ethan is not a knight\". In Oliver's words: \"Ethan is a knight and James is a knight\". Victoria noted, \"Ethan is a knave or Ava is a knave\". In Ethan's words: \"If Isabella is a knave then Victoria is a knight\". So who is a knight and who is a knave?", "names": ["Isabella", "James", "Lucas", "Ella", "Ava", "Oliver", "Victoria", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, false, true, true], "solution_text": "Isabella is a knight, James is a knave, Lucas is a knave, Ella is a knight, Ava is a knave, Oliver is a knave, Victoria is a knight, and Ethan is a knight.", "solution_text_format": "(1) Isabella is a knight\n(2) James is a knave\n(3) Lucas is a knave\n(4) Ella is a knight\n(5) Ava is a knave\n(6) Oliver is a knave\n(7) Victoria is a knight\n(8) Ethan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Oliver is a knave or Ava is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Ethan is a knight and James is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If Isabella is a knave then Victoria is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Ethan is a knave or Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Ethan is not a knight.", "Ava cannot be a knave, because this would contradict the claim of Isabella that Oliver is a knave or Ava is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Ethan is a knave or Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Ethan is not a knight.", "Ava cannot be a knave, because this would contradict the claim of Isabella that Oliver is a knave or Ava is a knight.", "We have exhausted all possibilities for Ava and Victoria, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the claim of Oliver that Ethan is a knight and James is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Ethan is a knight and James is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If Isabella is a knave then Victoria is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Ethan is a knave or Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Ethan is not a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Ethan is not a knight.", "James cannot be a knight, because this would contradict the claim of their own that Oliver is a knight and Isabella is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Oliver is a knight and Isabella is a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Oliver is a knave if and only if Isabella is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Oliver is a knave if and only if Isabella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Isabella is a knight and James is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 5), ('telling-truth', 4)), ('and', ('telling-truth', 5), ('telling-truth', 0)), ('<=>', ('lying', 5), ('lying', 0)), ('and', ('telling-truth', 0), ('lying', 1)), ('not', ('telling-truth', 7)), ('and', ('telling-truth', 7), ('telling-truth', 1)), ('or', ('lying', 7), ('lying', 4)), ('->', ('lying', 0), ('telling-truth', 6)))", "index": 885}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sofia, Jack, Jackson, Matthew, James, Daniel, Olivia, and Penelope. Sofia was heard saying, \"Jack is a knave or Jackson is a knight\". \"James is a knight,\" Jack claimed. Jackson stated, \"Sofia is a knight if and only if Daniel is a knave\". \"James is a knave and Penelope is a knave,\" Matthew mentioned. James was heard saying, \"Penelope is not a knight\". As Daniel put it, \"Sofia is a knave\". Olivia commented, \"Sofia is not a knight\". Penelope noted, \"Jackson is a knight or Olivia is a knave\". So who is a knight and who is a knave?", "names": ["Sofia", "Jack", "Jackson", "Matthew", "James", "Daniel", "Olivia", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, false, false, true], "solution_text": "Sofia is a knight, Jack is a knave, Jackson is a knight, Matthew is a knave, James is a knave, Daniel is a knave, Olivia is a knave, and Penelope is a knight.", "solution_text_format": "(1) Sofia is a knight\n(2) Jack is a knave\n(3) Jackson is a knight\n(4) Matthew is a knave\n(5) James is a knave\n(6) Daniel is a knave\n(7) Olivia is a knave\n(8) Penelope is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Jack is a knave or Jackson is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that James is a knight.", "Assume James is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Penelope cannot be a knight, because this would contradict the claim of James that Penelope is not a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Jackson is a knight or Olivia is a knave.", "Jackson cannot be a knight, because this would contradict the false claim of Penelope that Jackson is a knight or Olivia is a knave.", "Jackson cannot be a knave, because this would contradict the claim of Sofia that Jack is a knave or Jackson is a knight.", "We have exhausted all possibilities for Jackson and Penelope, so let us go back and reconsider James.", "James cannot be a knave, because this would contradict the claim of Jack that James is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that James is a knight.", "James cannot be a knight, because this would contradict the false claim of Jack that James is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Penelope is not a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Jackson is a knight or Olivia is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Sofia is a knight if and only if Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of Jackson that Sofia is a knight if and only if Daniel is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Sofia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that Sofia is not a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Sofia is not a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that James is a knave and Penelope is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that James is a knave and Penelope is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('telling-truth', 2)), ('telling-truth', 4), ('<=>', ('telling-truth', 0), ('lying', 5)), ('and', ('lying', 4), ('lying', 7)), ('not', ('telling-truth', 7)), ('lying', 0), ('not', ('telling-truth', 0)), ('or', ('telling-truth', 2), ('lying', 6)))", "index": 886}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: David, Henry, William, Avery, Elizabeth, Mia, Michael, and Emma. In a statement by David: \"Michael is not a knight\". Henry expressed that If William is a knight then Emma is a knave. As William put it, \"William is a knight and Henry is a knight\". Avery said that David is a knight or Henry is a knight. Elizabeth remarked, \"Mia is a knight if and only if David is a knave\". In a statement by Mia: \"Avery is a knight\". Michael said that Henry is a knight or David is a knight. Emma said, \"If Elizabeth is a knight then Henry is a knight.\" So who is a knight and who is a knave?", "names": ["David", "Henry", "William", "Avery", "Elizabeth", "Mia", "Michael", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true, true, true], "solution_text": "David is a knave, Henry is a knight, William is a knave, Avery is a knight, Elizabeth is a knight, Mia is a knight, Michael is a knight, and Emma is a knight.", "solution_text_format": "(1) David is a knave\n(2) Henry is a knight\n(3) William is a knave\n(4) Avery is a knight\n(5) Elizabeth is a knight\n(6) Mia is a knight\n(7) Michael is a knight\n(8) Emma is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Michael is not a knight.", "Michael cannot be a knight, because this would contradict the claim of David that Michael is not a knight.", "Michael cannot be a knave, because this would contradict the false claim of their own that Henry is a knight or David is a knight.", "We have exhausted all possibilities for Michael, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Michael is not a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Henry is a knight or David is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that If William is a knight then Emma is a knave.", "Assume William is a knight. No contradiction is found in their claim that William is a knight and Henry is a knight.", "Emma cannot be a knight, because this would contradict the claim of Henry that If William is a knight then Emma is a knave.", "Emma cannot be a knave, because this would contradict the false claim of their own that If Elizabeth is a knight then Henry is a knight.", "We have exhausted all possibilities for Emma, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that William is a knight and Henry is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If Elizabeth is a knight then Henry is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Mia is a knight if and only if David is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Avery is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that David is a knight or Henry is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 6)), ('->', ('telling-truth', 2), ('lying', 7)), ('and', ('telling-truth', 2), ('telling-truth', 1)), ('or', ('telling-truth', 0), ('telling-truth', 1)), ('<=>', ('telling-truth', 5), ('lying', 0)), ('telling-truth', 3), ('or', ('telling-truth', 1), ('telling-truth', 0)), ('->', ('telling-truth', 4), ('telling-truth', 1)))", "index": 887}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Oliver, Emily, Ethan, Isabella, Jacob, Jackson, Sophia, and Penelope. Oliver noted, \"Jackson is a knight and Jacob is a knight\". According to Emily, \"Oliver is a knave if and only if Jackson is a knave\". \"Emily is a knight if and only if Sophia is a knight\" - Ethan. Isabella commented, \"Ethan is a knight or Ethan is a knave\". Jacob said, \"Isabella is a knave.\" Jackson asserted: \"Sophia is a knave\". Sophia remarked, \"If Isabella is a knave then Emily is a knight\". \"Emily is not a knight,\" Penelope claimed. So who is a knight and who is a knave?", "names": ["Oliver", "Emily", "Ethan", "Isabella", "Jacob", "Jackson", "Sophia", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false, true, false], "solution_text": "Oliver is a knave, Emily is a knight, Ethan is a knight, Isabella is a knight, Jacob is a knave, Jackson is a knave, Sophia is a knight, and Penelope is a knave.", "solution_text_format": "(1) Oliver is a knave\n(2) Emily is a knight\n(3) Ethan is a knight\n(4) Isabella is a knight\n(5) Jacob is a knave\n(6) Jackson is a knave\n(7) Sophia is a knight\n(8) Penelope is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Jackson is a knight and Jacob is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Sophia is a knave.", "Sophia cannot be a knight, because this would contradict the claim of Jackson that Sophia is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that If Isabella is a knave then Emily is a knight.", "Isabella cannot be a knight, because this would contradict the false claim of Sophia that If Isabella is a knave then Emily is a knight.", "Isabella cannot be a knave, because this would contradict the false claim of their own that Ethan is a knight or Ethan is a knave.", "We have exhausted all possibilities for Isabella and Sophia, so let us go back and reconsider Jackson.", "Jackson cannot be a knave, because this would contradict the claim of Oliver that Jackson is a knight and Jacob is a knight.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Jackson is a knight and Jacob is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Sophia is a knave.", "Sophia cannot be a knight, because this would contradict the claim of Jackson that Sophia is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that If Isabella is a knave then Emily is a knight.", "Isabella cannot be a knight, because this would contradict the false claim of Sophia that If Isabella is a knave then Emily is a knight.", "Isabella cannot be a knave, because this would contradict the false claim of their own that Ethan is a knight or Ethan is a knave.", "We have exhausted all possibilities for Isabella and Sophia, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Sophia is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that If Isabella is a knave then Emily is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Ethan is a knight or Ethan is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Emily is a knight if and only if Sophia is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Oliver is a knave if and only if Jackson is a knave.", "Jacob cannot be a knight, because this would contradict the claim of their own that Isabella is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Isabella is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Emily is not a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Emily is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('telling-truth', 4)), ('<=>', ('lying', 0), ('lying', 5)), ('<=>', ('telling-truth', 1), ('telling-truth', 6)), ('or', ('telling-truth', 2), ('lying', 2)), ('lying', 3), ('lying', 6), ('->', ('lying', 3), ('telling-truth', 1)), ('not', ('telling-truth', 1)))", "index": 888}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Daniel, Joseph, Benjamin, Mia, Ella, Riley, Chloe, and Penelope. Daniel commented, \"Ella is a knave if and only if Penelope is a knave\". According to Joseph, \"Mia is a knave and Chloe is a knave\". As Benjamin put it, \"Chloe is a knave if and only if Joseph is a knight\". Mia remarked, \"Riley is a knight and Daniel is a knave\". Ella asserted: \"Riley is a knight and Benjamin is a knight\". In a statement by Riley: \"Benjamin is a knave or Joseph is a knave\". Chloe was heard saying, \"Benjamin is a knight or Joseph is a knight\". Penelope asserted: \"Mia is a knave or Chloe is a knight\". So who is a knight and who is a knave?", "names": ["Daniel", "Joseph", "Benjamin", "Mia", "Ella", "Riley", "Chloe", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true, true, true], "solution_text": "Daniel is a knight, Joseph is a knave, Benjamin is a knight, Mia is a knave, Ella is a knight, Riley is a knight, Chloe is a knight, and Penelope is a knight.", "solution_text_format": "(1) Daniel is a knight\n(2) Joseph is a knave\n(3) Benjamin is a knight\n(4) Mia is a knave\n(5) Ella is a knight\n(6) Riley is a knight\n(7) Chloe is a knight\n(8) Penelope is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that Ella is a knave if and only if Penelope is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Riley is a knight and Benjamin is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Benjamin is a knave or Joseph is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Chloe is a knave if and only if Joseph is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Benjamin is a knight or Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Mia is a knave and Chloe is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Mia is a knave and Chloe is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Riley is a knight and Daniel is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Riley is a knight and Daniel is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Mia is a knave or Chloe is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 4), ('lying', 7)), ('and', ('lying', 3), ('lying', 6)), ('<=>', ('lying', 6), ('telling-truth', 1)), ('and', ('telling-truth', 5), ('lying', 0)), ('and', ('telling-truth', 5), ('telling-truth', 2)), ('or', ('lying', 2), ('lying', 1)), ('or', ('telling-truth', 2), ('telling-truth', 1)), ('or', ('lying', 3), ('telling-truth', 6)))", "index": 889}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Evelyn, Penelope, Benjamin, Avery, Samuel, Matthew, Grace, and Liam. Evelyn noted, \"If Matthew is a knave then Benjamin is a knave\". Penelope said that Benjamin is a knight and Samuel is a knave. \"Avery is not a knight,\" Benjamin mentioned. In a statement by Avery: \"Evelyn is a knight if and only if Grace is a knight\". In a statement by Samuel: \"Liam is not a knave\". According to Matthew, \"Grace is not a knight\". Grace stated, \"Evelyn is a knight and Penelope is a knight\". Liam said, \"Matthew is a knave or Avery is a knave.\" So who is a knight and who is a knave?", "names": ["Evelyn", "Penelope", "Benjamin", "Avery", "Samuel", "Matthew", "Grace", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true, false, true], "solution_text": "Evelyn is a knight, Penelope is a knave, Benjamin is a knight, Avery is a knave, Samuel is a knight, Matthew is a knight, Grace is a knave, and Liam is a knight.", "solution_text_format": "(1) Evelyn is a knight\n(2) Penelope is a knave\n(3) Benjamin is a knight\n(4) Avery is a knave\n(5) Samuel is a knight\n(6) Matthew is a knight\n(7) Grace is a knave\n(8) Liam is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that If Matthew is a knave then Benjamin is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Grace is not a knight.", "Grace cannot be a knight, because this would contradict the claim of Matthew that Grace is not a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Evelyn is a knight and Penelope is a knight.", "Penelope cannot be a knight, because this would contradict the false claim of Grace that Evelyn is a knight and Penelope is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Benjamin is a knight and Samuel is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Avery is not a knight.", "Avery cannot be a knight, because this would contradict the claim of Benjamin that Avery is not a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Evelyn is a knight if and only if Grace is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Liam is not a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Matthew is a knave or Avery is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('lying', 2)), ('and', ('telling-truth', 2), ('lying', 4)), ('not', ('telling-truth', 3)), ('<=>', ('telling-truth', 0), ('telling-truth', 6)), ('not', ('lying', 7)), ('not', ('telling-truth', 6)), ('and', ('telling-truth', 0), ('telling-truth', 1)), ('or', ('lying', 5), ('lying', 3)))", "index": 890}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mason, Aiden, Henry, Jacob, Jack, Owen, Abigail, and Riley. \"Owen is a knight or Jacob is a knight,\" Mason declared. Aiden told you that Jack is a knight if and only if Abigail is a knight. Henry told you that Abigail is a knave or Owen is a knave. Jacob asserted: \"Aiden is not a knave\". Jack stated, \"Jacob is a knight\". According to Owen, \"Aiden is a knight\". In Abigail's words: \"Henry is a knave or Mason is a knight\". Riley said that Abigail is a knave and Abigail is a knight. So who is a knight and who is a knave?", "names": ["Mason", "Aiden", "Henry", "Jacob", "Jack", "Owen", "Abigail", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true, true, false], "solution_text": "Mason is a knight, Aiden is a knight, Henry is a knave, Jacob is a knight, Jack is a knight, Owen is a knight, Abigail is a knight, and Riley is a knave.", "solution_text_format": "(1) Mason is a knight\n(2) Aiden is a knight\n(3) Henry is a knave\n(4) Jacob is a knight\n(5) Jack is a knight\n(6) Owen is a knight\n(7) Abigail is a knight\n(8) Riley is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Owen is a knight or Jacob is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Jack is a knight if and only if Abigail is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Aiden is not a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Henry is a knave or Mason is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Abigail is a knave or Owen is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Abigail is a knave or Owen is a knave.", "Riley cannot be a knight, because this would contradict the claim of their own that Abigail is a knave and Abigail is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Abigail is a knave and Abigail is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('telling-truth', 3)), ('<=>', ('telling-truth', 4), ('telling-truth', 6)), ('or', ('lying', 6), ('lying', 5)), ('not', ('lying', 1)), ('telling-truth', 3), ('telling-truth', 1), ('or', ('lying', 2), ('telling-truth', 0)), ('and', ('lying', 6), ('telling-truth', 6)))", "index": 891}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Owen, Lucas, Amelia, Aurora, Henry, Sebastian, Charlotte, and William. Owen remarked, \"Henry is a knave and Aurora is a knight\". \"William is a knight if and only if Henry is a knight,\" Lucas declared. According to Amelia, \"Charlotte is a knave or Henry is a knave\". Aurora asserted: \"If William is a knight then Amelia is a knight\". According to Henry, \"Amelia is a knave if and only if Sebastian is a knight\". Sebastian told you that If Aurora is a knight then Charlotte is a knave. \"Owen is a knave,\" Charlotte declared. William noted, \"Henry is not a knight\". So who is a knight and who is a knave?", "names": ["Owen", "Lucas", "Amelia", "Aurora", "Henry", "Sebastian", "Charlotte", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true, false, true], "solution_text": "Owen is a knight, Lucas is a knave, Amelia is a knight, Aurora is a knight, Henry is a knave, Sebastian is a knight, Charlotte is a knave, and William is a knight.", "solution_text_format": "(1) Owen is a knight\n(2) Lucas is a knave\n(3) Amelia is a knight\n(4) Aurora is a knight\n(5) Henry is a knave\n(6) Sebastian is a knight\n(7) Charlotte is a knave\n(8) William is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Henry is a knave and Aurora is a knight.", "Henry cannot be a knight, because this would contradict the claim of Owen that Henry is a knave and Aurora is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Amelia is a knave if and only if Sebastian is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Charlotte is a knave or Henry is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Owen is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Owen is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Aurora is a knight then Charlotte is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that If William is a knight then Amelia is a knight.", "Assume William is a knight. No contradiction is found in their claim that Henry is not a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that William is a knight if and only if Henry is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that William is a knight if and only if Henry is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('telling-truth', 3)), ('<=>', ('telling-truth', 7), ('telling-truth', 4)), ('or', ('lying', 6), ('lying', 4)), ('->', ('telling-truth', 7), ('telling-truth', 2)), ('<=>', ('lying', 2), ('telling-truth', 5)), ('->', ('telling-truth', 3), ('lying', 6)), ('lying', 0), ('not', ('telling-truth', 4)))", "index": 892}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ella, Samuel, Elizabeth, Lily, Daniel, David, Sofia, and Oliver. \"David is a knight and Sofia is a knight,\" Ella declared. In a statement by Samuel: \"Oliver is a knight if and only if Ella is a knight\". Elizabeth was heard saying, \"David is a knave if and only if Lily is a knave\". Lily asserted: \"David is a knave and Sofia is a knight\". Daniel asserted: \"Ella is not a knave\". In David's words: \"Elizabeth is a knight\". Sofia was heard saying, \"Oliver is a knave and Ella is a knave\". In a statement by Oliver: \"If Sofia is a knight then Ella is a knight\". So who is a knight and who is a knave?", "names": ["Ella", "Samuel", "Elizabeth", "Lily", "Daniel", "David", "Sofia", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, false, true, false], "solution_text": "Ella is a knave, Samuel is a knight, Elizabeth is a knave, Lily is a knight, Daniel is a knave, David is a knave, Sofia is a knight, and Oliver is a knave.", "solution_text_format": "(1) Ella is a knave\n(2) Samuel is a knight\n(3) Elizabeth is a knave\n(4) Lily is a knight\n(5) Daniel is a knave\n(6) David is a knave\n(7) Sofia is a knight\n(8) Oliver is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that David is a knight and Sofia is a knight.", "Assume David is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that David is a knave if and only if Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of their own that David is a knave and Sofia is a knight.", "Lily cannot be a knave, because this would contradict the claim of Elizabeth that David is a knave if and only if Lily is a knave.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Elizabeth.", "Elizabeth cannot be a knave, because this would contradict the claim of David that Elizabeth is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the claim of Ella that David is a knight and Sofia is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that David is a knight and Sofia is a knight.", "Assume David is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that David is a knave if and only if Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of their own that David is a knave and Sofia is a knight.", "Lily cannot be a knave, because this would contradict the claim of Elizabeth that David is a knave if and only if Lily is a knave.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Elizabeth.", "Elizabeth cannot be a knave, because this would contradict the claim of David that Elizabeth is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the false claim of David that Elizabeth is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that David is a knave if and only if Lily is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that David is a knave and Sofia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Oliver is a knave and Ella is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Sofia that Oliver is a knave and Ella is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that If Sofia is a knight then Ella is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Oliver is a knight if and only if Ella is a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that Ella is not a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Ella is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('telling-truth', 6)), ('<=>', ('telling-truth', 7), ('telling-truth', 0)), ('<=>', ('lying', 5), ('lying', 3)), ('and', ('lying', 5), ('telling-truth', 6)), ('not', ('lying', 0)), ('telling-truth', 2), ('and', ('lying', 7), ('lying', 0)), ('->', ('telling-truth', 6), ('telling-truth', 0)))", "index": 893}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emily, Penelope, Owen, Abigail, Ethan, Riley, Jack, and Ella. Emily was heard saying, \"Penelope is not a knight\". \"Penelope is a knight and Ella is a knight\" - Penelope. \"If Owen is a knight then Abigail is a knight,\" Owen mentioned. As Abigail put it, \"Ella is a knave and Ethan is a knight\". \"Ella is a knave or Ethan is a knight,\" Ethan mentioned. Riley stated, \"Jack is a knight and Abigail is a knave\". As Jack put it, \"If Riley is a knave then Abigail is a knave\". Ella asserted: \"Owen is a knave\". So who is a knight and who is a knave?", "names": ["Emily", "Penelope", "Owen", "Abigail", "Ethan", "Riley", "Jack", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false, false, false], "solution_text": "Emily is a knight, Penelope is a knave, Owen is a knight, Abigail is a knight, Ethan is a knight, Riley is a knave, Jack is a knave, and Ella is a knave.", "solution_text_format": "(1) Emily is a knight\n(2) Penelope is a knave\n(3) Owen is a knight\n(4) Abigail is a knight\n(5) Ethan is a knight\n(6) Riley is a knave\n(7) Jack is a knave\n(8) Ella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Penelope cannot be a knight, because this would contradict the claim of Emily that Penelope is not a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Penelope is a knight and Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of Ella that Owen is a knave.", "Owen cannot be a knave, because this would contradict the false claim of their own that If Owen is a knight then Abigail is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Owen is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that If Owen is a knight then Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Ella is a knave and Ethan is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Ella is a knave or Ethan is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Jack is a knight and Abigail is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Jack is a knight and Abigail is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that If Riley is a knave then Abigail is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that If Riley is a knave then Abigail is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 1)), ('and', ('telling-truth', 1), ('telling-truth', 7)), ('->', ('telling-truth', 2), ('telling-truth', 3)), ('and', ('lying', 7), ('telling-truth', 4)), ('or', ('lying', 7), ('telling-truth', 4)), ('and', ('telling-truth', 6), ('lying', 3)), ('->', ('lying', 5), ('lying', 3)), ('lying', 2))", "index": 894}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Owen, Liam, Penelope, James, Daniel, Chloe, Luke, and Jacob. Owen remarked, \"Penelope is a knight\". Liam noted, \"Owen is a knight\". Penelope commented, \"If Jacob is a knight then Luke is a knight\". \"Liam is a knight and Liam is a knave,\" James declared. Daniel was heard saying, \"If Liam is a knave then Jacob is a knave\". Chloe noted, \"If Luke is a knight then Luke is a knave\". Luke said, \"Liam is not a knight.\" Jacob remarked, \"Luke is a knight and Liam is a knave\". So who is a knight and who is a knave?", "names": ["Owen", "Liam", "Penelope", "James", "Daniel", "Chloe", "Luke", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true, false, false], "solution_text": "Owen is a knight, Liam is a knight, Penelope is a knight, James is a knave, Daniel is a knight, Chloe is a knight, Luke is a knave, and Jacob is a knave.", "solution_text_format": "(1) Owen is a knight\n(2) Liam is a knight\n(3) Penelope is a knight\n(4) James is a knave\n(5) Daniel is a knight\n(6) Chloe is a knight\n(7) Luke is a knave\n(8) Jacob is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that If Jacob is a knight then Luke is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Luke is a knight and Liam is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Liam is not a knight.", "Liam cannot be a knight, because this would contradict the claim of Luke that Liam is not a knight.", "Liam cannot be a knave, because this would contradict the false claim of their own that Owen is a knight.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the claim of Penelope that If Jacob is a knight then Luke is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Luke is a knight and Liam is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Liam is not a knight.", "Liam cannot be a knight, because this would contradict the claim of Luke that Liam is not a knight.", "Liam cannot be a knave, because this would contradict the false claim of their own that Owen is a knight.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Liam is not a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Owen is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Liam is a knight and Liam is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Liam is a knight and Liam is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that If Liam is a knave then Jacob is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that If Luke is a knight then Luke is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('telling-truth', 0), ('->', ('telling-truth', 7), ('telling-truth', 6)), ('and', ('telling-truth', 1), ('lying', 1)), ('->', ('lying', 1), ('lying', 7)), ('->', ('telling-truth', 6), ('lying', 6)), ('not', ('telling-truth', 1)), ('and', ('telling-truth', 6), ('lying', 1)))", "index": 895}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emma, Oliver, Avery, Matthew, Scarlett, Mason, Liam, and Lucas. \"Lucas is a knave if and only if Mason is a knave\" - Emma. Oliver commented, \"Matthew is a knave if and only if Matthew is a knight\". Avery was heard saying, \"Emma is not a knave\". Matthew asserted: \"Scarlett is not a knave\". Scarlett noted, \"Emma is a knight or Mason is a knave\". \"Oliver is a knave and Liam is a knight\" - Mason. Liam asserted: \"Oliver is not a knight\". \"If Matthew is a knight then Avery is a knight\" - Lucas. So who is a knight and who is a knave?", "names": ["Emma", "Oliver", "Avery", "Matthew", "Scarlett", "Mason", "Liam", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true, true, true], "solution_text": "Emma is a knight, Oliver is a knave, Avery is a knight, Matthew is a knight, Scarlett is a knight, Mason is a knight, Liam is a knight, and Lucas is a knight.", "solution_text_format": "(1) Emma is a knight\n(2) Oliver is a knave\n(3) Avery is a knight\n(4) Matthew is a knight\n(5) Scarlett is a knight\n(6) Mason is a knight\n(7) Liam is a knight\n(8) Lucas is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Lucas is a knave if and only if Mason is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that If Matthew is a knight then Avery is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Emma is a knight or Mason is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Oliver is a knave and Liam is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Matthew is a knave if and only if Matthew is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Matthew is a knave if and only if Matthew is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Oliver is not a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Emma is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 7), ('lying', 5)), ('<=>', ('lying', 3), ('telling-truth', 3)), ('not', ('lying', 0)), ('not', ('lying', 4)), ('or', ('telling-truth', 0), ('lying', 5)), ('and', ('lying', 1), ('telling-truth', 6)), ('not', ('telling-truth', 1)), ('->', ('telling-truth', 3), ('telling-truth', 2)))", "index": 896}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aria, William, Samuel, Olivia, Michael, Evelyn, Elizabeth, and Jacob. In Aria's words: \"William is not a knave\". \"If Jacob is a knight then Michael is a knight,\" William claimed. Samuel expressed that William is a knave and Michael is a knight. Olivia expressed that Evelyn is a knight. In Michael's words: \"Elizabeth is not a knight\". Evelyn told you that Aria is a knave and William is a knight. In a statement by Elizabeth: \"Olivia is a knight or Samuel is a knight\". Jacob was heard saying, \"Aria is not a knave\". So who is a knight and who is a knave?", "names": ["Aria", "William", "Samuel", "Olivia", "Michael", "Evelyn", "Elizabeth", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, false, false, true], "solution_text": "Aria is a knight, William is a knight, Samuel is a knave, Olivia is a knave, Michael is a knight, Evelyn is a knave, Elizabeth is a knave, and Jacob is a knight.", "solution_text_format": "(1) Aria is a knight\n(2) William is a knight\n(3) Samuel is a knave\n(4) Olivia is a knave\n(5) Michael is a knight\n(6) Evelyn is a knave\n(7) Elizabeth is a knave\n(8) Jacob is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that William is not a knave.", "Assume William is a knight. No contradiction is found in their claim that If Jacob is a knight then Michael is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Aria is not a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Elizabeth is not a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Michael that Elizabeth is not a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Olivia is a knight or Samuel is a knight.", "Olivia cannot be a knight, because this would contradict the false claim of Elizabeth that Olivia is a knight or Samuel is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Evelyn is a knight.", "Evelyn cannot be a knight, because this would contradict the false claim of Olivia that Evelyn is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Aria is a knave and William is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that William is a knave and Michael is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that William is a knave and Michael is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('->', ('telling-truth', 7), ('telling-truth', 4)), ('and', ('lying', 1), ('telling-truth', 4)), ('telling-truth', 5), ('not', ('telling-truth', 6)), ('and', ('lying', 0), ('telling-truth', 1)), ('or', ('telling-truth', 3), ('telling-truth', 2)), ('not', ('lying', 0)))", "index": 897}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Henry, Oliver, Samuel, Aurora, William, Chloe, Avery, and Emma. Henry remarked, \"William is a knave\". As Oliver put it, \"If Samuel is a knight then Aurora is a knight\". Samuel remarked, \"Henry is a knave and Henry is a knight\". In Aurora's words: \"If Henry is a knight then Oliver is a knight\". William commented, \"If Samuel is a knave then Emma is a knave\". According to Chloe, \"Oliver is a knight\". According to Avery, \"Aurora is a knave if and only if Oliver is a knight\". \"Aurora is a knight or Avery is a knave,\" Emma claimed. So who is a knight and who is a knave?", "names": ["Henry", "Oliver", "Samuel", "Aurora", "William", "Chloe", "Avery", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true, false, true], "solution_text": "Henry is a knight, Oliver is a knight, Samuel is a knave, Aurora is a knight, William is a knave, Chloe is a knight, Avery is a knave, and Emma is a knight.", "solution_text_format": "(1) Henry is a knight\n(2) Oliver is a knight\n(3) Samuel is a knave\n(4) Aurora is a knight\n(5) William is a knave\n(6) Chloe is a knight\n(7) Avery is a knave\n(8) Emma is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that William is a knave.", "William cannot be a knight, because this would contradict the claim of Henry that William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that If Samuel is a knave then Emma is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that Henry is a knave and Henry is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Henry is a knave and Henry is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Aurora is a knight or Avery is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that If Henry is a knight then Oliver is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that If Samuel is a knight then Aurora is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Aurora is a knave if and only if Oliver is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Aurora is a knave if and only if Oliver is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Oliver is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('->', ('telling-truth', 2), ('telling-truth', 3)), ('and', ('lying', 0), ('telling-truth', 0)), ('->', ('telling-truth', 0), ('telling-truth', 1)), ('->', ('lying', 2), ('lying', 7)), ('telling-truth', 1), ('<=>', ('lying', 3), ('telling-truth', 1)), ('or', ('telling-truth', 3), ('lying', 6)))", "index": 898}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sebastian, Lily, Aurora, James, Oliver, Benjamin, Chloe, and Jack. Sebastian expressed that Jack is a knight and Aurora is a knave. Lily noted, \"Jack is a knight if and only if Aurora is a knave\". \"Benjamin is a knave or Lily is a knight,\" Aurora declared. James said that Sebastian is a knight or Lily is a knave. \"Aurora is a knave,\" Oliver declared. Benjamin expressed that Jack is a knave and Lily is a knave. \"Sebastian is a knight or Aurora is a knight\" - Chloe. Jack commented, \"James is a knave\". So who is a knight and who is a knave?", "names": ["Sebastian", "Lily", "Aurora", "James", "Oliver", "Benjamin", "Chloe", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true, false, false], "solution_text": "Sebastian is a knave, Lily is a knave, Aurora is a knave, James is a knight, Oliver is a knight, Benjamin is a knight, Chloe is a knave, and Jack is a knave.", "solution_text_format": "(1) Sebastian is a knave\n(2) Lily is a knave\n(3) Aurora is a knave\n(4) James is a knight\n(5) Oliver is a knight\n(6) Benjamin is a knight\n(7) Chloe is a knave\n(8) Jack is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that Jack is a knight and Aurora is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that James is a knave.", "James cannot be a knight, because this would contradict the claim of Jack that James is a knave.", "James cannot be a knave, because this would contradict the false claim of their own that Sebastian is a knight or Lily is a knave.", "We have exhausted all possibilities for James, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the claim of Sebastian that Jack is a knight and Aurora is a knave.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Jack is a knight and Aurora is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that James is a knave.", "James cannot be a knight, because this would contradict the claim of Jack that James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Sebastian is a knight or Lily is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Jack is a knight if and only if Aurora is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Lily that Jack is a knight if and only if Aurora is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of Sebastian that Jack is a knight and Aurora is a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the false claim of James that Sebastian is a knight or Lily is a knave.", "We have exhausted all possibilities for Lily and James, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that James is a knave.", "Assume James is a knight. No contradiction is found in their claim that Sebastian is a knight or Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of James that Sebastian is a knight or Lily is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Jack is a knight if and only if Aurora is a knave.", "Aurora cannot be a knight, because this would contradict the false claim of Lily that Jack is a knight if and only if Aurora is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Benjamin is a knave or Lily is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Jack is a knave and Lily is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Aurora is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight or Aurora is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Sebastian is a knight or Aurora is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 7), ('lying', 2)), ('<=>', ('telling-truth', 7), ('lying', 2)), ('or', ('lying', 5), ('telling-truth', 1)), ('or', ('telling-truth', 0), ('lying', 1)), ('lying', 2), ('and', ('lying', 7), ('lying', 1)), ('or', ('telling-truth', 0), ('telling-truth', 2)), ('lying', 3))", "index": 899}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emily, Sebastian, Sofia, Daniel, Mason, Chloe, Lucas, and Ethan. As Emily put it, \"Sebastian is not a knave\". Sebastian commented, \"Lucas is a knight or Chloe is a knight\". \"If Ethan is a knave then Emily is a knight,\" Sofia claimed. Daniel said that Ethan is a knave if and only if Mason is a knave. According to Mason, \"Ethan is a knave or Emily is a knave\". Chloe commented, \"Emily is a knight if and only if Emily is a knave\". Lucas commented, \"Lucas is a knight if and only if Emily is a knave\". Ethan expressed that Lucas is a knave. So who is a knight and who is a knave?", "names": ["Emily", "Sebastian", "Sofia", "Daniel", "Mason", "Chloe", "Lucas", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false, false, true], "solution_text": "Emily is a knave, Sebastian is a knave, Sofia is a knight, Daniel is a knight, Mason is a knight, Chloe is a knave, Lucas is a knave, and Ethan is a knight.", "solution_text_format": "(1) Emily is a knave\n(2) Sebastian is a knave\n(3) Sofia is a knight\n(4) Daniel is a knight\n(5) Mason is a knight\n(6) Chloe is a knave\n(7) Lucas is a knave\n(8) Ethan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Sebastian is not a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Lucas is a knight or Chloe is a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Lucas is a knight if and only if Emily is a knave.", "Lucas cannot be a knave, because this would contradict the false claim of their own that Lucas is a knight if and only if Emily is a knave.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the claim of Emily that Sebastian is not a knave.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Sebastian is not a knave.", "Sebastian cannot be a knight, because this would contradict the false claim of Emily that Sebastian is not a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Lucas is a knight or Chloe is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of Sebastian that Lucas is a knight or Chloe is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Lucas is a knight if and only if Emily is a knave.", "Chloe cannot be a knight, because this would contradict the false claim of Sebastian that Lucas is a knight or Chloe is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Emily is a knight if and only if Emily is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that If Ethan is a knave then Emily is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Lucas is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Ethan is a knave if and only if Mason is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Ethan is a knave or Emily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('or', ('telling-truth', 6), ('telling-truth', 5)), ('->', ('lying', 7), ('telling-truth', 0)), ('<=>', ('lying', 7), ('lying', 4)), ('or', ('lying', 7), ('lying', 0)), ('<=>', ('telling-truth', 0), ('lying', 0)), ('<=>', ('telling-truth', 6), ('lying', 0)), ('lying', 6))", "index": 900}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aiden, Penelope, Abigail, Alexander, Sofia, Luke, Oliver, and Joseph. \"Oliver is a knave or Abigail is a knight,\" Aiden claimed. In Penelope's words: \"Abigail is a knight and Alexander is a knight\". Abigail noted, \"Penelope is a knave and Sofia is a knave\". As Alexander put it, \"Sofia is a knave and Sofia is a knight\". Sofia told you that Joseph is a knave or Alexander is a knave. Luke remarked, \"Sofia is a knave if and only if Oliver is a knight\". Oliver commented, \"Abigail is a knight if and only if Alexander is a knave\". Joseph told you that Alexander is a knave. So who is a knight and who is a knave?", "names": ["Aiden", "Penelope", "Abigail", "Alexander", "Sofia", "Luke", "Oliver", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true, false, true], "solution_text": "Aiden is a knight, Penelope is a knave, Abigail is a knave, Alexander is a knave, Sofia is a knight, Luke is a knight, Oliver is a knave, and Joseph is a knight.", "solution_text_format": "(1) Aiden is a knight\n(2) Penelope is a knave\n(3) Abigail is a knave\n(4) Alexander is a knave\n(5) Sofia is a knight\n(6) Luke is a knight\n(7) Oliver is a knave\n(8) Joseph is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Oliver is a knave or Abigail is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Abigail is a knight if and only if Alexander is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Penelope is a knave and Sofia is a knave.", "Penelope cannot be a knight, because this would contradict the claim of Abigail that Penelope is a knave and Sofia is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Abigail is a knight and Alexander is a knight.", "Alexander cannot be a knight, because this would contradict the false claim of Penelope that Abigail is a knight and Alexander is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Sofia is a knave and Sofia is a knight.", "Sofia cannot be a knight, because this would contradict the claim of Abigail that Penelope is a knave and Sofia is a knave.", "Sofia cannot be a knave, because this would contradict the false claim of their own that Joseph is a knave or Alexander is a knave.", "We have exhausted all possibilities for Sofia, Alexander, and Penelope, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the claim of Aiden that Oliver is a knave or Abigail is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Abigail is a knight if and only if Alexander is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Penelope is a knave and Sofia is a knave.", "Penelope cannot be a knight, because this would contradict the claim of Abigail that Penelope is a knave and Sofia is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Abigail is a knight and Alexander is a knight.", "Alexander cannot be a knight, because this would contradict the false claim of Penelope that Abigail is a knight and Alexander is a knight.", "Alexander cannot be a knave, because this would contradict the false claim of Oliver that Abigail is a knight if and only if Alexander is a knave.", "We have exhausted all possibilities for Alexander and Penelope, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Penelope is a knave and Sofia is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Abigail is a knight and Alexander is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Abigail is a knight and Alexander is a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that Sofia is a knave and Sofia is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Sofia is a knave and Sofia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Joseph is a knave or Alexander is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Alexander is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Sofia is a knave if and only if Oliver is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 6), ('telling-truth', 2)), ('and', ('telling-truth', 2), ('telling-truth', 3)), ('and', ('lying', 1), ('lying', 4)), ('and', ('lying', 4), ('telling-truth', 4)), ('or', ('lying', 7), ('lying', 3)), ('<=>', ('lying', 4), ('telling-truth', 6)), ('<=>', ('telling-truth', 2), ('lying', 3)), ('lying', 3))", "index": 901}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lily, Isabella, Emily, Penelope, Grace, Olivia, Aria, and Abigail. Lily noted, \"Grace is a knight and Abigail is a knight\". In a statement by Isabella: \"Penelope is not a knight\". Emily expressed that Penelope is a knave. According to Penelope, \"Grace is a knight and Olivia is a knave\". Grace commented, \"Lily is a knave if and only if Lily is a knight\". Olivia told you that Abigail is not a knave. \"Olivia is a knight,\" Aria mentioned. Abigail remarked, \"Isabella is not a knight\". So who is a knight and who is a knave?", "names": ["Lily", "Isabella", "Emily", "Penelope", "Grace", "Olivia", "Aria", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false, false, false], "solution_text": "Lily is a knave, Isabella is a knight, Emily is a knight, Penelope is a knave, Grace is a knave, Olivia is a knave, Aria is a knave, and Abigail is a knave.", "solution_text_format": "(1) Lily is a knave\n(2) Isabella is a knight\n(3) Emily is a knight\n(4) Penelope is a knave\n(5) Grace is a knave\n(6) Olivia is a knave\n(7) Aria is a knave\n(8) Abigail is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that Grace is a knight and Abigail is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Lily is a knave if and only if Lily is a knight.", "Grace cannot be a knave, because this would contradict the claim of Lily that Grace is a knight and Abigail is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Grace is a knight and Abigail is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Lily is a knave if and only if Lily is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Lily is a knave if and only if Lily is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Isabella is not a knight.", "Isabella cannot be a knight, because this would contradict the claim of Abigail that Isabella is not a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Penelope is not a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Grace is a knight and Olivia is a knave.", "Penelope cannot be a knave, because this would contradict the false claim of Isabella that Penelope is not a knight.", "We have exhausted all possibilities for Penelope and Isabella, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Isabella is not a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Penelope cannot be a knight, because this would contradict the claim of Isabella that Penelope is not a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Grace is a knight and Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that Abigail is not a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Abigail is not a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Penelope is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Olivia is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Olivia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 4), ('telling-truth', 7)), ('not', ('telling-truth', 3)), ('lying', 3), ('and', ('telling-truth', 4), ('lying', 5)), ('<=>', ('lying', 0), ('telling-truth', 0)), ('not', ('lying', 7)), ('telling-truth', 5), ('not', ('telling-truth', 1)))", "index": 902}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Avery, Henry, David, Alexander, Zoey, Harper, Aurora, and Joseph. Avery commented, \"Harper is not a knight\". Henry noted, \"Alexander is a knave or Joseph is a knight\". David noted, \"Avery is not a knight\". Alexander asserted: \"Joseph is a knave\". In a statement by Zoey: \"Zoey is a knight and Joseph is a knave\". \"Harper is a knight and Aurora is a knight\" - Harper. According to Aurora, \"Avery is a knight and Henry is a knave\". \"Zoey is a knight if and only if Joseph is a knight,\" Joseph claimed. So who is a knight and who is a knave?", "names": ["Avery", "Henry", "David", "Alexander", "Zoey", "Harper", "Aurora", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false, true, false], "solution_text": "Avery is a knight, Henry is a knave, David is a knave, Alexander is a knight, Zoey is a knight, Harper is a knave, Aurora is a knight, and Joseph is a knave.", "solution_text_format": "(1) Avery is a knight\n(2) Henry is a knave\n(3) David is a knave\n(4) Alexander is a knight\n(5) Zoey is a knight\n(6) Harper is a knave\n(7) Aurora is a knight\n(8) Joseph is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Harper is not a knight.", "Harper cannot be a knight, because this would contradict the claim of Avery that Harper is not a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Harper is a knight and Aurora is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Avery is a knight and Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of Aurora that Avery is a knight and Henry is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Alexander is a knave or Joseph is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the false claim of Henry that Alexander is a knave or Joseph is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Zoey is a knight if and only if Joseph is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Zoey is a knight and Joseph is a knave.", "David cannot be a knight, because this would contradict the claim of their own that Avery is not a knight.", "Assume David is a knave. No contradiction is found in their false claim that Avery is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 5)), ('or', ('lying', 3), ('telling-truth', 7)), ('not', ('telling-truth', 0)), ('lying', 7), ('and', ('telling-truth', 4), ('lying', 7)), ('and', ('telling-truth', 5), ('telling-truth', 6)), ('and', ('telling-truth', 0), ('lying', 1)), ('<=>', ('telling-truth', 4), ('telling-truth', 7)))", "index": 903}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Evelyn, Daniel, Jack, Oliver, Grace, Luke, Victoria, and Harper. Evelyn asserted: \"Jack is not a knave\". Daniel told you that Luke is not a knight. Jack stated, \"Grace is not a knight\". Oliver commented, \"Harper is a knight and Grace is a knight\". Grace remarked, \"Victoria is a knave\". Luke remarked, \"If Evelyn is a knight then Grace is a knave\". \"If Grace is a knight then Oliver is a knave\" - Victoria. Harper expressed that Luke is a knave or Victoria is a knight. So who is a knight and who is a knave?", "names": ["Evelyn", "Daniel", "Jack", "Oliver", "Grace", "Luke", "Victoria", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true, true, true], "solution_text": "Evelyn is a knight, Daniel is a knave, Jack is a knight, Oliver is a knave, Grace is a knave, Luke is a knight, Victoria is a knight, and Harper is a knight.", "solution_text_format": "(1) Evelyn is a knight\n(2) Daniel is a knave\n(3) Jack is a knight\n(4) Oliver is a knave\n(5) Grace is a knave\n(6) Luke is a knight\n(7) Victoria is a knight\n(8) Harper is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Jack is not a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Grace is not a knight.", "Grace cannot be a knight, because this would contradict the claim of Jack that Grace is not a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that If Grace is a knight then Oliver is a knave.", "Oliver cannot be a knight, because this would contradict the claim of their own that Harper is a knight and Grace is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Harper is a knight and Grace is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Luke is a knave or Victoria is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that If Evelyn is a knight then Grace is a knave.", "Daniel cannot be a knight, because this would contradict the claim of their own that Luke is not a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Luke is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('not', ('telling-truth', 5)), ('not', ('telling-truth', 4)), ('and', ('telling-truth', 7), ('telling-truth', 4)), ('lying', 6), ('->', ('telling-truth', 0), ('lying', 4)), ('->', ('telling-truth', 4), ('lying', 3)), ('or', ('lying', 5), ('telling-truth', 6)))", "index": 904}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Penelope, Amelia, Grace, Mia, Owen, Mason, Zoey, and Harper. \"Mia is a knave and Grace is a knight,\" Penelope claimed. \"Mia is a knight,\" Amelia mentioned. Grace expressed that Mason is not a knave. \"If Harper is a knight then Amelia is a knave,\" Mia declared. Owen remarked, \"Penelope is a knave if and only if Harper is a knight\". \"Penelope is a knave,\" Mason mentioned. Zoey asserted: \"Mason is not a knight\". Harper stated, \"Grace is a knave and Mia is a knight\". So who is a knight and who is a knave?", "names": ["Penelope", "Amelia", "Grace", "Mia", "Owen", "Mason", "Zoey", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true, false, false], "solution_text": "Penelope is a knave, Amelia is a knight, Grace is a knight, Mia is a knight, Owen is a knave, Mason is a knight, Zoey is a knave, and Harper is a knave.", "solution_text_format": "(1) Penelope is a knave\n(2) Amelia is a knight\n(3) Grace is a knight\n(4) Mia is a knight\n(5) Owen is a knave\n(6) Mason is a knight\n(7) Zoey is a knave\n(8) Harper is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that Mia is a knave and Grace is a knight.", "Mia cannot be a knight, because this would contradict the claim of Penelope that Mia is a knave and Grace is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that If Harper is a knight then Amelia is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Grace is a knave and Mia is a knight.", "Harper cannot be a knave, because this would contradict the false claim of Mia that If Harper is a knight then Amelia is a knave.", "We have exhausted all possibilities for Harper and Mia, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Mia is a knave and Grace is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that If Harper is a knight then Amelia is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Grace is a knave and Mia is a knight.", "Grace cannot be a knight, because this would contradict the claim of Harper that Grace is a knave and Mia is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Mason is not a knave.", "Mason cannot be a knight, because this would contradict the false claim of Grace that Mason is not a knave.", "Mason cannot be a knave, because this would contradict the false claim of their own that Penelope is a knave.", "We have exhausted all possibilities for Mason and Grace, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Grace is a knave and Mia is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Mason is not a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Penelope is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Mia is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Penelope is a knave if and only if Harper is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Penelope is a knave if and only if Harper is a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that Mason is not a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Mason is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('telling-truth', 2)), ('telling-truth', 3), ('not', ('lying', 5)), ('->', ('telling-truth', 7), ('lying', 1)), ('<=>', ('lying', 0), ('telling-truth', 7)), ('lying', 0), ('not', ('telling-truth', 5)), ('and', ('lying', 2), ('telling-truth', 3)))", "index": 905}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Avery, Liam, Jacob, Sophia, Ava, Logan, Lucas, and Isabella. \"Lucas is a knight if and only if Liam is a knave,\" Avery declared. \"Lucas is a knave and Isabella is a knave\" - Liam. As Jacob put it, \"Lucas is a knave\". According to Sophia, \"Lucas is a knave if and only if Ava is a knight\". Ava asserted: \"If Jacob is a knight then Logan is a knight\". As Logan put it, \"If Jacob is a knave then Lucas is a knave\". Lucas said that Isabella is a knave or Liam is a knight. Isabella was heard saying, \"Ava is a knave and Jacob is a knave\". So who is a knight and who is a knave?", "names": ["Avery", "Liam", "Jacob", "Sophia", "Ava", "Logan", "Lucas", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, false, true, false], "solution_text": "Avery is a knight, Liam is a knave, Jacob is a knave, Sophia is a knave, Ava is a knight, Logan is a knave, Lucas is a knight, and Isabella is a knave.", "solution_text_format": "(1) Avery is a knight\n(2) Liam is a knave\n(3) Jacob is a knave\n(4) Sophia is a knave\n(5) Ava is a knight\n(6) Logan is a knave\n(7) Lucas is a knight\n(8) Isabella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Lucas is a knight if and only if Liam is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Isabella is a knave or Liam is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Ava is a knave and Jacob is a knave.", "Ava cannot be a knight, because this would contradict the claim of Isabella that Ava is a knave and Jacob is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that If Jacob is a knight then Logan is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Lucas is a knave.", "Jacob cannot be a knave, because this would contradict the false claim of Ava that If Jacob is a knight then Logan is a knight.", "We have exhausted all possibilities for Jacob and Ava, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Ava is a knave and Jacob is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that If Jacob is a knight then Logan is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Lucas is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Lucas is a knave.", "Logan cannot be a knight, because this would contradict the claim of their own that If Jacob is a knave then Lucas is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that If Jacob is a knave then Lucas is a knave.", "Liam cannot be a knight, because this would contradict the claim of Avery that Lucas is a knight if and only if Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Lucas is a knave and Isabella is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that Lucas is a knave if and only if Ava is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Lucas is a knave if and only if Ava is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 6), ('lying', 1)), ('and', ('lying', 6), ('lying', 7)), ('lying', 6), ('<=>', ('lying', 6), ('telling-truth', 4)), ('->', ('telling-truth', 2), ('telling-truth', 5)), ('->', ('lying', 2), ('lying', 6)), ('or', ('lying', 7), ('telling-truth', 1)), ('and', ('lying', 4), ('lying', 2)))", "index": 906}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Owen, Henry, Olivia, Sophia, Jack, Matthew, Michael, and Jackson. Owen noted, \"Henry is a knave and Matthew is a knave\". Henry told you that Sophia is a knight or Owen is a knave. According to Olivia, \"Olivia is a knight and Michael is a knave\". Sophia stated, \"Olivia is a knave or Matthew is a knave\". Jack was heard saying, \"Michael is a knave if and only if Sophia is a knight\". Matthew asserted: \"Jack is a knave if and only if Sophia is a knave\". \"Henry is a knave if and only if Olivia is a knave\" - Michael. Jackson told you that Jackson is a knight and Owen is a knight. So who is a knight and who is a knave?", "names": ["Owen", "Henry", "Olivia", "Sophia", "Jack", "Matthew", "Michael", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true, false, false], "solution_text": "Owen is a knave, Henry is a knight, Olivia is a knave, Sophia is a knight, Jack is a knight, Matthew is a knight, Michael is a knave, and Jackson is a knave.", "solution_text_format": "(1) Owen is a knave\n(2) Henry is a knight\n(3) Olivia is a knave\n(4) Sophia is a knight\n(5) Jack is a knight\n(6) Matthew is a knight\n(7) Michael is a knave\n(8) Jackson is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Henry is a knave and Matthew is a knave.", "Henry cannot be a knight, because this would contradict the claim of Owen that Henry is a knave and Matthew is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Sophia is a knight or Owen is a knave.", "Sophia cannot be a knight, because this would contradict the false claim of Henry that Sophia is a knight or Owen is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Olivia is a knave or Matthew is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Olivia is a knight and Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of Olivia that Olivia is a knight and Michael is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Henry is a knave if and only if Olivia is a knave.", "Matthew cannot be a knight, because this would contradict the claim of Owen that Henry is a knave and Matthew is a knave.", "Matthew cannot be a knave, because this would contradict the false claim of Sophia that Olivia is a knave or Matthew is a knave.", "We have exhausted all possibilities for Matthew and Michael, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the false claim of Sophia that Olivia is a knave or Matthew is a knave.", "We have exhausted all possibilities for Olivia, Sophia, and Henry, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Henry is a knave and Matthew is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Sophia is a knight or Owen is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Olivia is a knave or Matthew is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Olivia is a knight and Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of Olivia that Olivia is a knight and Michael is a knave.", "Michael cannot be a knave, because this would contradict the false claim of their own that Henry is a knave if and only if Olivia is a knave.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Olivia is a knight and Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Henry is a knave if and only if Olivia is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Henry is a knave if and only if Olivia is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Jack is a knave if and only if Sophia is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Michael is a knave if and only if Sophia is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Jackson is a knight and Owen is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Jackson is a knight and Owen is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 1), ('lying', 5)), ('or', ('telling-truth', 3), ('lying', 0)), ('and', ('telling-truth', 2), ('lying', 6)), ('or', ('lying', 2), ('lying', 5)), ('<=>', ('lying', 6), ('telling-truth', 3)), ('<=>', ('lying', 4), ('lying', 3)), ('<=>', ('lying', 1), ('lying', 2)), ('and', ('telling-truth', 7), ('telling-truth', 0)))", "index": 907}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Samuel, Aiden, Joseph, Jackson, Olivia, Sebastian, Daniel, and Ava. Samuel told you that Daniel is a knave if and only if Jackson is a knight. In a statement by Aiden: \"Sebastian is a knight and Samuel is a knight\". As Joseph put it, \"Samuel is not a knight\". According to Jackson, \"Aiden is not a knight\". Olivia said that Daniel is a knave if and only if Jackson is a knight. Sebastian asserted: \"Ava is not a knave\". Daniel commented, \"If Olivia is a knave then Samuel is a knight\". \"Olivia is a knight,\" Ava claimed. So who is a knight and who is a knave?", "names": ["Samuel", "Aiden", "Joseph", "Jackson", "Olivia", "Sebastian", "Daniel", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true, true, true], "solution_text": "Samuel is a knight, Aiden is a knight, Joseph is a knave, Jackson is a knave, Olivia is a knight, Sebastian is a knight, Daniel is a knight, and Ava is a knight.", "solution_text_format": "(1) Samuel is a knight\n(2) Aiden is a knight\n(3) Joseph is a knave\n(4) Jackson is a knave\n(5) Olivia is a knight\n(6) Sebastian is a knight\n(7) Daniel is a knight\n(8) Ava is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that Daniel is a knave if and only if Jackson is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that If Olivia is a knave then Samuel is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Daniel is a knave if and only if Jackson is a knight.", "Jackson cannot be a knight, because this would contradict the claim of Samuel that Daniel is a knave if and only if Jackson is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Aiden is not a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Sebastian is a knight and Samuel is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Ava is not a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Olivia is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Samuel is not a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Samuel is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 6), ('telling-truth', 3)), ('and', ('telling-truth', 5), ('telling-truth', 0)), ('not', ('telling-truth', 0)), ('not', ('telling-truth', 1)), ('<=>', ('lying', 6), ('telling-truth', 3)), ('not', ('lying', 7)), ('->', ('lying', 4), ('telling-truth', 0)), ('telling-truth', 4))", "index": 908}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Michael, Amelia, Chloe, Ava, Ella, Logan, Jackson, and James. Michael commented, \"Logan is a knave and Amelia is a knight\". As Amelia put it, \"Logan is not a knight\". \"Michael is a knave\" - Chloe. Ava expressed that Michael is not a knight. Ella asserted: \"Chloe is a knight\". Logan commented, \"James is a knave and Jackson is a knight\". \"If Ava is a knight then Amelia is a knave,\" Jackson mentioned. According to James, \"If Jackson is a knave then Chloe is a knight\". So who is a knight and who is a knave?", "names": ["Michael", "Amelia", "Chloe", "Ava", "Ella", "Logan", "Jackson", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, false, true, true], "solution_text": "Michael is a knight, Amelia is a knight, Chloe is a knave, Ava is a knave, Ella is a knave, Logan is a knave, Jackson is a knight, and James is a knight.", "solution_text_format": "(1) Michael is a knight\n(2) Amelia is a knight\n(3) Chloe is a knave\n(4) Ava is a knave\n(5) Ella is a knave\n(6) Logan is a knave\n(7) Jackson is a knight\n(8) James is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Logan is a knave and Amelia is a knight.", "Logan cannot be a knight, because this would contradict the claim of Michael that Logan is a knave and Amelia is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that James is a knave and Jackson is a knight.", "Assume James is a knight. No contradiction is found in their claim that If Jackson is a knave then Chloe is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that If Ava is a knight then Amelia is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Michael is not a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Michael is not a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Logan is not a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Michael is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Michael is a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Chloe is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Chloe is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 5), ('telling-truth', 1)), ('not', ('telling-truth', 5)), ('lying', 0), ('not', ('telling-truth', 0)), ('telling-truth', 2), ('and', ('lying', 7), ('telling-truth', 6)), ('->', ('telling-truth', 3), ('lying', 1)), ('->', ('lying', 6), ('telling-truth', 2)))", "index": 909}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sofia, Noah, Aiden, Aria, Ava, Scarlett, Riley, and Isabella. Sofia asserted: \"Riley is a knave and Aria is a knight\". \"Aria is a knave,\" Noah declared. \"Scarlett is a knave,\" Aiden claimed. Aria asserted: \"If Isabella is a knight then Aiden is a knave\". Ava stated, \"Aiden is a knight or Scarlett is a knave\". \"Aiden is a knave and Sofia is a knave,\" Scarlett claimed. According to Riley, \"Aiden is a knight or Scarlett is a knave\". Isabella said that Aria is a knight or Isabella is a knight. So who is a knight and who is a knave?", "names": ["Sofia", "Noah", "Aiden", "Aria", "Ava", "Scarlett", "Riley", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, false, true, true], "solution_text": "Sofia is a knave, Noah is a knight, Aiden is a knight, Aria is a knave, Ava is a knight, Scarlett is a knave, Riley is a knight, and Isabella is a knight.", "solution_text_format": "(1) Sofia is a knave\n(2) Noah is a knight\n(3) Aiden is a knight\n(4) Aria is a knave\n(5) Ava is a knight\n(6) Scarlett is a knave\n(7) Riley is a knight\n(8) Isabella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Riley is a knave and Aria is a knight.", "Riley cannot be a knight, because this would contradict the claim of Sofia that Riley is a knave and Aria is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Aiden is a knight or Scarlett is a knave.", "Aiden cannot be a knight, because this would contradict the false claim of Riley that Aiden is a knight or Scarlett is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Aiden is a knave and Sofia is a knave.", "Scarlett cannot be a knave, because this would contradict the false claim of Aiden that Scarlett is a knave.", "We have exhausted all possibilities for Scarlett, Aiden, and Riley, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Riley is a knave and Aria is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Aiden is a knight or Scarlett is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Aiden that Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Aiden is a knave and Sofia is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that If Isabella is a knight then Aiden is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Aria that If Isabella is a knight then Aiden is a knave.", "Isabella cannot be a knave, because this would contradict the false claim of their own that Aria is a knight or Isabella is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that If Isabella is a knight then Aiden is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Aria is a knight or Isabella is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Aria is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Aiden is a knight or Scarlett is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 6), ('telling-truth', 3)), ('lying', 3), ('lying', 5), ('->', ('telling-truth', 7), ('lying', 2)), ('or', ('telling-truth', 2), ('lying', 5)), ('and', ('lying', 2), ('lying', 0)), ('or', ('telling-truth', 2), ('lying', 5)), ('or', ('telling-truth', 3), ('telling-truth', 7)))", "index": 910}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Luke, Lucas, Aiden, Matthew, Jackson, Emily, Sebastian, and Owen. Luke commented, \"Matthew is a knight\". Lucas expressed that If Jackson is a knave then Owen is a knave. \"Lucas is not a knave,\" Aiden claimed. \"Owen is not a knave,\" Matthew claimed. As Jackson put it, \"Matthew is a knave or Sebastian is a knight\". As Emily put it, \"Luke is not a knave\". Sebastian remarked, \"Lucas is a knave and Luke is a knave\". Owen stated, \"If Matthew is a knight then Jackson is a knave\". So who is a knight and who is a knave?", "names": ["Luke", "Lucas", "Aiden", "Matthew", "Jackson", "Emily", "Sebastian", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, true, false, true], "solution_text": "Luke is a knight, Lucas is a knave, Aiden is a knave, Matthew is a knight, Jackson is a knave, Emily is a knight, Sebastian is a knave, and Owen is a knight.", "solution_text_format": "(1) Luke is a knight\n(2) Lucas is a knave\n(3) Aiden is a knave\n(4) Matthew is a knight\n(5) Jackson is a knave\n(6) Emily is a knight\n(7) Sebastian is a knave\n(8) Owen is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Owen is not a knave.", "Assume Owen is a knight. No contradiction is found in their claim that If Matthew is a knight then Jackson is a knave.", "Jackson cannot be a knight, because this would contradict the claim of Owen that If Matthew is a knight then Jackson is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Matthew is a knave or Sebastian is a knight.", "Sebastian cannot be a knight, because this would contradict the false claim of Jackson that Matthew is a knave or Sebastian is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Lucas is a knave and Luke is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that If Jackson is a knave then Owen is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that If Jackson is a knave then Owen is a knave.", "Aiden cannot be a knight, because this would contradict the claim of their own that Lucas is not a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Lucas is not a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Luke is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 3), ('->', ('lying', 4), ('lying', 7)), ('not', ('lying', 1)), ('not', ('lying', 7)), ('or', ('lying', 3), ('telling-truth', 6)), ('not', ('lying', 0)), ('and', ('lying', 1), ('lying', 0)), ('->', ('telling-truth', 3), ('lying', 4)))", "index": 911}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: David, Ava, Ethan, Isabella, Abigail, Owen, Chloe, and Samuel. David remarked, \"Ethan is a knave\". Ava remarked, \"Ethan is a knight or Isabella is a knight\". Ethan expressed that Isabella is a knave or Abigail is a knight. Isabella expressed that Abigail is not a knave. Abigail asserted: \"Owen is not a knight\". Owen was heard saying, \"Owen is a knight or Ethan is a knight\". \"Ava is a knight and Ava is a knave\" - Chloe. Samuel expressed that Chloe is a knave. So who is a knight and who is a knave?", "names": ["David", "Ava", "Ethan", "Isabella", "Abigail", "Owen", "Chloe", "Samuel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true, false, true], "solution_text": "David is a knave, Ava is a knight, Ethan is a knight, Isabella is a knave, Abigail is a knave, Owen is a knight, Chloe is a knave, and Samuel is a knight.", "solution_text_format": "(1) David is a knave\n(2) Ava is a knight\n(3) Ethan is a knight\n(4) Isabella is a knave\n(5) Abigail is a knave\n(6) Owen is a knight\n(7) Chloe is a knave\n(8) Samuel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Ethan is a knave.", "Ethan cannot be a knight, because this would contradict the claim of David that Ethan is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Isabella is a knave or Abigail is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Abigail is not a knave.", "Abigail cannot be a knight, because this would contradict the false claim of Ethan that Isabella is a knave or Abigail is a knight.", "Abigail cannot be a knave, because this would contradict the claim of Isabella that Abigail is not a knave.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the false claim of Ethan that Isabella is a knave or Abigail is a knight.", "We have exhausted all possibilities for Isabella and Ethan, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Ethan is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Isabella is a knave or Abigail is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Abigail is not a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Owen is not a knight.", "Owen cannot be a knight, because this would contradict the claim of Abigail that Owen is not a knight.", "Owen cannot be a knave, because this would contradict the false claim of their own that Owen is a knight or Ethan is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the claim of Ethan that Isabella is a knave or Abigail is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Abigail is not a knave.", "Abigail cannot be a knight, because this would contradict the false claim of Isabella that Abigail is not a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Owen is not a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Owen is a knight or Ethan is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Ethan is a knight or Isabella is a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Ava is a knight and Ava is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Ava is a knight and Ava is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Chloe is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('or', ('telling-truth', 2), ('telling-truth', 3)), ('or', ('lying', 3), ('telling-truth', 4)), ('not', ('lying', 4)), ('not', ('telling-truth', 5)), ('or', ('telling-truth', 5), ('telling-truth', 2)), ('and', ('telling-truth', 1), ('lying', 1)), ('lying', 6))", "index": 912}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jacob, Zoey, Alexander, Henry, Ella, Aurora, Benjamin, and Jack. Jacob remarked, \"Henry is a knave or Alexander is a knight\". In Zoey's words: \"Henry is not a knave\". Alexander remarked, \"Henry is a knave and Jacob is a knight\". Henry told you that Benjamin is a knight or Henry is a knight. Ella stated, \"Jacob is a knight if and only if Zoey is a knave\". Aurora commented, \"If Jack is a knave then Alexander is a knave\". Benjamin asserted: \"Ella is a knight and Henry is a knave\". Jack said that If Aurora is a knight then Aurora is a knave. So who is a knight and who is a knave?", "names": ["Jacob", "Zoey", "Alexander", "Henry", "Ella", "Aurora", "Benjamin", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true, false, false], "solution_text": "Jacob is a knave, Zoey is a knight, Alexander is a knave, Henry is a knight, Ella is a knight, Aurora is a knight, Benjamin is a knave, and Jack is a knave.", "solution_text_format": "(1) Jacob is a knave\n(2) Zoey is a knight\n(3) Alexander is a knave\n(4) Henry is a knight\n(5) Ella is a knight\n(6) Aurora is a knight\n(7) Benjamin is a knave\n(8) Jack is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that Henry is a knave or Alexander is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Benjamin is a knight or Henry is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Ella is a knight and Henry is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Ella is a knight and Henry is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Jacob is a knight if and only if Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Ella that Jacob is a knight if and only if Zoey is a knave.", "Zoey cannot be a knave, because this would contradict the false claim of their own that Henry is not a knave.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Jacob is a knight if and only if Zoey is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Henry is not a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that Henry is a knave and Jacob is a knight.", "Alexander cannot be a knave, because this would contradict the claim of Jacob that Henry is a knave or Alexander is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Zoey.", "Zoey cannot be a knave, because this would contradict the false claim of their own that Henry is not a knave.", "We have exhausted all possibilities for Zoey, Ella, and Benjamin, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Benjamin is a knight or Henry is a knight.", "Benjamin cannot be a knight, because this would contradict the false claim of Henry that Benjamin is a knight or Henry is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Ella is a knight and Henry is a knave.", "Ella cannot be a knight, because this would contradict the false claim of Benjamin that Ella is a knight and Henry is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Jacob is a knight if and only if Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that Henry is not a knave.", "Zoey cannot be a knave, because this would contradict the false claim of Ella that Jacob is a knight if and only if Zoey is a knave.", "We have exhausted all possibilities for Zoey, Ella, Benjamin, and Henry, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Henry is a knave or Alexander is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Benjamin is a knight or Henry is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Ella is a knight and Henry is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Ella is a knight and Henry is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Jacob is a knight if and only if Zoey is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Henry is not a knave.", "Alexander cannot be a knight, because this would contradict the false claim of Jacob that Henry is a knave or Alexander is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Henry is a knave and Jacob is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that If Jack is a knave then Alexander is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that If Aurora is a knight then Aurora is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that If Aurora is a knight then Aurora is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('telling-truth', 2)), ('not', ('lying', 3)), ('and', ('lying', 3), ('telling-truth', 0)), ('or', ('telling-truth', 6), ('telling-truth', 3)), ('<=>', ('telling-truth', 0), ('lying', 1)), ('->', ('lying', 7), ('lying', 2)), ('and', ('telling-truth', 4), ('lying', 3)), ('->', ('telling-truth', 5), ('lying', 5)))", "index": 913}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Henry, Elizabeth, Lucas, Sofia, Scarlett, Oliver, Chloe, and Charlotte. In Henry's words: \"If Chloe is a knave then Lucas is a knight\". Elizabeth noted, \"Scarlett is not a knave\". Lucas expressed that Charlotte is a knave if and only if Scarlett is a knave. In a statement by Sofia: \"Elizabeth is a knave and Chloe is a knave\". Scarlett told you that Lucas is a knight. According to Oliver, \"Henry is not a knight\". Chloe expressed that Lucas is a knight and Elizabeth is a knight. Charlotte expressed that Oliver is a knave. So who is a knight and who is a knave?", "names": ["Henry", "Elizabeth", "Lucas", "Sofia", "Scarlett", "Oliver", "Chloe", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false, true, true], "solution_text": "Henry is a knight, Elizabeth is a knight, Lucas is a knight, Sofia is a knave, Scarlett is a knight, Oliver is a knave, Chloe is a knight, and Charlotte is a knight.", "solution_text_format": "(1) Henry is a knight\n(2) Elizabeth is a knight\n(3) Lucas is a knight\n(4) Sofia is a knave\n(5) Scarlett is a knight\n(6) Oliver is a knave\n(7) Chloe is a knight\n(8) Charlotte is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that If Chloe is a knave then Lucas is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Lucas is a knight and Elizabeth is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Charlotte is a knave if and only if Scarlett is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Oliver is a knave.", "Oliver cannot be a knight, because this would contradict the claim of their own that Henry is not a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Henry is not a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Lucas is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave and Chloe is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Elizabeth is a knave and Chloe is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 6), ('telling-truth', 2)), ('not', ('lying', 4)), ('<=>', ('lying', 7), ('lying', 4)), ('and', ('lying', 1), ('lying', 6)), ('telling-truth', 2), ('not', ('telling-truth', 0)), ('and', ('telling-truth', 2), ('telling-truth', 1)), ('lying', 5))", "index": 914}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Noah, Mia, David, Joseph, Aria, Daniel, Emily, and Ava. In Noah's words: \"Mia is a knight if and only if Mia is a knave\". Mia told you that Daniel is a knight if and only if Emily is a knight. \"Joseph is a knight or Daniel is a knave,\" David claimed. Joseph said, \"Noah is a knave or Noah is a knight.\" As Aria put it, \"Mia is a knight\". Daniel was heard saying, \"Noah is a knight or David is a knight\". Emily said, \"If Daniel is a knight then Joseph is a knave.\" Ava said that Joseph is a knave or Joseph is a knight. So who is a knight and who is a knave?", "names": ["Noah", "Mia", "David", "Joseph", "Aria", "Daniel", "Emily", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, true, false, true], "solution_text": "Noah is a knave, Mia is a knave, David is a knight, Joseph is a knight, Aria is a knave, Daniel is a knight, Emily is a knave, and Ava is a knight.", "solution_text_format": "(1) Noah is a knave\n(2) Mia is a knave\n(3) David is a knight\n(4) Joseph is a knight\n(5) Aria is a knave\n(6) Daniel is a knight\n(7) Emily is a knave\n(8) Ava is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Noah cannot be a knight, because this would contradict the claim of their own that Mia is a knight if and only if Mia is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Mia is a knight if and only if Mia is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Daniel is a knight if and only if Emily is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Noah is a knight or David is a knight.", "Assume David is a knight. No contradiction is found in their claim that Joseph is a knight or Daniel is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Noah is a knave or Noah is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that If Daniel is a knight then Joseph is a knave.", "Emily cannot be a knave, because this would contradict the claim of Mia that Daniel is a knight if and only if Emily is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of David that Joseph is a knight or Daniel is a knave.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the claim of Daniel that Noah is a knight or David is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Noah is a knight or David is a knight.", "David cannot be a knight, because this would contradict the false claim of Daniel that Noah is a knight or David is a knight.", "David cannot be a knave, because this would contradict the false claim of their own that Joseph is a knight or Daniel is a knave.", "We have exhausted all possibilities for David and Daniel, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Daniel is a knight if and only if Emily is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Noah is a knight or David is a knight.", "Assume David is a knight. No contradiction is found in their claim that Joseph is a knight or Daniel is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Noah is a knave or Noah is a knight.", "Emily cannot be a knight, because this would contradict the false claim of Mia that Daniel is a knight if and only if Emily is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that If Daniel is a knight then Joseph is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Mia is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Mia is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Joseph is a knave or Joseph is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('lying', 1)), ('<=>', ('telling-truth', 5), ('telling-truth', 6)), ('or', ('telling-truth', 3), ('lying', 5)), ('or', ('lying', 0), ('telling-truth', 0)), ('telling-truth', 1), ('or', ('telling-truth', 0), ('telling-truth', 2)), ('->', ('telling-truth', 5), ('lying', 3)), ('or', ('lying', 3), ('telling-truth', 3)))", "index": 915}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ella, Jacob, Samuel, David, Mason, Grace, Jackson, and Sofia. In Ella's words: \"If Sofia is a knave then Jacob is a knave\". Jacob was heard saying, \"Mason is not a knight\". \"Ella is a knight or Jackson is a knave,\" Samuel claimed. In David's words: \"Grace is a knight if and only if Samuel is a knight\". \"Samuel is not a knave,\" Mason declared. In Grace's words: \"Mason is a knave and Sofia is a knave\". Jackson remarked, \"If Sofia is a knave then Jacob is a knight\". Sofia told you that Grace is a knave if and only if David is a knight. So who is a knight and who is a knave?", "names": ["Ella", "Jacob", "Samuel", "David", "Mason", "Grace", "Jackson", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, false, false, false], "solution_text": "Ella is a knight, Jacob is a knave, Samuel is a knight, David is a knave, Mason is a knight, Grace is a knave, Jackson is a knave, and Sofia is a knave.", "solution_text_format": "(1) Ella is a knight\n(2) Jacob is a knave\n(3) Samuel is a knight\n(4) David is a knave\n(5) Mason is a knight\n(6) Grace is a knave\n(7) Jackson is a knave\n(8) Sofia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that If Sofia is a knave then Jacob is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Grace is a knave if and only if David is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Mason is a knave and Sofia is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Mason is a knave and Sofia is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Samuel is not a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Ella is a knight or Jackson is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that If Sofia is a knave then Jacob is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Mason is not a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Mason is not a knight.", "David cannot be a knight, because this would contradict the claim of their own that Grace is a knight if and only if Samuel is a knight.", "David cannot be a knave, because this would contradict the claim of Sofia that Grace is a knave if and only if David is a knight.", "We have exhausted all possibilities for David and Jacob, so let us go back and reconsider Jackson.", "Jackson cannot be a knave, because this would contradict the false claim of their own that If Sofia is a knave then Jacob is a knight.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Samuel.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Ella is a knight or Jackson is a knave.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Samuel is not a knave.", "Samuel cannot be a knight, because this would contradict the false claim of Mason that Samuel is not a knave.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Ella is a knight or Jackson is a knave.", "We have exhausted all possibilities for Samuel, Mason, and Grace, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Grace is a knave if and only if David is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Mason is a knave and Sofia is a knave.", "Mason cannot be a knight, because this would contradict the claim of Grace that Mason is a knave and Sofia is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Samuel is not a knave.", "Samuel cannot be a knight, because this would contradict the false claim of Mason that Samuel is not a knave.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Ella is a knight or Jackson is a knave.", "We have exhausted all possibilities for Samuel and Mason, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Mason is a knave and Sofia is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Samuel is not a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Ella is a knight or Jackson is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that If Sofia is a knave then Jacob is a knight.", "Jacob cannot be a knight, because this would contradict the claim of Ella that If Sofia is a knave then Jacob is a knave.", "Jacob cannot be a knave, because this would contradict the claim of Jackson that If Sofia is a knave then Jacob is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that If Sofia is a knave then Jacob is a knight.", "Jacob cannot be a knight, because this would contradict the claim of Ella that If Sofia is a knave then Jacob is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Mason is not a knight.", "David cannot be a knight, because this would contradict the claim of their own that Grace is a knight if and only if Samuel is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Grace is a knight if and only if Samuel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 7), ('lying', 1)), ('not', ('telling-truth', 4)), ('or', ('telling-truth', 0), ('lying', 6)), ('<=>', ('telling-truth', 5), ('telling-truth', 2)), ('not', ('lying', 2)), ('and', ('lying', 4), ('lying', 7)), ('->', ('lying', 7), ('telling-truth', 1)), ('<=>', ('lying', 5), ('telling-truth', 3)))", "index": 916}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Penelope, Oliver, Avery, Lucas, Grace, Ella, Logan, and Evelyn. As Penelope put it, \"Oliver is a knight and Lucas is a knave\". Oliver said, \"Lucas is a knight if and only if Penelope is a knave.\" In Avery's words: \"If Lucas is a knight then Logan is a knight\". Lucas expressed that Penelope is not a knave. Grace stated, \"Grace is a knight and Logan is a knight\". \"If Avery is a knave then Evelyn is a knave,\" Ella claimed. Logan said, \"Ella is a knave or Avery is a knave.\" Evelyn remarked, \"Grace is a knight and Lucas is a knight\". So who is a knight and who is a knave?", "names": ["Penelope", "Oliver", "Avery", "Lucas", "Grace", "Ella", "Logan", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, true, false, false], "solution_text": "Penelope is a knave, Oliver is a knave, Avery is a knight, Lucas is a knave, Grace is a knave, Ella is a knight, Logan is a knave, and Evelyn is a knave.", "solution_text_format": "(1) Penelope is a knave\n(2) Oliver is a knave\n(3) Avery is a knight\n(4) Lucas is a knave\n(5) Grace is a knave\n(6) Ella is a knight\n(7) Logan is a knave\n(8) Evelyn is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that Oliver is a knight and Lucas is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Lucas is a knight if and only if Penelope is a knave.", "Lucas cannot be a knight, because this would contradict the claim of Penelope that Oliver is a knight and Lucas is a knave.", "Lucas cannot be a knave, because this would contradict the false claim of their own that Penelope is not a knave.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the claim of Penelope that Oliver is a knight and Lucas is a knave.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Oliver is a knight and Lucas is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Lucas is a knight if and only if Penelope is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Penelope is not a knave.", "Lucas cannot be a knave, because this would contradict the false claim of Penelope that Oliver is a knight and Lucas is a knave.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Lucas is a knight if and only if Penelope is a knave.", "Lucas cannot be a knight, because this would contradict the false claim of Oliver that Lucas is a knight if and only if Penelope is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Penelope is not a knave.", "Assume Avery is a knight. No contradiction is found in their claim that If Lucas is a knight then Logan is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Ella is a knave or Avery is a knave.", "Ella cannot be a knight, because this would contradict the claim of Logan that Ella is a knave or Avery is a knave.", "Ella cannot be a knave, because this would contradict the false claim of their own that If Avery is a knave then Evelyn is a knave.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Ella is a knave or Avery is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that If Avery is a knave then Evelyn is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Grace is a knight and Lucas is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Grace is a knight and Lucas is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Grace is a knight and Logan is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Grace is a knight and Logan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('lying', 3)), ('<=>', ('telling-truth', 3), ('lying', 0)), ('->', ('telling-truth', 3), ('telling-truth', 6)), ('not', ('lying', 0)), ('and', ('telling-truth', 4), ('telling-truth', 6)), ('->', ('lying', 2), ('lying', 7)), ('or', ('lying', 5), ('lying', 2)), ('and', ('telling-truth', 4), ('telling-truth', 3)))", "index": 917}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Alexander, David, Jack, Daniel, Samuel, Lily, Lucas, and Riley. Alexander stated, \"Daniel is not a knave\". \"Lily is a knave or Riley is a knight,\" David claimed. Jack asserted: \"Lily is a knave if and only if Alexander is a knave\". Daniel asserted: \"If Samuel is a knight then Samuel is a knave\". Samuel asserted: \"David is a knight if and only if David is a knave\". As Lily put it, \"Samuel is not a knight\". \"Alexander is not a knave\" - Lucas. Riley asserted: \"If Samuel is a knave then Alexander is a knave\". So who is a knight and who is a knave?", "names": ["Alexander", "David", "Jack", "Daniel", "Samuel", "Lily", "Lucas", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true, true, false], "solution_text": "Alexander is a knight, David is a knave, Jack is a knight, Daniel is a knight, Samuel is a knave, Lily is a knight, Lucas is a knight, and Riley is a knave.", "solution_text_format": "(1) Alexander is a knight\n(2) David is a knave\n(3) Jack is a knight\n(4) Daniel is a knight\n(5) Samuel is a knave\n(6) Lily is a knight\n(7) Lucas is a knight\n(8) Riley is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that Daniel is not a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that If Samuel is a knight then Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Daniel that If Samuel is a knight then Samuel is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that David is a knight if and only if David is a knave.", "Assume David is a knight. No contradiction is found in their claim that Lily is a knave or Riley is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Samuel is not a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that If Samuel is a knave then Alexander is a knave.", "Riley cannot be a knave, because this would contradict the claim of David that Lily is a knave or Riley is a knight.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the false claim of their own that Samuel is not a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Lily is a knave or Riley is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Samuel is not a knight.", "Riley cannot be a knight, because this would contradict the false claim of David that Lily is a knave or Riley is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that If Samuel is a knave then Alexander is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Lily is a knave if and only if Alexander is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Alexander is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 3)), ('or', ('lying', 5), ('telling-truth', 7)), ('<=>', ('lying', 5), ('lying', 0)), ('->', ('telling-truth', 4), ('lying', 4)), ('<=>', ('telling-truth', 1), ('lying', 1)), ('not', ('telling-truth', 4)), ('not', ('lying', 0)), ('->', ('lying', 4), ('lying', 0)))", "index": 918}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Isabella, Evelyn, Matthew, Ella, Grace, Liam, Daniel, and Samuel. In a statement by Isabella: \"Ella is a knave\". Evelyn expressed that Ella is not a knight. \"Evelyn is a knight if and only if Isabella is a knight,\" Matthew mentioned. \"Samuel is a knave if and only if Grace is a knight,\" Ella claimed. \"Ella is a knave if and only if Ella is a knight,\" Grace claimed. In a statement by Liam: \"Isabella is a knave and Liam is a knight\". Daniel was heard saying, \"Ella is not a knave\". \"Liam is a knave,\" Samuel mentioned. So who is a knight and who is a knave?", "names": ["Isabella", "Evelyn", "Matthew", "Ella", "Grace", "Liam", "Daniel", "Samuel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false, true, true], "solution_text": "Isabella is a knave, Evelyn is a knave, Matthew is a knight, Ella is a knight, Grace is a knave, Liam is a knave, Daniel is a knight, and Samuel is a knight.", "solution_text_format": "(1) Isabella is a knave\n(2) Evelyn is a knave\n(3) Matthew is a knight\n(4) Ella is a knight\n(5) Grace is a knave\n(6) Liam is a knave\n(7) Daniel is a knight\n(8) Samuel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of Isabella that Ella is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Samuel is a knave if and only if Grace is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Isabella is a knave and Liam is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Isabella is a knave and Liam is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Ella is a knave if and only if Ella is a knight.", "Grace cannot be a knave, because this would contradict the false claim of Ella that Samuel is a knave if and only if Grace is a knight.", "We have exhausted all possibilities for Grace and Liam, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Isabella is a knave and Liam is a knight.", "Liam cannot be a knave, because this would contradict the false claim of Samuel that Liam is a knave.", "We have exhausted all possibilities for Liam, Samuel, and Ella, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Grace is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of Samuel that Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Isabella is a knave and Liam is a knight.", "Grace cannot be a knight, because this would contradict the claim of Ella that Samuel is a knave if and only if Grace is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Ella is a knave if and only if Ella is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Ella is not a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Ella is not a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Evelyn is a knight if and only if Isabella is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Ella is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('not', ('telling-truth', 3)), ('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('<=>', ('lying', 7), ('telling-truth', 4)), ('<=>', ('lying', 3), ('telling-truth', 3)), ('and', ('lying', 0), ('telling-truth', 5)), ('not', ('lying', 3)), ('lying', 5))", "index": 919}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Evelyn, Avery, Emily, Isabella, Oliver, Penelope, Sofia, and Ella. Evelyn noted, \"Oliver is not a knight\". Avery stated, \"If Evelyn is a knight then Oliver is a knave\". \"If Isabella is a knight then Isabella is a knave,\" Emily declared. \"Oliver is a knight and Emily is a knave,\" Isabella mentioned. Oliver remarked, \"Avery is a knave and Ella is a knight\". Penelope noted, \"Ella is a knight if and only if Avery is a knave\". \"Evelyn is a knave if and only if Oliver is a knave,\" Sofia declared. Ella asserted: \"Isabella is a knight and Emily is a knave\". So who is a knight and who is a knave?", "names": ["Evelyn", "Avery", "Emily", "Isabella", "Oliver", "Penelope", "Sofia", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true, false, false], "solution_text": "Evelyn is a knight, Avery is a knight, Emily is a knight, Isabella is a knave, Oliver is a knave, Penelope is a knight, Sofia is a knave, and Ella is a knave.", "solution_text_format": "(1) Evelyn is a knight\n(2) Avery is a knight\n(3) Emily is a knight\n(4) Isabella is a knave\n(5) Oliver is a knave\n(6) Penelope is a knight\n(7) Sofia is a knave\n(8) Ella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Oliver is not a knight.", "Oliver cannot be a knight, because this would contradict the claim of Evelyn that Oliver is not a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Avery is a knave and Ella is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that If Evelyn is a knight then Oliver is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Isabella is a knight and Emily is a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that Oliver is a knight and Emily is a knave.", "Isabella cannot be a knave, because this would contradict the claim of Ella that Isabella is a knight and Emily is a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Isabella is a knight and Emily is a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that Oliver is a knight and Emily is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Oliver is a knight and Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that If Isabella is a knight then Isabella is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Ella is a knight if and only if Avery is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave if and only if Oliver is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Evelyn is a knave if and only if Oliver is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 4)), ('->', ('telling-truth', 0), ('lying', 4)), ('->', ('telling-truth', 3), ('lying', 3)), ('and', ('telling-truth', 4), ('lying', 2)), ('and', ('lying', 1), ('telling-truth', 7)), ('<=>', ('telling-truth', 7), ('lying', 1)), ('<=>', ('lying', 0), ('lying', 4)), ('and', ('telling-truth', 3), ('lying', 2)))", "index": 920}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aurora, Aiden, William, Chloe, Benjamin, Aria, Luke, and Isabella. Aurora noted, \"Aurora is a knight or Aiden is a knave\". \"Aria is a knave or Chloe is a knight,\" Aiden declared. As William put it, \"Chloe is a knave\". According to Chloe, \"Luke is a knight and Isabella is a knight\". Benjamin commented, \"Aurora is not a knight\". \"Aurora is a knave or Aiden is a knave,\" Aria claimed. Luke said, \"Aiden is a knight and William is a knight.\" \"If Aurora is a knight then Aiden is a knight\" - Isabella. So who is a knight and who is a knave?", "names": ["Aurora", "Aiden", "William", "Chloe", "Benjamin", "Aria", "Luke", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true, false, false], "solution_text": "Aurora is a knight, Aiden is a knave, William is a knight, Chloe is a knave, Benjamin is a knave, Aria is a knight, Luke is a knave, and Isabella is a knave.", "solution_text_format": "(1) Aurora is a knight\n(2) Aiden is a knave\n(3) William is a knight\n(4) Chloe is a knave\n(5) Benjamin is a knave\n(6) Aria is a knight\n(7) Luke is a knave\n(8) Isabella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that Aurora is a knight or Aiden is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Aria is a knave or Chloe is a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that Aurora is a knave or Aiden is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Aurora is a knave or Aiden is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Luke is a knight and Isabella is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Aiden is a knight and William is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Chloe is a knave.", "William cannot be a knave, because this would contradict the claim of Luke that Aiden is a knight and William is a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the claim of Chloe that Luke is a knight and Isabella is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Luke is a knight and Isabella is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Aiden is a knight and William is a knight.", "Assume William is a knight. No contradiction is found in their claim that Chloe is a knave.", "Isabella cannot be a knight, because this would contradict the false claim of Chloe that Luke is a knight and Isabella is a knight.", "Isabella cannot be a knave, because this would contradict the false claim of their own that If Aurora is a knight then Aiden is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the false claim of their own that Chloe is a knave.", "We have exhausted all possibilities for William, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Aiden is a knight and William is a knight.", "William cannot be a knight, because this would contradict the false claim of Luke that Aiden is a knight and William is a knight.", "William cannot be a knave, because this would contradict the false claim of their own that Chloe is a knave.", "We have exhausted all possibilities for William, Luke, Chloe, and Aria, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Aria is a knave or Chloe is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Aurora is a knave or Aiden is a knave.", "Chloe cannot be a knight, because this would contradict the false claim of Aiden that Aria is a knave or Chloe is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Luke is a knight and Isabella is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Aiden is a knight and William is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Aiden is a knight and William is a knight.", "Assume William is a knight. No contradiction is found in their claim that Chloe is a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that If Aurora is a knight then Aiden is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that If Aurora is a knight then Aiden is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Aurora is not a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Aurora is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 0), ('lying', 1)), ('or', ('lying', 5), ('telling-truth', 3)), ('lying', 3), ('and', ('telling-truth', 6), ('telling-truth', 7)), ('not', ('telling-truth', 0)), ('or', ('lying', 0), ('lying', 1)), ('and', ('telling-truth', 1), ('telling-truth', 2)), ('->', ('telling-truth', 0), ('telling-truth', 1)))", "index": 921}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lily, Jack, Elizabeth, Ava, Isabella, Jackson, Lucas, and Olivia. Lily expressed that Isabella is not a knave. As Jack put it, \"Elizabeth is not a knave\". Elizabeth said that Olivia is a knight and Ava is a knave. Ava told you that Lucas is a knave. \"Lucas is a knave,\" Isabella claimed. Jackson asserted: \"Jack is not a knave\". Lucas commented, \"If Jack is a knight then Isabella is a knight\". Olivia noted, \"Elizabeth is a knave and Isabella is a knight\". So who is a knight and who is a knave?", "names": ["Lily", "Jack", "Elizabeth", "Ava", "Isabella", "Jackson", "Lucas", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, false, true, false], "solution_text": "Lily is a knave, Jack is a knave, Elizabeth is a knave, Ava is a knave, Isabella is a knave, Jackson is a knave, Lucas is a knight, and Olivia is a knave.", "solution_text_format": "(1) Lily is a knave\n(2) Jack is a knave\n(3) Elizabeth is a knave\n(4) Ava is a knave\n(5) Isabella is a knave\n(6) Jackson is a knave\n(7) Lucas is a knight\n(8) Olivia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that Isabella is not a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the claim of Isabella that Lucas is a knave.", "Lucas cannot be a knave, because this would contradict the false claim of their own that If Jack is a knight then Isabella is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the claim of Lily that Isabella is not a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Isabella is not a knave.", "Isabella cannot be a knight, because this would contradict the false claim of Lily that Isabella is not a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Lucas is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that If Jack is a knight then Isabella is a knight.", "Jack cannot be a knight, because this would contradict the claim of Lucas that If Jack is a knight then Isabella is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Elizabeth is not a knave.", "Elizabeth cannot be a knight, because this would contradict the false claim of Jack that Elizabeth is not a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Olivia is a knight and Ava is a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave and Isabella is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Elizabeth is a knave and Isabella is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Lucas is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Lucas is a knave.", "Jackson cannot be a knight, because this would contradict the claim of their own that Jack is not a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Jack is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('not', ('lying', 2)), ('and', ('telling-truth', 7), ('lying', 3)), ('lying', 6), ('lying', 6), ('not', ('lying', 1)), ('->', ('telling-truth', 1), ('telling-truth', 4)), ('and', ('lying', 2), ('telling-truth', 4)))", "index": 922}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ella, Lucas, Sofia, Victoria, Aurora, Samuel, Aiden, and Grace. According to Ella, \"Aiden is a knight and Ella is a knight\". As Lucas put it, \"Ella is a knight and Samuel is a knave\". Sofia commented, \"Aiden is not a knight\". \"Victoria is a knight if and only if Sofia is a knave\" - Victoria. Aurora noted, \"Victoria is not a knight\". \"Lucas is a knight,\" Samuel declared. \"If Victoria is a knight then Lucas is a knight,\" Aiden claimed. As Grace put it, \"Aiden is a knight\". So who is a knight and who is a knave?", "names": ["Ella", "Lucas", "Sofia", "Victoria", "Aurora", "Samuel", "Aiden", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, false, true, true], "solution_text": "Ella is a knave, Lucas is a knave, Sofia is a knave, Victoria is a knave, Aurora is a knight, Samuel is a knave, Aiden is a knight, and Grace is a knight.", "solution_text_format": "(1) Ella is a knave\n(2) Lucas is a knave\n(3) Sofia is a knave\n(4) Victoria is a knave\n(5) Aurora is a knight\n(6) Samuel is a knave\n(7) Aiden is a knight\n(8) Grace is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Aiden is a knight and Ella is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that If Victoria is a knight then Lucas is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Aiden is not a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Aiden is not a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Ella is a knight and Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Lucas that Ella is a knight and Samuel is a knave.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Lucas is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the claim of Aiden that If Victoria is a knight then Lucas is a knight.", "We have exhausted all possibilities for Lucas and Sofia, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Victoria is a knight if and only if Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Aiden is not a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Aiden is not a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Ella is a knight and Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Lucas that Ella is a knight and Samuel is a knave.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Lucas is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Ella is a knight and Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that Lucas is a knight.", "Samuel cannot be a knave, because this would contradict the false claim of Lucas that Ella is a knight and Samuel is a knave.", "We have exhausted all possibilities for Samuel, Lucas, Sofia, and Victoria, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the claim of Ella that Aiden is a knight and Ella is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Aiden is a knight and Ella is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that If Victoria is a knight then Lucas is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Aiden is not a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Aiden is not a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Ella is a knight and Samuel is a knave.", "Lucas cannot be a knave, because this would contradict the claim of Aiden that If Victoria is a knight then Lucas is a knight.", "We have exhausted all possibilities for Lucas and Sofia, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Victoria is a knight if and only if Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Aiden is not a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Aiden is not a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Ella is a knight and Samuel is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Ella is a knight and Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that Lucas is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Lucas is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Victoria is not a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Aiden is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 6), ('telling-truth', 0)), ('and', ('telling-truth', 0), ('lying', 5)), ('not', ('telling-truth', 6)), ('<=>', ('telling-truth', 3), ('lying', 2)), ('not', ('telling-truth', 3)), ('telling-truth', 1), ('->', ('telling-truth', 3), ('telling-truth', 1)), ('telling-truth', 6))", "index": 923}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Harper, Samuel, Luke, Amelia, Victoria, Scarlett, Benjamin, and Charlotte. As Harper put it, \"Luke is not a knight\". Samuel asserted: \"Scarlett is a knight if and only if Luke is a knave\". Luke expressed that Scarlett is a knave and Charlotte is a knave. Amelia asserted: \"Harper is a knight\". \"Samuel is a knight and Benjamin is a knight,\" Victoria declared. Scarlett noted, \"Harper is a knight and Samuel is a knight\". Benjamin commented, \"If Victoria is a knave then Luke is a knave\". As Charlotte put it, \"Scarlett is a knight if and only if Amelia is a knight\". So who is a knight and who is a knave?", "names": ["Harper", "Samuel", "Luke", "Amelia", "Victoria", "Scarlett", "Benjamin", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true, true, true], "solution_text": "Harper is a knight, Samuel is a knight, Luke is a knave, Amelia is a knight, Victoria is a knight, Scarlett is a knight, Benjamin is a knight, and Charlotte is a knight.", "solution_text_format": "(1) Harper is a knight\n(2) Samuel is a knight\n(3) Luke is a knave\n(4) Amelia is a knight\n(5) Victoria is a knight\n(6) Scarlett is a knight\n(7) Benjamin is a knight\n(8) Charlotte is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that Luke is not a knight.", "Luke cannot be a knight, because this would contradict the claim of Harper that Luke is not a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Scarlett is a knave and Charlotte is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Harper is a knight and Samuel is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Scarlett is a knight if and only if Luke is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Scarlett is a knight if and only if Amelia is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Harper is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Samuel is a knight and Benjamin is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Victoria is a knave then Luke is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('<=>', ('telling-truth', 5), ('lying', 2)), ('and', ('lying', 5), ('lying', 7)), ('telling-truth', 0), ('and', ('telling-truth', 1), ('telling-truth', 6)), ('and', ('telling-truth', 0), ('telling-truth', 1)), ('->', ('lying', 4), ('lying', 2)), ('<=>', ('telling-truth', 5), ('telling-truth', 3)))", "index": 924}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lily, Lucas, Victoria, Aiden, Charlotte, Sophia, Alexander, and Ella. Lily told you that Sophia is a knight and Lucas is a knight. Lucas expressed that Lily is a knight if and only if Aiden is a knave. In Victoria's words: \"Alexander is not a knave\". Aiden was heard saying, \"Alexander is a knight\". Charlotte asserted: \"Aiden is a knave\". Sophia commented, \"Victoria is not a knave\". In Alexander's words: \"Victoria is a knight\". As Ella put it, \"Victoria is not a knight\". So who is a knight and who is a knave?", "names": ["Lily", "Lucas", "Victoria", "Aiden", "Charlotte", "Sophia", "Alexander", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, false, false, true], "solution_text": "Lily is a knave, Lucas is a knave, Victoria is a knave, Aiden is a knave, Charlotte is a knight, Sophia is a knave, Alexander is a knave, and Ella is a knight.", "solution_text_format": "(1) Lily is a knave\n(2) Lucas is a knave\n(3) Victoria is a knave\n(4) Aiden is a knave\n(5) Charlotte is a knight\n(6) Sophia is a knave\n(7) Alexander is a knave\n(8) Ella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that Sophia is a knight and Lucas is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Victoria is not a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Alexander is not a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Victoria is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Lily is a knight if and only if Aiden is a knave.", "Aiden cannot be a knight, because this would contradict the claim of Lucas that Lily is a knight if and only if Aiden is a knave.", "Aiden cannot be a knave, because this would contradict the false claim of their own that Alexander is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the claim of Lily that Sophia is a knight and Lucas is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Alexander.", "Alexander cannot be a knave, because this would contradict the claim of Victoria that Alexander is not a knave.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Victoria.", "Victoria cannot be a knave, because this would contradict the claim of Sophia that Victoria is not a knave.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the claim of Lily that Sophia is a knight and Lucas is a knight.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Sophia is a knight and Lucas is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Victoria is not a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Alexander is not a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Victoria is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of Lily that Sophia is a knight and Lucas is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Lily is a knight if and only if Aiden is a knave.", "Aiden cannot be a knight, because this would contradict the false claim of Lucas that Lily is a knight if and only if Aiden is a knave.", "Aiden cannot be a knave, because this would contradict the false claim of their own that Alexander is a knight.", "We have exhausted all possibilities for Aiden and Lucas, so let us go back and reconsider Alexander.", "Alexander cannot be a knave, because this would contradict the claim of Victoria that Alexander is not a knave.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Victoria.", "Victoria cannot be a knave, because this would contradict the claim of Sophia that Victoria is not a knave.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Victoria is not a knave.", "Victoria cannot be a knight, because this would contradict the false claim of Sophia that Victoria is not a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Alexander is not a knave.", "Alexander cannot be a knight, because this would contradict the false claim of Victoria that Alexander is not a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Victoria is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Lily is a knight if and only if Aiden is a knave.", "Aiden cannot be a knight, because this would contradict the claim of their own that Alexander is a knight.", "Aiden cannot be a knave, because this would contradict the claim of Lucas that Lily is a knight if and only if Aiden is a knave.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Lily is a knight if and only if Aiden is a knave.", "Aiden cannot be a knight, because this would contradict the false claim of Lucas that Lily is a knight if and only if Aiden is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Alexander is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Aiden is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Victoria is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('telling-truth', 1)), ('<=>', ('telling-truth', 0), ('lying', 3)), ('not', ('lying', 6)), ('telling-truth', 6), ('lying', 3), ('not', ('lying', 2)), ('telling-truth', 2), ('not', ('telling-truth', 2)))", "index": 925}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jackson, Noah, Riley, Evelyn, Jacob, Scarlett, Victoria, and Charlotte. In a statement by Jackson: \"Riley is a knight or Victoria is a knight\". Noah commented, \"If Noah is a knight then Jacob is a knight\". Riley told you that Scarlett is a knave or Charlotte is a knight. In a statement by Evelyn: \"Riley is a knave or Charlotte is a knave\". Jacob asserted: \"Victoria is not a knave\". Scarlett said, \"Jackson is a knave if and only if Charlotte is a knight.\" Victoria stated, \"Charlotte is a knight or Riley is a knave\". Charlotte told you that Evelyn is a knight and Jacob is a knave. So who is a knight and who is a knave?", "names": ["Jackson", "Noah", "Riley", "Evelyn", "Jacob", "Scarlett", "Victoria", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true, true, false], "solution_text": "Jackson is a knight, Noah is a knight, Riley is a knave, Evelyn is a knight, Jacob is a knight, Scarlett is a knight, Victoria is a knight, and Charlotte is a knave.", "solution_text_format": "(1) Jackson is a knight\n(2) Noah is a knight\n(3) Riley is a knave\n(4) Evelyn is a knight\n(5) Jacob is a knight\n(6) Scarlett is a knight\n(7) Victoria is a knight\n(8) Charlotte is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Riley is a knight or Victoria is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Scarlett is a knave or Charlotte is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Jackson is a knave if and only if Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Scarlett that Jackson is a knave if and only if Charlotte is a knight.", "Charlotte cannot be a knave, because this would contradict the claim of Riley that Scarlett is a knave or Charlotte is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Jackson is a knave if and only if Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Evelyn is a knight and Jacob is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Riley is a knave or Charlotte is a knave.", "Evelyn cannot be a knave, because this would contradict the claim of Charlotte that Evelyn is a knight and Jacob is a knave.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the false claim of Scarlett that Jackson is a knave if and only if Charlotte is a knight.", "We have exhausted all possibilities for Charlotte and Scarlett, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Scarlett is a knave or Charlotte is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Jackson is a knave if and only if Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of Riley that Scarlett is a knave or Charlotte is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Evelyn is a knight and Jacob is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Riley is a knave or Charlotte is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Victoria is not a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Charlotte is a knight or Riley is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that If Noah is a knight then Jacob is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('telling-truth', 6)), ('->', ('telling-truth', 1), ('telling-truth', 4)), ('or', ('lying', 5), ('telling-truth', 7)), ('or', ('lying', 2), ('lying', 7)), ('not', ('lying', 6)), ('<=>', ('lying', 0), ('telling-truth', 7)), ('or', ('telling-truth', 7), ('lying', 2)), ('and', ('telling-truth', 3), ('lying', 4)))", "index": 926}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mason, Lily, James, Sofia, Ella, Joseph, Avery, and Luke. \"Ella is a knight or Lily is a knight,\" Mason claimed. Lily expressed that Ella is a knave if and only if Ella is a knight. \"Lily is a knight,\" James mentioned. Sofia told you that Mason is not a knave. Ella said, \"Mason is a knight and Joseph is a knight.\" Joseph was heard saying, \"If Luke is a knight then Ella is a knave\". According to Avery, \"James is a knave if and only if Mason is a knave\". Luke said that James is a knight or Joseph is a knight. So who is a knight and who is a knave?", "names": ["Mason", "Lily", "James", "Sofia", "Ella", "Joseph", "Avery", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, true, true, true], "solution_text": "Mason is a knave, Lily is a knave, James is a knave, Sofia is a knave, Ella is a knave, Joseph is a knight, Avery is a knight, and Luke is a knight.", "solution_text_format": "(1) Mason is a knave\n(2) Lily is a knave\n(3) James is a knave\n(4) Sofia is a knave\n(5) Ella is a knave\n(6) Joseph is a knight\n(7) Avery is a knight\n(8) Luke is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Ella is a knight or Lily is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Mason is a knight and Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Luke is a knight then Ella is a knave.", "Luke cannot be a knight, because this would contradict the claim of Joseph that If Luke is a knight then Ella is a knave.", "Luke cannot be a knave, because this would contradict the false claim of their own that James is a knight or Joseph is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of Ella that Mason is a knight and Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Mason is a knight and Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of Ella that Mason is a knight and Joseph is a knight.", "Joseph cannot be a knave, because this would contradict the false claim of their own that If Luke is a knight then Ella is a knave.", "We have exhausted all possibilities for Joseph and Ella, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Ella is a knight or Lily is a knight.", "Ella cannot be a knight, because this would contradict the false claim of Mason that Ella is a knight or Lily is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Mason is a knight and Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Luke is a knight then Ella is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that James is a knight or Joseph is a knight.", "Assume James is a knight. No contradiction is found in their claim that Lily is a knight.", "Lily cannot be a knight, because this would contradict the false claim of Mason that Ella is a knight or Lily is a knight.", "Lily cannot be a knave, because this would contradict the claim of James that Lily is a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Lily is a knight.", "Lily cannot be a knight, because this would contradict the false claim of Mason that Ella is a knight or Lily is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Ella is a knave if and only if Ella is a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that Mason is not a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Mason is not a knave.", "Assume Avery is a knight. No contradiction is found in their claim that James is a knave if and only if Mason is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('telling-truth', 1)), ('<=>', ('lying', 4), ('telling-truth', 4)), ('telling-truth', 1), ('not', ('lying', 0)), ('and', ('telling-truth', 0), ('telling-truth', 5)), ('->', ('telling-truth', 7), ('lying', 4)), ('<=>', ('lying', 2), ('lying', 0)), ('or', ('telling-truth', 2), ('telling-truth', 5)))", "index": 927}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Oliver, Riley, Aria, Logan, Avery, Mason, Henry, and Charlotte. Oliver said, \"Avery is a knave if and only if Charlotte is a knight.\" In Riley's words: \"Logan is a knight and Charlotte is a knight\". Aria expressed that Avery is a knave or Charlotte is a knave. \"Charlotte is a knight\" - Logan. \"If Henry is a knight then Aria is a knight,\" Avery claimed. Mason told you that If Logan is a knight then Riley is a knave. \"Logan is a knight and Mason is a knight,\" Henry claimed. Charlotte was heard saying, \"Aria is a knight if and only if Mason is a knight\". So who is a knight and who is a knave?", "names": ["Oliver", "Riley", "Aria", "Logan", "Avery", "Mason", "Henry", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false, false, true], "solution_text": "Oliver is a knave, Riley is a knight, Aria is a knave, Logan is a knight, Avery is a knight, Mason is a knave, Henry is a knave, and Charlotte is a knight.", "solution_text_format": "(1) Oliver is a knave\n(2) Riley is a knight\n(3) Aria is a knave\n(4) Logan is a knight\n(5) Avery is a knight\n(6) Mason is a knave\n(7) Henry is a knave\n(8) Charlotte is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Avery is a knave if and only if Charlotte is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that If Henry is a knight then Aria is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Logan is a knight and Mason is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Oliver that Avery is a knave if and only if Charlotte is a knight.", "Charlotte cannot be a knave, because this would contradict the claim of Logan that Charlotte is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the claim of Henry that Logan is a knight and Mason is a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Logan is a knight and Mason is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Oliver that Avery is a knave if and only if Charlotte is a knight.", "Charlotte cannot be a knave, because this would contradict the claim of Logan that Charlotte is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Oliver that Avery is a knave if and only if Charlotte is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Aria is a knight if and only if Mason is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Avery is a knave or Charlotte is a knave.", "Mason cannot be a knight, because this would contradict the false claim of Charlotte that Aria is a knight if and only if Mason is a knight.", "Mason cannot be a knave, because this would contradict the false claim of their own that If Logan is a knight then Riley is a knave.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Aria.", "Aria cannot be a knave, because this would contradict the false claim of their own that Avery is a knave or Charlotte is a knave.", "We have exhausted all possibilities for Aria, Charlotte, Logan, and Henry, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that If Henry is a knight then Aria is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Logan is a knight and Mason is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Aria is a knight if and only if Mason is a knight.", "Aria cannot be a knight, because this would contradict the false claim of Avery that If Henry is a knight then Aria is a knight.", "Aria cannot be a knave, because this would contradict the false claim of their own that Avery is a knave or Charlotte is a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the claim of Oliver that Avery is a knave if and only if Charlotte is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the claim of Henry that Logan is a knight and Mason is a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the false claim of Avery that If Henry is a knight then Aria is a knight.", "We have exhausted all possibilities for Henry and Avery, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Avery is a knave if and only if Charlotte is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that If Henry is a knight then Aria is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Logan is a knight and Mason is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Aria is a knight if and only if Mason is a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that Avery is a knave or Charlotte is a knave.", "Aria cannot be a knave, because this would contradict the claim of Avery that If Henry is a knight then Aria is a knight.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the false claim of Oliver that Avery is a knave if and only if Charlotte is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the claim of Henry that Logan is a knight and Mason is a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Logan is a knight and Mason is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Aria is a knight if and only if Mason is a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that Avery is a knave or Charlotte is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Avery is a knave or Charlotte is a knave.", "Mason cannot be a knight, because this would contradict the false claim of Henry that Logan is a knight and Mason is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that If Logan is a knight then Riley is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Logan is a knight and Charlotte is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 4), ('telling-truth', 7)), ('and', ('telling-truth', 3), ('telling-truth', 7)), ('or', ('lying', 4), ('lying', 7)), ('telling-truth', 7), ('->', ('telling-truth', 6), ('telling-truth', 2)), ('->', ('telling-truth', 3), ('lying', 1)), ('and', ('telling-truth', 3), ('telling-truth', 5)), ('<=>', ('telling-truth', 2), ('telling-truth', 5)))", "index": 928}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ella, Ethan, Chloe, Aiden, Emma, Michael, Charlotte, and Elizabeth. Ella stated, \"Charlotte is a knight\". In Ethan's words: \"Aiden is a knight\". In Chloe's words: \"If Emma is a knave then Ethan is a knight\". In Aiden's words: \"Ella is a knight or Aiden is a knight\". In a statement by Emma: \"Ethan is a knight or Aiden is a knight\". Michael commented, \"Elizabeth is a knight if and only if Emma is a knight\". \"Emma is a knave or Elizabeth is a knave\" - Charlotte. Elizabeth expressed that Chloe is not a knave. So who is a knight and who is a knave?", "names": ["Ella", "Ethan", "Chloe", "Aiden", "Emma", "Michael", "Charlotte", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true, false, true], "solution_text": "Ella is a knave, Ethan is a knight, Chloe is a knight, Aiden is a knight, Emma is a knight, Michael is a knight, Charlotte is a knave, and Elizabeth is a knight.", "solution_text_format": "(1) Ella is a knave\n(2) Ethan is a knight\n(3) Chloe is a knight\n(4) Aiden is a knight\n(5) Emma is a knight\n(6) Michael is a knight\n(7) Charlotte is a knave\n(8) Elizabeth is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Emma is a knave or Elizabeth is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Ethan is a knight or Aiden is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Ella is a knight or Aiden is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Charlotte that Emma is a knave or Elizabeth is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Chloe is not a knave.", "Chloe cannot be a knight, because this would contradict the false claim of Elizabeth that Chloe is not a knave.", "Chloe cannot be a knave, because this would contradict the false claim of their own that If Emma is a knave then Ethan is a knight.", "We have exhausted all possibilities for Chloe and Elizabeth, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the claim of Ethan that Aiden is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the false claim of Ethan that Aiden is a knight.", "Aiden cannot be a knave, because this would contradict the false claim of their own that Ella is a knight or Aiden is a knight.", "We have exhausted all possibilities for Aiden and Ethan, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Ethan is a knight or Aiden is a knight.", "Ethan cannot be a knight, because this would contradict the false claim of Emma that Ethan is a knight or Aiden is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the false claim of Ethan that Aiden is a knight.", "Aiden cannot be a knave, because this would contradict the false claim of their own that Ella is a knight or Aiden is a knight.", "We have exhausted all possibilities for Aiden, Ethan, and Emma, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the claim of Ella that Charlotte is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of Ella that Charlotte is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Emma is a knave or Elizabeth is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Ethan is a knight or Aiden is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Ella is a knight or Aiden is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Chloe is not a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that If Emma is a knave then Ethan is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Elizabeth is a knight if and only if Emma is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 6), ('telling-truth', 3), ('->', ('lying', 4), ('telling-truth', 1)), ('or', ('telling-truth', 0), ('telling-truth', 3)), ('or', ('telling-truth', 1), ('telling-truth', 3)), ('<=>', ('telling-truth', 7), ('telling-truth', 4)), ('or', ('lying', 4), ('lying', 7)), ('not', ('lying', 2)))", "index": 929}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Scarlett, Zoey, William, Lucas, Samuel, Luke, Oliver, and Penelope. Scarlett asserted: \"Oliver is a knave if and only if William is a knave\". In Zoey's words: \"Lucas is a knave if and only if Luke is a knight\". \"Lucas is a knight if and only if Lucas is a knave\" - William. \"William is not a knave,\" Lucas declared. According to Samuel, \"Oliver is a knight if and only if Scarlett is a knave\". Luke remarked, \"Penelope is a knave if and only if Penelope is a knight\". Oliver said, \"Samuel is a knight.\" \"Luke is a knight\" - Penelope. So who is a knight and who is a knave?", "names": ["Scarlett", "Zoey", "William", "Lucas", "Samuel", "Luke", "Oliver", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, false, true, false], "solution_text": "Scarlett is a knave, Zoey is a knave, William is a knave, Lucas is a knave, Samuel is a knight, Luke is a knave, Oliver is a knight, and Penelope is a knave.", "solution_text_format": "(1) Scarlett is a knave\n(2) Zoey is a knave\n(3) William is a knave\n(4) Lucas is a knave\n(5) Samuel is a knight\n(6) Luke is a knave\n(7) Oliver is a knight\n(8) Penelope is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Oliver is a knave if and only if William is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Samuel is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Oliver is a knight if and only if Scarlett is a knave.", "Samuel cannot be a knave, because this would contradict the claim of Oliver that Samuel is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Samuel is a knight.", "Samuel cannot be a knight, because this would contradict the false claim of Oliver that Samuel is a knight.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Oliver is a knight if and only if Scarlett is a knave.", "We have exhausted all possibilities for Samuel and Oliver, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Oliver is a knave if and only if William is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Samuel is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Oliver is a knight if and only if Scarlett is a knave.", "William cannot be a knight, because this would contradict the false claim of Scarlett that Oliver is a knave if and only if William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Lucas is a knight if and only if Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that William is not a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that William is not a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Lucas is a knave if and only if Luke is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Penelope is a knave if and only if Penelope is a knight.", "Luke cannot be a knave, because this would contradict the claim of Zoey that Lucas is a knave if and only if Luke is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Lucas is a knave if and only if Luke is a knight.", "Luke cannot be a knight, because this would contradict the false claim of Zoey that Lucas is a knave if and only if Luke is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Penelope is a knave if and only if Penelope is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Luke is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Luke is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 6), ('lying', 2)), ('<=>', ('lying', 3), ('telling-truth', 5)), ('<=>', ('telling-truth', 3), ('lying', 3)), ('not', ('lying', 2)), ('<=>', ('telling-truth', 6), ('lying', 0)), ('<=>', ('lying', 7), ('telling-truth', 7)), ('telling-truth', 4), ('telling-truth', 5))", "index": 930}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Abigail, Henry, Chloe, Avery, Luke, Joseph, James, and Aiden. Abigail expressed that If Aiden is a knight then Joseph is a knave. According to Henry, \"Luke is a knave and Chloe is a knight\". In Chloe's words: \"Avery is a knight and James is a knight\". Avery commented, \"Henry is not a knave\". Luke stated, \"James is not a knave\". \"If Henry is a knight then Avery is a knight,\" Joseph declared. James said that Avery is not a knave. In Aiden's words: \"If Avery is a knave then Chloe is a knave\". So who is a knight and who is a knave?", "names": ["Abigail", "Henry", "Chloe", "Avery", "Luke", "Joseph", "James", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, true, false, true], "solution_text": "Abigail is a knave, Henry is a knave, Chloe is a knave, Avery is a knave, Luke is a knave, Joseph is a knight, James is a knave, and Aiden is a knight.", "solution_text_format": "(1) Abigail is a knave\n(2) Henry is a knave\n(3) Chloe is a knave\n(4) Avery is a knave\n(5) Luke is a knave\n(6) Joseph is a knight\n(7) James is a knave\n(8) Aiden is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that If Aiden is a knight then Joseph is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Avery is a knave then Chloe is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Henry is not a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Luke is a knave and Chloe is a knight.", "Luke cannot be a knight, because this would contradict the claim of Henry that Luke is a knave and Chloe is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that James is not a knave.", "James cannot be a knight, because this would contradict the false claim of Luke that James is not a knave.", "James cannot be a knave, because this would contradict the false claim of their own that Avery is not a knave.", "We have exhausted all possibilities for James and Luke, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the claim of Avery that Henry is not a knave.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Henry is not a knave.", "Henry cannot be a knight, because this would contradict the false claim of Avery that Henry is not a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Luke is a knave and Chloe is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that James is not a knave.", "James cannot be a knight, because this would contradict the claim of their own that Avery is not a knave.", "James cannot be a knave, because this would contradict the claim of Luke that James is not a knave.", "We have exhausted all possibilities for James, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that James is not a knave.", "James cannot be a knight, because this would contradict the false claim of Luke that James is not a knave.", "Assume James is a knave. No contradiction is found in their false claim that Avery is not a knave.", "Chloe cannot be a knight, because this would contradict the false claim of Henry that Luke is a knave and Chloe is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Avery is a knight and James is a knight.", "Joseph cannot be a knight, because this would contradict the claim of Abigail that If Aiden is a knight then Joseph is a knave.", "Joseph cannot be a knave, because this would contradict the false claim of their own that If Henry is a knight then Avery is a knight.", "We have exhausted all possibilities for Joseph, Chloe, James, Luke, Henry, and Avery, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that If Avery is a knave then Chloe is a knave.", "Avery cannot be a knight, because this would contradict the false claim of Aiden that If Avery is a knave then Chloe is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Henry is not a knave.", "Henry cannot be a knight, because this would contradict the false claim of Avery that Henry is not a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Luke is a knave and Chloe is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that James is not a knave.", "James cannot be a knight, because this would contradict the claim of their own that Avery is not a knave.", "James cannot be a knave, because this would contradict the claim of Luke that James is not a knave.", "We have exhausted all possibilities for James, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that James is not a knave.", "James cannot be a knight, because this would contradict the false claim of Luke that James is not a knave.", "Assume James is a knave. No contradiction is found in their false claim that Avery is not a knave.", "Chloe cannot be a knight, because this would contradict the false claim of Henry that Luke is a knave and Chloe is a knight.", "Chloe cannot be a knave, because this would contradict the false claim of Aiden that If Avery is a knave then Chloe is a knave.", "We have exhausted all possibilities for Chloe, James, Luke, Henry, Avery, and Aiden, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that If Aiden is a knight then Joseph is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Avery is a knave then Chloe is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Henry is not a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Luke is a knave and Chloe is a knight.", "Luke cannot be a knight, because this would contradict the claim of Henry that Luke is a knave and Chloe is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that James is not a knave.", "James cannot be a knight, because this would contradict the false claim of Luke that James is not a knave.", "James cannot be a knave, because this would contradict the false claim of their own that Avery is not a knave.", "We have exhausted all possibilities for James and Luke, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the claim of Avery that Henry is not a knave.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Henry is not a knave.", "Henry cannot be a knight, because this would contradict the false claim of Avery that Henry is not a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Luke is a knave and Chloe is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that James is not a knave.", "James cannot be a knight, because this would contradict the claim of their own that Avery is not a knave.", "James cannot be a knave, because this would contradict the claim of Luke that James is not a knave.", "We have exhausted all possibilities for James, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that James is not a knave.", "James cannot be a knight, because this would contradict the false claim of Luke that James is not a knave.", "Assume James is a knave. No contradiction is found in their false claim that Avery is not a knave.", "Chloe cannot be a knight, because this would contradict the false claim of Henry that Luke is a knave and Chloe is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Avery is a knight and James is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Henry is a knight then Avery is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 7), ('lying', 5)), ('and', ('lying', 4), ('telling-truth', 2)), ('and', ('telling-truth', 3), ('telling-truth', 6)), ('not', ('lying', 1)), ('not', ('lying', 6)), ('->', ('telling-truth', 1), ('telling-truth', 3)), ('not', ('lying', 3)), ('->', ('lying', 3), ('lying', 2)))", "index": 931}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Liam, Lucas, Noah, Ethan, Sofia, Chloe, Emily, and Benjamin. As Liam put it, \"Lucas is not a knave\". Lucas asserted: \"If Sofia is a knight then Ethan is a knave\". \"Emily is a knave and Chloe is a knight\" - Noah. Ethan expressed that Liam is a knave or Lucas is a knight. \"Sofia is a knight if and only if Liam is a knight,\" Sofia mentioned. \"Liam is a knight or Emily is a knave,\" Chloe declared. Emily was heard saying, \"Lucas is a knight and Sofia is a knave\". \"Ethan is a knave\" - Benjamin. So who is a knight and who is a knave?", "names": ["Liam", "Lucas", "Noah", "Ethan", "Sofia", "Chloe", "Emily", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true, true, false], "solution_text": "Liam is a knight, Lucas is a knight, Noah is a knave, Ethan is a knight, Sofia is a knave, Chloe is a knight, Emily is a knight, and Benjamin is a knave.", "solution_text_format": "(1) Liam is a knight\n(2) Lucas is a knight\n(3) Noah is a knave\n(4) Ethan is a knight\n(5) Sofia is a knave\n(6) Chloe is a knight\n(7) Emily is a knight\n(8) Benjamin is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Lucas is not a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that If Sofia is a knight then Ethan is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Sofia is a knight if and only if Liam is a knight.", "Ethan cannot be a knight, because this would contradict the claim of Lucas that If Sofia is a knight then Ethan is a knave.", "Ethan cannot be a knave, because this would contradict the false claim of their own that Liam is a knave or Lucas is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Sofia is a knight if and only if Liam is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Liam is a knave or Lucas is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Emily is a knave and Chloe is a knight.", "Emily cannot be a knight, because this would contradict the claim of Noah that Emily is a knave and Chloe is a knight.", "Emily cannot be a knave, because this would contradict the false claim of their own that Lucas is a knight and Sofia is a knave.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Emily is a knave and Chloe is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Lucas is a knight and Sofia is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Liam is a knight or Emily is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Ethan is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Ethan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('->', ('telling-truth', 4), ('lying', 3)), ('and', ('lying', 6), ('telling-truth', 5)), ('or', ('lying', 0), ('telling-truth', 1)), ('<=>', ('telling-truth', 4), ('telling-truth', 0)), ('or', ('telling-truth', 0), ('lying', 6)), ('and', ('telling-truth', 1), ('lying', 4)), ('lying', 3))", "index": 932}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Olivia, Henry, Lily, Owen, Liam, Sebastian, Victoria, and Elizabeth. In a statement by Olivia: \"Lily is a knave\". Henry said that Henry is a knight if and only if Sebastian is a knave. Lily noted, \"Lily is a knight or Victoria is a knave\". Owen noted, \"Henry is a knave if and only if Liam is a knight\". As Liam put it, \"Henry is a knave or Victoria is a knave\". According to Sebastian, \"If Olivia is a knight then Olivia is a knave\". Victoria was heard saying, \"Henry is a knight or Lily is a knight\". Elizabeth commented, \"Henry is not a knight\". So who is a knight and who is a knave?", "names": ["Olivia", "Henry", "Lily", "Owen", "Liam", "Sebastian", "Victoria", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false, true, false], "solution_text": "Olivia is a knight, Henry is a knight, Lily is a knave, Owen is a knight, Liam is a knave, Sebastian is a knave, Victoria is a knight, and Elizabeth is a knave.", "solution_text_format": "(1) Olivia is a knight\n(2) Henry is a knight\n(3) Lily is a knave\n(4) Owen is a knight\n(5) Liam is a knave\n(6) Sebastian is a knave\n(7) Victoria is a knight\n(8) Elizabeth is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of Olivia that Lily is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Lily is a knight or Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Henry is a knight or Lily is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Henry is a knight if and only if Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Henry that Henry is a knight if and only if Sebastian is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that If Olivia is a knight then Olivia is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Henry is a knave if and only if Liam is a knight.", "Liam cannot be a knight, because this would contradict the claim of Owen that Henry is a knave if and only if Liam is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Henry is a knave or Victoria is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Henry is not a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Henry is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('<=>', ('telling-truth', 1), ('lying', 5)), ('or', ('telling-truth', 2), ('lying', 6)), ('<=>', ('lying', 1), ('telling-truth', 4)), ('or', ('lying', 1), ('lying', 6)), ('->', ('telling-truth', 0), ('lying', 0)), ('or', ('telling-truth', 1), ('telling-truth', 2)), ('not', ('telling-truth', 1)))", "index": 933}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mason, Ava, Liam, Amelia, Luke, Daniel, Charlotte, and Zoey. Mason asserted: \"If Luke is a knight then Ava is a knave\". \"Daniel is a knight if and only if Mason is a knave,\" Ava declared. Liam was heard saying, \"Amelia is not a knave\". Amelia told you that Ava is a knight if and only if Ava is a knave. Luke commented, \"Amelia is a knave or Amelia is a knight\". In Daniel's words: \"Mason is a knight or Ava is a knave\". Charlotte expressed that Liam is not a knave. Zoey noted, \"Luke is a knight or Mason is a knave\". So who is a knight and who is a knave?", "names": ["Mason", "Ava", "Liam", "Amelia", "Luke", "Daniel", "Charlotte", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true, false, true], "solution_text": "Mason is a knight, Ava is a knave, Liam is a knave, Amelia is a knave, Luke is a knight, Daniel is a knight, Charlotte is a knave, and Zoey is a knight.", "solution_text_format": "(1) Mason is a knight\n(2) Ava is a knave\n(3) Liam is a knave\n(4) Amelia is a knave\n(5) Luke is a knight\n(6) Daniel is a knight\n(7) Charlotte is a knave\n(8) Zoey is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that If Luke is a knight then Ava is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Amelia is a knave or Amelia is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Ava is a knight if and only if Ava is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Ava is a knight if and only if Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of Mason that If Luke is a knight then Ava is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Daniel is a knight if and only if Mason is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Mason is a knight or Ava is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Amelia is not a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Amelia is not a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Liam is not a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Liam is not a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Luke is a knight or Mason is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 4), ('lying', 1)), ('<=>', ('telling-truth', 5), ('lying', 0)), ('not', ('lying', 3)), ('<=>', ('telling-truth', 1), ('lying', 1)), ('or', ('lying', 3), ('telling-truth', 3)), ('or', ('telling-truth', 0), ('lying', 1)), ('not', ('lying', 2)), ('or', ('telling-truth', 4), ('lying', 0)))", "index": 934}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Chloe, Scarlett, Sofia, Mason, Owen, Mia, Emma, and Logan. Chloe stated, \"Scarlett is a knight or Mason is a knight\". In Scarlett's words: \"Owen is a knight\". In a statement by Sofia: \"If Sofia is a knight then Owen is a knight\". \"Sofia is a knave,\" Mason mentioned. In a statement by Owen: \"Logan is a knight if and only if Mia is a knave\". Mia noted, \"Mason is a knight and Logan is a knave\". Emma stated, \"Mia is a knave or Emma is a knight\". In Logan's words: \"Scarlett is a knight or Owen is a knave\". So who is a knight and who is a knave?", "names": ["Chloe", "Scarlett", "Sofia", "Mason", "Owen", "Mia", "Emma", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false, true, true], "solution_text": "Chloe is a knight, Scarlett is a knight, Sofia is a knight, Mason is a knave, Owen is a knight, Mia is a knave, Emma is a knight, and Logan is a knight.", "solution_text_format": "(1) Chloe is a knight\n(2) Scarlett is a knight\n(3) Sofia is a knight\n(4) Mason is a knave\n(5) Owen is a knight\n(6) Mia is a knave\n(7) Emma is a knight\n(8) Logan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Scarlett is a knight or Mason is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Owen is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Logan is a knight if and only if Mia is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Scarlett is a knight or Owen is a knave.", "Mia cannot be a knight, because this would contradict the claim of Owen that Logan is a knight if and only if Mia is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Mason is a knight and Logan is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Mason that Sofia is a knave.", "Sofia cannot be a knave, because this would contradict the false claim of their own that If Sofia is a knight then Owen is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that If Sofia is a knight then Owen is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Mia is a knave or Emma is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('telling-truth', 3)), ('telling-truth', 4), ('->', ('telling-truth', 2), ('telling-truth', 4)), ('lying', 2), ('<=>', ('telling-truth', 7), ('lying', 5)), ('and', ('telling-truth', 3), ('lying', 7)), ('or', ('lying', 5), ('telling-truth', 6)), ('or', ('telling-truth', 1), ('lying', 4)))", "index": 935}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Penelope, Charlotte, James, Alexander, Isabella, Luke, Emma, and Liam. Penelope said, \"Isabella is a knight and Emma is a knave.\" According to Charlotte, \"Charlotte is a knight if and only if Liam is a knight\". In a statement by James: \"If Luke is a knight then Penelope is a knight\". As Alexander put it, \"Luke is a knight if and only if Charlotte is a knave\". In a statement by Isabella: \"Liam is a knight and Emma is a knight\". \"Charlotte is a knight or Isabella is a knight,\" Luke claimed. Emma expressed that Liam is a knave if and only if Alexander is a knave. Liam asserted: \"Isabella is a knight and Alexander is a knight\". So who is a knight and who is a knave?", "names": ["Penelope", "Charlotte", "James", "Alexander", "Isabella", "Luke", "Emma", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true, true, true], "solution_text": "Penelope is a knave, Charlotte is a knave, James is a knave, Alexander is a knight, Isabella is a knight, Luke is a knight, Emma is a knight, and Liam is a knight.", "solution_text_format": "(1) Penelope is a knave\n(2) Charlotte is a knave\n(3) James is a knave\n(4) Alexander is a knight\n(5) Isabella is a knight\n(6) Luke is a knight\n(7) Emma is a knight\n(8) Liam is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that Isabella is a knight and Emma is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Liam is a knight and Emma is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Isabella is a knight and Alexander is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Luke is a knight if and only if Charlotte is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Charlotte is a knight or Isabella is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Alexander that Luke is a knight if and only if Charlotte is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Charlotte is a knight if and only if Liam is a knight.", "Emma cannot be a knight, because this would contradict the claim of Penelope that Isabella is a knight and Emma is a knave.", "Emma cannot be a knave, because this would contradict the claim of Isabella that Liam is a knight and Emma is a knight.", "We have exhausted all possibilities for Emma and Charlotte, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the false claim of their own that Charlotte is a knight or Isabella is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Alexander.", "Alexander cannot be a knave, because this would contradict the claim of Liam that Isabella is a knight and Alexander is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the claim of Isabella that Liam is a knight and Emma is a knight.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the claim of Penelope that Isabella is a knight and Emma is a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Isabella is a knight and Emma is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Liam is a knight and Emma is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Isabella is a knight and Alexander is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Luke is a knight if and only if Charlotte is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Charlotte is a knight or Isabella is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Alexander that Luke is a knight if and only if Charlotte is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Charlotte is a knight if and only if Liam is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Liam is a knave if and only if Alexander is a knave.", "James cannot be a knight, because this would contradict the claim of their own that If Luke is a knight then Penelope is a knight.", "Assume James is a knave. No contradiction is found in their false claim that If Luke is a knight then Penelope is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 4), ('lying', 6)), ('<=>', ('telling-truth', 1), ('telling-truth', 7)), ('->', ('telling-truth', 5), ('telling-truth', 0)), ('<=>', ('telling-truth', 5), ('lying', 1)), ('and', ('telling-truth', 7), ('telling-truth', 6)), ('or', ('telling-truth', 1), ('telling-truth', 4)), ('<=>', ('lying', 7), ('lying', 3)), ('and', ('telling-truth', 4), ('telling-truth', 3)))", "index": 936}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Oliver, Penelope, Aiden, Abigail, Samuel, Emma, Michael, and Elizabeth. In Oliver's words: \"Aiden is a knight if and only if Oliver is a knight\". Penelope remarked, \"Aiden is not a knave\". Aiden said that Emma is a knave if and only if Elizabeth is a knave. As Abigail put it, \"Samuel is a knave\". Samuel was heard saying, \"Penelope is a knight or Aiden is a knight\". According to Emma, \"Oliver is a knave\". \"Elizabeth is a knight or Penelope is a knave,\" Michael mentioned. In a statement by Elizabeth: \"Penelope is a knight\". So who is a knight and who is a knave?", "names": ["Oliver", "Penelope", "Aiden", "Abigail", "Samuel", "Emma", "Michael", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true, true, true], "solution_text": "Oliver is a knave, Penelope is a knight, Aiden is a knight, Abigail is a knave, Samuel is a knight, Emma is a knight, Michael is a knight, and Elizabeth is a knight.", "solution_text_format": "(1) Oliver is a knave\n(2) Penelope is a knight\n(3) Aiden is a knight\n(4) Abigail is a knave\n(5) Samuel is a knight\n(6) Emma is a knight\n(7) Michael is a knight\n(8) Elizabeth is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Aiden is a knight if and only if Oliver is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Emma is a knave if and only if Elizabeth is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Oliver is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Oliver is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of Aiden that Emma is a knave if and only if Elizabeth is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Penelope is a knight.", "Penelope cannot be a knight, because this would contradict the false claim of Elizabeth that Penelope is a knight.", "Penelope cannot be a knave, because this would contradict the false claim of their own that Aiden is not a knave.", "We have exhausted all possibilities for Penelope, Elizabeth, and Emma, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the claim of Oliver that Aiden is a knight if and only if Oliver is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Aiden is a knight if and only if Oliver is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Emma is a knave if and only if Elizabeth is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Oliver is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Aiden is not a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Abigail that Samuel is a knave.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Penelope is a knight or Aiden is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Samuel is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Penelope is a knight or Aiden is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Elizabeth is a knight or Penelope is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('telling-truth', 0)), ('not', ('lying', 2)), ('<=>', ('lying', 5), ('lying', 7)), ('lying', 4), ('or', ('telling-truth', 1), ('telling-truth', 2)), ('lying', 0), ('or', ('telling-truth', 7), ('lying', 1)), ('telling-truth', 1))", "index": 937}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Michael, Logan, Harper, William, Penelope, Aiden, Avery, and Evelyn. Michael expressed that Logan is a knave if and only if Penelope is a knight. In a statement by Logan: \"Aiden is a knave and Avery is a knave\". Harper was heard saying, \"Avery is a knight or Logan is a knight\". William was heard saying, \"Aiden is a knight or Harper is a knave\". In Penelope's words: \"Penelope is a knight if and only if Logan is a knave\". \"Harper is a knight if and only if Avery is a knave\" - Aiden. Avery said that Penelope is not a knight. In a statement by Evelyn: \"If Evelyn is a knight then Aiden is a knave\". So who is a knight and who is a knave?", "names": ["Michael", "Logan", "Harper", "William", "Penelope", "Aiden", "Avery", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, false, true, true], "solution_text": "Michael is a knave, Logan is a knave, Harper is a knight, William is a knave, Penelope is a knave, Aiden is a knave, Avery is a knight, and Evelyn is a knight.", "solution_text_format": "(1) Michael is a knave\n(2) Logan is a knave\n(3) Harper is a knight\n(4) William is a knave\n(5) Penelope is a knave\n(6) Aiden is a knave\n(7) Avery is a knight\n(8) Evelyn is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Logan is a knave if and only if Penelope is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Aiden is a knave and Avery is a knave.", "Aiden cannot be a knight, because this would contradict the claim of Logan that Aiden is a knave and Avery is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Harper is a knight if and only if Avery is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Avery is a knight or Logan is a knight.", "Avery cannot be a knight, because this would contradict the claim of Logan that Aiden is a knave and Avery is a knave.", "Avery cannot be a knave, because this would contradict the false claim of Aiden that Harper is a knight if and only if Avery is a knave.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the false claim of their own that Avery is a knight or Logan is a knight.", "We have exhausted all possibilities for Harper and Aiden, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Aiden is a knave and Avery is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Harper is a knight if and only if Avery is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Avery is a knight or Logan is a knight.", "Avery cannot be a knight, because this would contradict the claim of Aiden that Harper is a knight if and only if Avery is a knave.", "Avery cannot be a knave, because this would contradict the claim of Harper that Avery is a knight or Logan is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Avery is a knight or Logan is a knight.", "Avery cannot be a knight, because this would contradict the false claim of Harper that Avery is a knight or Logan is a knight.", "Avery cannot be a knave, because this would contradict the claim of Aiden that Harper is a knight if and only if Avery is a knave.", "We have exhausted all possibilities for Avery and Harper, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Harper is a knight if and only if Avery is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Avery is a knight or Logan is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Penelope cannot be a knight, because this would contradict the claim of Avery that Penelope is not a knight.", "Penelope cannot be a knave, because this would contradict the claim of Michael that Logan is a knave if and only if Penelope is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Avery.", "Avery cannot be a knave, because this would contradict the false claim of Logan that Aiden is a knave and Avery is a knave.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Avery is a knight or Logan is a knight.", "Avery cannot be a knight, because this would contradict the false claim of Harper that Avery is a knight or Logan is a knight.", "Avery cannot be a knave, because this would contradict the false claim of Logan that Aiden is a knave and Avery is a knave.", "We have exhausted all possibilities for Avery, Harper, Aiden, and Logan, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Logan is a knave if and only if Penelope is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Aiden is a knave and Avery is a knave.", "Aiden cannot be a knight, because this would contradict the claim of Logan that Aiden is a knave and Avery is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Harper is a knight if and only if Avery is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Avery is a knight or Logan is a knight.", "Avery cannot be a knight, because this would contradict the claim of Logan that Aiden is a knave and Avery is a knave.", "Avery cannot be a knave, because this would contradict the false claim of Aiden that Harper is a knight if and only if Avery is a knave.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the false claim of their own that Avery is a knight or Logan is a knight.", "We have exhausted all possibilities for Harper and Aiden, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Aiden is a knave and Avery is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Harper is a knight if and only if Avery is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Avery is a knight or Logan is a knight.", "Avery cannot be a knight, because this would contradict the claim of Aiden that Harper is a knight if and only if Avery is a knave.", "Avery cannot be a knave, because this would contradict the claim of Harper that Avery is a knight or Logan is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Avery is a knight or Logan is a knight.", "Avery cannot be a knight, because this would contradict the false claim of Harper that Avery is a knight or Logan is a knight.", "Avery cannot be a knave, because this would contradict the claim of Aiden that Harper is a knight if and only if Avery is a knave.", "We have exhausted all possibilities for Avery and Harper, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Harper is a knight if and only if Avery is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Avery is a knight or Logan is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Penelope cannot be a knight, because this would contradict the false claim of Michael that Logan is a knave if and only if Penelope is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Penelope is a knight if and only if Logan is a knave.", "William cannot be a knight, because this would contradict the claim of their own that Aiden is a knight or Harper is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Aiden is a knight or Harper is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Evelyn is a knight then Aiden is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('telling-truth', 4)), ('and', ('lying', 5), ('lying', 6)), ('or', ('telling-truth', 6), ('telling-truth', 1)), ('or', ('telling-truth', 5), ('lying', 2)), ('<=>', ('telling-truth', 4), ('lying', 1)), ('<=>', ('telling-truth', 2), ('lying', 6)), ('not', ('telling-truth', 4)), ('->', ('telling-truth', 7), ('lying', 5)))", "index": 938}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Joseph, Aiden, Sebastian, Zoey, Luke, Avery, Benjamin, and Alexander. Joseph said, \"Zoey is a knave if and only if Avery is a knight.\" Aiden said, \"Benjamin is not a knave.\" Sebastian noted, \"Avery is a knave or Aiden is a knight\". In a statement by Zoey: \"Alexander is not a knave\". \"Alexander is not a knave,\" Luke declared. \"If Zoey is a knight then Aiden is a knave,\" Avery mentioned. Benjamin told you that Zoey is a knave. Alexander noted, \"Aiden is a knight or Zoey is a knight\". So who is a knight and who is a knave?", "names": ["Joseph", "Aiden", "Sebastian", "Zoey", "Luke", "Avery", "Benjamin", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true, false, true], "solution_text": "Joseph is a knave, Aiden is a knave, Sebastian is a knave, Zoey is a knight, Luke is a knight, Avery is a knight, Benjamin is a knave, and Alexander is a knight.", "solution_text_format": "(1) Joseph is a knave\n(2) Aiden is a knave\n(3) Sebastian is a knave\n(4) Zoey is a knight\n(5) Luke is a knight\n(6) Avery is a knight\n(7) Benjamin is a knave\n(8) Alexander is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that Zoey is a knave if and only if Avery is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Alexander is not a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Aiden is a knight or Zoey is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Benjamin is not a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Zoey is a knave.", "Benjamin cannot be a knave, because this would contradict the claim of Aiden that Benjamin is not a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Benjamin is not a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Aiden that Benjamin is not a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Zoey is a knave.", "Avery cannot be a knight, because this would contradict the claim of Joseph that Zoey is a knave if and only if Avery is a knight.", "Avery cannot be a knave, because this would contradict the false claim of their own that If Zoey is a knight then Aiden is a knave.", "We have exhausted all possibilities for Avery, Benjamin, and Aiden, so let us go back and reconsider Alexander.", "Alexander cannot be a knave, because this would contradict the claim of Zoey that Alexander is not a knave.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Alexander is not a knave.", "Alexander cannot be a knight, because this would contradict the false claim of Zoey that Alexander is not a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Aiden is a knight or Zoey is a knight.", "Aiden cannot be a knight, because this would contradict the false claim of Alexander that Aiden is a knight or Zoey is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Benjamin is not a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Aiden that Benjamin is not a knave.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that Zoey is a knave.", "We have exhausted all possibilities for Benjamin, Aiden, Alexander, and Zoey, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Zoey is a knave if and only if Avery is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Alexander is not a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Aiden is a knight or Zoey is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Benjamin is not a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Zoey is a knave.", "Benjamin cannot be a knave, because this would contradict the claim of Aiden that Benjamin is not a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Benjamin is not a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Aiden that Benjamin is not a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Zoey is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that If Zoey is a knight then Aiden is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Avery is a knave or Aiden is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Avery is a knave or Aiden is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Alexander is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('telling-truth', 5)), ('not', ('lying', 6)), ('or', ('lying', 5), ('telling-truth', 1)), ('not', ('lying', 7)), ('not', ('lying', 7)), ('->', ('telling-truth', 3), ('lying', 1)), ('lying', 3), ('or', ('telling-truth', 1), ('telling-truth', 3)))", "index": 939}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sebastian, Matthew, Elizabeth, Alexander, Logan, Scarlett, Michael, and Avery. Sebastian said that Matthew is a knave if and only if Scarlett is a knave. In a statement by Matthew: \"If Scarlett is a knave then Sebastian is a knave\". According to Elizabeth, \"Avery is a knight if and only if Logan is a knave\". In Alexander's words: \"Sebastian is a knight\". As Logan put it, \"Michael is a knight if and only if Scarlett is a knave\". As Scarlett put it, \"Logan is a knave\". Michael commented, \"If Logan is a knave then Matthew is a knave\". Avery said, \"Alexander is a knight or Elizabeth is a knight.\" So who is a knight and who is a knave?", "names": ["Sebastian", "Matthew", "Elizabeth", "Alexander", "Logan", "Scarlett", "Michael", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false, true, true], "solution_text": "Sebastian is a knight, Matthew is a knave, Elizabeth is a knave, Alexander is a knight, Logan is a knight, Scarlett is a knave, Michael is a knight, and Avery is a knight.", "solution_text_format": "(1) Sebastian is a knight\n(2) Matthew is a knave\n(3) Elizabeth is a knave\n(4) Alexander is a knight\n(5) Logan is a knight\n(6) Scarlett is a knave\n(7) Michael is a knight\n(8) Avery is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that Matthew is a knave if and only if Scarlett is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that If Scarlett is a knave then Sebastian is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of Scarlett that Logan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Michael is a knight if and only if Scarlett is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that If Logan is a knave then Matthew is a knave.", "Michael cannot be a knave, because this would contradict the false claim of Logan that Michael is a knight if and only if Scarlett is a knave.", "We have exhausted all possibilities for Michael and Logan, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the claim of Sebastian that Matthew is a knave if and only if Scarlett is a knave.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that If Scarlett is a knave then Sebastian is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Sebastian that Matthew is a knave if and only if Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Logan is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Michael is a knight if and only if Scarlett is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that If Logan is a knave then Matthew is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Avery is a knight if and only if Logan is a knave.", "Avery cannot be a knight, because this would contradict the claim of Elizabeth that Avery is a knight if and only if Logan is a knave.", "Avery cannot be a knave, because this would contradict the false claim of their own that Alexander is a knight or Elizabeth is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Avery is a knight if and only if Logan is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Alexander is a knight or Elizabeth is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Sebastian is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('lying', 5)), ('->', ('lying', 5), ('lying', 0)), ('<=>', ('telling-truth', 7), ('lying', 4)), ('telling-truth', 0), ('<=>', ('telling-truth', 6), ('lying', 5)), ('lying', 4), ('->', ('lying', 4), ('lying', 1)), ('or', ('telling-truth', 3), ('telling-truth', 2)))", "index": 940}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sophia, Lucas, Harper, Elizabeth, Charlotte, Amelia, William, and Aiden. In a statement by Sophia: \"Elizabeth is not a knight\". Lucas asserted: \"William is a knave if and only if Amelia is a knave\". Harper noted, \"Amelia is a knight or Sophia is a knave\". Elizabeth said that Sophia is a knave or Harper is a knave. Charlotte noted, \"Amelia is a knave if and only if Elizabeth is a knight\". Amelia noted, \"Lucas is a knave if and only if Aiden is a knave\". William asserted: \"William is a knight and Harper is a knave\". Aiden said that Charlotte is a knight or Sophia is a knight. So who is a knight and who is a knave?", "names": ["Sophia", "Lucas", "Harper", "Elizabeth", "Charlotte", "Amelia", "William", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, true, false, false], "solution_text": "Sophia is a knave, Lucas is a knave, Harper is a knight, Elizabeth is a knight, Charlotte is a knave, Amelia is a knight, William is a knave, and Aiden is a knave.", "solution_text_format": "(1) Sophia is a knave\n(2) Lucas is a knave\n(3) Harper is a knight\n(4) Elizabeth is a knight\n(5) Charlotte is a knave\n(6) Amelia is a knight\n(7) William is a knave\n(8) Aiden is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Elizabeth is not a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Sophia that Elizabeth is not a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Sophia is a knave or Harper is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Amelia is a knight or Sophia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Lucas is a knave if and only if Aiden is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that William is a knave if and only if Amelia is a knave.", "William cannot be a knight, because this would contradict the claim of their own that William is a knight and Harper is a knave.", "William cannot be a knave, because this would contradict the claim of Lucas that William is a knave if and only if Amelia is a knave.", "We have exhausted all possibilities for William, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that William is a knave if and only if Amelia is a knave.", "William cannot be a knight, because this would contradict the false claim of Lucas that William is a knave if and only if Amelia is a knave.", "Assume William is a knave. No contradiction is found in their false claim that William is a knight and Harper is a knave.", "Aiden cannot be a knight, because this would contradict the claim of Amelia that Lucas is a knave if and only if Aiden is a knave.", "Aiden cannot be a knave, because this would contradict the false claim of their own that Charlotte is a knight or Sophia is a knight.", "We have exhausted all possibilities for Aiden, William, and Lucas, so let us go back and reconsider Amelia.", "Amelia cannot be a knave, because this would contradict the claim of Harper that Amelia is a knight or Sophia is a knave.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the false claim of Elizabeth that Sophia is a knave or Harper is a knave.", "We have exhausted all possibilities for Harper and Elizabeth, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Elizabeth is not a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Sophia is a knave or Harper is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Amelia is a knight or Sophia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Lucas is a knave if and only if Aiden is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that William is a knave if and only if Amelia is a knave.", "William cannot be a knight, because this would contradict the claim of their own that William is a knight and Harper is a knave.", "William cannot be a knave, because this would contradict the claim of Lucas that William is a knave if and only if Amelia is a knave.", "We have exhausted all possibilities for William, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that William is a knave if and only if Amelia is a knave.", "William cannot be a knight, because this would contradict the false claim of Lucas that William is a knave if and only if Amelia is a knave.", "Assume William is a knave. No contradiction is found in their false claim that William is a knight and Harper is a knave.", "Aiden cannot be a knight, because this would contradict the claim of Amelia that Lucas is a knave if and only if Aiden is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Charlotte is a knight or Sophia is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Amelia is a knave if and only if Elizabeth is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Amelia is a knave if and only if Elizabeth is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 3)), ('<=>', ('lying', 6), ('lying', 5)), ('or', ('telling-truth', 5), ('lying', 0)), ('or', ('lying', 0), ('lying', 2)), ('<=>', ('lying', 5), ('telling-truth', 3)), ('<=>', ('lying', 1), ('lying', 7)), ('and', ('telling-truth', 6), ('lying', 2)), ('or', ('telling-truth', 4), ('telling-truth', 0)))", "index": 941}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Alexander, Jack, Zoey, Scarlett, Ava, Amelia, Owen, and Michael. \"Michael is not a knave\" - Alexander. \"Ava is a knight and Amelia is a knave,\" Jack claimed. In a statement by Zoey: \"Owen is a knave\". Scarlett asserted: \"Michael is a knight\". \"Michael is a knave or Alexander is a knight,\" Ava mentioned. Amelia was heard saying, \"Zoey is a knave if and only if Ava is a knave\". In a statement by Owen: \"Michael is a knave and Michael is a knight\". As Michael put it, \"Jack is a knave and Owen is a knight\". So who is a knight and who is a knave?", "names": ["Alexander", "Jack", "Zoey", "Scarlett", "Ava", "Amelia", "Owen", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true, false, false], "solution_text": "Alexander is a knave, Jack is a knave, Zoey is a knight, Scarlett is a knave, Ava is a knight, Amelia is a knight, Owen is a knave, and Michael is a knave.", "solution_text_format": "(1) Alexander is a knave\n(2) Jack is a knave\n(3) Zoey is a knight\n(4) Scarlett is a knave\n(5) Ava is a knight\n(6) Amelia is a knight\n(7) Owen is a knave\n(8) Michael is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that Michael is not a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Jack is a knave and Owen is a knight.", "Jack cannot be a knight, because this would contradict the claim of Michael that Jack is a knave and Owen is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Ava is a knight and Amelia is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Michael is a knave or Alexander is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Zoey is a knave if and only if Ava is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of Zoey that Owen is a knave.", "Owen cannot be a knave, because this would contradict the claim of Michael that Jack is a knave and Owen is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Zoey.", "Zoey cannot be a knave, because this would contradict the claim of Amelia that Zoey is a knave if and only if Ava is a knave.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Amelia.", "Amelia cannot be a knave, because this would contradict the false claim of Jack that Ava is a knight and Amelia is a knave.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the false claim of their own that Michael is a knave or Alexander is a knight.", "We have exhausted all possibilities for Ava and Jack, so let us go back and reconsider Michael.", "Michael cannot be a knave, because this would contradict the claim of Alexander that Michael is not a knave.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Michael is not a knave.", "Michael cannot be a knight, because this would contradict the false claim of Alexander that Michael is not a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Jack is a knave and Owen is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Ava is a knight and Amelia is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Michael is a knave or Alexander is a knight.", "Amelia cannot be a knight, because this would contradict the claim of Jack that Ava is a knight and Amelia is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Zoey is a knave if and only if Ava is a knave.", "Zoey cannot be a knight, because this would contradict the false claim of Amelia that Zoey is a knave if and only if Ava is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Michael is a knight.", "Owen cannot be a knave, because this would contradict the false claim of Zoey that Owen is a knave.", "We have exhausted all possibilities for Owen, Zoey, and Amelia, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the claim of Jack that Ava is a knight and Amelia is a knave.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Ava is a knight and Amelia is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Michael is a knave or Alexander is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Zoey is a knave if and only if Ava is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of Zoey that Owen is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Michael is a knave and Michael is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Michael is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Michael is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 7)), ('and', ('telling-truth', 4), ('lying', 5)), ('lying', 6), ('telling-truth', 7), ('or', ('lying', 7), ('telling-truth', 0)), ('<=>', ('lying', 2), ('lying', 4)), ('and', ('lying', 7), ('telling-truth', 7)), ('and', ('lying', 1), ('telling-truth', 6)))", "index": 942}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Liam, Mason, Jacob, Zoey, James, Samuel, Riley, and Chloe. \"Jacob is a knave\" - Liam. In a statement by Mason: \"Riley is not a knave\". According to Jacob, \"Zoey is a knave\". Zoey stated, \"If Chloe is a knave then Samuel is a knight\". In James's words: \"Mason is a knave and Samuel is a knight\". Samuel told you that Chloe is a knave and Riley is a knave. Riley remarked, \"If James is a knight then Jacob is a knight\". Chloe remarked, \"Jacob is a knight or Liam is a knight\". So who is a knight and who is a knave?", "names": ["Liam", "Mason", "Jacob", "Zoey", "James", "Samuel", "Riley", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false, true, true], "solution_text": "Liam is a knight, Mason is a knight, Jacob is a knave, Zoey is a knight, James is a knave, Samuel is a knave, Riley is a knight, and Chloe is a knight.", "solution_text_format": "(1) Liam is a knight\n(2) Mason is a knight\n(3) Jacob is a knave\n(4) Zoey is a knight\n(5) James is a knave\n(6) Samuel is a knave\n(7) Riley is a knight\n(8) Chloe is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Liam that Jacob is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Zoey is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that If Chloe is a knave then Samuel is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Jacob is a knight or Liam is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Chloe is a knave and Riley is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Chloe is a knave and Riley is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that If James is a knight then Jacob is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Mason is a knave and Samuel is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Mason is a knave and Samuel is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Riley is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('not', ('lying', 6)), ('lying', 3), ('->', ('lying', 7), ('telling-truth', 5)), ('and', ('lying', 1), ('telling-truth', 5)), ('and', ('lying', 7), ('lying', 6)), ('->', ('telling-truth', 4), ('telling-truth', 2)), ('or', ('telling-truth', 2), ('telling-truth', 0)))", "index": 943}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Scarlett, Daniel, Emma, Sofia, Jacob, Ethan, James, and Mason. Scarlett told you that Emma is not a knight. Daniel noted, \"Mason is not a knight\". Emma said that James is a knave if and only if Scarlett is a knave. Sofia commented, \"Emma is a knight\". Jacob commented, \"Mason is a knight if and only if Emma is a knave\". Ethan commented, \"Sofia is not a knight\". \"Ethan is a knight,\" James claimed. Mason was heard saying, \"Scarlett is a knave if and only if Ethan is a knight\". So who is a knight and who is a knave?", "names": ["Scarlett", "Daniel", "Emma", "Sofia", "Jacob", "Ethan", "James", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false, false, false], "solution_text": "Scarlett is a knave, Daniel is a knight, Emma is a knight, Sofia is a knight, Jacob is a knight, Ethan is a knave, James is a knave, and Mason is a knave.", "solution_text_format": "(1) Scarlett is a knave\n(2) Daniel is a knight\n(3) Emma is a knight\n(4) Sofia is a knight\n(5) Jacob is a knight\n(6) Ethan is a knave\n(7) James is a knave\n(8) Mason is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Emma is not a knight.", "Emma cannot be a knight, because this would contradict the claim of Scarlett that Emma is not a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that James is a knave if and only if Scarlett is a knave.", "James cannot be a knight, because this would contradict the false claim of Emma that James is a knave if and only if Scarlett is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Ethan is a knight.", "Ethan cannot be a knight, because this would contradict the false claim of James that Ethan is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Sofia is not a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that Emma is a knight.", "Sofia cannot be a knave, because this would contradict the false claim of Ethan that Sofia is not a knight.", "We have exhausted all possibilities for Sofia, Ethan, James, and Emma, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Emma is not a knight.", "Assume Emma is a knight. No contradiction is found in their claim that James is a knave if and only if Scarlett is a knave.", "James cannot be a knight, because this would contradict the claim of Emma that James is a knave if and only if Scarlett is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Ethan is a knight.", "Ethan cannot be a knight, because this would contradict the false claim of James that Ethan is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Sofia is not a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Emma is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Mason is not a knight.", "Mason cannot be a knight, because this would contradict the claim of Daniel that Mason is not a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Scarlett is a knave if and only if Ethan is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Mason is a knight if and only if Emma is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('not', ('telling-truth', 7)), ('<=>', ('lying', 6), ('lying', 0)), ('telling-truth', 2), ('<=>', ('telling-truth', 7), ('lying', 2)), ('not', ('telling-truth', 3)), ('telling-truth', 5), ('<=>', ('lying', 0), ('telling-truth', 5)))", "index": 944}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aurora, Ava, Jackson, Aiden, Olivia, Zoey, Lily, and Abigail. Aurora expressed that Zoey is a knave if and only if Ava is a knave. Ava asserted: \"If Zoey is a knave then Zoey is a knight\". Jackson expressed that Zoey is a knave and Lily is a knight. In a statement by Aiden: \"Jackson is not a knight\". According to Olivia, \"Aurora is not a knight\". Zoey was heard saying, \"Ava is a knave and Lily is a knight\". \"Ava is a knight if and only if Abigail is a knave\" - Lily. Abigail was heard saying, \"Zoey is a knight and Zoey is a knave\". So who is a knight and who is a knave?", "names": ["Aurora", "Ava", "Jackson", "Aiden", "Olivia", "Zoey", "Lily", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, false, false, false], "solution_text": "Aurora is a knight, Ava is a knave, Jackson is a knave, Aiden is a knight, Olivia is a knave, Zoey is a knave, Lily is a knave, and Abigail is a knave.", "solution_text_format": "(1) Aurora is a knight\n(2) Ava is a knave\n(3) Jackson is a knave\n(4) Aiden is a knight\n(5) Olivia is a knave\n(6) Zoey is a knave\n(7) Lily is a knave\n(8) Abigail is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that Zoey is a knave if and only if Ava is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Ava is a knave and Lily is a knight.", "Ava cannot be a knight, because this would contradict the claim of Zoey that Ava is a knave and Lily is a knight.", "Ava cannot be a knave, because this would contradict the claim of Aurora that Zoey is a knave if and only if Ava is a knave.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Ava is a knave and Lily is a knight.", "Ava cannot be a knight, because this would contradict the claim of Aurora that Zoey is a knave if and only if Ava is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that If Zoey is a knave then Zoey is a knight.", "Lily cannot be a knight, because this would contradict the false claim of Zoey that Ava is a knave and Lily is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Ava is a knight if and only if Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the false claim of Lily that Ava is a knight if and only if Abigail is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Zoey is a knight and Zoey is a knave.", "Jackson cannot be a knight, because this would contradict the claim of their own that Zoey is a knave and Lily is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Zoey is a knave and Lily is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Jackson is not a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that Aurora is not a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Aurora is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 5), ('lying', 1)), ('->', ('lying', 5), ('telling-truth', 5)), ('and', ('lying', 5), ('telling-truth', 6)), ('not', ('telling-truth', 2)), ('not', ('telling-truth', 0)), ('and', ('lying', 1), ('telling-truth', 6)), ('<=>', ('telling-truth', 1), ('lying', 7)), ('and', ('telling-truth', 5), ('lying', 5)))", "index": 945}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: James, Logan, Mia, Zoey, Jackson, Aria, Michael, and Owen. \"Logan is a knave or Aria is a knave,\" James claimed. Logan asserted: \"Aria is not a knave\". Mia stated, \"Michael is a knight\". \"If Logan is a knight then Michael is a knight\" - Zoey. Jackson commented, \"James is not a knight\". \"If Owen is a knave then Zoey is a knight,\" Aria claimed. Michael commented, \"If Zoey is a knight then Logan is a knight\". As Owen put it, \"James is a knight and Michael is a knave\". So who is a knight and who is a knave?", "names": ["James", "Logan", "Mia", "Zoey", "Jackson", "Aria", "Michael", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true, true, false], "solution_text": "James is a knave, Logan is a knight, Mia is a knight, Zoey is a knight, Jackson is a knight, Aria is a knight, Michael is a knight, and Owen is a knave.", "solution_text_format": "(1) James is a knave\n(2) Logan is a knight\n(3) Mia is a knight\n(4) Zoey is a knight\n(5) Jackson is a knight\n(6) Aria is a knight\n(7) Michael is a knight\n(8) Owen is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Logan is a knave or Aria is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Aria is not a knave.", "Aria cannot be a knight, because this would contradict the claim of James that Logan is a knave or Aria is a knave.", "Aria cannot be a knave, because this would contradict the claim of Logan that Aria is not a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Aria is not a knave.", "Aria cannot be a knight, because this would contradict the false claim of Logan that Aria is not a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that If Owen is a knave then Zoey is a knight.", "Owen cannot be a knight, because this would contradict the false claim of Aria that If Owen is a knave then Zoey is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that James is a knight and Michael is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that If Zoey is a knight then Logan is a knight.", "Zoey cannot be a knight, because this would contradict the false claim of Aria that If Owen is a knave then Zoey is a knight.", "Zoey cannot be a knave, because this would contradict the false claim of their own that If Logan is a knight then Michael is a knight.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Michael.", "Michael cannot be a knave, because this would contradict the false claim of Owen that James is a knight and Michael is a knave.", "We have exhausted all possibilities for Michael, Owen, Aria, and Logan, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Logan is a knave or Aria is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Aria is not a knave.", "Assume Aria is a knight. No contradiction is found in their claim that If Owen is a knave then Zoey is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that James is a knight and Michael is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that James is a knight and Michael is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that If Zoey is a knight then Logan is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that If Logan is a knight then Michael is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Michael is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that James is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('lying', 5)), ('not', ('lying', 5)), ('telling-truth', 6), ('->', ('telling-truth', 1), ('telling-truth', 6)), ('not', ('telling-truth', 0)), ('->', ('lying', 7), ('telling-truth', 3)), ('->', ('telling-truth', 3), ('telling-truth', 1)), ('and', ('telling-truth', 0), ('lying', 6)))", "index": 946}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ella, Isabella, Logan, Ethan, William, Henry, Jack, and Victoria. Ella remarked, \"Isabella is a knight if and only if Jack is a knight\". In a statement by Isabella: \"Henry is a knave\". According to Logan, \"Isabella is a knave and Ethan is a knave\". Ethan asserted: \"Ella is a knave\". William told you that Ethan is a knight if and only if Jack is a knight. \"If Victoria is a knave then Logan is a knave,\" Henry declared. As Jack put it, \"Victoria is a knight or Henry is a knave\". Victoria said, \"Logan is a knave.\" So who is a knight and who is a knave?", "names": ["Ella", "Isabella", "Logan", "Ethan", "William", "Henry", "Jack", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true, true, true], "solution_text": "Ella is a knave, Isabella is a knave, Logan is a knave, Ethan is a knight, William is a knight, Henry is a knight, Jack is a knight, and Victoria is a knight.", "solution_text_format": "(1) Ella is a knave\n(2) Isabella is a knave\n(3) Logan is a knave\n(4) Ethan is a knight\n(5) William is a knight\n(6) Henry is a knight\n(7) Jack is a knight\n(8) Victoria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Jack is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of Isabella that Henry is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that If Victoria is a knave then Logan is a knave.", "Victoria cannot be a knight, because this would contradict the false claim of Henry that If Victoria is a knave then Logan is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of their own that Isabella is a knave and Ethan is a knave.", "Logan cannot be a knave, because this would contradict the false claim of Henry that If Victoria is a knave then Logan is a knave.", "We have exhausted all possibilities for Logan, Victoria, and Henry, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Henry is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Victoria is a knave then Logan is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of Victoria that Logan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Isabella is a knave and Ethan is a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Ella is a knave.", "Ethan cannot be a knave, because this would contradict the false claim of Logan that Isabella is a knave and Ethan is a knave.", "We have exhausted all possibilities for Ethan and Logan, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of Henry that If Victoria is a knave then Logan is a knave.", "Logan cannot be a knave, because this would contradict the false claim of Victoria that Logan is a knave.", "We have exhausted all possibilities for Logan and Victoria, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the false claim of Isabella that Henry is a knave.", "We have exhausted all possibilities for Henry and Isabella, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Isabella is a knight if and only if Jack is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of Isabella that Henry is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that If Victoria is a knave then Logan is a knave.", "Victoria cannot be a knight, because this would contradict the false claim of Henry that If Victoria is a knave then Logan is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of their own that Isabella is a knave and Ethan is a knave.", "Logan cannot be a knave, because this would contradict the false claim of Henry that If Victoria is a knave then Logan is a knave.", "We have exhausted all possibilities for Logan, Victoria, and Henry, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Henry is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Victoria is a knave then Logan is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of Victoria that Logan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Isabella is a knave and Ethan is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Ella is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Victoria is a knight or Henry is a knave.", "Assume William is a knight. No contradiction is found in their claim that Ethan is a knight if and only if Jack is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('telling-truth', 6)), ('lying', 5), ('and', ('lying', 1), ('lying', 3)), ('lying', 0), ('<=>', ('telling-truth', 3), ('telling-truth', 6)), ('->', ('lying', 7), ('lying', 2)), ('or', ('telling-truth', 7), ('lying', 5)), ('lying', 2))", "index": 947}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aiden, Noah, Scarlett, James, Avery, Jack, Zoey, and Michael. Aiden commented, \"Scarlett is a knave or Zoey is a knight\". \"Zoey is a knave or Jack is a knave,\" Noah mentioned. Scarlett was heard saying, \"Zoey is a knave if and only if Noah is a knight\". As James put it, \"Aiden is a knight if and only if Avery is a knight\". Avery was heard saying, \"Scarlett is a knave if and only if Noah is a knight\". In Jack's words: \"Noah is a knight and James is a knight\". As Zoey put it, \"Zoey is a knight\". Michael noted, \"Aiden is a knave or Jack is a knight\". So who is a knight and who is a knave?", "names": ["Aiden", "Noah", "Scarlett", "James", "Avery", "Jack", "Zoey", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true, false, true], "solution_text": "Aiden is a knave, Noah is a knight, Scarlett is a knight, James is a knight, Avery is a knave, Jack is a knight, Zoey is a knave, and Michael is a knight.", "solution_text_format": "(1) Aiden is a knave\n(2) Noah is a knight\n(3) Scarlett is a knight\n(4) James is a knight\n(5) Avery is a knave\n(6) Jack is a knight\n(7) Zoey is a knave\n(8) Michael is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Scarlett is a knave or Zoey is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Zoey is a knave if and only if Noah is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Zoey is a knight.", "Noah cannot be a knight, because this would contradict the claim of Scarlett that Zoey is a knave if and only if Noah is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Zoey is a knave or Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Noah is a knight and James is a knight.", "Jack cannot be a knave, because this would contradict the false claim of Noah that Zoey is a knave or Jack is a knave.", "We have exhausted all possibilities for Jack and Noah, so let us go back and reconsider Zoey.", "Zoey cannot be a knave, because this would contradict the claim of Aiden that Scarlett is a knave or Zoey is a knight.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Zoey is a knave if and only if Noah is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Zoey is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Zoey is a knave or Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of Noah that Zoey is a knave or Jack is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Noah is a knight and James is a knight.", "James cannot be a knight, because this would contradict the false claim of Jack that Noah is a knight and James is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Aiden is a knight if and only if Avery is a knight.", "Avery cannot be a knight, because this would contradict the false claim of James that Aiden is a knight if and only if Avery is a knight.", "Avery cannot be a knave, because this would contradict the false claim of their own that Scarlett is a knave if and only if Noah is a knight.", "We have exhausted all possibilities for Avery, James, and Jack, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the false claim of Scarlett that Zoey is a knave if and only if Noah is a knight.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Zoey is a knight.", "Noah cannot be a knight, because this would contradict the false claim of Scarlett that Zoey is a knave if and only if Noah is a knight.", "Noah cannot be a knave, because this would contradict the false claim of their own that Zoey is a knave or Jack is a knave.", "We have exhausted all possibilities for Noah, Zoey, and Scarlett, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Scarlett is a knave or Zoey is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Zoey is a knave if and only if Noah is a knight.", "Zoey cannot be a knight, because this would contradict the false claim of Aiden that Scarlett is a knave or Zoey is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Zoey is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Zoey is a knave or Jack is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Noah is a knight and James is a knight.", "Assume James is a knight. No contradiction is found in their claim that Aiden is a knight if and only if Avery is a knight.", "Avery cannot be a knight, because this would contradict the claim of James that Aiden is a knight if and only if Avery is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Scarlett is a knave if and only if Noah is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Aiden is a knave or Jack is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('telling-truth', 6)), ('or', ('lying', 6), ('lying', 5)), ('<=>', ('lying', 6), ('telling-truth', 1)), ('<=>', ('telling-truth', 0), ('telling-truth', 4)), ('<=>', ('lying', 2), ('telling-truth', 1)), ('and', ('telling-truth', 1), ('telling-truth', 3)), ('telling-truth', 6), ('or', ('lying', 0), ('telling-truth', 5)))", "index": 948}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mia, William, Michael, Sophia, David, Abigail, Riley, and Sofia. Mia said, \"Sophia is a knight and Michael is a knight.\" William noted, \"Riley is a knight and David is a knave\". Michael commented, \"Sofia is a knight and Abigail is a knight\". Sophia said, \"Abigail is not a knight.\" As David put it, \"Sophia is not a knight\". According to Abigail, \"Riley is not a knave\". In Riley's words: \"If Riley is a knight then Michael is a knave\". Sofia told you that Sofia is a knight and Michael is a knight. So who is a knight and who is a knave?", "names": ["Mia", "William", "Michael", "Sophia", "David", "Abigail", "Riley", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, true, true, false], "solution_text": "Mia is a knave, William is a knave, Michael is a knave, Sophia is a knave, David is a knight, Abigail is a knight, Riley is a knight, and Sofia is a knave.", "solution_text_format": "(1) Mia is a knave\n(2) William is a knave\n(3) Michael is a knave\n(4) Sophia is a knave\n(5) David is a knight\n(6) Abigail is a knight\n(7) Riley is a knight\n(8) Sofia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Sophia is a knight and Michael is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Abigail is not a knight.", "Abigail cannot be a knight, because this would contradict the claim of Sophia that Abigail is not a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Riley is not a knave.", "Riley cannot be a knight, because this would contradict the false claim of Abigail that Riley is not a knave.", "Riley cannot be a knave, because this would contradict the false claim of their own that If Riley is a knight then Michael is a knave.", "We have exhausted all possibilities for Riley and Abigail, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the claim of Mia that Sophia is a knight and Michael is a knight.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Sophia is a knight and Michael is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Abigail is not a knight.", "Abigail cannot be a knight, because this would contradict the claim of Sophia that Abigail is not a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Riley is not a knave.", "Riley cannot be a knight, because this would contradict the false claim of Abigail that Riley is not a knave.", "Riley cannot be a knave, because this would contradict the false claim of their own that If Riley is a knight then Michael is a knave.", "We have exhausted all possibilities for Riley and Abigail, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Abigail is not a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Riley is not a knave.", "Assume Riley is a knight. No contradiction is found in their claim that If Riley is a knight then Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of Riley that If Riley is a knight then Michael is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Sofia is a knight and Abigail is a knight.", "Sofia cannot be a knight, because this would contradict the false claim of Michael that Sofia is a knight and Abigail is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Sofia is a knight and Michael is a knight.", "Assume William is a knight. No contradiction is found in their claim that Riley is a knight and David is a knave.", "David cannot be a knight, because this would contradict the claim of William that Riley is a knight and David is a knave.", "David cannot be a knave, because this would contradict the false claim of their own that Sophia is not a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Riley is a knight and David is a knave.", "Assume David is a knight. No contradiction is found in their claim that Sophia is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('telling-truth', 2)), ('and', ('telling-truth', 6), ('lying', 4)), ('and', ('telling-truth', 7), ('telling-truth', 5)), ('not', ('telling-truth', 5)), ('not', ('telling-truth', 3)), ('not', ('lying', 6)), ('->', ('telling-truth', 6), ('lying', 2)), ('and', ('telling-truth', 7), ('telling-truth', 2)))", "index": 949}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Chloe, Joseph, Mia, Samuel, James, Amelia, Zoey, and Matthew. Chloe was heard saying, \"Zoey is a knave and James is a knave\". Joseph noted, \"Chloe is a knave if and only if James is a knave\". \"Samuel is a knave if and only if James is a knight,\" Mia declared. According to Samuel, \"If Samuel is a knight then Zoey is a knight\". According to James, \"Samuel is a knight if and only if Mia is a knave\". Amelia noted, \"Samuel is a knave\". Zoey stated, \"Joseph is not a knave\". Matthew stated, \"James is not a knight\". So who is a knight and who is a knave?", "names": ["Chloe", "Joseph", "Mia", "Samuel", "James", "Amelia", "Zoey", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false, true, true], "solution_text": "Chloe is a knave, Joseph is a knight, Mia is a knight, Samuel is a knight, James is a knave, Amelia is a knave, Zoey is a knight, and Matthew is a knight.", "solution_text_format": "(1) Chloe is a knave\n(2) Joseph is a knight\n(3) Mia is a knight\n(4) Samuel is a knight\n(5) James is a knave\n(6) Amelia is a knave\n(7) Zoey is a knight\n(8) Matthew is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Zoey is a knave and James is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Chloe that Zoey is a knave and James is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Joseph is not a knave.", "Joseph cannot be a knight, because this would contradict the false claim of Zoey that Joseph is not a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Chloe is a knave if and only if James is a knave.", "James cannot be a knight, because this would contradict the claim of Chloe that Zoey is a knave and James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Samuel is a knight if and only if Mia is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that If Samuel is a knight then Zoey is a knight.", "Samuel cannot be a knave, because this would contradict the false claim of their own that If Samuel is a knight then Zoey is a knight.", "We have exhausted all possibilities for Samuel, James, Joseph, and Zoey, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Zoey is a knave and James is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Joseph is not a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Chloe is a knave if and only if James is a knave.", "James cannot be a knight, because this would contradict the claim of Joseph that Chloe is a knave if and only if James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Samuel is a knight if and only if Mia is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that If Samuel is a knight then Zoey is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Samuel is a knave if and only if James is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Samuel is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Samuel is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that James is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 6), ('lying', 4)), ('<=>', ('lying', 0), ('lying', 4)), ('<=>', ('lying', 3), ('telling-truth', 4)), ('->', ('telling-truth', 3), ('telling-truth', 6)), ('<=>', ('telling-truth', 3), ('lying', 2)), ('lying', 3), ('not', ('lying', 1)), ('not', ('telling-truth', 4)))", "index": 950}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Joseph, Aiden, Ella, Olivia, Penelope, Samuel, Avery, and Chloe. Joseph expressed that Chloe is not a knave. In Aiden's words: \"Penelope is not a knight\". \"Avery is a knight and Joseph is a knight,\" Ella claimed. In a statement by Olivia: \"Penelope is a knave\". Penelope expressed that Joseph is a knave or Joseph is a knight. In a statement by Samuel: \"Aiden is a knave or Avery is a knight\". Avery noted, \"Aiden is a knave\". Chloe remarked, \"If Aiden is a knight then Joseph is a knight\". So who is a knight and who is a knave?", "names": ["Joseph", "Aiden", "Ella", "Olivia", "Penelope", "Samuel", "Avery", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true, true, true], "solution_text": "Joseph is a knight, Aiden is a knave, Ella is a knight, Olivia is a knave, Penelope is a knight, Samuel is a knight, Avery is a knight, and Chloe is a knight.", "solution_text_format": "(1) Joseph is a knight\n(2) Aiden is a knave\n(3) Ella is a knight\n(4) Olivia is a knave\n(5) Penelope is a knight\n(6) Samuel is a knight\n(7) Avery is a knight\n(8) Chloe is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that Chloe is not a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that If Aiden is a knight then Joseph is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Penelope cannot be a knight, because this would contradict the claim of Aiden that Penelope is not a knight.", "Penelope cannot be a knave, because this would contradict the false claim of their own that Joseph is a knave or Joseph is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Penelope is not a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Joseph is a knave or Joseph is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Avery is a knight and Joseph is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Aiden is a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that Penelope is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Penelope is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Aiden is a knave or Avery is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 7)), ('not', ('telling-truth', 4)), ('and', ('telling-truth', 6), ('telling-truth', 0)), ('lying', 4), ('or', ('lying', 0), ('telling-truth', 0)), ('or', ('lying', 1), ('telling-truth', 6)), ('lying', 1), ('->', ('telling-truth', 1), ('telling-truth', 0)))", "index": 951}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jackson, Sofia, Henry, Logan, Avery, Mason, Lucas, and Harper. \"Mason is a knight and Avery is a knight,\" Jackson claimed. Sofia asserted: \"Jackson is a knight if and only if Avery is a knave\". In Henry's words: \"If Lucas is a knave then Avery is a knave\". \"Harper is a knight or Avery is a knight\" - Logan. In a statement by Avery: \"Lucas is a knave or Mason is a knave\". Mason said that Harper is not a knave. Lucas commented, \"Logan is a knave\". Harper stated, \"Avery is not a knight\". So who is a knight and who is a knave?", "names": ["Jackson", "Sofia", "Henry", "Logan", "Avery", "Mason", "Lucas", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false, false, false], "solution_text": "Jackson is a knave, Sofia is a knight, Henry is a knave, Logan is a knight, Avery is a knight, Mason is a knave, Lucas is a knave, and Harper is a knave.", "solution_text_format": "(1) Jackson is a knave\n(2) Sofia is a knight\n(3) Henry is a knave\n(4) Logan is a knight\n(5) Avery is a knight\n(6) Mason is a knave\n(7) Lucas is a knave\n(8) Harper is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Mason is a knight and Avery is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Harper is not a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Avery is not a knight.", "Avery cannot be a knight, because this would contradict the claim of Harper that Avery is not a knight.", "Avery cannot be a knave, because this would contradict the claim of Jackson that Mason is a knight and Avery is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the claim of Mason that Harper is not a knave.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Mason.", "Mason cannot be a knave, because this would contradict the claim of Jackson that Mason is a knight and Avery is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Mason is a knight and Avery is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Harper is not a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Avery is not a knight.", "Avery cannot be a knight, because this would contradict the false claim of Jackson that Mason is a knight and Avery is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Lucas is a knave or Mason is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of Lucas that Logan is a knave.", "Logan cannot be a knave, because this would contradict the false claim of their own that Harper is a knight or Avery is a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the false claim of Avery that Lucas is a knave or Mason is a knave.", "We have exhausted all possibilities for Lucas and Avery, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the claim of Mason that Harper is not a knave.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Harper is not a knave.", "Harper cannot be a knight, because this would contradict the false claim of Mason that Harper is not a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Avery is not a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Lucas is a knave or Mason is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of Lucas that Logan is a knave.", "Logan cannot be a knave, because this would contradict the false claim of their own that Harper is a knight or Avery is a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Logan is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Harper is a knight or Avery is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Avery is a knave.", "Henry cannot be a knight, because this would contradict the claim of their own that If Lucas is a knave then Avery is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that If Lucas is a knave then Avery is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('telling-truth', 4)), ('<=>', ('telling-truth', 0), ('lying', 4)), ('->', ('lying', 6), ('lying', 4)), ('or', ('telling-truth', 7), ('telling-truth', 4)), ('or', ('lying', 6), ('lying', 5)), ('not', ('lying', 7)), ('lying', 3), ('not', ('telling-truth', 4)))", "index": 952}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: William, Sophia, David, Aurora, Harper, Samuel, Elizabeth, and Noah. William said, \"Elizabeth is a knave or Sophia is a knight.\" Sophia remarked, \"If Elizabeth is a knave then David is a knave\". According to David, \"Samuel is not a knight\". Aurora said that William is a knave. \"Noah is a knave\" - Harper. Samuel said, \"William is a knight or William is a knave.\" Elizabeth remarked, \"Aurora is a knave and Samuel is a knave\". Noah told you that If Samuel is a knave then Elizabeth is a knave. So who is a knight and who is a knave?", "names": ["William", "Sophia", "David", "Aurora", "Harper", "Samuel", "Elizabeth", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, true, false, true], "solution_text": "William is a knight, Sophia is a knight, David is a knave, Aurora is a knave, Harper is a knave, Samuel is a knight, Elizabeth is a knave, and Noah is a knight.", "solution_text_format": "(1) William is a knight\n(2) Sophia is a knight\n(3) David is a knave\n(4) Aurora is a knave\n(5) Harper is a knave\n(6) Samuel is a knight\n(7) Elizabeth is a knave\n(8) Noah is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Elizabeth is a knave or Sophia is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Aurora is a knave and Samuel is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that William is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that William is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Elizabeth that Aurora is a knave and Samuel is a knave.", "Samuel cannot be a knave, because this would contradict the false claim of their own that William is a knight or William is a knave.", "We have exhausted all possibilities for Samuel and Aurora, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Aurora is a knave and Samuel is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that William is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that William is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that William is a knight or William is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that If Elizabeth is a knave then David is a knave.", "David cannot be a knight, because this would contradict the claim of Sophia that If Elizabeth is a knave then David is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Samuel is not a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of Harper that Noah is a knave.", "Noah cannot be a knave, because this would contradict the false claim of their own that If Samuel is a knave then Elizabeth is a knave.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Noah is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that If Samuel is a knave then Elizabeth is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 6), ('telling-truth', 1)), ('->', ('lying', 6), ('lying', 2)), ('not', ('telling-truth', 5)), ('lying', 0), ('lying', 7), ('or', ('telling-truth', 0), ('lying', 0)), ('and', ('lying', 3), ('lying', 5)), ('->', ('lying', 5), ('lying', 6)))", "index": 953}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Avery, James, Jack, Lily, Harper, Sophia, Evelyn, and Benjamin. \"James is a knight or Avery is a knight,\" Avery declared. James was heard saying, \"Avery is a knave if and only if Sophia is a knight\". \"James is not a knave,\" Jack mentioned. Lily said that Avery is a knight. \"Evelyn is a knight and Benjamin is a knave,\" Harper declared. Sophia asserted: \"Lily is a knight if and only if Evelyn is a knight\". Evelyn said that Sophia is a knight or Avery is a knight. Benjamin was heard saying, \"Jack is a knight if and only if Sophia is a knave\". So who is a knight and who is a knave?", "names": ["Avery", "James", "Jack", "Lily", "Harper", "Sophia", "Evelyn", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, true, true, true], "solution_text": "Avery is a knight, James is a knave, Jack is a knave, Lily is a knight, Harper is a knave, Sophia is a knight, Evelyn is a knight, and Benjamin is a knight.", "solution_text_format": "(1) Avery is a knight\n(2) James is a knave\n(3) Jack is a knave\n(4) Lily is a knight\n(5) Harper is a knave\n(6) Sophia is a knight\n(7) Evelyn is a knight\n(8) Benjamin is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that James is a knight or Avery is a knight.", "Assume James is a knight. No contradiction is found in their claim that Avery is a knave if and only if Sophia is a knight.", "Sophia cannot be a knight, because this would contradict the claim of James that Avery is a knave if and only if Sophia is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Lily is a knight if and only if Evelyn is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Avery is a knight.", "Evelyn cannot be a knight, because this would contradict the false claim of Sophia that Lily is a knight if and only if Evelyn is a knight.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that Sophia is a knight or Avery is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the false claim of their own that Avery is a knight.", "We have exhausted all possibilities for Lily and Sophia, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Avery is a knave if and only if Sophia is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Lily is a knight if and only if Evelyn is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Avery is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Sophia is a knight or Avery is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that James is not a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that James is not a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Evelyn is a knight and Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Harper that Evelyn is a knight and Benjamin is a knave.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that Jack is a knight if and only if Sophia is a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Evelyn is a knight and Benjamin is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Jack is a knight if and only if Sophia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('telling-truth', 0)), ('<=>', ('lying', 0), ('telling-truth', 5)), ('not', ('lying', 1)), ('telling-truth', 0), ('and', ('telling-truth', 6), ('lying', 7)), ('<=>', ('telling-truth', 3), ('telling-truth', 6)), ('or', ('telling-truth', 5), ('telling-truth', 0)), ('<=>', ('telling-truth', 2), ('lying', 5)))", "index": 954}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: James, Liam, Ethan, Joseph, Henry, Evelyn, Scarlett, and Elizabeth. In a statement by James: \"Elizabeth is a knave and Scarlett is a knight\". Liam told you that James is a knight. \"If Scarlett is a knight then Henry is a knight,\" Ethan declared. Joseph noted, \"If James is a knight then Evelyn is a knight\". Henry stated, \"Liam is a knight and Elizabeth is a knave\". \"James is a knight or Scarlett is a knave,\" Evelyn mentioned. Scarlett remarked, \"If Elizabeth is a knight then Ethan is a knight\". Elizabeth was heard saying, \"Elizabeth is a knight\". So who is a knight and who is a knave?", "names": ["James", "Liam", "Ethan", "Joseph", "Henry", "Evelyn", "Scarlett", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true, true, false], "solution_text": "James is a knight, Liam is a knight, Ethan is a knight, Joseph is a knight, Henry is a knight, Evelyn is a knight, Scarlett is a knight, and Elizabeth is a knave.", "solution_text_format": "(1) James is a knight\n(2) Liam is a knight\n(3) Ethan is a knight\n(4) Joseph is a knight\n(5) Henry is a knight\n(6) Evelyn is a knight\n(7) Scarlett is a knight\n(8) Elizabeth is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Elizabeth is a knave and Scarlett is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of James that Elizabeth is a knave and Scarlett is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Elizabeth is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Elizabeth is a knight then Ethan is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If Scarlett is a knight then Henry is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Liam is a knight and Elizabeth is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that James is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If James is a knight then Evelyn is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that James is a knight or Scarlett is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 7), ('telling-truth', 6)), ('telling-truth', 0), ('->', ('telling-truth', 6), ('telling-truth', 4)), ('->', ('telling-truth', 0), ('telling-truth', 5)), ('and', ('telling-truth', 1), ('lying', 7)), ('or', ('telling-truth', 0), ('lying', 6)), ('->', ('telling-truth', 7), ('telling-truth', 2)), ('telling-truth', 7))", "index": 955}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Charlotte, Jacob, Oliver, Mason, Aurora, Victoria, Henry, and Ethan. In a statement by Charlotte: \"Ethan is a knight\". Jacob commented, \"Victoria is not a knave\". Oliver said that Henry is a knight or Henry is a knave. Mason commented, \"Henry is a knight and Jacob is a knave\". According to Aurora, \"Charlotte is a knave\". Victoria commented, \"Oliver is a knight or Jacob is a knight\". Henry was heard saying, \"Mason is a knight or Ethan is a knave\". Ethan stated, \"Jacob is a knave and Henry is a knave\". So who is a knight and who is a knave?", "names": ["Charlotte", "Jacob", "Oliver", "Mason", "Aurora", "Victoria", "Henry", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true, true, false], "solution_text": "Charlotte is a knave, Jacob is a knight, Oliver is a knight, Mason is a knave, Aurora is a knight, Victoria is a knight, Henry is a knight, and Ethan is a knave.", "solution_text_format": "(1) Charlotte is a knave\n(2) Jacob is a knight\n(3) Oliver is a knight\n(4) Mason is a knave\n(5) Aurora is a knight\n(6) Victoria is a knight\n(7) Henry is a knight\n(8) Ethan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that Ethan is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Jacob is a knave and Henry is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Ethan that Jacob is a knave and Henry is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Victoria is not a knave.", "Victoria cannot be a knight, because this would contradict the false claim of Jacob that Victoria is not a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Oliver is a knight or Jacob is a knight.", "Oliver cannot be a knight, because this would contradict the false claim of Victoria that Oliver is a knight or Jacob is a knight.", "Oliver cannot be a knave, because this would contradict the false claim of their own that Henry is a knight or Henry is a knave.", "We have exhausted all possibilities for Oliver, Victoria, and Jacob, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the claim of Charlotte that Ethan is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Ethan is a knight.", "Ethan cannot be a knight, because this would contradict the false claim of Charlotte that Ethan is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Jacob is a knave and Henry is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Victoria is not a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Oliver is a knight or Jacob is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Henry is a knight or Henry is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Mason is a knight or Ethan is a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Henry is a knight and Jacob is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Henry is a knight and Jacob is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Charlotte is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 7), ('not', ('lying', 5)), ('or', ('telling-truth', 6), ('lying', 6)), ('and', ('telling-truth', 6), ('lying', 1)), ('lying', 0), ('or', ('telling-truth', 2), ('telling-truth', 1)), ('or', ('telling-truth', 3), ('lying', 7)), ('and', ('lying', 1), ('lying', 6)))", "index": 956}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emily, Charlotte, Lucas, James, Aria, David, Owen, and Benjamin. Emily noted, \"Owen is a knight and Lucas is a knave\". \"David is a knight if and only if Charlotte is a knight,\" Charlotte mentioned. Lucas said, \"Charlotte is not a knave.\" James was heard saying, \"Emily is a knight if and only if Aria is a knave\". Aria said, \"David is a knight if and only if Emily is a knight.\" According to David, \"If Owen is a knight then Charlotte is a knight\". Owen asserted: \"Charlotte is a knave\". As Benjamin put it, \"David is not a knave\". So who is a knight and who is a knave?", "names": ["Emily", "Charlotte", "Lucas", "James", "Aria", "David", "Owen", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true, false, true], "solution_text": "Emily is a knave, Charlotte is a knight, Lucas is a knight, James is a knave, Aria is a knave, David is a knight, Owen is a knave, and Benjamin is a knight.", "solution_text_format": "(1) Emily is a knave\n(2) Charlotte is a knight\n(3) Lucas is a knight\n(4) James is a knave\n(5) Aria is a knave\n(6) David is a knight\n(7) Owen is a knave\n(8) Benjamin is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Owen is a knight and Lucas is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Owen that Charlotte is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that David is a knight if and only if Charlotte is a knight.", "David cannot be a knight, because this would contradict the claim of their own that If Owen is a knight then Charlotte is a knight.", "David cannot be a knave, because this would contradict the false claim of Charlotte that David is a knight if and only if Charlotte is a knight.", "We have exhausted all possibilities for David and Charlotte, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the claim of Emily that Owen is a knight and Lucas is a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Owen is a knight and Lucas is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Owen that Charlotte is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that David is a knight if and only if Charlotte is a knight.", "David cannot be a knight, because this would contradict the claim of their own that If Owen is a knight then Charlotte is a knight.", "David cannot be a knave, because this would contradict the false claim of Charlotte that David is a knight if and only if Charlotte is a knight.", "We have exhausted all possibilities for David and Charlotte, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Charlotte is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that David is a knight if and only if Charlotte is a knight.", "Assume David is a knight. No contradiction is found in their claim that If Owen is a knight then Charlotte is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Charlotte is not a knave.", "Assume James is a knight. No contradiction is found in their claim that Emily is a knight if and only if Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that David is a knight if and only if Emily is a knight.", "Aria cannot be a knave, because this would contradict the claim of James that Emily is a knight if and only if Aria is a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Emily is a knight if and only if Aria is a knave.", "Aria cannot be a knight, because this would contradict the false claim of James that Emily is a knight if and only if Aria is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that David is a knight if and only if Emily is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that David is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 6), ('lying', 2)), ('<=>', ('telling-truth', 5), ('telling-truth', 1)), ('not', ('lying', 1)), ('<=>', ('telling-truth', 0), ('lying', 4)), ('<=>', ('telling-truth', 5), ('telling-truth', 0)), ('->', ('telling-truth', 6), ('telling-truth', 1)), ('lying', 1), ('not', ('lying', 5)))", "index": 957}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Logan, Ella, Zoey, Sofia, Mia, James, Sophia, and Liam. In a statement by Logan: \"Sophia is a knight or Logan is a knight\". In a statement by Ella: \"Sofia is a knave and Liam is a knight\". Zoey told you that Logan is a knave. Sofia asserted: \"Mia is a knight\". Mia was heard saying, \"Sophia is a knight if and only if Logan is a knight\". James told you that Ella is not a knight. \"Ella is a knave or Sofia is a knave\" - Sophia. Liam told you that If Mia is a knight then James is a knight. So who is a knight and who is a knave?", "names": ["Logan", "Ella", "Zoey", "Sofia", "Mia", "James", "Sophia", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true, true, true], "solution_text": "Logan is a knight, Ella is a knave, Zoey is a knave, Sofia is a knight, Mia is a knight, James is a knight, Sophia is a knight, and Liam is a knight.", "solution_text_format": "(1) Logan is a knight\n(2) Ella is a knave\n(3) Zoey is a knave\n(4) Sofia is a knight\n(5) Mia is a knight\n(6) James is a knight\n(7) Sophia is a knight\n(8) Liam is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that Sophia is a knight or Logan is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Ella is a knave or Sofia is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Sofia is a knave and Liam is a knight.", "Sofia cannot be a knight, because this would contradict the claim of Ella that Sofia is a knave and Liam is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Mia is a knight.", "Mia cannot be a knight, because this would contradict the false claim of Sofia that Mia is a knight.", "Mia cannot be a knave, because this would contradict the false claim of their own that Sophia is a knight if and only if Logan is a knight.", "We have exhausted all possibilities for Mia and Sofia, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Sofia is a knave and Liam is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Sophia is a knight if and only if Logan is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that If Mia is a knight then James is a knight.", "Assume James is a knight. No contradiction is found in their claim that Ella is not a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that Logan is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Logan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 6), ('telling-truth', 0)), ('and', ('lying', 3), ('telling-truth', 7)), ('lying', 0), ('telling-truth', 4), ('<=>', ('telling-truth', 6), ('telling-truth', 0)), ('not', ('telling-truth', 1)), ('or', ('lying', 1), ('lying', 3)), ('->', ('telling-truth', 4), ('telling-truth', 5)))", "index": 958}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Penelope, Avery, Oliver, Daniel, Zoey, Samuel, Aurora, and Abigail. \"If Avery is a knight then Oliver is a knight,\" Penelope declared. Avery expressed that Daniel is a knight. \"Avery is a knave or Zoey is a knight,\" Oliver claimed. As Daniel put it, \"Avery is a knave and Samuel is a knave\". Zoey asserted: \"Penelope is a knight or Zoey is a knight\". As Samuel put it, \"If Daniel is a knight then Aurora is a knight\". Aurora said that If Samuel is a knight then Abigail is a knave. As Abigail put it, \"If Aurora is a knight then Zoey is a knight\". So who is a knight and who is a knave?", "names": ["Penelope", "Avery", "Oliver", "Daniel", "Zoey", "Samuel", "Aurora", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true, false, true], "solution_text": "Penelope is a knight, Avery is a knave, Oliver is a knight, Daniel is a knave, Zoey is a knight, Samuel is a knight, Aurora is a knave, and Abigail is a knight.", "solution_text_format": "(1) Penelope is a knight\n(2) Avery is a knave\n(3) Oliver is a knight\n(4) Daniel is a knave\n(5) Zoey is a knight\n(6) Samuel is a knight\n(7) Aurora is a knave\n(8) Abigail is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that If Avery is a knight then Oliver is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that Avery is a knave and Samuel is a knave.", "Daniel cannot be a knave, because this would contradict the claim of Avery that Daniel is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of Avery that Daniel is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Avery is a knave and Samuel is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that If Daniel is a knight then Aurora is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that If Samuel is a knight then Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Aurora that If Samuel is a knight then Abigail is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that If Aurora is a knight then Zoey is a knight.", "Zoey cannot be a knight, because this would contradict the false claim of Abigail that If Aurora is a knight then Zoey is a knight.", "Zoey cannot be a knave, because this would contradict the false claim of their own that Penelope is a knight or Zoey is a knight.", "We have exhausted all possibilities for Zoey and Abigail, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that If Samuel is a knight then Abigail is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that If Aurora is a knight then Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Penelope is a knight or Zoey is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Avery is a knave or Zoey is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 1), ('telling-truth', 2)), ('telling-truth', 3), ('or', ('lying', 1), ('telling-truth', 4)), ('and', ('lying', 1), ('lying', 5)), ('or', ('telling-truth', 0), ('telling-truth', 4)), ('->', ('telling-truth', 3), ('telling-truth', 6)), ('->', ('telling-truth', 5), ('lying', 7)), ('->', ('telling-truth', 6), ('telling-truth', 4)))", "index": 959}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Joseph, Penelope, Noah, William, Lily, Alexander, Michael, and Riley. Joseph said that William is a knave. As Penelope put it, \"If Michael is a knave then Lily is a knight\". Noah expressed that Alexander is a knight if and only if Lily is a knave. William asserted: \"Alexander is not a knave\". In Lily's words: \"Alexander is a knight and Michael is a knave\". In a statement by Alexander: \"Lily is a knight or Lily is a knave\". Michael said that Joseph is not a knave. In a statement by Riley: \"Alexander is a knight\". So who is a knight and who is a knave?", "names": ["Joseph", "Penelope", "Noah", "William", "Lily", "Alexander", "Michael", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true, false, true], "solution_text": "Joseph is a knave, Penelope is a knight, Noah is a knave, William is a knight, Lily is a knight, Alexander is a knight, Michael is a knave, and Riley is a knight.", "solution_text_format": "(1) Joseph is a knave\n(2) Penelope is a knight\n(3) Noah is a knave\n(4) William is a knight\n(5) Lily is a knight\n(6) Alexander is a knight\n(7) Michael is a knave\n(8) Riley is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that William is a knave.", "William cannot be a knight, because this would contradict the claim of Joseph that William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Alexander is not a knave.", "Alexander cannot be a knight, because this would contradict the false claim of William that Alexander is not a knave.", "Alexander cannot be a knave, because this would contradict the false claim of their own that Lily is a knight or Lily is a knave.", "We have exhausted all possibilities for Alexander and William, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that William is a knave.", "Assume William is a knight. No contradiction is found in their claim that Alexander is not a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Lily is a knight or Lily is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Alexander is a knight and Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of Lily that Alexander is a knight and Michael is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Joseph is not a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that If Michael is a knave then Lily is a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that Alexander is a knight if and only if Lily is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Alexander is a knight if and only if Lily is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Alexander is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('->', ('lying', 6), ('telling-truth', 4)), ('<=>', ('telling-truth', 5), ('lying', 4)), ('not', ('lying', 5)), ('and', ('telling-truth', 5), ('lying', 6)), ('or', ('telling-truth', 4), ('lying', 4)), ('not', ('lying', 0)), ('telling-truth', 5))", "index": 960}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aurora, Ava, Daniel, Matthew, Owen, William, Jackson, and Avery. Aurora asserted: \"Matthew is a knight and Owen is a knave\". \"Avery is not a knave,\" Ava mentioned. Daniel was heard saying, \"Jackson is a knave\". In Matthew's words: \"Avery is a knave\". Owen stated, \"Daniel is not a knight\". William said, \"Ava is a knave or Avery is a knight.\" According to Jackson, \"Jackson is a knight or Matthew is a knight\". Avery asserted: \"If Ava is a knight then Daniel is a knave\". So who is a knight and who is a knave?", "names": ["Aurora", "Ava", "Daniel", "Matthew", "Owen", "William", "Jackson", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true, true, true], "solution_text": "Aurora is a knave, Ava is a knight, Daniel is a knave, Matthew is a knave, Owen is a knight, William is a knight, Jackson is a knight, and Avery is a knight.", "solution_text_format": "(1) Aurora is a knave\n(2) Ava is a knight\n(3) Daniel is a knave\n(4) Matthew is a knave\n(5) Owen is a knight\n(6) William is a knight\n(7) Jackson is a knight\n(8) Avery is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that Matthew is a knight and Owen is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Avery is a knave.", "Avery cannot be a knight, because this would contradict the claim of Matthew that Avery is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that If Ava is a knight then Daniel is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Avery is not a knave.", "Ava cannot be a knave, because this would contradict the false claim of Avery that If Ava is a knight then Daniel is a knave.", "We have exhausted all possibilities for Ava and Avery, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the claim of Aurora that Matthew is a knight and Owen is a knave.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Matthew is a knight and Owen is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Avery is a knave.", "Avery cannot be a knight, because this would contradict the claim of Matthew that Avery is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that If Ava is a knight then Daniel is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Avery is not a knave.", "Ava cannot be a knave, because this would contradict the false claim of Avery that If Ava is a knight then Daniel is a knave.", "We have exhausted all possibilities for Ava and Avery, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Avery is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that If Ava is a knight then Daniel is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Avery is not a knave.", "Daniel cannot be a knight, because this would contradict the claim of Avery that If Ava is a knight then Daniel is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Jackson is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Jackson is a knight or Matthew is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Daniel is not a knight.", "Assume William is a knight. No contradiction is found in their claim that Ava is a knave or Avery is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('lying', 4)), ('not', ('lying', 7)), ('lying', 6), ('lying', 7), ('not', ('telling-truth', 2)), ('or', ('lying', 1), ('telling-truth', 7)), ('or', ('telling-truth', 6), ('telling-truth', 3)), ('->', ('telling-truth', 1), ('lying', 2)))", "index": 961}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aiden, Grace, Matthew, Jacob, Daniel, Amelia, Ethan, and Isabella. Aiden said, \"If Ethan is a knight then Daniel is a knave.\" Grace expressed that Matthew is a knave if and only if Amelia is a knave. Matthew expressed that If Amelia is a knave then Matthew is a knight. Jacob was heard saying, \"Isabella is a knave and Grace is a knight\". Daniel was heard saying, \"If Daniel is a knight then Grace is a knight\". Amelia asserted: \"Aiden is a knave if and only if Daniel is a knave\". According to Ethan, \"Isabella is a knight or Daniel is a knight\". Isabella stated, \"Aiden is a knight and Matthew is a knight\". So who is a knight and who is a knave?", "names": ["Aiden", "Grace", "Matthew", "Jacob", "Daniel", "Amelia", "Ethan", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false, true, false], "solution_text": "Aiden is a knave, Grace is a knight, Matthew is a knave, Jacob is a knight, Daniel is a knight, Amelia is a knave, Ethan is a knight, and Isabella is a knave.", "solution_text_format": "(1) Aiden is a knave\n(2) Grace is a knight\n(3) Matthew is a knave\n(4) Jacob is a knight\n(5) Daniel is a knight\n(6) Amelia is a knave\n(7) Ethan is a knight\n(8) Isabella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that If Ethan is a knight then Daniel is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Isabella is a knight or Daniel is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Aiden is a knight and Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that If Amelia is a knave then Matthew is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Aiden is a knave if and only if Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of Aiden that If Ethan is a knight then Daniel is a knave.", "Daniel cannot be a knave, because this would contradict the false claim of their own that If Daniel is a knight then Grace is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of Aiden that If Ethan is a knight then Daniel is a knave.", "Daniel cannot be a knave, because this would contradict the false claim of their own that If Daniel is a knight then Grace is a knight.", "We have exhausted all possibilities for Daniel and Amelia, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the claim of Isabella that Aiden is a knight and Matthew is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Aiden is a knight and Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the false claim of Isabella that Aiden is a knight and Matthew is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that If Amelia is a knave then Matthew is a knight.", "Amelia cannot be a knight, because this would contradict the false claim of Matthew that If Amelia is a knave then Matthew is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of Aiden that If Ethan is a knight then Daniel is a knave.", "Daniel cannot be a knave, because this would contradict the false claim of their own that If Daniel is a knight then Grace is a knight.", "We have exhausted all possibilities for Daniel, Amelia, Matthew, and Isabella, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Isabella is a knight or Daniel is a knight.", "Isabella cannot be a knight, because this would contradict the false claim of Ethan that Isabella is a knight or Daniel is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Aiden is a knight and Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the false claim of Isabella that Aiden is a knight and Matthew is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that If Amelia is a knave then Matthew is a knight.", "Amelia cannot be a knight, because this would contradict the false claim of Matthew that If Amelia is a knave then Matthew is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the false claim of Amelia that Aiden is a knave if and only if Daniel is a knave.", "Daniel cannot be a knave, because this would contradict the false claim of their own that If Daniel is a knight then Grace is a knight.", "We have exhausted all possibilities for Daniel, Amelia, Matthew, Isabella, and Ethan, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that If Ethan is a knight then Daniel is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Isabella is a knight or Daniel is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Aiden is a knight and Matthew is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Aiden is a knight and Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that If Amelia is a knave then Matthew is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Aiden is a knave if and only if Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of Amelia that Aiden is a knave if and only if Daniel is a knave.", "Daniel cannot be a knave, because this would contradict the false claim of Aiden that If Ethan is a knight then Daniel is a knave.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if Daniel is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that If Daniel is a knight then Grace is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Matthew is a knave if and only if Amelia is a knave.", "Grace cannot be a knave, because this would contradict the claim of Daniel that If Daniel is a knight then Grace is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the false claim of Aiden that If Ethan is a knight then Daniel is a knave.", "We have exhausted all possibilities for Daniel and Amelia, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that If Amelia is a knave then Matthew is a knight.", "Amelia cannot be a knight, because this would contradict the false claim of Matthew that If Amelia is a knave then Matthew is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if Daniel is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that If Daniel is a knight then Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Matthew is a knave if and only if Amelia is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Isabella is a knave and Grace is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 6), ('lying', 4)), ('<=>', ('lying', 2), ('lying', 5)), ('->', ('lying', 5), ('telling-truth', 2)), ('and', ('lying', 7), ('telling-truth', 1)), ('->', ('telling-truth', 4), ('telling-truth', 1)), ('<=>', ('lying', 0), ('lying', 4)), ('or', ('telling-truth', 7), ('telling-truth', 4)), ('and', ('telling-truth', 0), ('telling-truth', 2)))", "index": 962}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: James, William, Isabella, Abigail, Sofia, Avery, Jack, and Zoey. James expressed that Avery is a knave if and only if Sofia is a knave. \"Abigail is not a knight\" - William. In a statement by Isabella: \"James is a knave\". In Abigail's words: \"James is not a knight\". In a statement by Sofia: \"Avery is a knight or Sofia is a knight\". Avery asserted: \"William is a knave or Abigail is a knave\". Jack remarked, \"James is a knave and William is a knave\". According to Zoey, \"Sofia is a knave if and only if James is a knight\". So who is a knight and who is a knave?", "names": ["James", "William", "Isabella", "Abigail", "Sofia", "Avery", "Jack", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true, false, false], "solution_text": "James is a knight, William is a knight, Isabella is a knave, Abigail is a knave, Sofia is a knight, Avery is a knight, Jack is a knave, and Zoey is a knave.", "solution_text_format": "(1) James is a knight\n(2) William is a knight\n(3) Isabella is a knave\n(4) Abigail is a knave\n(5) Sofia is a knight\n(6) Avery is a knight\n(7) Jack is a knave\n(8) Zoey is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Avery is a knave if and only if Sofia is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that William is a knave or Abigail is a knave.", "Assume William is a knight. No contradiction is found in their claim that Abigail is not a knight.", "Abigail cannot be a knight, because this would contradict the claim of William that Abigail is not a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that James is not a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Avery is a knight or Sofia is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that James is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that James is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that James is a knave and William is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that James is a knave and William is a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that Sofia is a knave if and only if James is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Sofia is a knave if and only if James is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 5), ('lying', 4)), ('not', ('telling-truth', 3)), ('lying', 0), ('not', ('telling-truth', 0)), ('or', ('telling-truth', 5), ('telling-truth', 4)), ('or', ('lying', 1), ('lying', 3)), ('and', ('lying', 0), ('lying', 1)), ('<=>', ('lying', 4), ('telling-truth', 0)))", "index": 963}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Benjamin, Ava, Grace, Amelia, Emily, Aria, Lily, and David. Benjamin told you that David is a knave. Ava commented, \"Emily is a knave\". Grace commented, \"Emily is a knave if and only if Aria is a knight\". \"Emily is a knight if and only if Ava is a knight,\" Amelia declared. \"Amelia is a knight or David is a knight,\" Emily declared. In a statement by Aria: \"Grace is a knight and Emily is a knave\". \"If Grace is a knave then Lily is a knight,\" Lily claimed. As David put it, \"Grace is a knave\". So who is a knight and who is a knave?", "names": ["Benjamin", "Ava", "Grace", "Amelia", "Emily", "Aria", "Lily", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true, true, false], "solution_text": "Benjamin is a knight, Ava is a knight, Grace is a knight, Amelia is a knave, Emily is a knave, Aria is a knight, Lily is a knight, and David is a knave.", "solution_text_format": "(1) Benjamin is a knight\n(2) Ava is a knight\n(3) Grace is a knight\n(4) Amelia is a knave\n(5) Emily is a knave\n(6) Aria is a knight\n(7) Lily is a knight\n(8) David is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that David is a knave.", "David cannot be a knight, because this would contradict the claim of Benjamin that David is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Grace is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Emily is a knave if and only if Aria is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Amelia is a knight or David is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Emily is a knight if and only if Ava is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Emily is a knave.", "Ava cannot be a knave, because this would contradict the claim of Amelia that Emily is a knight if and only if Ava is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Amelia.", "Amelia cannot be a knave, because this would contradict the claim of Emily that Amelia is a knight or David is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Amelia is a knight or David is a knight.", "Amelia cannot be a knight, because this would contradict the false claim of Emily that Amelia is a knight or David is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Emily is a knight if and only if Ava is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Emily is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Grace is a knight and Emily is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that If Grace is a knave then Lily is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 7), ('lying', 4), ('<=>', ('lying', 4), ('telling-truth', 5)), ('<=>', ('telling-truth', 4), ('telling-truth', 1)), ('or', ('telling-truth', 3), ('telling-truth', 7)), ('and', ('telling-truth', 2), ('lying', 4)), ('->', ('lying', 2), ('telling-truth', 6)), ('lying', 2))", "index": 964}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lucas, Ethan, Isabella, Grace, William, Sofia, Lily, and Benjamin. Lucas told you that William is a knave and Ethan is a knight. Ethan remarked, \"If Ethan is a knight then William is a knave\". As Isabella put it, \"Lily is a knight and William is a knave\". Grace told you that If Lily is a knight then William is a knave. \"Lily is a knave\" - William. Sofia said, \"Ethan is a knave or Isabella is a knave.\" Lily stated, \"If Sofia is a knave then Lucas is a knight\". Benjamin told you that Ethan is a knight. So who is a knight and who is a knave?", "names": ["Lucas", "Ethan", "Isabella", "Grace", "William", "Sofia", "Lily", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false, true, true], "solution_text": "Lucas is a knight, Ethan is a knight, Isabella is a knight, Grace is a knight, William is a knave, Sofia is a knave, Lily is a knight, and Benjamin is a knight.", "solution_text_format": "(1) Lucas is a knight\n(2) Ethan is a knight\n(3) Isabella is a knight\n(4) Grace is a knight\n(5) William is a knave\n(6) Sofia is a knave\n(7) Lily is a knight\n(8) Benjamin is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that William is a knave and Ethan is a knight.", "William cannot be a knight, because this would contradict the claim of Lucas that William is a knave and Ethan is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Lily is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that If Sofia is a knave then Lucas is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Ethan is a knave or Isabella is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that If Ethan is a knight then William is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Sofia that Ethan is a knave or Isabella is a knave.", "Isabella cannot be a knave, because this would contradict the false claim of their own that Lily is a knight and William is a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the claim of Lucas that William is a knave and Ethan is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Ethan is a knave or Isabella is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that If Ethan is a knight then William is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Lily is a knight and William is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that If Lily is a knight then William is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Ethan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('telling-truth', 1)), ('->', ('telling-truth', 1), ('lying', 4)), ('and', ('telling-truth', 6), ('lying', 4)), ('->', ('telling-truth', 6), ('lying', 4)), ('lying', 6), ('or', ('lying', 1), ('lying', 2)), ('->', ('lying', 5), ('telling-truth', 0)), ('telling-truth', 1))", "index": 965}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Oliver, David, Benjamin, Sebastian, Liam, William, Matthew, and Joseph. Oliver told you that David is a knight if and only if Benjamin is a knight. In David's words: \"Oliver is a knave or Matthew is a knight\". Benjamin told you that Oliver is a knight or William is a knave. \"William is not a knave\" - Sebastian. Liam said that Matthew is a knight if and only if Benjamin is a knight. In William's words: \"If Matthew is a knave then Liam is a knave\". Matthew stated, \"Benjamin is a knave\". Joseph was heard saying, \"David is a knave and Benjamin is a knight\". So who is a knight and who is a knave?", "names": ["Oliver", "David", "Benjamin", "Sebastian", "Liam", "William", "Matthew", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, true, true, false], "solution_text": "Oliver is a knave, David is a knight, Benjamin is a knave, Sebastian is a knight, Liam is a knave, William is a knight, Matthew is a knight, and Joseph is a knave.", "solution_text_format": "(1) Oliver is a knave\n(2) David is a knight\n(3) Benjamin is a knave\n(4) Sebastian is a knight\n(5) Liam is a knave\n(6) William is a knight\n(7) Matthew is a knight\n(8) Joseph is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that David is a knight if and only if Benjamin is a knight.", "Assume David is a knight. No contradiction is found in their claim that Oliver is a knave or Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Matthew that Benjamin is a knave.", "Benjamin cannot be a knave, because this would contradict the claim of Oliver that David is a knight if and only if Benjamin is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the claim of David that Oliver is a knave or Matthew is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Oliver is a knave or Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the false claim of David that Oliver is a knave or Matthew is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Oliver that David is a knight if and only if Benjamin is a knight.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that Oliver is a knight or William is a knave.", "We have exhausted all possibilities for Benjamin, Matthew, and David, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that David is a knight if and only if Benjamin is a knight.", "Assume David is a knight. No contradiction is found in their claim that Oliver is a knave or Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Oliver that David is a knight if and only if Benjamin is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Oliver is a knight or William is a knave.", "Assume William is a knight. No contradiction is found in their claim that If Matthew is a knave then Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Matthew is a knight if and only if Benjamin is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Matthew is a knight if and only if Benjamin is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that William is not a knave.", "Joseph cannot be a knight, because this would contradict the claim of their own that David is a knave and Benjamin is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that David is a knave and Benjamin is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('telling-truth', 2)), ('or', ('lying', 0), ('telling-truth', 6)), ('or', ('telling-truth', 0), ('lying', 5)), ('not', ('lying', 5)), ('<=>', ('telling-truth', 6), ('telling-truth', 2)), ('->', ('lying', 6), ('lying', 4)), ('lying', 2), ('and', ('lying', 1), ('telling-truth', 2)))", "index": 966}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jack, Sophia, Penelope, Scarlett, Harper, Aiden, Ethan, and Owen. Jack commented, \"Penelope is a knight if and only if Sophia is a knight\". Sophia asserted: \"Sophia is a knight if and only if Ethan is a knight\". Penelope noted, \"Harper is a knight or Scarlett is a knight\". Scarlett said, \"Owen is a knave or Jack is a knight.\" Harper was heard saying, \"If Sophia is a knave then Jack is a knave\". Aiden said that Sophia is a knave and Harper is a knight. In Ethan's words: \"Ethan is a knight if and only if Aiden is a knave\". Owen noted, \"Ethan is a knave or Aiden is a knave\". So who is a knight and who is a knave?", "names": ["Jack", "Sophia", "Penelope", "Scarlett", "Harper", "Aiden", "Ethan", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false, true, true], "solution_text": "Jack is a knight, Sophia is a knight, Penelope is a knight, Scarlett is a knight, Harper is a knight, Aiden is a knave, Ethan is a knight, and Owen is a knight.", "solution_text_format": "(1) Jack is a knight\n(2) Sophia is a knight\n(3) Penelope is a knight\n(4) Scarlett is a knight\n(5) Harper is a knight\n(6) Aiden is a knave\n(7) Ethan is a knight\n(8) Owen is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Penelope is a knight if and only if Sophia is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Harper is a knight or Scarlett is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that If Sophia is a knave then Jack is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Sophia is a knight if and only if Ethan is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Ethan is a knight if and only if Aiden is a knave.", "Aiden cannot be a knight, because this would contradict the claim of their own that Sophia is a knave and Harper is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Sophia is a knave and Harper is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Owen is a knave or Jack is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Ethan is a knave or Aiden is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('telling-truth', 1)), ('<=>', ('telling-truth', 1), ('telling-truth', 6)), ('or', ('telling-truth', 4), ('telling-truth', 3)), ('or', ('lying', 7), ('telling-truth', 0)), ('->', ('lying', 1), ('lying', 0)), ('and', ('lying', 1), ('telling-truth', 4)), ('<=>', ('telling-truth', 6), ('lying', 5)), ('or', ('lying', 6), ('lying', 5)))", "index": 967}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sebastian, Ava, Penelope, Sophia, William, Benjamin, Grace, and Michael. Sebastian said, \"Penelope is a knight if and only if Penelope is a knave.\" Ava expressed that If William is a knight then Michael is a knight. Penelope remarked, \"Benjamin is a knight or William is a knave\". \"Grace is a knight if and only if Ava is a knave,\" Sophia claimed. As William put it, \"Michael is not a knave\". Benjamin expressed that If Penelope is a knave then Michael is a knave. Grace expressed that Penelope is a knave or Benjamin is a knave. According to Michael, \"Grace is a knight and William is a knave\". So who is a knight and who is a knave?", "names": ["Sebastian", "Ava", "Penelope", "Sophia", "William", "Benjamin", "Grace", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true, false, false], "solution_text": "Sebastian is a knave, Ava is a knight, Penelope is a knight, Sophia is a knight, William is a knave, Benjamin is a knight, Grace is a knave, and Michael is a knave.", "solution_text_format": "(1) Sebastian is a knave\n(2) Ava is a knight\n(3) Penelope is a knight\n(4) Sophia is a knight\n(5) William is a knave\n(6) Benjamin is a knight\n(7) Grace is a knave\n(8) Michael is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Sebastian cannot be a knight, because this would contradict the claim of their own that Penelope is a knight if and only if Penelope is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Penelope is a knight if and only if Penelope is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Benjamin is a knight or William is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Penelope is a knave then Michael is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Grace is a knight and William is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Penelope is a knave or Benjamin is a knave.", "Grace cannot be a knave, because this would contradict the claim of Michael that Grace is a knight and William is a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Grace is a knight and William is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Penelope is a knave or Benjamin is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Penelope is a knave or Benjamin is a knave.", "William cannot be a knight, because this would contradict the claim of their own that Michael is not a knave.", "Assume William is a knave. No contradiction is found in their false claim that Michael is not a knave.", "Assume Ava is a knight. No contradiction is found in their claim that If William is a knight then Michael is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Grace is a knight if and only if Ava is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('lying', 2)), ('->', ('telling-truth', 4), ('telling-truth', 7)), ('or', ('telling-truth', 5), ('lying', 4)), ('<=>', ('telling-truth', 6), ('lying', 1)), ('not', ('lying', 7)), ('->', ('lying', 2), ('lying', 7)), ('or', ('lying', 2), ('lying', 5)), ('and', ('telling-truth', 6), ('lying', 4)))", "index": 968}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Liam, Harper, Benjamin, Isabella, Aurora, Mia, Emily, and Ava. As Liam put it, \"Isabella is a knight\". Harper remarked, \"Benjamin is a knave and Ava is a knave\". Benjamin said that Benjamin is a knight and Emily is a knight. Isabella remarked, \"Mia is a knight if and only if Benjamin is a knight\". According to Aurora, \"Benjamin is a knave or Mia is a knight\". \"If Harper is a knave then Emily is a knave,\" Mia mentioned. In a statement by Emily: \"If Harper is a knight then Liam is a knight\". Ava commented, \"Mia is a knight or Aurora is a knave\". So who is a knight and who is a knave?", "names": ["Liam", "Harper", "Benjamin", "Isabella", "Aurora", "Mia", "Emily", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, false, true, true], "solution_text": "Liam is a knave, Harper is a knave, Benjamin is a knight, Isabella is a knave, Aurora is a knave, Mia is a knave, Emily is a knight, and Ava is a knight.", "solution_text_format": "(1) Liam is a knave\n(2) Harper is a knave\n(3) Benjamin is a knight\n(4) Isabella is a knave\n(5) Aurora is a knave\n(6) Mia is a knave\n(7) Emily is a knight\n(8) Ava is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Isabella is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Mia is a knight if and only if Benjamin is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that If Harper is a knave then Emily is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Benjamin is a knave and Ava is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Harper that Benjamin is a knave and Ava is a knave.", "Benjamin cannot be a knave, because this would contradict the claim of Isabella that Mia is a knight if and only if Benjamin is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Benjamin is a knave and Ava is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Benjamin is a knight and Emily is a knight.", "Emily cannot be a knight, because this would contradict the claim of Mia that If Harper is a knave then Emily is a knave.", "Emily cannot be a knave, because this would contradict the claim of Benjamin that Benjamin is a knight and Emily is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the claim of Isabella that Mia is a knight if and only if Benjamin is a knight.", "We have exhausted all possibilities for Benjamin and Harper, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that If Harper is a knave then Emily is a knave.", "Harper cannot be a knight, because this would contradict the false claim of Mia that If Harper is a knave then Emily is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Benjamin is a knave and Ava is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Isabella that Mia is a knight if and only if Benjamin is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Benjamin is a knight and Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that If Harper is a knight then Liam is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Mia is a knight or Aurora is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Ava that Mia is a knight or Aurora is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of their own that Benjamin is a knave or Mia is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the false claim of Harper that Benjamin is a knave and Ava is a knave.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the false claim of Mia that If Harper is a knave then Emily is a knave.", "We have exhausted all possibilities for Emily, Benjamin, Harper, and Mia, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the claim of Liam that Isabella is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Isabella is a knight.", "Isabella cannot be a knight, because this would contradict the false claim of Liam that Isabella is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Mia is a knight if and only if Benjamin is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that If Harper is a knave then Emily is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Benjamin is a knave and Ava is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Harper that Benjamin is a knave and Ava is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Benjamin is a knight and Emily is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that If Harper is a knight then Liam is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that If Harper is a knight then Liam is a knight.", "Ava cannot be a knight, because this would contradict the claim of Harper that Benjamin is a knave and Ava is a knave.", "Ava cannot be a knave, because this would contradict the false claim of their own that Mia is a knight or Aurora is a knave.", "We have exhausted all possibilities for Ava, Emily, and Benjamin, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Benjamin is a knave and Ava is a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Isabella that Mia is a knight if and only if Benjamin is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Benjamin is a knight and Emily is a knight.", "Emily cannot be a knight, because this would contradict the claim of Mia that If Harper is a knave then Emily is a knave.", "Emily cannot be a knave, because this would contradict the false claim of their own that If Harper is a knight then Liam is a knight.", "We have exhausted all possibilities for Emily, Benjamin, and Harper, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that If Harper is a knave then Emily is a knave.", "Harper cannot be a knight, because this would contradict the false claim of Mia that If Harper is a knave then Emily is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Benjamin is a knave and Ava is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Benjamin is a knight and Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that If Harper is a knight then Liam is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Mia is a knight or Aurora is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave or Mia is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Benjamin is a knave or Mia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 3), ('and', ('lying', 2), ('lying', 7)), ('and', ('telling-truth', 2), ('telling-truth', 6)), ('<=>', ('telling-truth', 5), ('telling-truth', 2)), ('or', ('lying', 2), ('telling-truth', 5)), ('->', ('lying', 1), ('lying', 6)), ('->', ('telling-truth', 1), ('telling-truth', 0)), ('or', ('telling-truth', 5), ('lying', 4)))", "index": 969}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ava, Alexander, Jacob, Aria, Avery, Chloe, Joseph, and James. Ava was heard saying, \"Aria is a knight and James is a knave\". \"Joseph is a knight\" - Alexander. \"Ava is a knight or Joseph is a knave,\" Jacob declared. Aria said that If Ava is a knight then Jacob is a knight. Avery expressed that If Chloe is a knave then Avery is a knight. Chloe commented, \"James is a knave and Ava is a knight\". In Joseph's words: \"Alexander is a knave and Chloe is a knave\". James stated, \"Alexander is a knight\". So who is a knight and who is a knave?", "names": ["Ava", "Alexander", "Jacob", "Aria", "Avery", "Chloe", "Joseph", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true, false, false], "solution_text": "Ava is a knight, Alexander is a knave, Jacob is a knight, Aria is a knight, Avery is a knight, Chloe is a knight, Joseph is a knave, and James is a knave.", "solution_text_format": "(1) Ava is a knight\n(2) Alexander is a knave\n(3) Jacob is a knight\n(4) Aria is a knight\n(5) Avery is a knight\n(6) Chloe is a knight\n(7) Joseph is a knave\n(8) James is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Aria is a knight and James is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that If Ava is a knight then Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Ava is a knight or Joseph is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Alexander is a knave and Chloe is a knave.", "Alexander cannot be a knight, because this would contradict the claim of Joseph that Alexander is a knave and Chloe is a knave.", "Alexander cannot be a knave, because this would contradict the false claim of their own that Joseph is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Alexander is a knave and Chloe is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that Joseph is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Joseph is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that James is a knave and Ava is a knight.", "James cannot be a knight, because this would contradict the claim of Ava that Aria is a knight and James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Alexander is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that If Chloe is a knave then Avery is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('lying', 7)), ('telling-truth', 6), ('or', ('telling-truth', 0), ('lying', 6)), ('->', ('telling-truth', 0), ('telling-truth', 2)), ('->', ('lying', 5), ('telling-truth', 4)), ('and', ('lying', 7), ('telling-truth', 0)), ('and', ('lying', 1), ('lying', 5)), ('telling-truth', 1))", "index": 970}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aiden, Samuel, Henry, Riley, Jack, Oliver, Abigail, and Daniel. \"Abigail is a knave or Oliver is a knave,\" Aiden claimed. Samuel said, \"Daniel is not a knight.\" As Henry put it, \"If Jack is a knight then Riley is a knave\". Riley expressed that Abigail is a knave or Aiden is a knave. Jack asserted: \"If Aiden is a knight then Oliver is a knight\". Oliver noted, \"Abigail is a knave\". In a statement by Abigail: \"Daniel is a knave if and only if Abigail is a knight\". Daniel asserted: \"Oliver is not a knave\". So who is a knight and who is a knave?", "names": ["Aiden", "Samuel", "Henry", "Riley", "Jack", "Oliver", "Abigail", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false, true, false], "solution_text": "Aiden is a knight, Samuel is a knight, Henry is a knight, Riley is a knave, Jack is a knave, Oliver is a knave, Abigail is a knight, and Daniel is a knave.", "solution_text_format": "(1) Aiden is a knight\n(2) Samuel is a knight\n(3) Henry is a knight\n(4) Riley is a knave\n(5) Jack is a knave\n(6) Oliver is a knave\n(7) Abigail is a knight\n(8) Daniel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Abigail is a knave or Oliver is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Daniel is a knave if and only if Abigail is a knight.", "Daniel cannot be a knight, because this would contradict the claim of Abigail that Daniel is a knave if and only if Abigail is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Oliver is not a knave.", "Oliver cannot be a knight, because this would contradict the claim of Aiden that Abigail is a knave or Oliver is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Abigail is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Daniel is not a knight.", "Assume Henry is a knight. No contradiction is found in their claim that If Jack is a knight then Riley is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that If Aiden is a knight then Oliver is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that If Aiden is a knight then Oliver is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Abigail is a knave or Aiden is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Abigail is a knave or Aiden is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 6), ('lying', 5)), ('not', ('telling-truth', 7)), ('->', ('telling-truth', 4), ('lying', 3)), ('or', ('lying', 6), ('lying', 0)), ('->', ('telling-truth', 0), ('telling-truth', 5)), ('lying', 6), ('<=>', ('lying', 7), ('telling-truth', 6)), ('not', ('lying', 5)))", "index": 971}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Chloe, Liam, Owen, Jackson, Alexander, Riley, Oliver, and Avery. Chloe said that Avery is a knave if and only if Alexander is a knave. Liam remarked, \"Chloe is a knave and Alexander is a knight\". Owen expressed that If Liam is a knave then Oliver is a knave. Jackson said, \"Jackson is a knight if and only if Chloe is a knave.\" In a statement by Alexander: \"Chloe is not a knight\". Riley asserted: \"Chloe is not a knave\". In a statement by Oliver: \"Chloe is a knight\". Avery said that If Jackson is a knight then Oliver is a knight. So who is a knight and who is a knave?", "names": ["Chloe", "Liam", "Owen", "Jackson", "Alexander", "Riley", "Oliver", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false, false, false], "solution_text": "Chloe is a knave, Liam is a knight, Owen is a knight, Jackson is a knight, Alexander is a knight, Riley is a knave, Oliver is a knave, and Avery is a knave.", "solution_text_format": "(1) Chloe is a knave\n(2) Liam is a knight\n(3) Owen is a knight\n(4) Jackson is a knight\n(5) Alexander is a knight\n(6) Riley is a knave\n(7) Oliver is a knave\n(8) Avery is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Avery is a knave if and only if Alexander is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that If Jackson is a knight then Oliver is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Jackson is a knight if and only if Chloe is a knave.", "Jackson cannot be a knave, because this would contradict the false claim of their own that Jackson is a knight if and only if Chloe is a knave.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that If Jackson is a knight then Oliver is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Jackson is a knight if and only if Chloe is a knave.", "Jackson cannot be a knave, because this would contradict the false claim of their own that Jackson is a knight if and only if Chloe is a knave.", "We have exhausted all possibilities for Jackson and Avery, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Avery is a knave if and only if Alexander is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that If Jackson is a knight then Oliver is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Chloe is a knave.", "Oliver cannot be a knight, because this would contradict the claim of their own that Chloe is a knight.", "Oliver cannot be a knave, because this would contradict the claim of Avery that If Jackson is a knight then Oliver is a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Jackson is a knight if and only if Chloe is a knave.", "Oliver cannot be a knight, because this would contradict the claim of their own that Chloe is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Chloe is a knight.", "Alexander cannot be a knight, because this would contradict the false claim of Chloe that Avery is a knave if and only if Alexander is a knave.", "Alexander cannot be a knave, because this would contradict the false claim of their own that Chloe is not a knight.", "We have exhausted all possibilities for Alexander, Oliver, and Jackson, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that If Jackson is a knight then Oliver is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Chloe is a knave.", "Oliver cannot be a knight, because this would contradict the claim of their own that Chloe is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Chloe is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Chloe is not a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Chloe is a knave and Alexander is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that If Liam is a knave then Oliver is a knave.", "Riley cannot be a knight, because this would contradict the claim of their own that Chloe is not a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Chloe is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 7), ('lying', 4)), ('and', ('lying', 0), ('telling-truth', 4)), ('->', ('lying', 1), ('lying', 6)), ('<=>', ('telling-truth', 3), ('lying', 0)), ('not', ('telling-truth', 0)), ('not', ('lying', 0)), ('telling-truth', 0), ('->', ('telling-truth', 3), ('telling-truth', 6)))", "index": 972}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: David, Samuel, Sebastian, Ella, Daniel, Ava, James, and Jackson. David noted, \"Sebastian is a knave\". Samuel remarked, \"David is a knave if and only if Samuel is a knight\". Sebastian asserted: \"If Sebastian is a knight then Samuel is a knave\". \"If Sebastian is a knight then Ava is a knave,\" Ella claimed. \"Ella is not a knight\" - Daniel. Ava remarked, \"David is a knight if and only if Sebastian is a knave\". James stated, \"Sebastian is a knave and James is a knight\". Jackson said that Ava is a knight. So who is a knight and who is a knave?", "names": ["David", "Samuel", "Sebastian", "Ella", "Daniel", "Ava", "James", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true, false, true], "solution_text": "David is a knave, Samuel is a knave, Sebastian is a knight, Ella is a knave, Daniel is a knight, Ava is a knight, James is a knave, and Jackson is a knight.", "solution_text_format": "(1) David is a knave\n(2) Samuel is a knave\n(3) Sebastian is a knight\n(4) Ella is a knave\n(5) Daniel is a knight\n(6) Ava is a knight\n(7) James is a knave\n(8) Jackson is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of David that Sebastian is a knave.", "Sebastian cannot be a knave, because this would contradict the false claim of their own that If Sebastian is a knight then Samuel is a knave.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Sebastian is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Sebastian is a knight then Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Sebastian that If Sebastian is a knight then Samuel is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that David is a knave if and only if Samuel is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that If Sebastian is a knight then Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of Ella that If Sebastian is a knight then Ava is a knave.", "Ava cannot be a knave, because this would contradict the false claim of their own that David is a knight if and only if Sebastian is a knave.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that If Sebastian is a knight then Ava is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that David is a knight if and only if Sebastian is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Ella is not a knight.", "James cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave and James is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Sebastian is a knave and James is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Ava is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('<=>', ('lying', 0), ('telling-truth', 1)), ('->', ('telling-truth', 2), ('lying', 1)), ('->', ('telling-truth', 2), ('lying', 5)), ('not', ('telling-truth', 3)), ('<=>', ('telling-truth', 0), ('lying', 2)), ('and', ('lying', 2), ('telling-truth', 6)), ('telling-truth', 5))", "index": 973}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Grace, Chloe, Logan, Emily, James, Aiden, Lucas, and Sophia. Grace noted, \"Logan is a knight or Logan is a knave\". As Chloe put it, \"Lucas is a knave and Emily is a knave\". Logan commented, \"If James is a knight then Emily is a knave\". Emily said, \"Grace is a knave.\" James told you that Grace is a knave or Lucas is a knave. Aiden said, \"Chloe is a knave.\" According to Lucas, \"Sophia is a knave\". As Sophia put it, \"Chloe is a knave and Sophia is a knight\". So who is a knight and who is a knave?", "names": ["Grace", "Chloe", "Logan", "Emily", "James", "Aiden", "Lucas", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true, true, false], "solution_text": "Grace is a knight, Chloe is a knave, Logan is a knight, Emily is a knave, James is a knave, Aiden is a knight, Lucas is a knight, and Sophia is a knave.", "solution_text_format": "(1) Grace is a knight\n(2) Chloe is a knave\n(3) Logan is a knight\n(4) Emily is a knave\n(5) James is a knave\n(6) Aiden is a knight\n(7) Lucas is a knight\n(8) Sophia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Logan is a knight or Logan is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that If James is a knight then Emily is a knave.", "Assume James is a knight. No contradiction is found in their claim that Grace is a knave or Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the claim of James that Grace is a knave or Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Sophia is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Chloe is a knave and Sophia is a knight.", "Chloe cannot be a knight, because this would contradict the claim of Sophia that Chloe is a knave and Sophia is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Lucas is a knave and Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of Logan that If James is a knight then Emily is a knave.", "Emily cannot be a knave, because this would contradict the false claim of Chloe that Lucas is a knave and Emily is a knave.", "We have exhausted all possibilities for Emily and Chloe, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the false claim of Lucas that Sophia is a knave.", "We have exhausted all possibilities for Sophia and Lucas, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Grace is a knave or Lucas is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Sophia is a knave.", "Sophia cannot be a knight, because this would contradict the claim of Lucas that Sophia is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Chloe is a knave and Sophia is a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Lucas is a knave and Emily is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Lucas is a knave and Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Grace is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Grace is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Chloe is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('lying', 2)), ('and', ('lying', 6), ('lying', 3)), ('->', ('telling-truth', 4), ('lying', 3)), ('lying', 0), ('or', ('lying', 0), ('lying', 6)), ('lying', 1), ('lying', 7), ('and', ('lying', 1), ('telling-truth', 7)))", "index": 974}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mia, Aiden, Noah, Harper, Luke, Avery, Amelia, and Olivia. \"Harper is not a knave,\" Mia mentioned. Aiden expressed that Avery is a knave. Noah said that Amelia is a knave if and only if Luke is a knave. According to Harper, \"Amelia is not a knave\". \"If Amelia is a knave then Avery is a knave,\" Luke declared. Avery was heard saying, \"Harper is a knight or Luke is a knave\". Amelia asserted: \"Mia is a knave if and only if Noah is a knight\". In Olivia's words: \"Avery is not a knight\". So who is a knight and who is a knave?", "names": ["Mia", "Aiden", "Noah", "Harper", "Luke", "Avery", "Amelia", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, false, false, true], "solution_text": "Mia is a knave, Aiden is a knight, Noah is a knave, Harper is a knave, Luke is a knight, Avery is a knave, Amelia is a knave, and Olivia is a knight.", "solution_text_format": "(1) Mia is a knave\n(2) Aiden is a knight\n(3) Noah is a knave\n(4) Harper is a knave\n(5) Luke is a knight\n(6) Avery is a knave\n(7) Amelia is a knave\n(8) Olivia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Harper is not a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Amelia is not a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Mia is a knave if and only if Noah is a knight.", "Noah cannot be a knight, because this would contradict the claim of Amelia that Mia is a knave if and only if Noah is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Amelia is a knave if and only if Luke is a knave.", "Luke cannot be a knight, because this would contradict the false claim of Noah that Amelia is a knave if and only if Luke is a knave.", "Luke cannot be a knave, because this would contradict the false claim of their own that If Amelia is a knave then Avery is a knave.", "We have exhausted all possibilities for Luke and Noah, so let us go back and reconsider Amelia.", "Amelia cannot be a knave, because this would contradict the claim of Harper that Amelia is not a knave.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the claim of Mia that Harper is not a knave.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Harper is not a knave.", "Harper cannot be a knight, because this would contradict the false claim of Mia that Harper is not a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Amelia is not a knave.", "Amelia cannot be a knight, because this would contradict the false claim of Harper that Amelia is not a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Mia is a knave if and only if Noah is a knight.", "Noah cannot be a knight, because this would contradict the false claim of Amelia that Mia is a knave if and only if Noah is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Amelia is a knave if and only if Luke is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that If Amelia is a knave then Avery is a knave.", "Avery cannot be a knight, because this would contradict the claim of Luke that If Amelia is a knave then Avery is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Harper is a knight or Luke is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Avery is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Avery is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 3)), ('lying', 5), ('<=>', ('lying', 6), ('lying', 4)), ('not', ('lying', 6)), ('->', ('lying', 6), ('lying', 5)), ('or', ('telling-truth', 3), ('lying', 4)), ('<=>', ('lying', 0), ('telling-truth', 2)), ('not', ('telling-truth', 5)))", "index": 975}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aiden, Ella, Isabella, Logan, David, Mia, Evelyn, and Grace. Aiden was heard saying, \"Grace is not a knight\". Ella stated, \"Aiden is a knave if and only if Logan is a knight\". Isabella asserted: \"If David is a knight then Evelyn is a knight\". Logan told you that If Ella is a knave then Ella is a knight. According to David, \"Grace is not a knave\". As Mia put it, \"David is a knave\". Evelyn was heard saying, \"If David is a knave then Evelyn is a knight\". Grace was heard saying, \"Mia is a knight or Ella is a knave\". So who is a knight and who is a knave?", "names": ["Aiden", "Ella", "Isabella", "Logan", "David", "Mia", "Evelyn", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, false, true, true], "solution_text": "Aiden is a knave, Ella is a knave, Isabella is a knight, Logan is a knave, David is a knight, Mia is a knave, Evelyn is a knight, and Grace is a knight.", "solution_text_format": "(1) Aiden is a knave\n(2) Ella is a knave\n(3) Isabella is a knight\n(4) Logan is a knave\n(5) David is a knight\n(6) Mia is a knave\n(7) Evelyn is a knight\n(8) Grace is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Grace is not a knight.", "Grace cannot be a knight, because this would contradict the claim of Aiden that Grace is not a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Mia is a knight or Ella is a knave.", "Mia cannot be a knight, because this would contradict the false claim of Grace that Mia is a knight or Ella is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that David is a knave.", "David cannot be a knight, because this would contradict the claim of their own that Grace is not a knave.", "David cannot be a knave, because this would contradict the false claim of Mia that David is a knave.", "We have exhausted all possibilities for David, Mia, and Grace, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Grace is not a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Mia is a knight or Ella is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that David is a knave.", "David cannot be a knight, because this would contradict the claim of Mia that David is a knave.", "David cannot be a knave, because this would contradict the false claim of their own that Grace is not a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that David is a knave.", "Assume David is a knight. No contradiction is found in their claim that Grace is not a knave.", "Ella cannot be a knight, because this would contradict the claim of Grace that Mia is a knight or Ella is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if Logan is a knight.", "Logan cannot be a knight, because this would contradict the false claim of Ella that Aiden is a knave if and only if Logan is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that If Ella is a knave then Ella is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that If David is a knight then Evelyn is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If David is a knave then Evelyn is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 7)), ('<=>', ('lying', 0), ('telling-truth', 3)), ('->', ('telling-truth', 4), ('telling-truth', 6)), ('->', ('lying', 1), ('telling-truth', 1)), ('not', ('lying', 7)), ('lying', 4), ('->', ('lying', 4), ('telling-truth', 6)), ('or', ('telling-truth', 5), ('lying', 1)))", "index": 976}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Scarlett, Olivia, Sofia, Avery, Jackson, Emma, Noah, and Grace. Scarlett expressed that Jackson is a knave. Olivia remarked, \"Grace is a knave or Avery is a knave\". According to Sofia, \"Jackson is a knight\". Avery told you that Scarlett is a knave if and only if Sofia is a knight. \"Olivia is a knave and Sofia is a knight,\" Jackson declared. Emma was heard saying, \"Scarlett is a knave if and only if Sofia is a knight\". Noah noted, \"If Jackson is a knave then Jackson is a knight\". As Grace put it, \"Sofia is a knave and Avery is a knave\". So who is a knight and who is a knave?", "names": ["Scarlett", "Olivia", "Sofia", "Avery", "Jackson", "Emma", "Noah", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true, false, false], "solution_text": "Scarlett is a knight, Olivia is a knight, Sofia is a knave, Avery is a knight, Jackson is a knave, Emma is a knight, Noah is a knave, and Grace is a knave.", "solution_text_format": "(1) Scarlett is a knight\n(2) Olivia is a knight\n(3) Sofia is a knave\n(4) Avery is a knight\n(5) Jackson is a knave\n(6) Emma is a knight\n(7) Noah is a knave\n(8) Grace is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Jackson is a knave.", "Jackson cannot be a knight, because this would contradict the claim of Scarlett that Jackson is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Olivia is a knave and Sofia is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Grace is a knave or Avery is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Sofia is a knave and Avery is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Jackson is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Jackson is a knight.", "Avery cannot be a knight, because this would contradict the claim of Olivia that Grace is a knave or Avery is a knave.", "Avery cannot be a knave, because this would contradict the false claim of their own that Scarlett is a knave if and only if Sofia is a knight.", "We have exhausted all possibilities for Avery and Sofia, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Sofia is a knave and Avery is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Jackson is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Jackson is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Scarlett is a knave if and only if Sofia is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Scarlett is a knave if and only if Sofia is a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that If Jackson is a knave then Jackson is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that If Jackson is a knave then Jackson is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('or', ('lying', 7), ('lying', 3)), ('telling-truth', 4), ('<=>', ('lying', 0), ('telling-truth', 2)), ('and', ('lying', 1), ('telling-truth', 2)), ('<=>', ('lying', 0), ('telling-truth', 2)), ('->', ('lying', 4), ('telling-truth', 4)), ('and', ('lying', 2), ('lying', 3)))", "index": 977}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Riley, Emma, Henry, Mason, Jackson, Chloe, Emily, and Noah. Riley was heard saying, \"Emma is a knight\". Emma said that Chloe is a knave or Henry is a knight. Henry told you that If Henry is a knight then Jackson is a knight. As Mason put it, \"Riley is not a knave\". Jackson told you that Emily is not a knight. Chloe was heard saying, \"Henry is a knave if and only if Noah is a knight\". As Emily put it, \"Emily is a knight if and only if Chloe is a knave\". Noah remarked, \"Riley is a knight and Emma is a knight\". So who is a knight and who is a knave?", "names": ["Riley", "Emma", "Henry", "Mason", "Jackson", "Chloe", "Emily", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false, false, true], "solution_text": "Riley is a knight, Emma is a knight, Henry is a knight, Mason is a knight, Jackson is a knight, Chloe is a knave, Emily is a knave, and Noah is a knight.", "solution_text_format": "(1) Riley is a knight\n(2) Emma is a knight\n(3) Henry is a knight\n(4) Mason is a knight\n(5) Jackson is a knight\n(6) Chloe is a knave\n(7) Emily is a knave\n(8) Noah is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Emma is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Chloe is a knave or Henry is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Henry is a knave if and only if Noah is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that If Henry is a knight then Jackson is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Emily is not a knight.", "Emily cannot be a knight, because this would contradict the claim of Jackson that Emily is not a knight.", "Emily cannot be a knave, because this would contradict the false claim of their own that Emily is a knight if and only if Chloe is a knave.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Jackson.", "Jackson cannot be a knave, because this would contradict the claim of Henry that If Henry is a knight then Jackson is a knight.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the claim of Emma that Chloe is a knave or Henry is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Henry is a knave if and only if Noah is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that If Henry is a knight then Jackson is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Emily is not a knight.", "Emily cannot be a knight, because this would contradict the claim of Jackson that Emily is not a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Emily is a knight if and only if Chloe is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Riley is a knight and Emma is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Riley is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('or', ('lying', 5), ('telling-truth', 2)), ('->', ('telling-truth', 2), ('telling-truth', 4)), ('not', ('lying', 0)), ('not', ('telling-truth', 6)), ('<=>', ('lying', 2), ('telling-truth', 7)), ('<=>', ('telling-truth', 6), ('lying', 5)), ('and', ('telling-truth', 0), ('telling-truth', 1)))", "index": 978}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Michael, Samuel, Noah, Evelyn, Riley, Victoria, Sebastian, and Emma. In Michael's words: \"Noah is a knave and Samuel is a knight\". \"Samuel is a knight,\" Samuel mentioned. Noah stated, \"Evelyn is a knave\". Evelyn said that Riley is a knave and Victoria is a knight. Riley was heard saying, \"Victoria is not a knave\". \"Evelyn is a knave if and only if Samuel is a knave,\" Victoria declared. \"If Sebastian is a knight then Samuel is a knight,\" Sebastian mentioned. \"Noah is not a knight,\" Emma declared. So who is a knight and who is a knave?", "names": ["Michael", "Samuel", "Noah", "Evelyn", "Riley", "Victoria", "Sebastian", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false, true, false], "solution_text": "Michael is a knave, Samuel is a knight, Noah is a knight, Evelyn is a knave, Riley is a knave, Victoria is a knave, Sebastian is a knight, and Emma is a knave.", "solution_text_format": "(1) Michael is a knave\n(2) Samuel is a knight\n(3) Noah is a knight\n(4) Evelyn is a knave\n(5) Riley is a knave\n(6) Victoria is a knave\n(7) Sebastian is a knight\n(8) Emma is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Noah is a knave and Samuel is a knight.", "Noah cannot be a knight, because this would contradict the claim of Michael that Noah is a knave and Samuel is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Evelyn is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Riley is a knave and Victoria is a knight.", "Riley cannot be a knight, because this would contradict the claim of Evelyn that Riley is a knave and Victoria is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Victoria is not a knave.", "Victoria cannot be a knight, because this would contradict the false claim of Riley that Victoria is not a knave.", "Victoria cannot be a knave, because this would contradict the claim of Evelyn that Riley is a knave and Victoria is a knight.", "We have exhausted all possibilities for Victoria and Riley, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the false claim of Noah that Evelyn is a knave.", "We have exhausted all possibilities for Evelyn and Noah, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Noah is a knave and Samuel is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Evelyn is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of Noah that Evelyn is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Riley is a knave and Victoria is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Victoria is not a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Evelyn is a knave if and only if Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Victoria that Evelyn is a knave if and only if Samuel is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Samuel is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that If Sebastian is a knight then Samuel is a knight.", "Sebastian cannot be a knave, because this would contradict the false claim of their own that If Sebastian is a knight then Samuel is a knight.", "We have exhausted all possibilities for Sebastian and Samuel, so let us go back and reconsider Victoria.", "Victoria cannot be a knave, because this would contradict the claim of Riley that Victoria is not a knave.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Victoria is not a knave.", "Victoria cannot be a knight, because this would contradict the false claim of Evelyn that Riley is a knave and Victoria is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Evelyn is a knave if and only if Samuel is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Samuel is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Sebastian is a knight then Samuel is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Noah is not a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Noah is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('telling-truth', 1)), ('telling-truth', 1), ('lying', 3), ('and', ('lying', 4), ('telling-truth', 5)), ('not', ('lying', 5)), ('<=>', ('lying', 3), ('lying', 1)), ('->', ('telling-truth', 6), ('telling-truth', 1)), ('not', ('telling-truth', 2)))", "index": 979}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Matthew, Mason, Joseph, Ethan, Lucas, Chloe, Ava, and Benjamin. In Matthew's words: \"Joseph is a knave\". Mason noted, \"Lucas is not a knight\". Joseph remarked, \"If Ethan is a knave then Mason is a knave\". In Ethan's words: \"Benjamin is a knight if and only if Lucas is a knight\". Lucas asserted: \"Ethan is a knight if and only if Joseph is a knight\". As Chloe put it, \"Lucas is a knight and Benjamin is a knave\". Ava was heard saying, \"Chloe is a knave\". Benjamin was heard saying, \"If Lucas is a knave then Lucas is a knight\". So who is a knight and who is a knave?", "names": ["Matthew", "Mason", "Joseph", "Ethan", "Lucas", "Chloe", "Ava", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false, true, true], "solution_text": "Matthew is a knave, Mason is a knave, Joseph is a knight, Ethan is a knight, Lucas is a knight, Chloe is a knave, Ava is a knight, and Benjamin is a knight.", "solution_text_format": "(1) Matthew is a knave\n(2) Mason is a knave\n(3) Joseph is a knight\n(4) Ethan is a knight\n(5) Lucas is a knight\n(6) Chloe is a knave\n(7) Ava is a knight\n(8) Benjamin is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Matthew that Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that If Ethan is a knave then Mason is a knave.", "Ethan cannot be a knight, because this would contradict the false claim of Joseph that If Ethan is a knave then Mason is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Benjamin is a knight if and only if Lucas is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Lucas is a knave then Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of Ethan that Benjamin is a knight if and only if Lucas is a knight.", "Lucas cannot be a knave, because this would contradict the false claim of their own that Ethan is a knight if and only if Joseph is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that If Lucas is a knave then Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of Benjamin that If Lucas is a knave then Lucas is a knight.", "Lucas cannot be a knave, because this would contradict the false claim of Ethan that Benjamin is a knight if and only if Lucas is a knight.", "We have exhausted all possibilities for Lucas, Benjamin, Ethan, and Joseph, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Joseph is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that If Ethan is a knave then Mason is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Benjamin is a knight if and only if Lucas is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Lucas is a knave then Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Ethan is a knight if and only if Joseph is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Lucas is not a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Lucas is not a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Lucas is a knight and Benjamin is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Lucas is a knight and Benjamin is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Chloe is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('not', ('telling-truth', 4)), ('->', ('lying', 3), ('lying', 1)), ('<=>', ('telling-truth', 7), ('telling-truth', 4)), ('<=>', ('telling-truth', 3), ('telling-truth', 2)), ('and', ('telling-truth', 4), ('lying', 7)), ('lying', 5), ('->', ('lying', 4), ('telling-truth', 4)))", "index": 980}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Matthew, Amelia, Ava, Grace, Elizabeth, Sofia, Joseph, and Jack. Matthew commented, \"Grace is not a knave\". Amelia was heard saying, \"Joseph is a knave\". \"Matthew is a knight and Sofia is a knave,\" Ava declared. Grace was heard saying, \"Matthew is a knight or Elizabeth is a knave\". In a statement by Elizabeth: \"Amelia is a knave if and only if Jack is a knight\". \"Ava is a knight and Joseph is a knight,\" Sofia claimed. Joseph told you that Ava is a knave. In Jack's words: \"Matthew is not a knave\". So who is a knight and who is a knave?", "names": ["Matthew", "Amelia", "Ava", "Grace", "Elizabeth", "Sofia", "Joseph", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false, false, true], "solution_text": "Matthew is a knight, Amelia is a knight, Ava is a knight, Grace is a knight, Elizabeth is a knave, Sofia is a knave, Joseph is a knave, and Jack is a knight.", "solution_text_format": "(1) Matthew is a knight\n(2) Amelia is a knight\n(3) Ava is a knight\n(4) Grace is a knight\n(5) Elizabeth is a knave\n(6) Sofia is a knave\n(7) Joseph is a knave\n(8) Jack is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that Grace is not a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Matthew is a knight or Elizabeth is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Amelia is a knave if and only if Jack is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Amelia that Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Ava is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Matthew is a knight and Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Ava that Matthew is a knight and Sofia is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Ava is a knight and Joseph is a knight.", "Jack cannot be a knight, because this would contradict the claim of Elizabeth that Amelia is a knave if and only if Jack is a knight.", "Jack cannot be a knave, because this would contradict the false claim of their own that Matthew is not a knave.", "We have exhausted all possibilities for Jack and Sofia, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the false claim of Joseph that Ava is a knave.", "We have exhausted all possibilities for Ava and Joseph, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Joseph is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of Joseph that Ava is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Matthew is a knight and Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Ava is a knight and Joseph is a knight.", "Sofia cannot be a knave, because this would contradict the false claim of Ava that Matthew is a knight and Sofia is a knave.", "We have exhausted all possibilities for Sofia and Ava, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the false claim of Amelia that Joseph is a knave.", "We have exhausted all possibilities for Joseph and Amelia, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Amelia is a knave if and only if Jack is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Amelia that Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Ava is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Matthew is a knight and Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Ava that Matthew is a knight and Sofia is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Ava is a knight and Joseph is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Matthew is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 3)), ('lying', 6), ('and', ('telling-truth', 0), ('lying', 5)), ('or', ('telling-truth', 0), ('lying', 4)), ('<=>', ('lying', 1), ('telling-truth', 7)), ('and', ('telling-truth', 2), ('telling-truth', 6)), ('lying', 2), ('not', ('lying', 0)))", "index": 981}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mia, Abigail, Sofia, Penelope, Grace, Victoria, Aria, and Lily. Mia said, \"Victoria is a knight if and only if Abigail is a knave.\" \"Grace is a knave if and only if Lily is a knave,\" Abigail mentioned. Sofia said, \"Victoria is a knight.\" Penelope asserted: \"Sofia is a knight if and only if Lily is a knight\". Grace said that Mia is a knight if and only if Abigail is a knight. \"Aria is a knight if and only if Grace is a knave\" - Victoria. Aria said, \"Mia is a knave.\" \"Mia is a knave and Victoria is a knave,\" Lily mentioned. So who is a knight and who is a knave?", "names": ["Mia", "Abigail", "Sofia", "Penelope", "Grace", "Victoria", "Aria", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true, true, false], "solution_text": "Mia is a knave, Abigail is a knight, Sofia is a knight, Penelope is a knave, Grace is a knave, Victoria is a knight, Aria is a knight, and Lily is a knave.", "solution_text_format": "(1) Mia is a knave\n(2) Abigail is a knight\n(3) Sofia is a knight\n(4) Penelope is a knave\n(5) Grace is a knave\n(6) Victoria is a knight\n(7) Aria is a knight\n(8) Lily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Abigail is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Aria is a knight if and only if Grace is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Mia is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Mia is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Mia is a knight if and only if Abigail is a knight.", "Abigail cannot be a knight, because this would contradict the claim of Mia that Victoria is a knight if and only if Abigail is a knave.", "Abigail cannot be a knave, because this would contradict the claim of Grace that Mia is a knight if and only if Abigail is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Grace.", "Grace cannot be a knave, because this would contradict the claim of Victoria that Aria is a knight if and only if Grace is a knave.", "We have exhausted all possibilities for Grace and Aria, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Aria is a knight if and only if Grace is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Mia is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Mia is a knave.", "Grace cannot be a knight, because this would contradict the false claim of Victoria that Aria is a knight if and only if Grace is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Mia is a knight if and only if Abigail is a knight.", "Abigail cannot be a knight, because this would contradict the false claim of Grace that Mia is a knight if and only if Abigail is a knight.", "Abigail cannot be a knave, because this would contradict the claim of Mia that Victoria is a knight if and only if Abigail is a knave.", "We have exhausted all possibilities for Abigail, Grace, Aria, and Victoria, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Victoria is a knight if and only if Abigail is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Aria is a knight if and only if Grace is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Mia is a knave.", "Grace cannot be a knight, because this would contradict the claim of Victoria that Aria is a knight if and only if Grace is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Mia is a knight if and only if Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Grace is a knave if and only if Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of Abigail that Grace is a knave if and only if Lily is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Mia is a knave and Victoria is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Victoria is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Sofia is a knight if and only if Lily is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Sofia is a knight if and only if Lily is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 5), ('lying', 1)), ('<=>', ('lying', 4), ('lying', 7)), ('telling-truth', 5), ('<=>', ('telling-truth', 2), ('telling-truth', 7)), ('<=>', ('telling-truth', 0), ('telling-truth', 1)), ('<=>', ('telling-truth', 6), ('lying', 4)), ('lying', 0), ('and', ('lying', 0), ('lying', 5)))", "index": 982}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Zoey, Oliver, Alexander, Benjamin, Evelyn, Harper, Logan, and Ethan. In Zoey's words: \"Ethan is a knight or Oliver is a knight\". According to Oliver, \"Alexander is not a knave\". Alexander said that Evelyn is a knave or Logan is a knave. As Benjamin put it, \"Evelyn is a knave or Harper is a knight\". \"Logan is not a knave,\" Evelyn mentioned. Harper expressed that Evelyn is a knight if and only if Alexander is a knave. \"Benjamin is not a knave,\" Logan declared. Ethan stated, \"Harper is not a knave\". So who is a knight and who is a knave?", "names": ["Zoey", "Oliver", "Alexander", "Benjamin", "Evelyn", "Harper", "Logan", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true, true, true], "solution_text": "Zoey is a knight, Oliver is a knave, Alexander is a knave, Benjamin is a knight, Evelyn is a knight, Harper is a knight, Logan is a knight, and Ethan is a knight.", "solution_text_format": "(1) Zoey is a knight\n(2) Oliver is a knave\n(3) Alexander is a knave\n(4) Benjamin is a knight\n(5) Evelyn is a knight\n(6) Harper is a knight\n(7) Logan is a knight\n(8) Ethan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Zoey is a knight. No contradiction is found in their claim that Ethan is a knight or Oliver is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Harper is not a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Evelyn is a knight if and only if Alexander is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Logan is not a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Benjamin is not a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Evelyn is a knave or Harper is a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave or Logan is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Evelyn is a knave or Logan is a knave.", "Oliver cannot be a knight, because this would contradict the claim of their own that Alexander is not a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Alexander is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 7), ('telling-truth', 1)), ('not', ('lying', 2)), ('or', ('lying', 4), ('lying', 6)), ('or', ('lying', 4), ('telling-truth', 5)), ('not', ('lying', 6)), ('<=>', ('telling-truth', 4), ('lying', 2)), ('not', ('lying', 3)), ('not', ('lying', 5)))", "index": 983}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Grace, Mia, Chloe, William, Liam, Sebastian, Charlotte, and Henry. Grace noted, \"Henry is a knave\". \"Liam is a knave,\" Mia claimed. Chloe said that Mia is a knight. \"Henry is a knight if and only if Henry is a knave\" - William. Liam was heard saying, \"Grace is a knight\". In a statement by Sebastian: \"Grace is not a knight\". According to Charlotte, \"If Liam is a knight then Grace is a knight\". Henry noted, \"William is a knave or Grace is a knave\". So who is a knight and who is a knave?", "names": ["Grace", "Mia", "Chloe", "William", "Liam", "Sebastian", "Charlotte", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true, true, true], "solution_text": "Grace is a knave, Mia is a knight, Chloe is a knight, William is a knave, Liam is a knave, Sebastian is a knight, Charlotte is a knight, and Henry is a knight.", "solution_text_format": "(1) Grace is a knave\n(2) Mia is a knight\n(3) Chloe is a knight\n(4) William is a knave\n(5) Liam is a knave\n(6) Sebastian is a knight\n(7) Charlotte is a knight\n(8) Henry is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of Grace that Henry is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that William is a knave or Grace is a knave.", "William cannot be a knight, because this would contradict the claim of their own that Henry is a knight if and only if Henry is a knave.", "William cannot be a knave, because this would contradict the false claim of Henry that William is a knave or Grace is a knave.", "We have exhausted all possibilities for William and Henry, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Henry is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that William is a knave or Grace is a knave.", "William cannot be a knight, because this would contradict the claim of their own that Henry is a knight if and only if Henry is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Henry is a knight if and only if Henry is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of Mia that Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Grace is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Mia is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Grace is not a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Liam is a knight then Grace is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 7), ('lying', 4), ('telling-truth', 1), ('<=>', ('telling-truth', 7), ('lying', 7)), ('telling-truth', 0), ('not', ('telling-truth', 0)), ('->', ('telling-truth', 4), ('telling-truth', 0)), ('or', ('lying', 3), ('lying', 0)))", "index": 984}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Henry, Emma, Michael, Ella, Logan, Sebastian, Sophia, and Daniel. Henry noted, \"If Sebastian is a knight then Ella is a knight\". \"Michael is a knave if and only if Henry is a knave,\" Emma mentioned. \"Daniel is a knave or Emma is a knave,\" Michael mentioned. Ella remarked, \"Sophia is a knight or Daniel is a knight\". \"If Daniel is a knave then Ella is a knight,\" Logan mentioned. According to Sebastian, \"If Logan is a knight then Sophia is a knight\". Sophia noted, \"Emma is a knave if and only if Logan is a knight\". Daniel stated, \"Ella is a knight or Sebastian is a knave\". So who is a knight and who is a knave?", "names": ["Henry", "Emma", "Michael", "Ella", "Logan", "Sebastian", "Sophia", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, true, false, false], "solution_text": "Henry is a knave, Emma is a knave, Michael is a knight, Ella is a knave, Logan is a knave, Sebastian is a knight, Sophia is a knave, and Daniel is a knave.", "solution_text_format": "(1) Henry is a knave\n(2) Emma is a knave\n(3) Michael is a knight\n(4) Ella is a knave\n(5) Logan is a knave\n(6) Sebastian is a knight\n(7) Sophia is a knave\n(8) Daniel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that If Sebastian is a knight then Ella is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Logan is a knight then Sophia is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that If Daniel is a knave then Ella is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Ella is a knight or Sebastian is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Sophia is a knight or Daniel is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Emma is a knave if and only if Logan is a knight.", "Emma cannot be a knight, because this would contradict the claim of Sophia that Emma is a knave if and only if Logan is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Michael is a knave if and only if Henry is a knave.", "Michael cannot be a knight, because this would contradict the false claim of Emma that Michael is a knave if and only if Henry is a knave.", "Michael cannot be a knave, because this would contradict the false claim of their own that Daniel is a knave or Emma is a knave.", "We have exhausted all possibilities for Michael and Emma, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the claim of Sebastian that If Logan is a knight then Sophia is a knight.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the claim of Henry that If Sebastian is a knight then Ella is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Ella is a knight or Sebastian is a knave.", "Ella cannot be a knight, because this would contradict the false claim of Daniel that Ella is a knight or Sebastian is a knave.", "Ella cannot be a knave, because this would contradict the claim of Henry that If Sebastian is a knight then Ella is a knight.", "We have exhausted all possibilities for Ella and Daniel, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that If Daniel is a knave then Ella is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of Logan that If Daniel is a knave then Ella is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Ella is a knight or Sebastian is a knave.", "Ella cannot be a knight, because this would contradict the false claim of Logan that If Daniel is a knave then Ella is a knight.", "Ella cannot be a knave, because this would contradict the claim of Henry that If Sebastian is a knight then Ella is a knight.", "We have exhausted all possibilities for Ella, Daniel, and Logan, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that If Logan is a knight then Sophia is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that If Daniel is a knave then Ella is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Ella is a knight or Sebastian is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Sophia is a knight or Daniel is a knight.", "Sophia cannot be a knight, because this would contradict the false claim of Sebastian that If Logan is a knight then Sophia is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Emma is a knave if and only if Logan is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Michael is a knave if and only if Henry is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Daniel is a knave or Emma is a knave.", "Michael cannot be a knave, because this would contradict the claim of Emma that Michael is a knave if and only if Henry is a knave.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Emma.", "Emma cannot be a knave, because this would contradict the false claim of Sophia that Emma is a knave if and only if Logan is a knight.", "We have exhausted all possibilities for Emma and Sophia, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the false claim of their own that Sophia is a knight or Daniel is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the false claim of their own that Ella is a knight or Sebastian is a knave.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the false claim of Sebastian that If Logan is a knight then Sophia is a knight.", "We have exhausted all possibilities for Logan and Sebastian, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that If Sebastian is a knight then Ella is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Logan is a knight then Sophia is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that If Daniel is a knave then Ella is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Ella is a knight or Sebastian is a knave.", "Ella cannot be a knight, because this would contradict the false claim of Henry that If Sebastian is a knight then Ella is a knight.", "Ella cannot be a knave, because this would contradict the false claim of their own that Sophia is a knight or Daniel is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Ella is a knight or Sebastian is a knave.", "Ella cannot be a knight, because this would contradict the false claim of Henry that If Sebastian is a knight then Ella is a knight.", "Ella cannot be a knave, because this would contradict the claim of Logan that If Daniel is a knave then Ella is a knight.", "We have exhausted all possibilities for Ella and Daniel, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that If Daniel is a knave then Ella is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of Logan that If Daniel is a knave then Ella is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Ella is a knight or Sebastian is a knave.", "Ella cannot be a knight, because this would contradict the false claim of Henry that If Sebastian is a knight then Ella is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Sophia is a knight or Daniel is a knight.", "Sophia cannot be a knight, because this would contradict the false claim of Ella that Sophia is a knight or Daniel is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Emma is a knave if and only if Logan is a knight.", "Emma cannot be a knight, because this would contradict the false claim of Sophia that Emma is a knave if and only if Logan is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Michael is a knave if and only if Henry is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Daniel is a knave or Emma is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 5), ('telling-truth', 3)), ('<=>', ('lying', 2), ('lying', 0)), ('or', ('lying', 7), ('lying', 1)), ('or', ('telling-truth', 6), ('telling-truth', 7)), ('->', ('lying', 7), ('telling-truth', 3)), ('->', ('telling-truth', 4), ('telling-truth', 6)), ('<=>', ('lying', 1), ('telling-truth', 4)), ('or', ('telling-truth', 3), ('lying', 5)))", "index": 985}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sebastian, Chloe, Scarlett, Matthew, Luke, Jacob, Olivia, and Lucas. According to Sebastian, \"Scarlett is a knight if and only if Luke is a knight\". According to Chloe, \"Sebastian is a knight or Sebastian is a knave\". In Scarlett's words: \"Luke is a knight and Lucas is a knight\". According to Matthew, \"Lucas is a knave if and only if Scarlett is a knave\". As Luke put it, \"Chloe is not a knight\". Jacob said, \"Chloe is a knight or Olivia is a knave.\" \"Luke is a knight or Lucas is a knight,\" Olivia claimed. As Lucas put it, \"Scarlett is a knave and Chloe is a knight\". So who is a knight and who is a knave?", "names": ["Sebastian", "Chloe", "Scarlett", "Matthew", "Luke", "Jacob", "Olivia", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, true, true, true], "solution_text": "Sebastian is a knight, Chloe is a knight, Scarlett is a knave, Matthew is a knave, Luke is a knave, Jacob is a knight, Olivia is a knight, and Lucas is a knight.", "solution_text_format": "(1) Sebastian is a knight\n(2) Chloe is a knight\n(3) Scarlett is a knave\n(4) Matthew is a knave\n(5) Luke is a knave\n(6) Jacob is a knight\n(7) Olivia is a knight\n(8) Lucas is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that Scarlett is a knight if and only if Luke is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Luke is a knight and Lucas is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Chloe is not a knight.", "Chloe cannot be a knight, because this would contradict the claim of Luke that Chloe is not a knight.", "Chloe cannot be a knave, because this would contradict the false claim of their own that Sebastian is a knight or Sebastian is a knave.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the claim of Sebastian that Scarlett is a knight if and only if Luke is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Luke is a knight and Lucas is a knight.", "Luke cannot be a knight, because this would contradict the claim of Sebastian that Scarlett is a knight if and only if Luke is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Chloe is not a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Sebastian is a knight or Sebastian is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Scarlett is a knave and Chloe is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Lucas is a knave if and only if Scarlett is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Lucas is a knave if and only if Scarlett is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Chloe is a knight or Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Luke is a knight or Lucas is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('telling-truth', 4)), ('or', ('telling-truth', 0), ('lying', 0)), ('and', ('telling-truth', 4), ('telling-truth', 7)), ('<=>', ('lying', 7), ('lying', 2)), ('not', ('telling-truth', 1)), ('or', ('telling-truth', 1), ('lying', 6)), ('or', ('telling-truth', 4), ('telling-truth', 7)), ('and', ('lying', 2), ('telling-truth', 1)))", "index": 986}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Harper, Emma, Chloe, Amelia, Luke, Jacob, Zoey, and Joseph. Harper was heard saying, \"If Harper is a knight then Emma is a knave\". Emma said that Joseph is a knave. In a statement by Chloe: \"Zoey is not a knave\". \"Chloe is a knave,\" Amelia declared. Luke asserted: \"Harper is a knight or Luke is a knight\". \"Zoey is a knight if and only if Amelia is a knight\" - Jacob. Zoey noted, \"If Chloe is a knave then Zoey is a knight\". Joseph remarked, \"Amelia is not a knight\". So who is a knight and who is a knave?", "names": ["Harper", "Emma", "Chloe", "Amelia", "Luke", "Jacob", "Zoey", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, false, true, true], "solution_text": "Harper is a knight, Emma is a knave, Chloe is a knight, Amelia is a knave, Luke is a knight, Jacob is a knave, Zoey is a knight, and Joseph is a knight.", "solution_text_format": "(1) Harper is a knight\n(2) Emma is a knave\n(3) Chloe is a knight\n(4) Amelia is a knave\n(5) Luke is a knight\n(6) Jacob is a knave\n(7) Zoey is a knight\n(8) Joseph is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that If Harper is a knight then Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of Harper that If Harper is a knight then Emma is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Joseph is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Amelia is not a knight.", "Amelia cannot be a knight, because this would contradict the claim of Joseph that Amelia is not a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Chloe is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Zoey is not a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that If Chloe is a knave then Zoey is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Harper is a knight or Luke is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Zoey is a knight if and only if Amelia is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Zoey is a knight if and only if Amelia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 0), ('lying', 1)), ('lying', 7), ('not', ('lying', 6)), ('lying', 2), ('or', ('telling-truth', 0), ('telling-truth', 4)), ('<=>', ('telling-truth', 6), ('telling-truth', 3)), ('->', ('lying', 2), ('telling-truth', 6)), ('not', ('telling-truth', 3)))", "index": 987}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Charlotte, Luke, Owen, Amelia, Mason, Lucas, Daniel, and Olivia. Charlotte was heard saying, \"Amelia is a knave and Amelia is a knight\". \"Daniel is a knave if and only if Amelia is a knight,\" Luke mentioned. Owen noted, \"Amelia is not a knave\". Amelia commented, \"Daniel is not a knight\". As Mason put it, \"Owen is a knight\". Lucas stated, \"Amelia is a knave or Owen is a knight\". Daniel asserted: \"Luke is a knave\". \"Owen is a knight or Amelia is a knight,\" Olivia declared. So who is a knight and who is a knave?", "names": ["Charlotte", "Luke", "Owen", "Amelia", "Mason", "Lucas", "Daniel", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true, false, true], "solution_text": "Charlotte is a knave, Luke is a knight, Owen is a knight, Amelia is a knight, Mason is a knight, Lucas is a knight, Daniel is a knave, and Olivia is a knight.", "solution_text_format": "(1) Charlotte is a knave\n(2) Luke is a knight\n(3) Owen is a knight\n(4) Amelia is a knight\n(5) Mason is a knight\n(6) Lucas is a knight\n(7) Daniel is a knave\n(8) Olivia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Charlotte cannot be a knight, because this would contradict the claim of their own that Amelia is a knave and Amelia is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Amelia is a knave and Amelia is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Daniel is not a knight.", "Daniel cannot be a knight, because this would contradict the claim of Amelia that Daniel is not a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Luke is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Daniel is a knave if and only if Amelia is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Amelia is not a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Owen is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Amelia is a knave or Owen is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Owen is a knight or Amelia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('telling-truth', 3)), ('<=>', ('lying', 6), ('telling-truth', 3)), ('not', ('lying', 3)), ('not', ('telling-truth', 6)), ('telling-truth', 2), ('or', ('lying', 3), ('telling-truth', 2)), ('lying', 1), ('or', ('telling-truth', 2), ('telling-truth', 3)))", "index": 988}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Abigail, Avery, William, Chloe, Zoey, Matthew, Aiden, and Sebastian. Abigail expressed that Zoey is a knight or Abigail is a knight. As Avery put it, \"Chloe is a knave or Sebastian is a knave\". In William's words: \"Sebastian is not a knight\". \"Zoey is a knight,\" Chloe mentioned. In Zoey's words: \"If Sebastian is a knight then Abigail is a knave\". As Matthew put it, \"If Aiden is a knave then Abigail is a knave\". \"Zoey is a knave or Aiden is a knight,\" Aiden claimed. Sebastian was heard saying, \"William is a knight or Zoey is a knave\". So who is a knight and who is a knave?", "names": ["Abigail", "Avery", "William", "Chloe", "Zoey", "Matthew", "Aiden", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, true, true, true], "solution_text": "Abigail is a knight, Avery is a knight, William is a knave, Chloe is a knave, Zoey is a knave, Matthew is a knight, Aiden is a knight, and Sebastian is a knight.", "solution_text_format": "(1) Abigail is a knight\n(2) Avery is a knight\n(3) William is a knave\n(4) Chloe is a knave\n(5) Zoey is a knave\n(6) Matthew is a knight\n(7) Aiden is a knight\n(8) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Zoey is a knight or Abigail is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that If Sebastian is a knight then Abigail is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Zoey that If Sebastian is a knight then Abigail is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that William is a knight or Zoey is a knave.", "William cannot be a knight, because this would contradict the false claim of Sebastian that William is a knight or Zoey is a knave.", "William cannot be a knave, because this would contradict the false claim of their own that Sebastian is not a knight.", "We have exhausted all possibilities for William and Sebastian, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that If Sebastian is a knight then Abigail is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that William is a knight or Zoey is a knave.", "William cannot be a knight, because this would contradict the claim of their own that Sebastian is not a knight.", "Assume William is a knave. No contradiction is found in their false claim that Sebastian is not a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Chloe is a knave or Sebastian is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Avery that Chloe is a knave or Sebastian is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Zoey is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that If Aiden is a knave then Abigail is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Zoey is a knave or Aiden is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('telling-truth', 0)), ('or', ('lying', 3), ('lying', 7)), ('not', ('telling-truth', 7)), ('telling-truth', 4), ('->', ('telling-truth', 7), ('lying', 0)), ('->', ('lying', 6), ('lying', 0)), ('or', ('lying', 4), ('telling-truth', 6)), ('or', ('telling-truth', 2), ('lying', 4)))", "index": 989}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Luke, Sebastian, Sophia, Chloe, Victoria, Emma, Elizabeth, and Penelope. \"Sophia is a knight or Chloe is a knight,\" Luke mentioned. Sebastian told you that Luke is a knave or Penelope is a knight. Sophia noted, \"Sebastian is not a knight\". According to Chloe, \"If Elizabeth is a knight then Luke is a knave\". \"Emma is a knight\" - Victoria. In Emma's words: \"Victoria is a knight\". Elizabeth stated, \"If Penelope is a knight then Chloe is a knight\". In a statement by Penelope: \"Victoria is a knight or Sebastian is a knight\". So who is a knight and who is a knave?", "names": ["Luke", "Sebastian", "Sophia", "Chloe", "Victoria", "Emma", "Elizabeth", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, false, true, false], "solution_text": "Luke is a knight, Sebastian is a knave, Sophia is a knight, Chloe is a knave, Victoria is a knave, Emma is a knave, Elizabeth is a knight, and Penelope is a knave.", "solution_text_format": "(1) Luke is a knight\n(2) Sebastian is a knave\n(3) Sophia is a knight\n(4) Chloe is a knave\n(5) Victoria is a knave\n(6) Emma is a knave\n(7) Elizabeth is a knight\n(8) Penelope is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Sophia is a knight or Chloe is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Sebastian is not a knight.", "Sebastian cannot be a knight, because this would contradict the claim of Sophia that Sebastian is not a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Luke is a knave or Penelope is a knight.", "Penelope cannot be a knight, because this would contradict the false claim of Sebastian that Luke is a knave or Penelope is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Victoria is a knight or Sebastian is a knight.", "Victoria cannot be a knight, because this would contradict the false claim of Penelope that Victoria is a knight or Sebastian is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Emma is a knight.", "Emma cannot be a knight, because this would contradict the false claim of Victoria that Emma is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Victoria is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that If Elizabeth is a knight then Luke is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of Chloe that If Elizabeth is a knight then Luke is a knave.", "Elizabeth cannot be a knave, because this would contradict the false claim of their own that If Penelope is a knight then Chloe is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that If Elizabeth is a knight then Luke is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Penelope is a knight then Chloe is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('telling-truth', 3)), ('or', ('lying', 0), ('telling-truth', 7)), ('not', ('telling-truth', 1)), ('->', ('telling-truth', 6), ('lying', 0)), ('telling-truth', 5), ('telling-truth', 4), ('->', ('telling-truth', 7), ('telling-truth', 3)), ('or', ('telling-truth', 4), ('telling-truth', 1)))", "index": 990}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jacob, Jack, Ava, Grace, Noah, James, Olivia, and David. Jacob was heard saying, \"Noah is not a knight\". As Jack put it, \"Jacob is not a knight\". In Ava's words: \"Noah is not a knight\". Grace commented, \"David is not a knight\". Noah told you that James is a knight if and only if Olivia is a knight. \"Jack is a knight and Noah is a knight\" - James. Olivia commented, \"If Jack is a knave then James is a knight\". David asserted: \"Olivia is not a knight\". So who is a knight and who is a knave?", "names": ["Jacob", "Jack", "Ava", "Grace", "Noah", "James", "Olivia", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true, true, false], "solution_text": "Jacob is a knave, Jack is a knight, Ava is a knave, Grace is a knight, Noah is a knight, James is a knight, Olivia is a knight, and David is a knave.", "solution_text_format": "(1) Jacob is a knave\n(2) Jack is a knight\n(3) Ava is a knave\n(4) Grace is a knight\n(5) Noah is a knight\n(6) James is a knight\n(7) Olivia is a knight\n(8) David is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that Noah is not a knight.", "Noah cannot be a knight, because this would contradict the claim of Jacob that Noah is not a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that James is a knight if and only if Olivia is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Jack is a knight and Noah is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Jack is a knight and Noah is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Jacob is not a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Jacob is not a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that If Jack is a knave then James is a knight.", "Olivia cannot be a knave, because this would contradict the false claim of Noah that James is a knight if and only if Olivia is a knight.", "We have exhausted all possibilities for Olivia, Jack, James, and Noah, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Noah is not a knight.", "Assume Noah is a knight. No contradiction is found in their claim that James is a knight if and only if Olivia is a knight.", "Assume James is a knight. No contradiction is found in their claim that Jack is a knight and Noah is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Jacob is not a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that If Jack is a knave then James is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Noah is not a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Noah is not a knight.", "Assume Grace is a knight. No contradiction is found in their claim that David is not a knight.", "David cannot be a knight, because this would contradict the claim of Grace that David is not a knight.", "Assume David is a knave. No contradiction is found in their false claim that Olivia is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 4)), ('not', ('telling-truth', 0)), ('not', ('telling-truth', 4)), ('not', ('telling-truth', 7)), ('<=>', ('telling-truth', 5), ('telling-truth', 6)), ('and', ('telling-truth', 1), ('telling-truth', 4)), ('->', ('lying', 1), ('telling-truth', 5)), ('not', ('telling-truth', 6)))", "index": 991}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Alexander, Emily, David, Grace, Oliver, Ava, Owen, and Sebastian. According to Alexander, \"Emily is a knave and David is a knight\". According to Emily, \"Grace is not a knight\". \"Grace is not a knight,\" David mentioned. Grace remarked, \"Oliver is a knight\". \"If Sebastian is a knight then David is a knave,\" Oliver mentioned. Ava expressed that Grace is a knight or Oliver is a knave. \"Oliver is a knight or Grace is a knave\" - Owen. \"Emily is a knave and Grace is a knight\" - Sebastian. So who is a knight and who is a knave?", "names": ["Alexander", "Emily", "David", "Grace", "Oliver", "Ava", "Owen", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true, true, true], "solution_text": "Alexander is a knave, Emily is a knave, David is a knave, Grace is a knight, Oliver is a knight, Ava is a knight, Owen is a knight, and Sebastian is a knight.", "solution_text_format": "(1) Alexander is a knave\n(2) Emily is a knave\n(3) David is a knave\n(4) Grace is a knight\n(5) Oliver is a knight\n(6) Ava is a knight\n(7) Owen is a knight\n(8) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that Emily is a knave and David is a knight.", "Emily cannot be a knight, because this would contradict the claim of Alexander that Emily is a knave and David is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Grace is not a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Oliver is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that If Sebastian is a knight then David is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Emily is a knave and Grace is a knight.", "David cannot be a knight, because this would contradict the claim of their own that Grace is not a knight.", "David cannot be a knave, because this would contradict the claim of Alexander that Emily is a knave and David is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the false claim of their own that Emily is a knave and Grace is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the claim of Grace that Oliver is a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Grace.", "Grace cannot be a knave, because this would contradict the false claim of Emily that Grace is not a knight.", "We have exhausted all possibilities for Grace and Emily, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Emily is a knave and David is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Grace is not a knight.", "Grace cannot be a knight, because this would contradict the claim of Emily that Grace is not a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Oliver is a knight.", "Oliver cannot be a knight, because this would contradict the false claim of Grace that Oliver is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that If Sebastian is a knight then David is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Emily is a knave and Grace is a knight.", "Sebastian cannot be a knave, because this would contradict the false claim of Oliver that If Sebastian is a knight then David is a knave.", "We have exhausted all possibilities for Sebastian, Oliver, and Grace, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Grace is not a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Oliver is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that If Sebastian is a knight then David is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Emily is a knave and Grace is a knight.", "David cannot be a knight, because this would contradict the false claim of Alexander that Emily is a knave and David is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Grace is not a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Grace is a knight or Oliver is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Oliver is a knight or Grace is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 1), ('telling-truth', 2)), ('not', ('telling-truth', 3)), ('not', ('telling-truth', 3)), ('telling-truth', 4), ('->', ('telling-truth', 7), ('lying', 2)), ('or', ('telling-truth', 3), ('lying', 4)), ('or', ('telling-truth', 4), ('lying', 3)), ('and', ('lying', 1), ('telling-truth', 3)))", "index": 992}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mason, Jackson, Emma, Elizabeth, Jack, Avery, Harper, and Aria. \"Jack is a knave or Avery is a knave,\" Mason declared. Jackson noted, \"Avery is a knave or Jack is a knight\". Emma stated, \"Elizabeth is a knight and Aria is a knight\". In a statement by Elizabeth: \"Aria is not a knave\". Jack said, \"Emma is a knight and Emma is a knave.\" According to Avery, \"Avery is a knight and Aria is a knave\". According to Harper, \"Elizabeth is a knave and Jack is a knave\". In Aria's words: \"If Harper is a knave then Aria is a knight\". So who is a knight and who is a knave?", "names": ["Mason", "Jackson", "Emma", "Elizabeth", "Jack", "Avery", "Harper", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false, false, true], "solution_text": "Mason is a knight, Jackson is a knight, Emma is a knight, Elizabeth is a knight, Jack is a knave, Avery is a knave, Harper is a knave, and Aria is a knight.", "solution_text_format": "(1) Mason is a knight\n(2) Jackson is a knight\n(3) Emma is a knight\n(4) Elizabeth is a knight\n(5) Jack is a knave\n(6) Avery is a knave\n(7) Harper is a knave\n(8) Aria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Jack is a knave or Avery is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Emma is a knight and Emma is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Emma is a knight and Emma is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Elizabeth is a knight and Aria is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Aria is not a knave.", "Assume Aria is a knight. No contradiction is found in their claim that If Harper is a knave then Aria is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave and Jack is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Elizabeth is a knave and Jack is a knave.", "Avery cannot be a knight, because this would contradict the claim of their own that Avery is a knight and Aria is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Avery is a knight and Aria is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Avery is a knave or Jack is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 4), ('lying', 5)), ('or', ('lying', 5), ('telling-truth', 4)), ('and', ('telling-truth', 3), ('telling-truth', 7)), ('not', ('lying', 7)), ('and', ('telling-truth', 2), ('lying', 2)), ('and', ('telling-truth', 5), ('lying', 7)), ('and', ('lying', 3), ('lying', 4)), ('->', ('lying', 6), ('telling-truth', 7)))", "index": 993}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sebastian, Michael, Benjamin, Henry, Aria, Riley, Aiden, and Grace. In a statement by Sebastian: \"If Benjamin is a knight then Henry is a knight\". As Michael put it, \"Aria is not a knave\". Benjamin told you that Aiden is not a knight. Henry said, \"Grace is not a knave.\" Aria stated, \"If Aria is a knight then Sebastian is a knight\". Riley expressed that Sebastian is a knight if and only if Aria is a knight. \"Aria is a knight or Sebastian is a knight\" - Aiden. In a statement by Grace: \"Michael is a knight if and only if Aria is a knave\". So who is a knight and who is a knave?", "names": ["Sebastian", "Michael", "Benjamin", "Henry", "Aria", "Riley", "Aiden", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true, true, false], "solution_text": "Sebastian is a knight, Michael is a knight, Benjamin is a knave, Henry is a knave, Aria is a knight, Riley is a knight, Aiden is a knight, and Grace is a knave.", "solution_text_format": "(1) Sebastian is a knight\n(2) Michael is a knight\n(3) Benjamin is a knave\n(4) Henry is a knave\n(5) Aria is a knight\n(6) Riley is a knight\n(7) Aiden is a knight\n(8) Grace is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that If Benjamin is a knight then Henry is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Aiden is not a knight.", "Aiden cannot be a knight, because this would contradict the claim of Benjamin that Aiden is not a knight.", "Aiden cannot be a knave, because this would contradict the false claim of their own that Aria is a knight or Sebastian is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Aiden is not a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Aria is a knight or Sebastian is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that If Aria is a knight then Sebastian is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Grace is not a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Michael is a knight if and only if Aria is a knave.", "Michael cannot be a knight, because this would contradict the claim of Grace that Michael is a knight if and only if Aria is a knave.", "Michael cannot be a knave, because this would contradict the false claim of their own that Aria is not a knave.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Grace.", "Grace cannot be a knave, because this would contradict the claim of Henry that Grace is not a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Grace is not a knave.", "Grace cannot be a knight, because this would contradict the false claim of Henry that Grace is not a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Michael is a knight if and only if Aria is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Aria is not a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Sebastian is a knight if and only if Aria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('telling-truth', 3)), ('not', ('lying', 4)), ('not', ('telling-truth', 6)), ('not', ('lying', 7)), ('->', ('telling-truth', 4), ('telling-truth', 0)), ('<=>', ('telling-truth', 0), ('telling-truth', 4)), ('or', ('telling-truth', 4), ('telling-truth', 0)), ('<=>', ('telling-truth', 1), ('lying', 4)))", "index": 994}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emma, Sofia, Noah, Grace, Henry, Avery, Jacob, and Riley. Emma expressed that Sofia is a knight or Grace is a knight. Sofia said that Emma is a knight. Noah remarked, \"Emma is not a knight\". \"Jacob is a knight\" - Grace. Henry was heard saying, \"If Emma is a knight then Grace is a knave\". As Avery put it, \"Emma is not a knight\". Jacob told you that Riley is a knave if and only if Grace is a knight. Riley commented, \"If Noah is a knight then Noah is a knave\". So who is a knight and who is a knave?", "names": ["Emma", "Sofia", "Noah", "Grace", "Henry", "Avery", "Jacob", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true, false, false], "solution_text": "Emma is a knave, Sofia is a knave, Noah is a knight, Grace is a knave, Henry is a knight, Avery is a knight, Jacob is a knave, and Riley is a knave.", "solution_text_format": "(1) Emma is a knave\n(2) Sofia is a knave\n(3) Noah is a knight\n(4) Grace is a knave\n(5) Henry is a knight\n(6) Avery is a knight\n(7) Jacob is a knave\n(8) Riley is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Sofia is a knight or Grace is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Emma is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Riley is a knave if and only if Grace is a knight.", "Riley cannot be a knight, because this would contradict the claim of Jacob that Riley is a knave if and only if Grace is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that If Noah is a knight then Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of their own that Emma is not a knight.", "Noah cannot be a knave, because this would contradict the false claim of Riley that If Noah is a knight then Noah is a knave.", "We have exhausted all possibilities for Noah and Riley, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the claim of Grace that Jacob is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Jacob is a knight.", "Jacob cannot be a knight, because this would contradict the false claim of Grace that Jacob is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Riley is a knave if and only if Grace is a knight.", "Riley cannot be a knight, because this would contradict the false claim of Jacob that Riley is a knave if and only if Grace is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that If Noah is a knight then Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of their own that Emma is not a knight.", "Noah cannot be a knave, because this would contradict the false claim of Riley that If Noah is a knight then Noah is a knave.", "We have exhausted all possibilities for Noah, Riley, Jacob, and Grace, so let us go back and reconsider Sofia.", "Sofia cannot be a knave, because this would contradict the false claim of their own that Emma is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Sofia is a knight or Grace is a knight.", "Sofia cannot be a knight, because this would contradict the false claim of Emma that Sofia is a knight or Grace is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Emma is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Emma that Sofia is a knight or Grace is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Jacob is a knight.", "Jacob cannot be a knight, because this would contradict the false claim of Grace that Jacob is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Riley is a knave if and only if Grace is a knight.", "Riley cannot be a knight, because this would contradict the false claim of Jacob that Riley is a knave if and only if Grace is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that If Noah is a knight then Noah is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Emma is not a knight.", "Assume Henry is a knight. No contradiction is found in their claim that If Emma is a knight then Grace is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Emma is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('telling-truth', 3)), ('telling-truth', 0), ('not', ('telling-truth', 0)), ('telling-truth', 6), ('->', ('telling-truth', 0), ('lying', 3)), ('not', ('telling-truth', 0)), ('<=>', ('lying', 7), ('telling-truth', 3)), ('->', ('telling-truth', 2), ('lying', 2)))", "index": 995}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Penelope, Owen, Ava, Ethan, Charlotte, Avery, Zoey, and Aria. Penelope commented, \"Avery is not a knave\". Owen said that Penelope is a knight or Aria is a knight. In a statement by Ava: \"Charlotte is not a knave\". Ethan told you that Zoey is a knave. As Charlotte put it, \"Penelope is a knave or Aria is a knave\". \"Penelope is a knave or Avery is a knight,\" Avery mentioned. Zoey remarked, \"If Penelope is a knave then Ava is a knave\". \"Charlotte is a knight or Penelope is a knight,\" Aria claimed. So who is a knight and who is a knave?", "names": ["Penelope", "Owen", "Ava", "Ethan", "Charlotte", "Avery", "Zoey", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, true, true, true], "solution_text": "Penelope is a knight, Owen is a knight, Ava is a knave, Ethan is a knave, Charlotte is a knave, Avery is a knight, Zoey is a knight, and Aria is a knight.", "solution_text_format": "(1) Penelope is a knight\n(2) Owen is a knight\n(3) Ava is a knave\n(4) Ethan is a knave\n(5) Charlotte is a knave\n(6) Avery is a knight\n(7) Zoey is a knight\n(8) Aria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that Avery is not a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Penelope is a knave or Avery is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Penelope is a knight or Aria is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Charlotte is a knight or Penelope is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Penelope is a knave or Aria is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Penelope is a knave or Aria is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Charlotte is not a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Charlotte is not a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Ethan that Zoey is a knave.", "Zoey cannot be a knave, because this would contradict the false claim of their own that If Penelope is a knave then Ava is a knave.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Zoey is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that If Penelope is a knave then Ava is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 5)), ('or', ('telling-truth', 0), ('telling-truth', 7)), ('not', ('lying', 4)), ('lying', 6), ('or', ('lying', 0), ('lying', 7)), ('or', ('lying', 0), ('telling-truth', 5)), ('->', ('lying', 0), ('lying', 2)), ('or', ('telling-truth', 4), ('telling-truth', 0)))", "index": 996}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Riley, Aria, Aurora, Ella, Luke, Penelope, Michael, and Logan. Riley asserted: \"Penelope is not a knave\". According to Aria, \"Ella is a knight\". Aurora remarked, \"Penelope is a knight\". Ella remarked, \"Riley is a knave and Luke is a knight\". Luke said that Ella is not a knave. As Penelope put it, \"If Michael is a knight then Ella is a knight\". Michael said, \"Aria is a knight and Luke is a knight.\" According to Logan, \"Logan is a knight or Riley is a knight\". So who is a knight and who is a knave?", "names": ["Riley", "Aria", "Aurora", "Ella", "Luke", "Penelope", "Michael", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true, false, true], "solution_text": "Riley is a knight, Aria is a knave, Aurora is a knight, Ella is a knave, Luke is a knave, Penelope is a knight, Michael is a knave, and Logan is a knight.", "solution_text_format": "(1) Riley is a knight\n(2) Aria is a knave\n(3) Aurora is a knight\n(4) Ella is a knave\n(5) Luke is a knave\n(6) Penelope is a knight\n(7) Michael is a knave\n(8) Logan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Penelope is not a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that If Michael is a knight then Ella is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Aria is a knight and Luke is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Ella is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Riley is a knave and Luke is a knight.", "Ella cannot be a knave, because this would contradict the claim of Aria that Ella is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Aria.", "Aria cannot be a knave, because this would contradict the claim of Michael that Aria is a knight and Luke is a knight.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Aria is a knight and Luke is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Ella is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Riley is a knave and Luke is a knight.", "Ella cannot be a knave, because this would contradict the claim of Aria that Ella is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Ella is a knight.", "Ella cannot be a knight, because this would contradict the false claim of Aria that Ella is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Riley is a knave and Luke is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Ella is not a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Ella is not a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Penelope is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Logan is a knight or Riley is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 5)), ('telling-truth', 3), ('telling-truth', 5), ('and', ('lying', 0), ('telling-truth', 4)), ('not', ('lying', 3)), ('->', ('telling-truth', 6), ('telling-truth', 3)), ('and', ('telling-truth', 1), ('telling-truth', 4)), ('or', ('telling-truth', 7), ('telling-truth', 0)))", "index": 997}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aiden, Jack, Sebastian, Aria, Mason, Victoria, Liam, and Joseph. According to Aiden, \"Sebastian is a knight or Victoria is a knave\". Jack noted, \"Victoria is a knight or Joseph is a knave\". Sebastian remarked, \"Joseph is a knave\". Aria said, \"Sebastian is not a knave.\" Mason commented, \"If Victoria is a knight then Aria is a knave\". Victoria said, \"Joseph is not a knave.\" Liam was heard saying, \"If Aiden is a knight then Sebastian is a knave\". Joseph told you that Aiden is a knave and Victoria is a knave. So who is a knight and who is a knave?", "names": ["Aiden", "Jack", "Sebastian", "Aria", "Mason", "Victoria", "Liam", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false, false, false], "solution_text": "Aiden is a knight, Jack is a knight, Sebastian is a knight, Aria is a knight, Mason is a knight, Victoria is a knave, Liam is a knave, and Joseph is a knave.", "solution_text_format": "(1) Aiden is a knight\n(2) Jack is a knight\n(3) Sebastian is a knight\n(4) Aria is a knight\n(5) Mason is a knight\n(6) Victoria is a knave\n(7) Liam is a knave\n(8) Joseph is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Sebastian is a knight or Victoria is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Sebastian that Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Aiden is a knave and Victoria is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that Joseph is not a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Joseph is not a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Victoria is a knight or Joseph is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Sebastian is not a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Victoria is a knight then Aria is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that If Aiden is a knight then Sebastian is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that If Aiden is a knight then Sebastian is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('lying', 5)), ('or', ('telling-truth', 5), ('lying', 7)), ('lying', 7), ('not', ('lying', 2)), ('->', ('telling-truth', 5), ('lying', 3)), ('not', ('lying', 7)), ('->', ('telling-truth', 0), ('lying', 2)), ('and', ('lying', 0), ('lying', 5)))", "index": 998}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Alexander, Sophia, Michael, Amelia, Benjamin, Lily, Joseph, and Ethan. Alexander told you that Ethan is not a knight. \"Alexander is a knight or Benjamin is a knave\" - Sophia. Michael asserted: \"Amelia is a knave if and only if Sophia is a knave\". Amelia asserted: \"Joseph is a knave and Ethan is a knight\". Benjamin told you that Michael is a knight. Lily remarked, \"If Michael is a knight then Benjamin is a knight\". Joseph was heard saying, \"Benjamin is a knave\". Ethan commented, \"Joseph is a knight\". So who is a knight and who is a knave?", "names": ["Alexander", "Sophia", "Michael", "Amelia", "Benjamin", "Lily", "Joseph", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, true, true, true], "solution_text": "Alexander is a knave, Sophia is a knight, Michael is a knave, Amelia is a knave, Benjamin is a knave, Lily is a knight, Joseph is a knight, and Ethan is a knight.", "solution_text_format": "(1) Alexander is a knave\n(2) Sophia is a knight\n(3) Michael is a knave\n(4) Amelia is a knave\n(5) Benjamin is a knave\n(6) Lily is a knight\n(7) Joseph is a knight\n(8) Ethan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that Ethan is not a knight.", "Ethan cannot be a knight, because this would contradict the claim of Alexander that Ethan is not a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of Ethan that Joseph is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Benjamin is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Michael is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Amelia is a knave if and only if Sophia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Joseph is a knave and Ethan is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Joseph is a knave and Ethan is a knight.", "Sophia cannot be a knight, because this would contradict the claim of Michael that Amelia is a knave if and only if Sophia is a knave.", "Sophia cannot be a knave, because this would contradict the false claim of their own that Alexander is a knight or Benjamin is a knave.", "We have exhausted all possibilities for Sophia and Amelia, so let us go back and reconsider Michael.", "Michael cannot be a knave, because this would contradict the claim of Benjamin that Michael is a knight.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the false claim of Joseph that Benjamin is a knave.", "We have exhausted all possibilities for Benjamin, Joseph, and Ethan, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Ethan is not a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Joseph that Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Michael is a knight.", "Michael cannot be a knight, because this would contradict the false claim of Benjamin that Michael is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Amelia is a knave if and only if Sophia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Joseph is a knave and Ethan is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Joseph is a knave and Ethan is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Alexander is a knight or Benjamin is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that If Michael is a knight then Benjamin is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 7)), ('or', ('telling-truth', 0), ('lying', 4)), ('<=>', ('lying', 3), ('lying', 1)), ('and', ('lying', 6), ('telling-truth', 7)), ('telling-truth', 2), ('->', ('telling-truth', 2), ('telling-truth', 4)), ('lying', 4), ('telling-truth', 6))", "index": 999}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Luke, Avery, Benjamin, Harper, Penelope, Olivia, Ella, and Daniel. Luke commented, \"Benjamin is a knave\". Avery stated, \"If Penelope is a knave then Avery is a knight\". Benjamin told you that Olivia is a knight and Avery is a knight. Harper said that Ella is a knight and Luke is a knave. Penelope told you that Daniel is a knave or Benjamin is a knave. \"Penelope is a knight and Harper is a knave\" - Olivia. \"Olivia is a knave,\" Ella declared. In a statement by Daniel: \"If Harper is a knave then Penelope is a knave\". So who is a knight and who is a knave?", "names": ["Luke", "Avery", "Benjamin", "Harper", "Penelope", "Olivia", "Ella", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true, false, false], "solution_text": "Luke is a knave, Avery is a knight, Benjamin is a knight, Harper is a knave, Penelope is a knight, Olivia is a knight, Ella is a knave, and Daniel is a knave.", "solution_text_format": "(1) Luke is a knave\n(2) Avery is a knight\n(3) Benjamin is a knight\n(4) Harper is a knave\n(5) Penelope is a knight\n(6) Olivia is a knight\n(7) Ella is a knave\n(8) Daniel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Luke that Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Olivia is a knight and Avery is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Penelope is a knight and Harper is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Daniel is a knave or Benjamin is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that If Harper is a knave then Penelope is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Ella is a knight and Luke is a knave.", "Harper cannot be a knave, because this would contradict the claim of Daniel that If Harper is a knave then Penelope is a knave.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that If Harper is a knave then Penelope is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Ella is a knight and Luke is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Ella is a knight and Luke is a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Olivia is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Olivia is a knave.", "Avery cannot be a knight, because this would contradict the false claim of Benjamin that Olivia is a knight and Avery is a knight.", "Avery cannot be a knave, because this would contradict the false claim of their own that If Penelope is a knave then Avery is a knight.", "We have exhausted all possibilities for Avery, Ella, Harper, and Daniel, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the false claim of their own that Daniel is a knave or Benjamin is a knave.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Penelope is a knight and Harper is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Daniel is a knave or Benjamin is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that If Harper is a knave then Penelope is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Ella is a knight and Luke is a knave.", "Harper cannot be a knave, because this would contradict the false claim of Olivia that Penelope is a knight and Harper is a knave.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that If Harper is a knave then Penelope is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Ella is a knight and Luke is a knave.", "Harper cannot be a knave, because this would contradict the false claim of Olivia that Penelope is a knight and Harper is a knave.", "We have exhausted all possibilities for Harper and Daniel, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the false claim of their own that Daniel is a knave or Benjamin is a knave.", "We have exhausted all possibilities for Penelope, Olivia, and Benjamin, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Benjamin is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Olivia is a knight and Avery is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Penelope is a knight and Harper is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Daniel is a knave or Benjamin is a knave.", "Daniel cannot be a knight, because this would contradict the claim of Penelope that Daniel is a knave or Benjamin is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that If Harper is a knave then Penelope is a knave.", "Harper cannot be a knight, because this would contradict the claim of Olivia that Penelope is a knight and Harper is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Ella is a knight and Luke is a knave.", "Ella cannot be a knight, because this would contradict the false claim of Harper that Ella is a knight and Luke is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Olivia is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that If Penelope is a knave then Avery is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('->', ('lying', 4), ('telling-truth', 1)), ('and', ('telling-truth', 5), ('telling-truth', 1)), ('and', ('telling-truth', 6), ('lying', 0)), ('or', ('lying', 7), ('lying', 2)), ('and', ('telling-truth', 4), ('lying', 3)), ('lying', 5), ('->', ('lying', 3), ('lying', 4)))", "index": 1000}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Grace, Alexander, Harper, Olivia, Scarlett, Abigail, Ava, and Owen. Grace asserted: \"Ava is a knave or Abigail is a knight\". Alexander expressed that Olivia is a knave or Ava is a knave. As Harper put it, \"Grace is a knave\". Olivia said, \"Harper is not a knave.\" \"If Grace is a knight then Ava is a knight\" - Scarlett. Abigail commented, \"If Olivia is a knight then Abigail is a knight\". \"Harper is a knave or Grace is a knight,\" Ava mentioned. In Owen's words: \"Ava is a knave or Grace is a knight\". So who is a knight and who is a knave?", "names": ["Grace", "Alexander", "Harper", "Olivia", "Scarlett", "Abigail", "Ava", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true, true, true], "solution_text": "Grace is a knight, Alexander is a knight, Harper is a knave, Olivia is a knave, Scarlett is a knight, Abigail is a knight, Ava is a knight, and Owen is a knight.", "solution_text_format": "(1) Grace is a knight\n(2) Alexander is a knight\n(3) Harper is a knave\n(4) Olivia is a knave\n(5) Scarlett is a knight\n(6) Abigail is a knight\n(7) Ava is a knight\n(8) Owen is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Ava is a knave or Abigail is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Harper is a knave or Grace is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that Grace is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Grace is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that If Olivia is a knight then Abigail is a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that Harper is not a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Harper is not a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Olivia is a knave or Ava is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Grace is a knight then Ava is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Ava is a knave or Grace is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 6), ('telling-truth', 5)), ('or', ('lying', 3), ('lying', 6)), ('lying', 0), ('not', ('lying', 2)), ('->', ('telling-truth', 0), ('telling-truth', 6)), ('->', ('telling-truth', 3), ('telling-truth', 5)), ('or', ('lying', 2), ('telling-truth', 0)), ('or', ('lying', 6), ('telling-truth', 0)))", "index": 1001}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Henry, Sebastian, Logan, Jack, Penelope, Isabella, Ava, and James. Henry noted, \"Jack is a knight or Logan is a knight\". \"Ava is a knight if and only if Henry is a knight\" - Sebastian. \"Isabella is a knight and Jack is a knight,\" Logan mentioned. In a statement by Jack: \"Jack is a knight or Henry is a knave\". Penelope told you that Sebastian is a knave or Jack is a knave. \"Penelope is a knave,\" Isabella declared. In a statement by Ava: \"Isabella is a knave if and only if Penelope is a knave\". James noted, \"Isabella is a knight if and only if Logan is a knight\". So who is a knight and who is a knave?", "names": ["Henry", "Sebastian", "Logan", "Jack", "Penelope", "Isabella", "Ava", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false, false, true], "solution_text": "Henry is a knight, Sebastian is a knave, Logan is a knave, Jack is a knight, Penelope is a knight, Isabella is a knave, Ava is a knave, and James is a knight.", "solution_text_format": "(1) Henry is a knight\n(2) Sebastian is a knave\n(3) Logan is a knave\n(4) Jack is a knight\n(5) Penelope is a knight\n(6) Isabella is a knave\n(7) Ava is a knave\n(8) James is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that Jack is a knight or Logan is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Jack is a knight or Henry is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Isabella is a knight and Jack is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the claim of Isabella that Penelope is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Sebastian is a knave or Jack is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Ava is a knight if and only if Henry is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Isabella is a knave if and only if Penelope is a knave.", "Ava cannot be a knave, because this would contradict the claim of Sebastian that Ava is a knight if and only if Henry is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the false claim of Penelope that Sebastian is a knave or Jack is a knave.", "We have exhausted all possibilities for Sebastian and Penelope, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the claim of Logan that Isabella is a knight and Jack is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Isabella is a knight and Jack is a knight.", "Isabella cannot be a knight, because this would contradict the false claim of Logan that Isabella is a knight and Jack is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Penelope is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Sebastian is a knave or Jack is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Penelope that Sebastian is a knave or Jack is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Ava is a knight if and only if Henry is a knight.", "Ava cannot be a knight, because this would contradict the false claim of Sebastian that Ava is a knight if and only if Henry is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Isabella is a knave if and only if Penelope is a knave.", "Assume James is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Logan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('telling-truth', 2)), ('<=>', ('telling-truth', 6), ('telling-truth', 0)), ('and', ('telling-truth', 5), ('telling-truth', 3)), ('or', ('telling-truth', 3), ('lying', 0)), ('or', ('lying', 1), ('lying', 3)), ('lying', 4), ('<=>', ('lying', 5), ('lying', 4)), ('<=>', ('telling-truth', 5), ('telling-truth', 2)))", "index": 1002}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Logan, Harper, Riley, Aiden, Scarlett, Jacob, Michael, and Evelyn. Logan expressed that Aiden is a knight or Scarlett is a knight. Harper noted, \"Logan is a knave\". Riley was heard saying, \"If Aiden is a knave then Jacob is a knight\". Aiden remarked, \"Jacob is a knave or Jacob is a knight\". Scarlett commented, \"Michael is a knight and Michael is a knave\". Jacob asserted: \"Evelyn is a knight if and only if Scarlett is a knight\". \"Scarlett is a knight if and only if Scarlett is a knave,\" Michael declared. Evelyn remarked, \"Logan is a knave\". So who is a knight and who is a knave?", "names": ["Logan", "Harper", "Riley", "Aiden", "Scarlett", "Jacob", "Michael", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true, false, false], "solution_text": "Logan is a knight, Harper is a knave, Riley is a knight, Aiden is a knight, Scarlett is a knave, Jacob is a knight, Michael is a knave, and Evelyn is a knave.", "solution_text_format": "(1) Logan is a knight\n(2) Harper is a knave\n(3) Riley is a knight\n(4) Aiden is a knight\n(5) Scarlett is a knave\n(6) Jacob is a knight\n(7) Michael is a knave\n(8) Evelyn is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that Aiden is a knight or Scarlett is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Jacob is a knave or Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Evelyn is a knight if and only if Scarlett is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Logan is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Logan is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Michael is a knight and Michael is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Michael is a knight and Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight if and only if Scarlett is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Scarlett is a knight if and only if Scarlett is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Logan is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Logan is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that If Aiden is a knave then Jacob is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('telling-truth', 4)), ('lying', 0), ('->', ('lying', 3), ('telling-truth', 5)), ('or', ('lying', 5), ('telling-truth', 5)), ('and', ('telling-truth', 6), ('lying', 6)), ('<=>', ('telling-truth', 7), ('telling-truth', 4)), ('<=>', ('telling-truth', 4), ('lying', 4)), ('lying', 0))", "index": 1003}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mia, Aurora, Jacob, Jackson, Evelyn, Henry, Michael, and Aria. In a statement by Mia: \"Evelyn is a knight or Aurora is a knight\". Aurora noted, \"Evelyn is a knight if and only if Jacob is a knave\". Jacob said that If Aria is a knave then Aurora is a knave. \"Mia is not a knave,\" Jackson claimed. According to Evelyn, \"Michael is a knave if and only if Aurora is a knave\". \"Jackson is a knave or Aria is a knave,\" Henry claimed. Michael asserted: \"Michael is a knight\". Aria stated, \"If Evelyn is a knave then Henry is a knight\". So who is a knight and who is a knave?", "names": ["Mia", "Aurora", "Jacob", "Jackson", "Evelyn", "Henry", "Michael", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false, false, true], "solution_text": "Mia is a knight, Aurora is a knave, Jacob is a knight, Jackson is a knight, Evelyn is a knight, Henry is a knave, Michael is a knave, and Aria is a knight.", "solution_text_format": "(1) Mia is a knight\n(2) Aurora is a knave\n(3) Jacob is a knight\n(4) Jackson is a knight\n(5) Evelyn is a knight\n(6) Henry is a knave\n(7) Michael is a knave\n(8) Aria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Evelyn is a knight or Aurora is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Michael is a knave if and only if Aurora is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Michael is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Evelyn is a knight if and only if Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Aurora that Evelyn is a knight if and only if Jacob is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that If Aria is a knave then Aurora is a knave.", "Aria cannot be a knight, because this would contradict the false claim of Jacob that If Aria is a knave then Aurora is a knave.", "Aria cannot be a knave, because this would contradict the false claim of their own that If Evelyn is a knave then Henry is a knight.", "We have exhausted all possibilities for Aria and Jacob, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the claim of Evelyn that Michael is a knave if and only if Aurora is a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Michael is a knight.", "Aurora cannot be a knight, because this would contradict the claim of Evelyn that Michael is a knave if and only if Aurora is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Evelyn is a knight if and only if Jacob is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that If Aria is a knave then Aurora is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that If Evelyn is a knave then Henry is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Jackson is a knave or Aria is a knave.", "Jackson cannot be a knight, because this would contradict the claim of Henry that Jackson is a knave or Aria is a knave.", "Jackson cannot be a knave, because this would contradict the false claim of their own that Mia is not a knave.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Jackson is a knave or Aria is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Mia is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('telling-truth', 1)), ('<=>', ('telling-truth', 4), ('lying', 2)), ('->', ('lying', 7), ('lying', 1)), ('not', ('lying', 0)), ('<=>', ('lying', 6), ('lying', 1)), ('or', ('lying', 3), ('lying', 7)), ('telling-truth', 6), ('->', ('lying', 4), ('telling-truth', 5)))", "index": 1004}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mia, Aiden, Ava, Chloe, Jack, Ella, Lily, and Penelope. Mia stated, \"Aiden is a knight if and only if Lily is a knight\". Aiden said, \"If Aiden is a knight then Ella is a knight.\" In Ava's words: \"Mia is a knight if and only if Penelope is a knight\". In Chloe's words: \"Ella is a knight\". Jack was heard saying, \"Penelope is a knave and Mia is a knight\". Ella said that Mia is a knave. As Lily put it, \"If Jack is a knave then Jack is a knight\". Penelope noted, \"Jack is a knave and Chloe is a knave\". So who is a knight and who is a knave?", "names": ["Mia", "Aiden", "Ava", "Chloe", "Jack", "Ella", "Lily", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true, false, false], "solution_text": "Mia is a knave, Aiden is a knight, Ava is a knight, Chloe is a knight, Jack is a knave, Ella is a knight, Lily is a knave, and Penelope is a knave.", "solution_text_format": "(1) Mia is a knave\n(2) Aiden is a knight\n(3) Ava is a knight\n(4) Chloe is a knight\n(5) Jack is a knave\n(6) Ella is a knight\n(7) Lily is a knave\n(8) Penelope is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Aiden is a knight if and only if Lily is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that If Aiden is a knight then Ella is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Mia is a knave.", "Ella cannot be a knave, because this would contradict the claim of Aiden that If Aiden is a knight then Ella is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the false claim of their own that If Aiden is a knight then Ella is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Aiden is a knight if and only if Lily is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that If Aiden is a knight then Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Mia is a knave.", "Lily cannot be a knight, because this would contradict the false claim of Mia that Aiden is a knight if and only if Lily is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that If Jack is a knave then Jack is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Penelope is a knave and Mia is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Penelope is a knave and Mia is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Jack is a knave and Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Penelope that Jack is a knave and Chloe is a knave.", "Chloe cannot be a knave, because this would contradict the false claim of their own that Ella is a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Jack is a knave and Chloe is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Ella is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Mia is a knight if and only if Penelope is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('telling-truth', 6)), ('->', ('telling-truth', 1), ('telling-truth', 5)), ('<=>', ('telling-truth', 0), ('telling-truth', 7)), ('telling-truth', 5), ('and', ('lying', 7), ('telling-truth', 0)), ('lying', 0), ('->', ('lying', 4), ('telling-truth', 4)), ('and', ('lying', 4), ('lying', 3)))", "index": 1005}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aiden, Isabella, Abigail, Zoey, Alexander, Samuel, Liam, and Lily. \"Lily is not a knave,\" Aiden claimed. As Isabella put it, \"Isabella is a knight or Aiden is a knight\". As Abigail put it, \"Isabella is a knight or Liam is a knight\". Zoey was heard saying, \"If Abigail is a knight then Isabella is a knight\". Alexander said, \"Zoey is a knight if and only if Isabella is a knight.\" Samuel remarked, \"Abigail is a knave\". Liam remarked, \"Alexander is a knave if and only if Abigail is a knave\". Lily stated, \"Zoey is a knave and Isabella is a knave\". So who is a knight and who is a knave?", "names": ["Aiden", "Isabella", "Abigail", "Zoey", "Alexander", "Samuel", "Liam", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false, true, false], "solution_text": "Aiden is a knave, Isabella is a knight, Abigail is a knight, Zoey is a knight, Alexander is a knight, Samuel is a knave, Liam is a knight, and Lily is a knave.", "solution_text_format": "(1) Aiden is a knave\n(2) Isabella is a knight\n(3) Abigail is a knight\n(4) Zoey is a knight\n(5) Alexander is a knight\n(6) Samuel is a knave\n(7) Liam is a knight\n(8) Lily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Lily is not a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Zoey is a knave and Isabella is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Lily that Zoey is a knave and Isabella is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that If Abigail is a knight then Isabella is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Isabella is a knight or Liam is a knight.", "Isabella cannot be a knight, because this would contradict the false claim of Zoey that If Abigail is a knight then Isabella is a knight.", "Isabella cannot be a knave, because this would contradict the false claim of their own that Isabella is a knight or Aiden is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the false claim of Zoey that If Abigail is a knight then Isabella is a knight.", "We have exhausted all possibilities for Abigail and Zoey, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the claim of Aiden that Lily is not a knave.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Lily is not a knave.", "Lily cannot be a knight, because this would contradict the false claim of Aiden that Lily is not a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Zoey is a knave and Isabella is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that If Abigail is a knight then Isabella is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Isabella is a knight or Liam is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Isabella is a knight or Aiden is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Alexander is a knave if and only if Abigail is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Zoey is a knight if and only if Isabella is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Abigail is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Abigail is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 7)), ('or', ('telling-truth', 1), ('telling-truth', 0)), ('or', ('telling-truth', 1), ('telling-truth', 6)), ('->', ('telling-truth', 2), ('telling-truth', 1)), ('<=>', ('telling-truth', 3), ('telling-truth', 1)), ('lying', 2), ('<=>', ('lying', 4), ('lying', 2)), ('and', ('lying', 3), ('lying', 1)))", "index": 1006}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lily, Mason, Scarlett, Benjamin, Luke, Jacob, Owen, and William. Lily asserted: \"If Luke is a knave then Lily is a knight\". Mason expressed that William is a knave. Scarlett asserted: \"Lily is a knave if and only if Jacob is a knight\". According to Benjamin, \"Jacob is not a knave\". As Luke put it, \"Mason is a knight if and only if Owen is a knight\". Jacob stated, \"Scarlett is not a knave\". Owen commented, \"Mason is a knave or Lily is a knight\". \"Jacob is a knave or Owen is a knave,\" William mentioned. So who is a knight and who is a knave?", "names": ["Lily", "Mason", "Scarlett", "Benjamin", "Luke", "Jacob", "Owen", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, false, true, true], "solution_text": "Lily is a knave, Mason is a knave, Scarlett is a knave, Benjamin is a knave, Luke is a knave, Jacob is a knave, Owen is a knight, and William is a knight.", "solution_text_format": "(1) Lily is a knave\n(2) Mason is a knave\n(3) Scarlett is a knave\n(4) Benjamin is a knave\n(5) Luke is a knave\n(6) Jacob is a knave\n(7) Owen is a knight\n(8) William is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that If Luke is a knave then Lily is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Mason is a knight if and only if Owen is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that William is a knave.", "William cannot be a knight, because this would contradict the claim of Mason that William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Jacob is a knave or Owen is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Lily is a knave if and only if Jacob is a knight.", "Scarlett cannot be a knave, because this would contradict the claim of Jacob that Scarlett is not a knave.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the false claim of William that Jacob is a knave or Owen is a knave.", "We have exhausted all possibilities for Jacob and William, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that William is a knave.", "Assume William is a knight. No contradiction is found in their claim that Jacob is a knave or Owen is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Lily is a knave if and only if Jacob is a knight.", "Scarlett cannot be a knave, because this would contradict the claim of Jacob that Scarlett is not a knave.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Scarlett is not a knave.", "Scarlett cannot be a knight, because this would contradict the false claim of Jacob that Scarlett is not a knave.", "Scarlett cannot be a knave, because this would contradict the false claim of their own that Lily is a knave if and only if Jacob is a knight.", "We have exhausted all possibilities for Scarlett and Jacob, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the false claim of Mason that William is a knave.", "We have exhausted all possibilities for William and Mason, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Mason is a knight if and only if Owen is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that William is a knave.", "William cannot be a knight, because this would contradict the claim of Mason that William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Jacob is a knave or Owen is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Lily is a knave if and only if Jacob is a knight.", "Scarlett cannot be a knave, because this would contradict the claim of Jacob that Scarlett is not a knave.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the false claim of William that Jacob is a knave or Owen is a knave.", "We have exhausted all possibilities for Jacob and William, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that William is a knave.", "Assume William is a knight. No contradiction is found in their claim that Jacob is a knave or Owen is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Lily is a knave if and only if Jacob is a knight.", "Scarlett cannot be a knave, because this would contradict the claim of Jacob that Scarlett is not a knave.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Scarlett is not a knave.", "Scarlett cannot be a knight, because this would contradict the false claim of Jacob that Scarlett is not a knave.", "Scarlett cannot be a knave, because this would contradict the false claim of their own that Lily is a knave if and only if Jacob is a knight.", "We have exhausted all possibilities for Scarlett and Jacob, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the false claim of Mason that William is a knave.", "We have exhausted all possibilities for William, Mason, and Luke, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that If Luke is a knave then Lily is a knight.", "Luke cannot be a knight, because this would contradict the false claim of Lily that If Luke is a knave then Lily is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Mason is a knight if and only if Owen is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that William is a knave.", "William cannot be a knight, because this would contradict the claim of Mason that William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Jacob is a knave or Owen is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Lily is a knave if and only if Jacob is a knight.", "Owen cannot be a knight, because this would contradict the false claim of Luke that Mason is a knight if and only if Owen is a knight.", "Owen cannot be a knave, because this would contradict the false claim of William that Jacob is a knave or Owen is a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the false claim of their own that Lily is a knave if and only if Jacob is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the false claim of William that Jacob is a knave or Owen is a knave.", "We have exhausted all possibilities for Jacob and William, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that William is a knave.", "Assume William is a knight. No contradiction is found in their claim that Jacob is a knave or Owen is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Lily is a knave if and only if Jacob is a knight.", "Owen cannot be a knight, because this would contradict the claim of William that Jacob is a knave or Owen is a knave.", "Owen cannot be a knave, because this would contradict the false claim of Luke that Mason is a knight if and only if Owen is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the false claim of their own that Lily is a knave if and only if Jacob is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Scarlett is not a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Lily is a knave if and only if Jacob is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Lily is a knave if and only if Jacob is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Mason is a knave or Lily is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Jacob is not a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Jacob is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 4), ('telling-truth', 0)), ('lying', 7), ('<=>', ('lying', 0), ('telling-truth', 5)), ('not', ('lying', 5)), ('<=>', ('telling-truth', 1), ('telling-truth', 6)), ('not', ('lying', 2)), ('or', ('lying', 1), ('telling-truth', 0)), ('or', ('lying', 5), ('lying', 6)))", "index": 1007}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ella, Riley, Ava, Zoey, Chloe, Owen, Aria, and Charlotte. Ella said, \"Chloe is a knight and Aria is a knave.\" Riley noted, \"Ella is a knight or Riley is a knight\". \"Charlotte is a knight or Owen is a knave,\" Ava claimed. Zoey stated, \"Chloe is not a knight\". Chloe was heard saying, \"Charlotte is a knave\". Owen was heard saying, \"Zoey is a knave\". Aria said, \"Zoey is a knight and Owen is a knave.\" \"Aria is a knave and Ella is a knave,\" Charlotte declared. So who is a knight and who is a knave?", "names": ["Ella", "Riley", "Ava", "Zoey", "Chloe", "Owen", "Aria", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true, false, false], "solution_text": "Ella is a knight, Riley is a knight, Ava is a knave, Zoey is a knave, Chloe is a knight, Owen is a knight, Aria is a knave, and Charlotte is a knave.", "solution_text_format": "(1) Ella is a knight\n(2) Riley is a knight\n(3) Ava is a knave\n(4) Zoey is a knave\n(5) Chloe is a knight\n(6) Owen is a knight\n(7) Aria is a knave\n(8) Charlotte is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Chloe is a knight and Aria is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Chloe that Charlotte is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Aria is a knave and Ella is a knave.", "Aria cannot be a knight, because this would contradict the claim of Ella that Chloe is a knight and Aria is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Zoey is a knight and Owen is a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that Chloe is not a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Chloe is not a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Zoey is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Ella is a knight or Riley is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Charlotte is a knight or Owen is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Charlotte is a knight or Owen is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 4), ('lying', 6)), ('or', ('telling-truth', 0), ('telling-truth', 1)), ('or', ('telling-truth', 7), ('lying', 5)), ('not', ('telling-truth', 4)), ('lying', 7), ('lying', 3), ('and', ('telling-truth', 3), ('lying', 5)), ('and', ('lying', 6), ('lying', 0)))", "index": 1008}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Oliver, Ella, Jackson, Avery, Noah, Aurora, Abigail, and Henry. Oliver expressed that Henry is a knight if and only if Ella is a knight. As Ella put it, \"If Noah is a knave then Aurora is a knight\". Jackson noted, \"Aurora is a knight and Oliver is a knight\". Avery noted, \"Ella is a knave\". \"If Avery is a knave then Aurora is a knight\" - Noah. \"Jackson is not a knight,\" Aurora declared. As Abigail put it, \"Jackson is a knight or Avery is a knight\". Henry told you that Abigail is a knight and Henry is a knight. So who is a knight and who is a knave?", "names": ["Oliver", "Ella", "Jackson", "Avery", "Noah", "Aurora", "Abigail", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true, false, false], "solution_text": "Oliver is a knave, Ella is a knight, Jackson is a knave, Avery is a knave, Noah is a knight, Aurora is a knight, Abigail is a knave, and Henry is a knave.", "solution_text_format": "(1) Oliver is a knave\n(2) Ella is a knight\n(3) Jackson is a knave\n(4) Avery is a knave\n(5) Noah is a knight\n(6) Aurora is a knight\n(7) Abigail is a knave\n(8) Henry is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Henry is a knight if and only if Ella is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Abigail is a knight and Henry is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Jackson is a knight or Avery is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Aurora is a knight and Oliver is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Jackson is not a knight.", "Aurora cannot be a knave, because this would contradict the claim of Jackson that Aurora is a knight and Oliver is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Aurora is a knight and Oliver is a knight.", "Aurora cannot be a knight, because this would contradict the false claim of Jackson that Aurora is a knight and Oliver is a knight.", "Aurora cannot be a knave, because this would contradict the false claim of their own that Jackson is not a knight.", "We have exhausted all possibilities for Aurora and Jackson, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the claim of Henry that Abigail is a knight and Henry is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Abigail is a knight and Henry is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Jackson is a knight or Avery is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Aurora is a knight and Oliver is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Jackson is not a knight.", "Aurora cannot be a knave, because this would contradict the claim of Jackson that Aurora is a knight and Oliver is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Aurora is a knight and Oliver is a knight.", "Aurora cannot be a knight, because this would contradict the false claim of Jackson that Aurora is a knight and Oliver is a knight.", "Aurora cannot be a knave, because this would contradict the false claim of their own that Jackson is not a knight.", "We have exhausted all possibilities for Aurora and Jackson, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Jackson is a knight or Avery is a knight.", "Jackson cannot be a knight, because this would contradict the false claim of Abigail that Jackson is a knight or Avery is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Aurora is a knight and Oliver is a knight.", "Aurora cannot be a knight, because this would contradict the false claim of Jackson that Aurora is a knight and Oliver is a knight.", "Aurora cannot be a knave, because this would contradict the false claim of their own that Jackson is not a knight.", "We have exhausted all possibilities for Aurora, Jackson, Abigail, and Henry, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Henry is a knight if and only if Ella is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Abigail is a knight and Henry is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Jackson is a knight or Avery is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Aurora is a knight and Oliver is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Aurora is a knight and Oliver is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Jackson is not a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Ella is a knave.", "Ella cannot be a knight, because this would contradict the false claim of Oliver that Henry is a knight if and only if Ella is a knight.", "Ella cannot be a knave, because this would contradict the false claim of their own that If Noah is a knave then Aurora is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Avery.", "Avery cannot be a knave, because this would contradict the claim of Abigail that Jackson is a knight or Avery is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the false claim of their own that Jackson is not a knight.", "We have exhausted all possibilities for Aurora and Jackson, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the claim of Henry that Abigail is a knight and Henry is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Abigail is a knight and Henry is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Jackson is a knight or Avery is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Aurora is a knight and Oliver is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Aurora is a knight and Oliver is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Jackson is not a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of Avery that Ella is a knave.", "Ella cannot be a knave, because this would contradict the false claim of Oliver that Henry is a knight if and only if Ella is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Avery.", "Avery cannot be a knave, because this would contradict the claim of Abigail that Jackson is a knight or Avery is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the false claim of their own that Jackson is not a knight.", "We have exhausted all possibilities for Aurora and Jackson, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Jackson is a knight or Avery is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Aurora is a knight and Oliver is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Aurora is a knight and Oliver is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Jackson is not a knight.", "Avery cannot be a knight, because this would contradict the false claim of Abigail that Jackson is a knight or Avery is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that If Noah is a knave then Aurora is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that If Avery is a knave then Aurora is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 7), ('telling-truth', 1)), ('->', ('lying', 4), ('telling-truth', 5)), ('and', ('telling-truth', 5), ('telling-truth', 0)), ('lying', 1), ('->', ('lying', 3), ('telling-truth', 5)), ('not', ('telling-truth', 2)), ('or', ('telling-truth', 2), ('telling-truth', 3)), ('and', ('telling-truth', 6), ('telling-truth', 7)))", "index": 1009}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Elizabeth, Mia, Matthew, Benjamin, Alexander, Charlotte, Harper, and Lily. Elizabeth remarked, \"Charlotte is a knight\". Mia expressed that If Matthew is a knave then Benjamin is a knight. \"Alexander is a knight if and only if Harper is a knave,\" Matthew mentioned. Benjamin said that Elizabeth is not a knight. Alexander stated, \"Lily is a knave and Lily is a knight\". Charlotte said, \"Mia is a knave if and only if Lily is a knight.\" \"If Benjamin is a knave then Harper is a knight,\" Harper mentioned. Lily told you that Elizabeth is a knight. So who is a knight and who is a knave?", "names": ["Elizabeth", "Mia", "Matthew", "Benjamin", "Alexander", "Charlotte", "Harper", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, true, false, true], "solution_text": "Elizabeth is a knight, Mia is a knave, Matthew is a knave, Benjamin is a knave, Alexander is a knave, Charlotte is a knight, Harper is a knave, and Lily is a knight.", "solution_text_format": "(1) Elizabeth is a knight\n(2) Mia is a knave\n(3) Matthew is a knave\n(4) Benjamin is a knave\n(5) Alexander is a knave\n(6) Charlotte is a knight\n(7) Harper is a knave\n(8) Lily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Mia is a knave if and only if Lily is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that If Matthew is a knave then Benjamin is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Alexander is a knight if and only if Harper is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that Lily is a knave and Lily is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Lily is a knave and Lily is a knight.", "Lily cannot be a knight, because this would contradict the claim of Charlotte that Mia is a knave if and only if Lily is a knight.", "Lily cannot be a knave, because this would contradict the false claim of their own that Elizabeth is a knight.", "We have exhausted all possibilities for Lily and Alexander, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Alexander is a knight if and only if Harper is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that Lily is a knave and Lily is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Lily is a knave and Lily is a knight.", "Lily cannot be a knight, because this would contradict the claim of Charlotte that Mia is a knave if and only if Lily is a knight.", "Lily cannot be a knave, because this would contradict the false claim of their own that Elizabeth is a knight.", "We have exhausted all possibilities for Lily, Alexander, and Matthew, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that If Matthew is a knave then Benjamin is a knight.", "Matthew cannot be a knight, because this would contradict the false claim of Mia that If Matthew is a knave then Benjamin is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Alexander is a knight if and only if Harper is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that Lily is a knave and Lily is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Lily is a knave and Lily is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Harper cannot be a knight, because this would contradict the false claim of Matthew that Alexander is a knight if and only if Harper is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that If Benjamin is a knave then Harper is a knight.", "Benjamin cannot be a knight, because this would contradict the false claim of Mia that If Matthew is a knave then Benjamin is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Elizabeth is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 5), ('->', ('lying', 2), ('telling-truth', 3)), ('<=>', ('telling-truth', 4), ('lying', 6)), ('not', ('telling-truth', 0)), ('and', ('lying', 7), ('telling-truth', 7)), ('<=>', ('lying', 1), ('telling-truth', 7)), ('->', ('lying', 3), ('telling-truth', 6)), ('telling-truth', 0))", "index": 1010}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ella, Avery, Abigail, David, Aria, Owen, Luke, and Jacob. \"David is a knight\" - Ella. Avery was heard saying, \"Abigail is a knave and Owen is a knight\". Abigail said, \"If Ella is a knight then Aria is a knave.\" \"Avery is a knight and Ella is a knave,\" David declared. \"Aria is a knight and Ella is a knight,\" Aria declared. As Owen put it, \"Luke is a knave or Luke is a knight\". \"Jacob is a knight or Abigail is a knave,\" Luke declared. Jacob commented, \"If Owen is a knave then Avery is a knight\". So who is a knight and who is a knave?", "names": ["Ella", "Avery", "Abigail", "David", "Aria", "Owen", "Luke", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, true, true, true], "solution_text": "Ella is a knave, Avery is a knave, Abigail is a knight, David is a knave, Aria is a knave, Owen is a knight, Luke is a knight, and Jacob is a knight.", "solution_text_format": "(1) Ella is a knave\n(2) Avery is a knave\n(3) Abigail is a knight\n(4) David is a knave\n(5) Aria is a knave\n(6) Owen is a knight\n(7) Luke is a knight\n(8) Jacob is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that David is a knight.", "David cannot be a knight, because this would contradict the claim of their own that Avery is a knight and Ella is a knave.", "David cannot be a knave, because this would contradict the claim of Ella that David is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that David is a knight.", "David cannot be a knight, because this would contradict the false claim of Ella that David is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Avery is a knight and Ella is a knave.", "Avery cannot be a knight, because this would contradict the false claim of David that Avery is a knight and Ella is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Abigail is a knave and Owen is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If Ella is a knight then Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Aria is a knight and Ella is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Aria is a knight and Ella is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Luke is a knave or Luke is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Jacob is a knight or Abigail is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that If Owen is a knave then Avery is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 3), ('and', ('lying', 2), ('telling-truth', 5)), ('->', ('telling-truth', 0), ('lying', 4)), ('and', ('telling-truth', 1), ('lying', 0)), ('and', ('telling-truth', 4), ('telling-truth', 0)), ('or', ('lying', 6), ('telling-truth', 6)), ('or', ('telling-truth', 7), ('lying', 2)), ('->', ('lying', 5), ('telling-truth', 1)))", "index": 1011}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lily, Ethan, Alexander, Mia, Harper, Aurora, Olivia, and Emma. Lily said that If Mia is a knave then Aurora is a knight. Ethan said, \"If Aurora is a knight then Alexander is a knight.\" Alexander was heard saying, \"Mia is a knave if and only if Aurora is a knave\". \"Mia is a knight and Olivia is a knave\" - Mia. \"Emma is a knight and Lily is a knight,\" Harper mentioned. \"Ethan is a knight if and only if Lily is a knight\" - Aurora. Olivia stated, \"Olivia is a knight if and only if Harper is a knave\". Emma expressed that If Emma is a knight then Olivia is a knave. So who is a knight and who is a knave?", "names": ["Lily", "Ethan", "Alexander", "Mia", "Harper", "Aurora", "Olivia", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false, false, true], "solution_text": "Lily is a knave, Ethan is a knight, Alexander is a knight, Mia is a knave, Harper is a knave, Aurora is a knave, Olivia is a knave, and Emma is a knight.", "solution_text_format": "(1) Lily is a knave\n(2) Ethan is a knight\n(3) Alexander is a knight\n(4) Mia is a knave\n(5) Harper is a knave\n(6) Aurora is a knave\n(7) Olivia is a knave\n(8) Emma is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that If Mia is a knave then Aurora is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Mia is a knight and Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Mia that Mia is a knight and Olivia is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Olivia is a knight if and only if Harper is a knave.", "Harper cannot be a knight, because this would contradict the false claim of Olivia that Olivia is a knight if and only if Harper is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Emma is a knight and Lily is a knight.", "Emma cannot be a knight, because this would contradict the false claim of Harper that Emma is a knight and Lily is a knight.", "Emma cannot be a knave, because this would contradict the false claim of their own that If Emma is a knight then Olivia is a knave.", "We have exhausted all possibilities for Emma, Harper, and Olivia, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Mia is a knight and Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Harper is a knave.", "Harper cannot be a knight, because this would contradict the claim of Olivia that Olivia is a knight if and only if Harper is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Emma is a knight and Lily is a knight.", "Emma cannot be a knight, because this would contradict the false claim of Harper that Emma is a knight and Lily is a knight.", "Emma cannot be a knave, because this would contradict the false claim of their own that If Emma is a knight then Olivia is a knave.", "We have exhausted all possibilities for Emma and Harper, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Olivia is a knight if and only if Harper is a knave.", "Harper cannot be a knight, because this would contradict the false claim of Olivia that Olivia is a knight if and only if Harper is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Emma is a knight and Lily is a knight.", "Emma cannot be a knight, because this would contradict the false claim of Harper that Emma is a knight and Lily is a knight.", "Emma cannot be a knave, because this would contradict the false claim of their own that If Emma is a knight then Olivia is a knave.", "We have exhausted all possibilities for Emma, Harper, Olivia, and Mia, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that If Mia is a knave then Aurora is a knight.", "Mia cannot be a knight, because this would contradict the false claim of Lily that If Mia is a knave then Aurora is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Mia is a knight and Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Harper is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Emma is a knight and Lily is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Emma is a knight and Lily is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that If Emma is a knight then Olivia is a knave.", "Emma cannot be a knave, because this would contradict the false claim of their own that If Emma is a knight then Olivia is a knave.", "We have exhausted all possibilities for Emma and Harper, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Olivia is a knight if and only if Harper is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Emma is a knight and Lily is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Emma is a knight and Lily is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If Emma is a knight then Olivia is a knave.", "Aurora cannot be a knight, because this would contradict the false claim of Lily that If Mia is a knave then Aurora is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Ethan is a knight if and only if Lily is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If Aurora is a knight then Alexander is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Mia is a knave if and only if Aurora is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('telling-truth', 5)), ('->', ('telling-truth', 5), ('telling-truth', 2)), ('<=>', ('lying', 3), ('lying', 5)), ('and', ('telling-truth', 3), ('lying', 6)), ('and', ('telling-truth', 7), ('telling-truth', 0)), ('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('<=>', ('telling-truth', 6), ('lying', 4)), ('->', ('telling-truth', 7), ('lying', 6)))", "index": 1012}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Logan, Lucas, William, Olivia, Ethan, Aiden, Abigail, and Jackson. \"Olivia is a knight and Logan is a knight,\" Logan declared. \"Aiden is a knight and Logan is a knight,\" Lucas mentioned. According to William, \"Abigail is a knight or Logan is a knight\". Olivia commented, \"Ethan is a knave and William is a knave\". In a statement by Ethan: \"Logan is a knight or Jackson is a knight\". \"Lucas is not a knave,\" Aiden mentioned. Abigail said, \"If Logan is a knight then Aiden is a knave.\" Jackson asserted: \"William is a knave\". So who is a knight and who is a knave?", "names": ["Logan", "Lucas", "William", "Olivia", "Ethan", "Aiden", "Abigail", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, false, true, false], "solution_text": "Logan is a knave, Lucas is a knave, William is a knight, Olivia is a knave, Ethan is a knave, Aiden is a knave, Abigail is a knight, and Jackson is a knave.", "solution_text_format": "(1) Logan is a knave\n(2) Lucas is a knave\n(3) William is a knight\n(4) Olivia is a knave\n(5) Ethan is a knave\n(6) Aiden is a knave\n(7) Abigail is a knight\n(8) Jackson is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that Olivia is a knight and Logan is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Ethan is a knave and William is a knave.", "Ethan cannot be a knight, because this would contradict the claim of Olivia that Ethan is a knave and William is a knave.", "Ethan cannot be a knave, because this would contradict the false claim of their own that Logan is a knight or Jackson is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the claim of Logan that Olivia is a knight and Logan is a knight.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Olivia is a knight and Logan is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Ethan is a knave and William is a knave.", "Ethan cannot be a knight, because this would contradict the claim of Olivia that Ethan is a knave and William is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Logan is a knight or Jackson is a knight.", "Jackson cannot be a knight, because this would contradict the false claim of Ethan that Logan is a knight or Jackson is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that William is a knave.", "William cannot be a knight, because this would contradict the claim of Olivia that Ethan is a knave and William is a knave.", "William cannot be a knave, because this would contradict the false claim of Jackson that William is a knave.", "We have exhausted all possibilities for William, Jackson, and Ethan, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Ethan is a knave and William is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Logan is a knight or Jackson is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that William is a knave.", "William cannot be a knight, because this would contradict the claim of Jackson that William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Abigail is a knight or Logan is a knight.", "Abigail cannot be a knight, because this would contradict the false claim of William that Abigail is a knight or Logan is a knight.", "Abigail cannot be a knave, because this would contradict the false claim of their own that If Logan is a knight then Aiden is a knave.", "We have exhausted all possibilities for Abigail and William, so let us go back and reconsider Jackson.", "Jackson cannot be a knave, because this would contradict the claim of Ethan that Logan is a knight or Jackson is a knight.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Logan is a knight or Jackson is a knight.", "Jackson cannot be a knight, because this would contradict the false claim of Ethan that Logan is a knight or Jackson is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that William is a knave.", "Assume William is a knight. No contradiction is found in their claim that Abigail is a knight or Logan is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If Logan is a knight then Aiden is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Lucas is not a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Aiden is a knight and Logan is a knight.", "Lucas cannot be a knave, because this would contradict the claim of Aiden that Lucas is not a knave.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Lucas is not a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Aiden is a knight and Logan is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Aiden is a knight and Logan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('telling-truth', 0)), ('and', ('telling-truth', 5), ('telling-truth', 0)), ('or', ('telling-truth', 6), ('telling-truth', 0)), ('and', ('lying', 4), ('lying', 2)), ('or', ('telling-truth', 0), ('telling-truth', 7)), ('not', ('lying', 1)), ('->', ('telling-truth', 0), ('lying', 5)), ('lying', 2))", "index": 1013}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emily, Elizabeth, Henry, Lucas, Oliver, Charlotte, Ella, and Joseph. Emily stated, \"If Ella is a knave then Elizabeth is a knight\". In Elizabeth's words: \"Charlotte is not a knave\". Henry noted, \"Elizabeth is a knave\". According to Lucas, \"Elizabeth is a knight\". \"If Charlotte is a knave then Oliver is a knight\" - Oliver. Charlotte was heard saying, \"Emily is a knight and Lucas is a knight\". Ella asserted: \"Elizabeth is a knave and Emily is a knave\". \"Charlotte is a knight or Henry is a knave,\" Joseph mentioned. So who is a knight and who is a knave?", "names": ["Emily", "Elizabeth", "Henry", "Lucas", "Oliver", "Charlotte", "Ella", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true, false, true], "solution_text": "Emily is a knight, Elizabeth is a knight, Henry is a knave, Lucas is a knight, Oliver is a knight, Charlotte is a knight, Ella is a knave, and Joseph is a knight.", "solution_text_format": "(1) Emily is a knight\n(2) Elizabeth is a knight\n(3) Henry is a knave\n(4) Lucas is a knight\n(5) Oliver is a knight\n(6) Charlotte is a knight\n(7) Ella is a knave\n(8) Joseph is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that If Ella is a knave then Elizabeth is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave and Emily is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Elizabeth is a knave and Emily is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Charlotte is not a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Emily is a knight and Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Elizabeth is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that If Charlotte is a knave then Oliver is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Charlotte is a knight or Henry is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 6), ('telling-truth', 1)), ('not', ('lying', 5)), ('lying', 1), ('telling-truth', 1), ('->', ('lying', 5), ('telling-truth', 4)), ('and', ('telling-truth', 0), ('telling-truth', 3)), ('and', ('lying', 1), ('lying', 0)), ('or', ('telling-truth', 5), ('lying', 2)))", "index": 1014}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Daniel, Chloe, James, Jack, Logan, Sebastian, Elizabeth, and Scarlett. In a statement by Daniel: \"If Elizabeth is a knight then Elizabeth is a knave\". Chloe was heard saying, \"Daniel is a knave\". James stated, \"Sebastian is a knave\". Jack noted, \"Sebastian is a knave if and only if Scarlett is a knight\". Logan was heard saying, \"Daniel is a knave or Jack is a knight\". Sebastian noted, \"Daniel is a knave or Chloe is a knight\". Elizabeth said, \"Chloe is a knave or Chloe is a knight.\" Scarlett noted, \"If James is a knave then Chloe is a knave\". So who is a knight and who is a knave?", "names": ["Daniel", "Chloe", "James", "Jack", "Logan", "Sebastian", "Elizabeth", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true, true, false], "solution_text": "Daniel is a knave, Chloe is a knight, James is a knave, Jack is a knight, Logan is a knight, Sebastian is a knight, Elizabeth is a knight, and Scarlett is a knave.", "solution_text_format": "(1) Daniel is a knave\n(2) Chloe is a knight\n(3) James is a knave\n(4) Jack is a knight\n(5) Logan is a knight\n(6) Sebastian is a knight\n(7) Elizabeth is a knight\n(8) Scarlett is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that If Elizabeth is a knight then Elizabeth is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of Daniel that If Elizabeth is a knight then Elizabeth is a knave.", "Elizabeth cannot be a knave, because this would contradict the false claim of their own that Chloe is a knave or Chloe is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that If Elizabeth is a knight then Elizabeth is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Chloe is a knave or Chloe is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Daniel is a knave.", "Assume James is a knight. No contradiction is found in their claim that Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of James that Sebastian is a knave.", "Sebastian cannot be a knave, because this would contradict the false claim of their own that Daniel is a knave or Chloe is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Sebastian is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Daniel is a knave or Chloe is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Sebastian is a knave if and only if Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of Jack that Sebastian is a knave if and only if Scarlett is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that If James is a knave then Chloe is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Daniel is a knave or Jack is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 6), ('lying', 6)), ('lying', 0), ('lying', 5), ('<=>', ('lying', 5), ('telling-truth', 7)), ('or', ('lying', 0), ('telling-truth', 3)), ('or', ('lying', 0), ('telling-truth', 1)), ('or', ('lying', 1), ('telling-truth', 1)), ('->', ('lying', 2), ('lying', 1)))", "index": 1015}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Henry, Jacob, Lucas, Abigail, James, Alexander, Victoria, and Ethan. In Henry's words: \"Victoria is a knave if and only if Lucas is a knight\". Jacob was heard saying, \"Ethan is a knight or Henry is a knave\". Lucas told you that Alexander is a knave and Henry is a knight. Abigail noted, \"Ethan is a knight\". James said, \"Alexander is a knight.\" Alexander told you that Victoria is a knight if and only if Abigail is a knight. Victoria told you that If Alexander is a knave then Henry is a knight. Ethan remarked, \"Henry is a knave and Lucas is a knave\". So who is a knight and who is a knave?", "names": ["Henry", "Jacob", "Lucas", "Abigail", "James", "Alexander", "Victoria", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, false, false, true], "solution_text": "Henry is a knave, Jacob is a knight, Lucas is a knave, Abigail is a knight, James is a knave, Alexander is a knave, Victoria is a knave, and Ethan is a knight.", "solution_text_format": "(1) Henry is a knave\n(2) Jacob is a knight\n(3) Lucas is a knave\n(4) Abigail is a knight\n(5) James is a knave\n(6) Alexander is a knave\n(7) Victoria is a knave\n(8) Ethan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that Victoria is a knave if and only if Lucas is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that If Alexander is a knave then Henry is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Ethan is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Henry is a knave and Lucas is a knave.", "Ethan cannot be a knave, because this would contradict the claim of Abigail that Ethan is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the claim of Alexander that Victoria is a knight if and only if Abigail is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Victoria is a knight if and only if Abigail is a knight.", "Abigail cannot be a knight, because this would contradict the false claim of Alexander that Victoria is a knight if and only if Abigail is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Ethan is a knight.", "Ethan cannot be a knight, because this would contradict the false claim of Abigail that Ethan is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Henry is a knave and Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the claim of Henry that Victoria is a knave if and only if Lucas is a knight.", "Lucas cannot be a knave, because this would contradict the false claim of their own that Alexander is a knave and Henry is a knight.", "We have exhausted all possibilities for Lucas, Ethan, Abigail, and Alexander, so let us go back and reconsider Victoria.", "Victoria cannot be a knave, because this would contradict the false claim of their own that If Alexander is a knave then Henry is a knight.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Victoria is a knave if and only if Lucas is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that If Alexander is a knave then Henry is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Ethan is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Henry is a knave and Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Alexander is a knave and Henry is a knight.", "Lucas cannot be a knave, because this would contradict the false claim of Henry that Victoria is a knave if and only if Lucas is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the claim of Abigail that Ethan is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the claim of Alexander that Victoria is a knight if and only if Abigail is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Alexander.", "Alexander cannot be a knave, because this would contradict the claim of Victoria that If Alexander is a knave then Henry is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that If Alexander is a knave then Henry is a knight.", "Alexander cannot be a knight, because this would contradict the false claim of Victoria that If Alexander is a knave then Henry is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Victoria is a knight if and only if Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Ethan is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Henry is a knave and Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the false claim of Henry that Victoria is a knave if and only if Lucas is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Alexander is a knave and Henry is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Ethan is a knight or Henry is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Alexander is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Alexander is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 6), ('telling-truth', 2)), ('or', ('telling-truth', 7), ('lying', 0)), ('and', ('lying', 5), ('telling-truth', 0)), ('telling-truth', 7), ('telling-truth', 5), ('<=>', ('telling-truth', 6), ('telling-truth', 3)), ('->', ('lying', 5), ('telling-truth', 0)), ('and', ('lying', 0), ('lying', 2)))", "index": 1016}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: James, Riley, Jackson, Charlotte, Henry, Evelyn, Owen, and Avery. James said that Jackson is a knave if and only if Henry is a knight. According to Riley, \"Riley is a knight if and only if Jackson is a knave\". Jackson expressed that Riley is a knave. Charlotte told you that Riley is a knave. In Henry's words: \"Jackson is a knight\". Evelyn told you that Riley is a knight and James is a knave. Owen expressed that James is a knave or Avery is a knave. Avery expressed that Henry is a knave. So who is a knight and who is a knave?", "names": ["James", "Riley", "Jackson", "Charlotte", "Henry", "Evelyn", "Owen", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, true, true, true], "solution_text": "James is a knave, Riley is a knight, Jackson is a knave, Charlotte is a knave, Henry is a knave, Evelyn is a knight, Owen is a knight, and Avery is a knight.", "solution_text_format": "(1) James is a knave\n(2) Riley is a knight\n(3) Jackson is a knave\n(4) Charlotte is a knave\n(5) Henry is a knave\n(6) Evelyn is a knight\n(7) Owen is a knight\n(8) Avery is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Jackson is a knave if and only if Henry is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Riley is a knave.", "Riley cannot be a knight, because this would contradict the claim of their own that Riley is a knight if and only if Jackson is a knave.", "Riley cannot be a knave, because this would contradict the false claim of their own that Riley is a knight if and only if Jackson is a knave.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Riley is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Riley is a knight if and only if Jackson is a knave.", "Henry cannot be a knight, because this would contradict the claim of their own that Jackson is a knight.", "Henry cannot be a knave, because this would contradict the claim of James that Jackson is a knave if and only if Henry is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Riley.", "Riley cannot be a knave, because this would contradict the false claim of Jackson that Riley is a knave.", "We have exhausted all possibilities for Riley and Jackson, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Jackson is a knave if and only if Henry is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Riley is a knave.", "Riley cannot be a knight, because this would contradict the claim of their own that Riley is a knight if and only if Jackson is a knave.", "Riley cannot be a knave, because this would contradict the false claim of their own that Riley is a knight if and only if Jackson is a knave.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Riley is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Riley is a knight if and only if Jackson is a knave.", "Henry cannot be a knight, because this would contradict the false claim of James that Jackson is a knave if and only if Henry is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Jackson is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Riley is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Riley is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Riley is a knight and James is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that James is a knave or Avery is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Henry is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('telling-truth', 4)), ('<=>', ('telling-truth', 1), ('lying', 2)), ('lying', 1), ('lying', 1), ('telling-truth', 2), ('and', ('telling-truth', 1), ('lying', 0)), ('or', ('lying', 0), ('lying', 7)), ('lying', 4))", "index": 1017}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: William, Ella, Avery, Mia, Sofia, Ava, Michael, and Daniel. In William's words: \"William is a knight and Ella is a knave\". In a statement by Ella: \"Ava is a knave or Daniel is a knave\". Avery remarked, \"Michael is a knight if and only if Avery is a knight\". In a statement by Mia: \"If Avery is a knight then Sofia is a knight\". \"Mia is a knight if and only if Ella is a knave,\" Sofia claimed. According to Ava, \"Daniel is a knave if and only if Avery is a knight\". \"William is not a knave\" - Michael. Daniel stated, \"Mia is a knight or Ava is a knave\". So who is a knight and who is a knave?", "names": ["William", "Ella", "Avery", "Mia", "Sofia", "Ava", "Michael", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true, true, true], "solution_text": "William is a knight, Ella is a knave, Avery is a knave, Mia is a knight, Sofia is a knight, Ava is a knight, Michael is a knight, and Daniel is a knight.", "solution_text_format": "(1) William is a knight\n(2) Ella is a knave\n(3) Avery is a knave\n(4) Mia is a knight\n(5) Sofia is a knight\n(6) Ava is a knight\n(7) Michael is a knight\n(8) Daniel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that William is a knight and Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of William that William is a knight and Ella is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Ava is a knave or Daniel is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Daniel is a knave if and only if Avery is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Mia is a knight or Ava is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that If Avery is a knight then Sofia is a knight.", "Avery cannot be a knight, because this would contradict the claim of Ava that Daniel is a knave if and only if Avery is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Michael is a knight if and only if Avery is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that William is not a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Mia is a knight if and only if Ella is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 0), ('lying', 1)), ('or', ('lying', 5), ('lying', 7)), ('<=>', ('telling-truth', 6), ('telling-truth', 2)), ('->', ('telling-truth', 2), ('telling-truth', 4)), ('<=>', ('telling-truth', 3), ('lying', 1)), ('<=>', ('lying', 7), ('telling-truth', 2)), ('not', ('lying', 0)), ('or', ('telling-truth', 3), ('lying', 5)))", "index": 1018}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ella, Aiden, Isabella, Aria, Ethan, Emily, Owen, and Emma. Ella noted, \"If Emma is a knight then Emma is a knave\". Aiden was heard saying, \"Ella is a knave\". Isabella remarked, \"Emily is a knave or Ella is a knave\". Aria said that Ella is a knave if and only if Emily is a knave. According to Ethan, \"Ella is a knight if and only if Owen is a knave\". Emily expressed that If Owen is a knave then Aiden is a knight. \"Isabella is not a knight,\" Owen declared. Emma commented, \"Ella is a knight and Emily is a knave\". So who is a knight and who is a knave?", "names": ["Ella", "Aiden", "Isabella", "Aria", "Ethan", "Emily", "Owen", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, true, true, false], "solution_text": "Ella is a knight, Aiden is a knave, Isabella is a knave, Aria is a knight, Ethan is a knave, Emily is a knight, Owen is a knight, and Emma is a knave.", "solution_text_format": "(1) Ella is a knight\n(2) Aiden is a knave\n(3) Isabella is a knave\n(4) Aria is a knight\n(5) Ethan is a knave\n(6) Emily is a knight\n(7) Owen is a knight\n(8) Emma is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that If Emma is a knight then Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of Ella that If Emma is a knight then Emma is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Ella is a knight and Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that If Owen is a knave then Aiden is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Isabella is not a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Emily is a knave or Ella is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Emily is a knave or Ella is a knave.", "Aiden cannot be a knight, because this would contradict the claim of their own that Ella is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Ella is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Ella is a knave if and only if Emily is a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Ella is a knight if and only if Owen is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Ella is a knight if and only if Owen is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 7), ('lying', 7)), ('lying', 0), ('or', ('lying', 5), ('lying', 0)), ('<=>', ('lying', 0), ('lying', 5)), ('<=>', ('telling-truth', 0), ('lying', 6)), ('->', ('lying', 6), ('telling-truth', 1)), ('not', ('telling-truth', 2)), ('and', ('telling-truth', 0), ('lying', 5)))", "index": 1019}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Abigail, Oliver, Ella, James, Penelope, Aria, Olivia, and Zoey. As Abigail put it, \"If Zoey is a knave then Aria is a knight\". \"Olivia is a knave if and only if Abigail is a knave,\" Oliver claimed. Ella noted, \"Oliver is not a knave\". James said that Abigail is a knave. Penelope noted, \"If Oliver is a knave then Olivia is a knight\". Aria noted, \"Penelope is a knave or Olivia is a knave\". \"Oliver is a knave,\" Olivia claimed. According to Zoey, \"If Ella is a knave then Penelope is a knave\". So who is a knight and who is a knave?", "names": ["Abigail", "Oliver", "Ella", "James", "Penelope", "Aria", "Olivia", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, false, true, false], "solution_text": "Abigail is a knave, Oliver is a knave, Ella is a knave, James is a knight, Penelope is a knight, Aria is a knave, Olivia is a knight, and Zoey is a knave.", "solution_text_format": "(1) Abigail is a knave\n(2) Oliver is a knave\n(3) Ella is a knave\n(4) James is a knight\n(5) Penelope is a knight\n(6) Aria is a knave\n(7) Olivia is a knight\n(8) Zoey is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that If Zoey is a knave then Aria is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that If Ella is a knave then Penelope is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Oliver is not a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Olivia is a knave if and only if Abigail is a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that Oliver is a knave.", "Olivia cannot be a knave, because this would contradict the claim of Oliver that Olivia is a knave if and only if Abigail is a knave.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the claim of Ella that Oliver is not a knave.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Oliver is not a knave.", "Oliver cannot be a knight, because this would contradict the false claim of Ella that Oliver is not a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Olivia is a knave if and only if Abigail is a knave.", "Olivia cannot be a knight, because this would contradict the false claim of Oliver that Olivia is a knave if and only if Abigail is a knave.", "Olivia cannot be a knave, because this would contradict the false claim of their own that Oliver is a knave.", "We have exhausted all possibilities for Olivia, Oliver, and Ella, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that If Ella is a knave then Penelope is a knave.", "Ella cannot be a knight, because this would contradict the false claim of Zoey that If Ella is a knave then Penelope is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Oliver is not a knave.", "Oliver cannot be a knight, because this would contradict the false claim of Ella that Oliver is not a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Olivia is a knave if and only if Abigail is a knave.", "Olivia cannot be a knight, because this would contradict the false claim of Oliver that Olivia is a knave if and only if Abigail is a knave.", "Olivia cannot be a knave, because this would contradict the false claim of their own that Oliver is a knave.", "We have exhausted all possibilities for Olivia, Oliver, Ella, and Zoey, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that If Zoey is a knave then Aria is a knight.", "Zoey cannot be a knight, because this would contradict the false claim of Abigail that If Zoey is a knave then Aria is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that If Ella is a knave then Penelope is a knave.", "Ella cannot be a knight, because this would contradict the false claim of Zoey that If Ella is a knave then Penelope is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Oliver is not a knave.", "Oliver cannot be a knight, because this would contradict the false claim of Ella that Oliver is not a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Olivia is a knave if and only if Abigail is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Oliver is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that If Oliver is a knave then Olivia is a knight.", "Aria cannot be a knight, because this would contradict the false claim of Abigail that If Zoey is a knave then Aria is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Penelope is a knave or Olivia is a knave.", "Assume James is a knight. No contradiction is found in their claim that Abigail is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 7), ('telling-truth', 5)), ('<=>', ('lying', 6), ('lying', 0)), ('not', ('lying', 1)), ('lying', 0), ('->', ('lying', 1), ('telling-truth', 6)), ('or', ('lying', 4), ('lying', 6)), ('lying', 1), ('->', ('lying', 2), ('lying', 4)))", "index": 1020}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Henry, Jack, Olivia, Daniel, Aiden, Joseph, Penelope, and Ava. \"If Aiden is a knight then Jack is a knave,\" Henry mentioned. \"If Daniel is a knave then Henry is a knight,\" Jack declared. According to Olivia, \"If Daniel is a knight then Penelope is a knight\". Daniel noted, \"If Aiden is a knight then Henry is a knave\". Aiden said that Joseph is a knave or Aiden is a knight. \"Joseph is a knight and Ava is a knight\" - Joseph. \"Daniel is a knave or Ava is a knight\" - Penelope. In Ava's words: \"If Jack is a knight then Joseph is a knave\". So who is a knight and who is a knave?", "names": ["Henry", "Jack", "Olivia", "Daniel", "Aiden", "Joseph", "Penelope", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false, true, true], "solution_text": "Henry is a knave, Jack is a knight, Olivia is a knight, Daniel is a knight, Aiden is a knight, Joseph is a knave, Penelope is a knight, and Ava is a knight.", "solution_text_format": "(1) Henry is a knave\n(2) Jack is a knight\n(3) Olivia is a knight\n(4) Daniel is a knight\n(5) Aiden is a knight\n(6) Joseph is a knave\n(7) Penelope is a knight\n(8) Ava is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that If Aiden is a knight then Jack is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Joseph is a knave or Aiden is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Joseph is a knight and Ava is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that If Jack is a knight then Joseph is a knave.", "Jack cannot be a knight, because this would contradict the claim of Henry that If Aiden is a knight then Jack is a knave.", "Jack cannot be a knave, because this would contradict the false claim of their own that If Daniel is a knave then Henry is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the claim of Joseph that Joseph is a knight and Ava is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Joseph is a knight and Ava is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that If Jack is a knight then Joseph is a knave.", "Jack cannot be a knight, because this would contradict the claim of Henry that If Aiden is a knight then Jack is a knave.", "Jack cannot be a knave, because this would contradict the false claim of their own that If Daniel is a knave then Henry is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the false claim of their own that If Jack is a knight then Joseph is a knave.", "We have exhausted all possibilities for Ava and Joseph, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Joseph is a knave or Aiden is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Joseph is a knight and Ava is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that If Jack is a knight then Joseph is a knave.", "Jack cannot be a knight, because this would contradict the claim of Ava that If Jack is a knight then Joseph is a knave.", "Jack cannot be a knave, because this would contradict the false claim of their own that If Daniel is a knave then Henry is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the claim of Joseph that Joseph is a knight and Ava is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the false claim of Aiden that Joseph is a knave or Aiden is a knight.", "We have exhausted all possibilities for Joseph and Aiden, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that If Aiden is a knight then Jack is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Joseph is a knave or Aiden is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Joseph is a knight and Ava is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that If Jack is a knight then Joseph is a knave.", "Jack cannot be a knight, because this would contradict the claim of Ava that If Jack is a knight then Joseph is a knave.", "Jack cannot be a knave, because this would contradict the false claim of Henry that If Aiden is a knight then Jack is a knave.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the claim of Joseph that Joseph is a knight and Ava is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Joseph is a knight and Ava is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that If Jack is a knight then Joseph is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that If Daniel is a knave then Henry is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that If Aiden is a knight then Henry is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that If Daniel is a knight then Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Daniel is a knave or Ava is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 4), ('lying', 1)), ('->', ('lying', 3), ('telling-truth', 0)), ('->', ('telling-truth', 3), ('telling-truth', 6)), ('->', ('telling-truth', 4), ('lying', 0)), ('or', ('lying', 5), ('telling-truth', 4)), ('and', ('telling-truth', 5), ('telling-truth', 7)), ('or', ('lying', 3), ('telling-truth', 7)), ('->', ('telling-truth', 1), ('lying', 5)))", "index": 1021}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ava, Lily, Evelyn, Victoria, Alexander, Ella, Emma, and Ethan. Ava commented, \"Evelyn is a knight if and only if Emma is a knave\". In Lily's words: \"If Ethan is a knave then Alexander is a knave\". Evelyn was heard saying, \"Ella is a knave if and only if Emma is a knave\". Victoria said, \"Alexander is not a knave.\" \"Ella is a knave,\" Alexander mentioned. \"If Ella is a knight then Emma is a knight,\" Ella claimed. Emma said, \"Ethan is not a knave.\" Ethan noted, \"Emma is a knave if and only if Ella is a knave\". So who is a knight and who is a knave?", "names": ["Ava", "Lily", "Evelyn", "Victoria", "Alexander", "Ella", "Emma", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true, true, true], "solution_text": "Ava is a knave, Lily is a knight, Evelyn is a knight, Victoria is a knave, Alexander is a knave, Ella is a knight, Emma is a knight, and Ethan is a knight.", "solution_text_format": "(1) Ava is a knave\n(2) Lily is a knight\n(3) Evelyn is a knight\n(4) Victoria is a knave\n(5) Alexander is a knave\n(6) Ella is a knight\n(7) Emma is a knight\n(8) Ethan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Evelyn is a knight if and only if Emma is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Ella is a knave if and only if Emma is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that If Ella is a knight then Emma is a knight.", "Emma cannot be a knight, because this would contradict the claim of Ava that Evelyn is a knight if and only if Emma is a knave.", "Emma cannot be a knave, because this would contradict the claim of Evelyn that Ella is a knave if and only if Emma is a knave.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the false claim of their own that If Ella is a knight then Emma is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Ella is a knave if and only if Emma is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that If Ella is a knight then Emma is a knight.", "Emma cannot be a knight, because this would contradict the false claim of Evelyn that Ella is a knave if and only if Emma is a knave.", "Emma cannot be a knave, because this would contradict the claim of Ava that Evelyn is a knight if and only if Emma is a knave.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the false claim of their own that If Ella is a knight then Emma is a knight.", "We have exhausted all possibilities for Ella and Evelyn, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Evelyn is a knight if and only if Emma is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Ella is a knave if and only if Emma is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that If Ella is a knight then Emma is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Ethan is not a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Emma is a knave if and only if Ella is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that If Ethan is a knave then Alexander is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that Ella is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Ella is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that Alexander is not a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Alexander is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('lying', 6)), ('->', ('lying', 7), ('lying', 4)), ('<=>', ('lying', 5), ('lying', 6)), ('not', ('lying', 4)), ('lying', 5), ('->', ('telling-truth', 5), ('telling-truth', 6)), ('not', ('lying', 7)), ('<=>', ('lying', 6), ('lying', 5)))", "index": 1022}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Luke, Alexander, Grace, Sofia, Benjamin, Amelia, David, and Logan. In Luke's words: \"David is a knave\". In Alexander's words: \"Grace is a knight\". Grace asserted: \"Amelia is a knight or Logan is a knave\". Sofia expressed that David is a knave and Amelia is a knave. Benjamin asserted: \"If David is a knave then Grace is a knight\". \"Sofia is a knight and Luke is a knight,\" Amelia declared. David expressed that Amelia is a knave. Logan stated, \"Luke is not a knight\". So who is a knight and who is a knave?", "names": ["Luke", "Alexander", "Grace", "Sofia", "Benjamin", "Amelia", "David", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, false, true, true], "solution_text": "Luke is a knave, Alexander is a knave, Grace is a knave, Sofia is a knave, Benjamin is a knight, Amelia is a knave, David is a knight, and Logan is a knight.", "solution_text_format": "(1) Luke is a knave\n(2) Alexander is a knave\n(3) Grace is a knave\n(4) Sofia is a knave\n(5) Benjamin is a knight\n(6) Amelia is a knave\n(7) David is a knight\n(8) Logan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that David is a knave.", "David cannot be a knight, because this would contradict the claim of Luke that David is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Amelia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Sofia is a knight and Luke is a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that David is a knave and Amelia is a knave.", "Sofia cannot be a knave, because this would contradict the claim of Amelia that Sofia is a knight and Luke is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Amelia.", "Amelia cannot be a knave, because this would contradict the false claim of David that Amelia is a knave.", "We have exhausted all possibilities for Amelia and David, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that David is a knave.", "Assume David is a knight. No contradiction is found in their claim that Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Sofia is a knight and Luke is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Sofia is a knight and Luke is a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that David is a knave and Amelia is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that David is a knave and Amelia is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Amelia is a knight or Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of Grace that Amelia is a knight or Logan is a knave.", "Logan cannot be a knave, because this would contradict the false claim of their own that Luke is not a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Grace.", "Grace cannot be a knave, because this would contradict the claim of Alexander that Grace is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Grace is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Alexander that Grace is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Amelia is a knight or Logan is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Luke is not a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that If David is a knave then Grace is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 6), ('telling-truth', 2), ('or', ('telling-truth', 5), ('lying', 7)), ('and', ('lying', 6), ('lying', 5)), ('->', ('lying', 6), ('telling-truth', 2)), ('and', ('telling-truth', 3), ('telling-truth', 0)), ('lying', 5), ('not', ('telling-truth', 0)))", "index": 1023}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: William, Ella, David, Ethan, Scarlett, James, Henry, and Charlotte. William stated, \"Ethan is a knave\". \"James is a knave,\" Ella declared. As David put it, \"Ethan is not a knave\". \"Charlotte is a knave\" - Ethan. Scarlett noted, \"William is a knight\". James said that William is a knave and Ethan is a knight. Henry said, \"If Ella is a knight then William is a knight.\" Charlotte said, \"Scarlett is a knave if and only if William is a knave.\" So who is a knight and who is a knave?", "names": ["William", "Ella", "David", "Ethan", "Scarlett", "James", "Henry", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, false, true, true], "solution_text": "William is a knight, Ella is a knight, David is a knave, Ethan is a knave, Scarlett is a knight, James is a knave, Henry is a knight, and Charlotte is a knight.", "solution_text_format": "(1) William is a knight\n(2) Ella is a knight\n(3) David is a knave\n(4) Ethan is a knave\n(5) Scarlett is a knight\n(6) James is a knave\n(7) Henry is a knight\n(8) Charlotte is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Ethan is a knave.", "Ethan cannot be a knight, because this would contradict the claim of William that Ethan is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Charlotte is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Scarlett is a knave if and only if William is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that William is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that James is a knave.", "James cannot be a knight, because this would contradict the claim of Ella that James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that William is a knave and Ethan is a knight.", "David cannot be a knight, because this would contradict the claim of their own that Ethan is not a knave.", "Assume David is a knave. No contradiction is found in their false claim that Ethan is not a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Ella is a knight then William is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('lying', 5), ('not', ('lying', 3)), ('lying', 7), ('telling-truth', 0), ('and', ('lying', 0), ('telling-truth', 3)), ('->', ('telling-truth', 1), ('telling-truth', 0)), ('<=>', ('lying', 4), ('lying', 0)))", "index": 1024}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: James, Avery, Logan, Daniel, Ava, Jackson, Aiden, and Ella. \"Aiden is a knight\" - James. Avery said, \"If Daniel is a knave then Ella is a knight.\" Logan asserted: \"Aiden is a knave and James is a knight\". Daniel said, \"Daniel is a knight and Avery is a knave.\" As Ava put it, \"Ella is a knave if and only if Jackson is a knight\". Jackson said, \"If Daniel is a knight then Avery is a knave.\" \"Jackson is not a knave\" - Aiden. Ella said that If Logan is a knight then James is a knave. So who is a knight and who is a knave?", "names": ["James", "Avery", "Logan", "Daniel", "Ava", "Jackson", "Aiden", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, true, true, true], "solution_text": "James is a knight, Avery is a knight, Logan is a knave, Daniel is a knave, Ava is a knave, Jackson is a knight, Aiden is a knight, and Ella is a knight.", "solution_text_format": "(1) James is a knight\n(2) Avery is a knight\n(3) Logan is a knave\n(4) Daniel is a knave\n(5) Ava is a knave\n(6) Jackson is a knight\n(7) Aiden is a knight\n(8) Ella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Jackson is not a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that If Daniel is a knight then Avery is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Daniel is a knight and Avery is a knave.", "Avery cannot be a knight, because this would contradict the claim of Daniel that Daniel is a knight and Avery is a knave.", "Avery cannot be a knave, because this would contradict the false claim of their own that If Daniel is a knave then Ella is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Daniel is a knight and Avery is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that If Daniel is a knave then Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that If Logan is a knight then James is a knave.", "Logan cannot be a knight, because this would contradict the claim of their own that Aiden is a knave and James is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Aiden is a knave and James is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Ella is a knave if and only if Jackson is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Ella is a knave if and only if Jackson is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 6), ('->', ('lying', 3), ('telling-truth', 7)), ('and', ('lying', 6), ('telling-truth', 0)), ('and', ('telling-truth', 3), ('lying', 1)), ('<=>', ('lying', 7), ('telling-truth', 5)), ('->', ('telling-truth', 3), ('lying', 1)), ('not', ('lying', 5)), ('->', ('telling-truth', 2), ('lying', 0)))", "index": 1025}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Oliver, Emma, Logan, Samuel, Olivia, Zoey, Chloe, and Henry. In Oliver's words: \"Olivia is not a knave\". Emma expressed that Chloe is a knight or Chloe is a knave. \"Samuel is not a knave,\" Logan claimed. \"Olivia is not a knight,\" Samuel mentioned. Olivia stated, \"If Chloe is a knight then Zoey is a knave\". \"Chloe is a knave and Logan is a knave,\" Zoey mentioned. Chloe said that Logan is a knight. Henry noted, \"Samuel is a knave if and only if Oliver is a knight\". So who is a knight and who is a knave?", "names": ["Oliver", "Emma", "Logan", "Samuel", "Olivia", "Zoey", "Chloe", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true, false, true], "solution_text": "Oliver is a knight, Emma is a knight, Logan is a knave, Samuel is a knave, Olivia is a knight, Zoey is a knight, Chloe is a knave, and Henry is a knight.", "solution_text_format": "(1) Oliver is a knight\n(2) Emma is a knight\n(3) Logan is a knave\n(4) Samuel is a knave\n(5) Olivia is a knight\n(6) Zoey is a knight\n(7) Chloe is a knave\n(8) Henry is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Olivia is not a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that If Chloe is a knight then Zoey is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Logan is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Samuel is not a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that Olivia is not a knight.", "Samuel cannot be a knave, because this would contradict the claim of Logan that Samuel is not a knave.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the claim of Chloe that Logan is a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Logan is a knight.", "Logan cannot be a knight, because this would contradict the false claim of Chloe that Logan is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Samuel is not a knave.", "Samuel cannot be a knight, because this would contradict the false claim of Logan that Samuel is not a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Olivia is not a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Chloe is a knave and Logan is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Chloe is a knight or Chloe is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Oliver is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('or', ('telling-truth', 6), ('lying', 6)), ('not', ('lying', 3)), ('not', ('telling-truth', 4)), ('->', ('telling-truth', 6), ('lying', 5)), ('and', ('lying', 6), ('lying', 2)), ('telling-truth', 2), ('<=>', ('lying', 3), ('telling-truth', 0)))", "index": 1026}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Zoey, Luke, Benjamin, Lucas, Joseph, Aria, Scarlett, and Jackson. Zoey was heard saying, \"Joseph is a knight if and only if Scarlett is a knight\". Luke said that Benjamin is a knave or Scarlett is a knight. Benjamin told you that Lucas is a knave or Benjamin is a knight. Lucas said, \"Aria is a knave.\" Joseph noted, \"Luke is a knave if and only if Scarlett is a knight\". As Aria put it, \"Joseph is a knave\". \"Aria is a knight or Jackson is a knight\" - Scarlett. Jackson commented, \"Lucas is a knight or Joseph is a knave\". So who is a knight and who is a knave?", "names": ["Zoey", "Luke", "Benjamin", "Lucas", "Joseph", "Aria", "Scarlett", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true, true, true], "solution_text": "Zoey is a knave, Luke is a knight, Benjamin is a knight, Lucas is a knave, Joseph is a knave, Aria is a knight, Scarlett is a knight, and Jackson is a knight.", "solution_text_format": "(1) Zoey is a knave\n(2) Luke is a knight\n(3) Benjamin is a knight\n(4) Lucas is a knave\n(5) Joseph is a knave\n(6) Aria is a knight\n(7) Scarlett is a knight\n(8) Jackson is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Zoey is a knight. No contradiction is found in their claim that Joseph is a knight if and only if Scarlett is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Luke is a knave if and only if Scarlett is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Benjamin is a knave or Scarlett is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Lucas is a knave or Benjamin is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of Lucas that Aria is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Joseph is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Joseph that Luke is a knave if and only if Scarlett is a knight.", "Scarlett cannot be a knave, because this would contradict the claim of Zoey that Joseph is a knight if and only if Scarlett is a knight.", "We have exhausted all possibilities for Scarlett and Aria, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Joseph is a knave.", "Aria cannot be a knave, because this would contradict the false claim of Lucas that Aria is a knave.", "We have exhausted all possibilities for Aria and Lucas, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Lucas is a knave or Benjamin is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of Lucas that Aria is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Joseph is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Joseph that Luke is a knave if and only if Scarlett is a knight.", "Scarlett cannot be a knave, because this would contradict the claim of Zoey that Joseph is a knight if and only if Scarlett is a knight.", "We have exhausted all possibilities for Scarlett and Aria, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the false claim of Benjamin that Lucas is a knave or Benjamin is a knight.", "We have exhausted all possibilities for Lucas and Benjamin, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Benjamin is a knave or Scarlett is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Lucas is a knave or Benjamin is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of Lucas that Aria is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Joseph is a knave.", "Scarlett cannot be a knight, because this would contradict the false claim of Luke that Benjamin is a knave or Scarlett is a knight.", "Scarlett cannot be a knave, because this would contradict the claim of Zoey that Joseph is a knight if and only if Scarlett is a knight.", "We have exhausted all possibilities for Scarlett and Aria, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Joseph is a knave.", "Aria cannot be a knave, because this would contradict the false claim of Lucas that Aria is a knave.", "We have exhausted all possibilities for Aria and Lucas, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the false claim of Luke that Benjamin is a knave or Scarlett is a knight.", "We have exhausted all possibilities for Benjamin and Luke, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Luke is a knave if and only if Scarlett is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Benjamin is a knave or Scarlett is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Lucas is a knave or Benjamin is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of Lucas that Aria is a knave.", "Aria cannot be a knave, because this would contradict the false claim of their own that Joseph is a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Aria is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Joseph is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Zoey that Joseph is a knight if and only if Scarlett is a knight.", "Scarlett cannot be a knave, because this would contradict the claim of Luke that Benjamin is a knave or Scarlett is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Aria.", "Aria cannot be a knave, because this would contradict the false claim of Lucas that Aria is a knave.", "We have exhausted all possibilities for Aria and Lucas, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Lucas is a knave or Benjamin is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of Lucas that Aria is a knave.", "Aria cannot be a knave, because this would contradict the false claim of their own that Joseph is a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the false claim of Benjamin that Lucas is a knave or Benjamin is a knight.", "We have exhausted all possibilities for Lucas and Benjamin, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Benjamin is a knave or Scarlett is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Lucas is a knave or Benjamin is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of Lucas that Aria is a knave.", "Aria cannot be a knave, because this would contradict the false claim of their own that Joseph is a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Aria is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Joseph is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Zoey that Joseph is a knight if and only if Scarlett is a knight.", "Scarlett cannot be a knave, because this would contradict the false claim of their own that Aria is a knight or Jackson is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Aria.", "Aria cannot be a knave, because this would contradict the false claim of Lucas that Aria is a knave.", "We have exhausted all possibilities for Aria and Lucas, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the false claim of Luke that Benjamin is a knave or Scarlett is a knight.", "We have exhausted all possibilities for Benjamin, Luke, and Joseph, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Joseph is a knight if and only if Scarlett is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Luke is a knave if and only if Scarlett is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Benjamin is a knave or Scarlett is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Lucas is a knave or Benjamin is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of Lucas that Aria is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Joseph is a knave.", "Scarlett cannot be a knight, because this would contradict the false claim of Zoey that Joseph is a knight if and only if Scarlett is a knight.", "Scarlett cannot be a knave, because this would contradict the claim of Luke that Benjamin is a knave or Scarlett is a knight.", "We have exhausted all possibilities for Scarlett and Aria, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Joseph is a knave.", "Aria cannot be a knave, because this would contradict the false claim of Lucas that Aria is a knave.", "We have exhausted all possibilities for Aria and Lucas, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Lucas is a knave or Benjamin is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of Lucas that Aria is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Joseph is a knave.", "Scarlett cannot be a knight, because this would contradict the false claim of Zoey that Joseph is a knight if and only if Scarlett is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Aria is a knight or Jackson is a knight.", "Jackson cannot be a knight, because this would contradict the false claim of Scarlett that Aria is a knight or Jackson is a knight.", "Jackson cannot be a knave, because this would contradict the false claim of their own that Lucas is a knight or Joseph is a knave.", "We have exhausted all possibilities for Jackson, Scarlett, and Aria, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the false claim of Benjamin that Lucas is a knave or Benjamin is a knight.", "We have exhausted all possibilities for Lucas and Benjamin, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Benjamin is a knave or Scarlett is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Lucas is a knave or Benjamin is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of Lucas that Aria is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Joseph is a knave.", "Scarlett cannot be a knight, because this would contradict the false claim of Zoey that Joseph is a knight if and only if Scarlett is a knight.", "Scarlett cannot be a knave, because this would contradict the claim of Joseph that Luke is a knave if and only if Scarlett is a knight.", "We have exhausted all possibilities for Scarlett and Aria, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Joseph is a knave.", "Aria cannot be a knave, because this would contradict the false claim of Lucas that Aria is a knave.", "We have exhausted all possibilities for Aria and Lucas, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the false claim of Luke that Benjamin is a knave or Scarlett is a knight.", "We have exhausted all possibilities for Benjamin and Luke, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Luke is a knave if and only if Scarlett is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Benjamin is a knave or Scarlett is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Lucas is a knave or Benjamin is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of Lucas that Aria is a knave.", "Aria cannot be a knave, because this would contradict the false claim of their own that Joseph is a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Aria is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Joseph is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Aria is a knight or Jackson is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Lucas is a knight or Joseph is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 4), ('telling-truth', 6)), ('or', ('lying', 2), ('telling-truth', 6)), ('or', ('lying', 3), ('telling-truth', 2)), ('lying', 5), ('<=>', ('lying', 1), ('telling-truth', 6)), ('lying', 4), ('or', ('telling-truth', 5), ('telling-truth', 7)), ('or', ('telling-truth', 3), ('lying', 4)))", "index": 1027}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Luke, Jack, Scarlett, Emily, Owen, Zoey, Evelyn, and Emma. \"Evelyn is a knight,\" Luke declared. Jack told you that Emily is a knave and Evelyn is a knave. Scarlett told you that If Luke is a knave then Luke is a knight. Emily asserted: \"Jack is a knave\". Owen told you that Evelyn is a knave or Emma is a knight. Zoey asserted: \"Emma is a knight\". Evelyn remarked, \"Scarlett is a knight or Owen is a knight\". In a statement by Emma: \"Jack is a knight\". So who is a knight and who is a knave?", "names": ["Luke", "Jack", "Scarlett", "Emily", "Owen", "Zoey", "Evelyn", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, false, true, false], "solution_text": "Luke is a knight, Jack is a knave, Scarlett is a knight, Emily is a knight, Owen is a knave, Zoey is a knave, Evelyn is a knight, and Emma is a knave.", "solution_text_format": "(1) Luke is a knight\n(2) Jack is a knave\n(3) Scarlett is a knight\n(4) Emily is a knight\n(5) Owen is a knave\n(6) Zoey is a knave\n(7) Evelyn is a knight\n(8) Emma is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Evelyn is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Scarlett is a knight or Owen is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Luke is a knave then Luke is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Evelyn is a knave or Emma is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Jack is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Emily is a knave and Evelyn is a knave.", "Jack cannot be a knave, because this would contradict the claim of Emma that Jack is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Emma.", "Emma cannot be a knave, because this would contradict the claim of Owen that Evelyn is a knave or Emma is a knight.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Evelyn is a knave or Emma is a knight.", "Emma cannot be a knight, because this would contradict the false claim of Owen that Evelyn is a knave or Emma is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Jack is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Emily is a knave and Evelyn is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Emily is a knave and Evelyn is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Jack is a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that Emma is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Emma is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 6), ('and', ('lying', 3), ('lying', 6)), ('->', ('lying', 0), ('telling-truth', 0)), ('lying', 1), ('or', ('lying', 6), ('telling-truth', 7)), ('telling-truth', 7), ('or', ('telling-truth', 2), ('telling-truth', 4)), ('telling-truth', 1))", "index": 1028}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Chloe, Owen, Aria, Victoria, Penelope, Alexander, Joseph, and Riley. \"Penelope is not a knight,\" Chloe declared. Owen told you that Riley is a knave and Penelope is a knight. \"If Joseph is a knave then Aria is a knight,\" Aria claimed. \"Chloe is a knave\" - Victoria. Penelope remarked, \"Alexander is a knight and Alexander is a knave\". As Alexander put it, \"Owen is not a knave\". As Joseph put it, \"Victoria is a knave if and only if Penelope is a knave\". Riley said, \"Owen is a knight or Joseph is a knave.\" So who is a knight and who is a knave?", "names": ["Chloe", "Owen", "Aria", "Victoria", "Penelope", "Alexander", "Joseph", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, false, true, false], "solution_text": "Chloe is a knight, Owen is a knave, Aria is a knight, Victoria is a knave, Penelope is a knave, Alexander is a knave, Joseph is a knight, and Riley is a knave.", "solution_text_format": "(1) Chloe is a knight\n(2) Owen is a knave\n(3) Aria is a knight\n(4) Victoria is a knave\n(5) Penelope is a knave\n(6) Alexander is a knave\n(7) Joseph is a knight\n(8) Riley is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Penelope cannot be a knight, because this would contradict the claim of Chloe that Penelope is not a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Alexander is a knight and Alexander is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Owen is not a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Riley is a knave and Penelope is a knight.", "Owen cannot be a knave, because this would contradict the claim of Alexander that Owen is not a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Owen is not a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Riley is a knave and Penelope is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Riley is a knave and Penelope is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Owen is a knight or Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Riley that Owen is a knight or Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Victoria is a knave if and only if Penelope is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that Chloe is a knave.", "Victoria cannot be a knave, because this would contradict the false claim of Joseph that Victoria is a knave if and only if Penelope is a knave.", "We have exhausted all possibilities for Victoria and Joseph, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Owen is a knight or Joseph is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Victoria is a knave if and only if Penelope is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that Chloe is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Chloe is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that If Joseph is a knave then Aria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 4)), ('and', ('lying', 7), ('telling-truth', 4)), ('->', ('lying', 6), ('telling-truth', 2)), ('lying', 0), ('and', ('telling-truth', 5), ('lying', 5)), ('not', ('lying', 1)), ('<=>', ('lying', 3), ('lying', 4)), ('or', ('telling-truth', 1), ('lying', 6)))", "index": 1029}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Evelyn, Harper, Benjamin, Zoey, Oliver, Grace, Sofia, and Joseph. Evelyn remarked, \"Oliver is a knave and Harper is a knave\". \"If Joseph is a knight then Zoey is a knight,\" Harper declared. According to Benjamin, \"Harper is a knight\". Zoey said, \"If Harper is a knave then Sofia is a knight.\" Oliver commented, \"Benjamin is a knave and Benjamin is a knight\". Grace stated, \"Zoey is a knight or Harper is a knight\". Sofia stated, \"Evelyn is a knight if and only if Benjamin is a knave\". Joseph told you that If Sofia is a knight then Evelyn is a knave. So who is a knight and who is a knave?", "names": ["Evelyn", "Harper", "Benjamin", "Zoey", "Oliver", "Grace", "Sofia", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true, true, true], "solution_text": "Evelyn is a knave, Harper is a knight, Benjamin is a knight, Zoey is a knight, Oliver is a knave, Grace is a knight, Sofia is a knight, and Joseph is a knight.", "solution_text_format": "(1) Evelyn is a knave\n(2) Harper is a knight\n(3) Benjamin is a knight\n(4) Zoey is a knight\n(5) Oliver is a knave\n(6) Grace is a knight\n(7) Sofia is a knight\n(8) Joseph is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Oliver is a knave and Harper is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Evelyn that Oliver is a knave and Harper is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Benjamin is a knave and Benjamin is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Harper is a knight.", "Harper cannot be a knight, because this would contradict the claim of Evelyn that Oliver is a knave and Harper is a knave.", "Harper cannot be a knave, because this would contradict the claim of Benjamin that Harper is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Harper is a knight.", "Harper cannot be a knight, because this would contradict the claim of Evelyn that Oliver is a knave and Harper is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that If Joseph is a knight then Zoey is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Sofia is a knight then Evelyn is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Joseph that If Sofia is a knight then Evelyn is a knave.", "Sofia cannot be a knave, because this would contradict the false claim of their own that Evelyn is a knight if and only if Benjamin is a knave.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the false claim of Harper that If Joseph is a knight then Zoey is a knight.", "We have exhausted all possibilities for Joseph, Harper, Benjamin, and Oliver, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Oliver is a knave and Harper is a knave.", "Oliver cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave and Benjamin is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Benjamin is a knave and Benjamin is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Harper is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that If Joseph is a knight then Zoey is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Sofia is a knight then Evelyn is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Evelyn is a knight if and only if Benjamin is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that If Harper is a knave then Sofia is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Zoey is a knight or Harper is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('lying', 1)), ('->', ('telling-truth', 7), ('telling-truth', 3)), ('telling-truth', 1), ('->', ('lying', 1), ('telling-truth', 6)), ('and', ('lying', 2), ('telling-truth', 2)), ('or', ('telling-truth', 3), ('telling-truth', 1)), ('<=>', ('telling-truth', 0), ('lying', 2)), ('->', ('telling-truth', 6), ('lying', 0)))", "index": 1030}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Scarlett, Ella, Evelyn, Noah, Aria, Ava, Sofia, and Mia. Scarlett said, \"Mia is a knight if and only if Ava is a knight.\" Ella stated, \"Aria is a knave or Evelyn is a knight\". Evelyn said, \"Ava is not a knave.\" \"If Ella is a knight then Sofia is a knave,\" Noah declared. \"Evelyn is not a knave\" - Aria. Ava commented, \"Sofia is a knave if and only if Mia is a knight\". Sofia said, \"Noah is a knave if and only if Noah is a knight.\" Mia said that If Noah is a knight then Noah is a knave. So who is a knight and who is a knave?", "names": ["Scarlett", "Ella", "Evelyn", "Noah", "Aria", "Ava", "Sofia", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false, false, false], "solution_text": "Scarlett is a knight, Ella is a knight, Evelyn is a knave, Noah is a knight, Aria is a knave, Ava is a knave, Sofia is a knave, and Mia is a knave.", "solution_text_format": "(1) Scarlett is a knight\n(2) Ella is a knight\n(3) Evelyn is a knave\n(4) Noah is a knight\n(5) Aria is a knave\n(6) Ava is a knave\n(7) Sofia is a knave\n(8) Mia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Mia is a knight if and only if Ava is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that If Noah is a knight then Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of Mia that If Noah is a knight then Noah is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that If Ella is a knight then Sofia is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Aria is a knave or Evelyn is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Evelyn is not a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Ava is not a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Sofia is a knave if and only if Mia is a knight.", "Sofia cannot be a knight, because this would contradict the claim of Ava that Sofia is a knave if and only if Mia is a knight.", "Sofia cannot be a knave, because this would contradict the false claim of Noah that If Ella is a knight then Sofia is a knave.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the claim of Scarlett that Mia is a knight if and only if Ava is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the claim of Ella that Aria is a knave or Evelyn is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Evelyn is not a knave.", "Evelyn cannot be a knight, because this would contradict the false claim of Aria that Evelyn is not a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Ava is not a knave.", "Ava cannot be a knight, because this would contradict the false claim of Evelyn that Ava is not a knave.", "Ava cannot be a knave, because this would contradict the claim of Scarlett that Mia is a knight if and only if Ava is a knight.", "We have exhausted all possibilities for Ava, Evelyn, and Aria, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the false claim of Noah that If Ella is a knight then Sofia is a knave.", "We have exhausted all possibilities for Ella and Noah, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that If Noah is a knight then Noah is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that If Ella is a knight then Sofia is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Aria is a knave or Evelyn is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Evelyn is not a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Ava is not a knave.", "Ava cannot be a knight, because this would contradict the claim of Scarlett that Mia is a knight if and only if Ava is a knight.", "Ava cannot be a knave, because this would contradict the claim of Evelyn that Ava is not a knave.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the claim of Ella that Aria is a knave or Evelyn is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Evelyn is not a knave.", "Evelyn cannot be a knight, because this would contradict the false claim of Aria that Evelyn is not a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Ava is not a knave.", "Ava cannot be a knight, because this would contradict the claim of Scarlett that Mia is a knight if and only if Ava is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Sofia is a knave if and only if Mia is a knight.", "Sofia cannot be a knight, because this would contradict the claim of Noah that If Ella is a knight then Sofia is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Noah is a knave if and only if Noah is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 7), ('telling-truth', 5)), ('or', ('lying', 4), ('telling-truth', 2)), ('not', ('lying', 5)), ('->', ('telling-truth', 1), ('lying', 6)), ('not', ('lying', 2)), ('<=>', ('lying', 6), ('telling-truth', 7)), ('<=>', ('lying', 3), ('telling-truth', 3)), ('->', ('telling-truth', 3), ('lying', 3)))", "index": 1031}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: William, Owen, Evelyn, James, Mason, Jack, Chloe, and Emily. William was heard saying, \"Owen is a knave and James is a knave\". Owen commented, \"James is a knave\". Evelyn told you that William is not a knave. \"Emily is not a knave\" - James. \"If Jack is a knight then Emily is a knave\" - Mason. Jack stated, \"Mason is a knight if and only if William is a knave\". Chloe stated, \"If William is a knave then Owen is a knight\". Emily commented, \"Emily is a knight or Jack is a knave\". So who is a knight and who is a knave?", "names": ["William", "Owen", "Evelyn", "James", "Mason", "Jack", "Chloe", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true, true, false], "solution_text": "William is a knave, Owen is a knight, Evelyn is a knave, James is a knave, Mason is a knight, Jack is a knight, Chloe is a knight, and Emily is a knave.", "solution_text_format": "(1) William is a knave\n(2) Owen is a knight\n(3) Evelyn is a knave\n(4) James is a knave\n(5) Mason is a knight\n(6) Jack is a knight\n(7) Chloe is a knight\n(8) Emily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Owen is a knave and James is a knave.", "Owen cannot be a knight, because this would contradict the claim of William that Owen is a knave and James is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that James is a knave.", "James cannot be a knight, because this would contradict the claim of William that Owen is a knave and James is a knave.", "James cannot be a knave, because this would contradict the false claim of Owen that James is a knave.", "We have exhausted all possibilities for James and Owen, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Owen is a knave and James is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that James is a knave.", "James cannot be a knight, because this would contradict the claim of Owen that James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Emily is not a knave.", "Emily cannot be a knight, because this would contradict the false claim of James that Emily is not a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Emily is a knight or Jack is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Mason is a knight if and only if William is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Jack is a knight then Emily is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that William is not a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that William is not a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that If William is a knave then Owen is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 1), ('lying', 3)), ('lying', 3), ('not', ('lying', 0)), ('not', ('lying', 7)), ('->', ('telling-truth', 5), ('lying', 7)), ('<=>', ('telling-truth', 4), ('lying', 0)), ('->', ('lying', 0), ('telling-truth', 1)), ('or', ('telling-truth', 7), ('lying', 5)))", "index": 1032}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ethan, Benjamin, Zoey, Sofia, Avery, Abigail, Noah, and Alexander. Ethan remarked, \"Noah is a knight\". Benjamin was heard saying, \"Alexander is a knight if and only if Zoey is a knight\". In a statement by Zoey: \"If Avery is a knight then Sofia is a knave\". Sofia stated, \"Noah is a knight or Avery is a knight\". In Avery's words: \"If Noah is a knight then Sofia is a knave\". As Abigail put it, \"Benjamin is a knave and Benjamin is a knight\". In Noah's words: \"Alexander is not a knave\". Alexander said, \"If Sofia is a knight then Abigail is a knave.\" So who is a knight and who is a knave?", "names": ["Ethan", "Benjamin", "Zoey", "Sofia", "Avery", "Abigail", "Noah", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false, true, true], "solution_text": "Ethan is a knight, Benjamin is a knight, Zoey is a knight, Sofia is a knight, Avery is a knave, Abigail is a knave, Noah is a knight, and Alexander is a knight.", "solution_text_format": "(1) Ethan is a knight\n(2) Benjamin is a knight\n(3) Zoey is a knight\n(4) Sofia is a knight\n(5) Avery is a knave\n(6) Abigail is a knave\n(7) Noah is a knight\n(8) Alexander is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Noah is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Alexander is not a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that If Sofia is a knight then Abigail is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Noah is a knight or Avery is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that If Noah is a knight then Sofia is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that If Noah is a knight then Sofia is a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave and Benjamin is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Benjamin is a knave and Benjamin is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Alexander is a knight if and only if Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that If Avery is a knight then Sofia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 6), ('<=>', ('telling-truth', 7), ('telling-truth', 2)), ('->', ('telling-truth', 4), ('lying', 3)), ('or', ('telling-truth', 6), ('telling-truth', 4)), ('->', ('telling-truth', 6), ('lying', 3)), ('and', ('lying', 1), ('telling-truth', 1)), ('not', ('lying', 7)), ('->', ('telling-truth', 3), ('lying', 5)))", "index": 1033}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Oliver, Lucas, William, Elizabeth, Jack, Ella, Scarlett, and Henry. Oliver noted, \"Jack is a knave or Lucas is a knight\". Lucas asserted: \"Oliver is a knave\". William expressed that If Lucas is a knight then Ella is a knave. Elizabeth told you that Oliver is a knave and Scarlett is a knave. Jack remarked, \"Scarlett is a knight and Scarlett is a knave\". \"Oliver is a knave or William is a knave,\" Ella mentioned. Scarlett commented, \"Lucas is a knave and Ella is a knight\". \"Jack is a knave or Lucas is a knight\" - Henry. So who is a knight and who is a knave?", "names": ["Oliver", "Lucas", "William", "Elizabeth", "Jack", "Ella", "Scarlett", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, false, false, true], "solution_text": "Oliver is a knight, Lucas is a knave, William is a knight, Elizabeth is a knave, Jack is a knave, Ella is a knave, Scarlett is a knave, and Henry is a knight.", "solution_text_format": "(1) Oliver is a knight\n(2) Lucas is a knave\n(3) William is a knight\n(4) Elizabeth is a knave\n(5) Jack is a knave\n(6) Ella is a knave\n(7) Scarlett is a knave\n(8) Henry is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Jack is a knave or Lucas is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight and Scarlett is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Scarlett is a knight and Scarlett is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Lucas is a knave and Ella is a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Oliver is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Oliver is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Oliver is a knave or William is a knave.", "William cannot be a knight, because this would contradict the claim of Ella that Oliver is a knave or William is a knave.", "William cannot be a knave, because this would contradict the false claim of their own that If Lucas is a knight then Ella is a knave.", "We have exhausted all possibilities for William, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the claim of Scarlett that Lucas is a knave and Ella is a knight.", "We have exhausted all possibilities for Ella and Lucas, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Lucas is a knave and Ella is a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Oliver is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Oliver is a knave.", "Ella cannot be a knight, because this would contradict the false claim of Scarlett that Lucas is a knave and Ella is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Oliver is a knave or William is a knave.", "Assume William is a knight. No contradiction is found in their claim that If Lucas is a knight then Ella is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Oliver is a knave and Scarlett is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Oliver is a knave and Scarlett is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Jack is a knave or Lucas is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 4), ('telling-truth', 1)), ('lying', 0), ('->', ('telling-truth', 1), ('lying', 5)), ('and', ('lying', 0), ('lying', 6)), ('and', ('telling-truth', 6), ('lying', 6)), ('or', ('lying', 0), ('lying', 2)), ('and', ('lying', 1), ('telling-truth', 5)), ('or', ('lying', 4), ('telling-truth', 1)))", "index": 1034}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Penelope, William, Harper, Zoey, Owen, Isabella, Ella, and Evelyn. \"Ella is not a knave,\" Penelope declared. In William's words: \"Penelope is a knave\". In Harper's words: \"If Evelyn is a knight then Owen is a knight\". Zoey remarked, \"Penelope is a knight\". Owen expressed that Zoey is not a knight. \"Owen is not a knave,\" Isabella declared. \"Penelope is a knave if and only if Harper is a knave,\" Ella mentioned. As Evelyn put it, \"If William is a knave then Owen is a knave\". So who is a knight and who is a knave?", "names": ["Penelope", "William", "Harper", "Zoey", "Owen", "Isabella", "Ella", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true, false, true], "solution_text": "Penelope is a knave, William is a knight, Harper is a knight, Zoey is a knave, Owen is a knight, Isabella is a knight, Ella is a knave, and Evelyn is a knight.", "solution_text_format": "(1) Penelope is a knave\n(2) William is a knight\n(3) Harper is a knight\n(4) Zoey is a knave\n(5) Owen is a knight\n(6) Isabella is a knight\n(7) Ella is a knave\n(8) Evelyn is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that Ella is not a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Penelope is a knave if and only if Harper is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that If Evelyn is a knight then Owen is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If William is a knave then Owen is a knave.", "William cannot be a knight, because this would contradict the claim of their own that Penelope is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Penelope is a knave.", "Owen cannot be a knight, because this would contradict the claim of Evelyn that If William is a knave then Owen is a knave.", "Owen cannot be a knave, because this would contradict the claim of Harper that If Evelyn is a knight then Owen is a knight.", "We have exhausted all possibilities for Owen and William, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that If William is a knave then Owen is a knave.", "William cannot be a knight, because this would contradict the claim of their own that Penelope is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Penelope is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Zoey is not a knight.", "Zoey cannot be a knight, because this would contradict the claim of Owen that Zoey is not a knight.", "Zoey cannot be a knave, because this would contradict the false claim of their own that Penelope is a knight.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the false claim of Evelyn that If William is a knave then Owen is a knave.", "We have exhausted all possibilities for Owen, William, and Evelyn, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the claim of Ella that Penelope is a knave if and only if Harper is a knave.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the claim of Penelope that Ella is not a knave.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Ella is not a knave.", "Ella cannot be a knight, because this would contradict the false claim of Penelope that Ella is not a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Penelope is a knave if and only if Harper is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that If Evelyn is a knight then Owen is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If William is a knave then Owen is a knave.", "Assume William is a knight. No contradiction is found in their claim that Penelope is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Zoey is not a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that Penelope is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Penelope is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Owen is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 6)), ('lying', 0), ('->', ('telling-truth', 7), ('telling-truth', 4)), ('telling-truth', 0), ('not', ('telling-truth', 3)), ('not', ('lying', 4)), ('<=>', ('lying', 0), ('lying', 2)), ('->', ('lying', 1), ('lying', 4)))", "index": 1035}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Owen, Chloe, Luke, Lucas, Scarlett, Liam, Daniel, and Avery. \"If Daniel is a knight then Owen is a knight,\" Owen claimed. Chloe expressed that Owen is a knave. Luke expressed that If Owen is a knave then Daniel is a knight. Lucas said that Avery is a knight and Luke is a knight. \"Chloe is a knight and Daniel is a knave,\" Scarlett claimed. \"Daniel is a knave or Lucas is a knight,\" Liam mentioned. Daniel said that Liam is a knight and Scarlett is a knight. Avery said, \"Luke is a knave if and only if Daniel is a knave.\" So who is a knight and who is a knave?", "names": ["Owen", "Chloe", "Luke", "Lucas", "Scarlett", "Liam", "Daniel", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true, false, false], "solution_text": "Owen is a knight, Chloe is a knave, Luke is a knight, Lucas is a knave, Scarlett is a knave, Liam is a knight, Daniel is a knave, and Avery is a knave.", "solution_text_format": "(1) Owen is a knight\n(2) Chloe is a knave\n(3) Luke is a knight\n(4) Lucas is a knave\n(5) Scarlett is a knave\n(6) Liam is a knight\n(7) Daniel is a knave\n(8) Avery is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that If Daniel is a knight then Owen is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Liam is a knight and Scarlett is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Daniel is a knave or Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Avery is a knight and Luke is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Luke is a knave if and only if Daniel is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that If Owen is a knave then Daniel is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Chloe is a knight and Daniel is a knave.", "Scarlett cannot be a knave, because this would contradict the claim of Daniel that Liam is a knight and Scarlett is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the false claim of their own that If Owen is a knave then Daniel is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Avery.", "Avery cannot be a knave, because this would contradict the claim of Lucas that Avery is a knight and Luke is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the claim of Liam that Daniel is a knave or Lucas is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the claim of Daniel that Liam is a knight and Scarlett is a knight.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Liam is a knight and Scarlett is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Daniel is a knave or Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Avery is a knight and Luke is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Luke is a knave if and only if Daniel is a knave.", "Luke cannot be a knight, because this would contradict the claim of Avery that Luke is a knave if and only if Daniel is a knave.", "Luke cannot be a knave, because this would contradict the false claim of their own that If Owen is a knave then Daniel is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Avery.", "Avery cannot be a knave, because this would contradict the claim of Lucas that Avery is a knight and Luke is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Avery is a knight and Luke is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Luke is a knave if and only if Daniel is a knave.", "Luke cannot be a knight, because this would contradict the false claim of Lucas that Avery is a knight and Luke is a knight.", "Luke cannot be a knave, because this would contradict the false claim of their own that If Owen is a knave then Daniel is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Luke is a knave if and only if Daniel is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that If Owen is a knave then Daniel is a knight.", "Scarlett cannot be a knight, because this would contradict the false claim of Daniel that Liam is a knight and Scarlett is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Chloe is a knight and Daniel is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Owen is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Owen is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 6), ('telling-truth', 0)), ('lying', 0), ('->', ('lying', 0), ('telling-truth', 6)), ('and', ('telling-truth', 7), ('telling-truth', 2)), ('and', ('telling-truth', 1), ('lying', 6)), ('or', ('lying', 6), ('telling-truth', 3)), ('and', ('telling-truth', 5), ('telling-truth', 4)), ('<=>', ('lying', 2), ('lying', 6)))", "index": 1036}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jacob, Ava, Avery, Harper, Jackson, Mason, Aria, and Penelope. \"If Penelope is a knight then Penelope is a knave,\" Jacob claimed. Ava told you that Aria is not a knight. Avery commented, \"Aria is a knave if and only if Jackson is a knave\". \"Ava is a knave,\" Harper declared. \"Harper is a knight and Aria is a knight,\" Jackson mentioned. In a statement by Mason: \"Ava is a knight\". Aria noted, \"Jackson is a knave or Penelope is a knave\". In Penelope's words: \"Mason is a knight and Aria is a knight\". So who is a knight and who is a knave?", "names": ["Jacob", "Ava", "Avery", "Harper", "Jackson", "Mason", "Aria", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false, true, false], "solution_text": "Jacob is a knight, Ava is a knave, Avery is a knight, Harper is a knight, Jackson is a knight, Mason is a knave, Aria is a knight, and Penelope is a knave.", "solution_text_format": "(1) Jacob is a knight\n(2) Ava is a knave\n(3) Avery is a knight\n(4) Harper is a knight\n(5) Jackson is a knight\n(6) Mason is a knave\n(7) Aria is a knight\n(8) Penelope is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that If Penelope is a knight then Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the claim of Jacob that If Penelope is a knight then Penelope is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Mason is a knight and Aria is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Ava is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Aria is not a knight.", "Aria cannot be a knight, because this would contradict the claim of Ava that Aria is not a knight.", "Aria cannot be a knave, because this would contradict the false claim of their own that Jackson is a knave or Penelope is a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the claim of Mason that Ava is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Ava is a knight.", "Ava cannot be a knight, because this would contradict the false claim of Mason that Ava is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Aria is not a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Jackson is a knave or Penelope is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Harper is a knight and Aria is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Ava is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Aria is a knave if and only if Jackson is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 7), ('lying', 7)), ('not', ('telling-truth', 6)), ('<=>', ('lying', 6), ('lying', 4)), ('lying', 1), ('and', ('telling-truth', 3), ('telling-truth', 6)), ('telling-truth', 1), ('or', ('lying', 4), ('lying', 7)), ('and', ('telling-truth', 5), ('telling-truth', 6)))", "index": 1037}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: James, Noah, Grace, Riley, Jackson, Joseph, Samuel, and Scarlett. \"Samuel is a knave,\" James declared. Noah told you that Noah is a knight and Jackson is a knave. Grace told you that Scarlett is not a knave. According to Riley, \"Joseph is a knave and Samuel is a knight\". Jackson was heard saying, \"Noah is not a knave\". Joseph said, \"If James is a knight then Jackson is a knight.\" Samuel remarked, \"Jackson is a knight and Scarlett is a knave\". According to Scarlett, \"Jackson is a knight if and only if Riley is a knave\". So who is a knight and who is a knave?", "names": ["James", "Noah", "Grace", "Riley", "Jackson", "Joseph", "Samuel", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, false, false, false], "solution_text": "James is a knight, Noah is a knave, Grace is a knave, Riley is a knave, Jackson is a knave, Joseph is a knave, Samuel is a knave, and Scarlett is a knave.", "solution_text_format": "(1) James is a knight\n(2) Noah is a knave\n(3) Grace is a knave\n(4) Riley is a knave\n(5) Jackson is a knave\n(6) Joseph is a knave\n(7) Samuel is a knave\n(8) Scarlett is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of James that Samuel is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Jackson is a knight and Scarlett is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Noah is not a knave.", "Noah cannot be a knight, because this would contradict the claim of their own that Noah is a knight and Jackson is a knave.", "Noah cannot be a knave, because this would contradict the claim of Jackson that Noah is not a knave.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Noah is not a knave.", "Noah cannot be a knight, because this would contradict the false claim of Jackson that Noah is not a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Noah is a knight and Jackson is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Riley is a knave.", "Riley cannot be a knight, because this would contradict the claim of their own that Joseph is a knave and Samuel is a knight.", "Riley cannot be a knave, because this would contradict the claim of Scarlett that Jackson is a knight if and only if Riley is a knave.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Jackson is a knight if and only if Riley is a knave.", "Riley cannot be a knight, because this would contradict the claim of their own that Joseph is a knave and Samuel is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Joseph is a knave and Samuel is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that If James is a knight then Jackson is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that If James is a knight then Jackson is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Scarlett is not a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Scarlett is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 6), ('and', ('telling-truth', 1), ('lying', 4)), ('not', ('lying', 7)), ('and', ('lying', 5), ('telling-truth', 6)), ('not', ('lying', 1)), ('->', ('telling-truth', 0), ('telling-truth', 4)), ('and', ('telling-truth', 4), ('lying', 7)), ('<=>', ('telling-truth', 4), ('lying', 3)))", "index": 1038}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jack, Henry, Ethan, Isabella, Alexander, Grace, Aria, and Olivia. Jack said that Olivia is a knave and Isabella is a knight. Henry asserted: \"Jack is not a knave\". Ethan told you that Jack is a knave. Isabella noted, \"Olivia is a knave\". \"Aria is not a knight,\" Alexander mentioned. Grace noted, \"Henry is a knave or Jack is a knave\". \"Grace is a knight and Grace is a knave,\" Aria claimed. \"Grace is a knight and Ethan is a knave,\" Olivia claimed. So who is a knight and who is a knave?", "names": ["Jack", "Henry", "Ethan", "Isabella", "Alexander", "Grace", "Aria", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false, false, false], "solution_text": "Jack is a knight, Henry is a knight, Ethan is a knave, Isabella is a knight, Alexander is a knight, Grace is a knave, Aria is a knave, and Olivia is a knave.", "solution_text_format": "(1) Jack is a knight\n(2) Henry is a knight\n(3) Ethan is a knave\n(4) Isabella is a knight\n(5) Alexander is a knight\n(6) Grace is a knave\n(7) Aria is a knave\n(8) Olivia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Olivia is a knave and Isabella is a knight.", "Olivia cannot be a knight, because this would contradict the claim of Jack that Olivia is a knave and Isabella is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Grace is a knight and Ethan is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Henry is a knave or Jack is a knave.", "Henry cannot be a knight, because this would contradict the claim of Grace that Henry is a knave or Jack is a knave.", "Henry cannot be a knave, because this would contradict the false claim of their own that Jack is not a knave.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Henry is a knave or Jack is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Jack is not a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Jack is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Jack is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Olivia is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Aria is not a knight.", "Aria cannot be a knight, because this would contradict the claim of Alexander that Aria is not a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Grace is a knight and Grace is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 7), ('telling-truth', 3)), ('not', ('lying', 0)), ('lying', 0), ('lying', 7), ('not', ('telling-truth', 6)), ('or', ('lying', 1), ('lying', 0)), ('and', ('telling-truth', 5), ('lying', 5)), ('and', ('telling-truth', 5), ('lying', 2)))", "index": 1039}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Zoey, Amelia, William, Sophia, Scarlett, Chloe, Benjamin, and Lily. Zoey stated, \"Zoey is a knight or Chloe is a knight\". Amelia said that Benjamin is a knave. William noted, \"Lily is a knight or Zoey is a knight\". In Sophia's words: \"Benjamin is a knight and Lily is a knave\". Scarlett was heard saying, \"William is a knave or William is a knight\". As Chloe put it, \"Lily is a knight if and only if Amelia is a knight\". Benjamin commented, \"Lily is a knave\". \"Scarlett is a knave and Sophia is a knave\" - Lily. So who is a knight and who is a knave?", "names": ["Zoey", "Amelia", "William", "Sophia", "Scarlett", "Chloe", "Benjamin", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true, true, false], "solution_text": "Zoey is a knight, Amelia is a knave, William is a knight, Sophia is a knight, Scarlett is a knight, Chloe is a knight, Benjamin is a knight, and Lily is a knave.", "solution_text_format": "(1) Zoey is a knight\n(2) Amelia is a knave\n(3) William is a knight\n(4) Sophia is a knight\n(5) Scarlett is a knight\n(6) Chloe is a knight\n(7) Benjamin is a knight\n(8) Lily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Zoey is a knight. No contradiction is found in their claim that Zoey is a knight or Chloe is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Lily is a knight if and only if Amelia is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Scarlett is a knave and Sophia is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Lily that Scarlett is a knave and Sophia is a knave.", "Scarlett cannot be a knave, because this would contradict the false claim of their own that William is a knave or William is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Scarlett is a knave and Sophia is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that William is a knave or William is a knight.", "Assume William is a knight. No contradiction is found in their claim that Lily is a knight or Zoey is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Benjamin is a knight and Lily is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Lily is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Benjamin is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 0), ('telling-truth', 5)), ('lying', 6), ('or', ('telling-truth', 7), ('telling-truth', 0)), ('and', ('telling-truth', 6), ('lying', 7)), ('or', ('lying', 2), ('telling-truth', 2)), ('<=>', ('telling-truth', 7), ('telling-truth', 1)), ('lying', 7), ('and', ('lying', 4), ('lying', 3)))", "index": 1040}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: James, Liam, Avery, Riley, Oliver, Emma, Chloe, and Logan. James said that Liam is a knight and Oliver is a knave. \"If Avery is a knight then James is a knight,\" Liam declared. As Avery put it, \"Chloe is a knave and Logan is a knave\". Riley asserted: \"Chloe is a knave\". Oliver said that If Liam is a knight then Logan is a knave. Emma commented, \"Liam is not a knight\". As Chloe put it, \"If Avery is a knave then Oliver is a knight\". \"Chloe is a knight if and only if Riley is a knight\" - Logan. So who is a knight and who is a knave?", "names": ["James", "Liam", "Avery", "Riley", "Oliver", "Emma", "Chloe", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, false, true, false], "solution_text": "James is a knave, Liam is a knight, Avery is a knave, Riley is a knave, Oliver is a knight, Emma is a knave, Chloe is a knight, and Logan is a knave.", "solution_text_format": "(1) James is a knave\n(2) Liam is a knight\n(3) Avery is a knave\n(4) Riley is a knave\n(5) Oliver is a knight\n(6) Emma is a knave\n(7) Chloe is a knight\n(8) Logan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Liam is a knight and Oliver is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that If Avery is a knight then James is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Chloe is a knave and Logan is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Avery that Chloe is a knave and Logan is a knave.", "Chloe cannot be a knave, because this would contradict the false claim of their own that If Avery is a knave then Oliver is a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Chloe is a knave and Logan is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that If Avery is a knave then Oliver is a knight.", "Oliver cannot be a knight, because this would contradict the claim of James that Liam is a knight and Oliver is a knave.", "Oliver cannot be a knave, because this would contradict the claim of Chloe that If Avery is a knave then Oliver is a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that If Avery is a knave then Oliver is a knight.", "Oliver cannot be a knight, because this would contradict the claim of James that Liam is a knight and Oliver is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that If Liam is a knight then Logan is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Chloe is a knight if and only if Riley is a knight.", "Riley cannot be a knight, because this would contradict the claim of Logan that Chloe is a knight if and only if Riley is a knight.", "Riley cannot be a knave, because this would contradict the false claim of their own that Chloe is a knave.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the false claim of Avery that Chloe is a knave and Logan is a knave.", "We have exhausted all possibilities for Logan, Oliver, Chloe, and Avery, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the claim of James that Liam is a knight and Oliver is a knave.", "We have exhausted all possibilities for Liam, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Liam is a knight and Oliver is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that If Avery is a knight then James is a knight.", "Avery cannot be a knight, because this would contradict the claim of Liam that If Avery is a knight then James is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Chloe is a knave and Logan is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that If Avery is a knave then Oliver is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that If Liam is a knight then Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of Oliver that If Liam is a knight then Logan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Chloe is a knight if and only if Riley is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Chloe is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Chloe is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Liam is not a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Liam is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('lying', 4)), ('->', ('telling-truth', 2), ('telling-truth', 0)), ('and', ('lying', 6), ('lying', 7)), ('lying', 6), ('->', ('telling-truth', 1), ('lying', 7)), ('not', ('telling-truth', 1)), ('->', ('lying', 2), ('telling-truth', 4)), ('<=>', ('telling-truth', 6), ('telling-truth', 3)))", "index": 1041}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Avery, Jacob, Elizabeth, Riley, Amelia, Alexander, Henry, and Oliver. Avery commented, \"Oliver is a knight and Riley is a knight\". In Jacob's words: \"Oliver is a knight or Henry is a knight\". \"Henry is a knight,\" Elizabeth claimed. According to Riley, \"Elizabeth is a knight\". Amelia remarked, \"Oliver is not a knave\". Alexander asserted: \"If Amelia is a knave then Riley is a knight\". \"If Oliver is a knave then Amelia is a knave\" - Henry. Oliver asserted: \"Henry is not a knave\". So who is a knight and who is a knave?", "names": ["Avery", "Jacob", "Elizabeth", "Riley", "Amelia", "Alexander", "Henry", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true, true, true], "solution_text": "Avery is a knight, Jacob is a knight, Elizabeth is a knight, Riley is a knight, Amelia is a knight, Alexander is a knight, Henry is a knight, and Oliver is a knight.", "solution_text_format": "(1) Avery is a knight\n(2) Jacob is a knight\n(3) Elizabeth is a knight\n(4) Riley is a knight\n(5) Amelia is a knight\n(6) Alexander is a knight\n(7) Henry is a knight\n(8) Oliver is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Oliver is a knight and Riley is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Henry is not a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Oliver is a knave then Amelia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Oliver is not a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Henry is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Oliver is a knight or Henry is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that If Amelia is a knave then Riley is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 7), ('telling-truth', 3)), ('or', ('telling-truth', 7), ('telling-truth', 6)), ('telling-truth', 6), ('telling-truth', 2), ('not', ('lying', 7)), ('->', ('lying', 4), ('telling-truth', 3)), ('->', ('lying', 7), ('lying', 4)), ('not', ('lying', 6)))", "index": 1042}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ava, Logan, Penelope, Joseph, Mason, Liam, Evelyn, and Sophia. Ava noted, \"Penelope is a knight if and only if Sophia is a knight\". According to Logan, \"Sophia is a knave or Logan is a knight\". Penelope expressed that Sophia is a knave. Joseph said that Penelope is a knave or Logan is a knight. Mason commented, \"Evelyn is a knight and Logan is a knave\". Liam remarked, \"Ava is a knight\". Evelyn asserted: \"Sophia is a knave and Logan is a knave\". Sophia said that Ava is a knight if and only if Mason is a knave. So who is a knight and who is a knave?", "names": ["Ava", "Logan", "Penelope", "Joseph", "Mason", "Liam", "Evelyn", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false, false, false], "solution_text": "Ava is a knave, Logan is a knight, Penelope is a knight, Joseph is a knight, Mason is a knave, Liam is a knave, Evelyn is a knave, and Sophia is a knave.", "solution_text_format": "(1) Ava is a knave\n(2) Logan is a knight\n(3) Penelope is a knight\n(4) Joseph is a knight\n(5) Mason is a knave\n(6) Liam is a knave\n(7) Evelyn is a knave\n(8) Sophia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Penelope is a knight if and only if Sophia is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Sophia is a knave.", "Sophia cannot be a knight, because this would contradict the claim of Penelope that Sophia is a knave.", "Sophia cannot be a knave, because this would contradict the claim of Ava that Penelope is a knight if and only if Sophia is a knight.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Sophia is a knave.", "Sophia cannot be a knight, because this would contradict the claim of Ava that Penelope is a knight if and only if Sophia is a knight.", "Sophia cannot be a knave, because this would contradict the false claim of Penelope that Sophia is a knave.", "We have exhausted all possibilities for Sophia and Penelope, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Penelope is a knight if and only if Sophia is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Sophia is a knave.", "Sophia cannot be a knight, because this would contradict the false claim of Ava that Penelope is a knight if and only if Sophia is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Ava is a knight if and only if Mason is a knave.", "Mason cannot be a knight, because this would contradict the false claim of Sophia that Ava is a knight if and only if Mason is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Evelyn is a knight and Logan is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Sophia is a knave and Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of Evelyn that Sophia is a knave and Logan is a knave.", "Logan cannot be a knave, because this would contradict the false claim of their own that Sophia is a knave or Logan is a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Sophia is a knave and Logan is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Sophia is a knave or Logan is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Penelope is a knave or Logan is a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that Ava is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Ava is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('telling-truth', 7)), ('or', ('lying', 7), ('telling-truth', 1)), ('lying', 7), ('or', ('lying', 2), ('telling-truth', 1)), ('and', ('telling-truth', 6), ('lying', 1)), ('telling-truth', 0), ('and', ('lying', 7), ('lying', 1)), ('<=>', ('telling-truth', 0), ('lying', 4)))", "index": 1043}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Zoey, Charlotte, Mason, Jack, Jacob, Mia, Grace, and Riley. Zoey stated, \"Grace is a knave or Jack is a knave\". \"If Mia is a knave then Jacob is a knave\" - Charlotte. Mason was heard saying, \"Jack is a knave or Grace is a knave\". In a statement by Jack: \"Grace is a knight if and only if Jacob is a knave\". According to Jacob, \"Mason is a knight\". Mia was heard saying, \"Jack is a knight\". \"Mia is a knight or Mason is a knave\" - Grace. Riley remarked, \"Mason is a knave and Zoey is a knight\". So who is a knight and who is a knave?", "names": ["Zoey", "Charlotte", "Mason", "Jack", "Jacob", "Mia", "Grace", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, true, true, false], "solution_text": "Zoey is a knave, Charlotte is a knight, Mason is a knave, Jack is a knight, Jacob is a knave, Mia is a knight, Grace is a knight, and Riley is a knave.", "solution_text_format": "(1) Zoey is a knave\n(2) Charlotte is a knight\n(3) Mason is a knave\n(4) Jack is a knight\n(5) Jacob is a knave\n(6) Mia is a knight\n(7) Grace is a knight\n(8) Riley is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Zoey is a knight. No contradiction is found in their claim that Grace is a knave or Jack is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Mia is a knight or Mason is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Jack is a knight.", "Jack cannot be a knight, because this would contradict the claim of Zoey that Grace is a knave or Jack is a knave.", "Jack cannot be a knave, because this would contradict the claim of Mia that Jack is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Jack is a knight.", "Jack cannot be a knight, because this would contradict the claim of Zoey that Grace is a knave or Jack is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Grace is a knight if and only if Jacob is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Mason is a knight.", "Mason cannot be a knight, because this would contradict the claim of Grace that Mia is a knight or Mason is a knave.", "Mason cannot be a knave, because this would contradict the false claim of their own that Jack is a knave or Grace is a knave.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the false claim of Jack that Grace is a knight if and only if Jacob is a knave.", "We have exhausted all possibilities for Jacob, Jack, and Mia, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Mia is a knight or Mason is a knave.", "Mia cannot be a knight, because this would contradict the false claim of Grace that Mia is a knight or Mason is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Jack is a knight.", "Jack cannot be a knight, because this would contradict the false claim of Mia that Jack is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Grace is a knight if and only if Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the false claim of Jack that Grace is a knight if and only if Jacob is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Mason is a knight.", "Mason cannot be a knight, because this would contradict the false claim of Jacob that Mason is a knight.", "Mason cannot be a knave, because this would contradict the false claim of their own that Jack is a knave or Grace is a knave.", "We have exhausted all possibilities for Mason, Jacob, Jack, Mia, and Grace, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Grace is a knave or Jack is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Mia is a knight or Mason is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Grace is a knight if and only if Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Jack that Grace is a knight if and only if Jacob is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Mason is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Jack is a knave or Grace is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Jack is a knave or Grace is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Mia is a knave then Jacob is a knave.", "Riley cannot be a knight, because this would contradict the claim of their own that Mason is a knave and Zoey is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Mason is a knave and Zoey is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 6), ('lying', 3)), ('->', ('lying', 5), ('lying', 4)), ('or', ('lying', 3), ('lying', 6)), ('<=>', ('telling-truth', 6), ('lying', 4)), ('telling-truth', 2), ('telling-truth', 3), ('or', ('telling-truth', 5), ('lying', 2)), ('and', ('lying', 2), ('telling-truth', 0)))", "index": 1044}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jackson, Emma, Owen, Chloe, Matthew, Michael, Logan, and Liam. As Jackson put it, \"Chloe is a knave\". Emma stated, \"Jackson is a knight if and only if Michael is a knight\". \"Matthew is a knight,\" Owen mentioned. \"Jackson is a knight and Liam is a knave,\" Chloe mentioned. Matthew stated, \"Michael is a knight and Emma is a knave\". Michael remarked, \"Owen is a knight if and only if Liam is a knave\". Logan said, \"Chloe is a knave or Emma is a knave.\" \"Matthew is a knave or Michael is a knave,\" Liam claimed. So who is a knight and who is a knave?", "names": ["Jackson", "Emma", "Owen", "Chloe", "Matthew", "Michael", "Logan", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, true, true, true], "solution_text": "Jackson is a knight, Emma is a knight, Owen is a knave, Chloe is a knave, Matthew is a knave, Michael is a knight, Logan is a knight, and Liam is a knight.", "solution_text_format": "(1) Jackson is a knight\n(2) Emma is a knight\n(3) Owen is a knave\n(4) Chloe is a knave\n(5) Matthew is a knave\n(6) Michael is a knight\n(7) Logan is a knight\n(8) Liam is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Jackson that Chloe is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Jackson is a knight and Liam is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Matthew is a knave or Michael is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Michael is a knight and Emma is a knave.", "Michael cannot be a knight, because this would contradict the claim of Liam that Matthew is a knave or Michael is a knave.", "Michael cannot be a knave, because this would contradict the claim of Matthew that Michael is a knight and Emma is a knave.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Michael is a knight and Emma is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Owen is a knight if and only if Liam is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Matthew is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Matthew is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Michael is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Chloe is a knave or Emma is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('<=>', ('telling-truth', 0), ('telling-truth', 5)), ('telling-truth', 4), ('and', ('telling-truth', 0), ('lying', 7)), ('and', ('telling-truth', 5), ('lying', 1)), ('<=>', ('telling-truth', 2), ('lying', 7)), ('or', ('lying', 3), ('lying', 1)), ('or', ('lying', 4), ('lying', 5)))", "index": 1045}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mason, Ella, Zoey, Victoria, Liam, Owen, Lucas, and Elizabeth. In Mason's words: \"Lucas is a knight and Owen is a knight\". Ella stated, \"Victoria is a knave\". Zoey remarked, \"Victoria is not a knave\". \"Elizabeth is not a knave,\" Victoria declared. Liam told you that Zoey is a knave and Elizabeth is a knight. \"Liam is a knight,\" Owen declared. \"If Victoria is a knave then Elizabeth is a knave,\" Lucas mentioned. \"Owen is a knight and Lucas is a knave,\" Elizabeth mentioned. So who is a knight and who is a knave?", "names": ["Mason", "Ella", "Zoey", "Victoria", "Liam", "Owen", "Lucas", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, false, true, false], "solution_text": "Mason is a knave, Ella is a knight, Zoey is a knave, Victoria is a knave, Liam is a knave, Owen is a knave, Lucas is a knight, and Elizabeth is a knave.", "solution_text_format": "(1) Mason is a knave\n(2) Ella is a knight\n(3) Zoey is a knave\n(4) Victoria is a knave\n(5) Liam is a knave\n(6) Owen is a knave\n(7) Lucas is a knight\n(8) Elizabeth is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Lucas is a knight and Owen is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that If Victoria is a knave then Elizabeth is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Elizabeth is not a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Owen is a knight and Lucas is a knave.", "Elizabeth cannot be a knave, because this would contradict the claim of Victoria that Elizabeth is not a knave.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Elizabeth is not a knave.", "Elizabeth cannot be a knight, because this would contradict the false claim of Victoria that Elizabeth is not a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Owen is a knight and Lucas is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Liam is a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that Zoey is a knave and Elizabeth is a knight.", "Liam cannot be a knave, because this would contradict the claim of Owen that Liam is a knight.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the claim of Mason that Lucas is a knight and Owen is a knight.", "We have exhausted all possibilities for Owen, Elizabeth, and Victoria, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the claim of Mason that Lucas is a knight and Owen is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Lucas is a knight and Owen is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that If Victoria is a knave then Elizabeth is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Elizabeth is not a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Owen is a knight and Lucas is a knave.", "Elizabeth cannot be a knave, because this would contradict the claim of Victoria that Elizabeth is not a knave.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Elizabeth is not a knave.", "Elizabeth cannot be a knight, because this would contradict the false claim of Victoria that Elizabeth is not a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Owen is a knight and Lucas is a knave.", "Owen cannot be a knight, because this would contradict the false claim of Mason that Lucas is a knight and Owen is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Liam is a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that Zoey is a knave and Elizabeth is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Zoey is a knave and Elizabeth is a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that Victoria is not a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Victoria is not a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Victoria is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 6), ('telling-truth', 5)), ('lying', 3), ('not', ('lying', 3)), ('not', ('lying', 7)), ('and', ('lying', 2), ('telling-truth', 7)), ('telling-truth', 4), ('->', ('lying', 3), ('lying', 7)), ('and', ('telling-truth', 5), ('lying', 6)))", "index": 1046}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Charlotte, Mia, Scarlett, Emily, Jacob, Isabella, Matthew, and Benjamin. In Charlotte's words: \"Emily is a knight and Scarlett is a knave\". Mia said, \"Isabella is a knave and Scarlett is a knight.\" According to Scarlett, \"Mia is not a knave\". \"Matthew is a knave\" - Emily. Jacob stated, \"Scarlett is a knight or Benjamin is a knight\". \"If Mia is a knave then Benjamin is a knight\" - Isabella. Matthew noted, \"Jacob is a knave and Benjamin is a knight\". In Benjamin's words: \"Mia is a knight if and only if Charlotte is a knight\". So who is a knight and who is a knave?", "names": ["Charlotte", "Mia", "Scarlett", "Emily", "Jacob", "Isabella", "Matthew", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, false, false, false], "solution_text": "Charlotte is a knight, Mia is a knave, Scarlett is a knave, Emily is a knight, Jacob is a knave, Isabella is a knave, Matthew is a knave, and Benjamin is a knave.", "solution_text_format": "(1) Charlotte is a knight\n(2) Mia is a knave\n(3) Scarlett is a knave\n(4) Emily is a knight\n(5) Jacob is a knave\n(6) Isabella is a knave\n(7) Matthew is a knave\n(8) Benjamin is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that Emily is a knight and Scarlett is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Matthew is a knave.", "Matthew cannot be a knight, because this would contradict the claim of Emily that Matthew is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Jacob is a knave and Benjamin is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Scarlett is a knight or Benjamin is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of Charlotte that Emily is a knight and Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Mia is not a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Isabella is a knave and Scarlett is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Isabella is a knave and Scarlett is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that If Mia is a knave then Benjamin is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Mia is a knight if and only if Charlotte is a knight.", "Benjamin cannot be a knave, because this would contradict the claim of Jacob that Scarlett is a knight or Benjamin is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that If Mia is a knave then Benjamin is a knight.", "Benjamin cannot be a knight, because this would contradict the false claim of Isabella that If Mia is a knave then Benjamin is a knight.", "Benjamin cannot be a knave, because this would contradict the claim of Jacob that Scarlett is a knight or Benjamin is a knight.", "We have exhausted all possibilities for Benjamin, Isabella, Mia, and Scarlett, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Scarlett is a knight or Benjamin is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of Charlotte that Emily is a knight and Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Mia is not a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Isabella is a knave and Scarlett is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Isabella is a knave and Scarlett is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that If Mia is a knave then Benjamin is a knight.", "Benjamin cannot be a knight, because this would contradict the false claim of Jacob that Scarlett is a knight or Benjamin is a knight.", "Benjamin cannot be a knave, because this would contradict the claim of Isabella that If Mia is a knave then Benjamin is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that If Mia is a knave then Benjamin is a knight.", "Benjamin cannot be a knight, because this would contradict the false claim of Jacob that Scarlett is a knight or Benjamin is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Mia is a knight if and only if Charlotte is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('lying', 2)), ('and', ('lying', 5), ('telling-truth', 2)), ('not', ('lying', 1)), ('lying', 6), ('or', ('telling-truth', 2), ('telling-truth', 7)), ('->', ('lying', 1), ('telling-truth', 7)), ('and', ('lying', 4), ('telling-truth', 7)), ('<=>', ('telling-truth', 1), ('telling-truth', 0)))", "index": 1047}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jackson, Owen, Emma, Ella, Abigail, Penelope, Isabella, and Evelyn. In Jackson's words: \"Emma is a knave or Penelope is a knave\". Owen noted, \"Emma is a knight\". Emma expressed that Isabella is a knight if and only if Abigail is a knight. Ella commented, \"Penelope is a knight\". Abigail noted, \"Isabella is a knave if and only if Ella is a knight\". Penelope said, \"Jackson is a knight and Jackson is a knave.\" Isabella told you that Jackson is a knave. Evelyn remarked, \"Ella is not a knave\". So who is a knight and who is a knave?", "names": ["Jackson", "Owen", "Emma", "Ella", "Abigail", "Penelope", "Isabella", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false, false, false], "solution_text": "Jackson is a knight, Owen is a knight, Emma is a knight, Ella is a knave, Abigail is a knave, Penelope is a knave, Isabella is a knave, and Evelyn is a knave.", "solution_text_format": "(1) Jackson is a knight\n(2) Owen is a knight\n(3) Emma is a knight\n(4) Ella is a knave\n(5) Abigail is a knave\n(6) Penelope is a knave\n(7) Isabella is a knave\n(8) Evelyn is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Emma is a knave or Penelope is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Abigail is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Jackson is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Jackson is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Emma that Isabella is a knight if and only if Abigail is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Isabella is a knave if and only if Ella is a knight.", "Ella cannot be a knight, because this would contradict the false claim of Abigail that Isabella is a knave if and only if Ella is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Penelope is a knight.", "Penelope cannot be a knight, because this would contradict the claim of Jackson that Emma is a knave or Penelope is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Jackson is a knight and Jackson is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Emma is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Ella is not a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Ella is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('lying', 5)), ('telling-truth', 2), ('<=>', ('telling-truth', 6), ('telling-truth', 4)), ('telling-truth', 5), ('<=>', ('lying', 6), ('telling-truth', 3)), ('and', ('telling-truth', 0), ('lying', 0)), ('lying', 0), ('not', ('lying', 3)))", "index": 1048}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jack, Logan, Matthew, Benjamin, Chloe, Victoria, Abigail, and Jacob. \"Logan is a knight if and only if Matthew is a knight\" - Jack. According to Logan, \"Chloe is a knight or Matthew is a knight\". Matthew was heard saying, \"Chloe is a knight\". \"Logan is a knight if and only if Benjamin is a knight,\" Benjamin mentioned. \"Victoria is a knight if and only if Benjamin is a knave,\" Chloe claimed. \"Matthew is a knight if and only if Chloe is a knight,\" Victoria declared. Abigail expressed that Jacob is a knave or Benjamin is a knight. In a statement by Jacob: \"Chloe is not a knight\". So who is a knight and who is a knave?", "names": ["Jack", "Logan", "Matthew", "Benjamin", "Chloe", "Victoria", "Abigail", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true, true, false], "solution_text": "Jack is a knight, Logan is a knight, Matthew is a knight, Benjamin is a knave, Chloe is a knight, Victoria is a knight, Abigail is a knight, and Jacob is a knave.", "solution_text_format": "(1) Jack is a knight\n(2) Logan is a knight\n(3) Matthew is a knight\n(4) Benjamin is a knave\n(5) Chloe is a knight\n(6) Victoria is a knight\n(7) Abigail is a knight\n(8) Jacob is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Logan is a knight if and only if Matthew is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Chloe is a knight or Matthew is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Benjamin is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Matthew is a knight if and only if Chloe is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Chloe is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of Chloe that Victoria is a knight if and only if Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Logan is a knight if and only if Benjamin is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Jacob is a knave or Benjamin is a knight.", "Jacob cannot be a knight, because this would contradict the claim of Abigail that Jacob is a knave or Benjamin is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Chloe is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('telling-truth', 2)), ('or', ('telling-truth', 4), ('telling-truth', 2)), ('telling-truth', 4), ('<=>', ('telling-truth', 1), ('telling-truth', 3)), ('<=>', ('telling-truth', 5), ('lying', 3)), ('<=>', ('telling-truth', 2), ('telling-truth', 4)), ('or', ('lying', 7), ('telling-truth', 3)), ('not', ('telling-truth', 4)))", "index": 1049}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Luke, Charlotte, Jack, Owen, Ella, Samuel, Elizabeth, and Michael. As Luke put it, \"Samuel is not a knave\". Charlotte commented, \"Michael is not a knight\". \"Michael is not a knight\" - Jack. In a statement by Owen: \"Charlotte is a knight and Luke is a knight\". \"Samuel is a knight if and only if Luke is a knight,\" Ella declared. Samuel commented, \"If Michael is a knave then Elizabeth is a knave\". \"Michael is a knight\" - Elizabeth. Michael asserted: \"Charlotte is a knave or Jack is a knight\". So who is a knight and who is a knave?", "names": ["Luke", "Charlotte", "Jack", "Owen", "Ella", "Samuel", "Elizabeth", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true, true, true], "solution_text": "Luke is a knight, Charlotte is a knave, Jack is a knave, Owen is a knave, Ella is a knight, Samuel is a knight, Elizabeth is a knight, and Michael is a knight.", "solution_text_format": "(1) Luke is a knight\n(2) Charlotte is a knave\n(3) Jack is a knave\n(4) Owen is a knave\n(5) Ella is a knight\n(6) Samuel is a knight\n(7) Elizabeth is a knight\n(8) Michael is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Samuel is not a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that If Michael is a knave then Elizabeth is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Charlotte is a knave or Jack is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Michael is not a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Michael is not a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Michael is not a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Michael is not a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Michael is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Charlotte is a knight and Luke is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Charlotte is a knight and Luke is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Samuel is a knight if and only if Luke is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 5)), ('not', ('telling-truth', 7)), ('not', ('telling-truth', 7)), ('and', ('telling-truth', 1), ('telling-truth', 0)), ('<=>', ('telling-truth', 5), ('telling-truth', 0)), ('->', ('lying', 7), ('lying', 6)), ('telling-truth', 7), ('or', ('lying', 1), ('telling-truth', 2)))", "index": 1050}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Noah, Charlotte, Oliver, Mia, Jackson, Liam, Aurora, and Elizabeth. Noah expressed that Liam is a knight and Elizabeth is a knight. \"Mia is not a knight,\" Charlotte claimed. Oliver stated, \"If Elizabeth is a knave then Jackson is a knave\". Mia told you that Noah is a knave and Elizabeth is a knight. In a statement by Jackson: \"If Oliver is a knave then Jackson is a knight\". In a statement by Liam: \"Jackson is a knight\". In Aurora's words: \"Mia is a knight and Aurora is a knight\". Elizabeth commented, \"Jackson is a knight if and only if Liam is a knight\". So who is a knight and who is a knave?", "names": ["Noah", "Charlotte", "Oliver", "Mia", "Jackson", "Liam", "Aurora", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true, false, true], "solution_text": "Noah is a knight, Charlotte is a knight, Oliver is a knight, Mia is a knave, Jackson is a knight, Liam is a knight, Aurora is a knave, and Elizabeth is a knight.", "solution_text_format": "(1) Noah is a knight\n(2) Charlotte is a knight\n(3) Oliver is a knight\n(4) Mia is a knave\n(5) Jackson is a knight\n(6) Liam is a knight\n(7) Aurora is a knave\n(8) Elizabeth is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Noah is a knight. No contradiction is found in their claim that Liam is a knight and Elizabeth is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Jackson is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that If Oliver is a knave then Jackson is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Jackson is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Liam is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Mia is not a knight.", "Mia cannot be a knight, because this would contradict the claim of Charlotte that Mia is not a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Noah is a knave and Elizabeth is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Mia is a knight and Aurora is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Mia is a knight and Aurora is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('telling-truth', 7)), ('not', ('telling-truth', 3)), ('->', ('lying', 7), ('lying', 4)), ('and', ('lying', 0), ('telling-truth', 7)), ('->', ('lying', 2), ('telling-truth', 4)), ('telling-truth', 4), ('and', ('telling-truth', 3), ('telling-truth', 6)), ('<=>', ('telling-truth', 4), ('telling-truth', 5)))", "index": 1051}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Abigail, Sofia, Chloe, Jacob, Daniel, Alexander, Ava, and Ethan. According to Abigail, \"If Abigail is a knight then Alexander is a knight\". \"Jacob is not a knight,\" Sofia claimed. Chloe asserted: \"Jacob is a knight and Alexander is a knight\". \"Sofia is not a knight,\" Jacob mentioned. \"Abigail is not a knave\" - Daniel. Alexander commented, \"Jacob is a knight if and only if Daniel is a knave\". According to Ava, \"Chloe is a knight\". Ethan said that If Chloe is a knave then Jacob is a knight. So who is a knight and who is a knave?", "names": ["Abigail", "Sofia", "Chloe", "Jacob", "Daniel", "Alexander", "Ava", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true, false, false], "solution_text": "Abigail is a knight, Sofia is a knight, Chloe is a knave, Jacob is a knave, Daniel is a knight, Alexander is a knight, Ava is a knave, and Ethan is a knave.", "solution_text_format": "(1) Abigail is a knight\n(2) Sofia is a knight\n(3) Chloe is a knave\n(4) Jacob is a knave\n(5) Daniel is a knight\n(6) Alexander is a knight\n(7) Ava is a knave\n(8) Ethan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that If Abigail is a knight then Alexander is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Jacob is a knight if and only if Daniel is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Sofia is not a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that Jacob is not a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Jacob is not a knight.", "Daniel cannot be a knight, because this would contradict the claim of Alexander that Jacob is a knight if and only if Daniel is a knave.", "Daniel cannot be a knave, because this would contradict the false claim of their own that Abigail is not a knave.", "We have exhausted all possibilities for Daniel and Sofia, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Sofia is not a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Jacob is not a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Abigail is not a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Jacob is a knight and Alexander is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Jacob is a knight and Alexander is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Chloe is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Chloe is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that If Chloe is a knave then Jacob is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that If Chloe is a knave then Jacob is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 0), ('telling-truth', 5)), ('not', ('telling-truth', 3)), ('and', ('telling-truth', 3), ('telling-truth', 5)), ('not', ('telling-truth', 1)), ('not', ('lying', 0)), ('<=>', ('telling-truth', 3), ('lying', 4)), ('telling-truth', 2), ('->', ('lying', 2), ('telling-truth', 3)))", "index": 1052}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sofia, Aiden, Emma, Elizabeth, Mia, Avery, Sophia, and David. \"David is a knight and David is a knave\" - Sofia. Aiden told you that Sophia is a knave and Sofia is a knight. \"David is a knight,\" Emma mentioned. Elizabeth told you that Mia is not a knight. \"Emma is not a knave,\" Mia claimed. Avery told you that Elizabeth is a knave if and only if Elizabeth is a knight. \"Elizabeth is a knight or Sofia is a knave,\" Sophia claimed. According to David, \"Avery is a knave and Aiden is a knight\". So who is a knight and who is a knave?", "names": ["Sofia", "Aiden", "Emma", "Elizabeth", "Mia", "Avery", "Sophia", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, false, true, false], "solution_text": "Sofia is a knave, Aiden is a knave, Emma is a knave, Elizabeth is a knight, Mia is a knave, Avery is a knave, Sophia is a knight, and David is a knave.", "solution_text_format": "(1) Sofia is a knave\n(2) Aiden is a knave\n(3) Emma is a knave\n(4) Elizabeth is a knight\n(5) Mia is a knave\n(6) Avery is a knave\n(7) Sophia is a knight\n(8) David is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Sofia cannot be a knight, because this would contradict the claim of their own that David is a knight and David is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that David is a knight and David is a knave.", "Assume David is a knight. No contradiction is found in their claim that Avery is a knave and Aiden is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave if and only if Elizabeth is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Elizabeth is a knave if and only if Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Mia is not a knight.", "Mia cannot be a knight, because this would contradict the claim of Elizabeth that Mia is not a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Emma is not a knave.", "Emma cannot be a knight, because this would contradict the false claim of Mia that Emma is not a knave.", "Emma cannot be a knave, because this would contradict the false claim of their own that David is a knight.", "We have exhausted all possibilities for Emma and Mia, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Mia is not a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Emma is not a knave.", "Assume Emma is a knight. No contradiction is found in their claim that David is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Sophia is a knave and Sofia is a knight.", "Aiden cannot be a knave, because this would contradict the claim of David that Avery is a knave and Aiden is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Emma.", "Emma cannot be a knave, because this would contradict the false claim of their own that David is a knight.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the false claim of Elizabeth that Mia is not a knight.", "We have exhausted all possibilities for Mia, Elizabeth, and Avery, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Avery is a knave and Aiden is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave if and only if Elizabeth is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Elizabeth is a knave if and only if Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Mia is not a knight.", "Mia cannot be a knight, because this would contradict the claim of Elizabeth that Mia is not a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Emma is not a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that David is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that David is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Sophia is a knave and Sofia is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Sophia is a knave and Sofia is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Elizabeth is a knight or Sofia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 7), ('lying', 7)), ('and', ('lying', 6), ('telling-truth', 0)), ('telling-truth', 7), ('not', ('telling-truth', 4)), ('not', ('lying', 2)), ('<=>', ('lying', 3), ('telling-truth', 3)), ('or', ('telling-truth', 3), ('lying', 0)), ('and', ('lying', 5), ('telling-truth', 1)))", "index": 1053}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emily, Penelope, Riley, Aiden, Lily, Henry, Alexander, and William. In a statement by Emily: \"Aiden is not a knave\". Penelope stated, \"Riley is a knave if and only if Penelope is a knight\". Riley said that Emily is not a knight. Aiden expressed that If William is a knave then Lily is a knave. Lily noted, \"Penelope is a knave if and only if Alexander is a knave\". \"Emily is a knave if and only if Emily is a knight,\" Henry claimed. \"Penelope is a knave or Emily is a knight,\" Alexander claimed. As William put it, \"If William is a knight then Penelope is a knave\". So who is a knight and who is a knave?", "names": ["Emily", "Penelope", "Riley", "Aiden", "Lily", "Henry", "Alexander", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, false, true, true], "solution_text": "Emily is a knight, Penelope is a knave, Riley is a knave, Aiden is a knight, Lily is a knave, Henry is a knave, Alexander is a knight, and William is a knight.", "solution_text_format": "(1) Emily is a knight\n(2) Penelope is a knave\n(3) Riley is a knave\n(4) Aiden is a knight\n(5) Lily is a knave\n(6) Henry is a knave\n(7) Alexander is a knight\n(8) William is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Aiden is not a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If William is a knave then Lily is a knave.", "Assume William is a knight. No contradiction is found in their claim that If William is a knight then Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the claim of William that If William is a knight then Penelope is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Riley is a knave if and only if Penelope is a knight.", "Riley cannot be a knight, because this would contradict the false claim of Penelope that Riley is a knave if and only if Penelope is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Emily is not a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Penelope is a knave if and only if Alexander is a knave.", "Alexander cannot be a knight, because this would contradict the claim of Lily that Penelope is a knave if and only if Alexander is a knave.", "Alexander cannot be a knave, because this would contradict the false claim of their own that Penelope is a knave or Emily is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Penelope is a knave if and only if Alexander is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Penelope is a knave or Emily is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Emily is a knave if and only if Emily is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Emily is a knave if and only if Emily is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 3)), ('<=>', ('lying', 2), ('telling-truth', 1)), ('not', ('telling-truth', 0)), ('->', ('lying', 7), ('lying', 4)), ('<=>', ('lying', 1), ('lying', 6)), ('<=>', ('lying', 0), ('telling-truth', 0)), ('or', ('lying', 1), ('telling-truth', 0)), ('->', ('telling-truth', 7), ('lying', 1)))", "index": 1054}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jacob, Jack, Jackson, Harper, Emma, Grace, Scarlett, and Ava. Jacob was heard saying, \"Ava is a knave if and only if Emma is a knave\". According to Jack, \"Harper is not a knave\". Jackson said, \"Grace is a knave.\" Harper expressed that Emma is not a knave. Emma was heard saying, \"Scarlett is a knave and Jacob is a knave\". In a statement by Grace: \"Jackson is a knave if and only if Jack is a knave\". Scarlett said, \"Ava is a knave.\" \"Jackson is not a knave,\" Ava mentioned. So who is a knight and who is a knave?", "names": ["Jacob", "Jack", "Jackson", "Harper", "Emma", "Grace", "Scarlett", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, true, true, false], "solution_text": "Jacob is a knight, Jack is a knave, Jackson is a knave, Harper is a knave, Emma is a knave, Grace is a knight, Scarlett is a knight, and Ava is a knave.", "solution_text_format": "(1) Jacob is a knight\n(2) Jack is a knave\n(3) Jackson is a knave\n(4) Harper is a knave\n(5) Emma is a knave\n(6) Grace is a knight\n(7) Scarlett is a knight\n(8) Ava is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that Ava is a knave if and only if Emma is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Jackson is not a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Grace is a knave.", "Grace cannot be a knight, because this would contradict the claim of Jackson that Grace is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Jackson is a knave if and only if Jack is a knave.", "Jack cannot be a knight, because this would contradict the false claim of Grace that Jackson is a knave if and only if Jack is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Harper is not a knave.", "Harper cannot be a knight, because this would contradict the false claim of Jack that Harper is not a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Emma is not a knave.", "Emma cannot be a knight, because this would contradict the false claim of Harper that Emma is not a knave.", "Emma cannot be a knave, because this would contradict the claim of Jacob that Ava is a knave if and only if Emma is a knave.", "We have exhausted all possibilities for Emma, Harper, Jack, and Grace, so let us go back and reconsider Jackson.", "Jackson cannot be a knave, because this would contradict the claim of Ava that Jackson is not a knave.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Jackson is not a knave.", "Jackson cannot be a knight, because this would contradict the false claim of Ava that Jackson is not a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Grace is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Jackson is a knave if and only if Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of Grace that Jackson is a knave if and only if Jack is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Harper is not a knave.", "Harper cannot be a knight, because this would contradict the false claim of Jack that Harper is not a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Emma is not a knave.", "Emma cannot be a knight, because this would contradict the claim of Jacob that Ava is a knave if and only if Emma is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Scarlett is a knave and Jacob is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Ava is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 7), ('lying', 4)), ('not', ('lying', 3)), ('lying', 5), ('not', ('lying', 4)), ('and', ('lying', 6), ('lying', 0)), ('<=>', ('lying', 2), ('lying', 1)), ('lying', 7), ('not', ('lying', 2)))", "index": 1055}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Noah, Oliver, Chloe, Jack, Alexander, William, Elizabeth, and Liam. Noah told you that Chloe is a knight or Jack is a knave. \"Jack is a knave if and only if Elizabeth is a knave,\" Oliver claimed. Chloe said, \"Oliver is not a knight.\" Jack stated, \"William is a knave and Chloe is a knight\". \"Elizabeth is a knave if and only if Noah is a knight,\" Alexander mentioned. William remarked, \"Chloe is a knave and Noah is a knight\". \"Jack is a knight if and only if Liam is a knight,\" Elizabeth claimed. Liam remarked, \"Jack is a knave and Oliver is a knave\". So who is a knight and who is a knave?", "names": ["Noah", "Oliver", "Chloe", "Jack", "Alexander", "William", "Elizabeth", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false, false, false], "solution_text": "Noah is a knight, Oliver is a knave, Chloe is a knight, Jack is a knight, Alexander is a knight, William is a knave, Elizabeth is a knave, and Liam is a knave.", "solution_text_format": "(1) Noah is a knight\n(2) Oliver is a knave\n(3) Chloe is a knight\n(4) Jack is a knight\n(5) Alexander is a knight\n(6) William is a knave\n(7) Elizabeth is a knave\n(8) Liam is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Noah is a knight. No contradiction is found in their claim that Chloe is a knight or Jack is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Oliver is not a knight.", "Oliver cannot be a knight, because this would contradict the claim of Chloe that Oliver is not a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Jack is a knave if and only if Elizabeth is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that William is a knave and Chloe is a knight.", "William cannot be a knight, because this would contradict the claim of Jack that William is a knave and Chloe is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Chloe is a knave and Noah is a knight.", "Elizabeth cannot be a knight, because this would contradict the false claim of Oliver that Jack is a knave if and only if Elizabeth is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Jack is a knight if and only if Liam is a knight.", "Liam cannot be a knight, because this would contradict the false claim of Elizabeth that Jack is a knight if and only if Liam is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Jack is a knave and Oliver is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Elizabeth is a knave if and only if Noah is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('lying', 3)), ('<=>', ('lying', 3), ('lying', 6)), ('not', ('telling-truth', 1)), ('and', ('lying', 5), ('telling-truth', 2)), ('<=>', ('lying', 6), ('telling-truth', 0)), ('and', ('lying', 2), ('telling-truth', 0)), ('<=>', ('telling-truth', 3), ('telling-truth', 7)), ('and', ('lying', 3), ('lying', 1)))", "index": 1056}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ava, Harper, Ethan, Avery, Grace, Mason, Luke, and Michael. In a statement by Ava: \"If Luke is a knight then Harper is a knight\". \"If Michael is a knight then Mason is a knight\" - Harper. According to Ethan, \"Grace is a knight\". Avery said that Luke is a knight and Michael is a knight. Grace remarked, \"Ava is a knave if and only if Michael is a knave\". \"Luke is a knave if and only if Grace is a knave,\" Mason declared. \"Avery is a knight if and only if Ethan is a knave,\" Luke declared. \"If Avery is a knave then Grace is a knave,\" Michael mentioned. So who is a knight and who is a knave?", "names": ["Ava", "Harper", "Ethan", "Avery", "Grace", "Mason", "Luke", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, false, true, true], "solution_text": "Ava is a knave, Harper is a knave, Ethan is a knave, Avery is a knight, Grace is a knave, Mason is a knave, Luke is a knight, and Michael is a knight.", "solution_text_format": "(1) Ava is a knave\n(2) Harper is a knave\n(3) Ethan is a knave\n(4) Avery is a knight\n(5) Grace is a knave\n(6) Mason is a knave\n(7) Luke is a knight\n(8) Michael is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that If Luke is a knight then Harper is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Avery is a knight if and only if Ethan is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Luke is a knight and Michael is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that If Avery is a knave then Grace is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Ava is a knave if and only if Michael is a knave.", "Ethan cannot be a knight, because this would contradict the claim of Luke that Avery is a knight if and only if Ethan is a knave.", "Ethan cannot be a knave, because this would contradict the false claim of their own that Grace is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Grace.", "Grace cannot be a knave, because this would contradict the false claim of their own that Ava is a knave if and only if Michael is a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Michael.", "Michael cannot be a knave, because this would contradict the claim of Avery that Luke is a knight and Michael is a knight.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Luke is a knight and Michael is a knight.", "Michael cannot be a knight, because this would contradict the false claim of Avery that Luke is a knight and Michael is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that If Avery is a knave then Grace is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Ava is a knave if and only if Michael is a knave.", "Grace cannot be a knave, because this would contradict the false claim of Michael that If Avery is a knave then Grace is a knave.", "We have exhausted all possibilities for Grace, Michael, and Avery, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Avery is a knight if and only if Ethan is a knave.", "Avery cannot be a knight, because this would contradict the claim of their own that Luke is a knight and Michael is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Luke is a knight and Michael is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that If Avery is a knave then Grace is a knave.", "Grace cannot be a knight, because this would contradict the claim of Michael that If Avery is a knave then Grace is a knave.", "Grace cannot be a knave, because this would contradict the false claim of their own that Ava is a knave if and only if Michael is a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that If Avery is a knave then Grace is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Ava is a knave if and only if Michael is a knave.", "Grace cannot be a knave, because this would contradict the false claim of Michael that If Avery is a knave then Grace is a knave.", "We have exhausted all possibilities for Grace, Michael, Avery, and Luke, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that If Luke is a knight then Harper is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Avery is a knight if and only if Ethan is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Luke is a knight and Michael is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that If Avery is a knave then Grace is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Ava is a knave if and only if Michael is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Ava is a knave if and only if Michael is a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Grace is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Grace is a knight.", "Harper cannot be a knight, because this would contradict the false claim of Ava that If Luke is a knight then Harper is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that If Michael is a knight then Mason is a knight.", "Mason cannot be a knight, because this would contradict the false claim of Harper that If Michael is a knight then Mason is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Luke is a knave if and only if Grace is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 6), ('telling-truth', 1)), ('->', ('telling-truth', 7), ('telling-truth', 5)), ('telling-truth', 4), ('and', ('telling-truth', 6), ('telling-truth', 7)), ('<=>', ('lying', 0), ('lying', 7)), ('<=>', ('lying', 6), ('lying', 4)), ('<=>', ('telling-truth', 3), ('lying', 2)), ('->', ('lying', 3), ('lying', 4)))", "index": 1057}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Oliver, Lucas, Michael, Scarlett, Benjamin, Luke, Matthew, and Sofia. Oliver said, \"Sofia is a knight.\" \"Benjamin is a knave and Luke is a knave,\" Lucas claimed. \"Matthew is a knight or Benjamin is a knave,\" Michael declared. According to Scarlett, \"Michael is a knave if and only if Scarlett is a knight\". Benjamin was heard saying, \"Scarlett is a knave\". \"If Sofia is a knave then Oliver is a knight\" - Luke. Matthew asserted: \"Sofia is a knave\". Sofia said, \"Oliver is a knave if and only if Michael is a knight.\" So who is a knight and who is a knave?", "names": ["Oliver", "Lucas", "Michael", "Scarlett", "Benjamin", "Luke", "Matthew", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true, false, true], "solution_text": "Oliver is a knight, Lucas is a knave, Michael is a knave, Scarlett is a knave, Benjamin is a knight, Luke is a knight, Matthew is a knave, and Sofia is a knight.", "solution_text_format": "(1) Oliver is a knight\n(2) Lucas is a knave\n(3) Michael is a knave\n(4) Scarlett is a knave\n(5) Benjamin is a knight\n(6) Luke is a knight\n(7) Matthew is a knave\n(8) Sofia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Sofia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Oliver is a knave if and only if Michael is a knight.", "Michael cannot be a knight, because this would contradict the claim of Sofia that Oliver is a knave if and only if Michael is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Matthew is a knight or Benjamin is a knave.", "Matthew cannot be a knight, because this would contradict the false claim of Michael that Matthew is a knight or Benjamin is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Sofia is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Benjamin that Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Michael is a knave if and only if Scarlett is a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave and Luke is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Benjamin is a knave and Luke is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that If Sofia is a knave then Oliver is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 7), ('and', ('lying', 4), ('lying', 5)), ('or', ('telling-truth', 6), ('lying', 4)), ('<=>', ('lying', 2), ('telling-truth', 3)), ('lying', 3), ('->', ('lying', 7), ('telling-truth', 0)), ('lying', 7), ('<=>', ('lying', 0), ('telling-truth', 2)))", "index": 1058}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Elizabeth, Charlotte, Aurora, Amelia, James, Penelope, William, and Jackson. \"Jackson is a knight if and only if Penelope is a knight\" - Elizabeth. \"Aurora is a knave and James is a knight,\" Charlotte claimed. Aurora noted, \"William is a knave and Jackson is a knight\". \"William is a knight and Elizabeth is a knight,\" Amelia claimed. James asserted: \"James is a knight\". Penelope asserted: \"Elizabeth is a knight if and only if Amelia is a knave\". William told you that Aurora is a knight or Jackson is a knave. Jackson commented, \"James is not a knight\". So who is a knight and who is a knave?", "names": ["Elizabeth", "Charlotte", "Aurora", "Amelia", "James", "Penelope", "William", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false, true, false], "solution_text": "Elizabeth is a knight, Charlotte is a knight, Aurora is a knave, Amelia is a knight, James is a knight, Penelope is a knave, William is a knight, and Jackson is a knave.", "solution_text_format": "(1) Elizabeth is a knight\n(2) Charlotte is a knight\n(3) Aurora is a knave\n(4) Amelia is a knight\n(5) James is a knight\n(6) Penelope is a knave\n(7) William is a knight\n(8) Jackson is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Penelope is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that James is not a knight.", "James cannot be a knight, because this would contradict the claim of Jackson that James is not a knight.", "Assume James is a knave. No contradiction is found in their false claim that James is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Elizabeth is a knight if and only if Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Penelope that Elizabeth is a knight if and only if Amelia is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that William is a knight and Elizabeth is a knight.", "William cannot be a knight, because this would contradict the false claim of Amelia that William is a knight and Elizabeth is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Aurora is a knight or Jackson is a knave.", "Aurora cannot be a knight, because this would contradict the false claim of William that Aurora is a knight or Jackson is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of their own that William is a knave and Jackson is a knight.", "We have exhausted all possibilities for Aurora, William, and Amelia, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the claim of Elizabeth that Jackson is a knight if and only if Penelope is a knight.", "We have exhausted all possibilities for Penelope and James, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that James is not a knight.", "Assume James is a knight. No contradiction is found in their claim that James is a knight.", "Penelope cannot be a knight, because this would contradict the claim of Elizabeth that Jackson is a knight if and only if Penelope is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Elizabeth is a knight if and only if Amelia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that William is a knight and Elizabeth is a knight.", "Assume William is a knight. No contradiction is found in their claim that Aurora is a knight or Jackson is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that William is a knave and Jackson is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that William is a knave and Jackson is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Aurora is a knave and James is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 7), ('telling-truth', 5)), ('and', ('lying', 2), ('telling-truth', 4)), ('and', ('lying', 6), ('telling-truth', 7)), ('and', ('telling-truth', 6), ('telling-truth', 0)), ('telling-truth', 4), ('<=>', ('telling-truth', 0), ('lying', 3)), ('or', ('telling-truth', 2), ('lying', 7)), ('not', ('telling-truth', 4)))", "index": 1059}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Joseph, Chloe, James, Liam, Luke, Zoey, William, and Mason. Joseph expressed that Chloe is a knight. \"If James is a knave then Joseph is a knight,\" Chloe mentioned. James expressed that If James is a knight then Liam is a knave. Liam commented, \"Joseph is a knight and Liam is a knight\". \"If Zoey is a knight then Joseph is a knave,\" Luke claimed. \"James is a knave or James is a knight\" - Zoey. William remarked, \"Zoey is a knight if and only if Liam is a knave\". \"Liam is not a knight,\" Mason claimed. So who is a knight and who is a knave?", "names": ["Joseph", "Chloe", "James", "Liam", "Luke", "Zoey", "William", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true, true, true], "solution_text": "Joseph is a knight, Chloe is a knight, James is a knight, Liam is a knave, Luke is a knave, Zoey is a knight, William is a knight, and Mason is a knight.", "solution_text_format": "(1) Joseph is a knight\n(2) Chloe is a knight\n(3) James is a knight\n(4) Liam is a knave\n(5) Luke is a knave\n(6) Zoey is a knight\n(7) William is a knight\n(8) Mason is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that Chloe is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that If James is a knave then Joseph is a knight.", "Assume James is a knight. No contradiction is found in their claim that If James is a knight then Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of James that If James is a knight then Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Joseph is a knight and Liam is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that If Zoey is a knight then Joseph is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Luke that If Zoey is a knight then Joseph is a knave.", "Zoey cannot be a knave, because this would contradict the false claim of their own that James is a knave or James is a knight.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that If Zoey is a knight then Joseph is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that James is a knave or James is a knight.", "Assume William is a knight. No contradiction is found in their claim that Zoey is a knight if and only if Liam is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Liam is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('->', ('lying', 2), ('telling-truth', 0)), ('->', ('telling-truth', 2), ('lying', 3)), ('and', ('telling-truth', 0), ('telling-truth', 3)), ('->', ('telling-truth', 5), ('lying', 0)), ('or', ('lying', 2), ('telling-truth', 2)), ('<=>', ('telling-truth', 5), ('lying', 3)), ('not', ('telling-truth', 3)))", "index": 1060}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Henry, Daniel, Owen, William, Lily, Evelyn, Amelia, and Michael. Henry was heard saying, \"Lily is a knave if and only if Evelyn is a knave\". Daniel was heard saying, \"Amelia is a knave\". Owen told you that Henry is not a knight. \"Amelia is a knave if and only if Lily is a knave,\" William declared. In a statement by Lily: \"If Owen is a knight then Daniel is a knight\". Evelyn expressed that Amelia is a knight or William is a knight. \"Lily is not a knave,\" Amelia mentioned. Michael said, \"Amelia is a knight or William is a knave.\" So who is a knight and who is a knave?", "names": ["Henry", "Daniel", "Owen", "William", "Lily", "Evelyn", "Amelia", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true, true, true], "solution_text": "Henry is a knight, Daniel is a knave, Owen is a knave, William is a knight, Lily is a knight, Evelyn is a knight, Amelia is a knight, and Michael is a knight.", "solution_text_format": "(1) Henry is a knight\n(2) Daniel is a knave\n(3) Owen is a knave\n(4) William is a knight\n(5) Lily is a knight\n(6) Evelyn is a knight\n(7) Amelia is a knight\n(8) Michael is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that Lily is a knave if and only if Evelyn is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that If Owen is a knight then Daniel is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Henry is not a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Henry is not a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Daniel that Amelia is a knave.", "Amelia cannot be a knave, because this would contradict the false claim of their own that Lily is not a knave.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Amelia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Lily is not a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Amelia is a knight or William is a knight.", "Assume William is a knight. No contradiction is found in their claim that Amelia is a knave if and only if Lily is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Amelia is a knight or William is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 4), ('lying', 5)), ('lying', 6), ('not', ('telling-truth', 0)), ('<=>', ('lying', 6), ('lying', 4)), ('->', ('telling-truth', 2), ('telling-truth', 1)), ('or', ('telling-truth', 6), ('telling-truth', 3)), ('not', ('lying', 4)), ('or', ('telling-truth', 6), ('lying', 3)))", "index": 1061}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: William, Ethan, Matthew, Emma, Ava, Evelyn, Ella, and Owen. William noted, \"If Ava is a knight then Ethan is a knight\". \"Matthew is a knave or Evelyn is a knight\" - Ethan. Matthew said that Ella is a knight or Owen is a knight. \"If Owen is a knight then Ava is a knight,\" Emma claimed. Ava was heard saying, \"Ella is a knave or William is a knight\". \"Owen is a knave,\" Evelyn mentioned. Ella noted, \"Evelyn is not a knight\". \"Ella is a knight if and only if Ethan is a knight,\" Owen claimed. So who is a knight and who is a knave?", "names": ["William", "Ethan", "Matthew", "Emma", "Ava", "Evelyn", "Ella", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true, false, false], "solution_text": "William is a knight, Ethan is a knight, Matthew is a knave, Emma is a knight, Ava is a knight, Evelyn is a knight, Ella is a knave, and Owen is a knave.", "solution_text_format": "(1) William is a knight\n(2) Ethan is a knight\n(3) Matthew is a knave\n(4) Emma is a knight\n(5) Ava is a knight\n(6) Evelyn is a knight\n(7) Ella is a knave\n(8) Owen is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that If Ava is a knight then Ethan is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Ella is a knave or William is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Evelyn is not a knight.", "Evelyn cannot be a knight, because this would contradict the claim of Ella that Evelyn is not a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Owen is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Ella is a knight if and only if Ethan is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Matthew is a knave or Evelyn is a knight.", "Matthew cannot be a knight, because this would contradict the claim of Ethan that Matthew is a knave or Evelyn is a knight.", "Matthew cannot be a knave, because this would contradict the false claim of their own that Ella is a knight or Owen is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the claim of William that If Ava is a knight then Ethan is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the false claim of Evelyn that Owen is a knave.", "We have exhausted all possibilities for Owen and Evelyn, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Evelyn is not a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of Evelyn that Owen is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Ella is a knight if and only if Ethan is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Matthew is a knave or Evelyn is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Ella is a knight or Owen is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Ella is a knight or Owen is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If Owen is a knight then Ava is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 4), ('telling-truth', 1)), ('or', ('lying', 2), ('telling-truth', 5)), ('or', ('telling-truth', 6), ('telling-truth', 7)), ('->', ('telling-truth', 7), ('telling-truth', 4)), ('or', ('lying', 6), ('telling-truth', 0)), ('lying', 7), ('not', ('telling-truth', 5)), ('<=>', ('telling-truth', 6), ('telling-truth', 1)))", "index": 1062}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sofia, Sophia, Benjamin, Evelyn, Oliver, Grace, Samuel, and Luke. Sofia was heard saying, \"If Sophia is a knight then Luke is a knight\". Sophia commented, \"If Grace is a knave then Evelyn is a knave\". Benjamin noted, \"Benjamin is a knight\". \"Sofia is a knave,\" Evelyn mentioned. Oliver noted, \"Luke is a knight if and only if Grace is a knave\". According to Grace, \"If Sofia is a knave then Sophia is a knave\". Samuel stated, \"Grace is a knight\". According to Luke, \"Evelyn is a knight if and only if Benjamin is a knave\". So who is a knight and who is a knave?", "names": ["Sofia", "Sophia", "Benjamin", "Evelyn", "Oliver", "Grace", "Samuel", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true, true, true], "solution_text": "Sofia is a knight, Sophia is a knight, Benjamin is a knight, Evelyn is a knave, Oliver is a knave, Grace is a knight, Samuel is a knight, and Luke is a knight.", "solution_text_format": "(1) Sofia is a knight\n(2) Sophia is a knight\n(3) Benjamin is a knight\n(4) Evelyn is a knave\n(5) Oliver is a knave\n(6) Grace is a knight\n(7) Samuel is a knight\n(8) Luke is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that If Sophia is a knight then Luke is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that If Grace is a knave then Evelyn is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that If Sofia is a knave then Sophia is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Sofia is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Sofia is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Evelyn is a knight if and only if Benjamin is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Benjamin is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Luke is a knight if and only if Grace is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Luke is a knight if and only if Grace is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Grace is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 1), ('telling-truth', 7)), ('->', ('lying', 5), ('lying', 3)), ('telling-truth', 2), ('lying', 0), ('<=>', ('telling-truth', 7), ('lying', 5)), ('->', ('lying', 0), ('lying', 1)), ('telling-truth', 5), ('<=>', ('telling-truth', 3), ('lying', 2)))", "index": 1063}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jacob, Penelope, James, Daniel, Amelia, Scarlett, Ava, and Noah. \"Daniel is a knave or Ava is a knave\" - Jacob. \"Scarlett is a knave and Amelia is a knight,\" Penelope declared. James expressed that Jacob is a knight. In a statement by Daniel: \"Noah is a knave\". Amelia remarked, \"Amelia is a knight or Scarlett is a knight\". Scarlett said, \"Penelope is not a knight.\" In Ava's words: \"Penelope is a knave if and only if Noah is a knight\". \"Jacob is a knave or Ava is a knave\" - Noah. So who is a knight and who is a knave?", "names": ["Jacob", "Penelope", "James", "Daniel", "Amelia", "Scarlett", "Ava", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false, false, true], "solution_text": "Jacob is a knight, Penelope is a knight, James is a knight, Daniel is a knave, Amelia is a knight, Scarlett is a knave, Ava is a knave, and Noah is a knight.", "solution_text_format": "(1) Jacob is a knight\n(2) Penelope is a knight\n(3) James is a knight\n(4) Daniel is a knave\n(5) Amelia is a knight\n(6) Scarlett is a knave\n(7) Ava is a knave\n(8) Noah is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that Daniel is a knave or Ava is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of Daniel that Noah is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Jacob is a knave or Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of Jacob that Daniel is a knave or Ava is a knave.", "Ava cannot be a knave, because this would contradict the false claim of Noah that Jacob is a knave or Ava is a knave.", "We have exhausted all possibilities for Ava and Noah, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Noah is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Jacob is a knave or Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of Noah that Jacob is a knave or Ava is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Penelope is a knave if and only if Noah is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Scarlett is a knave and Amelia is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of Penelope that Scarlett is a knave and Amelia is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Penelope is not a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Amelia is a knight or Scarlett is a knight.", "Assume James is a knight. No contradiction is found in their claim that Jacob is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('lying', 6)), ('and', ('lying', 5), ('telling-truth', 4)), ('telling-truth', 0), ('lying', 7), ('or', ('telling-truth', 4), ('telling-truth', 5)), ('not', ('telling-truth', 1)), ('<=>', ('lying', 1), ('telling-truth', 7)), ('or', ('lying', 0), ('lying', 6)))", "index": 1064}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aiden, Oliver, David, Chloe, Riley, Ethan, Michael, and Jack. \"Ethan is a knight\" - Aiden. Oliver remarked, \"Aiden is a knight or Aiden is a knave\". \"Riley is not a knave\" - David. Chloe commented, \"Riley is a knave\". Riley asserted: \"If Jack is a knight then Aiden is a knave\". As Ethan put it, \"If Chloe is a knave then Michael is a knave\". In a statement by Michael: \"Aiden is a knave\". In a statement by Jack: \"Oliver is a knight and Chloe is a knave\". So who is a knight and who is a knave?", "names": ["Aiden", "Oliver", "David", "Chloe", "Riley", "Ethan", "Michael", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, false, true, true], "solution_text": "Aiden is a knave, Oliver is a knight, David is a knight, Chloe is a knave, Riley is a knight, Ethan is a knave, Michael is a knight, and Jack is a knight.", "solution_text_format": "(1) Aiden is a knave\n(2) Oliver is a knight\n(3) David is a knight\n(4) Chloe is a knave\n(5) Riley is a knight\n(6) Ethan is a knave\n(7) Michael is a knight\n(8) Jack is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Ethan is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If Chloe is a knave then Michael is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Riley is a knave.", "Riley cannot be a knight, because this would contradict the claim of Chloe that Riley is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that If Jack is a knight then Aiden is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Oliver is a knight and Chloe is a knave.", "Jack cannot be a knave, because this would contradict the false claim of Riley that If Jack is a knight then Aiden is a knave.", "We have exhausted all possibilities for Jack and Riley, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Riley is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that If Jack is a knight then Aiden is a knave.", "Jack cannot be a knight, because this would contradict the claim of Riley that If Jack is a knight then Aiden is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Oliver is a knight and Chloe is a knave.", "Oliver cannot be a knight, because this would contradict the false claim of Jack that Oliver is a knight and Chloe is a knave.", "Oliver cannot be a knave, because this would contradict the false claim of their own that Aiden is a knight or Aiden is a knave.", "We have exhausted all possibilities for Oliver and Jack, so let us go back and reconsider Riley.", "Riley cannot be a knave, because this would contradict the false claim of Chloe that Riley is a knave.", "We have exhausted all possibilities for Riley and Chloe, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the claim of Aiden that Ethan is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Ethan is a knight.", "Ethan cannot be a knight, because this would contradict the false claim of Aiden that Ethan is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that If Chloe is a knave then Michael is a knave.", "Chloe cannot be a knight, because this would contradict the false claim of Ethan that If Chloe is a knave then Michael is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Riley is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that If Jack is a knight then Aiden is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Oliver is a knight and Chloe is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Aiden is a knight or Aiden is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Aiden is a knave.", "Assume David is a knight. No contradiction is found in their claim that Riley is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 5), ('or', ('telling-truth', 0), ('lying', 0)), ('not', ('lying', 4)), ('lying', 4), ('->', ('telling-truth', 7), ('lying', 0)), ('->', ('lying', 3), ('lying', 6)), ('lying', 0), ('and', ('telling-truth', 1), ('lying', 3)))", "index": 1065}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emma, Jackson, Avery, Alexander, Zoey, Aria, Owen, and Luke. Emma commented, \"Avery is a knave and Owen is a knave\". Jackson stated, \"Zoey is not a knave\". Avery said, \"If Jackson is a knave then Aria is a knight.\" \"Luke is a knight and Zoey is a knave,\" Alexander claimed. As Zoey put it, \"Aria is not a knave\". \"Aria is a knight and Alexander is a knight,\" Aria declared. \"If Aria is a knight then Luke is a knight,\" Owen declared. \"If Emma is a knave then Aria is a knave,\" Luke declared. So who is a knight and who is a knave?", "names": ["Emma", "Jackson", "Avery", "Alexander", "Zoey", "Aria", "Owen", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, false, true, true], "solution_text": "Emma is a knave, Jackson is a knave, Avery is a knave, Alexander is a knight, Zoey is a knave, Aria is a knave, Owen is a knight, and Luke is a knight.", "solution_text_format": "(1) Emma is a knave\n(2) Jackson is a knave\n(3) Avery is a knave\n(4) Alexander is a knight\n(5) Zoey is a knave\n(6) Aria is a knave\n(7) Owen is a knight\n(8) Luke is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Avery is a knave and Owen is a knave.", "Avery cannot be a knight, because this would contradict the claim of Emma that Avery is a knave and Owen is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that If Jackson is a knave then Aria is a knight.", "Jackson cannot be a knight, because this would contradict the false claim of Avery that If Jackson is a knave then Aria is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Zoey is not a knave.", "Zoey cannot be a knight, because this would contradict the false claim of Jackson that Zoey is not a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Aria is not a knave.", "Aria cannot be a knight, because this would contradict the false claim of Avery that If Jackson is a knave then Aria is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Aria is a knight and Alexander is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Luke is a knight and Zoey is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that If Emma is a knave then Aria is a knave.", "Owen cannot be a knight, because this would contradict the claim of Emma that Avery is a knave and Owen is a knave.", "Owen cannot be a knave, because this would contradict the false claim of their own that If Aria is a knight then Luke is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the claim of Alexander that Luke is a knight and Zoey is a knave.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Luke is a knight and Zoey is a knave.", "Luke cannot be a knight, because this would contradict the false claim of Alexander that Luke is a knight and Zoey is a knave.", "Luke cannot be a knave, because this would contradict the false claim of their own that If Emma is a knave then Aria is a knave.", "We have exhausted all possibilities for Luke, Alexander, Aria, Zoey, Jackson, and Avery, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Avery is a knave and Owen is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that If Jackson is a knave then Aria is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Zoey is not a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Aria is not a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Aria is a knight and Alexander is a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that Luke is a knight and Zoey is a knave.", "Alexander cannot be a knave, because this would contradict the claim of Aria that Aria is a knight and Alexander is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Aria.", "Aria cannot be a knave, because this would contradict the claim of Zoey that Aria is not a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Zoey.", "Zoey cannot be a knave, because this would contradict the claim of Jackson that Zoey is not a knave.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Zoey is not a knave.", "Zoey cannot be a knight, because this would contradict the false claim of Jackson that Zoey is not a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Aria is not a knave.", "Aria cannot be a knight, because this would contradict the false claim of Zoey that Aria is not a knave.", "Aria cannot be a knave, because this would contradict the claim of Avery that If Jackson is a knave then Aria is a knight.", "We have exhausted all possibilities for Aria, Zoey, and Jackson, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that If Jackson is a knave then Aria is a knight.", "Jackson cannot be a knight, because this would contradict the false claim of Avery that If Jackson is a knave then Aria is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Zoey is not a knave.", "Zoey cannot be a knight, because this would contradict the false claim of Jackson that Zoey is not a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Aria is not a knave.", "Aria cannot be a knight, because this would contradict the false claim of Avery that If Jackson is a knave then Aria is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Aria is a knight and Alexander is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Luke is a knight and Zoey is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that If Emma is a knave then Aria is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that If Aria is a knight then Luke is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('lying', 6)), ('not', ('lying', 4)), ('->', ('lying', 1), ('telling-truth', 5)), ('and', ('telling-truth', 7), ('lying', 4)), ('not', ('lying', 5)), ('and', ('telling-truth', 5), ('telling-truth', 3)), ('->', ('telling-truth', 5), ('telling-truth', 7)), ('->', ('lying', 0), ('lying', 5)))", "index": 1066}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lucas, Samuel, Michael, Jack, David, Luke, Mason, and Daniel. Lucas noted, \"Daniel is not a knight\". Samuel was heard saying, \"Daniel is a knave if and only if Mason is a knave\". Michael expressed that David is not a knave. \"Lucas is a knight or Michael is a knave,\" Jack claimed. David said that Lucas is a knight. In Luke's words: \"Lucas is a knave if and only if Mason is a knight\". In Mason's words: \"If Luke is a knight then Michael is a knight\". Daniel told you that Michael is a knave and David is a knave. So who is a knight and who is a knave?", "names": ["Lucas", "Samuel", "Michael", "Jack", "David", "Luke", "Mason", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false, true, false], "solution_text": "Lucas is a knight, Samuel is a knave, Michael is a knight, Jack is a knight, David is a knight, Luke is a knave, Mason is a knight, and Daniel is a knave.", "solution_text_format": "(1) Lucas is a knight\n(2) Samuel is a knave\n(3) Michael is a knight\n(4) Jack is a knight\n(5) David is a knight\n(6) Luke is a knave\n(7) Mason is a knight\n(8) Daniel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that Daniel is not a knight.", "Daniel cannot be a knight, because this would contradict the claim of Lucas that Daniel is not a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Michael is a knave and David is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that David is not a knave.", "Assume David is a knight. No contradiction is found in their claim that Lucas is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Daniel is a knave if and only if Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of Samuel that Daniel is a knave if and only if Mason is a knave.", "Mason cannot be a knave, because this would contradict the false claim of their own that If Luke is a knight then Michael is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Daniel is a knave if and only if Mason is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Luke is a knight then Michael is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Lucas is a knave if and only if Mason is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Lucas is a knave if and only if Mason is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Lucas is a knight or Michael is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 7)), ('<=>', ('lying', 7), ('lying', 6)), ('not', ('lying', 4)), ('or', ('telling-truth', 0), ('lying', 2)), ('telling-truth', 0), ('<=>', ('lying', 0), ('telling-truth', 6)), ('->', ('telling-truth', 5), ('telling-truth', 2)), ('and', ('lying', 2), ('lying', 4)))", "index": 1067}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Chloe, Ethan, Lucas, Alexander, Charlotte, Penelope, Sophia, and Jack. As Chloe put it, \"Jack is a knave or Jack is a knight\". Ethan remarked, \"If Penelope is a knave then Charlotte is a knight\". Lucas said that If Ethan is a knight then Penelope is a knave. Alexander said, \"Jack is a knave.\" Charlotte commented, \"Penelope is a knight\". Penelope stated, \"Ethan is a knave if and only if Sophia is a knight\". As Sophia put it, \"Sophia is a knight or Jack is a knave\". In Jack's words: \"Penelope is not a knight\". So who is a knight and who is a knave?", "names": ["Chloe", "Ethan", "Lucas", "Alexander", "Charlotte", "Penelope", "Sophia", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, false, false, true], "solution_text": "Chloe is a knight, Ethan is a knave, Lucas is a knight, Alexander is a knave, Charlotte is a knave, Penelope is a knave, Sophia is a knave, and Jack is a knight.", "solution_text_format": "(1) Chloe is a knight\n(2) Ethan is a knave\n(3) Lucas is a knight\n(4) Alexander is a knave\n(5) Charlotte is a knave\n(6) Penelope is a knave\n(7) Sophia is a knave\n(8) Jack is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Jack is a knave or Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Penelope cannot be a knight, because this would contradict the claim of Jack that Penelope is not a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Ethan is a knave if and only if Sophia is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If Penelope is a knave then Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Penelope is a knight.", "Charlotte cannot be a knave, because this would contradict the claim of Ethan that If Penelope is a knave then Charlotte is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that If Penelope is a knave then Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of Ethan that If Penelope is a knave then Charlotte is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Penelope is a knight.", "Sophia cannot be a knight, because this would contradict the false claim of Penelope that Ethan is a knave if and only if Sophia is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Sophia is a knight or Jack is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that If Ethan is a knight then Penelope is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that Jack is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Jack is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 7), ('telling-truth', 7)), ('->', ('lying', 5), ('telling-truth', 4)), ('->', ('telling-truth', 1), ('lying', 5)), ('lying', 7), ('telling-truth', 5), ('<=>', ('lying', 1), ('telling-truth', 6)), ('or', ('telling-truth', 6), ('lying', 7)), ('not', ('telling-truth', 5)))", "index": 1068}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Scarlett, Zoey, Charlotte, Mason, Emily, James, Sofia, and Abigail. Scarlett asserted: \"Emily is a knight if and only if Sofia is a knave\". Zoey said that James is a knight or Sofia is a knave. Charlotte said that James is a knave if and only if Emily is a knight. Mason asserted: \"Zoey is a knave and Mason is a knight\". Emily commented, \"Zoey is not a knight\". James told you that Emily is a knight and James is a knight. Sofia expressed that Mason is a knight if and only if Emily is a knight. In Abigail's words: \"Charlotte is not a knight\". So who is a knight and who is a knave?", "names": ["Scarlett", "Zoey", "Charlotte", "Mason", "Emily", "James", "Sofia", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false, true, false], "solution_text": "Scarlett is a knave, Zoey is a knave, Charlotte is a knight, Mason is a knight, Emily is a knight, James is a knave, Sofia is a knight, and Abigail is a knave.", "solution_text_format": "(1) Scarlett is a knave\n(2) Zoey is a knave\n(3) Charlotte is a knight\n(4) Mason is a knight\n(5) Emily is a knight\n(6) James is a knave\n(7) Sofia is a knight\n(8) Abigail is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Emily is a knight if and only if Sofia is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Zoey is not a knight.", "Zoey cannot be a knight, because this would contradict the claim of Emily that Zoey is not a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that James is a knight or Sofia is a knave.", "James cannot be a knight, because this would contradict the false claim of Zoey that James is a knight or Sofia is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Emily is a knight and James is a knight.", "Sofia cannot be a knight, because this would contradict the claim of Scarlett that Emily is a knight if and only if Sofia is a knave.", "Sofia cannot be a knave, because this would contradict the false claim of Zoey that James is a knight or Sofia is a knave.", "We have exhausted all possibilities for Sofia, James, and Zoey, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Zoey is not a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that James is a knight or Sofia is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Emily is a knight and James is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Emily is a knight and James is a knight.", "Sofia cannot be a knight, because this would contradict the claim of Zoey that James is a knight or Sofia is a knave.", "Sofia cannot be a knave, because this would contradict the claim of Scarlett that Emily is a knight if and only if Sofia is a knave.", "We have exhausted all possibilities for Sofia and James, so let us go back and reconsider Zoey.", "Zoey cannot be a knave, because this would contradict the false claim of Emily that Zoey is not a knight.", "We have exhausted all possibilities for Zoey and Emily, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Emily is a knight if and only if Sofia is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Zoey is not a knight.", "Zoey cannot be a knight, because this would contradict the claim of Emily that Zoey is not a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that James is a knight or Sofia is a knave.", "James cannot be a knight, because this would contradict the false claim of Zoey that James is a knight or Sofia is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Emily is a knight and James is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Mason is a knight if and only if Emily is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Zoey is a knave and Mason is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that James is a knave if and only if Emily is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Charlotte is not a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Charlotte is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 4), ('lying', 6)), ('or', ('telling-truth', 5), ('lying', 6)), ('<=>', ('lying', 5), ('telling-truth', 4)), ('and', ('lying', 1), ('telling-truth', 3)), ('not', ('telling-truth', 1)), ('and', ('telling-truth', 4), ('telling-truth', 5)), ('<=>', ('telling-truth', 3), ('telling-truth', 4)), ('not', ('telling-truth', 2)))", "index": 1069}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Riley, Daniel, Benjamin, Liam, Logan, Penelope, Aria, and Emma. \"Emma is a knave if and only if Liam is a knave,\" Riley declared. Daniel expressed that Emma is not a knave. Benjamin remarked, \"Emma is a knight\". Liam commented, \"If Daniel is a knight then Emma is a knave\". Logan said, \"Daniel is not a knave.\" Penelope remarked, \"Benjamin is a knave if and only if Liam is a knight\". \"Daniel is a knight or Logan is a knave,\" Aria declared. According to Emma, \"If Penelope is a knave then Benjamin is a knave\". So who is a knight and who is a knave?", "names": ["Riley", "Daniel", "Benjamin", "Liam", "Logan", "Penelope", "Aria", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true, true, true], "solution_text": "Riley is a knave, Daniel is a knight, Benjamin is a knight, Liam is a knave, Logan is a knight, Penelope is a knight, Aria is a knight, and Emma is a knight.", "solution_text_format": "(1) Riley is a knave\n(2) Daniel is a knight\n(3) Benjamin is a knight\n(4) Liam is a knave\n(5) Logan is a knight\n(6) Penelope is a knight\n(7) Aria is a knight\n(8) Emma is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Emma is a knave if and only if Liam is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that If Penelope is a knave then Benjamin is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Benjamin is a knave if and only if Liam is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Emma is a knight.", "Liam cannot be a knight, because this would contradict the claim of Penelope that Benjamin is a knave if and only if Liam is a knight.", "Liam cannot be a knave, because this would contradict the claim of Riley that Emma is a knave if and only if Liam is a knave.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that Emma is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Benjamin is a knave if and only if Liam is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of Emma that If Penelope is a knave then Benjamin is a knave.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that Emma is a knight.", "We have exhausted all possibilities for Benjamin and Penelope, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that If Penelope is a knave then Benjamin is a knave.", "Penelope cannot be a knight, because this would contradict the false claim of Emma that If Penelope is a knave then Benjamin is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Benjamin is a knave if and only if Liam is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Emma is a knight.", "Benjamin cannot be a knave, because this would contradict the false claim of Emma that If Penelope is a knave then Benjamin is a knave.", "We have exhausted all possibilities for Benjamin, Penelope, and Emma, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Emma is a knave if and only if Liam is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that If Penelope is a knave then Benjamin is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Benjamin is a knave if and only if Liam is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Emma is a knight.", "Liam cannot be a knight, because this would contradict the false claim of Riley that Emma is a knave if and only if Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that If Daniel is a knight then Emma is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Emma is not a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Daniel is not a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Daniel is a knight or Logan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 7), ('lying', 3)), ('not', ('lying', 7)), ('telling-truth', 7), ('->', ('telling-truth', 1), ('lying', 7)), ('not', ('lying', 1)), ('<=>', ('lying', 2), ('telling-truth', 3)), ('or', ('telling-truth', 1), ('lying', 4)), ('->', ('lying', 5), ('lying', 2)))", "index": 1070}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Owen, Aiden, Amelia, Sofia, Jacob, Oliver, Lily, and Mason. Owen was heard saying, \"Sofia is a knight or Aiden is a knight\". In a statement by Aiden: \"If Lily is a knave then Sofia is a knight\". Amelia asserted: \"Mason is a knight if and only if Amelia is a knight\". In a statement by Sofia: \"Oliver is a knight if and only if Aiden is a knight\". Jacob said, \"Sofia is a knave if and only if Owen is a knight.\" \"Mason is a knave or Amelia is a knight,\" Oliver claimed. Lily said that Aiden is a knight if and only if Sofia is a knight. Mason asserted: \"If Amelia is a knave then Sofia is a knight\". So who is a knight and who is a knave?", "names": ["Owen", "Aiden", "Amelia", "Sofia", "Jacob", "Oliver", "Lily", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true, true, true], "solution_text": "Owen is a knight, Aiden is a knight, Amelia is a knight, Sofia is a knight, Jacob is a knave, Oliver is a knight, Lily is a knight, and Mason is a knight.", "solution_text_format": "(1) Owen is a knight\n(2) Aiden is a knight\n(3) Amelia is a knight\n(4) Sofia is a knight\n(5) Jacob is a knave\n(6) Oliver is a knight\n(7) Lily is a knight\n(8) Mason is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Sofia is a knight or Aiden is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Oliver is a knight if and only if Aiden is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Mason is a knave or Amelia is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that If Amelia is a knave then Sofia is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Mason is a knight if and only if Amelia is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that If Lily is a knave then Sofia is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Aiden is a knight if and only if Sofia is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Sofia is a knave if and only if Owen is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Sofia is a knave if and only if Owen is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('telling-truth', 1)), ('->', ('lying', 6), ('telling-truth', 3)), ('<=>', ('telling-truth', 7), ('telling-truth', 2)), ('<=>', ('telling-truth', 5), ('telling-truth', 1)), ('<=>', ('lying', 3), ('telling-truth', 0)), ('or', ('lying', 7), ('telling-truth', 2)), ('<=>', ('telling-truth', 1), ('telling-truth', 3)), ('->', ('lying', 2), ('telling-truth', 3)))", "index": 1071}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mia, Jackson, William, Amelia, Jack, Aria, David, and Elizabeth. In a statement by Mia: \"If Elizabeth is a knight then David is a knight\". Jackson stated, \"Amelia is a knave if and only if William is a knave\". According to William, \"Aria is a knight or Jackson is a knave\". Amelia commented, \"David is not a knave\". Jack was heard saying, \"David is not a knight\". \"Elizabeth is a knight or Mia is a knave,\" Aria claimed. David noted, \"Aria is not a knave\". Elizabeth expressed that Jackson is not a knight. So who is a knight and who is a knave?", "names": ["Mia", "Jackson", "William", "Amelia", "Jack", "Aria", "David", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, false, false, false], "solution_text": "Mia is a knight, Jackson is a knight, William is a knave, Amelia is a knave, Jack is a knight, Aria is a knave, David is a knave, and Elizabeth is a knave.", "solution_text_format": "(1) Mia is a knight\n(2) Jackson is a knight\n(3) William is a knave\n(4) Amelia is a knave\n(5) Jack is a knight\n(6) Aria is a knave\n(7) David is a knave\n(8) Elizabeth is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that If Elizabeth is a knight then David is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Jackson is not a knight.", "Jackson cannot be a knight, because this would contradict the claim of Elizabeth that Jackson is not a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Amelia is a knave if and only if William is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that David is not a knave.", "Assume David is a knight. No contradiction is found in their claim that Aria is not a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Elizabeth is a knight or Mia is a knave.", "William cannot be a knight, because this would contradict the false claim of Jackson that Amelia is a knave if and only if William is a knave.", "William cannot be a knave, because this would contradict the false claim of their own that Aria is a knight or Jackson is a knave.", "We have exhausted all possibilities for William, so let us go back and reconsider Aria.", "Aria cannot be a knave, because this would contradict the false claim of their own that Elizabeth is a knight or Mia is a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the claim of Mia that If Elizabeth is a knight then David is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that David is not a knave.", "David cannot be a knight, because this would contradict the false claim of Amelia that David is not a knave.", "David cannot be a knave, because this would contradict the claim of Mia that If Elizabeth is a knight then David is a knight.", "We have exhausted all possibilities for David, Amelia, and Jackson, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Jackson is not a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Amelia is a knave if and only if William is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that David is not a knave.", "Assume David is a knight. No contradiction is found in their claim that Aria is not a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight or Mia is a knave.", "Aria cannot be a knave, because this would contradict the claim of David that Aria is not a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the claim of Amelia that David is not a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that David is not a knave.", "David cannot be a knight, because this would contradict the false claim of Amelia that David is not a knave.", "Assume David is a knave. No contradiction is found in their false claim that Aria is not a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight or Mia is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Elizabeth is a knight or Mia is a knave.", "William cannot be a knight, because this would contradict the claim of Jackson that Amelia is a knave if and only if William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Aria is a knight or Jackson is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that David is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 7), ('telling-truth', 6)), ('<=>', ('lying', 3), ('lying', 2)), ('or', ('telling-truth', 5), ('lying', 1)), ('not', ('lying', 6)), ('not', ('telling-truth', 6)), ('or', ('telling-truth', 7), ('lying', 0)), ('not', ('lying', 5)), ('not', ('telling-truth', 1)))", "index": 1072}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Harper, Luke, Lucas, Grace, Daniel, Amelia, Penelope, and Michael. In a statement by Harper: \"Michael is not a knave\". Luke remarked, \"If Lucas is a knave then Grace is a knight\". Lucas said, \"Harper is a knight and Grace is a knave.\" \"Lucas is a knave if and only if Harper is a knave,\" Grace mentioned. Daniel told you that Lucas is a knave. Amelia was heard saying, \"Lucas is a knave or Amelia is a knight\". \"Luke is a knight or Penelope is a knight\" - Penelope. Michael stated, \"Amelia is a knight and Michael is a knight\". So who is a knight and who is a knave?", "names": ["Harper", "Luke", "Lucas", "Grace", "Daniel", "Amelia", "Penelope", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true, true, false], "solution_text": "Harper is a knave, Luke is a knight, Lucas is a knave, Grace is a knight, Daniel is a knight, Amelia is a knight, Penelope is a knight, and Michael is a knave.", "solution_text_format": "(1) Harper is a knave\n(2) Luke is a knight\n(3) Lucas is a knave\n(4) Grace is a knight\n(5) Daniel is a knight\n(6) Amelia is a knight\n(7) Penelope is a knight\n(8) Michael is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that Michael is not a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Amelia is a knight and Michael is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Lucas is a knave or Amelia is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Harper is a knight and Grace is a knave.", "Grace cannot be a knight, because this would contradict the claim of Lucas that Harper is a knight and Grace is a knave.", "Grace cannot be a knave, because this would contradict the false claim of their own that Lucas is a knave if and only if Harper is a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Harper is a knight and Grace is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Lucas is a knave if and only if Harper is a knave.", "Grace cannot be a knave, because this would contradict the false claim of Lucas that Harper is a knight and Grace is a knave.", "We have exhausted all possibilities for Grace and Lucas, so let us go back and reconsider Amelia.", "Amelia cannot be a knave, because this would contradict the claim of Michael that Amelia is a knight and Michael is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Michael.", "Michael cannot be a knave, because this would contradict the claim of Harper that Michael is not a knave.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Michael is not a knave.", "Michael cannot be a knight, because this would contradict the false claim of Harper that Michael is not a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Amelia is a knight and Michael is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Lucas is a knave or Amelia is a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Harper is a knight and Grace is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Harper is a knight and Grace is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Lucas is a knave if and only if Harper is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that If Lucas is a knave then Grace is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Lucas is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Luke is a knight or Penelope is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 7)), ('->', ('lying', 2), ('telling-truth', 3)), ('and', ('telling-truth', 0), ('lying', 3)), ('<=>', ('lying', 2), ('lying', 0)), ('lying', 2), ('or', ('lying', 2), ('telling-truth', 5)), ('or', ('telling-truth', 1), ('telling-truth', 6)), ('and', ('telling-truth', 5), ('telling-truth', 7)))", "index": 1073}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Oliver, Alexander, Riley, Luke, Victoria, Scarlett, Ethan, and Lucas. As Oliver put it, \"Lucas is a knight and Alexander is a knight\". In a statement by Alexander: \"Oliver is a knave if and only if Luke is a knave\". \"If Ethan is a knight then Luke is a knave\" - Riley. Luke said that Ethan is not a knave. Victoria noted, \"Scarlett is a knave\". In a statement by Scarlett: \"Riley is a knave if and only if Victoria is a knight\". Ethan asserted: \"Victoria is a knave\". In Lucas's words: \"Luke is a knight and Riley is a knave\". So who is a knight and who is a knave?", "names": ["Oliver", "Alexander", "Riley", "Luke", "Victoria", "Scarlett", "Ethan", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, false, false, false], "solution_text": "Oliver is a knave, Alexander is a knight, Riley is a knight, Luke is a knave, Victoria is a knight, Scarlett is a knave, Ethan is a knave, and Lucas is a knave.", "solution_text_format": "(1) Oliver is a knave\n(2) Alexander is a knight\n(3) Riley is a knight\n(4) Luke is a knave\n(5) Victoria is a knight\n(6) Scarlett is a knave\n(7) Ethan is a knave\n(8) Lucas is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Lucas is a knight and Alexander is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Luke is a knight and Riley is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Ethan is not a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Victoria is a knave.", "Victoria cannot be a knight, because this would contradict the claim of Ethan that Victoria is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Scarlett is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Riley is a knave if and only if Victoria is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that If Ethan is a knight then Luke is a knave.", "Riley cannot be a knave, because this would contradict the claim of Scarlett that Riley is a knave if and only if Victoria is a knight.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the false claim of Victoria that Scarlett is a knave.", "We have exhausted all possibilities for Scarlett and Victoria, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the claim of Luke that Ethan is not a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the claim of Lucas that Luke is a knight and Riley is a knave.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the claim of Oliver that Lucas is a knight and Alexander is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Lucas is a knight and Alexander is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Luke is a knight and Riley is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Ethan is not a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Victoria is a knave.", "Victoria cannot be a knight, because this would contradict the claim of Ethan that Victoria is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Scarlett is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Riley is a knave if and only if Victoria is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that If Ethan is a knight then Luke is a knave.", "Riley cannot be a knave, because this would contradict the claim of Scarlett that Riley is a knave if and only if Victoria is a knight.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the false claim of Victoria that Scarlett is a knave.", "We have exhausted all possibilities for Scarlett and Victoria, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the claim of Luke that Ethan is not a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the claim of Lucas that Luke is a knight and Riley is a knave.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Luke is a knight and Riley is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Ethan is not a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Victoria is a knave.", "Victoria cannot be a knight, because this would contradict the claim of Ethan that Victoria is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Scarlett is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Riley is a knave if and only if Victoria is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that If Ethan is a knight then Luke is a knave.", "Riley cannot be a knave, because this would contradict the claim of Scarlett that Riley is a knave if and only if Victoria is a knight.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the false claim of Victoria that Scarlett is a knave.", "We have exhausted all possibilities for Scarlett and Victoria, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the claim of Luke that Ethan is not a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Ethan is not a knave.", "Ethan cannot be a knight, because this would contradict the false claim of Luke that Ethan is not a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Victoria that Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Riley is a knave if and only if Victoria is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that If Ethan is a knight then Luke is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Oliver is a knave if and only if Luke is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 7), ('telling-truth', 1)), ('<=>', ('lying', 0), ('lying', 3)), ('->', ('telling-truth', 6), ('lying', 3)), ('not', ('lying', 6)), ('lying', 5), ('<=>', ('lying', 2), ('telling-truth', 4)), ('lying', 4), ('and', ('telling-truth', 3), ('lying', 2)))", "index": 1074}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Isabella, Scarlett, Emily, Aiden, James, Michael, Liam, and Penelope. Isabella asserted: \"If Emily is a knight then Aiden is a knave\". \"Penelope is a knight and Michael is a knight,\" Scarlett declared. Emily asserted: \"Michael is a knight if and only if Liam is a knave\". Aiden said that Michael is a knave or Aiden is a knight. According to James, \"Michael is a knight if and only if Scarlett is a knave\". Michael remarked, \"Emily is a knight\". Liam remarked, \"Penelope is a knight or Isabella is a knight\". According to Penelope, \"Emily is a knave or Isabella is a knight\". So who is a knight and who is a knave?", "names": ["Isabella", "Scarlett", "Emily", "Aiden", "James", "Michael", "Liam", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true, false, false], "solution_text": "Isabella is a knave, Scarlett is a knave, Emily is a knight, Aiden is a knight, James is a knight, Michael is a knight, Liam is a knave, and Penelope is a knave.", "solution_text_format": "(1) Isabella is a knave\n(2) Scarlett is a knave\n(3) Emily is a knight\n(4) Aiden is a knight\n(5) James is a knight\n(6) Michael is a knight\n(7) Liam is a knave\n(8) Penelope is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that If Emily is a knight then Aiden is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Michael is a knight if and only if Liam is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Emily is a knight.", "Liam cannot be a knight, because this would contradict the claim of Emily that Michael is a knight if and only if Liam is a knave.", "Liam cannot be a knave, because this would contradict the false claim of their own that Penelope is a knight or Isabella is a knight.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Michael.", "Michael cannot be a knave, because this would contradict the false claim of their own that Emily is a knight.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Michael is a knight if and only if Liam is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Emily is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Emily is a knight.", "Liam cannot be a knight, because this would contradict the false claim of Emily that Michael is a knight if and only if Liam is a knave.", "Liam cannot be a knave, because this would contradict the false claim of their own that Penelope is a knight or Isabella is a knight.", "We have exhausted all possibilities for Liam, Michael, and Emily, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that If Emily is a knight then Aiden is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Michael is a knight if and only if Liam is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Emily is a knight.", "Liam cannot be a knight, because this would contradict the claim of Emily that Michael is a knight if and only if Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Penelope is a knight or Isabella is a knight.", "Penelope cannot be a knight, because this would contradict the false claim of Liam that Penelope is a knight or Isabella is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Emily is a knave or Isabella is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Michael is a knave or Aiden is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Penelope is a knight and Michael is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Penelope is a knight and Michael is a knight.", "Assume James is a knight. No contradiction is found in their claim that Michael is a knight if and only if Scarlett is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('lying', 3)), ('and', ('telling-truth', 7), ('telling-truth', 5)), ('<=>', ('telling-truth', 5), ('lying', 6)), ('or', ('lying', 5), ('telling-truth', 3)), ('<=>', ('telling-truth', 5), ('lying', 1)), ('telling-truth', 2), ('or', ('telling-truth', 7), ('telling-truth', 0)), ('or', ('lying', 2), ('telling-truth', 0)))", "index": 1075}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Amelia, Logan, Aiden, Owen, Liam, Victoria, Samuel, and Sebastian. Amelia asserted: \"Liam is a knight if and only if Sebastian is a knight\". Logan was heard saying, \"Sebastian is a knave\". Aiden told you that Victoria is a knave if and only if Liam is a knight. \"Amelia is not a knave\" - Owen. Liam said, \"Owen is a knight.\" According to Victoria, \"If Liam is a knave then Liam is a knight\". As Samuel put it, \"Logan is a knave\". Sebastian remarked, \"If Logan is a knave then Victoria is a knave\". So who is a knight and who is a knave?", "names": ["Amelia", "Logan", "Aiden", "Owen", "Liam", "Victoria", "Samuel", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, false, true, true], "solution_text": "Amelia is a knave, Logan is a knave, Aiden is a knave, Owen is a knave, Liam is a knave, Victoria is a knave, Samuel is a knight, and Sebastian is a knight.", "solution_text_format": "(1) Amelia is a knave\n(2) Logan is a knave\n(3) Aiden is a knave\n(4) Owen is a knave\n(5) Liam is a knave\n(6) Victoria is a knave\n(7) Samuel is a knight\n(8) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Amelia is a knight. No contradiction is found in their claim that Liam is a knight if and only if Sebastian is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Owen is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Amelia is not a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Logan is a knave then Victoria is a knave.", "Logan cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Sebastian is a knave.", "Victoria cannot be a knight, because this would contradict the claim of Sebastian that If Logan is a knave then Victoria is a knave.", "Victoria cannot be a knave, because this would contradict the false claim of their own that If Liam is a knave then Liam is a knight.", "We have exhausted all possibilities for Victoria and Logan, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the claim of Amelia that Liam is a knight if and only if Sebastian is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the false claim of their own that Amelia is not a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Owen is a knight.", "Owen cannot be a knight, because this would contradict the false claim of Liam that Owen is a knight.", "Owen cannot be a knave, because this would contradict the false claim of their own that Amelia is not a knave.", "We have exhausted all possibilities for Owen and Liam, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Liam is a knight if and only if Sebastian is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Owen is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Amelia is not a knave.", "Owen cannot be a knave, because this would contradict the claim of Liam that Owen is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Owen is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Amelia is not a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Amelia is not a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Logan is a knave then Victoria is a knave.", "Logan cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Sebastian is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that If Liam is a knave then Liam is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that If Liam is a knave then Liam is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Victoria is a knave if and only if Liam is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Victoria is a knave if and only if Liam is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Logan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 4), ('telling-truth', 7)), ('lying', 7), ('<=>', ('lying', 5), ('telling-truth', 4)), ('not', ('lying', 0)), ('telling-truth', 3), ('->', ('lying', 4), ('telling-truth', 4)), ('lying', 1), ('->', ('lying', 1), ('lying', 5)))", "index": 1076}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Alexander, David, Harper, Isabella, Ethan, Liam, Ella, and Jacob. In Alexander's words: \"Jacob is a knave if and only if Harper is a knight\". \"Ethan is a knight if and only if Harper is a knave\" - David. Harper said, \"If Ethan is a knave then Alexander is a knight.\" As Isabella put it, \"Harper is a knight or Ella is a knave\". Ethan told you that Harper is a knight or Alexander is a knave. \"If Harper is a knave then Isabella is a knight\" - Liam. \"David is a knight if and only if Harper is a knight\" - Ella. Jacob noted, \"If Isabella is a knave then Liam is a knight\". So who is a knight and who is a knave?", "names": ["Alexander", "David", "Harper", "Isabella", "Ethan", "Liam", "Ella", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true, false, true], "solution_text": "Alexander is a knave, David is a knave, Harper is a knight, Isabella is a knight, Ethan is a knight, Liam is a knight, Ella is a knave, and Jacob is a knight.", "solution_text_format": "(1) Alexander is a knave\n(2) David is a knave\n(3) Harper is a knight\n(4) Isabella is a knight\n(5) Ethan is a knight\n(6) Liam is a knight\n(7) Ella is a knave\n(8) Jacob is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that Jacob is a knave if and only if Harper is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that If Isabella is a knave then Liam is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Harper is a knight or Ella is a knave.", "Harper cannot be a knight, because this would contradict the claim of Alexander that Jacob is a knave if and only if Harper is a knight.", "Harper cannot be a knave, because this would contradict the false claim of their own that If Ethan is a knave then Alexander is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Harper is a knight or Ella is a knave.", "Harper cannot be a knight, because this would contradict the claim of Alexander that Jacob is a knave if and only if Harper is a knight.", "Harper cannot be a knave, because this would contradict the false claim of their own that If Ethan is a knave then Alexander is a knight.", "We have exhausted all possibilities for Harper and Isabella, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that If Isabella is a knave then Liam is a knight.", "Isabella cannot be a knight, because this would contradict the false claim of Jacob that If Isabella is a knave then Liam is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Harper is a knight or Ella is a knave.", "Harper cannot be a knight, because this would contradict the false claim of Isabella that Harper is a knight or Ella is a knave.", "Harper cannot be a knave, because this would contradict the claim of Alexander that Jacob is a knave if and only if Harper is a knight.", "We have exhausted all possibilities for Harper, Isabella, and Jacob, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Jacob is a knave if and only if Harper is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that If Isabella is a knave then Liam is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Harper is a knight or Ella is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that If Ethan is a knave then Alexander is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Harper is a knight or Alexander is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that David is a knight if and only if Harper is a knight.", "David cannot be a knight, because this would contradict the claim of their own that Ethan is a knight if and only if Harper is a knave.", "David cannot be a knave, because this would contradict the claim of Ella that David is a knight if and only if Harper is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that David is a knight if and only if Harper is a knight.", "David cannot be a knight, because this would contradict the claim of their own that Ethan is a knight if and only if Harper is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Ethan is a knight if and only if Harper is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that If Harper is a knave then Isabella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 7), ('telling-truth', 2)), ('<=>', ('telling-truth', 4), ('lying', 2)), ('->', ('lying', 4), ('telling-truth', 0)), ('or', ('telling-truth', 2), ('lying', 6)), ('or', ('telling-truth', 2), ('lying', 0)), ('->', ('lying', 2), ('telling-truth', 3)), ('<=>', ('telling-truth', 1), ('telling-truth', 2)), ('->', ('lying', 3), ('telling-truth', 5)))", "index": 1077}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ava, Jack, Matthew, Aria, Michael, Abigail, Charlotte, and Logan. Ava expressed that Aria is a knight and Jack is a knave. Jack asserted: \"Aria is a knave if and only if Matthew is a knight\". \"If Aria is a knight then Jack is a knave\" - Matthew. Aria told you that Logan is a knave if and only if Ava is a knave. Michael noted, \"If Abigail is a knight then Logan is a knight\". \"Charlotte is a knight\" - Abigail. \"If Abigail is a knave then Michael is a knight,\" Charlotte mentioned. \"Charlotte is a knight and Charlotte is a knave\" - Logan. So who is a knight and who is a knave?", "names": ["Ava", "Jack", "Matthew", "Aria", "Michael", "Abigail", "Charlotte", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, true, true, false], "solution_text": "Ava is a knave, Jack is a knight, Matthew is a knave, Aria is a knight, Michael is a knave, Abigail is a knight, Charlotte is a knight, and Logan is a knave.", "solution_text_format": "(1) Ava is a knave\n(2) Jack is a knight\n(3) Matthew is a knave\n(4) Aria is a knight\n(5) Michael is a knave\n(6) Abigail is a knight\n(7) Charlotte is a knight\n(8) Logan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Aria is a knight and Jack is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Logan is a knave if and only if Ava is a knave.", "Logan cannot be a knight, because this would contradict the claim of their own that Charlotte is a knight and Charlotte is a knave.", "Logan cannot be a knave, because this would contradict the claim of Aria that Logan is a knave if and only if Ava is a knave.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Aria.", "Aria cannot be a knave, because this would contradict the claim of Ava that Aria is a knight and Jack is a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Aria is a knight and Jack is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Logan is a knave if and only if Ava is a knave.", "Logan cannot be a knight, because this would contradict the claim of Aria that Logan is a knave if and only if Ava is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Charlotte is a knight and Charlotte is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Abigail is a knave then Michael is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Charlotte is a knight.", "Michael cannot be a knight, because this would contradict the claim of their own that If Abigail is a knight then Logan is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that If Abigail is a knight then Logan is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Aria is a knave if and only if Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the claim of Jack that Aria is a knave if and only if Matthew is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that If Aria is a knight then Jack is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('lying', 1)), ('<=>', ('lying', 3), ('telling-truth', 2)), ('->', ('telling-truth', 3), ('lying', 1)), ('<=>', ('lying', 7), ('lying', 0)), ('->', ('telling-truth', 5), ('telling-truth', 7)), ('telling-truth', 6), ('->', ('lying', 5), ('telling-truth', 4)), ('and', ('telling-truth', 6), ('lying', 6)))", "index": 1078}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lucas, Alexander, Sofia, Daniel, Harper, James, Noah, and Joseph. Lucas told you that Alexander is a knight or Daniel is a knight. Alexander said that If Daniel is a knave then Lucas is a knight. In Sofia's words: \"If Joseph is a knight then Alexander is a knight\". Daniel remarked, \"James is a knight\". Harper asserted: \"Noah is a knave\". James was heard saying, \"Sofia is a knave or Lucas is a knave\". According to Noah, \"Sofia is a knave and Joseph is a knave\". \"Daniel is not a knave,\" Joseph mentioned. So who is a knight and who is a knave?", "names": ["Lucas", "Alexander", "Sofia", "Daniel", "Harper", "James", "Noah", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false, false, false], "solution_text": "Lucas is a knight, Alexander is a knight, Sofia is a knight, Daniel is a knave, Harper is a knight, James is a knave, Noah is a knave, and Joseph is a knave.", "solution_text_format": "(1) Lucas is a knight\n(2) Alexander is a knight\n(3) Sofia is a knight\n(4) Daniel is a knave\n(5) Harper is a knight\n(6) James is a knave\n(7) Noah is a knave\n(8) Joseph is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that Alexander is a knight or Daniel is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that If Daniel is a knave then Lucas is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that James is a knight.", "Assume James is a knight. No contradiction is found in their claim that Sofia is a knave or Lucas is a knave.", "Sofia cannot be a knight, because this would contradict the claim of James that Sofia is a knave or Lucas is a knave.", "Sofia cannot be a knave, because this would contradict the false claim of their own that If Joseph is a knight then Alexander is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider James.", "James cannot be a knave, because this would contradict the claim of Daniel that James is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that James is a knight.", "James cannot be a knight, because this would contradict the false claim of Daniel that James is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Sofia is a knave or Lucas is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that If Joseph is a knight then Alexander is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Daniel is not a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Daniel is not a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of Harper that Noah is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Sofia is a knave and Joseph is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('telling-truth', 3)), ('->', ('lying', 3), ('telling-truth', 0)), ('->', ('telling-truth', 7), ('telling-truth', 1)), ('telling-truth', 5), ('lying', 6), ('or', ('lying', 2), ('lying', 0)), ('and', ('lying', 2), ('lying', 7)), ('not', ('lying', 3)))", "index": 1079}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Matthew, Riley, David, Charlotte, Aurora, Daniel, William, and Sophia. \"Riley is a knave and Charlotte is a knave\" - Matthew. Riley asserted: \"If Aurora is a knave then Charlotte is a knight\". David expressed that Matthew is a knave and Aurora is a knight. As Charlotte put it, \"William is a knight\". Aurora remarked, \"Riley is a knave and William is a knave\". Daniel was heard saying, \"Riley is not a knave\". William was heard saying, \"David is a knave and Daniel is a knight\". Sophia was heard saying, \"William is a knave or Matthew is a knave\". So who is a knight and who is a knave?", "names": ["Matthew", "Riley", "David", "Charlotte", "Aurora", "Daniel", "William", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, true, true, true], "solution_text": "Matthew is a knave, Riley is a knight, David is a knave, Charlotte is a knight, Aurora is a knave, Daniel is a knight, William is a knight, and Sophia is a knight.", "solution_text_format": "(1) Matthew is a knave\n(2) Riley is a knight\n(3) David is a knave\n(4) Charlotte is a knight\n(5) Aurora is a knave\n(6) Daniel is a knight\n(7) William is a knight\n(8) Sophia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that Riley is a knave and Charlotte is a knave.", "Riley cannot be a knight, because this would contradict the claim of Matthew that Riley is a knave and Charlotte is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that If Aurora is a knave then Charlotte is a knight.", "Aurora cannot be a knight, because this would contradict the false claim of Riley that If Aurora is a knave then Charlotte is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Riley is a knave and William is a knave.", "Assume William is a knight. No contradiction is found in their claim that David is a knave and Daniel is a knight.", "David cannot be a knight, because this would contradict the claim of their own that Matthew is a knave and Aurora is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Matthew is a knave and Aurora is a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that Riley is not a knave.", "Daniel cannot be a knave, because this would contradict the claim of William that David is a knave and Daniel is a knight.", "We have exhausted all possibilities for Daniel and David, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the false claim of Aurora that Riley is a knave and William is a knave.", "We have exhausted all possibilities for William, Aurora, and Riley, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Riley is a knave and Charlotte is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that If Aurora is a knave then Charlotte is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Riley is a knave and William is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Riley is a knave and William is a knave.", "Assume William is a knight. No contradiction is found in their claim that David is a knave and Daniel is a knight.", "David cannot be a knight, because this would contradict the claim of their own that Matthew is a knave and Aurora is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Matthew is a knave and Aurora is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Riley is not a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that William is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that William is a knave or Matthew is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 1), ('lying', 3)), ('->', ('lying', 4), ('telling-truth', 3)), ('and', ('lying', 0), ('telling-truth', 4)), ('telling-truth', 6), ('and', ('lying', 1), ('lying', 6)), ('not', ('lying', 1)), ('and', ('lying', 2), ('telling-truth', 5)), ('or', ('lying', 6), ('lying', 0)))", "index": 1080}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Elizabeth, Aiden, Alexander, Matthew, Chloe, Penelope, Avery, and Liam. In a statement by Elizabeth: \"Alexander is a knight\". \"Liam is not a knight,\" Aiden declared. Alexander said that Chloe is a knight or Penelope is a knight. Matthew asserted: \"Alexander is not a knave\". Chloe was heard saying, \"Elizabeth is not a knave\". Penelope noted, \"Elizabeth is not a knight\". Avery was heard saying, \"Alexander is a knight\". Liam asserted: \"Matthew is not a knight\". So who is a knight and who is a knave?", "names": ["Elizabeth", "Aiden", "Alexander", "Matthew", "Chloe", "Penelope", "Avery", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false, true, false], "solution_text": "Elizabeth is a knight, Aiden is a knight, Alexander is a knight, Matthew is a knight, Chloe is a knight, Penelope is a knave, Avery is a knight, and Liam is a knave.", "solution_text_format": "(1) Elizabeth is a knight\n(2) Aiden is a knight\n(3) Alexander is a knight\n(4) Matthew is a knight\n(5) Chloe is a knight\n(6) Penelope is a knave\n(7) Avery is a knight\n(8) Liam is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Alexander is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Chloe is a knight or Penelope is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Elizabeth is not a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Elizabeth is not a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Elizabeth is not a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Liam is not a knight.", "Liam cannot be a knight, because this would contradict the claim of Aiden that Liam is not a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Matthew is not a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Alexander is not a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Alexander is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('not', ('telling-truth', 7)), ('or', ('telling-truth', 4), ('telling-truth', 5)), ('not', ('lying', 2)), ('not', ('lying', 0)), ('not', ('telling-truth', 0)), ('telling-truth', 2), ('not', ('telling-truth', 3)))", "index": 1081}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Elizabeth, Alexander, Chloe, James, Isabella, Aurora, Mason, and Samuel. \"James is not a knave,\" Elizabeth claimed. According to Alexander, \"Elizabeth is a knight\". Chloe commented, \"James is a knight\". James asserted: \"If Chloe is a knave then Samuel is a knight\". Isabella commented, \"Samuel is a knave\". In a statement by Aurora: \"James is a knight\". Mason commented, \"Elizabeth is a knave\". Samuel said, \"Alexander is a knight or Isabella is a knight.\" So who is a knight and who is a knave?", "names": ["Elizabeth", "Alexander", "Chloe", "James", "Isabella", "Aurora", "Mason", "Samuel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true, false, true], "solution_text": "Elizabeth is a knight, Alexander is a knight, Chloe is a knight, James is a knight, Isabella is a knave, Aurora is a knight, Mason is a knave, and Samuel is a knight.", "solution_text_format": "(1) Elizabeth is a knight\n(2) Alexander is a knight\n(3) Chloe is a knight\n(4) James is a knight\n(5) Isabella is a knave\n(6) Aurora is a knight\n(7) Mason is a knave\n(8) Samuel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that James is not a knave.", "Assume James is a knight. No contradiction is found in their claim that If Chloe is a knave then Samuel is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that James is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Alexander is a knight or Isabella is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Samuel is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Samuel is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that James is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Elizabeth is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 3)), ('telling-truth', 0), ('telling-truth', 3), ('->', ('lying', 2), ('telling-truth', 7)), ('lying', 7), ('telling-truth', 3), ('lying', 0), ('or', ('telling-truth', 1), ('telling-truth', 4)))", "index": 1082}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Mia, William, Daniel, Lily, Mason, Victoria, Charlotte, and Sebastian. Mia asserted: \"Mason is not a knave\". In a statement by William: \"Mason is a knight\". Daniel told you that Lily is not a knave. Lily said, \"If William is a knight then Daniel is a knight.\" Mason stated, \"Mia is a knave if and only if Victoria is a knight\". Victoria remarked, \"Mason is not a knave\". Charlotte was heard saying, \"Victoria is a knave\". In a statement by Sebastian: \"If Charlotte is a knave then Daniel is a knight\". So who is a knight and who is a knave?", "names": ["Mia", "William", "Daniel", "Lily", "Mason", "Victoria", "Charlotte", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false, true, true], "solution_text": "Mia is a knave, William is a knave, Daniel is a knight, Lily is a knight, Mason is a knave, Victoria is a knave, Charlotte is a knight, and Sebastian is a knight.", "solution_text_format": "(1) Mia is a knave\n(2) William is a knave\n(3) Daniel is a knight\n(4) Lily is a knight\n(5) Mason is a knave\n(6) Victoria is a knave\n(7) Charlotte is a knight\n(8) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Mason is not a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Mia is a knave if and only if Victoria is a knight.", "Victoria cannot be a knight, because this would contradict the claim of Mason that Mia is a knave if and only if Victoria is a knight.", "Victoria cannot be a knave, because this would contradict the false claim of their own that Mason is not a knave.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Mason.", "Mason cannot be a knave, because this would contradict the claim of Mia that Mason is not a knave.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Mason is not a knave.", "Mason cannot be a knight, because this would contradict the false claim of Mia that Mason is not a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Mia is a knave if and only if Victoria is a knight.", "Victoria cannot be a knight, because this would contradict the false claim of Mason that Mia is a knave if and only if Victoria is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Mason is not a knave.", "William cannot be a knight, because this would contradict the claim of their own that Mason is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Mason is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Lily is not a knave.", "Assume Lily is a knight. No contradiction is found in their claim that If William is a knight then Daniel is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Victoria is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Charlotte is a knave then Daniel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('telling-truth', 4), ('not', ('lying', 3)), ('->', ('telling-truth', 1), ('telling-truth', 2)), ('<=>', ('lying', 0), ('telling-truth', 5)), ('not', ('lying', 4)), ('lying', 5), ('->', ('lying', 6), ('telling-truth', 2)))", "index": 1083}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Riley, Liam, Jacob, Ella, Henry, Jack, Chloe, and Emily. Riley was heard saying, \"Ella is a knave if and only if Emily is a knave\". \"Jacob is a knight and Ella is a knight,\" Liam mentioned. Jacob commented, \"Liam is not a knight\". \"If Liam is a knave then Liam is a knight\" - Ella. In Henry's words: \"Jack is a knight\". \"If Chloe is a knave then Riley is a knight\" - Jack. In Chloe's words: \"Jack is a knight\". Emily said that Henry is not a knave. So who is a knight and who is a knave?", "names": ["Riley", "Liam", "Jacob", "Ella", "Henry", "Jack", "Chloe", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true, true, true], "solution_text": "Riley is a knave, Liam is a knave, Jacob is a knight, Ella is a knave, Henry is a knight, Jack is a knight, Chloe is a knight, and Emily is a knight.", "solution_text_format": "(1) Riley is a knave\n(2) Liam is a knave\n(3) Jacob is a knight\n(4) Ella is a knave\n(5) Henry is a knight\n(6) Jack is a knight\n(7) Chloe is a knight\n(8) Emily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Ella is a knave if and only if Emily is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that If Liam is a knave then Liam is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Jacob is a knight and Ella is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Liam is not a knight.", "Jacob cannot be a knave, because this would contradict the claim of Liam that Jacob is a knight and Ella is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the claim of Ella that If Liam is a knave then Liam is a knight.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that If Liam is a knave then Liam is a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that Jacob is a knight and Ella is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Jacob is a knight and Ella is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Liam is not a knight.", "Emily cannot be a knight, because this would contradict the claim of Riley that Ella is a knave if and only if Emily is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Henry is not a knave.", "Henry cannot be a knight, because this would contradict the false claim of Emily that Henry is not a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Jack is a knight.", "Jack cannot be a knight, because this would contradict the false claim of Henry that Jack is a knight.", "Jack cannot be a knave, because this would contradict the false claim of their own that If Chloe is a knave then Riley is a knight.", "We have exhausted all possibilities for Jack, Henry, and Emily, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the false claim of their own that Liam is not a knight.", "We have exhausted all possibilities for Jacob, Liam, and Ella, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Ella is a knave if and only if Emily is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that If Liam is a knave then Liam is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Jacob is a knight and Ella is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Liam is not a knight.", "Jacob cannot be a knave, because this would contradict the claim of Liam that Jacob is a knight and Ella is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the claim of Ella that If Liam is a knave then Liam is a knight.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that If Liam is a knave then Liam is a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that Jacob is a knight and Ella is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Jacob is a knight and Ella is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Liam is not a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Henry is not a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that If Chloe is a knave then Riley is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Jack is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('lying', 7)), ('and', ('telling-truth', 2), ('telling-truth', 3)), ('not', ('telling-truth', 1)), ('->', ('lying', 1), ('telling-truth', 1)), ('telling-truth', 5), ('->', ('lying', 6), ('telling-truth', 0)), ('telling-truth', 5), ('not', ('lying', 4)))", "index": 1084}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: David, Samuel, Sofia, Michael, Riley, Ava, Aiden, and Aria. \"Riley is a knight and Ava is a knight,\" David mentioned. Samuel was heard saying, \"Michael is not a knave\". Sofia told you that Michael is a knave. According to Michael, \"Aiden is a knight if and only if Ava is a knave\". Riley said that Michael is a knave and Aria is a knight. Ava told you that David is not a knave. Aiden said that If Aiden is a knight then David is a knave. \"Aiden is a knave if and only if Ava is a knave,\" Aria mentioned. So who is a knight and who is a knave?", "names": ["David", "Samuel", "Sofia", "Michael", "Riley", "Ava", "Aiden", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, false, true, false], "solution_text": "David is a knave, Samuel is a knight, Sofia is a knave, Michael is a knight, Riley is a knave, Ava is a knave, Aiden is a knight, and Aria is a knave.", "solution_text_format": "(1) David is a knave\n(2) Samuel is a knight\n(3) Sofia is a knave\n(4) Michael is a knight\n(5) Riley is a knave\n(6) Ava is a knave\n(7) Aiden is a knight\n(8) Aria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Riley is a knight and Ava is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Michael is a knave and Aria is a knight.", "Michael cannot be a knight, because this would contradict the claim of Riley that Michael is a knave and Aria is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Aiden is a knight if and only if Ava is a knave.", "Aiden cannot be a knight, because this would contradict the claim of their own that If Aiden is a knight then David is a knave.", "Aiden cannot be a knave, because this would contradict the false claim of their own that If Aiden is a knight then David is a knave.", "We have exhausted all possibilities for Aiden and Michael, so let us go back and reconsider Riley.", "Riley cannot be a knave, because this would contradict the claim of David that Riley is a knight and Ava is a knight.", "We have exhausted all possibilities for Riley, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Riley is a knight and Ava is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Michael is a knave and Aria is a knight.", "Michael cannot be a knight, because this would contradict the claim of Riley that Michael is a knave and Aria is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Aiden is a knight if and only if Ava is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Aiden is a knight then David is a knave.", "Ava cannot be a knight, because this would contradict the false claim of David that Riley is a knight and Ava is a knight.", "Ava cannot be a knave, because this would contradict the false claim of Michael that Aiden is a knight if and only if Ava is a knave.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the false claim of their own that If Aiden is a knight then David is a knave.", "We have exhausted all possibilities for Aiden and Michael, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Michael is a knave and Aria is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Aiden is a knight if and only if Ava is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Aiden is a knight then David is a knave.", "Ava cannot be a knight, because this would contradict the claim of Michael that Aiden is a knight if and only if Ava is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that David is not a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Aiden is a knave if and only if Ava is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if Ava is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Michael is not a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Michael is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Michael is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 4), ('telling-truth', 5)), ('not', ('lying', 3)), ('lying', 3), ('<=>', ('telling-truth', 6), ('lying', 5)), ('and', ('lying', 3), ('telling-truth', 7)), ('not', ('lying', 0)), ('->', ('telling-truth', 6), ('lying', 0)), ('<=>', ('lying', 6), ('lying', 5)))", "index": 1085}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Emily, Avery, Penelope, Emma, Chloe, David, Logan, and Lily. According to Emily, \"If Avery is a knave then David is a knight\". Avery noted, \"If Lily is a knight then David is a knight\". As Penelope put it, \"David is a knave or Logan is a knave\". Emma told you that Chloe is not a knight. According to Chloe, \"Logan is a knave\". As David put it, \"Emily is a knave if and only if Emma is a knight\". Logan asserted: \"Chloe is a knight and Lily is a knave\". Lily asserted: \"Avery is not a knave\". So who is a knight and who is a knave?", "names": ["Emily", "Avery", "Penelope", "Emma", "Chloe", "David", "Logan", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true, false, true], "solution_text": "Emily is a knight, Avery is a knight, Penelope is a knight, Emma is a knave, Chloe is a knight, David is a knight, Logan is a knave, and Lily is a knight.", "solution_text_format": "(1) Emily is a knight\n(2) Avery is a knight\n(3) Penelope is a knight\n(4) Emma is a knave\n(5) Chloe is a knight\n(6) David is a knight\n(7) Logan is a knave\n(8) Lily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that If Avery is a knave then David is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that If Lily is a knight then David is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Avery is not a knave.", "Assume David is a knight. No contradiction is found in their claim that Emily is a knave if and only if Emma is a knight.", "Emma cannot be a knight, because this would contradict the claim of David that Emily is a knave if and only if Emma is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Chloe is not a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of Chloe that Logan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Chloe is a knight and Lily is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that David is a knave or Logan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 1), ('telling-truth', 5)), ('->', ('telling-truth', 7), ('telling-truth', 5)), ('or', ('lying', 5), ('lying', 6)), ('not', ('telling-truth', 4)), ('lying', 6), ('<=>', ('lying', 0), ('telling-truth', 3)), ('and', ('telling-truth', 4), ('lying', 7)), ('not', ('lying', 1)))", "index": 1086}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Amelia, Scarlett, Chloe, Henry, Jacob, Emma, Ella, and Daniel. Amelia expressed that Ella is a knight or Chloe is a knight. According to Scarlett, \"Daniel is a knave if and only if Ella is a knave\". \"Henry is a knight and Daniel is a knave,\" Chloe mentioned. Henry remarked, \"Jacob is a knave if and only if Scarlett is a knave\". Jacob asserted: \"Scarlett is a knight or Henry is a knave\". Emma expressed that Chloe is a knave or Daniel is a knave. Ella said, \"Jacob is a knave.\" \"Ella is a knight\" - Daniel. So who is a knight and who is a knave?", "names": ["Amelia", "Scarlett", "Chloe", "Henry", "Jacob", "Emma", "Ella", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true, false, false], "solution_text": "Amelia is a knight, Scarlett is a knight, Chloe is a knight, Henry is a knight, Jacob is a knight, Emma is a knight, Ella is a knave, and Daniel is a knave.", "solution_text_format": "(1) Amelia is a knight\n(2) Scarlett is a knight\n(3) Chloe is a knight\n(4) Henry is a knight\n(5) Jacob is a knight\n(6) Emma is a knight\n(7) Ella is a knave\n(8) Daniel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Amelia is a knight. No contradiction is found in their claim that Ella is a knight or Chloe is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Ella that Jacob is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Scarlett is a knight or Henry is a knave.", "Scarlett cannot be a knight, because this would contradict the false claim of Jacob that Scarlett is a knight or Henry is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Daniel is a knave if and only if Ella is a knave.", "Daniel cannot be a knight, because this would contradict the false claim of Scarlett that Daniel is a knave if and only if Ella is a knave.", "Daniel cannot be a knave, because this would contradict the false claim of their own that Ella is a knight.", "We have exhausted all possibilities for Daniel, Scarlett, and Jacob, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Jacob is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Scarlett is a knight or Henry is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Daniel is a knave if and only if Ella is a knave.", "Daniel cannot be a knight, because this would contradict the claim of Scarlett that Daniel is a knave if and only if Ella is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Ella is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Jacob is a knave if and only if Scarlett is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Henry is a knight and Daniel is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Chloe is a knave or Daniel is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 6), ('telling-truth', 2)), ('<=>', ('lying', 7), ('lying', 6)), ('and', ('telling-truth', 3), ('lying', 7)), ('<=>', ('lying', 4), ('lying', 1)), ('or', ('telling-truth', 1), ('lying', 3)), ('or', ('lying', 2), ('lying', 7)), ('lying', 4), ('telling-truth', 6))", "index": 1087}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Harper, Michael, Lucas, Grace, Noah, Alexander, Aria, and Scarlett. Harper said, \"Alexander is a knight or Aria is a knave.\" \"Lucas is not a knight,\" Michael claimed. Lucas stated, \"Michael is a knave and Aria is a knight\". \"Michael is a knave,\" Grace claimed. Noah asserted: \"Grace is a knave or Noah is a knight\". \"If Harper is a knight then Lucas is a knave,\" Alexander mentioned. Aria said, \"If Alexander is a knight then Alexander is a knave.\" Scarlett was heard saying, \"Michael is a knave or Noah is a knave\". So who is a knight and who is a knave?", "names": ["Harper", "Michael", "Lucas", "Grace", "Noah", "Alexander", "Aria", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true, false, false], "solution_text": "Harper is a knight, Michael is a knight, Lucas is a knave, Grace is a knave, Noah is a knight, Alexander is a knight, Aria is a knave, and Scarlett is a knave.", "solution_text_format": "(1) Harper is a knight\n(2) Michael is a knight\n(3) Lucas is a knave\n(4) Grace is a knave\n(5) Noah is a knight\n(6) Alexander is a knight\n(7) Aria is a knave\n(8) Scarlett is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that Alexander is a knight or Aria is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that If Harper is a knight then Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the claim of Alexander that If Harper is a knight then Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Michael is a knave and Aria is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Lucas is not a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that If Alexander is a knight then Alexander is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that If Alexander is a knight then Alexander is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Michael is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Michael is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Grace is a knave or Noah is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Michael is a knave or Noah is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Michael is a knave or Noah is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('lying', 6)), ('not', ('telling-truth', 2)), ('and', ('lying', 1), ('telling-truth', 6)), ('lying', 1), ('or', ('lying', 3), ('telling-truth', 4)), ('->', ('telling-truth', 0), ('lying', 2)), ('->', ('telling-truth', 5), ('lying', 5)), ('or', ('lying', 1), ('lying', 4)))", "index": 1088}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aria, Noah, Avery, Olivia, Benjamin, Amelia, Victoria, and William. In Aria's words: \"Amelia is a knave and Olivia is a knave\". Noah said that Victoria is not a knave. Avery noted, \"Noah is a knight or Olivia is a knight\". Olivia remarked, \"William is a knight and Victoria is a knave\". \"If Amelia is a knight then Olivia is a knave,\" Benjamin claimed. Amelia asserted: \"Aria is a knight or William is a knave\". In Victoria's words: \"Olivia is a knave\". William was heard saying, \"If Olivia is a knave then Aria is a knave\". So who is a knight and who is a knave?", "names": ["Aria", "Noah", "Avery", "Olivia", "Benjamin", "Amelia", "Victoria", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false, false, true], "solution_text": "Aria is a knave, Noah is a knave, Avery is a knight, Olivia is a knight, Benjamin is a knight, Amelia is a knave, Victoria is a knave, and William is a knight.", "solution_text_format": "(1) Aria is a knave\n(2) Noah is a knave\n(3) Avery is a knight\n(4) Olivia is a knight\n(5) Benjamin is a knight\n(6) Amelia is a knave\n(7) Victoria is a knave\n(8) William is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that Amelia is a knave and Olivia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Aria that Amelia is a knave and Olivia is a knave.", "Amelia cannot be a knave, because this would contradict the false claim of their own that Aria is a knight or William is a knave.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Amelia is a knave and Olivia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Aria is a knight or William is a knave.", "William cannot be a knight, because this would contradict the claim of Amelia that Aria is a knight or William is a knave.", "William cannot be a knave, because this would contradict the false claim of their own that If Olivia is a knave then Aria is a knave.", "We have exhausted all possibilities for William, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Aria is a knight or William is a knave.", "Assume William is a knight. No contradiction is found in their claim that If Olivia is a knave then Aria is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that William is a knight and Victoria is a knave.", "Victoria cannot be a knight, because this would contradict the claim of Olivia that William is a knight and Victoria is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Olivia is a knave.", "Noah cannot be a knight, because this would contradict the claim of their own that Victoria is not a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Victoria is not a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Noah is a knight or Olivia is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Amelia is a knight then Olivia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 5), ('lying', 3)), ('not', ('lying', 6)), ('or', ('telling-truth', 1), ('telling-truth', 3)), ('and', ('telling-truth', 7), ('lying', 6)), ('->', ('telling-truth', 5), ('lying', 3)), ('or', ('telling-truth', 0), ('lying', 7)), ('lying', 3), ('->', ('lying', 3), ('lying', 0)))", "index": 1089}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Zoey, Evelyn, Aiden, Sophia, Ethan, Riley, Noah, and David. \"If Riley is a knight then Evelyn is a knave\" - Zoey. Evelyn stated, \"Ethan is a knight if and only if Ethan is a knave\". \"If Zoey is a knight then Ethan is a knave\" - Aiden. Sophia remarked, \"Ethan is a knave or Noah is a knave\". As Ethan put it, \"Sophia is a knight if and only if Aiden is a knave\". Riley stated, \"Sophia is a knight and David is a knight\". \"Ethan is not a knight,\" Noah claimed. David stated, \"Aiden is a knight and Riley is a knave\". So who is a knight and who is a knave?", "names": ["Zoey", "Evelyn", "Aiden", "Sophia", "Ethan", "Riley", "Noah", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false, false, false], "solution_text": "Zoey is a knight, Evelyn is a knave, Aiden is a knave, Sophia is a knight, Ethan is a knight, Riley is a knave, Noah is a knave, and David is a knave.", "solution_text_format": "(1) Zoey is a knight\n(2) Evelyn is a knave\n(3) Aiden is a knave\n(4) Sophia is a knight\n(5) Ethan is a knight\n(6) Riley is a knave\n(7) Noah is a knave\n(8) David is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Zoey is a knight. No contradiction is found in their claim that If Riley is a knight then Evelyn is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Sophia is a knight and David is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Ethan is a knave or Noah is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Sophia is a knight if and only if Aiden is a knave.", "Aiden cannot be a knight, because this would contradict the claim of their own that If Zoey is a knight then Ethan is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that If Zoey is a knight then Ethan is a knave.", "Noah cannot be a knight, because this would contradict the claim of Sophia that Ethan is a knave or Noah is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Ethan is not a knight.", "David cannot be a knight, because this would contradict the claim of their own that Aiden is a knight and Riley is a knave.", "David cannot be a knave, because this would contradict the claim of Riley that Sophia is a knight and David is a knight.", "We have exhausted all possibilities for David, Noah, and Aiden, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Sophia is a knight if and only if Aiden is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Zoey is a knight then Ethan is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Ethan is not a knight.", "David cannot be a knight, because this would contradict the claim of their own that Aiden is a knight and Riley is a knave.", "David cannot be a knave, because this would contradict the claim of Riley that Sophia is a knight and David is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the false claim of their own that Ethan is not a knight.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the false claim of their own that If Zoey is a knight then Ethan is a knave.", "We have exhausted all possibilities for Aiden and Ethan, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the claim of Riley that Sophia is a knight and David is a knight.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Sophia is a knight and David is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Ethan is a knave or Noah is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Sophia is a knight if and only if Aiden is a knave.", "Aiden cannot be a knight, because this would contradict the claim of their own that If Zoey is a knight then Ethan is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that If Zoey is a knight then Ethan is a knave.", "Noah cannot be a knight, because this would contradict the claim of Sophia that Ethan is a knave or Noah is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Ethan is not a knight.", "David cannot be a knight, because this would contradict the false claim of Riley that Sophia is a knight and David is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Aiden is a knight and Riley is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Ethan is a knight if and only if Ethan is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Ethan is a knight if and only if Ethan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 5), ('lying', 1)), ('<=>', ('telling-truth', 4), ('lying', 4)), ('->', ('telling-truth', 0), ('lying', 4)), ('or', ('lying', 4), ('lying', 6)), ('<=>', ('telling-truth', 3), ('lying', 2)), ('and', ('telling-truth', 3), ('telling-truth', 7)), ('not', ('telling-truth', 4)), ('and', ('telling-truth', 2), ('lying', 5)))", "index": 1090}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Abigail, Samuel, Sophia, Emma, Chloe, Matthew, Victoria, and Oliver. \"Abigail is a knight\" - Abigail. \"Oliver is a knave and Victoria is a knight,\" Samuel mentioned. \"Samuel is a knight\" - Sophia. In Emma's words: \"Sophia is a knight or Matthew is a knight\". In Chloe's words: \"Oliver is a knight or Abigail is a knave\". Matthew said that Samuel is a knave or Chloe is a knight. Victoria commented, \"Samuel is a knight if and only if Emma is a knave\". In Oliver's words: \"Abigail is not a knight\". So who is a knight and who is a knave?", "names": ["Abigail", "Samuel", "Sophia", "Emma", "Chloe", "Matthew", "Victoria", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true, true, true], "solution_text": "Abigail is a knave, Samuel is a knave, Sophia is a knave, Emma is a knight, Chloe is a knight, Matthew is a knight, Victoria is a knight, and Oliver is a knight.", "solution_text_format": "(1) Abigail is a knave\n(2) Samuel is a knave\n(3) Sophia is a knave\n(4) Emma is a knight\n(5) Chloe is a knight\n(6) Matthew is a knight\n(7) Victoria is a knight\n(8) Oliver is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Abigail is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Oliver is a knave and Victoria is a knight.", "Oliver cannot be a knight, because this would contradict the claim of Samuel that Oliver is a knave and Victoria is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Abigail is not a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Samuel is a knight if and only if Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of Victoria that Samuel is a knight if and only if Emma is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Sophia is a knight or Matthew is a knight.", "Sophia cannot be a knight, because this would contradict the false claim of Emma that Sophia is a knight or Matthew is a knight.", "Sophia cannot be a knave, because this would contradict the false claim of their own that Samuel is a knight.", "We have exhausted all possibilities for Sophia and Emma, so let us go back and reconsider Victoria.", "Victoria cannot be a knave, because this would contradict the claim of Samuel that Oliver is a knave and Victoria is a knight.", "We have exhausted all possibilities for Victoria and Oliver, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Oliver is a knave and Victoria is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Abigail is not a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Abigail is not a knight.", "Victoria cannot be a knight, because this would contradict the false claim of Samuel that Oliver is a knave and Victoria is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Samuel is a knight if and only if Emma is a knave.", "Emma cannot be a knight, because this would contradict the false claim of Victoria that Samuel is a knight if and only if Emma is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Sophia is a knight or Matthew is a knight.", "Sophia cannot be a knight, because this would contradict the claim of their own that Samuel is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Samuel is a knight.", "Matthew cannot be a knight, because this would contradict the false claim of Emma that Sophia is a knight or Matthew is a knight.", "Matthew cannot be a knave, because this would contradict the false claim of their own that Samuel is a knave or Chloe is a knight.", "We have exhausted all possibilities for Matthew, Sophia, Emma, Victoria, Oliver, and Samuel, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Abigail is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Oliver is a knave and Victoria is a knight.", "Oliver cannot be a knight, because this would contradict the claim of Samuel that Oliver is a knave and Victoria is a knight.", "Oliver cannot be a knave, because this would contradict the false claim of their own that Abigail is not a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Oliver is a knave and Victoria is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Abigail is not a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Samuel is a knight if and only if Emma is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Sophia is a knight or Matthew is a knight.", "Sophia cannot be a knight, because this would contradict the claim of their own that Samuel is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Samuel is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Samuel is a knave or Chloe is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Oliver is a knight or Abigail is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 0), ('and', ('lying', 7), ('telling-truth', 6)), ('telling-truth', 1), ('or', ('telling-truth', 2), ('telling-truth', 5)), ('or', ('telling-truth', 7), ('lying', 0)), ('or', ('lying', 1), ('telling-truth', 4)), ('<=>', ('telling-truth', 1), ('lying', 3)), ('not', ('telling-truth', 0)))", "index": 1091}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Owen, Samuel, David, Jack, Aurora, Alexander, Grace, and Aria. \"Jack is a knight if and only if David is a knight,\" Owen claimed. Samuel noted, \"Alexander is a knight\". David stated, \"David is a knight or Owen is a knave\". Jack told you that Samuel is a knave or David is a knight. According to Aurora, \"Aria is a knave\". As Alexander put it, \"Grace is a knight if and only if Aria is a knave\". Grace said, \"Alexander is a knave and Aria is a knight.\" Aria remarked, \"Aria is a knight and Owen is a knave\". So who is a knight and who is a knave?", "names": ["Owen", "Samuel", "David", "Jack", "Aurora", "Alexander", "Grace", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false, false, false], "solution_text": "Owen is a knight, Samuel is a knave, David is a knight, Jack is a knight, Aurora is a knight, Alexander is a knave, Grace is a knave, and Aria is a knave.", "solution_text_format": "(1) Owen is a knight\n(2) Samuel is a knave\n(3) David is a knight\n(4) Jack is a knight\n(5) Aurora is a knight\n(6) Alexander is a knave\n(7) Grace is a knave\n(8) Aria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Jack is a knight if and only if David is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Samuel is a knave or David is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Alexander is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Grace is a knight if and only if Aria is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Alexander is a knave and Aria is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Alexander is a knave and Aria is a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that Aria is a knight and Owen is a knave.", "Aria cannot be a knave, because this would contradict the claim of Alexander that Grace is a knight if and only if Aria is a knave.", "We have exhausted all possibilities for Aria and Grace, so let us go back and reconsider Alexander.", "Alexander cannot be a knave, because this would contradict the claim of Samuel that Alexander is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Alexander is a knight.", "Alexander cannot be a knight, because this would contradict the false claim of Samuel that Alexander is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Grace is a knight if and only if Aria is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Alexander is a knave and Aria is a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that Aria is a knight and Owen is a knave.", "Aria cannot be a knave, because this would contradict the false claim of Alexander that Grace is a knight if and only if Aria is a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Alexander is a knave and Aria is a knight.", "Aria cannot be a knight, because this would contradict the false claim of Alexander that Grace is a knight if and only if Aria is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Aria is a knight and Owen is a knave.", "Assume David is a knight. No contradiction is found in their claim that David is a knight or Owen is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Aria is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 3), ('telling-truth', 2)), ('telling-truth', 5), ('or', ('telling-truth', 2), ('lying', 0)), ('or', ('lying', 1), ('telling-truth', 2)), ('lying', 7), ('<=>', ('telling-truth', 6), ('lying', 7)), ('and', ('lying', 5), ('telling-truth', 7)), ('and', ('telling-truth', 7), ('lying', 0)))", "index": 1092}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Jacob, Jack, Michael, Matthew, Mason, Alexander, Sebastian, and Luke. \"Alexander is a knight if and only if Alexander is a knave,\" Jacob declared. \"If Alexander is a knight then Alexander is a knave,\" Jack mentioned. Michael said, \"If Sebastian is a knight then Luke is a knave.\" Matthew asserted: \"Sebastian is a knave or Alexander is a knight\". Mason said, \"Matthew is a knight.\" \"Sebastian is a knight or Michael is a knave,\" Alexander declared. Sebastian said that Sebastian is a knight and Michael is a knave. \"Sebastian is a knave if and only if Jack is a knave,\" Luke declared. So who is a knight and who is a knave?", "names": ["Jacob", "Jack", "Michael", "Matthew", "Mason", "Alexander", "Sebastian", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false, false, false], "solution_text": "Jacob is a knave, Jack is a knight, Michael is a knight, Matthew is a knight, Mason is a knight, Alexander is a knave, Sebastian is a knave, and Luke is a knave.", "solution_text_format": "(1) Jacob is a knave\n(2) Jack is a knight\n(3) Michael is a knight\n(4) Matthew is a knight\n(5) Mason is a knight\n(6) Alexander is a knave\n(7) Sebastian is a knave\n(8) Luke is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Jacob cannot be a knight, because this would contradict the claim of their own that Alexander is a knight if and only if Alexander is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Alexander is a knight if and only if Alexander is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Sebastian is a knight or Michael is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Sebastian is a knight and Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of Sebastian that Sebastian is a knight and Michael is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that If Sebastian is a knight then Luke is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Sebastian is a knave if and only if Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that If Alexander is a knight then Alexander is a knave.", "Jack cannot be a knave, because this would contradict the claim of Luke that Sebastian is a knave if and only if Jack is a knave.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the false claim of Michael that If Sebastian is a knight then Luke is a knave.", "We have exhausted all possibilities for Luke and Michael, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Sebastian is a knight and Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of Alexander that Sebastian is a knight or Michael is a knave.", "Michael cannot be a knave, because this would contradict the false claim of their own that If Sebastian is a knight then Luke is a knave.", "We have exhausted all possibilities for Michael and Sebastian, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Sebastian is a knight or Michael is a knave.", "Sebastian cannot be a knight, because this would contradict the false claim of Alexander that Sebastian is a knight or Michael is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Sebastian is a knight and Michael is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that If Sebastian is a knight then Luke is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Sebastian is a knave if and only if Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of Luke that Sebastian is a knave if and only if Jack is a knave.", "Jack cannot be a knave, because this would contradict the false claim of their own that If Alexander is a knight then Alexander is a knave.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Sebastian is a knave if and only if Jack is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that If Alexander is a knight then Alexander is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Sebastian is a knave or Alexander is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Matthew is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 5), ('lying', 5)), ('->', ('telling-truth', 5), ('lying', 5)), ('->', ('telling-truth', 6), ('lying', 7)), ('or', ('lying', 6), ('telling-truth', 5)), ('telling-truth', 3), ('or', ('telling-truth', 6), ('lying', 2)), ('and', ('telling-truth', 6), ('lying', 2)), ('<=>', ('lying', 6), ('lying', 1)))", "index": 1093}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Lily, Isabella, Noah, William, Joseph, Matthew, Zoey, and Aria. Lily said that Matthew is a knight if and only if Isabella is a knave. According to Isabella, \"Lily is not a knight\". Noah remarked, \"Lily is a knight\". William asserted: \"Matthew is a knave if and only if Noah is a knight\". Joseph was heard saying, \"If William is a knight then William is a knave\". Matthew was heard saying, \"Zoey is not a knight\". Zoey commented, \"Isabella is a knight and Lily is a knave\". As Aria put it, \"Lily is a knight if and only if Joseph is a knave\". So who is a knight and who is a knave?", "names": ["Lily", "Isabella", "Noah", "William", "Joseph", "Matthew", "Zoey", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true, false, false], "solution_text": "Lily is a knight, Isabella is a knave, Noah is a knight, William is a knave, Joseph is a knight, Matthew is a knight, Zoey is a knave, and Aria is a knave.", "solution_text_format": "(1) Lily is a knight\n(2) Isabella is a knave\n(3) Noah is a knight\n(4) William is a knave\n(5) Joseph is a knight\n(6) Matthew is a knight\n(7) Zoey is a knave\n(8) Aria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that Matthew is a knight if and only if Isabella is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Zoey is not a knight.", "Zoey cannot be a knight, because this would contradict the claim of Matthew that Zoey is not a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Isabella is a knight and Lily is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Lily that Matthew is a knight if and only if Isabella is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Lily is not a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Lily is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Matthew is a knave if and only if Noah is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Matthew is a knave if and only if Noah is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If William is a knight then William is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Lily is a knight if and only if Joseph is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Lily is a knight if and only if Joseph is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 5), ('lying', 1)), ('not', ('telling-truth', 0)), ('telling-truth', 0), ('<=>', ('lying', 5), ('telling-truth', 2)), ('->', ('telling-truth', 3), ('lying', 3)), ('not', ('telling-truth', 6)), ('and', ('telling-truth', 1), ('lying', 0)), ('<=>', ('telling-truth', 0), ('lying', 4)))", "index": 1094}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Aiden, Ava, Mia, Daniel, Lucas, Oliver, Amelia, and Ethan. Aiden said that Ava is a knight. Ava said, \"If Daniel is a knave then Aiden is a knight.\" Mia noted, \"Ava is not a knave\". Daniel said that If Ava is a knight then Oliver is a knave. Lucas remarked, \"Mia is a knight or Ethan is a knave\". \"Daniel is a knave and Amelia is a knave\" - Oliver. \"Daniel is a knave if and only if Amelia is a knight,\" Amelia mentioned. Ethan noted, \"Aiden is a knave if and only if Lucas is a knight\". So who is a knight and who is a knave?", "names": ["Aiden", "Ava", "Mia", "Daniel", "Lucas", "Oliver", "Amelia", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true, false, false], "solution_text": "Aiden is a knight, Ava is a knight, Mia is a knight, Daniel is a knave, Lucas is a knight, Oliver is a knight, Amelia is a knave, and Ethan is a knave.", "solution_text_format": "(1) Aiden is a knight\n(2) Ava is a knight\n(3) Mia is a knight\n(4) Daniel is a knave\n(5) Lucas is a knight\n(6) Oliver is a knight\n(7) Amelia is a knave\n(8) Ethan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Ava is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that If Daniel is a knave then Aiden is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that If Ava is a knight then Oliver is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Daniel that If Ava is a knight then Oliver is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Daniel is a knave and Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Daniel is a knave if and only if Amelia is a knight.", "Amelia cannot be a knave, because this would contradict the false claim of their own that Daniel is a knave if and only if Amelia is a knight.", "We have exhausted all possibilities for Amelia and Oliver, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that If Ava is a knight then Oliver is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Daniel is a knave and Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Oliver that Daniel is a knave and Amelia is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Daniel is a knave if and only if Amelia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Ava is not a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Mia is a knight or Ethan is a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Aiden is a knave if and only if Lucas is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if Lucas is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('->', ('lying', 3), ('telling-truth', 0)), ('not', ('lying', 1)), ('->', ('telling-truth', 1), ('lying', 5)), ('or', ('telling-truth', 2), ('lying', 7)), ('and', ('lying', 3), ('lying', 6)), ('<=>', ('lying', 3), ('telling-truth', 6)), ('<=>', ('lying', 0), ('telling-truth', 4)))", "index": 1095}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sofia, Avery, Penelope, Scarlett, Grace, Emily, William, and Emma. Sofia said, \"Avery is a knight.\" Avery noted, \"Sofia is a knight and Sofia is a knave\". Penelope said that Avery is a knight and Grace is a knight. Scarlett was heard saying, \"Avery is a knight if and only if Sofia is a knight\". Grace said that Avery is a knave if and only if Emma is a knave. Emily noted, \"Sofia is a knight and Scarlett is a knight\". As William put it, \"Emma is a knight and Emma is a knave\". Emma said, \"William is not a knave.\" So who is a knight and who is a knave?", "names": ["Sofia", "Avery", "Penelope", "Scarlett", "Grace", "Emily", "William", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, false, false, false], "solution_text": "Sofia is a knave, Avery is a knave, Penelope is a knave, Scarlett is a knight, Grace is a knight, Emily is a knave, William is a knave, and Emma is a knave.", "solution_text_format": "(1) Sofia is a knave\n(2) Avery is a knave\n(3) Penelope is a knave\n(4) Scarlett is a knight\n(5) Grace is a knight\n(6) Emily is a knave\n(7) William is a knave\n(8) Emma is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Avery is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Sofia is a knight and Sofia is a knave.", "Avery cannot be a knave, because this would contradict the claim of Sofia that Avery is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Avery is a knight.", "Avery cannot be a knight, because this would contradict the false claim of Sofia that Avery is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Sofia is a knight and Sofia is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Avery is a knight and Grace is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Avery is a knight and Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Avery is a knave if and only if Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of Grace that Avery is a knave if and only if Emma is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that William is not a knave.", "William cannot be a knight, because this would contradict the claim of their own that Emma is a knight and Emma is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Emma is a knight and Emma is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Avery is a knight if and only if Sofia is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Sofia is a knight and Scarlett is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Sofia is a knight and Scarlett is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('and', ('telling-truth', 0), ('lying', 0)), ('and', ('telling-truth', 1), ('telling-truth', 4)), ('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('<=>', ('lying', 1), ('lying', 7)), ('and', ('telling-truth', 0), ('telling-truth', 3)), ('and', ('telling-truth', 7), ('lying', 7)), ('not', ('lying', 6)))", "index": 1096}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Benjamin, Samuel, Sebastian, Grace, Alexander, Owen, Daniel, and Evelyn. \"Sebastian is a knight\" - Benjamin. \"Daniel is a knave and Daniel is a knight,\" Samuel declared. \"If Alexander is a knave then Owen is a knight,\" Sebastian mentioned. \"Daniel is a knave,\" Grace claimed. Alexander said that Daniel is a knave or Sebastian is a knave. Owen said that Samuel is a knave if and only if Benjamin is a knight. Daniel said, \"Sebastian is a knight or Sebastian is a knave.\" Evelyn noted, \"Benjamin is a knave if and only if Sebastian is a knight\". So who is a knight and who is a knave?", "names": ["Benjamin", "Samuel", "Sebastian", "Grace", "Alexander", "Owen", "Daniel", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true, true, false], "solution_text": "Benjamin is a knight, Samuel is a knave, Sebastian is a knight, Grace is a knave, Alexander is a knave, Owen is a knight, Daniel is a knight, and Evelyn is a knave.", "solution_text_format": "(1) Benjamin is a knight\n(2) Samuel is a knave\n(3) Sebastian is a knight\n(4) Grace is a knave\n(5) Alexander is a knave\n(6) Owen is a knight\n(7) Daniel is a knight\n(8) Evelyn is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Alexander is a knave then Owen is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Daniel is a knave or Sebastian is a knave.", "Daniel cannot be a knight, because this would contradict the claim of Alexander that Daniel is a knave or Sebastian is a knave.", "Daniel cannot be a knave, because this would contradict the false claim of their own that Sebastian is a knight or Sebastian is a knave.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Daniel is a knave or Sebastian is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Sebastian is a knight or Sebastian is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Benjamin is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Daniel is a knave and Daniel is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Daniel is a knave and Daniel is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Daniel is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Daniel is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave if and only if Sebastian is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Benjamin is a knave if and only if Sebastian is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('and', ('lying', 6), ('telling-truth', 6)), ('->', ('lying', 4), ('telling-truth', 5)), ('lying', 6), ('or', ('lying', 6), ('lying', 2)), ('<=>', ('lying', 1), ('telling-truth', 0)), ('or', ('telling-truth', 2), ('lying', 2)), ('<=>', ('lying', 0), ('telling-truth', 2)))", "index": 1097}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Ella, Mason, Riley, Ava, Penelope, Jack, Benjamin, and Mia. As Ella put it, \"Ava is a knave or Ava is a knight\". In a statement by Mason: \"Penelope is not a knight\". Riley commented, \"Benjamin is a knight if and only if Penelope is a knight\". In Ava's words: \"If Jack is a knave then Ava is a knight\". As Penelope put it, \"Mia is a knight and Ava is a knave\". \"Penelope is not a knave,\" Jack claimed. Benjamin noted, \"Penelope is a knight and Ella is a knave\". \"Penelope is a knight or Penelope is a knave,\" Mia declared. So who is a knight and who is a knave?", "names": ["Ella", "Mason", "Riley", "Ava", "Penelope", "Jack", "Benjamin", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false, false, true], "solution_text": "Ella is a knight, Mason is a knight, Riley is a knight, Ava is a knight, Penelope is a knave, Jack is a knave, Benjamin is a knave, and Mia is a knight.", "solution_text_format": "(1) Ella is a knight\n(2) Mason is a knight\n(3) Riley is a knight\n(4) Ava is a knight\n(5) Penelope is a knave\n(6) Jack is a knave\n(7) Benjamin is a knave\n(8) Mia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Ava is a knave or Ava is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that If Jack is a knave then Ava is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Penelope is not a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Mia is a knight and Ava is a knave.", "Penelope cannot be a knave, because this would contradict the claim of Jack that Penelope is not a knave.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Penelope is not a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Mia is a knight and Ava is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Mia is a knight and Ava is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Penelope is a knight or Penelope is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Benjamin is a knight if and only if Penelope is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of Riley that Benjamin is a knight if and only if Penelope is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Penelope is a knight and Ella is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('telling-truth', 3)), ('not', ('telling-truth', 4)), ('<=>', ('telling-truth', 6), ('telling-truth', 4)), ('->', ('lying', 5), ('telling-truth', 3)), ('and', ('telling-truth', 7), ('lying', 3)), ('not', ('lying', 4)), ('and', ('telling-truth', 4), ('lying', 0)), ('or', ('telling-truth', 4), ('lying', 4)))", "index": 1098}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Evelyn, Aria, Daniel, Joseph, Penelope, Harper, Liam, and Lily. Evelyn said, \"Aria is a knave if and only if Harper is a knave.\" Aria asserted: \"Lily is a knight if and only if Liam is a knave\". Daniel said, \"Harper is a knave if and only if Evelyn is a knight.\" Joseph noted, \"If Daniel is a knight then Penelope is a knight\". \"Daniel is not a knave,\" Penelope declared. As Harper put it, \"Aria is a knave or Daniel is a knave\". Liam stated, \"If Lily is a knave then Evelyn is a knave\". Lily said, \"Daniel is a knight or Liam is a knave.\" So who is a knight and who is a knave?", "names": ["Evelyn", "Aria", "Daniel", "Joseph", "Penelope", "Harper", "Liam", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true, true, true], "solution_text": "Evelyn is a knave, Aria is a knave, Daniel is a knight, Joseph is a knight, Penelope is a knight, Harper is a knight, Liam is a knight, and Lily is a knight.", "solution_text_format": "(1) Evelyn is a knave\n(2) Aria is a knave\n(3) Daniel is a knight\n(4) Joseph is a knight\n(5) Penelope is a knight\n(6) Harper is a knight\n(7) Liam is a knight\n(8) Lily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Aria is a knave if and only if Harper is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Lily is a knight if and only if Liam is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Daniel is a knight or Liam is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Harper is a knave if and only if Evelyn is a knight.", "Harper cannot be a knight, because this would contradict the claim of Daniel that Harper is a knave if and only if Evelyn is a knight.", "Harper cannot be a knave, because this would contradict the claim of Evelyn that Aria is a knave if and only if Harper is a knave.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Harper is a knave if and only if Evelyn is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Aria is a knave or Daniel is a knave.", "Liam cannot be a knight, because this would contradict the claim of Aria that Lily is a knight if and only if Liam is a knave.", "Liam cannot be a knave, because this would contradict the false claim of their own that If Lily is a knave then Evelyn is a knave.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the claim of Evelyn that Aria is a knave if and only if Harper is a knave.", "We have exhausted all possibilities for Harper and Daniel, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Daniel is a knight or Liam is a knave.", "Daniel cannot be a knight, because this would contradict the false claim of Lily that Daniel is a knight or Liam is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Harper is a knave if and only if Evelyn is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Aria is a knave or Daniel is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that If Lily is a knave then Evelyn is a knave.", "Liam cannot be a knave, because this would contradict the claim of Aria that Lily is a knight if and only if Liam is a knave.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the claim of Evelyn that Aria is a knave if and only if Harper is a knave.", "We have exhausted all possibilities for Harper, Daniel, and Lily, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Lily is a knight if and only if Liam is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Daniel is a knight or Liam is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Harper is a knave if and only if Evelyn is a knight.", "Harper cannot be a knight, because this would contradict the claim of Evelyn that Aria is a knave if and only if Harper is a knave.", "Harper cannot be a knave, because this would contradict the false claim of their own that Aria is a knave or Daniel is a knave.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Harper is a knave if and only if Evelyn is a knight.", "Harper cannot be a knight, because this would contradict the claim of Evelyn that Aria is a knave if and only if Harper is a knave.", "Harper cannot be a knave, because this would contradict the false claim of Daniel that Harper is a knave if and only if Evelyn is a knight.", "We have exhausted all possibilities for Harper and Daniel, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Daniel is a knight or Liam is a knave.", "Daniel cannot be a knight, because this would contradict the false claim of Lily that Daniel is a knight or Liam is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Harper is a knave if and only if Evelyn is a knight.", "Harper cannot be a knight, because this would contradict the claim of Evelyn that Aria is a knave if and only if Harper is a knave.", "Harper cannot be a knave, because this would contradict the false claim of Daniel that Harper is a knave if and only if Evelyn is a knight.", "We have exhausted all possibilities for Harper, Daniel, Lily, and Aria, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Aria is a knave if and only if Harper is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Lily is a knight if and only if Liam is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Daniel is a knight or Liam is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Harper is a knave if and only if Evelyn is a knight.", "Harper cannot be a knight, because this would contradict the false claim of Evelyn that Aria is a knave if and only if Harper is a knave.", "Harper cannot be a knave, because this would contradict the claim of Daniel that Harper is a knave if and only if Evelyn is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Harper is a knave if and only if Evelyn is a knight.", "Harper cannot be a knight, because this would contradict the false claim of Evelyn that Aria is a knave if and only if Harper is a knave.", "Harper cannot be a knave, because this would contradict the false claim of their own that Aria is a knave or Daniel is a knave.", "We have exhausted all possibilities for Harper and Daniel, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Daniel is a knight or Liam is a knave.", "Daniel cannot be a knight, because this would contradict the false claim of Lily that Daniel is a knight or Liam is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Harper is a knave if and only if Evelyn is a knight.", "Harper cannot be a knight, because this would contradict the false claim of Evelyn that Aria is a knave if and only if Harper is a knave.", "Harper cannot be a knave, because this would contradict the false claim of their own that Aria is a knave or Daniel is a knave.", "We have exhausted all possibilities for Harper, Daniel, and Lily, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Lily is a knight if and only if Liam is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Daniel is a knight or Liam is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Harper is a knave if and only if Evelyn is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Aria is a knave or Daniel is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that If Lily is a knave then Evelyn is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that If Daniel is a knight then Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Daniel is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('lying', 5)), ('<=>', ('telling-truth', 7), ('lying', 6)), ('<=>', ('lying', 5), ('telling-truth', 0)), ('->', ('telling-truth', 2), ('telling-truth', 4)), ('not', ('lying', 2)), ('or', ('lying', 1), ('lying', 2)), ('->', ('lying', 7), ('lying', 0)), ('or', ('telling-truth', 2), ('lying', 6)))", "index": 1099}