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-{"quiz": "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, Isabella, Zoey, Joseph, Henry, Luke, and Lily. In Ethan's words: \"Benjamin is a knight or Zoey is a knight\". Benjamin commented, \"Ethan is a knight and Henry is a knight\". \"Benjamin is a knight if and only if Lily is a knave,\" Isabella claimed. \"Benjamin is a knight or Lily is a knave,\" Zoey claimed. According to Joseph, \"Lily is a knight if and only if Luke is a knight\". \"Luke is a knave if and only if Isabella is a knave\" - Henry. \"Luke is a knight if and only if Zoey is a knave,\" Luke declared. According to Lily, \"Luke is a knight\". So who is a knight and who is a knave?", "names": ["Ethan", "Benjamin", "Isabella", "Zoey", "Joseph", "Henry", "Luke", "Lily"], "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": "Ethan is a knave, Benjamin is a knave, Isabella is a knight, Zoey is a knave, Joseph is a knight, Henry is a knight, Luke is a knight, and Lily is a knight.", "solution_text_format": "(1) Ethan is a knave\n(2) Benjamin is a knave\n(3) Isabella is a knight\n(4) Zoey is a knave\n(5) Joseph is a knight\n(6) Henry is a knight\n(7) Luke 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 Ethan is a knight. No contradiction is found in their claim that Benjamin is a knight or Zoey is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Ethan is a knight and Henry is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Luke is a knave if and only if Isabella is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Luke is a knight if and only if Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Luke that Luke 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 Benjamin is a knight or Lily is a knave.", "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 Luke is a knight if and only if Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the false claim of Luke that Luke 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 Benjamin is a knight or Lily is a knave.", "We have exhausted all possibilities for Zoey and Luke, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the claim of Benjamin that Ethan is a knight and Henry is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Ethan is a knight and Henry is a knight.", "Henry cannot be a knight, because this would contradict the false claim of Benjamin that Ethan is a knight and Henry 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 Isabella is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Luke is a knight if and only if Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Luke that Luke is a knight if and only if Zoey is a knave.", "Zoey cannot be a knave, because this would contradict the claim of Ethan that Benjamin is a knight or Zoey 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 Luke is a knight if and only if Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the false claim of Luke that Luke is a knight if and only if Zoey is a knave.", "Zoey cannot be a knave, because this would contradict the claim of Ethan that Benjamin is a knight or Zoey is a knight.", "We have exhausted all possibilities for Zoey, Luke, Henry, and Benjamin, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Benjamin is a knight or Zoey is a knight.", "Benjamin cannot be a knight, because this would contradict the false claim of Ethan that Benjamin is a knight or Zoey is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Ethan is a knight and Henry is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Luke is a knave if and only if Isabella is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Luke is a knight if and only if Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the false claim of Ethan that Benjamin is a knight or Zoey is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Benjamin is a knight or Lily is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Luke is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Benjamin is a knight if and only if Lily is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Lily is a knight if and only if Luke is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('telling-truth', 3)), ('and', ('telling-truth', 0), ('telling-truth', 5)), ('<=>', ('telling-truth', 1), ('lying', 7)), ('or', ('telling-truth', 1), ('lying', 7)), ('<=>', ('telling-truth', 7), ('telling-truth', 6)), ('<=>', ('lying', 6), ('lying', 2)), ('<=>', ('telling-truth', 6), ('lying', 3)), ('telling-truth', 6))", "index": 0}
-{"quiz": "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, Isabella, Jackson, Aria, Mason, Harper, Abigail, and Emily. \"Isabella is not a knave\" - Luke. In Isabella's words: \"If Mason is a knight then Emily is a knave\". Jackson said that Aria is a knight and Harper is a knight. Aria said, \"If Mason is a knave then Harper is a knight.\" As Mason put it, \"Emily is a knave or Aria is a knight\". Harper was heard saying, \"Emily is a knight\". \"Luke is a knave or Aria is a knight,\" Abigail declared. Emily asserted: \"Abigail is not a knight\". So who is a knight and who is a knave?", "names": ["Luke", "Isabella", "Jackson", "Aria", "Mason", "Harper", "Abigail", "Emily"], "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": "Luke is a knight, Isabella is a knight, Jackson is a knave, Aria is a knight, Mason is a knight, Harper is a knave, Abigail is a knight, and Emily is a knave.", "solution_text_format": "(1) Luke is a knight\n(2) Isabella is a knight\n(3) Jackson is a knave\n(4) Aria is a knight\n(5) Mason is a knight\n(6) Harper is a knave\n(7) Abigail 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 Luke 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 Mason is a knight then Emily is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Emily is a knave or Aria is a knight.", "Emily cannot be a knight, because this would contradict the claim of Isabella that If Mason is a knight then Emily is a knave.", "Assume Emily 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 Luke is a knave or Aria is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that If Mason is a knave then Harper is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that Emily is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Emily is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Aria is a knight and Harper is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Aria is a knight and Harper is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('->', ('telling-truth', 4), ('lying', 7)), ('and', ('telling-truth', 3), ('telling-truth', 5)), ('->', ('lying', 4), ('telling-truth', 5)), ('or', ('lying', 7), ('telling-truth', 3)), ('telling-truth', 7), ('or', ('lying', 0), ('telling-truth', 3)), ('not', ('telling-truth', 6)))", "index": 1}
-{"quiz": "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, Avery, Ella, Matthew, Luke, Mia, Scarlett, and Benjamin. \"Matthew is a knight,\" Isabella mentioned. \"If Ella is a knave then Matthew is a knave,\" Avery mentioned. Ella asserted: \"Luke is a knight\". Matthew told you that Avery is a knave and Isabella is a knave. Luke said, \"If Avery is a knave then Luke is a knight.\" Mia said, \"If Ella is a knave then Benjamin is a knave.\" Scarlett noted, \"Isabella is not a knave\". \"Mia is not a knave,\" Benjamin mentioned. So who is a knight and who is a knave?", "names": ["Isabella", "Avery", "Ella", "Matthew", "Luke", "Mia", "Scarlett", "Benjamin"], "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": "Isabella is a knave, Avery is a knight, Ella is a knight, Matthew is a knave, Luke is a knight, Mia is a knight, Scarlett is a knave, and Benjamin is a knight.", "solution_text_format": "(1) Isabella is a knave\n(2) Avery is a knight\n(3) Ella is a knight\n(4) Matthew is a knave\n(5) Luke is a knight\n(6) Mia is a knight\n(7) Scarlett 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 Isabella is a knight. No contradiction is found in their claim that Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Avery is a knave and Isabella is a knave.", "Matthew cannot be a knave, because this would contradict the claim of Isabella that 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 Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the false claim of Isabella that Matthew is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Avery is a knave and Isabella is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that If Ella is a knave then Matthew is a knave.", "Assume Ella 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 Avery is a knave then Luke is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that If Ella is a knave then Benjamin is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Mia is not a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Isabella is not a knave.", "Assume Scarlett 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": "(('telling-truth', 3), ('->', ('lying', 2), ('lying', 3)), ('telling-truth', 4), ('and', ('lying', 1), ('lying', 0)), ('->', ('lying', 1), ('telling-truth', 4)), ('->', ('lying', 2), ('lying', 7)), ('not', ('lying', 0)), ('not', ('lying', 5)))", "index": 2}
-{"quiz": "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, Sebastian, James, Emily, Olivia, Aria, Penelope, and Luke. Noah expressed that James is a knave and Luke is a knight. Sebastian said, \"Aria is a knave if and only if Noah is a knight.\" James commented, \"Emily is a knight or Emily is a knave\". Emily stated, \"Aria is a knight if and only if Penelope is a knave\". Olivia told you that Penelope is a knave or Noah is a knave. Aria stated, \"Luke is a knight if and only if Sebastian is a knave\". Penelope expressed that Noah is a knight. \"Sebastian is a knave\" - Luke. So who is a knight and who is a knave?", "names": ["Noah", "Sebastian", "James", "Emily", "Olivia", "Aria", "Penelope", "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, true, false, false], "solution_text": "Noah is a knave, Sebastian is a knight, James is a knight, Emily is a knight, Olivia is a knight, Aria is a knight, Penelope is a knave, and Luke is a knave.", "solution_text_format": "(1) Noah is a knave\n(2) Sebastian is a knight\n(3) James is a knight\n(4) Emily is a knight\n(5) Olivia is a knight\n(6) Aria is a knight\n(7) Penelope 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 Noah is a knight. No contradiction is found in their claim that James is a knave and Luke is a knight.", "James cannot be a knight, because this would contradict the claim of Noah that James is a knave and Luke is a knight.", "James cannot be a knave, because this would contradict the false claim of their own that Emily is a knight or Emily is a knave.", "We have exhausted all possibilities for James, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that James is a knave and Luke is a knight.", "Assume James 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 Aria is a knight if and only if Penelope is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Luke is a knight if and only if Sebastian is a knave.", "Assume Luke 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 Aria that Luke 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 Aria is a knave if and only if Noah is a knight.", "We have exhausted all possibilities for Sebastian, 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.", "Assume Sebastian is a knight. No contradiction is found in their claim that Aria is a knave if and only if Noah is a knight.", "Penelope cannot be a knight, because this would contradict the claim of Emily that Aria 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 Noah is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Penelope is a knave or Noah is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('telling-truth', 7)), ('<=>', ('lying', 5), ('telling-truth', 0)), ('or', ('telling-truth', 3), ('lying', 3)), ('<=>', ('telling-truth', 5), ('lying', 6)), ('or', ('lying', 6), ('lying', 0)), ('<=>', ('telling-truth', 7), ('lying', 1)), ('telling-truth', 0), ('lying', 1))", "index": 3}
-{"quiz": "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, Victoria, Aiden, Jackson, Liam, Aria, and Ethan. As Sofia put it, \"If William is a knave then Liam is a knave\". As William put it, \"Aria is a knave if and only if Sofia is a knave\". Victoria told you that Aria is a knave or William is a knave. Aiden asserted: \"If Aria is a knave then William is a knave\". According to Jackson, \"Ethan is a knight or Aiden is a knight\". Liam said that If Victoria is a knight then William is a knight. In a statement by Aria: \"Aiden is a knave and Liam is a knight\". Ethan was heard saying, \"If Liam is a knight then Jackson is a knight\". So who is a knight and who is a knave?", "names": ["Sofia", "William", "Victoria", "Aiden", "Jackson", "Liam", "Aria", "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, true], "solution_text": "Sofia is a knight, William is a knave, Victoria is a knight, Aiden is a knight, Jackson is a knight, Liam is a knave, Aria is a knave, and Ethan is a knight.", "solution_text_format": "(1) Sofia is a knight\n(2) William is a knave\n(3) Victoria is a knight\n(4) Aiden is a knight\n(5) Jackson is a knight\n(6) Liam is a knave\n(7) Aria 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 Sofia is a knight. No contradiction is found in their claim that If William is a knave then Liam is a knave.", "Assume William is a knight. No contradiction is found in their claim that Aria is a knave if and only if Sofia is a knave.", "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 If Aria is a knave then William is a knave.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Aria.", "Aria cannot be a knave, because this would contradict the claim of William that Aria is a knave if and only if Sofia is a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Aria is a knave if and only if Sofia is a knave.", "Aria cannot be a knight, because this would contradict the false claim of William that Aria is a knave if and only if Sofia is a knave.", "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 If Aria is a knave then William is a knave.", "Liam cannot be a knight, because this would contradict the claim of Sofia that If William is a knave then Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that If Victoria is a knight then William is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Aria is a knave or William is a knave.", "Assume Jackson 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 If Liam is a knight then Jackson is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 1), ('lying', 5)), ('<=>', ('lying', 6), ('lying', 0)), ('or', ('lying', 6), ('lying', 1)), ('->', ('lying', 6), ('lying', 1)), ('or', ('telling-truth', 7), ('telling-truth', 3)), ('->', ('telling-truth', 2), ('telling-truth', 1)), ('and', ('lying', 3), ('telling-truth', 5)), ('->', ('telling-truth', 5), ('telling-truth', 4)))", "index": 4}
-{"quiz": "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, Aurora, Jackson, Jacob, Chloe, Daniel, Luke, and Jack. According to Ethan, \"Jackson is a knight or Luke is a knight\". Aurora said, \"Jacob is a knight.\" Jackson said, \"Jacob is a knave if and only if Daniel is a knave.\" Jacob said, \"Jackson is a knight and Chloe is a knave.\" Chloe told you that Luke is a knight and Aurora is a knight. Daniel noted, \"Jacob is a knight\". Luke said, \"If Jackson is a knight then Ethan is a knave.\" In Jack's words: \"Jacob is a knave or Jackson is a knight\". So who is a knight and who is a knave?", "names": ["Ethan", "Aurora", "Jackson", "Jacob", "Chloe", "Daniel", "Luke", "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, false, true], "solution_text": "Ethan is a knight, Aurora is a knight, Jackson is a knight, Jacob is a knight, Chloe is a knave, Daniel is a knight, Luke is a knave, and Jack is a knight.", "solution_text_format": "(1) Ethan is a knight\n(2) Aurora is a knight\n(3) Jackson is a knight\n(4) Jacob is a knight\n(5) Chloe is a knave\n(6) Daniel is a knight\n(7) Luke 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 Ethan is a knight. No contradiction is found in their claim that Jackson is a knight or Luke is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Jacob is a knave if and only if Daniel is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Jackson is a knight and Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Jacob that Jackson is a knight and Chloe is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Luke is a knight and Aurora is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that If Jackson is a knight then Ethan is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that If Jackson is a knight then Ethan is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Jacob is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Jacob is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Jacob is a knave or Jackson is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('telling-truth', 6)), ('telling-truth', 3), ('<=>', ('lying', 3), ('lying', 5)), ('and', ('telling-truth', 2), ('lying', 4)), ('and', ('telling-truth', 6), ('telling-truth', 1)), ('telling-truth', 3), ('->', ('telling-truth', 2), ('lying', 0)), ('or', ('lying', 3), ('telling-truth', 2)))", "index": 5}
-{"quiz": "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, Oliver, Benjamin, Logan, Mia, Luke, and Olivia. Sophia said, \"Logan is a knave and Benjamin is a knave.\" \"Penelope is a knight or Logan is a knight,\" Penelope mentioned. \"Sophia is a knight or Mia is a knight,\" Oliver declared. In Benjamin's words: \"Penelope is not a knight\". \"Benjamin is a knight,\" Logan declared. Mia said, \"If Olivia is a knight then Oliver is a knave.\" Luke remarked, \"Benjamin is a knave or Penelope is a knight\". Olivia stated, \"Benjamin is a knight and Logan is a knight\". So who is a knight and who is a knave?", "names": ["Sophia", "Penelope", "Oliver", "Benjamin", "Logan", "Mia", "Luke", "Olivia"], "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": "Sophia is a knight, Penelope is a knight, Oliver is a knight, Benjamin is a knave, Logan is a knave, Mia is a knight, Luke is a knight, and Olivia is a knave.", "solution_text_format": "(1) Sophia is a knight\n(2) Penelope is a knight\n(3) Oliver is a knight\n(4) Benjamin is a knave\n(5) Logan is a knave\n(6) Mia is a knight\n(7) Luke 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 Sophia is a knight. No contradiction is found in their claim that Logan is a knave and Benjamin is a knave.", "Logan cannot be a knight, because this would contradict the claim of Sophia that Logan is a knave and Benjamin is a knave.", "Assume Logan 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 claim of Sophia that Logan is a knave and Benjamin is a knave.", "Assume Benjamin 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 Penelope is a knight or Logan is a knight.", "Assume Oliver 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 If Olivia is a knight then Oliver is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Mia that If Olivia is a knight then Oliver is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Benjamin is a knight and Logan is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Benjamin is a knave or Penelope is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('lying', 3)), ('or', ('telling-truth', 1), ('telling-truth', 4)), ('or', ('telling-truth', 0), ('telling-truth', 5)), ('not', ('telling-truth', 1)), ('telling-truth', 3), ('->', ('telling-truth', 7), ('lying', 2)), ('or', ('lying', 3), ('telling-truth', 1)), ('and', ('telling-truth', 3), ('telling-truth', 4)))", "index": 6}
-{"quiz": "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, Henry, Evelyn, Liam, Lily, Jack, Joseph, and Daniel. Aurora said, \"Evelyn is a knight or Jack is a knave.\" Henry noted, \"Evelyn is a knight and Daniel is a knight\". Evelyn told you that Lily is not a knight. Liam told you that Aurora is not a knave. Lily asserted: \"Joseph is a knight\". Jack commented, \"Daniel is a knight if and only if Henry is a knight\". \"Lily is a knight if and only if Evelyn is a knave,\" Joseph claimed. Daniel asserted: \"If Joseph is a knave then Henry is a knight\". So who is a knight and who is a knave?", "names": ["Aurora", "Henry", "Evelyn", "Liam", "Lily", "Jack", "Joseph", "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, false, true, true], "solution_text": "Aurora is a knight, Henry is a knave, Evelyn is a knave, Liam is a knight, Lily is a knight, Jack is a knave, Joseph is a knight, and Daniel is a knight.", "solution_text_format": "(1) Aurora is a knight\n(2) Henry is a knave\n(3) Evelyn is a knave\n(4) Liam is a knight\n(5) Lily is a knight\n(6) Jack is a knave\n(7) Joseph 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 Aurora is a knight. No contradiction is found in their claim that Evelyn is a knight or Jack is a knave.", "Assume Evelyn 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 Evelyn that Lily is not a knight.", "Assume Lily 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 Lily that Joseph is a knight.", "Joseph cannot be a knave, because this would contradict the false claim of their own that Lily is a knight if and only if Evelyn is a knave.", "We have exhausted all possibilities for Joseph and Lily, so let us go back and reconsider Evelyn.", "Assume Evelyn 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 Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Lily is a knight if and only if Evelyn is a knave.", "Jack cannot be a knight, because this would contradict the claim of Aurora that Evelyn is a knight or Jack is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Daniel is a knight if and only if Henry is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that If Joseph is a knave then Henry is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Evelyn is a knight and Daniel is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Evelyn is a knight and Daniel is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Aurora is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('lying', 5)), ('and', ('telling-truth', 2), ('telling-truth', 7)), ('not', ('telling-truth', 4)), ('not', ('lying', 0)), ('telling-truth', 6), ('<=>', ('telling-truth', 7), ('telling-truth', 1)), ('<=>', ('telling-truth', 4), ('lying', 2)), ('->', ('lying', 6), ('telling-truth', 1)))", "index": 7}
-{"quiz": "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, Aurora, Emily, Aria, Amelia, Abigail, William, and Logan. Ethan expressed that William is a knave if and only if Abigail is a knave. \"Logan is a knave if and only if Aria is a knave,\" Aurora claimed. Emily was heard saying, \"William is a knight if and only if Logan is a knight\". Aria stated, \"Emily is not a knave\". Amelia stated, \"Aria is a knave and William is a knight\". Abigail noted, \"Amelia is a knight or Amelia is a knave\". In William's words: \"Aria is a knight and Aurora is a knight\". \"Amelia is a knight\" - Logan. So who is a knight and who is a knave?", "names": ["Ethan", "Aurora", "Emily", "Aria", "Amelia", "Abigail", "William", "Logan"], "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": "Ethan is a knave, Aurora is a knave, Emily is a knight, Aria is a knight, Amelia is a knave, Abigail is a knight, William is a knave, and Logan is a knave.", "solution_text_format": "(1) Ethan is a knave\n(2) Aurora is a knave\n(3) Emily is a knight\n(4) Aria is a knight\n(5) Amelia is a knave\n(6) Abigail is a knight\n(7) William 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 William is a knave if and only if Abigail is a knave.", "Assume William is a knight. No contradiction is found in their claim that Aria is a knight and Aurora is a knight.", "Assume Aria 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 William is a knight if and only if Logan is a knight.", "Assume Logan 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 Aria is a knave and William is a knight.", "Amelia cannot be a knave, because this would contradict the claim of Logan that Amelia is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the claim of Emily that William 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 Emily.", "Emily cannot be a knave, because this would contradict the claim of Aria that Emily is not a knave.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Aria.", "Aria cannot be a knave, because this would contradict the claim of William that Aria is a knight and Aurora is a knight.", "We have exhausted all possibilities for Aria, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Aria is a knight and Aurora is a knight.", "Assume Aria 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 William is a knight if and only if Logan is a knight.", "Logan cannot be a knight, because this would contradict the claim of Emily that William 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 Amelia is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Aria is a knave and William is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Aria is a knave and William is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Logan is a knave if and only if Aria is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Logan is a knave if and only if Aria is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Ethan that William is a knave if and only if Abigail is a knave.", "Abigail cannot be a knave, because this would contradict the false claim of their own that Amelia is a knight or Amelia is a knave.", "We have exhausted all possibilities for Abigail, Aurora, Amelia, and Logan, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the claim of Aria that Emily is not a knave.", "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 not a knave.", "Emily cannot be a knight, because this would contradict the false claim of Aria that Emily is not a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that William is a knight if and only if Logan is a knight.", "Assume Logan 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 Aria is a knave and William is a knight.", "Amelia cannot be a knave, because this would contradict the claim of Logan that Amelia is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the false claim of Emily that William is a knight if and only if Logan is a knight.", "We have exhausted all possibilities for Logan, Emily, Aria, and William, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that William is a knave if and only if Abigail is a knave.", "Assume William is a knight. No contradiction is found in their claim that Aria is a knight and Aurora is a knight.", "Assume Aria 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 William is a knight if and only if Logan is a knight.", "Assume Logan 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 Aria is a knave and William is a knight.", "Amelia cannot be a knave, because this would contradict the claim of Logan that Amelia is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the claim of Emily that William 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 Emily.", "Emily cannot be a knave, because this would contradict the claim of Aria that Emily is not a knave.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Aria.", "Aria cannot be a knave, because this would contradict the claim of William that Aria is a knight and Aurora is a knight.", "We have exhausted all possibilities for Aria, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Aria is a knight and Aurora is a knight.", "Assume Aria 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 William is a knight if and only if Logan is a knight.", "Logan cannot be a knight, because this would contradict the claim of Emily that William 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 Amelia is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Aria is a knave and William is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Aria is a knave and William is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Logan is a knave if and only if Aria is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Logan is a knave if and only if Aria is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Amelia is a knight or Amelia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 6), ('lying', 5)), ('<=>', ('lying', 7), ('lying', 3)), ('<=>', ('telling-truth', 6), ('telling-truth', 7)), ('not', ('lying', 2)), ('and', ('lying', 3), ('telling-truth', 6)), ('or', ('telling-truth', 4), ('lying', 4)), ('and', ('telling-truth', 3), ('telling-truth', 1)), ('telling-truth', 4))", "index": 8}
-{"quiz": "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, Zoey, Sophia, Avery, Mia, Logan, and William. \"Charlotte is a knight if and only if Avery is a knave\" - Jackson. \"Logan is a knave\" - Charlotte. Zoey noted, \"Sophia is a knave or Jackson is a knight\". As Sophia put it, \"Avery is a knight or William is a knight\". As Avery put it, \"Jackson is a knave and Zoey is a knight\". According to Mia, \"Logan is a knave and Jackson is a knave\". Logan asserted: \"Sophia is not a knight\". William said, \"Sophia is a knave if and only if Charlotte is a knave.\" So who is a knight and who is a knave?", "names": ["Jackson", "Charlotte", "Zoey", "Sophia", "Avery", "Mia", "Logan", "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, false, false, true], "solution_text": "Jackson is a knight, Charlotte is a knight, Zoey is a knight, Sophia is a knight, Avery is a knave, Mia is a knave, Logan is a knave, and William is a knight.", "solution_text_format": "(1) Jackson is a knight\n(2) Charlotte is a knight\n(3) Zoey is a knight\n(4) Sophia is a knight\n(5) Avery is a knave\n(6) Mia is a knave\n(7) Logan 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 Jackson is a knight. No contradiction is found in their claim that Charlotte is a knight if and only if Avery is a knave.", "Assume Charlotte 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 Charlotte that Logan is a knave.", "Assume Logan 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 Avery is a knight or William is a knight.", "Avery cannot be a knight, because this would contradict the claim of Jackson that Charlotte 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 Jackson is a knave and Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Sophia is a knave or Jackson is a knight.", "Assume William is a knight. No contradiction is found in their claim that Sophia is a knave if and only if Charlotte is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Logan is a knave and Jackson is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Logan is a knave and Jackson is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('lying', 4)), ('lying', 6), ('or', ('lying', 3), ('telling-truth', 0)), ('or', ('telling-truth', 4), ('telling-truth', 7)), ('and', ('lying', 0), ('telling-truth', 2)), ('and', ('lying', 6), ('lying', 0)), ('not', ('telling-truth', 3)), ('<=>', ('lying', 3), ('lying', 1)))", "index": 9}
-{"quiz": "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, Charlotte, Emily, Noah, Victoria, Benjamin, Lily, and Mia. \"If Victoria is a knave then Benjamin is a knave,\" Amelia claimed. Charlotte expressed that Amelia is a knave and Noah is a knight. As Emily put it, \"Benjamin is a knight if and only if Noah is a knave\". Noah said that Emily is not a knave. \"Amelia is a knight and Noah is a knight,\" Victoria claimed. Benjamin noted, \"Mia is a knight if and only if Amelia is a knight\". Lily told you that Charlotte is not a knight. Mia told you that Emily is a knave or Victoria is a knave. So who is a knight and who is a knave?", "names": ["Amelia", "Charlotte", "Emily", "Noah", "Victoria", "Benjamin", "Lily", "Mia"], "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, Charlotte is a knave, Emily is a knight, Noah is a knight, Victoria is a knight, Benjamin is a knave, Lily is a knight, and Mia is a knave.", "solution_text_format": "(1) Amelia is a knight\n(2) Charlotte is a knave\n(3) Emily is a knight\n(4) Noah is a knight\n(5) Victoria is a knight\n(6) Benjamin is a knave\n(7) Lily 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 Amelia is a knight. No contradiction is found in their claim that If Victoria is a knave then Benjamin is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Amelia is a knight and Noah is a knight.", "Assume Noah 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 Benjamin is a knight if and only if Noah is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Emily that Benjamin is a knight if and only if Noah is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Mia is a knight if and only if Amelia is a knight.", "Mia cannot be a knight, because this would contradict the false claim of Benjamin that Mia is a knight if and only if Amelia is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Emily is a knave or Victoria is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Amelia is a knave and Noah is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Amelia is a knave and Noah is a knight.", "Assume Lily 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": "(('->', ('lying', 4), ('lying', 5)), ('and', ('lying', 0), ('telling-truth', 3)), ('<=>', ('telling-truth', 5), ('lying', 3)), ('not', ('lying', 2)), ('and', ('telling-truth', 0), ('telling-truth', 3)), ('<=>', ('telling-truth', 7), ('telling-truth', 0)), ('not', ('telling-truth', 1)), ('or', ('lying', 2), ('lying', 4)))", "index": 10}
-{"quiz": "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, Chloe, Matthew, Aurora, Ethan, Aiden, Emily, and Lily. Zoey commented, \"Aiden is a knight and Zoey is a knight\". According to Chloe, \"If Matthew is a knight then Aiden is a knave\". Matthew told you that Chloe is a knight. As Aurora put it, \"If Matthew is a knight then Matthew is a knave\". Ethan said, \"Aurora is a knave.\" \"Matthew is a knave,\" Aiden mentioned. Emily asserted: \"Zoey is a knave\". Lily remarked, \"Aiden is a knave and Chloe is a knight\". So who is a knight and who is a knave?", "names": ["Zoey", "Chloe", "Matthew", "Aurora", "Ethan", "Aiden", "Emily", "Lily"], "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": "Zoey is a knave, Chloe is a knight, Matthew is a knight, Aurora is a knave, Ethan is a knight, Aiden is a knave, Emily is a knight, and Lily is a knight.", "solution_text_format": "(1) Zoey is a knave\n(2) Chloe is a knight\n(3) Matthew is a knight\n(4) Aurora is a knave\n(5) Ethan is a knight\n(6) Aiden is a knave\n(7) Emily 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 Zoey is a knight. No contradiction is found in their claim that Aiden is a knight and Zoey is a knight.", "Assume Aiden 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 Aiden that Matthew is a knave.", "Assume Matthew 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 Matthew that Chloe is a knight.", "Chloe cannot be a knave, because this would contradict the false claim of their own that If Matthew is a knight then Aiden is a knave.", "We have exhausted all possibilities for Chloe and Matthew, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the claim of Zoey that Aiden is a knight and Zoey is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Aiden is a knight and Zoey is a knight.", "Assume Aiden 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 Aiden that Matthew is a knave.", "Assume Matthew 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 Matthew that Chloe is a knight.", "Chloe cannot be a knave, because this would contradict the false claim of their own that If Matthew is a knight then Aiden is a knave.", "We have exhausted all possibilities for Chloe and Matthew, so let us go back and reconsider Aiden.", "Assume Aiden 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 Chloe is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that If Matthew is a knight then Aiden is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that If Matthew is a knight then Matthew is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that If Matthew is a knight then Matthew is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Aurora is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Zoey is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Aiden is a knave and Chloe is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('telling-truth', 0)), ('->', ('telling-truth', 2), ('lying', 5)), ('telling-truth', 1), ('->', ('telling-truth', 2), ('lying', 2)), ('lying', 3), ('lying', 2), ('lying', 0), ('and', ('lying', 5), ('telling-truth', 1)))", "index": 11}
-{"quiz": "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, Jacob, Benjamin, Mia, Chloe, Logan, Sofia, and Owen. Ethan was heard saying, \"Chloe is a knight and Logan is a knave\". Jacob said that Chloe is not a knight. Benjamin stated, \"Logan is a knight if and only if Benjamin is a knight\". In a statement by Mia: \"If Ethan is a knave then Logan is a knight\". Chloe asserted: \"Mia is a knight\". Logan was heard saying, \"If Ethan is a knave then Benjamin is a knight\". \"Chloe is not a knight,\" Sofia mentioned. In Owen's words: \"If Chloe is a knight then Mia is a knave\". So who is a knight and who is a knave?", "names": ["Ethan", "Jacob", "Benjamin", "Mia", "Chloe", "Logan", "Sofia", "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, false, false], "solution_text": "Ethan is a knave, Jacob is a knave, Benjamin is a knight, Mia is a knight, Chloe is a knight, Logan is a knight, Sofia is a knave, and Owen is a knave.", "solution_text_format": "(1) Ethan is a knave\n(2) Jacob is a knave\n(3) Benjamin is a knight\n(4) Mia is a knight\n(5) Chloe is a knight\n(6) Logan is a knight\n(7) Sofia 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 Ethan is a knight. No contradiction is found in their claim that Chloe is a knight and Logan is a knave.", "Assume Chloe 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 If Ethan is a knave then Logan is a knight.", "Logan cannot be a knight, because this would contradict the claim of Ethan that Chloe is a knight and Logan is a knave.", "Logan cannot be a knave, because this would contradict the false claim of their own that If Ethan is a knave then Benjamin is a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the false claim of their own that If Ethan is a knave then Logan is a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the claim of Ethan that Chloe is a knight and Logan is a knave.", "We have exhausted all possibilities for 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 knight and Logan is a knave.", "Assume Chloe 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 If Ethan is a knave then Logan is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that If Ethan is a knave then Benjamin is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Logan is a knight if and only if Benjamin is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Chloe is not a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Chloe is not a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that Chloe is not a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Chloe is not a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that If Chloe is a knight then Mia is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that If Chloe is a knight then Mia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 4), ('lying', 5)), ('not', ('telling-truth', 4)), ('<=>', ('telling-truth', 5), ('telling-truth', 2)), ('->', ('lying', 0), ('telling-truth', 5)), ('telling-truth', 3), ('->', ('lying', 0), ('telling-truth', 2)), ('not', ('telling-truth', 4)), ('->', ('telling-truth', 4), ('lying', 3)))", "index": 12}
-{"quiz": "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, Sofia, Harper, Owen, Jackson, Sebastian, Lucas, and Aurora. James commented, \"If Lucas is a knight then Jackson is a knight\". \"Owen is a knave and Harper is a knave,\" Sofia mentioned. Harper was heard saying, \"If James is a knave then Sebastian is a knight\". Owen remarked, \"If James is a knave then Lucas is a knight\". Jackson expressed that Sebastian is a knight and Owen is a knave. Sebastian said that Lucas is a knave or Lucas is a knight. According to Lucas, \"Sofia is a knave\". Aurora stated, \"Lucas is a knave or Sofia is a knave\". So who is a knight and who is a knave?", "names": ["James", "Sofia", "Harper", "Owen", "Jackson", "Sebastian", "Lucas", "Aurora"], "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": "James is a knave, Sofia is a knave, Harper is a knight, Owen is a knight, Jackson is a knave, Sebastian is a knight, Lucas is a knight, and Aurora is a knight.", "solution_text_format": "(1) James is a knave\n(2) Sofia is a knave\n(3) Harper is a knight\n(4) Owen is a knight\n(5) Jackson is a knave\n(6) Sebastian is a knight\n(7) Lucas 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 Lucas is a knight then Jackson is a knight.", "Assume Lucas 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 Lucas that Sofia is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Owen is a knave and Harper is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that If James is a knave then Lucas is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that If James is a knave then Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Lucas is a knave or Lucas is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight and Owen is a knave.", "Jackson cannot be a knave, because this would contradict the claim of James that If Lucas is a knight then Jackson 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 false claim of their own that Lucas is a knave or Lucas is a knight.", "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 false claim of their own that If James is a knave then Sebastian is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the false claim of their own that If James is a knave then Lucas is a knight.", "We have exhausted all possibilities for Owen 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 a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Owen is a knave and Harper is a knave.", "Owen cannot be a knight, because this would contradict the claim of Sofia that Owen is a knave and Harper is a knave.", "Owen cannot be a knave, because this would contradict the false claim of their own that If James is a knave then Lucas is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Sofia.", "Sofia cannot be a knave, because this would contradict the false claim of Lucas that Sofia is a knave.", "We have exhausted all possibilities for Sofia and Lucas, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that If Lucas is a knight then Jackson is a knight.", "Assume Lucas 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 Lucas that Sofia is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Owen is a knave and Harper is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that If James is a knave then Lucas is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that If James is a knave then Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Lucas is a knave or Lucas is a knight.", "Jackson cannot be a knight, because this would contradict the false claim of James that If Lucas is a knight then Jackson is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Sebastian is a knight and Owen is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Lucas is a knave or Sofia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 6), ('telling-truth', 4)), ('and', ('lying', 3), ('lying', 2)), ('->', ('lying', 0), ('telling-truth', 5)), ('->', ('lying', 0), ('telling-truth', 6)), ('and', ('telling-truth', 5), ('lying', 3)), ('or', ('lying', 6), ('telling-truth', 6)), ('lying', 1), ('or', ('lying', 6), ('lying', 1)))", "index": 13}
-{"quiz": "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, Sophia, Lily, Penelope, Oliver, Jackson, Sebastian, and Samuel. In a statement by Avery: \"If Penelope is a knight then Lily is a knight\". According to Sophia, \"Lily is a knight and Sophia is a knight\". Lily stated, \"Avery is a knight if and only if Samuel is a knave\". \"Sebastian is not a knight\" - Penelope. \"Lily is a knave,\" Oliver claimed. Jackson said that Sophia is a knave and Samuel is a knight. Sebastian remarked, \"Samuel is a knight and Oliver is a knave\". Samuel asserted: \"Lily is a knave if and only if Sebastian is a knight\". So who is a knight and who is a knave?", "names": ["Avery", "Sophia", "Lily", "Penelope", "Oliver", "Jackson", "Sebastian", "Samuel"], "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": "Avery is a knave, Sophia is a knave, Lily is a knave, Penelope is a knight, Oliver is a knight, Jackson is a knave, Sebastian is a knave, and Samuel is a knave.", "solution_text_format": "(1) Avery is a knave\n(2) Sophia is a knave\n(3) Lily is a knave\n(4) Penelope is a knight\n(5) Oliver is a knight\n(6) Jackson is a knave\n(7) Sebastian 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 Avery is a knight. No contradiction is found in their claim that If Penelope is a knight then Lily is a knight.", "Assume Penelope 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 Penelope that Sebastian is not a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Samuel is a knight and Oliver is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Lily is a knave if and only if Sebastian is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Avery is a knight if and only if Samuel is a knave.", "Lily cannot be a knave, because this would contradict the claim of Avery that If Penelope is a knight then 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 knave if and only if Sebastian is a knight.", "Lily cannot be a knight, because this would contradict the false claim of Samuel that Lily is a knave if and only if Sebastian is a knight.", "Lily cannot be a knave, because this would contradict the claim of Avery that If Penelope is a knight then Lily is a knight.", "We have exhausted all possibilities for Lily, Samuel, 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 not a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Samuel is a knight and Oliver is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Lily is a knave if and only if Sebastian is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Avery is a knight if and only if Samuel is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Avery is a knight if and only if Samuel is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Sebastian that Samuel is a knight and Oliver is a knave.", "Oliver cannot be a knave, because this would contradict the false claim of their own that Lily is a knave.", "We have exhausted all possibilities for Oliver and Lily, so let us go back and reconsider Samuel.", "Samuel cannot be a knave, because this would contradict the claim of Sebastian that Samuel is a knight and Oliver is a knave.", "We have exhausted all possibilities for Samuel, 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 not a knight.", "We have exhausted all possibilities for Sebastian and Penelope, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that If Penelope is a knight then Lily is a knight.", "Assume Penelope 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 Penelope that Sebastian is not a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Samuel is a knight and Oliver is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Lily is a knave if and only if Sebastian is a knight.", "Lily cannot be a knight, because this would contradict the false claim of Avery that If Penelope is a knight then Lily is a knight.", "Lily cannot be a knave, because this would contradict the false claim of their own that Avery is a knight if and only if Samuel is a knave.", "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 knave if and only if Sebastian is a knight.", "Lily cannot be a knight, because this would contradict the false claim of Avery that If Penelope is a knight then Lily is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Avery is a knight if and only if Samuel is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Lily is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that Lily is a knight and Sophia is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Lily is a knight and Sophia is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Sophia is a knave and Samuel is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Sophia is a knave and Samuel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('telling-truth', 2)), ('and', ('telling-truth', 2), ('telling-truth', 1)), ('<=>', ('telling-truth', 0), ('lying', 7)), ('not', ('telling-truth', 6)), ('lying', 2), ('and', ('lying', 1), ('telling-truth', 7)), ('and', ('telling-truth', 7), ('lying', 4)), ('<=>', ('lying', 2), ('telling-truth', 6)))", "index": 14}
-{"quiz": "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, Scarlett, Emma, Penelope, David, Aurora, Amelia, and Alexander. \"Alexander is not a knight\" - Logan. Scarlett noted, \"Emma is a knave if and only if Penelope is a knight\". Emma stated, \"Scarlett is a knight\". In Penelope's words: \"Scarlett is not a knight\". According to David, \"If Emma is a knave then Logan is a knight\". According to Aurora, \"Amelia is a knight and Logan is a knave\". \"Scarlett is a knave if and only if David is a knave,\" Amelia declared. Alexander expressed that If Scarlett is a knave then David is a knave. So who is a knight and who is a knave?", "names": ["Logan", "Scarlett", "Emma", "Penelope", "David", "Aurora", "Amelia", "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, true, true], "solution_text": "Logan is a knave, Scarlett is a knight, Emma is a knight, Penelope is a knave, David is a knight, Aurora is a knight, Amelia is a knight, and Alexander is a knight.", "solution_text_format": "(1) Logan is a knave\n(2) Scarlett is a knight\n(3) Emma is a knight\n(4) Penelope is a knave\n(5) David is a knight\n(6) Aurora is a knight\n(7) Amelia 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 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 Logan that Alexander is not a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that If Scarlett is a knave then David is a knave.", "Scarlett cannot be a knight, because this would contradict the false claim of Alexander that If Scarlett is a knave then David is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Emma is a knave if and only if Penelope is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Scarlett is a knight.", "Penelope cannot be a knight, because this would contradict the false claim of Scarlett that Emma is a knave if and only if Penelope is a knight.", "Penelope 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 Penelope, Emma, Scarlett, and Alexander, so let us go back and reconsider Logan.", "Assume Logan 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 Scarlett is a knave then David is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Emma is a knave if and only if Penelope is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Scarlett is a knight.", "Penelope cannot be a knight, because this would contradict the claim of Scarlett that Emma 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 Scarlett is not a knight.", "Assume David is a knight. No contradiction is found in their claim that If Emma is a knave then Logan is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Amelia is a knight and Logan is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Scarlett is a knave if and only if David is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 7)), ('<=>', ('lying', 2), ('telling-truth', 3)), ('telling-truth', 1), ('not', ('telling-truth', 1)), ('->', ('lying', 2), ('telling-truth', 0)), ('and', ('telling-truth', 6), ('lying', 0)), ('<=>', ('lying', 1), ('lying', 4)), ('->', ('lying', 1), ('lying', 4)))", "index": 15}
-{"quiz": "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, Lily, Grace, Liam, Ella, Penelope, and David. In Luke's words: \"Jacob is a knight or Lily is a knight\". \"Ella is a knave if and only if Luke is a knight\" - Jacob. Lily remarked, \"Liam is a knight if and only if David is a knight\". Grace said, \"Jacob is a knight if and only if Jacob is a knave.\" \"If Luke is a knave then David is a knave,\" Liam declared. Ella asserted: \"Luke is a knave if and only if Lily is a knave\". In a statement by Penelope: \"Jacob is a knight and Liam is a knave\". According to David, \"Jacob is a knave or Grace is a knave\". So who is a knight and who is a knave?", "names": ["Luke", "Jacob", "Lily", "Grace", "Liam", "Ella", "Penelope", "David"], "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": "Luke is a knight, Jacob is a knave, Lily is a knight, Grace is a knave, Liam is a knight, Ella is a knight, Penelope is a knave, and David is a knight.", "solution_text_format": "(1) Luke is a knight\n(2) Jacob is a knave\n(3) Lily is a knight\n(4) Grace is a knave\n(5) Liam is a knight\n(6) Ella is a knight\n(7) Penelope 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 Jacob is a knight or Lily is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Ella is a knave if and only if Luke is a knight.", "Ella cannot be a knight, because this would contradict the claim of Jacob that Ella is a knave if and only if Luke is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Luke is a knave if and only if Lily is a knave.", "Lily cannot be a knight, because this would contradict the false claim of Ella that Luke 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 Liam is a knight if and only if David is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that If Luke is a knave then David is a knave.", "David cannot be a knight, because this would contradict the false claim of Lily that Liam 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 Jacob is a knave or Grace is a knave.", "Grace 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.", "Grace cannot be a knave, because this would contradict the false claim of David that Jacob is a knave or Grace is a knave.", "We have exhausted all possibilities for Grace and David, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the false claim of their own that If Luke is a knave then David is a knave.", "We have exhausted all possibilities for Liam, Lily, and Ella, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Ella is a knave if and only if Luke is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Luke is a knave if and only if Lily is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Liam is a knight if and only if David is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that If Luke is a knave then David is a knave.", "Assume David is a knight. No contradiction is found in their claim that Jacob is a knave or Grace is a knave.", "Grace 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 Grace is a knave. No contradiction is found in their false claim that Jacob is a knight if and only if Jacob is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Jacob is a knight and Liam is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Jacob is a knight and Liam is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('telling-truth', 2)), ('<=>', ('lying', 5), ('telling-truth', 0)), ('<=>', ('telling-truth', 4), ('telling-truth', 7)), ('<=>', ('telling-truth', 1), ('lying', 1)), ('->', ('lying', 0), ('lying', 7)), ('<=>', ('lying', 0), ('lying', 2)), ('and', ('telling-truth', 1), ('lying', 4)), ('or', ('lying', 1), ('lying', 3)))", "index": 16}
-{"quiz": "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, Michael, Aurora, Benjamin, Oliver, James, and Elizabeth. Luke told you that If Aurora is a knight then Aurora is a knave. As Sebastian put it, \"James is a knight and Elizabeth is a knave\". \"Sebastian is not a knight,\" Michael declared. As Aurora put it, \"Oliver is not a knight\". Benjamin remarked, \"Michael is a knight and Sebastian is a knave\". \"Elizabeth is not a knight,\" Oliver declared. In James's words: \"Elizabeth is a knight if and only if Sebastian is a knave\". As Elizabeth put it, \"If Benjamin is a knave then Aurora is a knave\". So who is a knight and who is a knave?", "names": ["Luke", "Sebastian", "Michael", "Aurora", "Benjamin", "Oliver", "James", "Elizabeth"], "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": "Luke is a knave, Sebastian is a knave, Michael is a knight, Aurora is a knight, Benjamin is a knight, Oliver is a knave, James is a knight, and Elizabeth is a knight.", "solution_text_format": "(1) Luke is a knave\n(2) Sebastian is a knave\n(3) Michael is a knight\n(4) Aurora is a knight\n(5) Benjamin is a knight\n(6) Oliver is a knave\n(7) James 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 Luke is a knight. No contradiction is found in their claim that If Aurora is a knight then Aurora is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Luke that If Aurora is a knight then Aurora is a knave.", "Assume Aurora 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 Elizabeth is not a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Oliver 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 Aurora is a knave.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the false claim of Aurora that Oliver is not a knight.", "We have exhausted all possibilities for Oliver and Aurora, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that If Aurora is a knight then Aurora is a knave.", "Assume Aurora 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 Aurora that Oliver is not a knight.", "Assume Oliver 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 Aurora is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Michael is a knight and Sebastian is a knave.", "Assume Michael 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 their own that James is a knight and Elizabeth is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that James is a knight and Elizabeth is a knave.", "Assume James is a knight. No contradiction is found in their claim that Elizabeth is a knight if and only if Sebastian is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('lying', 3)), ('and', ('telling-truth', 6), ('lying', 7)), ('not', ('telling-truth', 1)), ('not', ('telling-truth', 5)), ('and', ('telling-truth', 2), ('lying', 1)), ('not', ('telling-truth', 7)), ('<=>', ('telling-truth', 7), ('lying', 1)), ('->', ('lying', 4), ('lying', 3)))", "index": 17}
-{"quiz": "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, James, Jackson, Isabella, Charlotte, Joseph, David, and Liam. Harper remarked, \"David is a knave or Charlotte is a knave\". James remarked, \"Isabella is a knight if and only if Liam is a knight\". Jackson stated, \"Isabella is not a knave\". Isabella asserted: \"James is a knight if and only if Charlotte is a knave\". In Charlotte's words: \"Jackson is a knight if and only if Harper is a knave\". In Joseph's words: \"If Isabella is a knight then Liam is a knave\". David remarked, \"Isabella is a knave if and only if James is a knight\". Liam expressed that James is a knave and David is a knave. So who is a knight and who is a knave?", "names": ["Harper", "James", "Jackson", "Isabella", "Charlotte", "Joseph", "David", "Liam"], "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": "Harper is a knave, James is a knave, Jackson is a knight, Isabella is a knight, Charlotte is a knight, Joseph is a knight, David is a knight, and Liam is a knave.", "solution_text_format": "(1) Harper is a knave\n(2) James is a knave\n(3) Jackson is a knight\n(4) Isabella is a knight\n(5) Charlotte is a knight\n(6) Joseph is a knight\n(7) David 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 Harper is a knight. No contradiction is found in their claim that David is a knave or Charlotte is a knave.", "Assume David 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 James is a knight if and only if Charlotte is a knave.", "James cannot be a knight, because this would contradict the claim of David 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 Isabella is a knight if and only if Liam is a knight.", "Liam cannot be a knight, because this would contradict the false claim of James that Isabella 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 James is a knave and David is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Harper that David is a knave or Charlotte is a knave.", "Charlotte cannot be a knave, because this would contradict the claim of Isabella that James is a knight if and only if Charlotte is a knave.", "We have exhausted all possibilities for Charlotte, Liam, and James, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that James is a knight if and only if Charlotte is a knave.", "Assume James is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Liam is a knight.", "Liam cannot be a knight, because this would contradict the claim of James that Isabella 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 James is a knave and David is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Harper that David is a knave or Charlotte is a knave.", "Charlotte cannot be a knave, because this would contradict the false claim of Isabella that James is a knight if and only if Charlotte is a knave.", "We have exhausted all possibilities for Charlotte and Liam, so let us go back and reconsider James.", "James cannot be a knave, because this would contradict the claim of David 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 David.", "Assume David 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 James is a knight if and only if Charlotte is a knave.", "Assume James is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Liam is a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that James is a knave and David is a knave.", "Liam cannot be a knave, because this would contradict the claim of James that Isabella is a knight if and only if Liam is a knight.", "We have exhausted all possibilities for Liam, so let us go back and reconsider James.", "James cannot be a knave, because this would contradict the false claim of David that Isabella is a knave if and only if James is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that James is a knight if and only if Charlotte is a knave.", "James cannot be a knight, because this would contradict the false claim of David 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 Isabella is a knight if and only if Liam is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that James is a knave and David is a knave.", "Charlotte cannot be a knight, because this would contradict the false claim of Isabella that James 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 Jackson is a knight if and only if Harper is a knave.", "Jackson cannot be a knight, because this would contradict the claim of their own that Isabella is not a knave.", "Jackson cannot be a knave, because this would contradict the false claim of Charlotte that Jackson is a knight if and only if Harper is a knave.", "We have exhausted all possibilities for Jackson and Charlotte, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the false claim of James that Isabella is a knight if and only if Liam is a knight.", "We have exhausted all possibilities for Liam, James, Isabella, and David, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that David is a knave or Charlotte is a knave.", "Assume David 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 James is a knight if and only if Charlotte is a knave.", "James cannot be a knight, because this would contradict the claim of David 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 Isabella is a knight if and only if Liam is a knight.", "Liam cannot be a knight, because this would contradict the false claim of James that Isabella 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 James is a knave and David is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Harper is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Isabella is not a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that If Isabella is a knight then Liam is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 6), ('lying', 4)), ('<=>', ('telling-truth', 3), ('telling-truth', 7)), ('not', ('lying', 3)), ('<=>', ('telling-truth', 1), ('lying', 4)), ('<=>', ('telling-truth', 2), ('lying', 0)), ('->', ('telling-truth', 3), ('lying', 7)), ('<=>', ('lying', 3), ('telling-truth', 1)), ('and', ('lying', 1), ('lying', 6)))", "index": 18}
-{"quiz": "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, Penelope, Amelia, James, Scarlett, Lily, and Luke. Avery commented, \"James is a knight\". In Riley's words: \"Lily is a knave and Lily is a knight\". Penelope said, \"Riley is a knave or Lily is a knight.\" Amelia commented, \"Penelope is a knave and Riley is a knave\". James told you that If Penelope is a knave then Amelia is a knight. As Scarlett put it, \"Luke is a knave or Lily is a knight\". According to Lily, \"Penelope is a knave if and only if Avery is a knave\". In a statement by Luke: \"Lily is a knave if and only if Avery is a knight\". So who is a knight and who is a knave?", "names": ["Avery", "Riley", "Penelope", "Amelia", "James", "Scarlett", "Lily", "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, true, true, false], "solution_text": "Avery is a knight, Riley is a knave, Penelope is a knight, Amelia is a knave, James is a knight, Scarlett is a knight, Lily is a knight, and Luke is a knave.", "solution_text_format": "(1) Avery is a knight\n(2) Riley is a knave\n(3) Penelope is a knight\n(4) Amelia is a knave\n(5) James is a knight\n(6) Scarlett is a knight\n(7) Lily 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 Avery 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 Penelope is a knave then Amelia is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Riley is a knave or Lily is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Lily is a knave and Lily is a knight.", "Assume Riley 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 Penelope is a knave if and only if Avery is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Penelope is a knave and Riley is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Penelope is a knave and Riley is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Luke is a knave or Lily is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Lily is a knave if and only if Avery is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Lily is a knave if and only if Avery is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('and', ('lying', 6), ('telling-truth', 6)), ('or', ('lying', 1), ('telling-truth', 6)), ('and', ('lying', 2), ('lying', 1)), ('->', ('lying', 2), ('telling-truth', 3)), ('or', ('lying', 7), ('telling-truth', 6)), ('<=>', ('lying', 2), ('lying', 0)), ('<=>', ('lying', 6), ('telling-truth', 0)))", "index": 19}
-{"quiz": "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, Aurora, Luke, Abigail, Henry, Daniel, Charlotte, and Joseph. Owen said that Joseph is a knight or Joseph is a knave. Aurora was heard saying, \"Luke is a knight\". Luke said, \"Owen is a knave.\" Abigail commented, \"Joseph is a knave or Henry is a knave\". Henry said that Abigail is a knave if and only if Aurora is a knave. \"Owen is a knave if and only if Charlotte is a knave,\" Daniel declared. In Charlotte's words: \"Owen is not a knight\". In Joseph's words: \"Aurora is a knave if and only if Aurora is a knight\". So who is a knight and who is a knave?", "names": ["Owen", "Aurora", "Luke", "Abigail", "Henry", "Daniel", "Charlotte", "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, false, false, false], "solution_text": "Owen is a knight, Aurora is a knave, Luke is a knave, Abigail is a knight, Henry is a knave, Daniel is a knave, Charlotte is a knave, and Joseph is a knave.", "solution_text_format": "(1) Owen is a knight\n(2) Aurora is a knave\n(3) Luke is a knave\n(4) Abigail is a knight\n(5) Henry is a knave\n(6) Daniel is a knave\n(7) Charlotte 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 Owen is a knight. No contradiction is found in their claim that Joseph is a knight or Joseph is a knave.", "Joseph 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 Joseph 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 Luke is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Owen is a knave.", "Luke cannot be a knave, because this would contradict the claim of Aurora that Luke is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Aurora.", "Assume Aurora 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 Aurora that Luke is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Owen is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Joseph is a knave or Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of their own that Abigail is a knave if and only if Aurora is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Abigail is a knave if and only if Aurora is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Owen is a knave if and only if Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Owen is not a knight.", "Charlotte cannot be a knave, because this would contradict the claim of Daniel that Owen is a knave if and only if Charlotte is a knave.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Owen is a knave if and only if Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the false claim of Daniel that Owen is a knave if and only if Charlotte is a knave.", "Assume Charlotte 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": "(('or', ('telling-truth', 7), ('lying', 7)), ('telling-truth', 2), ('lying', 0), ('or', ('lying', 7), ('lying', 4)), ('<=>', ('lying', 3), ('lying', 1)), ('<=>', ('lying', 0), ('lying', 6)), ('not', ('telling-truth', 0)), ('<=>', ('lying', 1), ('telling-truth', 1)))", "index": 20}
-{"quiz": "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, Jackson, Liam, Daniel, Noah, Emily, Avery, and Mason. In Oliver's words: \"Liam is a knave or Emily is a knight\". \"If Liam is a knave then Emily is a knave,\" Jackson mentioned. \"Daniel is not a knave,\" Liam mentioned. Daniel said, \"Jackson is not a knave.\" Noah said that Mason is a knave if and only if Avery is a knave. According to Emily, \"Liam is a knave if and only if Oliver is a knight\". Avery stated, \"Mason is a knave\". Mason noted, \"If Noah is a knave then Liam is a knave\". So who is a knight and who is a knave?", "names": ["Oliver", "Jackson", "Liam", "Daniel", "Noah", "Emily", "Avery", "Mason"], "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": "Oliver is a knight, Jackson is a knave, Liam is a knave, Daniel is a knave, Noah is a knave, Emily is a knight, Avery is a knave, and Mason is a knight.", "solution_text_format": "(1) Oliver is a knight\n(2) Jackson is a knave\n(3) Liam is a knave\n(4) Daniel is a knave\n(5) Noah is a knave\n(6) Emily is a knight\n(7) Avery 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 Oliver is a knight. No contradiction is found in their claim that Liam is a knave or Emily is a knight.", "Assume Liam 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 Jackson is not a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that If Liam is a knave then Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Liam is a knave if and only if Oliver is a knight.", "Emily cannot be a knave, because this would contradict the claim of Oliver that Liam is a knave or Emily is a knight.", "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 false claim of their own that If Liam is a knave then Emily is a knave.", "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 claim of Liam that Daniel is not a knave.", "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 not a knave.", "Daniel cannot be a knight, because this would contradict the false claim of Liam that Daniel is not a knave.", "Assume Daniel 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 Daniel that Jackson is not a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that If Liam is a knave then Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Liam is a knave if and only if Oliver is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Mason is a knave if and only if Avery is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Noah is a knave then Liam is a knave.", "Avery cannot be a knight, because this would contradict the claim of their own that Mason is a knave.", "Avery cannot be a knave, because this would contradict the claim of Noah that Mason is a knave if and only if Avery is a knave.", "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 false claim of their own that If Noah is a knave then Liam is a knave.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Mason is a knave if and only if Avery is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Noah is a knave then Liam is a knave.", "Avery cannot be a knight, because this would contradict the false claim of Noah that Mason 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 Mason is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('telling-truth', 5)), ('->', ('lying', 2), ('lying', 5)), ('not', ('lying', 3)), ('not', ('lying', 1)), ('<=>', ('lying', 7), ('lying', 6)), ('<=>', ('lying', 2), ('telling-truth', 0)), ('lying', 7), ('->', ('lying', 4), ('lying', 2)))", "index": 21}
-{"quiz": "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, Emily, Charlotte, Abigail, Penelope, and David. Amelia was heard saying, \"Luke is not a knight\". Luke expressed that Abigail is a knight and Ethan is a knight. Ethan noted, \"If Luke is a knave then Luke is a knight\". Emily expressed that Charlotte is a knave or Abigail is a knight. In a statement by Charlotte: \"Penelope is a knight if and only if Luke is a knave\". \"Amelia is a knight and Ethan is a knave\" - Abigail. Penelope said that Ethan is not a knave. David remarked, \"Ethan is a knave or Amelia is a knight\". So who is a knight and who is a knave?", "names": ["Amelia", "Luke", "Ethan", "Emily", "Charlotte", "Abigail", "Penelope", "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": "Amelia is a knight, Luke is a knave, Ethan is a knave, Emily is a knight, Charlotte is a knave, Abigail is a knight, Penelope is a knave, and David 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) Emily is a knight\n(5) Charlotte is a knave\n(6) Abigail is a knight\n(7) Penelope 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 Amelia 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 Amelia that Luke is not a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Abigail is a knight and Ethan is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Amelia is a knight and Ethan is a knave.", "Ethan cannot be a knight, because this would contradict the false claim of Luke that Abigail is a knight and Ethan is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that If Luke is a knave then Luke is a knight.", "Assume Emily 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 Penelope is a knight if and only if Luke is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Ethan is not a knave.", "Penelope cannot be a knave, because this would contradict the claim of Charlotte that Penelope is a knight if and only if Luke is a knave.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Penelope is a knight if and only if Luke is a knave.", "Penelope cannot be a knight, because this would contradict the false claim of Charlotte that Penelope is a knight if and only if Luke is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Ethan is not a knave.", "Assume David is a knight. No contradiction is found in their claim that Ethan is a knave or Amelia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 1)), ('and', ('telling-truth', 5), ('telling-truth', 2)), ('->', ('lying', 1), ('telling-truth', 1)), ('or', ('lying', 4), ('telling-truth', 5)), ('<=>', ('telling-truth', 6), ('lying', 1)), ('and', ('telling-truth', 0), ('lying', 2)), ('not', ('lying', 2)), ('or', ('lying', 2), ('telling-truth', 0)))", "index": 22}
-{"quiz": "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, Liam, William, Abigail, Jack, David, Olivia, and Amelia. Ava told you that Liam is not a knight. Liam remarked, \"If Ava is a knight then William is a knight\". In a statement by William: \"Amelia is a knight and Olivia is a knave\". Abigail said, \"Liam is a knave or David is a knave.\" In a statement by Jack: \"David is a knight and Ava is a knave\". David said that Liam is a knave or Olivia is a knave. Olivia said that Jack is a knave if and only if David is a knave. Amelia noted, \"If William is a knight then Abigail is a knight\". So who is a knight and who is a knave?", "names": ["Ava", "Liam", "William", "Abigail", "Jack", "David", "Olivia", "Amelia"], "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": "Ava is a knave, Liam is a knight, William is a knave, Abigail is a knight, Jack is a knave, David is a knave, Olivia is a knight, and Amelia is a knight.", "solution_text_format": "(1) Ava is a knave\n(2) Liam is a knight\n(3) William is a knave\n(4) Abigail is a knight\n(5) Jack is a knave\n(6) David is a knave\n(7) Olivia 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 Ava 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 Ava that Liam is not a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that If Ava is a knight then William is a knight.", "William cannot be a knight, because this would contradict the false claim of Liam that If Ava is a knight then William is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Amelia is a knight and Olivia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that If William is a knight then Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Liam is a knave or David is a knave.", "Assume David is a knight. No contradiction is found in their claim that Liam is a knave or Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Jack is a knave if and only if David is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that David is a knight and Ava is a knave.", "Jack cannot be a knave, because this would contradict the claim of Olivia that Jack is a knave if and only if David is a knave.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the false claim of William that Amelia is a knight and Olivia is a knave.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the false claim of their own that Liam is a knave or Olivia is a knave.", "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 false claim of their own that Liam is a knave or David is a knave.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Amelia.", "Amelia cannot be a knave, because this would contradict the false claim of their own that If William is a knight then Abigail is a knight.", "We have exhausted all possibilities for Amelia, William, and Liam, so let us go back and reconsider Ava.", "Assume Ava 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 If Ava is a knight then William is a knight.", "Assume William 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 If William is a knight then Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Liam is a knave or David is a knave.", "David cannot be a knight, because this would contradict the claim of Abigail that Liam is a knave or David is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Liam is a knave or Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of William that Amelia is a knight and Olivia is a knave.", "Olivia cannot be a knave, because this would contradict the false claim of David that Liam is a knave or Olivia is a knave.", "We have exhausted all possibilities for Olivia and David, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the claim of Amelia 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 Amelia.", "Amelia cannot be a knave, because this would contradict the claim of William that Amelia is a knight and Olivia is a knave.", "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 Amelia is a knight and Olivia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that If William is a knight then Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Liam is a knave or David is a knave.", "David cannot be a knight, because this would contradict the claim of Abigail that Liam is a knave or David is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Liam is a knave or Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Jack is a knave if and only if David is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that David is a knight and Ava is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that David is a knight and Ava is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 1)), ('->', ('telling-truth', 0), ('telling-truth', 2)), ('and', ('telling-truth', 7), ('lying', 6)), ('or', ('lying', 1), ('lying', 5)), ('and', ('telling-truth', 5), ('lying', 0)), ('or', ('lying', 1), ('lying', 6)), ('<=>', ('lying', 4), ('lying', 5)), ('->', ('telling-truth', 2), ('telling-truth', 3)))", "index": 23}
-{"quiz": "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, Ava, James, Sebastian, Emma, Logan, and Elizabeth. Amelia said, \"Emma is a knave and Sebastian is a knave.\" Scarlett said that Sebastian is a knave or Amelia is a knight. Ava noted, \"Emma is not a knave\". According to James, \"Sebastian is a knight or Logan is a knight\". \"Emma is a knave and Logan is a knave,\" Sebastian claimed. According to Emma, \"Ava is a knight or Amelia is a knave\". Logan remarked, \"Ava is a knave and Ava is a knight\". \"Logan is a knave or Scarlett is a knight\" - Elizabeth. So who is a knight and who is a knave?", "names": ["Amelia", "Scarlett", "Ava", "James", "Sebastian", "Emma", "Logan", "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, true, false, true], "solution_text": "Amelia is a knave, Scarlett is a knight, Ava is a knight, James is a knave, Sebastian is a knave, Emma is a knight, Logan is a knave, and Elizabeth is a knight.", "solution_text_format": "(1) Amelia is a knave\n(2) Scarlett is a knight\n(3) Ava is a knight\n(4) James is a knave\n(5) Sebastian is a knave\n(6) Emma is a knight\n(7) Logan 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 Amelia is a knight. No contradiction is found in their claim that Emma is a knave and Sebastian is a knave.", "Emma cannot be a knight, because this would contradict the claim of Amelia that Emma is a knave and Sebastian is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Ava is a knight or Amelia is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Emma is not a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Emma is not a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Amelia that Emma is a knave and Sebastian is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Emma is a knave and Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of their own that Ava is a knave and Ava is a knight.", "Logan cannot be a knave, because this would contradict the false claim of Sebastian that Emma is a knave and Logan is a knave.", "We have exhausted all possibilities for Logan, Sebastian, Ava, and Emma, 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 knave and Sebastian is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Ava is a knight or Amelia is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Emma is not a knave.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Emma is a knave and Logan is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Emma is a knave and Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of their own that Ava is a knave and Ava is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Ava is a knave and Ava is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Sebastian is a knave or Amelia is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight or Logan is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Sebastian is a knight or Logan is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Logan is a knave or Scarlett is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 5), ('lying', 4)), ('or', ('lying', 4), ('telling-truth', 0)), ('not', ('lying', 5)), ('or', ('telling-truth', 4), ('telling-truth', 6)), ('and', ('lying', 5), ('lying', 6)), ('or', ('telling-truth', 2), ('lying', 0)), ('and', ('lying', 2), ('telling-truth', 2)), ('or', ('lying', 6), ('telling-truth', 1)))", "index": 24}
-{"quiz": "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, Alexander, Owen, Mason, Logan, Jackson, and Emma. Elizabeth remarked, \"If Alexander is a knight then Emma is a knave\". As Evelyn put it, \"Emma is a knave and Logan is a knight\". \"Jackson is a knight or Evelyn is a knave,\" Alexander claimed. In Owen's words: \"Alexander is a knave or Logan is a knave\". In a statement by Mason: \"Jackson is a knave\". Logan said, \"Emma is a knave and Owen is a knave.\" \"If Logan is a knave then Owen is a knight,\" Jackson claimed. \"Owen is a knight or Owen is a knave,\" Emma declared. So who is a knight and who is a knave?", "names": ["Elizabeth", "Evelyn", "Alexander", "Owen", "Mason", "Logan", "Jackson", "Emma"], "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": "Elizabeth is a knave, Evelyn is a knave, Alexander is a knight, Owen is a knight, Mason is a knave, Logan is a knave, Jackson is a knight, and Emma is a knight.", "solution_text_format": "(1) Elizabeth is a knave\n(2) Evelyn is a knave\n(3) Alexander is a knight\n(4) Owen is a knight\n(5) Mason is a knave\n(6) Logan is a knave\n(7) Jackson 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 Elizabeth is a knight. No contradiction is found in their claim that If Alexander is a knight then Emma is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Jackson is a knight or Evelyn is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that If Logan is a knave then Owen is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Emma is a knave and Owen is a knave.", "Emma cannot be a knight, because this would contradict the claim of Elizabeth that If Alexander is a knight then Emma is a knave.", "Emma cannot be a knave, because this would contradict the false claim of their own that Owen is a knight or Owen is a knave.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Emma is a knave and Owen is a knave.", "Emma cannot be a knight, because this would contradict the claim of Elizabeth that If Alexander is a knight then Emma is a knave.", "Emma cannot be a knave, because this would contradict the false claim of their own that Owen is a knight or Owen is a knave.", "We have exhausted all possibilities for Emma and Logan, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that If Logan is a knave then Owen is a knight.", "Logan cannot be a knight, because this would contradict the false claim of Jackson that If Logan is a knave then Owen is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Emma is a knave and Owen is a knave.", "Emma cannot be a knight, because this would contradict the claim of Elizabeth that If Alexander is a knight then Emma is a knave.", "Emma cannot be a knave, because this would contradict the false claim of their own that Owen is a knight or Owen is a knave.", "We have exhausted all possibilities for Emma, Logan, and Jackson, 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 knight or Evelyn is a knave.", "Jackson cannot be a knight, because this would contradict the false claim of Alexander that Jackson is a knight or Evelyn is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that If Logan is a knave then Owen is a knight.", "Logan cannot be a knight, because this would contradict the false claim of Jackson that If Logan is a knave then Owen is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Emma is a knave and Owen is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Owen is a knight or Owen is a knave.", "Owen cannot be a knight, because this would contradict the false claim of Jackson that If Logan is a knave then Owen is a knight.", "Owen cannot be a knave, because this would contradict the false claim of their own that Alexander is a knave or Logan is a knave.", "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 false claim of their own that Owen is a knight or Owen is a knave.", "We have exhausted all possibilities for Emma, Logan, Jackson, and Alexander, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that If Alexander is a knight then Emma is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Jackson is a knight or Evelyn is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that If Logan is a knave then Owen is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Emma is a knave and Owen is a knave.", "Emma cannot be a knight, because this would contradict the claim of Logan that Emma is a knave and Owen is a knave.", "Emma cannot be a knave, because this would contradict the false claim of Elizabeth that If Alexander is a knight then Emma is a knave.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Emma is a knave and Owen is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Owen is a knight or Owen is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Alexander is a knave or Logan is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Emma is a knave and Logan is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Emma is a knave and Logan is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Jackson is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Jackson is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('lying', 7)), ('and', ('lying', 7), ('telling-truth', 5)), ('or', ('telling-truth', 6), ('lying', 1)), ('or', ('lying', 2), ('lying', 5)), ('lying', 6), ('and', ('lying', 7), ('lying', 3)), ('->', ('lying', 5), ('telling-truth', 3)), ('or', ('telling-truth', 3), ('lying', 3)))", "index": 25}
-{"quiz": "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, Emily, Liam, Abigail, Mason, Chloe, Emma, and Jackson. Logan asserted: \"Chloe is not a knight\". \"If Chloe is a knave then Emily is a knight\" - Emily. Liam said, \"If Emma is a knave then Logan is a knave.\" According to Abigail, \"Jackson is a knave and Mason is a knight\". Mason was heard saying, \"Emily is not a knight\". \"Abigail is a knave,\" Chloe mentioned. Emma was heard saying, \"If Chloe is a knave then Emily is a knave\". Jackson said, \"Chloe is a knight or Emma is a knight.\" So who is a knight and who is a knave?", "names": ["Logan", "Emily", "Liam", "Abigail", "Mason", "Chloe", "Emma", "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": "Logan is a knave, Emily is a knight, Liam is a knight, Abigail is a knave, Mason is a knave, Chloe is a knight, Emma is a knight, and Jackson is a knight.", "solution_text_format": "(1) Logan is a knave\n(2) Emily is a knight\n(3) Liam is a knight\n(4) Abigail is a knave\n(5) Mason is a knave\n(6) Chloe 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 Logan 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 Logan that Chloe is not a knight.", "Assume Chloe 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 Jackson is a knave and Mason is a knight.", "Jackson cannot be a knight, because this would contradict the claim of Abigail that Jackson is a knave and Mason is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Chloe is a knight or Emma is a knight.", "Emma cannot be a knight, because this would contradict the false claim of Jackson that Chloe is a knight or Emma is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that If Chloe is a knave then Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that If Chloe is a knave then Emily is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Emily is not a knight.", "Mason cannot be a knave, because this would contradict the claim of Abigail that Jackson is a knave 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 false claim of Emma that If Chloe is a knave then Emily is a knave.", "We have exhausted all possibilities for Emily, Emma, and Jackson, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the false claim of Chloe that Abigail is a knave.", "We have exhausted all possibilities for Abigail 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 not 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 Jackson is a knave and Mason is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Chloe is a knight or Emma is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If Chloe is a knave then Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that If Chloe is a knave then Emily is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Emily is not a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Emily is not a knight.", "Assume Liam is a knight. No contradiction is found in their claim that If Emma is a knave then Logan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 5)), ('->', ('lying', 5), ('telling-truth', 1)), ('->', ('lying', 6), ('lying', 0)), ('and', ('lying', 7), ('telling-truth', 4)), ('not', ('telling-truth', 1)), ('lying', 3), ('->', ('lying', 5), ('lying', 1)), ('or', ('telling-truth', 5), ('telling-truth', 6)))", "index": 26}
-{"quiz": "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, Lucas, Samuel, Benjamin, Oliver, Penelope, and Aiden. \"Samuel is a knave and Aiden is a knave,\" Luke mentioned. Aria said that Luke is a knave and Oliver is a knave. \"Penelope is a knight or Samuel is a knave,\" Lucas claimed. In a statement by Samuel: \"Oliver is a knave\". Benjamin noted, \"Luke is a knight\". Oliver noted, \"Penelope is a knight if and only if Lucas is a knave\". Penelope asserted: \"Samuel is a knight or Aria is a knave\". Aiden noted, \"Benjamin is a knight or Luke is a knight\". So who is a knight and who is a knave?", "names": ["Luke", "Aria", "Lucas", "Samuel", "Benjamin", "Oliver", "Penelope", "Aiden"], "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": "Luke is a knave, Aria is a knight, Lucas is a knight, Samuel is a knight, Benjamin is a knave, Oliver is a knave, Penelope is a knight, and Aiden is a knave.", "solution_text_format": "(1) Luke is a knave\n(2) Aria is a knight\n(3) Lucas is a knight\n(4) Samuel is a knight\n(5) Benjamin is a knave\n(6) Oliver is a knave\n(7) Penelope is a knight\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 Luke is a knight. No contradiction is found in their claim that Samuel is a knave and Aiden is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Luke that Samuel is a knave and Aiden is a knave.", "Assume Samuel 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 a knight if and only if Lucas is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Samuel is a knight or Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Luke is a knave and Oliver is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Luke is a knave and Oliver is a knave.", "Lucas cannot be a knight, because this would contradict the claim of Oliver that Penelope 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 Penelope is a knight or Samuel is a knave.", "We have exhausted all possibilities for Lucas and Aria, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Samuel is a knight or Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Luke is a knave and Oliver is a knave.", "Aria cannot be a knave, because this would contradict the false claim of Penelope that Samuel is a knight or Aria is a knave.", "We have exhausted all possibilities for Aria and Penelope, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the false claim of Samuel that Oliver is a knave.", "We have exhausted all possibilities for Oliver 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 knave and Aiden is a knave.", "Assume Samuel 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 Samuel that Oliver is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Penelope is a knight if and only if Lucas is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Samuel is a knight or Aria is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Luke is a knave and Oliver is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Penelope is a knight or Samuel is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Benjamin is a knight or Luke is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Luke is a knight.", "Benjamin cannot be a knave, because this would contradict the claim of Aiden that Benjamin is a knight or Luke is a knight.", "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 a knight or Luke is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Luke is a knight.", "Assume Benjamin 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": "(('and', ('lying', 3), ('lying', 7)), ('and', ('lying', 0), ('lying', 5)), ('or', ('telling-truth', 6), ('lying', 3)), ('lying', 5), ('telling-truth', 0), ('<=>', ('telling-truth', 6), ('lying', 2)), ('or', ('telling-truth', 3), ('lying', 1)), ('or', ('telling-truth', 4), ('telling-truth', 0)))", "index": 27}
-{"quiz": "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, Zoey, Luke, Joseph, Matthew, and Ella. \"Sophia is a knight if and only if Luke is a knave,\" Sophia declared. According to Michael, \"Sophia is a knight\". In Grace's words: \"Matthew is a knave\". \"Ella is a knight,\" Zoey declared. As Luke put it, \"Sophia is a knight and Joseph is a knave\". Joseph asserted: \"Zoey is a knight or Luke is a knight\". Matthew stated, \"If Luke is a knave then Sophia is a knave\". In Ella's words: \"If Sophia is a knave then Zoey is a knave\". So who is a knight and who is a knave?", "names": ["Sophia", "Michael", "Grace", "Zoey", "Luke", "Joseph", "Matthew", "Ella"], "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, Michael is a knight, Grace is a knight, Zoey is a knight, Luke is a knave, Joseph is a knight, Matthew is a knave, and Ella is a knight.", "solution_text_format": "(1) Sophia is a knight\n(2) Michael is a knight\n(3) Grace is a knight\n(4) Zoey is a knight\n(5) Luke is a knave\n(6) Joseph is a knight\n(7) Matthew 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 Sophia is a knight. No contradiction is found in their claim that Sophia is a knight if and only if Luke is a knave.", "Luke cannot be a knight, because this would contradict the claim of Sophia that Sophia is a knight if and only if Luke is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Sophia is a knight and Joseph is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Zoey is a knight or Luke is a knight.", "Assume Zoey 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 Sophia is a knave then Zoey is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Sophia is a knight.", "Assume Grace 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 Grace that Matthew is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that If Luke is a knave then Sophia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 0), ('lying', 4)), ('telling-truth', 0), ('lying', 6), ('telling-truth', 7), ('and', ('telling-truth', 0), ('lying', 5)), ('or', ('telling-truth', 3), ('telling-truth', 4)), ('->', ('lying', 4), ('lying', 0)), ('->', ('lying', 0), ('lying', 3)))", "index": 28}
-{"quiz": "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, Penelope, Scarlett, Lucas, Jacob, Owen, Emily, and Oliver. Samuel told you that Penelope is a knave or Penelope is a knight. \"Owen is a knave,\" Penelope claimed. \"Oliver is not a knight,\" Scarlett claimed. \"Penelope is a knave or Oliver is a knight,\" Lucas declared. Jacob was heard saying, \"Samuel is not a knight\". Owen was heard saying, \"Owen is a knight or Oliver is a knave\". \"Emily is a knight or Owen is a knave,\" Emily mentioned. Oliver stated, \"Penelope is a knight if and only if Oliver is a knight\". So who is a knight and who is a knave?", "names": ["Samuel", "Penelope", "Scarlett", "Lucas", "Jacob", "Owen", "Emily", "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, false, true, true], "solution_text": "Samuel is a knight, Penelope is a knight, Scarlett is a knave, Lucas is a knight, Jacob is a knave, Owen is a knave, Emily is a knight, and Oliver is a knight.", "solution_text_format": "(1) Samuel is a knight\n(2) Penelope is a knight\n(3) Scarlett is a knave\n(4) Lucas is a knight\n(5) Jacob is a knave\n(6) Owen is a knave\n(7) Emily 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 Samuel is a knight. No contradiction is found in their claim that Penelope is a knave or Penelope is a knight.", "Assume Penelope 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 Penelope that Owen is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Owen is a knight or Oliver is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Penelope is a knight if and only if Oliver 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.", "Assume Lucas is a knight. No contradiction is found in their claim that Penelope is a knave or Oliver is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Samuel is not a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Samuel is not a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Emily is a knight or Owen is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('telling-truth', 1)), ('lying', 5), ('not', ('telling-truth', 7)), ('or', ('lying', 1), ('telling-truth', 7)), ('not', ('telling-truth', 0)), ('or', ('telling-truth', 5), ('lying', 7)), ('or', ('telling-truth', 6), ('lying', 5)), ('<=>', ('telling-truth', 1), ('telling-truth', 7)))", "index": 29}
-{"quiz": "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, Joseph, Ava, Penelope, Luke, Lily, Isabella, and Chloe. Aria noted, \"Luke is a knight if and only if Joseph is a knight\". Joseph was heard saying, \"Isabella is not a knave\". In a statement by Ava: \"Penelope is a knave and Chloe is a knight\". According to Penelope, \"Aria is a knave if and only if Ava is a knave\". Luke stated, \"Isabella is a knave if and only if Penelope is a knight\". Lily stated, \"Ava is a knight if and only if Luke is a knave\". Isabella commented, \"Chloe is not a knave\". According to Chloe, \"Ava is not a knight\". So who is a knight and who is a knave?", "names": ["Aria", "Joseph", "Ava", "Penelope", "Luke", "Lily", "Isabella", "Chloe"], "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": "Aria is a knave, Joseph is a knight, Ava is a knave, Penelope is a knight, Luke is a knave, Lily is a knave, Isabella is a knight, and Chloe is a knight.", "solution_text_format": "(1) Aria is a knave\n(2) Joseph is a knight\n(3) Ava is a knave\n(4) Penelope is a knight\n(5) Luke is a knave\n(6) Lily is a knave\n(7) Isabella 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 Aria is a knight. No contradiction is found in their claim that Luke is a knight if and only if Joseph is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Isabella is a knave if and only if Penelope is a knight.", "Assume Isabella 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 Ava is not a knight.", "Ava cannot be a knight, because this would contradict the claim of Chloe that Ava is not a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Penelope is a knave and Chloe is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Aria is a knave if and only if Ava is a knave.", "Penelope cannot be a knave, because this would contradict the false claim of Ava that Penelope is a knave and Chloe is a knight.", "We have exhausted all possibilities for Penelope and Ava, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the claim of Isabella that Chloe is not a knave.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Isabella.", "Assume Isabella 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 Isabella that Chloe is not a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Ava is not a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Penelope is a knave and Chloe is a knight.", "Ava cannot be a knave, because this would contradict the false claim of Chloe that Ava is not a knight.", "We have exhausted all possibilities for Ava, Chloe, and Isabella, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Isabella is a knave if and only if Penelope is a knight.", "Assume Isabella 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 Ava is not a knight.", "Ava cannot be a knight, because this would contradict the claim of Chloe that Ava is not a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Penelope is a knave and Chloe is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Aria is a knave if and only if Ava is a knave.", "Penelope cannot be a knave, because this would contradict the false claim of Ava that Penelope is a knave and Chloe is a knight.", "We have exhausted all possibilities for Penelope and Ava, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the claim of Isabella that Chloe is not a knave.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Isabella.", "Assume Isabella 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 Isabella that Chloe is not a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Ava is not a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Penelope is a knave and Chloe is a knight.", "Ava cannot be a knave, because this would contradict the false claim of Chloe that Ava is not a knight.", "We have exhausted all possibilities for Ava, Chloe, Isabella, and Luke, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Luke is a knight if and only if Joseph is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Isabella is a knave if and only if Penelope is a knight.", "Assume Isabella 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 Ava is not a knight.", "Ava cannot be a knight, because this would contradict the claim of Chloe that Ava is not a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Penelope is a knave and Chloe is a knight.", "Penelope cannot be a knight, because this would contradict the claim of Luke that Isabella is a knave if and only if Penelope is a knight.", "Penelope cannot be a knave, because this would contradict the false claim of Ava that Penelope is a knave and Chloe is a knight.", "We have exhausted all possibilities for Penelope and Ava, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the claim of Isabella that Chloe is not a knave.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Isabella.", "Assume Isabella 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 Isabella that Chloe is not a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Ava is not a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Penelope is a knave and Chloe is a knight.", "Ava cannot be a knave, because this would contradict the false claim of Chloe that Ava is not a knight.", "We have exhausted all possibilities for Ava, Chloe, and Isabella, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Isabella is a knave if and only if Penelope is a knight.", "Assume Isabella 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 Ava is not a knight.", "Ava cannot be a knight, because this would contradict the claim of Chloe that Ava is not a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Penelope is a knave and Chloe is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Aria is a knave if and only if Ava is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Isabella is not a knave.", "Lily cannot be a knight, because this would contradict the claim of their own that Ava is a knight if and only if Luke is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Ava is a knight if and only if Luke is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 4), ('telling-truth', 1)), ('not', ('lying', 6)), ('and', ('lying', 3), ('telling-truth', 7)), ('<=>', ('lying', 0), ('lying', 2)), ('<=>', ('lying', 6), ('telling-truth', 3)), ('<=>', ('telling-truth', 2), ('lying', 4)), ('not', ('lying', 7)), ('not', ('telling-truth', 2)))", "index": 30}
-{"quiz": "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, Michael, Samuel, Lucas, Olivia, Jack, Isabella, and Alexander. In Abigail's words: \"If Lucas is a knave then Lucas is a knight\". Michael commented, \"If Isabella is a knight then Jack is a knave\". In Samuel's words: \"Michael is a knave if and only if Michael is a knight\". Lucas stated, \"Samuel is a knight\". According to Olivia, \"Michael is not a knave\". Jack remarked, \"If Lucas is a knight then Olivia is a knave\". As Isabella put it, \"Lucas is a knight and Abigail is a knight\". Alexander noted, \"Michael is a knight if and only if Olivia is a knight\". So who is a knight and who is a knave?", "names": ["Abigail", "Michael", "Samuel", "Lucas", "Olivia", "Jack", "Isabella", "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, true, false, true], "solution_text": "Abigail is a knave, Michael is a knight, Samuel is a knave, Lucas is a knave, Olivia is a knight, Jack is a knight, Isabella is a knave, and Alexander is a knight.", "solution_text_format": "(1) Abigail is a knave\n(2) Michael is a knight\n(3) Samuel is a knave\n(4) Lucas is a knave\n(5) Olivia is a knight\n(6) Jack is a knight\n(7) Isabella 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 Abigail 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 Samuel is a knight.", "Samuel 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.", "Samuel cannot be a knave, because this would contradict the claim of Lucas that Samuel 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 Abigail that If Lucas is a knave then Lucas is a knight.", "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 If Lucas is a knave then Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of Abigail that If Lucas is a knave then Lucas is a knight.", "Assume Lucas 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 claim of their own that Michael is a knave if and only if Michael is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Michael is a knave if and only if Michael is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that If Isabella is a knight then Jack is a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that Lucas is a knight and Abigail is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Lucas is a knight and Abigail is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that If Lucas is a knight then Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Michael is not a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Michael is a knight if and only if Olivia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('telling-truth', 3)), ('->', ('telling-truth', 6), ('lying', 5)), ('<=>', ('lying', 1), ('telling-truth', 1)), ('telling-truth', 2), ('not', ('lying', 1)), ('->', ('telling-truth', 3), ('lying', 4)), ('and', ('telling-truth', 3), ('telling-truth', 0)), ('<=>', ('telling-truth', 1), ('telling-truth', 4)))", "index": 31}
-{"quiz": "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, Henry, William, Avery, Jack, Owen, Charlotte, and Luke. \"William is not a knight,\" Scarlett mentioned. In Henry's words: \"Charlotte is a knight\". William asserted: \"Luke is a knight if and only if Charlotte is a knave\". In Avery's words: \"Owen is a knight\". Jack asserted: \"Avery is a knight and Charlotte is a knave\". Owen told you that Avery is a knight or Scarlett is a knight. \"William is a knight and Luke is a knight,\" Charlotte mentioned. Luke was heard saying, \"If Owen is a knight then Henry is a knight\". So who is a knight and who is a knave?", "names": ["Scarlett", "Henry", "William", "Avery", "Jack", "Owen", "Charlotte", "Luke"], "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": "Scarlett is a knight, Henry is a knave, William is a knave, Avery is a knight, Jack is a knight, Owen is a knight, Charlotte is a knave, and Luke is a knave.", "solution_text_format": "(1) Scarlett is a knight\n(2) Henry is a knave\n(3) William is a knave\n(4) Avery is a knight\n(5) Jack is a knight\n(6) Owen is a knight\n(7) Charlotte 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 Scarlett 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 Scarlett that William is not a knight.", "Assume William is a knave. No contradiction is found in their false 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 If Owen is a knight then Henry is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Avery is a knight or Scarlett is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Owen is a knight.", "Assume Henry 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 William is a knight and Luke is a knight.", "Charlotte cannot be a knave, because this would contradict the claim of Henry that Charlotte is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the claim of Luke that If Owen is a knight then Henry is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Avery.", "Avery 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 Avery, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the false claim of their own that Avery is a knight or Scarlett is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Luke.", "Assume Luke 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 Avery is a knight or Scarlett is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Owen is a knight.", "Henry cannot be a knight, because this would contradict the false claim of Luke that If Owen is a knight then Henry is a knight.", "Assume Henry 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 Henry that Charlotte is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that William is a knight and Luke is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Avery is a knight and Charlotte is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('telling-truth', 6), ('<=>', ('telling-truth', 7), ('lying', 6)), ('telling-truth', 5), ('and', ('telling-truth', 3), ('lying', 6)), ('or', ('telling-truth', 3), ('telling-truth', 0)), ('and', ('telling-truth', 2), ('telling-truth', 7)), ('->', ('telling-truth', 5), ('telling-truth', 1)))", "index": 32}
-{"quiz": "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, Olivia, Grace, Scarlett, Sofia, Emma, and Ethan. \"If Sofia is a knight then Chloe is a knight,\" Evelyn claimed. \"Emma is not a knave,\" Chloe declared. \"Emma is a knave,\" Olivia mentioned. \"Emma is a knave or Olivia is a knight\" - Grace. In a statement by Scarlett: \"Grace is a knave and Olivia is a knave\". Sofia expressed that Ethan is a knave or Ethan is a knight. Emma remarked, \"Evelyn is a knight and Sofia is a knave\". In Ethan's words: \"Chloe is a knave\". So who is a knight and who is a knave?", "names": ["Evelyn", "Chloe", "Olivia", "Grace", "Scarlett", "Sofia", "Emma", "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, true, false, true], "solution_text": "Evelyn is a knave, Chloe is a knave, Olivia is a knight, Grace is a knight, Scarlett is a knave, Sofia is a knight, Emma is a knave, and Ethan is a knight.", "solution_text_format": "(1) Evelyn is a knave\n(2) Chloe is a knave\n(3) Olivia is a knight\n(4) Grace is a knight\n(5) Scarlett is a knave\n(6) Sofia is a knight\n(7) Emma 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 If Sofia is a knight then Chloe is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Ethan is a knave or Ethan is a knight.", "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.", "Chloe cannot be a knave, because this would contradict the claim of Evelyn that If Sofia is a knight then Chloe is a knight.", "We have exhausted all possibilities for 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 Emma is not a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Evelyn is a knight and Sofia is a knave.", "Emma cannot be a knave, because this would contradict the claim of Chloe that Emma is not a knave.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the claim of Evelyn that If Sofia is a knight then Chloe is a knight.", "We have exhausted all possibilities for Chloe and Ethan, so let us go back and reconsider Sofia.", "Sofia cannot be a knave, because this would contradict the false claim of their own that Ethan is a knave or Ethan is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that If Sofia is a knight then Chloe is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Ethan is a knave or Ethan is a knight.", "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 false claim of Evelyn that If Sofia is a knight then Chloe is a knight.", "Assume Chloe 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 Chloe that Emma is not a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Evelyn is a knight and Sofia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Emma is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Emma is a knave or Olivia is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Grace is a knave and Olivia is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Grace is a knave and Olivia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 5), ('telling-truth', 1)), ('not', ('lying', 6)), ('lying', 6), ('or', ('lying', 6), ('telling-truth', 2)), ('and', ('lying', 3), ('lying', 2)), ('or', ('lying', 7), ('telling-truth', 7)), ('and', ('telling-truth', 0), ('lying', 5)), ('lying', 1))", "index": 33}
-{"quiz": "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, Daniel, Benjamin, Aiden, Charlotte, Matthew, and Chloe. Mason was heard saying, \"Benjamin is a knave\". Ella commented, \"Benjamin is a knave or Matthew is a knave\". Daniel told you that Charlotte is not a knight. \"Aiden is a knight or Daniel is a knight,\" Benjamin mentioned. \"Charlotte is a knight if and only if Chloe is a knave,\" Aiden mentioned. Charlotte remarked, \"Daniel is a knave\". In a statement by Matthew: \"Benjamin is not a knight\". Chloe asserted: \"Benjamin is a knight or Aiden is a knight\". So who is a knight and who is a knave?", "names": ["Mason", "Ella", "Daniel", "Benjamin", "Aiden", "Charlotte", "Matthew", "Chloe"], "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, Ella is a knight, Daniel is a knight, Benjamin is a knight, Aiden is a knight, Charlotte is a knave, Matthew is a knave, and Chloe is a knight.", "solution_text_format": "(1) Mason is a knave\n(2) Ella is a knight\n(3) Daniel is a knight\n(4) Benjamin is a knight\n(5) Aiden is a knight\n(6) Charlotte is a knave\n(7) Matthew 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 Mason 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 Mason that Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Aiden is a knight or Daniel is a knight.", "Aiden cannot be a knight, because this would contradict the false claim of Benjamin that Aiden is a knight or Daniel is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Charlotte is a knight if and only if Chloe is a knave.", "Assume Charlotte 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 their own that Charlotte is not a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Charlotte is not a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight or Aiden is a knight.", "Chloe cannot be a knave, because this would contradict the false claim of Aiden that Charlotte is a knight if and only if Chloe is a knave.", "We have exhausted all possibilities for Chloe and Daniel, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the false claim of Benjamin that Aiden is a knight or Daniel is a knight.", "Daniel 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 Daniel, Charlotte, Aiden, and Benjamin, so let us go back and reconsider Mason.", "Assume Mason 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 Aiden is a knight or Daniel is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Charlotte is a knight if and only if Chloe is a knave.", "Assume Charlotte 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 their own that Charlotte is not a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Charlotte is not a knight.", "Chloe cannot be a knight, because this would contradict the claim of Aiden that Charlotte is a knight if and only if Chloe is a knave.", "Chloe cannot be a knave, because this would contradict the false claim of their own that Benjamin is a knight or Aiden is a knight.", "We have exhausted all possibilities for Chloe and Daniel, so let us go back and reconsider Charlotte.", "Assume Charlotte 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 Charlotte is not a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Benjamin is a knight or Aiden is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Benjamin is a knave or Matthew is a knave.", "Matthew cannot be a knight, because this would contradict the claim of Ella that Benjamin is a knave or Matthew is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Benjamin is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('or', ('lying', 3), ('lying', 6)), ('not', ('telling-truth', 5)), ('or', ('telling-truth', 4), ('telling-truth', 2)), ('<=>', ('telling-truth', 5), ('lying', 7)), ('lying', 2), ('not', ('telling-truth', 3)), ('or', ('telling-truth', 3), ('telling-truth', 4)))", "index": 34}
-{"quiz": "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, Aria, James, Lucas, Henry, Zoey, Penelope, and Michael. As Matthew put it, \"Michael is a knight or Lucas is a knight\". Aria said, \"Zoey is a knave if and only if Michael is a knave.\" \"If Penelope is a knave then Matthew is a knave,\" James declared. In Lucas's words: \"Aria is not a knave\". Henry remarked, \"If Michael is a knight then James is a knave\". Zoey expressed that If Zoey is a knight then Lucas is a knight. \"Henry is a knave\" - Penelope. \"Henry is a knave,\" Michael mentioned. So who is a knight and who is a knave?", "names": ["Matthew", "Aria", "James", "Lucas", "Henry", "Zoey", "Penelope", "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, true, true], "solution_text": "Matthew is a knight, Aria is a knight, James is a knight, Lucas is a knight, Henry is a knave, Zoey is a knight, Penelope is a knight, and Michael is a knight.", "solution_text_format": "(1) Matthew is a knight\n(2) Aria is a knight\n(3) James is a knight\n(4) Lucas is a knight\n(5) Henry is a knave\n(6) Zoey is a knight\n(7) Penelope 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 Matthew is a knight. No contradiction is found in their claim that Michael is a knight or Lucas is a knight.", "Assume Michael 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 Michael that Henry is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that If Michael is a knight then James is a knave.", "Assume James is a knight. No contradiction is found in their claim that If Penelope is a knave then Matthew is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Henry is a knave.", "Assume Lucas 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 Zoey is a knave if and only if Michael is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that If Zoey is a knight then Lucas is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 7), ('telling-truth', 3)), ('<=>', ('lying', 5), ('lying', 7)), ('->', ('lying', 6), ('lying', 0)), ('not', ('lying', 1)), ('->', ('telling-truth', 7), ('lying', 2)), ('->', ('telling-truth', 5), ('telling-truth', 3)), ('lying', 4), ('lying', 4))", "index": 35}
-{"quiz": "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, Isabella, Alexander, Samuel, Aria, Oliver, Penelope, and Noah. Jackson stated, \"Aria is a knave and Jackson is a knight\". Isabella said that Penelope is a knave if and only if Samuel is a knight. Alexander remarked, \"Samuel is a knight or Noah is a knight\". Samuel commented, \"Isabella is a knight and Jackson is a knave\". Aria told you that If Alexander is a knave then Samuel is a knave. \"Jackson is not a knight,\" Oliver claimed. Penelope was heard saying, \"Samuel is not a knight\". In Noah's words: \"Aria is a knight\". So who is a knight and who is a knave?", "names": ["Jackson", "Isabella", "Alexander", "Samuel", "Aria", "Oliver", "Penelope", "Noah"], "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": "Jackson is a knave, Isabella is a knight, Alexander is a knight, Samuel is a knight, Aria is a knight, Oliver is a knight, Penelope is a knave, and Noah is a knight.", "solution_text_format": "(1) Jackson is a knave\n(2) Isabella is a knight\n(3) Alexander is a knight\n(4) Samuel is a knight\n(5) Aria is a knight\n(6) Oliver is a knight\n(7) Penelope 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 Jackson is a knight. No contradiction is found in their claim that Aria is a knave and Jackson is a knight.", "Aria cannot be a knight, because this would contradict the claim of Jackson that Aria is a knave and Jackson is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that If Alexander is a knave then Samuel is a knave.", "Alexander cannot be a knight, because this would contradict the false claim of Aria that If Alexander is a knave then Samuel is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Samuel is a knight or Noah is a knight.", "Samuel cannot be a knight, because this would contradict the false claim of Alexander that Samuel is a knight or Noah is a knight.", "Samuel cannot be a knave, because this would contradict the false claim of Aria that If Alexander is a knave then Samuel is a knave.", "We have exhausted all possibilities for Samuel, Alexander, 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 knave and Jackson is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that If Alexander is a knave then Samuel is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Samuel is a knight or Noah is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Isabella is a knight and Jackson is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Penelope is a knave if and only if Samuel is a knight.", "Penelope cannot be a knight, because this would contradict the claim of Isabella that Penelope is a knave if and only if Samuel is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Samuel is not a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Aria is a knight.", "Assume Oliver 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', ('lying', 4), ('telling-truth', 0)), ('<=>', ('lying', 6), ('telling-truth', 3)), ('or', ('telling-truth', 3), ('telling-truth', 7)), ('and', ('telling-truth', 1), ('lying', 0)), ('->', ('lying', 2), ('lying', 3)), ('not', ('telling-truth', 0)), ('not', ('telling-truth', 3)), ('telling-truth', 4))", "index": 36}
-{"quiz": "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, Grace, Riley, James, Harper, Avery, Sofia, and Noah. In Ava's words: \"Avery is a knave if and only if Grace is a knave\". Grace expressed that James is a knight. Riley said that Ava is a knight if and only if Riley is a knight. James noted, \"If Ava is a knight then Riley is a knight\". As Harper put it, \"Ava is not a knight\". Avery noted, \"Grace is a knight if and only if Avery is a knight\". \"Avery is not a knight,\" Sofia mentioned. Noah noted, \"If Ava is a knave then Sofia is a knave\". So who is a knight and who is a knave?", "names": ["Ava", "Grace", "Riley", "James", "Harper", "Avery", "Sofia", "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, true], "solution_text": "Ava is a knight, Grace is a knight, Riley is a knight, James is a knight, Harper is a knave, Avery is a knight, Sofia is a knave, and Noah is a knight.", "solution_text_format": "(1) Ava is a knight\n(2) Grace is a knight\n(3) Riley is a knight\n(4) James is a knight\n(5) Harper is a knave\n(6) Avery is a knight\n(7) Sofia 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 Ava is a knight. No contradiction is found in their claim that Avery is a knave if and only if Grace is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Grace is a knight if and only if Avery is a knight.", "Assume Grace 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 Ava is a knight then Riley is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Ava is a knight if and only if Riley is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that Ava is not a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Ava is not a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that Avery is not a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Avery is not a knight.", "Assume Noah is a knight. No contradiction is found in their claim that If Ava is a knave then Sofia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 5), ('lying', 1)), ('telling-truth', 3), ('<=>', ('telling-truth', 0), ('telling-truth', 2)), ('->', ('telling-truth', 0), ('telling-truth', 2)), ('not', ('telling-truth', 0)), ('<=>', ('telling-truth', 1), ('telling-truth', 5)), ('not', ('telling-truth', 5)), ('->', ('lying', 0), ('lying', 6)))", "index": 37}
-{"quiz": "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, Joseph, Michael, Amelia, Jack, Emily, and Penelope. \"Emily is not a knave,\" Mia mentioned. \"Emily is not a knave,\" Luke claimed. Joseph said that Michael is a knave if and only if Emily is a knave. In a statement by Michael: \"Joseph is a knave or Emily is a knave\". Amelia stated, \"Jack is a knave if and only if Luke is a knight\". \"If Penelope is a knave then Amelia is a knight,\" Jack claimed. According to Emily, \"Joseph is a knight or Amelia is a knave\". \"Joseph is not a knight,\" Penelope claimed. So who is a knight and who is a knave?", "names": ["Mia", "Luke", "Joseph", "Michael", "Amelia", "Jack", "Emily", "Penelope"], "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, Luke is a knave, Joseph is a knave, Michael is a knight, Amelia is a knight, Jack is a knight, Emily is a knave, and Penelope is a knight.", "solution_text_format": "(1) Mia is a knave\n(2) Luke is a knave\n(3) Joseph is a knave\n(4) Michael is a knight\n(5) Amelia is a knight\n(6) Jack is a knight\n(7) Emily 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 Mia 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 knight or Amelia is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Michael is a knave if and only if Emily is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Joseph is a knave or Emily is a knave.", "Michael cannot be a knave, because this would contradict the claim of Joseph that Michael is a knave if and only if Emily is a knave.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Michael is a knave if and only if Emily is a knave.", "Michael cannot be a knight, because this would contradict the false claim of Joseph that Michael is a knave if and only if Emily is a knave.", "Michael cannot be a knave, because this would contradict the false claim of their own that Joseph is a knave or Emily is a knave.", "We have exhausted all possibilities for Michael and Joseph, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the claim of Mia that Emily is not a knave.", "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 not a knave.", "Emily cannot be a knight, because this would contradict the false claim of Mia that Emily is not a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Joseph is a knight or Amelia is a knave.", "Joseph cannot be a knight, because this would contradict the false claim of Emily that Joseph is a knight or Amelia is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Michael is a knave if and only if Emily is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Joseph is a knave or Emily is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Jack is a knave if and only if Luke is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that If Penelope is a knave then Amelia is a knight.", "Assume Penelope 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 Emily is not a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Emily is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 6)), ('not', ('lying', 6)), ('<=>', ('lying', 3), ('lying', 6)), ('or', ('lying', 2), ('lying', 6)), ('<=>', ('lying', 5), ('telling-truth', 1)), ('->', ('lying', 7), ('telling-truth', 4)), ('or', ('telling-truth', 2), ('lying', 4)), ('not', ('telling-truth', 2)))", "index": 38}
-{"quiz": "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, Mia, Sophia, Jack, Olivia, Sebastian, James, and Samuel. Emma commented, \"James is a knave\". According to Mia, \"Sebastian is a knight and Jack is a knave\". Sophia remarked, \"Samuel is not a knight\". As Jack put it, \"If Olivia is a knight then Sebastian is a knight\". Olivia expressed that If Samuel is a knight then Mia is a knight. Sebastian remarked, \"Samuel is a knight or Olivia is a knave\". \"Olivia is a knave,\" James claimed. \"Olivia is a knave and Sebastian is a knave,\" Samuel declared. So who is a knight and who is a knave?", "names": ["Emma", "Mia", "Sophia", "Jack", "Olivia", "Sebastian", "James", "Samuel"], "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": "Emma is a knight, Mia is a knave, Sophia is a knight, Jack is a knave, Olivia is a knight, Sebastian is a knave, James is a knave, and Samuel is a knave.", "solution_text_format": "(1) Emma is a knight\n(2) Mia is a knave\n(3) Sophia is a knight\n(4) Jack is a knave\n(5) Olivia is a knight\n(6) Sebastian is a knave\n(7) James 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 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 Emma that James is a knave.", "Assume James 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 Samuel is a knight then Mia is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Olivia is a knave and Sebastian is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Olivia is a knave and Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Samuel is a knight or Olivia is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Samuel is a knight or Olivia is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight and Jack is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Sebastian is a knight and Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that If Olivia is a knight then Sebastian is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that If Olivia is a knight then Sebastian is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Samuel is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 6), ('and', ('telling-truth', 5), ('lying', 3)), ('not', ('telling-truth', 7)), ('->', ('telling-truth', 4), ('telling-truth', 5)), ('->', ('telling-truth', 7), ('telling-truth', 1)), ('or', ('telling-truth', 7), ('lying', 4)), ('lying', 4), ('and', ('lying', 4), ('lying', 5)))", "index": 39}
-{"quiz": "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, William, Mia, Alexander, Ethan, Benjamin, and Abigail. According to Sofia, \"Mia is a knight and Abigail is a knight\". Daniel expressed that Benjamin is a knight if and only if Sofia is a knight. According to William, \"Benjamin is not a knave\". Mia said that If Benjamin is a knight then Daniel is a knave. \"Daniel is a knight,\" Alexander claimed. \"Abigail is a knight if and only if Benjamin is a knight,\" Ethan claimed. Benjamin noted, \"Abigail is a knave or Mia is a knave\". In a statement by Abigail: \"Mia is a knight or Sofia is a knave\". So who is a knight and who is a knave?", "names": ["Sofia", "Daniel", "William", "Mia", "Alexander", "Ethan", "Benjamin", "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, true], "solution_text": "Sofia is a knight, Daniel is a knave, William is a knave, Mia is a knight, Alexander is a knave, Ethan is a knave, Benjamin is a knave, and Abigail is a knight.", "solution_text_format": "(1) Sofia is a knight\n(2) Daniel is a knave\n(3) William is a knave\n(4) Mia is a knight\n(5) Alexander is a knave\n(6) Ethan is a knave\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 Sofia is a knight. No contradiction is found in their claim that Mia is a knight and Abigail is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that If Benjamin is a knight then Daniel is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Abigail is a knave or Mia is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Benjamin that Abigail is a knave or Mia is a knave.", "Abigail cannot be a knave, because this would contradict the claim of Sofia that Mia is a knight and Abigail is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Abigail is a knave or Mia is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Mia is a knight or Sofia is a knave.", "Daniel cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight if and only if Sofia is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Benjamin is a knight if and only if Sofia is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Benjamin is not a knave.", "Assume William is a knave. No contradiction is found in their false claim that Benjamin is not a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that Daniel is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Daniel is a knight.", "Ethan 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 knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Abigail is a knight if and only if Benjamin is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('telling-truth', 7)), ('<=>', ('telling-truth', 6), ('telling-truth', 0)), ('not', ('lying', 6)), ('->', ('telling-truth', 6), ('lying', 1)), ('telling-truth', 1), ('<=>', ('telling-truth', 7), ('telling-truth', 6)), ('or', ('lying', 7), ('lying', 3)), ('or', ('telling-truth', 3), ('lying', 0)))", "index": 40}
-{"quiz": "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, Joseph, Oliver, Avery, Noah, Harper, Penelope, and Lucas. \"Riley is a knight and Noah is a knight,\" Riley claimed. In Joseph's words: \"If Riley is a knight then Oliver is a knave\". Oliver said that Avery is a knight or Harper is a knight. Avery stated, \"Penelope is a knight\". Noah expressed that Joseph is a knave if and only if Oliver is a knave. \"If Lucas is a knave then Joseph is a knave,\" Harper mentioned. Penelope asserted: \"Harper is a knight and Oliver is a knight\". According to Lucas, \"Avery is a knave or Penelope is a knight\". So who is a knight and who is a knave?", "names": ["Riley", "Joseph", "Oliver", "Avery", "Noah", "Harper", "Penelope", "Lucas"], "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": "Riley is a knave, Joseph is a knight, Oliver is a knight, Avery is a knight, Noah is a knight, Harper is a knight, Penelope is a knight, and Lucas is a knight.", "solution_text_format": "(1) Riley is a knave\n(2) Joseph is a knight\n(3) Oliver is a knight\n(4) Avery is a knight\n(5) Noah is a knight\n(6) Harper is a knight\n(7) Penelope 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 Riley is a knight. No contradiction is found in their claim that Riley is a knight and Noah is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Joseph is a knave if and only if Oliver is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that If Riley is a knight then Oliver is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Joseph that If Riley is a knight then Oliver is a knave.", "Oliver cannot be a knave, because this would contradict the claim of Noah that Joseph is a knave if and only if Oliver is a knave.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that If Riley is a knight then Oliver is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Noah that Joseph is a knave if and only if Oliver is a knave.", "Oliver cannot be a knave, because this would contradict the false claim of Joseph that If Riley is a knight then Oliver is a knave.", "We have exhausted all possibilities for Oliver and Joseph, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the claim of Riley that Riley is a knight and Noah is a knight.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Riley is a knight and Noah is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Joseph is a knave if and only if Oliver is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that If Riley is a knight then Oliver is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Avery is a knight or Harper is a knight.", "Assume Avery 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 Harper is a knight and Oliver is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that If Lucas is a knave then Joseph is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Avery is a knave or Penelope is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 0), ('telling-truth', 4)), ('->', ('telling-truth', 0), ('lying', 2)), ('or', ('telling-truth', 3), ('telling-truth', 5)), ('telling-truth', 6), ('<=>', ('lying', 1), ('lying', 2)), ('->', ('lying', 7), ('lying', 1)), ('and', ('telling-truth', 5), ('telling-truth', 2)), ('or', ('lying', 3), ('telling-truth', 6)))", "index": 41}
-{"quiz": "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, Ava, Penelope, Scarlett, Emily, Alexander, and Evelyn. As Mason put it, \"Scarlett is a knave\". Avery said that Evelyn is not a knight. Ava expressed that Scarlett is a knave or Alexander is a knave. \"Scarlett is not a knave,\" Penelope mentioned. According to Scarlett, \"Penelope is a knave and Scarlett is a knight\". In a statement by Emily: \"Scarlett is a knight and Avery is a knight\". Alexander told you that If Evelyn is a knave then Avery is a knight. Evelyn noted, \"Evelyn is a knight and Avery is a knight\". So who is a knight and who is a knave?", "names": ["Mason", "Avery", "Ava", "Penelope", "Scarlett", "Emily", "Alexander", "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, false], "solution_text": "Mason is a knight, Avery is a knight, Ava is a knight, Penelope is a knave, Scarlett is a knave, Emily is a knave, Alexander is a knight, and Evelyn is a knave.", "solution_text_format": "(1) Mason is a knight\n(2) Avery is a knight\n(3) Ava is a knight\n(4) Penelope is a knave\n(5) Scarlett is a knave\n(6) Emily is a knave\n(7) Alexander 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 Mason 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 Mason that Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Penelope is a knave and Scarlett is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Scarlett is not a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Scarlett is not a knave.", "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 Evelyn is a knight and Avery is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Scarlett is a knave or Alexander is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that If Evelyn is a knave then Avery is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight and Avery is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Scarlett is a knight and Avery is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('not', ('telling-truth', 7)), ('or', ('lying', 4), ('lying', 6)), ('not', ('lying', 4)), ('and', ('lying', 3), ('telling-truth', 4)), ('and', ('telling-truth', 4), ('telling-truth', 1)), ('->', ('lying', 7), ('telling-truth', 1)), ('and', ('telling-truth', 7), ('telling-truth', 1)))", "index": 42}
-{"quiz": "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, Henry, Matthew, Zoey, James, Aurora, and David. Scarlett expressed that If Chloe is a knight then David is a knight. Chloe noted, \"Aurora is a knight and David is a knight\". Henry asserted: \"Zoey is a knave\". Matthew said, \"Zoey is a knave or David is a knight.\" \"If Matthew is a knave then Aurora is a knave,\" Zoey declared. In James's words: \"David is a knave or David is a knight\". In a statement by Aurora: \"David is not a knave\". In a statement by David: \"Chloe is a knave if and only if Aurora is a knight\". So who is a knight and who is a knave?", "names": ["Scarlett", "Chloe", "Henry", "Matthew", "Zoey", "James", "Aurora", "David"], "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, Henry is a knave, Matthew is a knave, Zoey is a knight, James is a knight, Aurora is a knave, and David is a knave.", "solution_text_format": "(1) Scarlett is a knight\n(2) Chloe is a knave\n(3) Henry is a knave\n(4) Matthew is a knave\n(5) Zoey is a knight\n(6) James is a knight\n(7) Aurora 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 Scarlett is a knight. No contradiction is found in their claim that If Chloe is a knight then David is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Aurora is a knight and David is a knight.", "Assume Aurora 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 Chloe is a knave if and only if Aurora is a knight.", "David cannot be a knave, because this would contradict the claim of Scarlett that If Chloe is a knight then David is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the claim of Chloe that Aurora is a knight and David is a knight.", "We have exhausted all possibilities for 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 knight and David is a knight.", "Assume Aurora 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 Chloe that Aurora is a knight and David is a knight.", "David cannot be a knave, because this would contradict the claim of Aurora that David is not a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Aurora.", "Assume Aurora 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 Aurora that David is not a knave.", "Assume David is a knave. No contradiction is found in their false claim that Chloe is a knave if and only if Aurora is a knight.", "Assume Henry 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 Henry that Zoey is a knave.", "Zoey cannot be a knave, because this would contradict the false claim of their own that If Matthew is a knave then Aurora is a knave.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Henry.", "Assume Henry 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 Matthew is a knave then Aurora is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Zoey is a knave or David is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Zoey is a knave or David is a knight.", "Assume James is a knight. No contradiction is found in their claim that David is a knave or David is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 1), ('telling-truth', 7)), ('and', ('telling-truth', 6), ('telling-truth', 7)), ('lying', 4), ('or', ('lying', 4), ('telling-truth', 7)), ('->', ('lying', 3), ('lying', 6)), ('or', ('lying', 7), ('telling-truth', 7)), ('not', ('lying', 7)), ('<=>', ('lying', 1), ('telling-truth', 6)))", "index": 43}
-{"quiz": "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, Penelope, Daniel, Joseph, Harper, Emma, Ella, and Jacob. In a statement by Charlotte: \"Emma is a knight and Joseph is a knight\". In a statement by Penelope: \"If Jacob is a knight then Harper is a knight\". Daniel asserted: \"If Ella is a knave then Joseph is a knave\". As Joseph put it, \"Harper is a knight\". Harper stated, \"Jacob is a knight if and only if Daniel is a knave\". \"Ella is a knave if and only if Charlotte is a knight,\" Emma claimed. Ella commented, \"Penelope is a knight if and only if Penelope is a knave\". Jacob asserted: \"Daniel is not a knave\". So who is a knight and who is a knave?", "names": ["Charlotte", "Penelope", "Daniel", "Joseph", "Harper", "Emma", "Ella", "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, false, false, true], "solution_text": "Charlotte is a knave, Penelope is a knave, Daniel is a knight, Joseph is a knave, Harper is a knave, Emma is a knave, Ella is a knave, and Jacob is a knight.", "solution_text_format": "(1) Charlotte is a knave\n(2) Penelope is a knave\n(3) Daniel is a knight\n(4) Joseph is a knave\n(5) Harper is a knave\n(6) Emma is a knave\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 Charlotte is a knight. No contradiction is found in their claim that Emma is a knight and Joseph is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Ella is a knave if and only if Charlotte is a knight.", "Ella cannot be a knight, because this would contradict the claim of Emma that Ella is a knave if and only if Charlotte is a knight.", "Assume Ella 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 If Jacob is a knight then Harper is a knight.", "Assume Jacob 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 Ella is a knave then Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Daniel that If Ella is a knave then Joseph is a knave.", "Joseph cannot be a knave, because this would contradict the claim of Charlotte that Emma is a knight and Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the claim of Jacob that Daniel is not a knave.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Jacob.", "Assume Jacob 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 Jacob that Daniel is not a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that If Ella is a knave then Joseph is a knave.", "Assume Joseph 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 their own that Jacob is a knight if and only if Daniel is a knave.", "Harper cannot be a knave, because this would contradict the claim of Joseph that Harper is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of Charlotte that Emma is a knight and Joseph is a knight.", "We have exhausted all possibilities for Joseph, Daniel, and Jacob, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that If Jacob is a knight then Harper is a knight.", "Assume Jacob 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 Ella is a knave then Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Daniel that If Ella is a knave then Joseph is a knave.", "Joseph cannot be a knave, because this would contradict the claim of Charlotte that Emma is a knight and Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the claim of Jacob that Daniel is not a knave.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the false claim of Penelope that If Jacob is a knight then Harper is a knight.", "We have exhausted all possibilities for Jacob, Penelope, and Ella, so let us go back and reconsider Emma.", "Emma cannot be a knave, because this would contradict the claim of Charlotte that Emma is a knight and Joseph is a knight.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Emma is a knight and Joseph is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Ella is a knave if and only if Charlotte is a knight.", "Ella 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.", "Ella cannot be a knave, because this would contradict the claim of Emma that Ella is a knave if and only if Charlotte is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Ella is a knave if and only if Charlotte is a knight.", "Ella cannot be a knight, because this would contradict the false claim of Emma that Ella is a knave if and only if Charlotte is a knight.", "Assume Ella 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 If Jacob is a knight then Harper is a knight.", "Assume Jacob 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 Ella is a knave then Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Daniel that If Ella is a knave then Joseph is a knave.", "Assume Joseph 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 Joseph that Harper is a knight.", "Harper cannot be a knave, because this would contradict the claim of Penelope that If Jacob is a knight then Harper is a knight.", "We have exhausted all possibilities for Harper and Joseph, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the claim of Jacob that Daniel is not a knave.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Jacob.", "Assume Jacob 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 Jacob that Daniel is not a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that If Ella is a knave then Joseph is a knave.", "Assume Joseph 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 their own that Jacob is a knight if and only if Daniel is a knave.", "Harper cannot be a knave, because this would contradict the claim of Joseph that Harper is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the false claim of Daniel that If Ella is a knave then Joseph is a knave.", "We have exhausted all possibilities for Joseph, Daniel, and Jacob, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that If Jacob is a knight then Harper is a knight.", "Assume Jacob 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 Ella is a knave then Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Daniel that If Ella is a knave then Joseph is a knave.", "Assume Joseph 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 Penelope that If Jacob is a knight then Harper is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Jacob is a knight if and only if Daniel is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('telling-truth', 3)), ('->', ('telling-truth', 7), ('telling-truth', 4)), ('->', ('lying', 6), ('lying', 3)), ('telling-truth', 4), ('<=>', ('telling-truth', 7), ('lying', 2)), ('<=>', ('lying', 6), ('telling-truth', 0)), ('<=>', ('telling-truth', 1), ('lying', 1)), ('not', ('lying', 2)))", "index": 44}
-{"quiz": "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, Isabella, Scarlett, Jackson, Riley, Zoey, Amelia, and Ava. \"Ava is a knave,\" Aria claimed. Isabella was heard saying, \"Zoey is not a knight\". \"Amelia is a knave or Ava is a knight,\" Scarlett declared. \"Amelia is a knave if and only if Ava is a knight,\" Jackson claimed. \"Ava is a knight and Jackson is a knave,\" Riley declared. \"Amelia is a knave or Isabella is a knave,\" Zoey declared. As Amelia put it, \"Zoey is not a knave\". Ava said that Aria is a knave and Amelia is a knave. So who is a knight and who is a knave?", "names": ["Aria", "Isabella", "Scarlett", "Jackson", "Riley", "Zoey", "Amelia", "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, true, true, false], "solution_text": "Aria is a knight, Isabella is a knave, Scarlett is a knave, Jackson is a knight, Riley is a knave, Zoey is a knight, Amelia is a knight, and Ava is a knave.", "solution_text_format": "(1) Aria is a knight\n(2) Isabella is a knave\n(3) Scarlett is a knave\n(4) Jackson is a knight\n(5) Riley is a knave\n(6) Zoey is a knight\n(7) Amelia 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 Aria 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 Aria that Ava is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Aria is a knave and Amelia is a knave.", "Assume Amelia 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 Amelia is a knave or Isabella is a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that Zoey is not a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Zoey is not a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Amelia is a knave or Ava is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Amelia is a knave or Ava is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Amelia is a knave if and only if Ava is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Ava is a knight and Jackson is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Ava is a knight and Jackson is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 7), ('not', ('telling-truth', 5)), ('or', ('lying', 6), ('telling-truth', 7)), ('<=>', ('lying', 6), ('telling-truth', 7)), ('and', ('telling-truth', 7), ('lying', 3)), ('or', ('lying', 6), ('lying', 1)), ('not', ('lying', 5)), ('and', ('lying', 0), ('lying', 6)))", "index": 45}
-{"quiz": "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, Aria, Penelope, Ella, Victoria, Luke, Owen, and Jack. Grace remarked, \"Victoria is a knave and Owen is a knight\". Aria noted, \"Luke is a knight if and only if Owen is a knave\". Penelope noted, \"Grace is a knight or Aria is a knave\". \"Grace is a knave or Ella is a knight,\" Ella mentioned. Victoria expressed that Ella is a knight or Owen is a knave. In Luke's words: \"Grace is a knight if and only if Aria is a knight\". \"Penelope is a knight,\" Owen claimed. \"Victoria is a knave and Owen is a knave,\" Jack declared. So who is a knight and who is a knave?", "names": ["Grace", "Aria", "Penelope", "Ella", "Victoria", "Luke", "Owen", "Jack"], "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": "Grace is a knave, Aria is a knave, Penelope is a knight, Ella is a knight, Victoria is a knight, Luke is a knight, Owen is a knight, and Jack is a knave.", "solution_text_format": "(1) Grace is a knave\n(2) Aria is a knave\n(3) Penelope is a knight\n(4) Ella is a knight\n(5) Victoria is a knight\n(6) Luke is a knight\n(7) Owen 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 Grace is a knight. No contradiction is found in their claim that Victoria is a knave and Owen is a knight.", "Victoria cannot be a knight, because this would contradict the claim of Grace that Victoria is a knave and Owen is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Ella is a knight or Owen is a knave.", "Ella cannot be a knight, because this would contradict the false claim of Victoria that Ella is a knight or Owen is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Grace is a knave or Ella is a knight.", "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 Grace is a knight or Aria is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Luke is a knight if and only if Owen is a knave.", "Luke cannot be a knight, because this would contradict the claim of Aria that Luke is a knight if and only if Owen is a knave.", "Luke cannot be a knave, because this would contradict the false claim of their own that Grace is a knight if and only if Aria is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Luke is a knight if and only if Owen is a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that Grace is a knight if and only if Aria is a knight.", "Luke cannot be a knave, because this would contradict the false claim of Aria that Luke is a knight if and only if Owen is a knave.", "We have exhausted all possibilities for Luke and Aria, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the false claim of their own that Grace is a knight or Aria is a knave.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the claim of Grace that Victoria is a knave and Owen is a knight.", "We have exhausted all possibilities for Owen, Ella, and Victoria, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Victoria is a knave and Owen is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Ella is a knight or Owen is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Grace is a knave or Ella is a knight.", "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 Grace is a knight or Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of Penelope that Grace is a knight or Aria is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Luke is a knight if and only if Owen is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Grace 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 Victoria is a knave and Owen is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Victoria is a knave and Owen is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('telling-truth', 6)), ('<=>', ('telling-truth', 5), ('lying', 6)), ('or', ('telling-truth', 0), ('lying', 1)), ('or', ('lying', 0), ('telling-truth', 3)), ('or', ('telling-truth', 3), ('lying', 6)), ('<=>', ('telling-truth', 0), ('telling-truth', 1)), ('telling-truth', 2), ('and', ('lying', 4), ('lying', 6)))", "index": 46}
-{"quiz": "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, Noah, Alexander, Aiden, Scarlett, Charlotte, Emily, and Aria. Owen told you that Scarlett is a knave and Aiden is a knight. Noah commented, \"Charlotte is a knight or Aria is a knight\". Alexander noted, \"If Scarlett is a knave then Aiden is a knave\". Aiden remarked, \"Noah is a knave or Scarlett is a knave\". As Scarlett put it, \"Aiden is a knight and Noah is a knave\". Charlotte stated, \"If Owen is a knight then Scarlett is a knave\". Emily asserted: \"Aiden is a knight\". Aria said that Aiden is a knave and Charlotte is a knight. So who is a knight and who is a knave?", "names": ["Owen", "Noah", "Alexander", "Aiden", "Scarlett", "Charlotte", "Emily", "Aria"], "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": "Owen is a knight, Noah is a knight, Alexander is a knave, Aiden is a knight, Scarlett is a knave, Charlotte is a knight, Emily is a knight, and Aria is a knave.", "solution_text_format": "(1) Owen is a knight\n(2) Noah is a knight\n(3) Alexander is a knave\n(4) Aiden is a knight\n(5) Scarlett is a knave\n(6) Charlotte is a knight\n(7) Emily 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 Owen is a knight. No contradiction is found in their claim that Scarlett is a knave and Aiden is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of Owen that Scarlett is a knave and Aiden is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Aiden is a knight and Noah is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Noah is a knave or Scarlett is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Charlotte is a knight or Aria is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Owen is a knight then Scarlett is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Aiden is a knave and Charlotte is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Aiden is a knave and Charlotte is a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that If Scarlett is a knave then Aiden is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that If Scarlett is a knave then Aiden is a knave.", "Assume Emily 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', ('lying', 4), ('telling-truth', 3)), ('or', ('telling-truth', 5), ('telling-truth', 7)), ('->', ('lying', 4), ('lying', 3)), ('or', ('lying', 1), ('lying', 4)), ('and', ('telling-truth', 3), ('lying', 1)), ('->', ('telling-truth', 0), ('lying', 4)), ('telling-truth', 3), ('and', ('lying', 3), ('telling-truth', 5)))", "index": 47}
-{"quiz": "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, Aurora, Harper, Grace, Jack, Evelyn, Olivia, and Samuel. According to Henry, \"Jack is a knave and Olivia is a knave\". Aurora commented, \"If Evelyn is a knave then Harper is a knight\". Harper was heard saying, \"Olivia is a knight or Olivia is a knave\". In a statement by Grace: \"If Grace is a knight then Aurora is a knight\". In Jack's words: \"If Grace is a knight then Evelyn is a knight\". \"If Grace is a knave then Aurora is a knave\" - Evelyn. In a statement by Olivia: \"If Evelyn is a knight then Evelyn is a knave\". Samuel stated, \"Harper is not a knave\". So who is a knight and who is a knave?", "names": ["Henry", "Aurora", "Harper", "Grace", "Jack", "Evelyn", "Olivia", "Samuel"], "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": "Henry is a knave, Aurora is a knight, Harper is a knight, Grace is a knight, Jack is a knight, Evelyn is a knight, Olivia is a knave, and Samuel is a knight.", "solution_text_format": "(1) Henry is a knave\n(2) Aurora is a knight\n(3) Harper is a knight\n(4) Grace is a knight\n(5) Jack is a knight\n(6) Evelyn is a knight\n(7) Olivia 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 Henry is a knight. No contradiction is found in their claim that Jack is a knave and Olivia is a knave.", "Jack cannot be a knight, because this would contradict the claim of Henry that Jack is a knave and Olivia is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that If Grace is a knight then Evelyn is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that If Grace is a knight then Aurora is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that If Evelyn is a knave then Harper is a knight.", "Evelyn cannot be a knight, because this would contradict the false claim of Jack that If Grace is a knight then Evelyn is a knight.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that If Grace is a knave then Aurora is a knave.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the claim of Grace that If Grace is a knight then Aurora is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Grace.", "Grace cannot be a knave, because this would contradict the false claim of their own that If Grace is a knight then Aurora is a knight.", "We have exhausted all possibilities for Grace and Jack, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Jack is a knave and Olivia is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that If Grace is a knight then Evelyn is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that If Grace is a knight then Aurora is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that If Evelyn is a knave then Harper is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Grace is a knave then Aurora is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Olivia is a knight or Olivia is a knave.", "Olivia 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 Olivia is a knave. No contradiction is found in their false claim that If Evelyn is a knight then Evelyn is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Harper is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('lying', 6)), ('->', ('lying', 5), ('telling-truth', 2)), ('or', ('telling-truth', 6), ('lying', 6)), ('->', ('telling-truth', 3), ('telling-truth', 1)), ('->', ('telling-truth', 3), ('telling-truth', 5)), ('->', ('lying', 3), ('lying', 1)), ('->', ('telling-truth', 5), ('lying', 5)), ('not', ('lying', 2)))", "index": 48}
-{"quiz": "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, Jacob, Grace, Owen, Liam, Isabella, Mia, and Amelia. Ethan remarked, \"If Owen is a knight then Mia is a knight\". According to Jacob, \"If Liam is a knave then Amelia is a knight\". Grace said that Isabella is a knave if and only if Jacob is a knight. Owen remarked, \"Amelia is a knave or Jacob is a knight\". \"Amelia is a knight,\" Liam claimed. Isabella was heard saying, \"Mia is a knave\". Mia said, \"If Owen is a knave then Ethan is a knave.\" \"Mia is not a knave,\" Amelia declared. So who is a knight and who is a knave?", "names": ["Ethan", "Jacob", "Grace", "Owen", "Liam", "Isabella", "Mia", "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": "Ethan is a knight, Jacob is a knight, Grace is a knight, Owen is a knight, Liam is a knight, Isabella is a knave, Mia is a knight, and Amelia is a knight.", "solution_text_format": "(1) Ethan is a knight\n(2) Jacob is a knight\n(3) Grace is a knight\n(4) Owen is a knight\n(5) Liam is a knight\n(6) Isabella is a knave\n(7) Mia 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 Ethan is a knight. No contradiction is found in their claim that If Owen is a knight then Mia is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Amelia is a knave or Jacob is a knight.", "Assume Amelia 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 Owen is a knave then Ethan is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that If Liam is a knave then Amelia is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Amelia is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Isabella is a knave if and only if Jacob is a knight.", "Isabella cannot be a knight, because this would contradict the claim of Grace that Isabella is a knave if and only if Jacob is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Mia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('telling-truth', 6)), ('->', ('lying', 4), ('telling-truth', 7)), ('<=>', ('lying', 5), ('telling-truth', 1)), ('or', ('lying', 7), ('telling-truth', 1)), ('telling-truth', 7), ('lying', 6), ('->', ('lying', 3), ('lying', 0)), ('not', ('lying', 6)))", "index": 49}
-{"quiz": "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, Alexander, Victoria, Mia, Ethan, Noah, and Charlotte. In Sophia's words: \"Charlotte is a knight\". William asserted: \"Sophia is a knight or Mia is a knight\". According to Alexander, \"Ethan is not a knave\". Victoria expressed that Noah is a knight and Mia is a knave. \"If William is a knave then Ethan is a knave,\" Mia claimed. As Ethan put it, \"Noah is a knave or Alexander is a knave\". \"If Victoria is a knave then Noah is a knight\" - Noah. According to Charlotte, \"Mia is a knight if and only if William is a knight\". So who is a knight and who is a knave?", "names": ["Sophia", "William", "Alexander", "Victoria", "Mia", "Ethan", "Noah", "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, true, false, true], "solution_text": "Sophia is a knight, William is a knight, Alexander is a knight, Victoria is a knave, Mia is a knight, Ethan is a knight, Noah is a knave, and Charlotte is a knight.", "solution_text_format": "(1) Sophia is a knight\n(2) William is a knight\n(3) Alexander is a knight\n(4) Victoria is a knave\n(5) Mia is a knight\n(6) Ethan is a knight\n(7) Noah 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 Sophia 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 knight if and only if William is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that If William is a knave then Ethan is a knave.", "Assume William is a knight. No contradiction is found in their claim that Sophia is a knight or Mia is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Noah is a knave or Alexander is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that If Victoria is a knave then Noah is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Noah is a knight and Mia is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Noah is a knight and Mia is a knave.", "Alexander cannot be a knight, because this would contradict the claim of Ethan that Noah is a knave or Alexander is a knave.", "Alexander 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 Alexander and Victoria, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that If Victoria is a knave then Noah is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Noah is a knight and Mia is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Noah is a knight and Mia is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Ethan is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 7), ('or', ('telling-truth', 0), ('telling-truth', 4)), ('not', ('lying', 5)), ('and', ('telling-truth', 6), ('lying', 4)), ('->', ('lying', 1), ('lying', 5)), ('or', ('lying', 6), ('lying', 2)), ('->', ('lying', 3), ('telling-truth', 6)), ('<=>', ('telling-truth', 4), ('telling-truth', 1)))", "index": 50}
-{"quiz": "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, Aria, Michael, Olivia, Noah, James, Liam, and Elizabeth. Ava told you that Aria is not a knight. Aria remarked, \"Liam is a knight\". Michael said, \"If James is a knight then Elizabeth is a knight.\" Olivia was heard saying, \"Michael is a knight or Liam is a knave\". In Noah's words: \"James is a knave and Michael is a knight\". In James's words: \"Elizabeth is a knight or Liam is a knight\". As Liam put it, \"Noah is a knight\". According to Elizabeth, \"Ava is a knight or James is a knight\". So who is a knight and who is a knave?", "names": ["Ava", "Aria", "Michael", "Olivia", "Noah", "James", "Liam", "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, false, true], "solution_text": "Ava is a knight, Aria is a knave, Michael is a knight, Olivia is a knight, Noah is a knave, James is a knight, Liam is a knave, and Elizabeth is a knight.", "solution_text_format": "(1) Ava is a knight\n(2) Aria is a knave\n(3) Michael is a knight\n(4) Olivia is a knight\n(5) Noah is a knave\n(6) James is a knight\n(7) Liam 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 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.", "Assume Aria 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 Aria that Liam is a knight.", "Assume Liam 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 Liam that Noah is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that James is a knave and Michael is a knight.", "Assume James is a knight. No contradiction is found in their claim that Elizabeth is a knight or Liam is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Ava is a knight or James is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that If James is a knight then Elizabeth is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Michael is a knight or Liam is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 1)), ('telling-truth', 6), ('->', ('telling-truth', 5), ('telling-truth', 7)), ('or', ('telling-truth', 2), ('lying', 6)), ('and', ('lying', 5), ('telling-truth', 2)), ('or', ('telling-truth', 7), ('telling-truth', 6)), ('telling-truth', 4), ('or', ('telling-truth', 0), ('telling-truth', 5)))", "index": 51}
-{"quiz": "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, Ethan, Michael, Jack, Lily, Olivia, Noah, and Logan. Oliver told you that Jack is a knave if and only if Olivia is a knave. Ethan told you that Lily is not a knave. As Michael put it, \"Ethan is a knight and Logan is a knave\". In Jack's words: \"Oliver is a knave if and only if Noah is a knight\". \"If Logan is a knave then Logan is a knight,\" Lily mentioned. \"Logan is not a knight\" - Olivia. In a statement by Noah: \"Jack is a knight and Oliver is a knight\". Logan noted, \"Oliver is a knight and Olivia is a knave\". So who is a knight and who is a knave?", "names": ["Oliver", "Ethan", "Michael", "Jack", "Lily", "Olivia", "Noah", "Logan"], "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": "Oliver is a knave, Ethan is a knave, Michael is a knave, Jack is a knave, Lily is a knave, Olivia is a knight, Noah is a knave, and Logan is a knave.", "solution_text_format": "(1) Oliver is a knave\n(2) Ethan is a knave\n(3) Michael is a knave\n(4) Jack is a knave\n(5) Lily is a knave\n(6) Olivia is a knight\n(7) Noah 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 Oliver is a knight. No contradiction is found in their claim that Jack is a knave if and only if Olivia is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Oliver is a knave if and only if Noah is a knight.", "Noah cannot be a knight, because this would contradict the claim of Jack that Oliver 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 Jack is a knight and Oliver is a knight.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Oliver is a knave if and only if Noah is a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that Jack is a knight and Oliver is a knight.", "Noah cannot be a knave, because this would contradict the false claim of Jack that Oliver is a knave if and only if Noah is a knight.", "We have exhausted all possibilities for Noah and Jack, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Jack is a knave if and only if Olivia is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Oliver is a knave if and only if Noah is a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that Jack is a knight and Oliver is a knight.", "Noah cannot be a knave, because this would contradict the claim of Jack that Oliver 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 Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Oliver is a knave if and only if Noah is a knight.", "Noah cannot be a knight, because this would contradict the false claim of Jack that Oliver 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 Jack is a knight and Oliver is a knight.", "Assume Olivia 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 Olivia that Logan is not a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Oliver is a knight and Olivia is a knave.", "Assume Ethan 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 Logan is a knave then Logan is a knight.", "Lily cannot be a knave, because this would contradict the claim of Ethan that Lily is not a knave.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Ethan.", "Assume Ethan 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 Ethan that Lily is not a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that If Logan is a knave then Logan is a knight.", "Michael cannot be a knight, because this would contradict the claim of their own that Ethan is a knight and Logan is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Ethan is a knight and Logan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('lying', 5)), ('not', ('lying', 4)), ('and', ('telling-truth', 1), ('lying', 7)), ('<=>', ('lying', 0), ('telling-truth', 6)), ('->', ('lying', 7), ('telling-truth', 7)), ('not', ('telling-truth', 7)), ('and', ('telling-truth', 3), ('telling-truth', 0)), ('and', ('telling-truth', 0), ('lying', 5)))", "index": 52}
-{"quiz": "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, Isabella, Liam, Lily, Logan, Jack, Grace, and Emma. According to Daniel, \"Logan is a knave\". As Isabella put it, \"Emma is a knave and Logan is a knight\". Liam asserted: \"If Logan is a knave then Daniel is a knave\". Lily commented, \"If Logan is a knave then Liam is a knave\". According to Logan, \"Jack is a knave\". As Jack put it, \"Lily is not a knave\". Grace said, \"If Emma is a knave then Logan is a knave.\" Emma noted, \"If Lily is a knave then Emma is a knight\". So who is a knight and who is a knave?", "names": ["Daniel", "Isabella", "Liam", "Lily", "Logan", "Jack", "Grace", "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, true], "solution_text": "Daniel is a knight, Isabella is a knave, Liam is a knave, Lily is a knight, Logan is a knave, Jack is a knight, Grace is a knight, and Emma is a knight.", "solution_text_format": "(1) Daniel is a knight\n(2) Isabella is a knave\n(3) Liam is a knave\n(4) Lily is a knight\n(5) Logan is a knave\n(6) Jack is a knight\n(7) Grace 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 Daniel 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 Daniel that Logan is a knave.", "Assume Logan 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 Lily is not a knave.", "Assume Lily is a knight. No contradiction is found in their claim that If Logan is a knave then Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that If Logan is a knave then Daniel is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that If Logan is a knave then Daniel is a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that Emma is a knave and Logan is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Emma is a knave and Logan is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If Lily is a knave then Emma is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that If Emma is a knave then Logan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('and', ('lying', 7), ('telling-truth', 4)), ('->', ('lying', 4), ('lying', 0)), ('->', ('lying', 4), ('lying', 2)), ('lying', 5), ('not', ('lying', 3)), ('->', ('lying', 7), ('lying', 4)), ('->', ('lying', 3), ('telling-truth', 7)))", "index": 53}
-{"quiz": "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, David, Ethan, Riley, Sofia, Emily, Lucas, and Liam. Jacob expressed that Riley is a knave. David noted, \"Riley is a knight and Riley is a knave\". Ethan noted, \"Riley is a knight if and only if Lucas is a knight\". Riley said, \"David is a knight and Ethan is a knight.\" Sofia told you that Liam is not a knave. Emily noted, \"If Jacob is a knight then Sofia is a knave\". In a statement by Lucas: \"Jacob is a knight if and only if Riley is a knight\". Liam commented, \"David is a knight and Riley is a knight\". So who is a knight and who is a knave?", "names": ["Jacob", "David", "Ethan", "Riley", "Sofia", "Emily", "Lucas", "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, true, false, false], "solution_text": "Jacob is a knight, David is a knave, Ethan is a knight, Riley is a knave, Sofia is a knave, Emily is a knight, Lucas is a knave, and Liam is a knave.", "solution_text_format": "(1) Jacob is a knight\n(2) David is a knave\n(3) Ethan is a knight\n(4) Riley is a knave\n(5) Sofia is a knave\n(6) Emily is a knight\n(7) Lucas 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 Jacob 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 Jacob that Riley is a knave.", "Assume Riley 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 Riley is a knight and Riley is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Riley is a knight and Riley is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Riley is a knight if and only if Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the claim of Ethan that Riley is a knight if and only if Lucas is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Jacob is a knight if and only if Riley is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Liam is not a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that David is a knight and Riley is a knight.", "Liam cannot be a knave, because this would contradict the claim of Sofia that Liam is not a knave.", "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 not a knave.", "Liam cannot be a knight, because this would contradict the false claim of Sofia that Liam is not a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that David is a knight and Riley is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that If Jacob is a knight then Sofia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('and', ('telling-truth', 3), ('lying', 3)), ('<=>', ('telling-truth', 3), ('telling-truth', 6)), ('and', ('telling-truth', 1), ('telling-truth', 2)), ('not', ('lying', 7)), ('->', ('telling-truth', 0), ('lying', 4)), ('<=>', ('telling-truth', 0), ('telling-truth', 3)), ('and', ('telling-truth', 1), ('telling-truth', 3)))", "index": 54}
-{"quiz": "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, Olivia, Liam, Aiden, Jacob, Alexander, and Matthew. Sophia told you that If Liam is a knave then Alexander is a knight. \"If Liam is a knight then Alexander is a knave\" - Victoria. Olivia expressed that If Liam is a knight then Jacob is a knave. \"Alexander is a knave and Olivia is a knight,\" Liam declared. Aiden told you that Jacob is a knave or Sophia is a knight. In a statement by Jacob: \"Sophia is a knave\". As Alexander put it, \"Olivia is a knight\". In Matthew's words: \"Jacob is a knave\". So who is a knight and who is a knave?", "names": ["Sophia", "Victoria", "Olivia", "Liam", "Aiden", "Jacob", "Alexander", "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, false, true, true], "solution_text": "Sophia is a knight, Victoria is a knight, Olivia is a knight, Liam is a knave, Aiden is a knight, Jacob is a knave, Alexander is a knight, and Matthew is a knight.", "solution_text_format": "(1) Sophia is a knight\n(2) Victoria is a knight\n(3) Olivia is a knight\n(4) Liam is a knave\n(5) Aiden is a knight\n(6) Jacob is a knave\n(7) Alexander 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 Sophia is a knight. No contradiction is found in their claim that If Liam is a knave then Alexander is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Alexander is a knave and Olivia is a knight.", "Alexander cannot be a knight, because this would contradict the claim of Liam that Alexander is a knave and Olivia is a knight.", "Assume Alexander 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 false claim of Alexander that Olivia is a knight.", "Olivia cannot be a knave, because this would contradict the claim of Liam that Alexander is a knave and Olivia is a knight.", "We have exhausted all possibilities for Olivia and 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 knave and Olivia is a knight.", "Assume Alexander 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 If Liam is a knight then Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of their own that Sophia is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Sophia is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that If Liam is a knight then Alexander is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Jacob is a knave or Sophia is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Jacob is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('telling-truth', 6)), ('->', ('telling-truth', 3), ('lying', 6)), ('->', ('telling-truth', 3), ('lying', 5)), ('and', ('lying', 6), ('telling-truth', 2)), ('or', ('lying', 5), ('telling-truth', 0)), ('lying', 0), ('telling-truth', 2), ('lying', 5))", "index": 55}
-{"quiz": "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, Isabella, Jacob, Aurora, Logan, Oliver, and Michael. Avery was heard saying, \"Aurora is a knight and Oliver is a knave\". Owen expressed that Jacob is a knave. Isabella told you that Owen is a knight and Aurora is a knave. Jacob told you that Logan is a knight or Oliver is a knave. Aurora stated, \"Logan is a knight if and only if Avery is a knight\". Logan noted, \"Jacob is not a knave\". Oliver remarked, \"Jacob is not a knave\". Michael said, \"If Avery is a knight then Owen is a knave.\" So who is a knight and who is a knave?", "names": ["Avery", "Owen", "Isabella", "Jacob", "Aurora", "Logan", "Oliver", "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, true, true, true], "solution_text": "Avery is a knave, Owen is a knave, Isabella is a knave, Jacob is a knight, Aurora is a knave, Logan is a knight, Oliver is a knight, and Michael is a knight.", "solution_text_format": "(1) Avery is a knave\n(2) Owen is a knave\n(3) Isabella is a knave\n(4) Jacob is a knight\n(5) Aurora is a knave\n(6) Logan is a knight\n(7) Oliver 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 Aurora is a knight and Oliver is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Logan is a knight if and only if Avery is a knight.", "Assume Logan 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 Logan is a knight or Oliver is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Avery that Aurora is a knight and Oliver is a knave.", "Oliver cannot be a knave, because this would contradict the false claim of their own that Jacob 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 false claim of their own that Logan is a knight or Oliver is a knave.", "We have exhausted all possibilities for Jacob, 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 if and only if Avery is a knight.", "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 claim of Avery that Aurora is a knight and Oliver is a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Aurora is a knight and Oliver is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Logan is a knight if and only if Avery is a knight.", "Logan cannot be a knight, because this would contradict the claim of Aurora that Logan is a knight if and only if Avery is a knight.", "Assume Logan 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 Logan that Jacob is not a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Logan is a knight or Oliver is a knave.", "Oliver cannot be a knight, because this would contradict the claim of their own that Jacob is not a knave.", "Oliver cannot be a knave, because this would contradict the false claim of Avery that Aurora is a knight and Oliver is a knave.", "We have exhausted all possibilities for Oliver, Jacob, and 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 a knight if and only if Avery is a knight.", "Assume Logan 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 Logan is a knight or Oliver is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Jacob is not a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Jacob is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Jacob is a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that Owen is a knight and Aurora is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Owen is a knight and Aurora is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that If Avery is a knight then Owen is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 4), ('lying', 6)), ('lying', 3), ('and', ('telling-truth', 1), ('lying', 4)), ('or', ('telling-truth', 5), ('lying', 6)), ('<=>', ('telling-truth', 5), ('telling-truth', 0)), ('not', ('lying', 3)), ('not', ('lying', 3)), ('->', ('telling-truth', 0), ('lying', 1)))", "index": 56}
-{"quiz": "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, Lily, Daniel, Sofia, James, Charlotte, Logan, and Ella. Victoria was heard saying, \"If Daniel is a knave then Lily is a knave\". Lily commented, \"Daniel is a knight\". Daniel noted, \"Victoria is a knight\". In a statement by Sofia: \"If Victoria is a knight then Lily is a knave\". James was heard saying, \"Lily is a knave\". Charlotte asserted: \"James is a knave and Lily is a knight\". In Logan's words: \"Sofia is a knight or Daniel is a knight\". In Ella's words: \"Logan is a knave\". So who is a knight and who is a knave?", "names": ["Victoria", "Lily", "Daniel", "Sofia", "James", "Charlotte", "Logan", "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, true, false], "solution_text": "Victoria is a knight, Lily is a knight, Daniel is a knight, Sofia is a knave, James is a knave, Charlotte is a knight, Logan is a knight, and Ella is a knave.", "solution_text_format": "(1) Victoria is a knight\n(2) Lily is a knight\n(3) Daniel is a knight\n(4) Sofia is a knave\n(5) James is a knave\n(6) Charlotte is a knight\n(7) Logan 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 Victoria is a knight. No contradiction is found in their claim that If Daniel is a knave then Lily is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Victoria is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Daniel is a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that If Victoria is a knight then Lily is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that If Victoria is a knight then Lily is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Lily is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Lily is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that James is a knave and Lily is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Sofia is a knight or Daniel is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Logan is a knave.", "Assume Ella 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": "(('->', ('lying', 2), ('lying', 1)), ('telling-truth', 2), ('telling-truth', 0), ('->', ('telling-truth', 0), ('lying', 1)), ('lying', 1), ('and', ('lying', 4), ('telling-truth', 1)), ('or', ('telling-truth', 3), ('telling-truth', 2)), ('lying', 6))", "index": 57}
-{"quiz": "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, Aiden, Olivia, Avery, Daniel, Grace, Scarlett, and Isabella. Henry noted, \"Daniel is not a knight\". Aiden commented, \"Scarlett is a knave or Aiden is a knight\". Olivia expressed that Daniel is a knight if and only if Aiden is a knight. Avery remarked, \"Henry is a knight or Aiden is a knave\". \"Aiden is a knight\" - Daniel. Grace commented, \"Daniel is not a knave\". Scarlett told you that Avery is a knave. In Isabella's words: \"Olivia is a knight or Aiden is a knave\". So who is a knight and who is a knave?", "names": ["Henry", "Aiden", "Olivia", "Avery", "Daniel", "Grace", "Scarlett", "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, true, true, true], "solution_text": "Henry is a knave, Aiden is a knight, Olivia is a knight, Avery is a knave, Daniel is a knight, Grace is a knight, Scarlett is a knight, and Isabella is a knight.", "solution_text_format": "(1) Henry is a knave\n(2) Aiden is a knight\n(3) Olivia is a knight\n(4) Avery is a knave\n(5) Daniel is a knight\n(6) Grace is a knight\n(7) Scarlett 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 Henry 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 Henry that Daniel is not a knight.", "Assume Daniel 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 Daniel that Aiden is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Scarlett is a knave or Aiden is a knight.", "Assume Scarlett 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 Scarlett that Avery is a knave.", "Avery cannot be a knave, because this would contradict the false claim of their own that Henry is a knight or Aiden is a knave.", "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 Aiden that Scarlett is a knave or Aiden is a knight.", "We have exhausted all possibilities for Scarlett, Aiden, and Daniel, so let us go back and reconsider Henry.", "Assume Henry 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 Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Scarlett is a knave or Aiden is a knight.", "Assume Scarlett 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 their own that Henry is a knight or Aiden is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Henry is a knight or Aiden is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Daniel is a knight if and only if Aiden is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Daniel is not a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Olivia is a knight or Aiden is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 4)), ('or', ('lying', 6), ('telling-truth', 1)), ('<=>', ('telling-truth', 4), ('telling-truth', 1)), ('or', ('telling-truth', 0), ('lying', 1)), ('telling-truth', 1), ('not', ('lying', 4)), ('lying', 3), ('or', ('telling-truth', 2), ('lying', 1)))", "index": 58}
-{"quiz": "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, James, Joseph, Mia, Samuel, Lily, Henry, and Mason. Matthew commented, \"Samuel is a knight or Matthew is a knight\". James asserted: \"Mia is a knave if and only if Matthew is a knave\". As Joseph put it, \"If Lily is a knave then Samuel is a knight\". \"Lily is a knight and James is a knight,\" Mia claimed. \"If Mia is a knight then Mia is a knave,\" Samuel mentioned. \"Mason is not a knave,\" Lily mentioned. Henry commented, \"If James is a knight then Joseph is a knight\". \"Samuel is not a knave\" - Mason. So who is a knight and who is a knave?", "names": ["Matthew", "James", "Joseph", "Mia", "Samuel", "Lily", "Henry", "Mason"], "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": "Matthew is a knight, James is a knave, Joseph is a knight, Mia is a knave, Samuel is a knight, Lily is a knight, Henry is a knight, and Mason is a knight.", "solution_text_format": "(1) Matthew is a knight\n(2) James is a knave\n(3) Joseph is a knight\n(4) Mia is a knave\n(5) Samuel is a knight\n(6) Lily is a knight\n(7) Henry 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 Matthew is a knight. No contradiction is found in their claim that Samuel is a knight or Matthew is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that If Mia is a knight then Mia is a knave.", "Mia cannot be a knight, because this would contradict the claim of Samuel that If Mia is a knight then Mia is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Lily is a knight and James is a knight.", "Assume Lily 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 Samuel is not a knave.", "James cannot be a knight, because this would contradict the claim of their own that Mia is a knave if and only if Matthew is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Mia is a knave if and only if Matthew is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that If Lily is a knave then Samuel is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that If James is a knight then Joseph is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('telling-truth', 0)), ('<=>', ('lying', 3), ('lying', 0)), ('->', ('lying', 5), ('telling-truth', 4)), ('and', ('telling-truth', 5), ('telling-truth', 1)), ('->', ('telling-truth', 3), ('lying', 3)), ('not', ('lying', 7)), ('->', ('telling-truth', 1), ('telling-truth', 2)), ('not', ('lying', 4)))", "index": 59}
-{"quiz": "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, Charlotte, Alexander, Aurora, Mason, Ella, Emma, and Avery. \"Charlotte is a knave if and only if Emma is a knave,\" Amelia declared. As Charlotte put it, \"Emma is a knave and Ella is a knight\". Alexander told you that Ella is a knave. Aurora remarked, \"Ella is a knave if and only if Amelia is a knight\". Mason was heard saying, \"Emma is a knight\". \"Charlotte is a knave,\" Ella mentioned. Emma said, \"Amelia is not a knight.\" In Avery's words: \"Mason is a knave if and only if Aurora is a knight\". So who is a knight and who is a knave?", "names": ["Amelia", "Charlotte", "Alexander", "Aurora", "Mason", "Ella", "Emma", "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": "Amelia is a knave, Charlotte is a knave, Alexander is a knave, Aurora is a knight, Mason is a knight, Ella is a knight, Emma is a knight, and Avery is a knave.", "solution_text_format": "(1) Amelia is a knave\n(2) Charlotte is a knave\n(3) Alexander is a knave\n(4) Aurora is a knight\n(5) Mason is a knight\n(6) Ella is a knight\n(7) Emma 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 Amelia is a knight. No contradiction is found in their claim that Charlotte is a knave if and only if Emma is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Emma is a knave and Ella is a knight.", "Emma cannot be a knight, because this would contradict the claim of Charlotte that Emma is a knave and Ella is a knight.", "Emma cannot be a knave, because this would contradict the claim of Amelia that Charlotte 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 Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Emma is a knave and Ella is a knight.", "Emma cannot be a knight, because this would contradict the claim of Amelia that Charlotte 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 Amelia is not a knight.", "Ella cannot be a knight, because this would contradict the false claim of Charlotte that Emma is a knave and Ella is a knight.", "Ella 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 Ella, Emma, and Charlotte, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Charlotte is a knave if and only if Emma is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Emma is a knave and Ella is a knight.", "Emma cannot be a knight, because this would contradict the false claim of Amelia that Charlotte is a knave if and only if Emma is a knave.", "Emma cannot be a knave, because this would contradict the false claim of their own that Amelia is not a knight.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Emma is a knave and Ella is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Amelia is not a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Charlotte 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.", "Assume Aurora is a knight. No contradiction is found in their claim that Ella is a knave if and only if Amelia is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Emma is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Mason is a knave if and only if Aurora is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Mason is a knave if and only if Aurora is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('lying', 6)), ('and', ('lying', 6), ('telling-truth', 5)), ('lying', 5), ('<=>', ('lying', 5), ('telling-truth', 0)), ('telling-truth', 6), ('lying', 1), ('not', ('telling-truth', 0)), ('<=>', ('lying', 4), ('telling-truth', 3)))", "index": 60}
-{"quiz": "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, James, Ava, Scarlett, Benjamin, Zoey, and Oliver. Emily asserted: \"Ava is not a knave\". Elizabeth told you that James is not a knave. In a statement by James: \"If James is a knight then Scarlett is a knight\". \"Oliver is a knight,\" Ava claimed. Scarlett told you that Oliver is a knight or Emily is a knave. Benjamin noted, \"If Oliver is a knave then Benjamin is a knight\". Zoey asserted: \"If James is a knave then James is a knight\". Oliver noted, \"Elizabeth is a knave if and only if James is a knave\". So who is a knight and who is a knave?", "names": ["Emily", "Elizabeth", "James", "Ava", "Scarlett", "Benjamin", "Zoey", "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": "Emily is a knight, Elizabeth is a knight, James is a knight, Ava is a knight, Scarlett is a knight, Benjamin is a knight, Zoey is a knight, and Oliver is a knight.", "solution_text_format": "(1) Emily is a knight\n(2) Elizabeth is a knight\n(3) James is a knight\n(4) Ava is a knight\n(5) Scarlett is a knight\n(6) Benjamin is a knight\n(7) Zoey 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 Emily 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 Oliver is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Elizabeth is a knave if and only if James is a knave.", "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 James is a knight then Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Oliver is a knight or Emily is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Oliver is a knave then Benjamin is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that If James is a knave then James is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 3)), ('not', ('lying', 2)), ('->', ('telling-truth', 2), ('telling-truth', 4)), ('telling-truth', 7), ('or', ('telling-truth', 7), ('lying', 0)), ('->', ('lying', 7), ('telling-truth', 5)), ('->', ('lying', 2), ('telling-truth', 2)), ('<=>', ('lying', 1), ('lying', 2)))", "index": 61}
-{"quiz": "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, Penelope, Daniel, Mia, Avery, Jacob, and Jackson. In Lucas's words: \"Mia is a knight or Mia is a knave\". Ella noted, \"If Jacob is a knave then Mia is a knave\". In Penelope's words: \"Mia is a knight and Penelope is a knight\". Daniel said that Penelope is a knight. \"Jackson is a knight and Lucas is a knight\" - Mia. In Avery's words: \"Mia is a knave if and only if Jackson is a knight\". Jacob asserted: \"Lucas is not a knight\". Jackson said, \"Lucas is a knave.\" So who is a knight and who is a knave?", "names": ["Lucas", "Ella", "Penelope", "Daniel", "Mia", "Avery", "Jacob", "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, false, false, false], "solution_text": "Lucas is a knight, Ella is a knight, Penelope is a knave, Daniel is a knave, Mia is a knave, Avery is a knave, Jacob is a knave, and Jackson is a knave.", "solution_text_format": "(1) Lucas is a knight\n(2) Ella is a knight\n(3) Penelope is a knave\n(4) Daniel is a knave\n(5) Mia is a knave\n(6) Avery is a knave\n(7) Jacob 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 Lucas is a knight. No contradiction is found in their claim that Mia is a knight or Mia is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Jackson is a knight and Lucas is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Lucas is a knave.", "Jackson cannot be a knave, because this would contradict the claim of Mia that Jackson is a knight and Lucas is a knight.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Jackson is a knight and Lucas is a knight.", "Jackson cannot be a knight, because this would contradict the false claim of Mia that Jackson is a knight and Lucas is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Lucas is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that If Jacob is a knave then Mia is a knave.", "Jacob cannot be a knight, because this would contradict the claim of their own that Lucas is not a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Lucas is not a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Mia is a knight and Penelope is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Mia is a knight and Penelope is a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that Penelope is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Penelope is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Mia is a knave if and only if Jackson is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Mia is a knave if and only if Jackson is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('lying', 4)), ('->', ('lying', 6), ('lying', 4)), ('and', ('telling-truth', 4), ('telling-truth', 2)), ('telling-truth', 2), ('and', ('telling-truth', 7), ('telling-truth', 0)), ('<=>', ('lying', 4), ('telling-truth', 7)), ('not', ('telling-truth', 0)), ('lying', 0))", "index": 62}
-{"quiz": "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, Jackson, Michael, Sofia, Noah, Abigail, and Aiden. Amelia said, \"Aiden is a knight if and only if Harper is a knight.\" Harper remarked, \"Michael is a knight\". \"Noah is a knave or Abigail is a knight\" - Jackson. \"Jackson is a knight if and only if Jackson is a knave,\" Michael declared. In Sofia's words: \"Noah is a knight or Harper is a knave\". Noah remarked, \"Harper is a knight\". Abigail was heard saying, \"Sofia is a knight or Noah is a knave\". In a statement by Aiden: \"If Abigail is a knave then Jackson is a knave\". So who is a knight and who is a knave?", "names": ["Amelia", "Harper", "Jackson", "Michael", "Sofia", "Noah", "Abigail", "Aiden"], "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": "Amelia is a knave, Harper is a knave, Jackson is a knight, Michael is a knave, Sofia is a knight, Noah is a knave, Abigail is a knight, and Aiden is a knight.", "solution_text_format": "(1) Amelia is a knave\n(2) Harper is a knave\n(3) Jackson is a knight\n(4) Michael is a knave\n(5) Sofia is a knight\n(6) Noah is a knave\n(7) Abigail 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 Aiden is a knight if and only if Harper is a knight.", "Assume Aiden 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 Sofia is a knight or Noah is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Noah is a knight or Harper is a knave.", "Assume Noah 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 Michael is a knight.", "Michael 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.", "Michael cannot be a knave, because this would contradict the claim of Harper that Michael is a knight.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the claim of Amelia that Aiden 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 Noah.", "Assume Noah 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 Sofia that Noah is a knight or Harper is a knave.", "Harper cannot be a knave, because this would contradict the claim of Amelia that Aiden is a knight if and only if Harper is a knight.", "We have exhausted all possibilities for Harper and Noah, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Noah is a knight or Harper is a knave.", "Noah cannot be a knight, because this would contradict the false claim of Sofia that Noah is a knight or Harper is a knave.", "Assume Noah 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 Noah that Harper is a knight.", "Harper cannot be a knave, because this would contradict the claim of Amelia that Aiden is a knight if and only if Harper is a knight.", "We have exhausted all possibilities for Harper, Noah, and Sofia, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Sofia is a knight or Noah is a knave.", "Sofia cannot be a knight, because this would contradict the false claim of Abigail that Sofia is a knight or Noah is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Noah is a knight or Harper is a knave.", "Noah cannot be a knight, because this would contradict the false claim of Sofia that Noah is a knight or Harper is a knave.", "Noah cannot be a knave, because this would contradict the false claim of Abigail that Sofia is a knight or Noah is a knave.", "We have exhausted all possibilities for Noah, Sofia, and Abigail, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that If Abigail is a knave then Jackson is a knave.", "Abigail cannot be a knight, because this would contradict the false claim of Aiden that If Abigail is a knave then Jackson is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Sofia is a knight or Noah is a knave.", "Sofia cannot be a knight, because this would contradict the false claim of Abigail that Sofia is a knight or Noah is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Noah is a knight or Harper is a knave.", "Noah cannot be a knight, because this would contradict the false claim of Sofia that Noah is a knight or Harper is a knave.", "Noah cannot be a knave, because this would contradict the false claim of Abigail that Sofia is a knight or Noah is a knave.", "We have exhausted all possibilities for Noah, Sofia, Abigail, and Aiden, 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 knight if and only if Harper is a knight.", "Assume Aiden 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 Sofia is a knight or Noah is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Noah is a knight or Harper is a knave.", "Assume Noah 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 false claim of Amelia that Aiden is a knight if and only if Harper is a knight.", "Harper cannot be a knave, because this would contradict the claim of Noah that Harper is a knight.", "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 a knight.", "Harper cannot be a knight, because this would contradict the false claim of Amelia that Aiden 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 Michael is a knight.", "Michael cannot be a knight, because this would contradict the false claim of Harper that Michael is a knight.", "Assume Michael 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 Jackson is a knight. No contradiction is found in their claim that Noah is a knave or Abigail is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 7), ('telling-truth', 1)), ('telling-truth', 3), ('or', ('lying', 5), ('telling-truth', 6)), ('<=>', ('telling-truth', 2), ('lying', 2)), ('or', ('telling-truth', 5), ('lying', 1)), ('telling-truth', 1), ('or', ('telling-truth', 4), ('lying', 5)), ('->', ('lying', 6), ('lying', 2)))", "index": 63}
-{"quiz": "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, Jacob, Amelia, Harper, Mia, William, Elizabeth, and Ella. \"If Jacob is a knave then Mia is a knight,\" Oliver declared. According to Jacob, \"Harper is a knight or Oliver is a knave\". Amelia asserted: \"Elizabeth is a knave or Mia is a knave\". In a statement by Harper: \"Jacob is a knave if and only if Elizabeth is a knave\". Mia asserted: \"William is a knave if and only if Oliver is a knave\". \"If Elizabeth is a knave then Elizabeth is a knight,\" William mentioned. Elizabeth expressed that If Oliver is a knight then Harper is a knight. Ella stated, \"Elizabeth is a knave if and only if Jacob is a knight\". So who is a knight and who is a knave?", "names": ["Oliver", "Jacob", "Amelia", "Harper", "Mia", "William", "Elizabeth", "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, true, false], "solution_text": "Oliver is a knight, Jacob is a knight, Amelia is a knave, Harper is a knight, Mia is a knight, William is a knight, Elizabeth is a knight, and Ella is a knave.", "solution_text_format": "(1) Oliver is a knight\n(2) Jacob is a knight\n(3) Amelia is a knave\n(4) Harper is a knight\n(5) Mia is a knight\n(6) William is a knight\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 Oliver is a knight. No contradiction is found in their claim that If Jacob is a knave then Mia is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Harper is a knight or Oliver is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Jacob is a knave if and only if Elizabeth is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Oliver is a knight then Harper is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that William is a knave if and only if Oliver is a knave.", "Assume William is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Elizabeth is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave or Mia is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Elizabeth is a knave or Mia is a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave if and only if Jacob is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Elizabeth is a knave if and only if Jacob is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 1), ('telling-truth', 4)), ('or', ('telling-truth', 3), ('lying', 0)), ('or', ('lying', 6), ('lying', 4)), ('<=>', ('lying', 1), ('lying', 6)), ('<=>', ('lying', 5), ('lying', 0)), ('->', ('lying', 6), ('telling-truth', 6)), ('->', ('telling-truth', 0), ('telling-truth', 3)), ('<=>', ('lying', 6), ('telling-truth', 1)))", "index": 64}
-{"quiz": "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, Ella, Jacob, Alexander, Evelyn, Lucas, Riley, and Luke. Noah said, \"If Lucas is a knave then Noah is a knight.\" Ella noted, \"Evelyn is a knight\". In a statement by Jacob: \"If Ella is a knave then Lucas is a knave\". According to Alexander, \"Evelyn is a knight or Jacob is a knight\". Evelyn noted, \"Luke is a knight or Luke is a knave\". Lucas said that Evelyn is a knight or Jacob is a knave. As Riley put it, \"Lucas is a knave or Ella is a knight\". \"Evelyn is a knave and Lucas is a knight,\" Luke claimed. So who is a knight and who is a knave?", "names": ["Noah", "Ella", "Jacob", "Alexander", "Evelyn", "Lucas", "Riley", "Luke"], "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": "Noah is a knight, Ella is a knight, Jacob is a knight, Alexander is a knight, Evelyn is a knight, Lucas is a knight, Riley is a knight, and Luke is a knave.", "solution_text_format": "(1) Noah is a knight\n(2) Ella is a knight\n(3) Jacob is a knight\n(4) Alexander is a knight\n(5) Evelyn is a knight\n(6) Lucas is a knight\n(7) Riley 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 If Lucas is a knave then Noah is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Evelyn is a knight or Jacob is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Luke is a knight or Luke is a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave and Lucas is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Evelyn is a knave and Lucas is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that If Ella is a knave then Lucas is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Evelyn is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Evelyn is a knight or Jacob is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Lucas is a knave or Ella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('telling-truth', 0)), ('telling-truth', 4), ('->', ('lying', 1), ('lying', 5)), ('or', ('telling-truth', 4), ('telling-truth', 2)), ('or', ('telling-truth', 7), ('lying', 7)), ('or', ('telling-truth', 4), ('lying', 2)), ('or', ('lying', 5), ('telling-truth', 1)), ('and', ('lying', 4), ('telling-truth', 5)))", "index": 65}
-{"quiz": "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, Ava, Benjamin, Matthew, Sofia, Lily, Noah, and Daniel. According to Emily, \"If Lily is a knave then Benjamin is a knave\". Ava told you that Benjamin is a knight. Benjamin expressed that Matthew is a knight and Lily is a knight. Matthew expressed that If Daniel is a knight then Lily is a knight. \"Daniel is a knight\" - Sofia. Lily expressed that If Daniel is a knight then Benjamin is a knave. Noah said that Daniel is not a knight. In Daniel's words: \"Benjamin is a knave\". So who is a knight and who is a knave?", "names": ["Emily", "Ava", "Benjamin", "Matthew", "Sofia", "Lily", "Noah", "Daniel"], "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": "Emily is a knight, Ava is a knight, Benjamin is a knight, Matthew is a knight, Sofia is a knave, Lily is a knight, Noah is a knight, and Daniel is a knave.", "solution_text_format": "(1) Emily is a knight\n(2) Ava is a knight\n(3) Benjamin is a knight\n(4) Matthew is a knight\n(5) Sofia is a knave\n(6) Lily is a knight\n(7) Noah 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 Emily is a knight. No contradiction is found in their claim that If Lily is a knave then Benjamin is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that If Daniel is a knight then Benjamin is a knave.", "Assume Daniel 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 Lily that If Daniel is a knight then Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Matthew is a knight and Lily is a knight.", "Matthew cannot be a knight, because this would contradict the false claim of Benjamin that Matthew is a knight and Lily is a knight.", "Matthew cannot be a knave, because this would contradict the false claim of their own that If Daniel is a knight then Lily is a knight.", "We have exhausted all possibilities for Matthew and Benjamin, so let us go back and reconsider Daniel.", "Assume Daniel 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 Matthew is a knight and Lily is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that If Daniel is a knight then Lily is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Benjamin is a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that Daniel is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Daniel is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Daniel is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('lying', 2)), ('telling-truth', 2), ('and', ('telling-truth', 3), ('telling-truth', 5)), ('->', ('telling-truth', 7), ('telling-truth', 5)), ('telling-truth', 7), ('->', ('telling-truth', 7), ('lying', 2)), ('not', ('telling-truth', 7)), ('lying', 2))", "index": 66}
-{"quiz": "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, Liam, Penelope, James, Avery, Riley, Ava, and William. Isabella commented, \"If William is a knave then Penelope is a knight\". \"If Riley is a knight then James is a knight,\" Liam claimed. In Penelope's words: \"Isabella is not a knave\". James stated, \"If James is a knight then Ava is a knave\". Avery told you that If Isabella is a knave then Avery is a knight. According to Riley, \"If Avery is a knight then James is a knight\". In Ava's words: \"Penelope is a knight if and only if Liam is a knave\". William told you that Avery is not a knight. So who is a knight and who is a knave?", "names": ["Isabella", "Liam", "Penelope", "James", "Avery", "Riley", "Ava", "William"], "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, Liam is a knight, Penelope is a knight, James is a knight, Avery is a knight, Riley is a knight, Ava is a knave, and William is a knave.", "solution_text_format": "(1) Isabella is a knight\n(2) Liam is a knight\n(3) Penelope is a knight\n(4) James is a knight\n(5) Avery is a knight\n(6) Riley is a knight\n(7) Ava 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 Isabella is a knight. No contradiction is found in their claim that If William is a knave then Penelope is a knight.", "Assume William 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 William that Avery is not a knight.", "Avery cannot be a knave, because this would contradict the false claim of their own that If Isabella is a knave then Avery is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider William.", "Assume William 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 If Isabella is a knave then Avery is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Isabella is not a knave.", "Assume Liam is a knight. No contradiction is found in their claim that If Riley is a knight then James is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that If Avery is a knight then James is a knight.", "Assume James is a knight. No contradiction is found in their claim that If James is a knight then Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of James that If James is a knight then Ava is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Penelope is a knight if and only if Liam is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 7), ('telling-truth', 2)), ('->', ('telling-truth', 5), ('telling-truth', 3)), ('not', ('lying', 0)), ('->', ('telling-truth', 3), ('lying', 6)), ('->', ('lying', 0), ('telling-truth', 4)), ('->', ('telling-truth', 4), ('telling-truth', 3)), ('<=>', ('telling-truth', 2), ('lying', 1)), ('not', ('telling-truth', 4)))", "index": 67}
-{"quiz": "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, Ava, Michael, Aria, Lily, Emily, James, and Sebastian. Jackson said, \"Sebastian is not a knave.\" Ava remarked, \"James is a knave or Emily is a knight\". Michael told you that If Aria is a knave then Sebastian is a knave. According to Aria, \"Michael is not a knight\". In Lily's words: \"James is a knight and Ava is a knave\". Emily remarked, \"If Ava is a knave then Emily is a knight\". \"If Jackson is a knight then James is a knight,\" James claimed. According to Sebastian, \"If Emily is a knave then James is a knave\". So who is a knight and who is a knave?", "names": ["Jackson", "Ava", "Michael", "Aria", "Lily", "Emily", "James", "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, false, true, false], "solution_text": "Jackson is a knave, Ava is a knave, Michael is a knight, Aria is a knave, Lily is a knight, Emily is a knave, James is a knight, and Sebastian is a knave.", "solution_text_format": "(1) Jackson is a knave\n(2) Ava is a knave\n(3) Michael is a knight\n(4) Aria is a knave\n(5) Lily is a knight\n(6) Emily is a knave\n(7) James 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 Jackson 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 Emily is a knave then James is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that If Ava is a knave then Emily is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that James is a knave or Emily is a knight.", "Assume James is a knight. No contradiction is found in their claim that If Jackson is a knight then James is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that If Aria is a knave then Sebastian is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Michael is not a knight.", "Aria cannot be a knave, because this would contradict the claim of Michael that If Aria is a knave then Sebastian is a knave.", "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 If Aria is a knave then Sebastian is a knave.", "Aria cannot be a knight, because this would contradict the false claim of Michael that If Aria is a knave then Sebastian is a knave.", "Aria 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 Aria and Michael, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that If Jackson is a knight then James is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that If Aria is a knave then Sebastian is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Michael is not a knight.", "Aria cannot be a knave, because this would contradict the claim of Michael that If Aria is a knave then Sebastian is a knave.", "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 If Aria is a knave then Sebastian is a knave.", "Aria cannot be a knight, because this would contradict the false claim of Michael that If Aria is a knave then Sebastian is a knave.", "Aria 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 Aria, Michael, and James, 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 knave or Emily 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 If Ava is a knave then Emily is a knight.", "Ava cannot be a knight, because this would contradict the false claim of Emily that If Ava is a knave then Emily is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that James is a knave or Emily is a knight.", "James cannot be a knight, because this would contradict the claim of Sebastian that If Emily is a knave then James is a knave.", "James cannot be a knave, because this would contradict the false claim of Ava that James is a knave or Emily is a knight.", "We have exhausted all possibilities for James, Ava, and Emily, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the claim of Jackson that Sebastian is not a knave.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Jackson.", "Assume Jackson 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 Jackson that Sebastian is not a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that If Emily is a knave then James is a knave.", "Emily cannot be a knight, because this would contradict the false claim of Sebastian that If Emily is a knave then James is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that If Ava is a knave then Emily is a knight.", "Ava cannot be a knight, because this would contradict the false claim of Emily that If Ava is a knave then Emily is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that James is a knave or Emily is a knight.", "Assume James is a knight. No contradiction is found in their claim that If Jackson is a knight then James is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that If Aria is a knave then Sebastian is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Michael is not a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Michael is not a knight.", "Assume Lily is a knight. No contradiction is found in their claim that James is a knight and Ava is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 7)), ('or', ('lying', 6), ('telling-truth', 5)), ('->', ('lying', 3), ('lying', 7)), ('not', ('telling-truth', 2)), ('and', ('telling-truth', 6), ('lying', 1)), ('->', ('lying', 1), ('telling-truth', 5)), ('->', ('telling-truth', 0), ('telling-truth', 6)), ('->', ('lying', 5), ('lying', 6)))", "index": 68}
-{"quiz": "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, Jacob, Jackson, Benjamin, Sophia, Ava, Ella, and Aiden. Isabella was heard saying, \"Benjamin is a knave and Jacob is a knave\". As Jacob put it, \"Sophia is a knight\". Jackson remarked, \"Ella is a knave or Sophia is a knight\". \"Sophia is a knave,\" Benjamin claimed. Sophia said, \"If Jackson is a knight then Aiden is a knave.\" Ava stated, \"Isabella is a knave or Jacob is a knave\". In Ella's words: \"If Ava is a knave then Jacob is a knave\". Aiden told you that Isabella is not a knave. So who is a knight and who is a knave?", "names": ["Isabella", "Jacob", "Jackson", "Benjamin", "Sophia", "Ava", "Ella", "Aiden"], "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, Jacob is a knight, Jackson is a knight, Benjamin is a knave, Sophia is a knight, Ava is a knight, Ella is a knight, and Aiden is a knave.", "solution_text_format": "(1) Isabella is a knave\n(2) Jacob is a knight\n(3) Jackson is a knight\n(4) Benjamin is a knave\n(5) Sophia is a knight\n(6) Ava is a knight\n(7) Ella is a knight\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 Isabella is a knight. No contradiction is found in their claim that Benjamin is a knave and Jacob is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Isabella that Benjamin is a knave and Jacob is a knave.", "Assume Benjamin 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 Jackson is a knight then Aiden is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Ella is a knave or Sophia is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that If Ava is a knave then Jacob is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Isabella is a knave or Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Isabella that Benjamin is a knave and Jacob is a knave.", "Jacob cannot be a knave, because this would contradict the false claim of their own that Sophia is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Isabella is a knave or Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Isabella that Benjamin is a knave and Jacob is a knave.", "Jacob cannot be a knave, because this would contradict the false claim of their own that Sophia is a knight.", "We have exhausted all possibilities for Jacob and Ava, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that If Ava is a knave then Jacob is a knave.", "Ava cannot be a knight, because this would contradict the false claim of Ella that If Ava is a knave then Jacob is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Isabella is a knave or Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Isabella that Benjamin is a knave and Jacob is a knave.", "Jacob cannot be a knave, because this would contradict the false claim of their own that Sophia is a knight.", "We have exhausted all possibilities for Jacob, Ava, and Ella, so let us go back and reconsider Jackson.", "Jackson cannot be a knave, because this would contradict the false claim of their own that Ella is a knave or Sophia is a knight.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the false claim of Benjamin that Sophia is a knave.", "We have exhausted all possibilities for Sophia and 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 knave and Jacob is a knave.", "Assume Benjamin 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 Benjamin that Sophia is a knave.", "Assume Sophia is a knave. No contradiction is found in their false 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 Ella is a knave or Sophia is a knight.", "Ella cannot be a knight, because this would contradict the claim of Jackson that Ella is a knave or Sophia is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that If Ava is a knave then Jacob is a knave.", "Ava cannot be a knight, because this would contradict the false claim of Ella that If Ava is a knave then Jacob is a knave.", "Ava cannot be a knave, because this would contradict the false claim of their own that Isabella is a knave or Jacob is a knave.", "We have exhausted all possibilities for Ava and Ella, so let us go back and reconsider Jackson.", "Jackson cannot be a knave, because this would contradict the false claim of Sophia that If Jackson is a knight then Aiden is a knave.", "We have exhausted all possibilities for Jackson and Sophia, so let us go back and reconsider Benjamin.", "Assume Benjamin 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 Jackson is a knight then Aiden is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Ella is a knave or Sophia is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that If Ava is a knave then Jacob is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Isabella is a knave or Jacob is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Sophia is a knight.", "Aiden cannot be a knight, because this would contradict the claim of Sophia that If Jackson is a knight then Aiden is a knave.", "Assume Aiden 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": "(('and', ('lying', 3), ('lying', 1)), ('telling-truth', 4), ('or', ('lying', 6), ('telling-truth', 4)), ('lying', 4), ('->', ('telling-truth', 2), ('lying', 7)), ('or', ('lying', 0), ('lying', 1)), ('->', ('lying', 5), ('lying', 1)), ('not', ('lying', 0)))", "index": 69}
-{"quiz": "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, Aurora, Grace, Oliver, Michael, Owen, and Liam. \"If Grace is a knave then Michael is a knight,\" Mia claimed. Joseph said, \"Aurora is a knight or Owen is a knight.\" In a statement by Aurora: \"Michael is a knave if and only if Mia is a knave\". Grace stated, \"Joseph is a knave if and only if Joseph is a knight\". \"Grace is a knave if and only if Liam is a knave,\" Oliver mentioned. Michael expressed that Aurora is not a knight. Owen expressed that Mia is a knight. In a statement by Liam: \"Grace is a knight if and only if Grace is a knave\". So who is a knight and who is a knave?", "names": ["Mia", "Joseph", "Aurora", "Grace", "Oliver", "Michael", "Owen", "Liam"], "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": "Mia is a knave, Joseph is a knight, Aurora is a knight, Grace is a knave, Oliver is a knight, Michael is a knave, Owen is a knave, and Liam is a knave.", "solution_text_format": "(1) Mia is a knave\n(2) Joseph is a knight\n(3) Aurora is a knight\n(4) Grace is a knave\n(5) Oliver is a knight\n(6) Michael is a knave\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 Mia is a knight. No contradiction is found in their claim that If Grace is a knave then Michael 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.", "Assume Joseph is a knight. No contradiction is found in their claim that Aurora is a knight or Owen is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Michael is a knave if and only if Mia is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Aurora is not a knight.", "Michael cannot be a knave, because this would contradict the claim of Mia that If Grace is a knave then Michael is a knight.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Michael is a knave if and only if Mia is a knave.", "Michael cannot be a knight, because this would contradict the false claim of Aurora that Michael is a knave if and only if Mia is a knave.", "Michael cannot be a knave, because this would contradict the claim of Mia that If Grace is a knave then Michael is a knight.", "We have exhausted all possibilities for Michael and Aurora, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Aurora is a knight or Owen is a knight.", "Aurora cannot be a knight, because this would contradict the false claim of Joseph that Aurora is a knight or Owen is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Michael is a knave if and only if Mia is a knave.", "Michael cannot be a knight, because this would contradict the false claim of Aurora that Michael is a knave if and only if Mia is a knave.", "Michael cannot be a knave, because this would contradict the claim of Mia that If Grace is a knave then Michael is a knight.", "We have exhausted all possibilities for Michael, Aurora, Joseph, and Grace, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that If Grace is a knave then Michael is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Mia that If Grace is a knave then Michael 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.", "Assume Joseph is a knight. No contradiction is found in their claim that Aurora is a knight or Owen is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Michael is a knave if and only if Mia is a knave.", "Michael cannot be a knight, because this would contradict the false claim of Mia that If Grace is a knave then Michael is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Aurora is not a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Mia is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Mia is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Grace is a knave if and only if Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of Oliver that Grace 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 Grace is a knight if and only if Grace is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('telling-truth', 5)), ('or', ('telling-truth', 2), ('telling-truth', 6)), ('<=>', ('lying', 5), ('lying', 0)), ('<=>', ('lying', 1), ('telling-truth', 1)), ('<=>', ('lying', 3), ('lying', 7)), ('not', ('telling-truth', 2)), ('telling-truth', 0), ('<=>', ('telling-truth', 3), ('lying', 3)))", "index": 70}
-{"quiz": "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, Benjamin, Noah, Lily, Sofia, Luke, and Michael. \"Noah is not a knight,\" Riley mentioned. \"Luke is a knave,\" James declared. Benjamin said, \"Michael is a knight.\" Noah noted, \"Riley is a knight and Sofia is a knave\". Lily stated, \"If James is a knave then Sofia is a knave\". \"If Michael is a knave then Michael is a knight,\" Sofia declared. \"Riley is a knight,\" Luke declared. In Michael's words: \"Sofia is a knave if and only if Lily is a knight\". So who is a knight and who is a knave?", "names": ["Riley", "James", "Benjamin", "Noah", "Lily", "Sofia", "Luke", "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": "Riley is a knight, James is a knave, Benjamin is a knight, Noah is a knave, Lily is a knave, Sofia is a knight, Luke is a knight, and Michael is a knight.", "solution_text_format": "(1) Riley is a knight\n(2) James is a knave\n(3) Benjamin is a knight\n(4) Noah is a knave\n(5) Lily is a knave\n(6) Sofia is a knight\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 Riley 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 Riley that Noah is not a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Riley is a knight and Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that If Michael is a knave then Michael is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Sofia 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 Sofia 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 James is a knave then Sofia is a knave.", "James cannot be a knight, because this would contradict the false claim of Lily that If James is a knave then Sofia is a knave.", "Assume James 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 Riley is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Michael is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 3)), ('lying', 6), ('telling-truth', 7), ('and', ('telling-truth', 0), ('lying', 5)), ('->', ('lying', 1), ('lying', 5)), ('->', ('lying', 7), ('telling-truth', 7)), ('telling-truth', 0), ('<=>', ('lying', 5), ('telling-truth', 4)))", "index": 71}
-{"quiz": "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, Sofia, Grace, Harper, Joseph, Noah, Victoria, and Matthew. Mia stated, \"Matthew is a knave if and only if Noah is a knight\". \"Joseph is a knight or Joseph is a knave\" - Sofia. Grace remarked, \"If Mia is a knight then Sofia is a knave\". Harper expressed that If Harper is a knight then Grace is a knight. Joseph commented, \"Grace is not a knight\". In a statement by Noah: \"Joseph is a knight and Noah is a knight\". As Victoria put it, \"Joseph is a knight and Noah is a knight\". \"Noah is a knight\" - Matthew. So who is a knight and who is a knave?", "names": ["Mia", "Sofia", "Grace", "Harper", "Joseph", "Noah", "Victoria", "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, false], "solution_text": "Mia is a knave, Sofia is a knight, Grace is a knight, Harper is a knight, Joseph is a knave, Noah is a knave, Victoria is a knave, and Matthew is a knave.", "solution_text_format": "(1) Mia is a knave\n(2) Sofia is a knight\n(3) Grace is a knight\n(4) Harper is a knight\n(5) Joseph is a knave\n(6) Noah is a knave\n(7) Victoria is a knave\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 Mia is a knight. No contradiction is found in their claim that Matthew is a knave if and only if Noah is a knight.", "Assume Matthew 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 Mia that Matthew is a knave if and only if Noah is a knight.", "Noah cannot be a knave, because this would contradict the claim of Matthew that Noah is a knight.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Matthew.", "Assume Matthew 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 Matthew that Noah is a knight.", "Noah cannot be a knave, because this would contradict the claim of Mia that Matthew is a knave if and only if Noah is a knight.", "We have exhausted all possibilities for Noah and Matthew, so let us go back and reconsider Mia.", "Assume Mia 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 Matthew 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 knight and Noah is a knight.", "Assume Joseph 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 Joseph that Grace is not a knight.", "Grace cannot be a knave, because this would contradict the false claim of their own that If Mia is a knight then Sofia is a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of Noah that Joseph is a knight and Noah is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the false claim of Mia that Matthew 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 Matthew.", "Assume Matthew 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 Matthew 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 Joseph is a knight and Noah is a knight.", "Assume Joseph 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 Joseph that Grace is not a knight.", "Grace cannot be a knave, because this would contradict the false claim of their own that If Mia is a knight then Sofia is a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Joseph.", "Assume Joseph 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 Mia is a knight then Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Joseph is a knight or Joseph is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that If Harper is a knight then Grace is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Joseph is a knight and Noah is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Joseph is a knight and Noah is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 7), ('telling-truth', 5)), ('or', ('telling-truth', 4), ('lying', 4)), ('->', ('telling-truth', 0), ('lying', 1)), ('->', ('telling-truth', 3), ('telling-truth', 2)), ('not', ('telling-truth', 2)), ('and', ('telling-truth', 4), ('telling-truth', 5)), ('and', ('telling-truth', 4), ('telling-truth', 5)), ('telling-truth', 5))", "index": 72}
-{"quiz": "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, Aurora, Daniel, Scarlett, Penelope, Mason, Jack, and Jacob. \"Jack is not a knight,\" Michael claimed. Aurora asserted: \"Michael is a knight if and only if Penelope is a knight\". Daniel was heard saying, \"Scarlett is not a knave\". In a statement by Scarlett: \"Daniel is a knight or Aurora is a knight\". \"Aurora is a knight or Michael is a knave,\" Penelope claimed. Mason said that If Aurora is a knight then Jack is a knave. Jack remarked, \"Aurora is a knave and Jacob is a knight\". \"Penelope is a knave,\" Jacob claimed. So who is a knight and who is a knave?", "names": ["Michael", "Aurora", "Daniel", "Scarlett", "Penelope", "Mason", "Jack", "Jacob"], "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": "Michael is a knight, Aurora is a knight, Daniel is a knight, Scarlett is a knight, Penelope is a knight, Mason is a knight, Jack is a knave, and Jacob is a knave.", "solution_text_format": "(1) Michael is a knight\n(2) Aurora is a knight\n(3) Daniel is a knight\n(4) Scarlett is a knight\n(5) Penelope is a knight\n(6) Mason is a knight\n(7) Jack 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 Michael 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 Michael that Jack is not a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Aurora is a knave and Jacob is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Michael is a knight if and only if Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Aurora is a knight or Michael is a knave.", "Jacob cannot be a knight, because this would contradict the claim of their own that Penelope is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Penelope is a knave.", "Assume Daniel 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 Daniel is a knight or Aurora is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that If Aurora is a knight then Jack is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 6)), ('<=>', ('telling-truth', 0), ('telling-truth', 4)), ('not', ('lying', 3)), ('or', ('telling-truth', 2), ('telling-truth', 1)), ('or', ('telling-truth', 1), ('lying', 0)), ('->', ('telling-truth', 1), ('lying', 6)), ('and', ('lying', 1), ('telling-truth', 7)), ('lying', 4))", "index": 73}
-{"quiz": "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, Riley, Oliver, Sofia, Elizabeth, Owen, and Samuel. \"Riley is a knave if and only if Elizabeth is a knave,\" Zoey claimed. \"Zoey is a knight,\" Emma claimed. \"Elizabeth is a knave if and only if Sofia is a knight,\" Riley mentioned. Oliver was heard saying, \"Sofia is not a knight\". As Sofia put it, \"If Sofia is a knight then Elizabeth is a knave\". Elizabeth was heard saying, \"Owen is a knight and Zoey is a knight\". Owen asserted: \"Sofia is a knave if and only if Zoey is a knight\". As Samuel put it, \"Sofia is a knave and Emma is a knight\". So who is a knight and who is a knave?", "names": ["Zoey", "Emma", "Riley", "Oliver", "Sofia", "Elizabeth", "Owen", "Samuel"], "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": "Zoey is a knave, Emma is a knave, Riley is a knight, Oliver is a knave, Sofia is a knight, Elizabeth is a knave, Owen is a knight, and Samuel is a knave.", "solution_text_format": "(1) Zoey is a knave\n(2) Emma is a knave\n(3) Riley is a knight\n(4) Oliver is a knave\n(5) Sofia is a knight\n(6) Elizabeth is a knave\n(7) Owen 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 Riley is a knave if and only if Elizabeth is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Elizabeth is a knave if and only if Sofia is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Owen is a knight and Zoey is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Sofia is a knave if and only if Zoey is a knight.", "Sofia cannot be a knight, because this would contradict the claim of Riley that Elizabeth is a knave if and only if Sofia 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 Elizabeth is a knave.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the claim of Elizabeth that Owen is a knight and Zoey is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Elizabeth.", "Elizabeth cannot be a knave, because this would contradict the claim of Zoey that Riley 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 Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Elizabeth is a knave if and only if Sofia is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Zoey that Riley 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 Owen is a knight and Zoey is a knight.", "Owen cannot be a knight, because this would contradict the false claim of Elizabeth that Owen is a knight and Zoey is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Sofia is a knave if and only if Zoey is a knight.", "Sofia cannot be a knight, because this would contradict the false claim of Riley that Elizabeth is a knave if and only if Sofia 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 Elizabeth is a knave.", "We have exhausted all possibilities for Sofia, Owen, Elizabeth, and Riley, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Riley is a knave if and only if Elizabeth is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Elizabeth is a knave if and only if Sofia is a knight.", "Elizabeth cannot be a knight, because this would contradict the false claim of Zoey that Riley 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 Owen is a knight and Zoey is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Sofia is a knave if and only if Zoey is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that If Sofia is a knight then Elizabeth is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Zoey is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Zoey is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Sofia is not a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Sofia is not a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Sofia is a knave and Emma is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Sofia is a knave and Emma is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('lying', 5)), ('telling-truth', 0), ('<=>', ('lying', 5), ('telling-truth', 4)), ('not', ('telling-truth', 4)), ('->', ('telling-truth', 4), ('lying', 5)), ('and', ('telling-truth', 6), ('telling-truth', 0)), ('<=>', ('lying', 4), ('telling-truth', 0)), ('and', ('lying', 4), ('telling-truth', 1)))", "index": 74}
-{"quiz": "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, Mia, Samuel, Amelia, Sophia, Jackson, Mason, and James. Lucas told you that James is a knight if and only if Lucas is a knight. Mia said that Lucas is a knave or Sophia is a knave. In Samuel's words: \"Mason is a knave or James is a knave\". In Amelia's words: \"Amelia is a knight or James is a knight\". Sophia stated, \"Amelia is a knave or Samuel is a knave\". Jackson told you that Sophia is a knight or Sophia is a knave. According to Mason, \"James is a knave and Amelia is a knight\". According to James, \"Lucas is a knave\". So who is a knight and who is a knave?", "names": ["Lucas", "Mia", "Samuel", "Amelia", "Sophia", "Jackson", "Mason", "James"], "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": "Lucas is a knave, Mia is a knight, Samuel is a knight, Amelia is a knight, Sophia is a knave, Jackson is a knight, Mason is a knave, and James is a knight.", "solution_text_format": "(1) Lucas is a knave\n(2) Mia is a knight\n(3) Samuel is a knight\n(4) Amelia is a knight\n(5) Sophia is a knave\n(6) Jackson is a knight\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 Lucas is a knight. No contradiction is found in their claim that James is a knight if and only if Lucas is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Lucas is a knave.", "James cannot be a knave, because this would contradict the claim of Lucas that James is a knight if and only if Lucas is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that James is a knight if and only if Lucas is a knight.", "Assume James is a knight. No contradiction is found in their claim that Lucas is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Lucas is a knave or Sophia is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Amelia is a knave or Samuel is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Amelia is a knight or James is a knight.", "Samuel cannot be a knight, because this would contradict the claim of Sophia that Amelia is a knave or Samuel is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Mason is a knave or James is a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that James is a knave and Amelia is a knight.", "Mason cannot be a knave, because this would contradict the false claim of Samuel that Mason is a knave or James is a knave.", "We have exhausted all possibilities for Mason and Samuel, so let us go back and reconsider Amelia.", "Amelia cannot be a knave, because this would contradict the false claim of their own that Amelia is a knight or James is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Amelia is a knave or Samuel is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Amelia is a knight or James is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Mason is a knave or James is a knave.", "Mason cannot be a knight, because this would contradict the claim of Samuel that Mason is a knave or James is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that James is a knave and Amelia is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Sophia is a knight or Sophia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 7), ('telling-truth', 0)), ('or', ('lying', 0), ('lying', 4)), ('or', ('lying', 6), ('lying', 7)), ('or', ('telling-truth', 3), ('telling-truth', 7)), ('or', ('lying', 3), ('lying', 2)), ('or', ('telling-truth', 4), ('lying', 4)), ('and', ('lying', 7), ('telling-truth', 3)), ('lying', 0))", "index": 75}
-{"quiz": "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, Victoria, Chloe, Noah, Mia, Mason, Michael, and Lily. Evelyn told you that Victoria is a knight if and only if Mia is a knight. \"Evelyn is a knave and Chloe is a knight,\" Victoria mentioned. \"Evelyn is a knave if and only if Evelyn is a knight\" - Chloe. Noah told you that Mia is a knave. Mia stated, \"Lily is a knave if and only if Chloe is a knave\". \"Mia is not a knave,\" Mason claimed. Michael noted, \"Evelyn is a knight and Lily is a knave\". As Lily put it, \"Lily is a knight if and only if Mia is a knave\". So who is a knight and who is a knave?", "names": ["Evelyn", "Victoria", "Chloe", "Noah", "Mia", "Mason", "Michael", "Lily"], "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": "Evelyn is a knight, Victoria is a knave, Chloe is a knave, Noah is a knight, Mia is a knave, Mason is a knave, Michael is a knave, and Lily is a knight.", "solution_text_format": "(1) Evelyn is a knight\n(2) Victoria is a knave\n(3) Chloe is a knave\n(4) Noah is a knight\n(5) Mia is a knave\n(6) Mason is a knave\n(7) Michael 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 Evelyn is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Mia is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave and Chloe is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Evelyn is a knave and Chloe is a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave if and only if Evelyn is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Evelyn is a knave if and only if Evelyn is a knight.", "Mia cannot be a knight, because this would contradict the claim of Evelyn that Victoria 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 Lily is a knave if and only if Chloe is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Lily is a knight if and only if Mia is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Mia is a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Mia is not a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Mia is not a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Evelyn is a knight and Lily is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Evelyn is a knight and Lily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('telling-truth', 4)), ('and', ('lying', 0), ('telling-truth', 2)), ('<=>', ('lying', 0), ('telling-truth', 0)), ('lying', 4), ('<=>', ('lying', 7), ('lying', 2)), ('not', ('lying', 4)), ('and', ('telling-truth', 0), ('lying', 7)), ('<=>', ('telling-truth', 7), ('lying', 4)))", "index": 76}
-{"quiz": "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, Harper, Liam, Lily, James, Zoey, Scarlett, and Joseph. \"If Scarlett is a knave then Liam is a knight,\" Avery claimed. Harper noted, \"Joseph is a knave\". Liam noted, \"Avery is not a knave\". Lily told you that Harper is a knight. James remarked, \"If Lily is a knave then Joseph is a knave\". Zoey was heard saying, \"Lily is not a knight\". In Scarlett's words: \"Liam is a knight if and only if James is a knave\". \"Scarlett is a knave and Scarlett is a knight,\" Joseph mentioned. So who is a knight and who is a knave?", "names": ["Avery", "Harper", "Liam", "Lily", "James", "Zoey", "Scarlett", "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": "Avery is a knight, Harper is a knight, Liam is a knight, Lily is a knight, James is a knight, Zoey is a knave, Scarlett is a knave, and Joseph is a knave.", "solution_text_format": "(1) Avery is a knight\n(2) Harper is a knight\n(3) Liam is a knight\n(4) Lily is a knight\n(5) James is a knight\n(6) Zoey is a knave\n(7) Scarlett 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 Avery is a knight. No contradiction is found in their claim that If Scarlett is a knave then Liam is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Liam is a knight if and only if James is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Avery is not a knave.", "James cannot be a knight, because this would contradict the claim of Scarlett 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 If Lily is a knave then Joseph is a knave.", "Lily cannot be a knight, because this would contradict the false claim of James that If Lily is a knave then Joseph is a knave.", "Assume Lily 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 Lily that Harper is a knight.", "Assume Harper 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 Scarlett is a knave and Scarlett is a knight.", "Joseph cannot be a knave, because this would contradict the false claim of Harper that Joseph is a knave.", "We have exhausted all possibilities for Joseph, Harper, Lily, and James, so let us go back and reconsider Liam.", "Liam 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 Liam, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Liam is a knight if and only if James is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Avery is not a knave.", "Assume James is a knight. No contradiction is found in their claim that If Lily is a knave then Joseph is a knave.", "Assume Lily 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 Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Harper that Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Scarlett is a knave and Scarlett is a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that Lily is not a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Lily is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 6), ('telling-truth', 2)), ('lying', 7), ('not', ('lying', 0)), ('telling-truth', 1), ('->', ('lying', 3), ('lying', 7)), ('not', ('telling-truth', 3)), ('<=>', ('telling-truth', 2), ('lying', 4)), ('and', ('lying', 6), ('telling-truth', 6)))", "index": 77}
-{"quiz": "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, Liam, Mason, Emma, Sebastian, Evelyn, Joseph, and Owen. \"Evelyn is not a knave,\" Isabella mentioned. According to Liam, \"Mason is a knight and Mason is a knave\". Mason said that Evelyn is a knave. Emma asserted: \"Evelyn is a knight and Mason is a knight\". Sebastian asserted: \"Isabella is a knight\". Evelyn asserted: \"If Joseph is a knight then Sebastian is a knight\". Joseph said that Emma is a knight if and only if Owen is a knave. \"Sebastian is a knave if and only if Evelyn is a knight,\" Owen mentioned. So who is a knight and who is a knave?", "names": ["Isabella", "Liam", "Mason", "Emma", "Sebastian", "Evelyn", "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, true, true, false, false], "solution_text": "Isabella is a knight, Liam is a knave, Mason is a knave, Emma is a knave, Sebastian is a knight, Evelyn is a knight, Joseph is a knave, and Owen is a knave.", "solution_text_format": "(1) Isabella is a knight\n(2) Liam is a knave\n(3) Mason is a knave\n(4) Emma is a knave\n(5) Sebastian is a knight\n(6) Evelyn 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 Isabella 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 If Joseph is a knight then Sebastian is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Emma is a knight if and only if Owen is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Evelyn is a knight and Mason is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave.", "Mason cannot be a knave, because this would contradict the claim of Emma that Evelyn is a knight and Mason is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Evelyn is a knight and Mason is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Evelyn is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Sebastian is a knave if and only if Evelyn is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of Owen that Sebastian is a knave if and only if Evelyn is a knight.", "Sebastian 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 Sebastian, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the claim of Joseph that Emma is a knight if and only if Owen is a knave.", "We have exhausted all possibilities for Owen, Mason, and Emma, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Emma is a knight if and only if Owen is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Evelyn is a knight and Mason is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave.", "Mason cannot be a knave, because this would contradict the claim of Emma that Evelyn is a knight and Mason is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Evelyn is a knight and Mason is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Evelyn is a knave.", "Owen cannot be a knight, because this would contradict the false claim of Joseph that Emma 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 Sebastian is a knave if and only if Evelyn is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Isabella is a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that Mason is a knight and Mason is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Mason is a knight and Mason is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 5)), ('and', ('telling-truth', 2), ('lying', 2)), ('lying', 5), ('and', ('telling-truth', 5), ('telling-truth', 2)), ('telling-truth', 0), ('->', ('telling-truth', 6), ('telling-truth', 4)), ('<=>', ('telling-truth', 3), ('lying', 7)), ('<=>', ('lying', 4), ('telling-truth', 5)))", "index": 78}
-{"quiz": "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, Lucas, Isabella, Riley, Emma, Jackson, Lily, and Sofia. Mia remarked, \"Lily is a knave\". Lucas said that Jackson is a knave. Isabella said, \"Emma is a knight and Riley is a knight.\" Riley asserted: \"Lily is a knight\". As Emma put it, \"Jackson is a knave or Emma is a knight\". According to Jackson, \"Mia is a knave if and only if Lucas is a knight\". Lily said that Isabella is a knave and Jackson is a knight. As Sofia put it, \"Jackson is not a knight\". So who is a knight and who is a knave?", "names": ["Mia", "Lucas", "Isabella", "Riley", "Emma", "Jackson", "Lily", "Sofia"], "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": "Mia is a knight, Lucas is a knight, Isabella is a knave, Riley is a knave, Emma is a knight, Jackson is a knave, Lily is a knave, and Sofia is a knight.", "solution_text_format": "(1) Mia is a knight\n(2) Lucas is a knight\n(3) Isabella is a knave\n(4) Riley is a knave\n(5) Emma is a knight\n(6) Jackson 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 Mia 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 Mia that Lily is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Isabella is a knave and Jackson is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Emma is a knight and Riley is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Jackson is a knave or Emma is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Mia is a knave if and only if Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Jackson is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Jackson is a knave.", "Riley cannot be a knight, because this would contradict the claim of their own that Lily is a knight.", "Riley cannot be a knave, because this would contradict the claim of Isabella that Emma is a knight and Riley is a knight.", "We have exhausted all possibilities for Riley and Lucas, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Mia is a knave if and only if Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Jackson is a knave.", "Riley cannot be a knight, because this would contradict the claim of their own that Lily is a knight.", "Riley cannot be a knave, because this would contradict the claim of Isabella that Emma is a knight and Riley is a knight.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Lucas.", "Lucas 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 Lucas and Jackson, so let us go back and reconsider Emma.", "Emma cannot be a knave, because this would contradict the claim of Isabella that Emma is a knight and Riley is a knight.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Emma is a knight and Riley is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Jackson is a knave or Emma is a knight.", "Jackson cannot be a knight, because this would contradict the false claim of Lily that Isabella is a knave and Jackson is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Mia is a knave if and only if Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Jackson is a knave.", "Riley cannot be a knight, because this would contradict the false claim of Isabella that Emma is a knight and Riley is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Lily is a knight.", "Assume Sofia 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', 6), ('lying', 5), ('and', ('telling-truth', 4), ('telling-truth', 3)), ('telling-truth', 6), ('or', ('lying', 5), ('telling-truth', 4)), ('<=>', ('lying', 0), ('telling-truth', 1)), ('and', ('lying', 2), ('telling-truth', 5)), ('not', ('telling-truth', 5)))", "index": 79}
-{"quiz": "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, Charlotte, Luke, Matthew, Liam, Evelyn, Penelope, and Aria. Samuel noted, \"Luke is not a knave\". Charlotte was heard saying, \"Aria is a knave\". Luke asserted: \"Liam is a knave or Matthew is a knight\". \"If Samuel is a knight then Charlotte is a knight,\" Matthew declared. In Liam's words: \"Liam is a knight and Evelyn is a knave\". Evelyn said, \"Charlotte is not a knave.\" Penelope stated, \"If Aria is a knave then Samuel is a knight\". Aria was heard saying, \"Liam is not a knave\". So who is a knight and who is a knave?", "names": ["Samuel", "Charlotte", "Luke", "Matthew", "Liam", "Evelyn", "Penelope", "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, false], "solution_text": "Samuel is a knight, Charlotte is a knight, Luke is a knight, Matthew is a knight, Liam is a knave, Evelyn is a knight, Penelope is a knight, and Aria is a knave.", "solution_text_format": "(1) Samuel is a knight\n(2) Charlotte is a knight\n(3) Luke is a knight\n(4) Matthew is a knight\n(5) Liam is a knave\n(6) Evelyn is a knight\n(7) Penelope 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 Samuel 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 Liam is a knave or Matthew is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Liam is a knight and Evelyn is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of Liam that Liam is a knight and Evelyn is a knave.", "Assume Evelyn 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 Evelyn that Charlotte is not a knave.", "Assume Charlotte 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 Liam is not a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that If Samuel is a knight then Charlotte is a knight.", "Matthew cannot be a knave, because this would contradict the claim of Luke that Liam is a knave or Matthew is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Aria.", "Aria cannot be a knave, because this would contradict the false claim of Charlotte that Aria is a knave.", "We have exhausted all possibilities for Aria, Charlotte, and Evelyn, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Liam is a knight and 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 Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of Charlotte that Aria is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Liam is not a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that If Samuel is a knight then Charlotte is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that If Aria is a knave then Samuel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('lying', 7), ('or', ('lying', 4), ('telling-truth', 3)), ('->', ('telling-truth', 0), ('telling-truth', 1)), ('and', ('telling-truth', 4), ('lying', 5)), ('not', ('lying', 1)), ('->', ('lying', 7), ('telling-truth', 0)), ('not', ('lying', 4)))", "index": 80}
-{"quiz": "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, Samuel, Sophia, Ella, Harper, Daniel, Emma, and Matthew. According to Jack, \"Samuel is a knight or Ella is a knave\". Samuel noted, \"If Jack is a knave then Daniel is a knave\". \"Samuel is a knight and Emma is a knight,\" Sophia mentioned. \"If Jack is a knave then Emma is a knight,\" Ella declared. Harper asserted: \"Ella is a knave if and only if Samuel is a knight\". Daniel expressed that Jack is a knave and Sophia is a knave. In a statement by Emma: \"Ella is not a knave\". According to Matthew, \"If Matthew is a knight then Sophia is a knight\". So who is a knight and who is a knave?", "names": ["Jack", "Samuel", "Sophia", "Ella", "Harper", "Daniel", "Emma", "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, true], "solution_text": "Jack is a knight, Samuel is a knight, Sophia is a knight, Ella is a knight, Harper is a knave, Daniel is a knave, Emma is a knight, and Matthew is a knight.", "solution_text_format": "(1) Jack is a knight\n(2) Samuel is a knight\n(3) Sophia is a knight\n(4) Ella is a knight\n(5) Harper is a knave\n(6) Daniel is a knave\n(7) Emma 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 Jack is a knight. No contradiction is found in their claim that Samuel is a knight or Ella is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that If Jack is a knave then Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of their own that Jack is a knave and Sophia is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Jack is a knave and Sophia is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Samuel is a knight and Emma is a knight.", "Assume Emma 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 If Jack is a knave then Emma is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that Ella is a knave if and only if Samuel is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Ella is a knave if and only if Samuel is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that If Matthew is a knight then Sophia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('lying', 3)), ('->', ('lying', 0), ('lying', 5)), ('and', ('telling-truth', 1), ('telling-truth', 6)), ('->', ('lying', 0), ('telling-truth', 6)), ('<=>', ('lying', 3), ('telling-truth', 1)), ('and', ('lying', 0), ('lying', 2)), ('not', ('lying', 3)), ('->', ('telling-truth', 7), ('telling-truth', 2)))", "index": 81}
-{"quiz": "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, Daniel, Abigail, Elizabeth, Aiden, Emma, Henry, and Jackson. Sebastian stated, \"Emma is a knight or Sebastian is a knight\". Daniel asserted: \"Jackson is a knight or Henry is a knave\". Abigail stated, \"If Aiden is a knave then Henry is a knave\". \"Sebastian is a knave and Aiden is a knight,\" Elizabeth declared. Aiden stated, \"If Sebastian is a knight then Emma is a knight\". In Emma's words: \"If Abigail is a knave then Elizabeth is a knave\". Henry commented, \"Daniel is a knave\". \"Henry is a knave if and only if Emma is a knave,\" Jackson claimed. So who is a knight and who is a knave?", "names": ["Sebastian", "Daniel", "Abigail", "Elizabeth", "Aiden", "Emma", "Henry", "Jackson"], "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": "Sebastian is a knight, Daniel is a knight, Abigail is a knight, Elizabeth is a knave, Aiden is a knight, Emma is a knight, Henry is a knave, and Jackson is a knave.", "solution_text_format": "(1) Sebastian is a knight\n(2) Daniel is a knight\n(3) Abigail is a knight\n(4) Elizabeth is a knave\n(5) Aiden is a knight\n(6) Emma is a knight\n(7) Henry 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 Sebastian is a knight. No contradiction is found in their claim that Emma is a knight or Sebastian is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If Abigail is a knave then Elizabeth is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that If Aiden is a knave then Henry is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Sebastian is a knight then Emma is a knight.", "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 Jackson is a knight or Henry is a knave.", "Jackson cannot be a knight, because this would contradict the false claim of Daniel that Jackson is a knight or Henry is a knave.", "Jackson cannot be a knave, because this would contradict the false claim of their own that Henry is a knave if and only if Emma is a knave.", "We have exhausted all possibilities for Jackson and Daniel, so let us go back and reconsider Henry.", "Assume Henry 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 Jackson is a knight or Henry is a knave.", "Jackson cannot be a knight, because this would contradict the claim of their own that Henry is a knave if and only if Emma is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Henry is a knave if and only if Emma is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave and Aiden is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Sebastian is a knave and Aiden is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('telling-truth', 0)), ('or', ('telling-truth', 7), ('lying', 6)), ('->', ('lying', 4), ('lying', 6)), ('and', ('lying', 0), ('telling-truth', 4)), ('->', ('telling-truth', 0), ('telling-truth', 5)), ('->', ('lying', 2), ('lying', 3)), ('lying', 1), ('<=>', ('lying', 6), ('lying', 5)))", "index": 82}
-{"quiz": "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, Noah, Ella, Logan, Aria, Oliver, and Jacob. In a statement by Elizabeth: \"Jacob is a knight\". Mia noted, \"Aria is a knave\". In Noah's words: \"Aria is a knave if and only if Logan is a knave\". Ella noted, \"Ella is a knight or Noah is a knight\". Logan noted, \"Oliver is a knight\". Aria remarked, \"Logan is not a knight\". Oliver stated, \"Elizabeth is a knave and Mia is a knave\". Jacob said, \"If Ella is a knight then Aria is a knave.\" So who is a knight and who is a knave?", "names": ["Elizabeth", "Mia", "Noah", "Ella", "Logan", "Aria", "Oliver", "Jacob"], "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, Noah is a knave, Ella is a knave, Logan is a knave, Aria is a knight, Oliver is a knave, and Jacob is a knight.", "solution_text_format": "(1) Elizabeth is a knight\n(2) Mia is a knave\n(3) Noah is a knave\n(4) Ella is a knave\n(5) Logan is a knave\n(6) Aria is a knight\n(7) Oliver 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 Elizabeth 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 If Ella is a knight then Aria is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Ella is a knight or Noah is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Aria is a knave if and only if Logan is a knave.", "Aria cannot be a knight, because this would contradict the claim of Jacob that If Ella is a knight then Aria is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Logan is not a knight.", "Logan cannot be a knight, because this would contradict the claim of Noah that Aria is a knave if and only if Logan is a knave.", "Logan cannot be a knave, because this would contradict the false claim of Aria that Logan is not a knight.", "We have exhausted all possibilities for Logan and Aria, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Aria is a knave if and only if Logan is a knave.", "Aria cannot be a knight, because this would contradict the claim of Jacob that If Ella is a knight then Aria is a knave.", "Assume Aria 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 Oliver is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave and Mia is a knave.", "Oliver cannot be a knave, because this would contradict the claim of Logan that Oliver is a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the false claim of Noah that Aria is a knave if and only if Logan is a knave.", "We have exhausted all possibilities for Logan, Aria, and Noah, 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 or Noah is a knight.", "Noah cannot be a knight, because this would contradict the false claim of Ella that Ella is a knight or Noah is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Aria is a knave if and only if Logan is a knave.", "Assume Aria 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 false claim of Noah that Aria is a knave if and only if Logan is a knave.", "Assume Logan 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 Logan that Oliver is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Elizabeth is a knave and Mia is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Aria is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Aria is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 7), ('lying', 5), ('<=>', ('lying', 5), ('lying', 4)), ('or', ('telling-truth', 3), ('telling-truth', 2)), ('telling-truth', 6), ('not', ('telling-truth', 4)), ('and', ('lying', 0), ('lying', 1)), ('->', ('telling-truth', 3), ('lying', 5)))", "index": 83}
-{"quiz": "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, Michael, William, Aurora, Jacob, Matthew, and Isabella. \"Matthew is a knight or Aurora is a knave\" - Elizabeth. Aiden expressed that Aurora is a knave or Matthew is a knave. \"If Elizabeth is a knight then Aiden is a knight,\" Michael mentioned. \"Isabella is a knave if and only if Jacob is a knight,\" William claimed. Aurora stated, \"Isabella is a knave and Isabella is a knight\". Jacob expressed that Matthew is not a knave. Matthew said that Aurora is a knight and William is a knave. Isabella stated, \"Jacob is a knight if and only if Michael is a knight\". So who is a knight and who is a knave?", "names": ["Elizabeth", "Aiden", "Michael", "William", "Aurora", "Jacob", "Matthew", "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, false, false], "solution_text": "Elizabeth is a knight, Aiden is a knight, Michael is a knight, William is a knave, Aurora is a knave, Jacob is a knave, Matthew is a knave, and Isabella is a knave.", "solution_text_format": "(1) Elizabeth is a knight\n(2) Aiden is a knight\n(3) Michael is a knight\n(4) William is a knave\n(5) Aurora is a knave\n(6) Jacob is a knave\n(7) Matthew 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 Elizabeth is a knight. No contradiction is found in their claim that Matthew is a knight or Aurora is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Aurora is a knight and William is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Isabella is a knave and Isabella is a knight.", "Aurora cannot be a knave, because this would contradict the claim of Matthew that Aurora is a knight and William is 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 and William is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Elizabeth that Matthew is a knight or Aurora is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Isabella is a knave and Isabella is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Jacob is a knight if and only if Michael is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Matthew is not a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Matthew is not a knave.", "Michael cannot be a knight, because this would contradict the claim of Isabella that Jacob is a knight if and only if Michael is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that If Elizabeth is a knight then Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the false claim of Michael that If Elizabeth is a knight then Aiden is a knight.", "Aiden cannot be a knave, because this would contradict the false claim of their own that Aurora is a knave or Matthew is a knave.", "We have exhausted all possibilities for Aiden, Michael, and Jacob, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Jacob is a knight if and only if Michael is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Matthew is not a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Matthew is not a knave.", "Assume Michael is a knight. No contradiction is found in their claim that If Elizabeth is a knight then Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Aurora is a knave or Matthew is a knave.", "William cannot be a knight, because this would contradict the claim of their own that Isabella is a knave if and only if Jacob is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Isabella is a knave if and only if Jacob is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 6), ('lying', 4)), ('or', ('lying', 4), ('lying', 6)), ('->', ('telling-truth', 0), ('telling-truth', 1)), ('<=>', ('lying', 7), ('telling-truth', 5)), ('and', ('lying', 7), ('telling-truth', 7)), ('not', ('lying', 6)), ('and', ('telling-truth', 4), ('lying', 3)), ('<=>', ('telling-truth', 5), ('telling-truth', 2)))", "index": 84}
-{"quiz": "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, Samuel, Noah, Penelope, Ella, Abigail, and Ava. Jack asserted: \"Samuel is a knave or Noah is a knight\". Luke asserted: \"Samuel is a knave\". Samuel said that If Samuel is a knight then Abigail is a knave. \"Luke is a knave or Ava is a knight,\" Noah mentioned. Penelope said, \"Noah is a knight if and only if Samuel is a knave.\" In a statement by Ella: \"Ava is a knave and Penelope is a knight\". Abigail said, \"Ella is a knight.\" Ava said, \"If Noah is a knave then Abigail is a knight.\" So who is a knight and who is a knave?", "names": ["Jack", "Luke", "Samuel", "Noah", "Penelope", "Ella", "Abigail", "Ava"], "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": "Jack is a knight, Luke is a knave, Samuel is a knight, Noah is a knight, Penelope is a knave, Ella is a knave, Abigail is a knave, and Ava is a knight.", "solution_text_format": "(1) Jack is a knight\n(2) Luke is a knave\n(3) Samuel is a knight\n(4) Noah is a knight\n(5) Penelope is a knave\n(6) Ella is a knave\n(7) Abigail 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 Jack is a knight. No contradiction is found in their claim that Samuel is a knave or Noah is a knight.", "Assume Samuel 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 Samuel 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 Ella is a knight.", "Ella cannot be a knight, because this would contradict the false claim of Abigail that Ella is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Ava is a knave and Penelope is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that If Noah is a knave then Abigail is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Luke is a knave or Ava is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Samuel is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Samuel is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Noah is a knight if and only if Samuel is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Noah is a knight if and only if Samuel is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('telling-truth', 3)), ('lying', 2), ('->', ('telling-truth', 2), ('lying', 6)), ('or', ('lying', 1), ('telling-truth', 7)), ('<=>', ('telling-truth', 3), ('lying', 2)), ('and', ('lying', 7), ('telling-truth', 4)), ('telling-truth', 5), ('->', ('lying', 3), ('telling-truth', 6)))", "index": 85}
-{"quiz": "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, Matthew, Charlotte, Oliver, Samuel, Riley, and Alexander. David stated, \"Riley is not a knave\". \"If Samuel is a knave then Oliver is a knight,\" Ella claimed. \"Samuel is a knight or Riley is a knave,\" Matthew declared. Charlotte asserted: \"Riley is not a knight\". Oliver commented, \"David is a knave\". \"Charlotte is a knight and Riley is a knave,\" Samuel mentioned. Riley remarked, \"If Matthew is a knave then Samuel is a knave\". Alexander stated, \"If Samuel is a knave then Oliver is a knave\". So who is a knight and who is a knave?", "names": ["David", "Ella", "Matthew", "Charlotte", "Oliver", "Samuel", "Riley", "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, true, true], "solution_text": "David is a knight, Ella is a knave, Matthew is a knave, Charlotte is a knave, Oliver is a knave, Samuel is a knave, Riley is a knight, and Alexander is a knight.", "solution_text_format": "(1) David is a knight\n(2) Ella is a knave\n(3) Matthew is a knave\n(4) Charlotte is a knave\n(5) Oliver is a knave\n(6) Samuel is a knave\n(7) Riley 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 David 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 Matthew is a knave then Samuel is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Samuel is a knight or Riley is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that Charlotte is a knight and Riley is a knave.", "Samuel cannot be a knave, because this would contradict the claim of Matthew that Samuel is a knight or Riley is a knave.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Samuel is a knight or Riley is a knave.", "Samuel cannot be a knight, because this would contradict the false claim of Matthew that Samuel is a knight or Riley is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Charlotte is a knight and Riley is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Riley is not a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Riley is not a knight.", "Assume Ella is a knight. No contradiction is found in their claim that If Samuel is a knave then Oliver is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that David is a knave.", "Oliver cannot be a knave, because this would contradict the claim of Ella that If Samuel is a knave then Oliver is a knight.", "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 If Samuel is a knave then Oliver is a knight.", "Oliver cannot be a knight, because this would contradict the false claim of Ella that If Samuel is a knave then Oliver is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that David is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that If Samuel is a knave then Oliver is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 6)), ('->', ('lying', 5), ('telling-truth', 4)), ('or', ('telling-truth', 5), ('lying', 6)), ('not', ('telling-truth', 6)), ('lying', 0), ('and', ('telling-truth', 3), ('lying', 6)), ('->', ('lying', 2), ('lying', 5)), ('->', ('lying', 5), ('lying', 4)))", "index": 86}
-{"quiz": "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, Liam, Alexander, Amelia, Riley, Jack, Emily, and Lily. \"Amelia is not a knight,\" Zoey claimed. Liam stated, \"Lily is a knight or Zoey is a knight\". In Alexander's words: \"Jack is a knight\". Amelia remarked, \"Riley is not a knave\". Riley was heard saying, \"Emily is a knight if and only if Zoey is a knave\". \"Zoey is a knave and Liam is a knight,\" Jack claimed. Emily expressed that Zoey is a knight and Liam is a knight. In a statement by Lily: \"Amelia is not a knight\". So who is a knight and who is a knave?", "names": ["Zoey", "Liam", "Alexander", "Amelia", "Riley", "Jack", "Emily", "Lily"], "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": "Zoey is a knight, Liam is a knight, Alexander is a knave, Amelia is a knave, Riley is a knave, Jack is a knave, Emily is a knight, and Lily is a knight.", "solution_text_format": "(1) Zoey is a knight\n(2) Liam is a knight\n(3) Alexander is a knave\n(4) Amelia is a knave\n(5) Riley is a knave\n(6) Jack is a knave\n(7) Emily 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 Zoey 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 Zoey that Amelia is not a knight.", "Assume Amelia 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 Amelia that Riley is not a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Emily is a knight if and only if Zoey is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Zoey is a knight and Liam is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Lily is a knight or Zoey is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Amelia is not a knight.", "Assume Alexander 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 Zoey is a knave and Liam is a knight.", "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 Zoey is a knave and Liam is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 3)), ('or', ('telling-truth', 7), ('telling-truth', 0)), ('telling-truth', 5), ('not', ('lying', 4)), ('<=>', ('telling-truth', 6), ('lying', 0)), ('and', ('lying', 0), ('telling-truth', 1)), ('and', ('telling-truth', 0), ('telling-truth', 1)), ('not', ('telling-truth', 3)))", "index": 87}
-{"quiz": "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, Owen, Zoey, Alexander, Benjamin, Aurora, Emily, and Aiden. \"Aurora is a knight if and only if Aurora is a knave,\" Noah declared. Owen said, \"Benjamin is a knave if and only if Noah is a knight.\" Zoey told you that If Emily is a knave then Aiden is a knight. Alexander asserted: \"Noah is a knight\". Benjamin expressed that Noah is a knight. Aurora commented, \"Alexander is not a knave\". In Emily's words: \"Alexander is a knight\". As Aiden put it, \"Owen is a knave if and only if Benjamin is a knight\". So who is a knight and who is a knave?", "names": ["Noah", "Owen", "Zoey", "Alexander", "Benjamin", "Aurora", "Emily", "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, false, false, false], "solution_text": "Noah is a knave, Owen is a knave, Zoey is a knave, Alexander is a knave, Benjamin is a knave, Aurora is a knave, Emily is a knave, and Aiden is a knave.", "solution_text_format": "(1) Noah is a knave\n(2) Owen is a knave\n(3) Zoey is a knave\n(4) Alexander is a knave\n(5) Benjamin is a knave\n(6) Aurora is a knave\n(7) Emily 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": ["Noah cannot be a knight, because this would contradict the claim of their own that Aurora is a knight if and only if Aurora is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Aurora is a knight if and only if Aurora is a knave.", "Assume Aurora 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 their own that Noah is a knight.", "Alexander cannot be a knave, because this would contradict the claim of Aurora that Alexander is not a knave.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Aurora.", "Assume Aurora 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 claim of their own that Noah is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Noah is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Benjamin is a knave if and only if Noah is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Noah is a knight.", "Benjamin cannot be a knave, because this would contradict the claim of Owen that Benjamin is a knave if and only if Noah is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Benjamin is a knave if and only if Noah is a knight.", "Benjamin cannot be a knight, because this would contradict the false claim of Owen that Benjamin is a knave if and only if Noah is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Noah is a knight.", "Assume Zoey 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 Alexander is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Alexander is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Owen is a knave if and only if Benjamin is a knight.", "Aiden cannot be a knave, because this would contradict the claim of Zoey that If Emily is a knave then Aiden is a knight.", "We have exhausted all possibilities for Aiden and Emily, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that If Emily is a knave then Aiden is a knight.", "Emily cannot be a knight, because this would contradict the false claim of Zoey that If Emily is a knave then Aiden is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Alexander is a knight.", "Aiden cannot be a knight, because this would contradict the false claim of Zoey that If Emily is a knave then Aiden is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Owen is a knave if and only if Benjamin is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 5), ('lying', 5)), ('<=>', ('lying', 4), ('telling-truth', 0)), ('->', ('lying', 6), ('telling-truth', 7)), ('telling-truth', 0), ('telling-truth', 0), ('not', ('lying', 3)), ('telling-truth', 3), ('<=>', ('lying', 1), ('telling-truth', 4)))", "index": 88}
-{"quiz": "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, Aurora, Aria, Benjamin, Emma, Charlotte, and Chloe. In a statement by Sebastian: \"Aria is not a knight\". \"Aria is not a knight,\" Evelyn declared. Aurora told you that Emma is a knight and Benjamin is a knave. According to Aria, \"Charlotte is a knave and Benjamin is a knave\". As Benjamin put it, \"Chloe is a knave\". Emma asserted: \"Charlotte is a knave if and only if Chloe is a knight\". \"Sebastian is a knave if and only if Emma is a knave,\" Charlotte mentioned. Chloe was heard saying, \"If Sebastian is a knight then Evelyn is a knight\". So who is a knight and who is a knave?", "names": ["Sebastian", "Evelyn", "Aurora", "Aria", "Benjamin", "Emma", "Charlotte", "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, true, false, true], "solution_text": "Sebastian is a knave, Evelyn is a knave, Aurora is a knight, Aria is a knight, Benjamin is a knave, Emma is a knight, Charlotte is a knave, and Chloe is a knight.", "solution_text_format": "(1) Sebastian is a knave\n(2) Evelyn is a knave\n(3) Aurora is a knight\n(4) Aria is a knight\n(5) Benjamin is a knave\n(6) Emma is a knight\n(7) Charlotte 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 Sebastian 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 Sebastian that Aria is not a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Charlotte is a knave and Benjamin is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Sebastian is a knave if and only if Emma is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Charlotte is a knave if and only if Chloe is a knight.", "Chloe cannot be a knight, because this would contradict the claim of Emma that Charlotte 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 Sebastian is a knight then Evelyn is a knight.", "Evelyn cannot be a knight, because this would contradict the false claim of Chloe that If Sebastian is a knight then Evelyn is a knight.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that Aria is not a knight.", "We have exhausted all possibilities for Evelyn and Chloe, so let us go back and reconsider Emma.", "Emma cannot be a knave, because this would contradict the claim of Charlotte that Sebastian 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 Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Sebastian is a knave if and only if Emma is a knave.", "Emma cannot be a knight, because this would contradict the false claim of Charlotte that Sebastian 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 Charlotte is a knave if and only if Chloe is a knight.", "Chloe cannot be a knight, because this would contradict the false claim of Emma that Charlotte 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 Sebastian is a knight then Evelyn is a knight.", "Evelyn cannot be a knight, because this would contradict the false claim of Chloe that If Sebastian is a knight then Evelyn is a knight.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that Aria is not a knight.", "We have exhausted all possibilities for Evelyn, Chloe, Emma, Charlotte, and Aria, so let us go back and reconsider Sebastian.", "Assume Sebastian 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 Charlotte is a knave and Benjamin is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Aria that Charlotte is a knave and Benjamin is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Sebastian is a knave if and only if Emma is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Charlotte is a knave if and only if Chloe is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that If Sebastian is a knight then Evelyn is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Aria is not a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Aria is not a knight.", "Benjamin cannot be a knight, because this would contradict the claim of Aria that Charlotte is a knave and Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Chloe is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Emma is a knight and Benjamin is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 3)), ('not', ('telling-truth', 3)), ('and', ('telling-truth', 5), ('lying', 4)), ('and', ('lying', 6), ('lying', 4)), ('lying', 7), ('<=>', ('lying', 6), ('telling-truth', 7)), ('<=>', ('lying', 0), ('lying', 5)), ('->', ('telling-truth', 0), ('telling-truth', 1)))", "index": 89}
-{"quiz": "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, Mason, Aria, Noah, Daniel, Liam, Logan, and Mia. Grace expressed that Mason is a knight if and only if Mia is a knave. According to Mason, \"Aria is a knight or Mia is a knave\". Aria said that Logan is a knave and Grace is a knave. Noah said that Grace is a knave and Daniel is a knight. According to Daniel, \"If Noah is a knave then Mason is a knight\". Liam noted, \"Daniel is a knight if and only if Mason is a knight\". Logan commented, \"Daniel is a knight or Logan is a knight\". \"Noah is a knight and Daniel is a knight\" - Mia. So who is a knight and who is a knave?", "names": ["Grace", "Mason", "Aria", "Noah", "Daniel", "Liam", "Logan", "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": "Grace is a knight, Mason is a knight, Aria is a knave, Noah is a knave, Daniel is a knight, Liam is a knight, Logan is a knight, and Mia is a knave.", "solution_text_format": "(1) Grace is a knight\n(2) Mason is a knight\n(3) Aria is a knave\n(4) Noah is a knave\n(5) Daniel is a knight\n(6) Liam is a knight\n(7) Logan 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 Grace is a knight. No contradiction is found in their claim that Mason is a knight if and only if Mia is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Aria is a knight or Mia is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Logan is a knave and Grace is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Logan is a knave and Grace is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Daniel is a knight or Logan is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that If Noah is a knave then Mason is a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that Grace is a knave and Daniel is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Grace is a knave and Daniel is a knight.", "Mia cannot be a knight, because this would contradict the claim of Grace that Mason 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 Noah is a knight and Daniel is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Daniel is a knight if and only if Mason is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('lying', 7)), ('or', ('telling-truth', 2), ('lying', 7)), ('and', ('lying', 6), ('lying', 0)), ('and', ('lying', 0), ('telling-truth', 4)), ('->', ('lying', 3), ('telling-truth', 1)), ('<=>', ('telling-truth', 4), ('telling-truth', 1)), ('or', ('telling-truth', 4), ('telling-truth', 6)), ('and', ('telling-truth', 3), ('telling-truth', 4)))", "index": 90}
-{"quiz": "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, Avery, Charlotte, Henry, Grace, Lucas, Jacob, and Olivia. In Lily's words: \"If Olivia is a knight then Avery is a knave\". Avery asserted: \"Grace is a knight and Grace is a knave\". According to Charlotte, \"Olivia is a knight and Grace is a knight\". Henry said that Jacob is a knight or Avery is a knight. Grace said that Henry is a knave if and only if Jacob is a knight. Lucas said that Charlotte is a knight and Henry is a knight. \"Jacob is a knight if and only if Henry is a knave\" - Jacob. According to Olivia, \"Lucas is a knight or Grace is a knight\". So who is a knight and who is a knave?", "names": ["Lily", "Avery", "Charlotte", "Henry", "Grace", "Lucas", "Jacob", "Olivia"], "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": "Lily is a knight, Avery is a knave, Charlotte is a knave, Henry is a knave, Grace is a knave, Lucas is a knave, Jacob is a knave, and Olivia is a knave.", "solution_text_format": "(1) Lily is a knight\n(2) Avery is a knave\n(3) Charlotte is a knave\n(4) Henry is a knave\n(5) Grace is a knave\n(6) Lucas is a knave\n(7) Jacob 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 Lily is a knight. No contradiction is found in their claim that If Olivia is a knight then Avery is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Lucas is a knight or Grace is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Charlotte is a knight and Henry is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Olivia is a knight and Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Henry is a knave if and only if Jacob is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Jacob is a knight or Avery is a knight.", "Jacob cannot be a knight, because this would contradict the claim of Grace that Henry 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 Jacob is a knight if and only if Henry is a knave.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the claim of Lucas that Charlotte is a knight and Henry is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Grace.", "Grace cannot be a knave, because this would contradict the claim of Charlotte that Olivia is a knight and Grace is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the claim of Lucas that Charlotte is a knight and Henry is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Charlotte is a knight and Henry is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Olivia is a knight and Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Henry is a knave if and only if Jacob is a knight.", "Henry cannot be a knight, because this would contradict the false claim of Lucas that Charlotte is a knight and Henry is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Jacob is a knight or Avery is a knight.", "Jacob cannot be a knight, because this would contradict the false claim of Henry that Jacob is a knight or Avery is a knight.", "Jacob cannot be a knave, because this would contradict the claim of Grace that Henry is a knave if and only if Jacob is a knight.", "We have exhausted all possibilities for Jacob and Henry, so let us go back and reconsider Grace.", "Grace cannot be a knave, because this would contradict the claim of Charlotte that Olivia is a knight and Grace is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Olivia is a knight and Grace is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Charlotte that Olivia is a knight and Grace is a knight.", "Grace cannot be a knave, because this would contradict the claim of Olivia that Lucas is a knight or Grace is a knight.", "We have exhausted all possibilities for Grace, Charlotte, and Lucas, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Lucas is a knight or Grace is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of Olivia that Lucas is a knight or Grace is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Charlotte is a knight and Henry is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Olivia is a knight and Grace is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Olivia is a knight and Grace is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Olivia that Lucas is a knight or Grace is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Henry is a knave if and only if Jacob is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Jacob is a knight or Avery is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Jacob is a knight if and only if Henry is a knave.", "Jacob cannot be a knave, because this would contradict the false claim of Grace that Henry 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 Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Jacob is a knight or Avery is a knight.", "Jacob cannot be a knight, because this would contradict the false claim of Henry that Jacob is a knight or Avery is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Jacob is a knight if and only if Henry is a knave.", "Avery cannot be a knight, because this would contradict the claim of their own that Grace is a knight and Grace is a knave.", "Assume Avery 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": "(('->', ('telling-truth', 7), ('lying', 1)), ('and', ('telling-truth', 4), ('lying', 4)), ('and', ('telling-truth', 7), ('telling-truth', 4)), ('or', ('telling-truth', 6), ('telling-truth', 1)), ('<=>', ('lying', 3), ('telling-truth', 6)), ('and', ('telling-truth', 2), ('telling-truth', 3)), ('<=>', ('telling-truth', 6), ('lying', 3)), ('or', ('telling-truth', 5), ('telling-truth', 4)))", "index": 91}
-{"quiz": "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, Abigail, Sophia, Grace, Sofia, Luke, Chloe, and Riley. According to Aria, \"Sophia is a knave or Sofia is a knave\". \"If Aria is a knave then Luke is a knight,\" Abigail declared. Sophia said that Aria is a knight if and only if Sofia is a knight. Grace was heard saying, \"Chloe is a knave\". According to Sofia, \"Sophia is a knight if and only if Sophia is a knave\". \"Sofia is not a knave,\" Luke claimed. Chloe noted, \"If Riley is a knave then Sophia is a knight\". In Riley's words: \"If Grace is a knight then Sophia is a knave\". So who is a knight and who is a knave?", "names": ["Aria", "Abigail", "Sophia", "Grace", "Sofia", "Luke", "Chloe", "Riley"], "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": "Aria is a knight, Abigail is a knight, Sophia is a knave, Grace is a knave, Sofia is a knave, Luke is a knave, Chloe is a knight, and Riley is a knight.", "solution_text_format": "(1) Aria is a knight\n(2) Abigail is a knight\n(3) Sophia is a knave\n(4) Grace is a knave\n(5) Sofia is a knave\n(6) Luke is a knave\n(7) Chloe 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 Sophia is a knave or Sofia is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Aria is a knight if and only if Sofia is a knight.", "Sofia cannot be a knight, because this would contradict the claim of Aria that Sophia is a knave or Sofia is a knave.", "Sofia cannot be a knave, because this would contradict the claim of Sophia that Aria 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 Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Aria is a knight if and only if Sofia is a knight.", "Sofia cannot be a knight, because this would contradict the false claim of Sophia that Aria 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 Sophia is a knight if and only if Sophia is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that If Aria is a knave then Luke is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Sofia is not a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Sofia is not a knave.", "Assume Grace 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 Grace that Chloe is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that If Riley is a knave then Sophia is a knight.", "Riley cannot be a knight, because this would contradict the false claim of Chloe that If Riley is a knave then Sophia is a knight.", "Riley cannot be a knave, because this would contradict the false claim of their own that If Grace is a knight then Sophia is a knave.", "We have exhausted all possibilities for Riley and Chloe, so let us go back and reconsider Grace.", "Assume Grace 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 If Riley is a knave then Sophia is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that If Grace is a knight then Sophia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('lying', 4)), ('->', ('lying', 0), ('telling-truth', 5)), ('<=>', ('telling-truth', 0), ('telling-truth', 4)), ('lying', 6), ('<=>', ('telling-truth', 2), ('lying', 2)), ('not', ('lying', 4)), ('->', ('lying', 7), ('telling-truth', 2)), ('->', ('telling-truth', 3), ('lying', 2)))", "index": 92}
-{"quiz": "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, Oliver, Logan, Scarlett, Liam, Benjamin, and Michael. Olivia commented, \"If Logan is a knave then Scarlett is a knave\". Harper told you that If Michael is a knave then Benjamin is a knave. Oliver stated, \"If Harper is a knave then Olivia is a knave\". Logan noted, \"Oliver is a knave if and only if Scarlett is a knave\". \"If Harper is a knave then Benjamin is a knight,\" Scarlett mentioned. Liam said that If Logan is a knave then Scarlett is a knave. In Benjamin's words: \"Oliver is a knight or Logan is a knight\". In a statement by Michael: \"Oliver is not a knave\". So who is a knight and who is a knave?", "names": ["Olivia", "Harper", "Oliver", "Logan", "Scarlett", "Liam", "Benjamin", "Michael"], "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": "Olivia is a knight, Harper is a knight, Oliver is a knight, Logan is a knight, Scarlett is a knight, Liam is a knight, Benjamin is a knight, and Michael is a knight.", "solution_text_format": "(1) Olivia is a knight\n(2) Harper is a knight\n(3) Oliver is a knight\n(4) Logan is a knight\n(5) Scarlett is a knight\n(6) Liam 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 Olivia is a knight. No contradiction is found in their claim that If Logan is a knave then Scarlett is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Oliver is a knave if and only if Scarlett is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that If Harper is a knave then Olivia is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that If Michael is a knave then Benjamin is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Oliver is not a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Oliver is a knight or Logan is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Harper is a knave then Benjamin is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that If Logan is a knave then Scarlett is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('lying', 4)), ('->', ('lying', 7), ('lying', 6)), ('->', ('lying', 1), ('lying', 0)), ('<=>', ('lying', 2), ('lying', 4)), ('->', ('lying', 1), ('telling-truth', 6)), ('->', ('lying', 3), ('lying', 4)), ('or', ('telling-truth', 2), ('telling-truth', 3)), ('not', ('lying', 2)))", "index": 93}
-{"quiz": "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, Aiden, Victoria, Amelia, Matthew, Evelyn, and Lily. Elizabeth commented, \"If Liam is a knight then Amelia is a knight\". Liam asserted: \"Amelia is a knave or Victoria is a knave\". Aiden remarked, \"If Liam is a knight then Elizabeth is a knight\". According to Victoria, \"If Lily is a knave then Elizabeth is a knave\". \"If Liam is a knave then Aiden is a knight,\" Amelia declared. Matthew said that Elizabeth is a knight or Lily is a knave. Evelyn expressed that Matthew is a knave or Aiden is a knave. \"Elizabeth is a knight and Matthew is a knave,\" Lily mentioned. So who is a knight and who is a knave?", "names": ["Elizabeth", "Liam", "Aiden", "Victoria", "Amelia", "Matthew", "Evelyn", "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, false], "solution_text": "Elizabeth is a knight, Liam is a knight, Aiden is a knight, Victoria is a knave, Amelia is a knight, Matthew is a knight, Evelyn is a knave, and Lily is a knave.", "solution_text_format": "(1) Elizabeth is a knight\n(2) Liam is a knight\n(3) Aiden is a knight\n(4) Victoria is a knave\n(5) Amelia is a knight\n(6) Matthew is a knight\n(7) Evelyn 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 Elizabeth is a knight. No contradiction is found in their claim that If Liam is a knight then Amelia is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Amelia is a knave or Victoria is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that If Liam is a knave then Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that If Liam is a knight then Elizabeth is a knight.", "Victoria cannot be a knight, because this would contradict the claim of Liam that Amelia is a knave or Victoria is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that If Lily is a knave then Elizabeth is a knave.", "Lily cannot be a knight, because this would contradict the false claim of Victoria that If Lily is a knave then Elizabeth is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Elizabeth is a knight and Matthew is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Elizabeth is a knight or Lily is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Matthew is a knave or Aiden is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Matthew is a knave or Aiden is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 1), ('telling-truth', 4)), ('or', ('lying', 4), ('lying', 3)), ('->', ('telling-truth', 1), ('telling-truth', 0)), ('->', ('lying', 7), ('lying', 0)), ('->', ('lying', 1), ('telling-truth', 2)), ('or', ('telling-truth', 0), ('lying', 7)), ('or', ('lying', 5), ('lying', 2)), ('and', ('telling-truth', 0), ('lying', 5)))", "index": 94}
-{"quiz": "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, Mia, Henry, Logan, Emma, Grace, and James. Lucas commented, \"Grace is not a knave\". Avery commented, \"Lucas is a knave and Logan is a knave\". Mia was heard saying, \"Mia is a knight and Logan is a knave\". \"Lucas is a knave or Grace is a knave,\" Henry mentioned. Logan remarked, \"Grace is a knight or Avery is a knave\". In Emma's words: \"Lucas is a knave or James is a knight\". \"Avery is not a knave,\" Grace claimed. According to James, \"Henry is a knight if and only if Emma is a knave\". So who is a knight and who is a knave?", "names": ["Lucas", "Avery", "Mia", "Henry", "Logan", "Emma", "Grace", "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, true, false, false], "solution_text": "Lucas is a knave, Avery is a knave, Mia is a knave, Henry is a knight, Logan is a knight, Emma is a knight, Grace is a knave, and James is a knave.", "solution_text_format": "(1) Lucas is a knave\n(2) Avery is a knave\n(3) Mia is a knave\n(4) Henry is a knight\n(5) Logan is a knight\n(6) Emma is a knight\n(7) Grace 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 Lucas 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 Avery is not a knave.", "Avery cannot be a knight, because this would contradict the claim of their own that Lucas is a knave and Logan is a knave.", "Avery cannot be a knave, because this would contradict the claim of Grace that Avery is not a knave.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Grace.", "Grace cannot be a knave, because this would contradict the claim of Lucas that Grace is not 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 Grace is not a knave.", "Grace cannot be a knight, because this would contradict the false claim of Lucas that Grace is not a knave.", "Assume Grace 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 Grace that Avery is not a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Lucas is a knave and Logan is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Grace is a knight or Avery is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Mia is a knight and Logan is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Mia is a knight and Logan is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Lucas is a knave or Grace is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Lucas is a knave or James is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Henry is a knight if and only if Emma is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Henry is a knight if and only if Emma is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 6)), ('and', ('lying', 0), ('lying', 4)), ('and', ('telling-truth', 2), ('lying', 4)), ('or', ('lying', 0), ('lying', 6)), ('or', ('telling-truth', 6), ('lying', 1)), ('or', ('lying', 0), ('telling-truth', 7)), ('not', ('lying', 1)), ('<=>', ('telling-truth', 3), ('lying', 5)))", "index": 95}
-{"quiz": "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, Amelia, Mason, Ava, Elizabeth, Benjamin, Victoria, and Penelope. Alexander asserted: \"Penelope is a knight and Amelia is a knight\". Amelia stated, \"If Alexander is a knight then Elizabeth is a knight\". As Mason put it, \"Amelia is a knave and Ava is a knight\". According to Ava, \"Amelia is a knight\". \"Ava is not a knave,\" Elizabeth claimed. \"Alexander is not a knave,\" Benjamin declared. \"Mason is a knave and Amelia is a knave\" - Victoria. \"Mason is a knight and Ava is a knight,\" Penelope claimed. So who is a knight and who is a knave?", "names": ["Alexander", "Amelia", "Mason", "Ava", "Elizabeth", "Benjamin", "Victoria", "Penelope"], "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": "Alexander is a knave, Amelia is a knight, Mason is a knave, Ava is a knight, Elizabeth is a knight, Benjamin is a knave, Victoria is a knave, and Penelope is a knave.", "solution_text_format": "(1) Alexander is a knave\n(2) Amelia is a knight\n(3) Mason is a knave\n(4) Ava is a knight\n(5) Elizabeth is a knight\n(6) Benjamin is a knave\n(7) Victoria 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 Alexander is a knight. No contradiction is found in their claim that Penelope is a knight and Amelia is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Mason is a knight and Ava is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Amelia is a knave and Ava is a knight.", "Amelia cannot be a knight, because this would contradict the claim of Mason that Amelia is a knave and Ava is a knight.", "Amelia cannot be a knave, because this would contradict the claim of Alexander that Penelope is a knight and Amelia is a knight.", "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 Penelope that Mason is a knight and Ava is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the claim of Alexander that Penelope is a knight and Amelia is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Penelope is a knight and Amelia is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Mason is a knight and Ava is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Amelia is a knave and Ava is a knight.", "Amelia cannot be a knight, because this would contradict the false claim of Alexander that Penelope is a knight and Amelia is a knight.", "Amelia cannot be a knave, because this would contradict the false claim of their own that If Alexander is a knight then Elizabeth is a knight.", "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 Penelope that Mason is a knight and Ava is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Mason is a knight and Ava is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Amelia is a knave and Ava is a knight.", "Amelia cannot be a knight, because this would contradict the claim of Mason that Amelia is a knave and Ava is a knight.", "Amelia cannot be a knave, because this would contradict the false claim of their own that If Alexander is a knight then Elizabeth is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Amelia is a knave and Ava is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that If Alexander is a knight then Elizabeth is a knight.", "Assume Elizabeth 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 Amelia is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Alexander is not a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Alexander is not a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that Mason is a knave and Amelia is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Mason is a knave and Amelia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 7), ('telling-truth', 1)), ('->', ('telling-truth', 0), ('telling-truth', 4)), ('and', ('lying', 1), ('telling-truth', 3)), ('telling-truth', 1), ('not', ('lying', 3)), ('not', ('lying', 0)), ('and', ('lying', 2), ('lying', 1)), ('and', ('telling-truth', 2), ('telling-truth', 3)))", "index": 96}
-{"quiz": "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, David, Jacob, Benjamin, Sebastian, Victoria, Ella, and Ava. Emma commented, \"Jacob is not a knave\". As David put it, \"If Sebastian is a knave then Sebastian is a knight\". Jacob remarked, \"Sebastian is a knave\". Benjamin commented, \"Ella is a knave or Jacob is a knave\". \"Victoria is a knave if and only if Sebastian is a knight,\" Sebastian declared. \"Sebastian is not a knave,\" Victoria mentioned. Ella said, \"Jacob is a knight or Sebastian is a knight.\" Ava expressed that Emma is a knight and Victoria is a knight. So who is a knight and who is a knave?", "names": ["Emma", "David", "Jacob", "Benjamin", "Sebastian", "Victoria", "Ella", "Ava"], "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": "Emma is a knight, David is a knave, Jacob is a knight, Benjamin is a knave, Sebastian is a knave, Victoria is a knave, Ella is a knight, and Ava is a knave.", "solution_text_format": "(1) Emma is a knight\n(2) David is a knave\n(3) Jacob is a knight\n(4) Benjamin is a knave\n(5) Sebastian is a knave\n(6) Victoria is a knave\n(7) Ella 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 Emma 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 Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Jacob that Sebastian is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Victoria is a knave if and only if Sebastian is a knight.", "Victoria cannot be a knight, because this would contradict the false claim of Sebastian that Victoria is a knave if and only if Sebastian is a knight.", "Assume Victoria 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 their own that If Sebastian is a knave then Sebastian is a knight.", "Assume David is a knave. No contradiction is found in their false claim that If Sebastian is a knave then Sebastian is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Ella is a knave or Jacob is a knave.", "Ella cannot be a knight, because this would contradict the claim of Benjamin that Ella is a knave or Jacob is a knave.", "Ella cannot be a knave, because this would contradict the false claim of their own that Jacob is a knight or Sebastian is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Ella is a knave or Jacob is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Jacob is a knight or Sebastian is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Emma is a knight and Victoria is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Emma is a knight and Victoria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('->', ('lying', 4), ('telling-truth', 4)), ('lying', 4), ('or', ('lying', 6), ('lying', 2)), ('<=>', ('lying', 5), ('telling-truth', 4)), ('not', ('lying', 4)), ('or', ('telling-truth', 2), ('telling-truth', 4)), ('and', ('telling-truth', 0), ('telling-truth', 5)))", "index": 97}
-{"quiz": "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, Aiden, Daniel, Henry, Aria, Mason, and Isabella. \"If Ella is a knight then Daniel is a knave,\" Luke declared. In Ella's words: \"Isabella is not a knight\". Aiden remarked, \"Ella is not a knave\". Daniel expressed that Daniel is a knight. \"Aria is a knave and Aiden is a knight,\" Henry declared. Aria asserted: \"Ella is a knight if and only if Daniel is a knave\". In Mason's words: \"Isabella is a knight\". Isabella was heard saying, \"Henry is a knight if and only if Ella is a knave\". So who is a knight and who is a knave?", "names": ["Luke", "Ella", "Aiden", "Daniel", "Henry", "Aria", "Mason", "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": "Luke is a knave, Ella is a knight, Aiden is a knight, Daniel is a knight, Henry is a knight, Aria is a knave, Mason is a knave, and Isabella is a knave.", "solution_text_format": "(1) Luke is a knave\n(2) Ella is a knight\n(3) Aiden is a knight\n(4) Daniel is a knight\n(5) Henry is a knight\n(6) Aria is a knave\n(7) Mason 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 Luke is a knight. No contradiction is found in their claim that If Ella is a knight then Daniel is a knave.", "Assume Ella 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 Ella that Isabella is not a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Henry is a knight if and only if Ella is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Aria is a knave and Aiden is a knight.", "Aria cannot be a knight, because this would contradict the claim of Henry that Aria is a knave and Aiden is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Ella is a knight if and only if Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of Luke that If Ella is a knight then Daniel is a knave.", "Daniel cannot be a knave, because this would contradict the false claim of Aria that Ella is a knight if and only if Daniel is a knave.", "We have exhausted all possibilities for Daniel and Aria, 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 knight if and only if Ella 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 not a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Henry is a knight if and only if Ella is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Aria is a knave and Aiden is a knight.", "Aria cannot be a knight, because this would contradict the claim of Henry that Aria is a knave and Aiden is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Ella is a knight if and only if Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the false claim of Aria that Ella 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 Daniel is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Ella is not a knave.", "Aiden cannot be a knave, because this would contradict the claim of Henry that Aria is a knave and Aiden is a knight.", "We have exhausted all possibilities for Aiden, Daniel, and Aria, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the claim of Isabella that Henry is a knight if and only if Ella is a knave.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the false claim of Ella that Isabella is not a knight.", "We have exhausted all possibilities for Isabella and Ella, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that If Ella is a knight then Daniel is a knave.", "Assume Ella 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 Ella that Isabella is not a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Henry is a knight if and only if Ella is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Aria is a knave and Aiden is a knight.", "Aria cannot be a knight, because this would contradict the claim of Henry that Aria is a knave and Aiden is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Ella is a knight if and only if Daniel is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Daniel is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Ella is not a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Isabella is a knight.", "Assume Mason 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', 1), ('lying', 3)), ('not', ('telling-truth', 7)), ('not', ('lying', 1)), ('telling-truth', 3), ('and', ('lying', 5), ('telling-truth', 2)), ('<=>', ('telling-truth', 1), ('lying', 3)), ('telling-truth', 7), ('<=>', ('telling-truth', 4), ('lying', 1)))", "index": 98}
-{"quiz": "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, Lucas, Emma, Evelyn, Aria, Mason, Penelope, and Avery. \"Evelyn is a knave,\" James claimed. Lucas said, \"If Emma is a knave then Mason is a knight.\" \"If Aria is a knight then Mason is a knight,\" Emma mentioned. As Evelyn put it, \"Penelope is a knight\". Aria remarked, \"Lucas is not a knave\". Mason told you that Lucas is not a knave. \"Avery is a knave,\" Penelope mentioned. According to Avery, \"Evelyn is a knight and Avery is a knight\". So who is a knight and who is a knave?", "names": ["James", "Lucas", "Emma", "Evelyn", "Aria", "Mason", "Penelope", "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, true, true, false], "solution_text": "James is a knave, Lucas is a knight, Emma is a knight, Evelyn is a knight, Aria is a knight, Mason is a knight, Penelope is a knight, and Avery is a knave.", "solution_text_format": "(1) James is a knave\n(2) Lucas is a knight\n(3) Emma is a knight\n(4) Evelyn is a knight\n(5) Aria is a knight\n(6) Mason is a knight\n(7) Penelope 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 James 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 James that Evelyn is a knave.", "Assume Evelyn 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 Evelyn that Penelope is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Avery is a knave.", "Avery cannot be a knight, because this would contradict the claim of their own that Evelyn is a knight and Avery is a knight.", "Avery cannot be a knave, because this would contradict the false claim of Penelope that Avery is a knave.", "We have exhausted all possibilities for Avery, Penelope, and Evelyn, so let us go back and reconsider James.", "Assume James 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 Penelope is a knight.", "Assume Penelope 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 Penelope that Avery is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Evelyn is a knight and Avery is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that If Emma is a knave then Mason is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If Aria is a knight then Mason is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Lucas is not a knave.", "Assume Mason 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": "(('lying', 3), ('->', ('lying', 2), ('telling-truth', 5)), ('->', ('telling-truth', 4), ('telling-truth', 5)), ('telling-truth', 6), ('not', ('lying', 1)), ('not', ('lying', 1)), ('lying', 7), ('and', ('telling-truth', 3), ('telling-truth', 7)))", "index": 99}