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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 6 inhabitants: David, Isabella, Evelyn, Penelope, Aurora, and Luke. David said, \"Isabella is a knight or Evelyn is a knight.\" Isabella commented, \"David is a knight and Penelope is a knight\". According to Evelyn, \"Isabella is a knight if and only if Luke is a knave\". Penelope commented, \"If Luke is a knave then Luke is a knight\". In Aurora's words: \"Luke is a knight if and only if Aurora is a knight\". Luke commented, \"Luke is a knight if and only if Aurora is a knight\". So who is a knight and who is a knave?", "names": ["David", "Isabella", "Evelyn", "Penelope", "Aurora", "Luke"], "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], "solution_text": "David is a knight, Isabella is a knight, Evelyn is a knave, Penelope is a knight, Aurora is a knight, and Luke is a knight.", "solution_text_format": "(1) David is a knight\n(2) Isabella is a knight\n(3) Evelyn is a knave\n(4) Penelope is a knight\n(5) Aurora is a knight\n(6) Luke is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Isabella is a knight or Evelyn is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that David is a knight and Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that If Luke is a knave then Luke is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Luke is a knight 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 if and only if Aurora is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Isabella is a knight if and only if Luke is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Isabella is a knight if and only if Luke is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('telling-truth', 2)), ('and', ('telling-truth', 0), ('telling-truth', 3)), ('<=>', ('telling-truth', 1), ('lying', 5)), ('->', ('lying', 5), ('telling-truth', 5)), ('<=>', ('telling-truth', 5), ('telling-truth', 4)), ('<=>', ('telling-truth', 5), ('telling-truth', 4)))", "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 6 inhabitants: Isabella, Henry, Michael, Mason, Daniel, and Zoey. In Isabella's words: \"Daniel is not a knave\". In Henry's words: \"Michael is a knight and Daniel is a knave\". According to Michael, \"Daniel is a knave or Isabella is a knight\". \"Michael is a knight or Michael is a knave,\" Mason mentioned. \"Daniel is a knight if and only if Isabella is a knave\" - Daniel. In Zoey's words: \"Daniel is a knave if and only if Isabella is a knave\". So who is a knight and who is a knave?", "names": ["Isabella", "Henry", "Michael", "Mason", "Daniel", "Zoey"], "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], "solution_text": "Isabella is a knave, Henry is a knight, Michael is a knight, Mason is a knight, Daniel is a knave, and Zoey is a knight.", "solution_text_format": "(1) Isabella is a knave\n(2) Henry is a knight\n(3) Michael is a knight\n(4) Mason is a knight\n(5) Daniel is a knave\n(6) Zoey is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Daniel is not a knave.", "Daniel cannot be a knight, because this would contradict the claim of their own that Daniel is a knight if and only if Isabella is a knave.", "Daniel cannot be a knave, because this would contradict the claim of Isabella that Daniel is not a knave.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Daniel is not a knave.", "Daniel cannot be a knight, because this would contradict the false claim of Isabella that Daniel is not a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Daniel is a knight if and only if Isabella is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Michael is a knight and Daniel is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Daniel is a knave or Isabella is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Michael is a knight or Michael is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Daniel is a knave if and only if Isabella is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('and', ('telling-truth', 2), ('lying', 4)), ('or', ('lying', 4), ('telling-truth', 0)), ('or', ('telling-truth', 2), ('lying', 2)), ('<=>', ('telling-truth', 4), ('lying', 0)), ('<=>', ('lying', 4), ('lying', 0)))", "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 6 inhabitants: David, Benjamin, Jackson, James, Sebastian, and Jack. As David put it, \"James is a knave and Jack is a knight\". Benjamin noted, \"James is a knave if and only if Jack is a knight\". Jackson said, \"Jack is a knight.\" James noted, \"David is a knight\". \"James is a knight if and only if Jackson is a knave,\" Sebastian mentioned. \"Sebastian is not a knave,\" Jack mentioned. So who is a knight and who is a knave?", "names": ["David", "Benjamin", "Jackson", "James", "Sebastian", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, false], "solution_text": "David is a knave, Benjamin is a knave, Jackson is a knave, James is a knave, Sebastian is a knave, and Jack is a knave.", "solution_text_format": "(1) David is a knave\n(2) Benjamin is a knave\n(3) Jackson is a knave\n(4) James is a knave\n(5) Sebastian is a knave\n(6) 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 David is a knight. No contradiction is found in their claim that James is a knave and Jack is a knight.", "James cannot be a knight, because this would contradict the claim of David that James is a knave and Jack is a knight.", "James cannot be a knave, because this would contradict the false claim of their own that David is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that James is a knave and Jack is a knight.", "James cannot be a knight, because this would contradict the claim of their own that David is a knight.", "Assume James is a knave. No contradiction is found in their false claim that David is a knight.", "Jack cannot be a knight, because this would contradict the false claim of David that James is a knave and Jack is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Sebastian is not a knave.", "Sebastian cannot be a knight, because this would contradict the false claim of Jack that Sebastian is not a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that James is a knight if and only if Jackson is a knave.", "Jackson cannot be a knight, because this would contradict the claim of their own that Jack is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Jack is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that James is a knave if and only if Jack is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that James is a knave if and only if Jack is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('telling-truth', 5)), ('<=>', ('lying', 3), ('telling-truth', 5)), ('telling-truth', 5), ('telling-truth', 0), ('<=>', ('telling-truth', 3), ('lying', 2)), ('not', ('lying', 4)))", "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 6 inhabitants: David, Ava, Scarlett, Daniel, James, and Lily. David expressed that Lily is not a knight. \"Scarlett is a knave or David is a knave,\" Ava declared. In Scarlett's words: \"Ava is a knight\". As Daniel put it, \"If Ava is a knave then Lily is a knave\". James expressed that Lily is a knight if and only if David is a knave. Lily said, \"If James is a knight then Lily is a knight.\" So who is a knight and who is a knave?", "names": ["David", "Ava", "Scarlett", "Daniel", "James", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true], "solution_text": "David is a knave, Ava is a knight, Scarlett is a knight, Daniel is a knight, James is a knight, and Lily is a knight.", "solution_text_format": "(1) David is a knave\n(2) Ava is a knight\n(3) Scarlett is a knight\n(4) Daniel is a knight\n(5) James is a knight\n(6) 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 David 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 David that Lily is not a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that If James is a knight then Lily is a knight.", "Assume James is a knight. No contradiction is found in their claim that Lily is a knight if and only if David is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Scarlett is a knave or David is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Ava that Scarlett is a knave or David is a knave.", "Scarlett cannot be a knave, because this would contradict the false claim of their own that Ava is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Scarlett is a knave or David is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Ava is a knight.", "Scarlett cannot be a knave, because this would contradict the false claim of Ava that Scarlett is a knave or David is a knave.", "We have exhausted all possibilities for Scarlett and Ava, so let us go back and reconsider James.", "James cannot be a knave, because this would contradict the false claim of their own that Lily is a knight if and only if David is a knave.", "We have exhausted all possibilities for James and Lily, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Lily is not a knight.", "Assume Lily is a knight. No contradiction is found in their claim that If James is a knight then Lily is a knight.", "Assume James is a knight. No contradiction is found in their claim that Lily is a knight if and only if David is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Scarlett is a knave or David is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Ava is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that If Ava is a knave then Lily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 5)), ('or', ('lying', 2), ('lying', 0)), ('telling-truth', 1), ('->', ('lying', 1), ('lying', 5)), ('<=>', ('telling-truth', 5), ('lying', 0)), ('->', ('telling-truth', 4), ('telling-truth', 5)))", "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 6 inhabitants: Samuel, Liam, Logan, Joseph, Ethan, and William. \"Joseph is a knave,\" Samuel declared. Liam remarked, \"Ethan is a knight if and only if Ethan is a knave\". Logan was heard saying, \"If Joseph is a knave then Samuel is a knave\". Joseph commented, \"Liam is a knave\". As Ethan put it, \"Joseph is a knave and William is a knight\". As William put it, \"Samuel is not a knight\". So who is a knight and who is a knave?", "names": ["Samuel", "Liam", "Logan", "Joseph", "Ethan", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, true], "solution_text": "Samuel is a knave, Liam is a knave, Logan is a knight, Joseph is a knight, Ethan is a knave, and William is a knight.", "solution_text_format": "(1) Samuel is a knave\n(2) Liam is a knave\n(3) Logan is a knight\n(4) Joseph is a knight\n(5) Ethan is a knave\n(6) 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 Samuel 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 Samuel that Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Ethan is a knight if and only if Ethan is a knave.", "Liam cannot be a knave, because this would contradict the false claim of Joseph that Liam is a knave.", "We have exhausted all possibilities for Liam and Joseph, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Joseph is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Ethan is a knight if and only if Ethan is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Ethan is a knight if and only if Ethan is a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Joseph is a knave and William is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Joseph is a knave and William is a knight.", "Assume William is a knight. No contradiction is found in their claim that Samuel is not a knight.", "Assume Logan is a knight. No contradiction is found in their claim that If Joseph is a knave then Samuel is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('<=>', ('telling-truth', 4), ('lying', 4)), ('->', ('lying', 3), ('lying', 0)), ('lying', 1), ('and', ('lying', 3), ('telling-truth', 5)), ('not', ('telling-truth', 0)))", "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 6 inhabitants: Sofia, David, Ella, Elizabeth, Owen, and Grace. Sofia said that Owen is a knight or Ella is a knight. David was heard saying, \"If Sofia is a knight then Elizabeth is a knave\". Ella was heard saying, \"David is a knight\". Elizabeth said that If Grace is a knight then Owen is a knave. According to Owen, \"Grace is not a knight\". Grace said, \"If Ella is a knave then Grace is a knight.\" So who is a knight and who is a knave?", "names": ["Sofia", "David", "Ella", "Elizabeth", "Owen", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false], "solution_text": "Sofia is a knight, David is a knave, Ella is a knave, Elizabeth is a knight, Owen is a knight, and Grace is a knave.", "solution_text_format": "(1) Sofia is a knight\n(2) David is a knave\n(3) Ella is a knave\n(4) Elizabeth is a knight\n(5) Owen is a knight\n(6) Grace is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Owen is a knight or Ella is a knight.", "Assume Owen 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 Owen that Grace is not a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that If Ella is a knave then Grace is a knight.", "Ella cannot be a knight, because this would contradict the false claim of Grace that If Ella is a knave then Grace is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that David is a knight.", "David cannot be a knight, because this would contradict the false claim of Ella that David is a knight.", "Assume David is a knave. No contradiction is found in their false claim that If Sofia is a knight then Elizabeth is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Grace is a knight then Owen is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('telling-truth', 2)), ('->', ('telling-truth', 0), ('lying', 3)), ('telling-truth', 1), ('->', ('telling-truth', 5), ('lying', 4)), ('not', ('telling-truth', 5)), ('->', ('lying', 2), ('telling-truth', 5)))", "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 6 inhabitants: Mia, Avery, Sophia, Benjamin, Olivia, and Aurora. \"Sophia is a knight\" - Mia. Avery stated, \"Sophia is a knight or Sophia is a knave\". Sophia stated, \"Olivia is a knave\". \"Mia is not a knave,\" Benjamin mentioned. Olivia said, \"Avery is a knave and Aurora is a knave.\" \"Benjamin is a knave and Sophia is a knight,\" Aurora mentioned. So who is a knight and who is a knave?", "names": ["Mia", "Avery", "Sophia", "Benjamin", "Olivia", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "Mia is a knight, Avery is a knight, Sophia is a knight, Benjamin is a knight, Olivia is a knave, and Aurora is a knave.", "solution_text_format": "(1) Mia is a knight\n(2) Avery is a knight\n(3) Sophia is a knight\n(4) Benjamin is a knight\n(5) Olivia is a knave\n(6) Aurora is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Sophia is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Sophia that Olivia is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Avery is a knave and Aurora is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Sophia is a knight or Sophia is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Benjamin is a knave and Sophia is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of Aurora that Benjamin is a knave and Sophia is a knight.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that Mia is not a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Benjamin is a knave and Sophia is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Mia is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('or', ('telling-truth', 2), ('lying', 2)), ('lying', 4), ('not', ('lying', 0)), ('and', ('lying', 1), ('lying', 5)), ('and', ('lying', 3), ('telling-truth', 2)))", "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 6 inhabitants: Liam, Grace, Aiden, Luke, Aurora, and Elizabeth. \"Grace is a knave or Elizabeth is a knight,\" Liam declared. Grace said, \"Grace is a knight if and only if Luke is a knave.\" \"Aiden is a knight if and only if Liam is a knight,\" Aiden mentioned. In a statement by Luke: \"Aiden is a knight if and only if Grace is a knight\". Aurora said, \"Elizabeth is a knave.\" Elizabeth noted, \"Aiden is not a knave\". So who is a knight and who is a knave?", "names": ["Liam", "Grace", "Aiden", "Luke", "Aurora", "Elizabeth"], "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], "solution_text": "Liam is a knight, Grace is a knave, Aiden is a knight, Luke is a knave, Aurora is a knave, and Elizabeth is a knight.", "solution_text_format": "(1) Liam is a knight\n(2) Grace is a knave\n(3) Aiden is a knight\n(4) Luke is a knave\n(5) Aurora is a knave\n(6) Elizabeth is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Grace is a knave or Elizabeth is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Grace is a knight if and only if Luke is a knave.", "Luke cannot be a knight, because this would contradict the claim of Grace that Grace 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 Aiden is a knight if and only if Grace is a knight.", "Aiden cannot be a knight, because this would contradict the false claim of Luke that Aiden is a knight if and only if Grace is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Aiden is a knight if and only if Liam is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Aiden is not a knave.", "Elizabeth cannot be a knave, because this would contradict the claim of Liam that Grace is a knave or Elizabeth is a knight.", "We have exhausted all possibilities for Elizabeth, Aiden, and Luke, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Grace is a knight if and only if Luke is a knave.", "Luke cannot be a knight, because this would contradict the false claim of Grace that Grace 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 Aiden is a knight if and only if Grace is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Aiden is a knight if and only if Liam is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Aiden is not a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Elizabeth is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('telling-truth', 5)), ('<=>', ('telling-truth', 1), ('lying', 3)), ('<=>', ('telling-truth', 2), ('telling-truth', 0)), ('<=>', ('telling-truth', 2), ('telling-truth', 1)), ('lying', 5), ('not', ('lying', 2)))", "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 6 inhabitants: Mia, Ethan, Michael, William, Amelia, and Avery. In a statement by Mia: \"William is not a knave\". \"Amelia is a knave and Michael is a knave,\" Ethan mentioned. As Michael put it, \"William is a knave or Avery is a knave\". William noted, \"Mia is a knave and Mia is a knight\". Amelia expressed that William is a knave and William is a knight. \"Amelia is a knave if and only if Mia is a knight,\" Avery claimed. So who is a knight and who is a knave?", "names": ["Mia", "Ethan", "Michael", "William", "Amelia", "Avery"], "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], "solution_text": "Mia is a knave, Ethan is a knave, Michael is a knight, William is a knave, Amelia is a knave, and Avery is a knave.", "solution_text_format": "(1) Mia is a knave\n(2) Ethan is a knave\n(3) Michael is a knight\n(4) William is a knave\n(5) Amelia is a knave\n(6) Avery is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that William is not a knave.", "William cannot be a knight, because this would contradict the claim of their own that Mia is a knave and Mia is a knight.", "William cannot be a knave, because this would contradict the claim of Mia that William is not a knave.", "We have exhausted all possibilities for William, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that William is not a knave.", "William cannot be a knight, because this would contradict the false claim of Mia that William is not a knave.", "Assume William is a knave. No contradiction is found in their false claim that Mia is a knave and Mia is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Amelia is a knave and Michael is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Ethan that Amelia is a knave and Michael is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that William is a knave and William is a knight.", "Michael cannot be a knight, because this would contradict the claim of Ethan that Amelia is a knave and Michael is a knave.", "Michael cannot be a knave, because this would contradict the false claim of their own that William is a knave or Avery is a knave.", "We have exhausted all possibilities for Michael and Amelia, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Amelia is a knave and Michael is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that William is a knave and William is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that William is a knave and William is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that William is a knave or Avery is a knave.", "Avery cannot be a knight, because this would contradict the claim of their own that Amelia is a knave if and only if Mia is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Amelia is a knave if and only if Mia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 3)), ('and', ('lying', 4), ('lying', 2)), ('or', ('lying', 3), ('lying', 5)), ('and', ('lying', 0), ('telling-truth', 0)), ('and', ('lying', 3), ('telling-truth', 3)), ('<=>', ('lying', 4), ('telling-truth', 0)))", "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 6 inhabitants: Mason, Mia, William, Ella, Sophia, and Avery. Mason asserted: \"If Avery is a knight then William is a knave\". Mia was heard saying, \"If Ella is a knave then William is a knight\". In William's words: \"Ella is not a knave\". Ella expressed that Avery is a knave if and only if Mia is a knave. \"Ella is a knight if and only if Mason is a knight\" - Sophia. \"Avery is a knight and Mason is a knave\" - Avery. So who is a knight and who is a knave?", "names": ["Mason", "Mia", "William", "Ella", "Sophia", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true], "solution_text": "Mason is a knave, Mia is a knight, William is a knight, Ella is a knight, Sophia is a knave, and Avery is a knight.", "solution_text_format": "(1) Mason is a knave\n(2) Mia is a knight\n(3) William is a knight\n(4) Ella is a knight\n(5) Sophia is a knave\n(6) Avery is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that If Avery is a knight then William is a knave.", "Avery cannot be a knight, because this would contradict the claim of their own that Avery is a knight and Mason is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Avery is a knight and Mason is a knave.", "Assume William 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 Avery is a knave if and only if Mia is a knave.", "Mia cannot be a knight, because this would contradict the claim of Ella that Avery is a knave if and only if Mia is a knave.", "Mia cannot be a knave, because this would contradict the false claim of their own that If Ella is a knave then William is a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the claim of William that Ella is not a knave.", "We have exhausted all possibilities for Ella, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Ella is not a knave.", "Ella cannot be a knight, because this would contradict the false claim of William that Ella is not a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Avery is a knave if and only if Mia is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that If Ella is a knave then William is a knight.", "Mia cannot be a knave, because this would contradict the false claim of Ella that Avery is a knave if and only if Mia is a knave.", "We have exhausted all possibilities for Mia, Ella, William, and Avery, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that If Avery is a knight then William is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Avery is a knight and Mason is a knave.", "Assume William 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 Avery is a knave if and only if Mia is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that If Ella is a knave then William is a knight.", "Sophia cannot be a knight, because this would contradict the claim of their own that Ella is a knight if and only if Mason is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Ella is a knight if and only if Mason is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 5), ('lying', 2)), ('->', ('lying', 3), ('telling-truth', 2)), ('not', ('lying', 3)), ('<=>', ('lying', 5), ('lying', 1)), ('<=>', ('telling-truth', 3), ('telling-truth', 0)), ('and', ('telling-truth', 5), ('lying', 0)))", "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 6 inhabitants: Mia, Aurora, Daniel, Benjamin, Riley, and Amelia. In Mia's words: \"If Riley is a knight then Riley is a knave\". \"Riley is a knave and Benjamin is a knave\" - Aurora. \"Riley is a knight and Daniel is a knight,\" Daniel claimed. Benjamin asserted: \"Daniel is a knave if and only if Riley is a knight\". \"Aurora is a knight if and only if Aurora is a knave,\" Riley claimed. Amelia expressed that Mia is a knight and Daniel is a knight. So who is a knight and who is a knave?", "names": ["Mia", "Aurora", "Daniel", "Benjamin", "Riley", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, false], "solution_text": "Mia is a knight, Aurora is a knight, Daniel is a knave, Benjamin is a knave, Riley is a knave, and Amelia is a knave.", "solution_text_format": "(1) Mia is a knight\n(2) Aurora is a knight\n(3) Daniel is a knave\n(4) Benjamin is a knave\n(5) Riley is a knave\n(6) Amelia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that If Riley is a knight then Riley is a knave.", "Riley cannot be a knight, because this would contradict the claim of Mia that If Riley is a knight then Riley is a knave.", "Assume Riley 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 Riley is a knave and Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Aurora that Riley is a knave and Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Daniel is a knave if and only if Riley is a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that Riley is a knight and Daniel is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Riley is a knight and Daniel is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Mia is a knight and Daniel is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Mia is a knight and Daniel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 4), ('lying', 4)), ('and', ('lying', 4), ('lying', 3)), ('and', ('telling-truth', 4), ('telling-truth', 2)), ('<=>', ('lying', 2), ('telling-truth', 4)), ('<=>', ('telling-truth', 1), ('lying', 1)), ('and', ('telling-truth', 0), ('telling-truth', 2)))", "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 6 inhabitants: Zoey, Victoria, Owen, Daniel, Aurora, and Aria. Zoey expressed that Daniel is a knight or Owen is a knight. Victoria commented, \"Aurora is not a knave\". Owen stated, \"Zoey is not a knave\". \"Aria is a knave or Victoria is a knave\" - Daniel. Aurora commented, \"Aria is a knave if and only if Zoey is a knave\". According to Aria, \"Daniel is a knight and Owen is a knave\". So who is a knight and who is a knave?", "names": ["Zoey", "Victoria", "Owen", "Daniel", "Aurora", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, false], "solution_text": "Zoey is a knight, Victoria is a knave, Owen is a knight, Daniel is a knight, Aurora is a knave, and Aria is a knave.", "solution_text_format": "(1) Zoey is a knight\n(2) Victoria is a knave\n(3) Owen is a knight\n(4) Daniel is a knight\n(5) Aurora is a knave\n(6) 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 Zoey is a knight. No contradiction is found in their claim that Daniel is a knight or Owen is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Aria is a knave or Victoria is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Daniel is a knight and Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of Aria that Daniel is a knight and Owen is a knave.", "Owen cannot be a knave, because this would contradict the false claim of their own that Zoey is not a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Daniel is a knight and Owen is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Zoey is not a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Aurora is not a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Aria is a knave if and only if Zoey is a knave.", "Aurora cannot be a knave, because this would contradict the claim of Victoria that Aurora is not a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Aurora is not a knave.", "Aurora cannot be a knight, because this would contradict the false claim of Victoria that Aurora is not a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Aria is a knave if and only if Zoey is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('telling-truth', 2)), ('not', ('lying', 4)), ('not', ('lying', 0)), ('or', ('lying', 5), ('lying', 1)), ('<=>', ('lying', 5), ('lying', 0)), ('and', ('telling-truth', 3), ('lying', 2)))", "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 6 inhabitants: Mia, Owen, Jackson, Amelia, Samuel, and Logan. According to Mia, \"Amelia is a knight\". Owen expressed that Jackson is a knight. \"If Samuel is a knight then Logan is a knave,\" Jackson declared. \"Logan is a knave\" - Amelia. Samuel was heard saying, \"Owen is a knight if and only if Amelia is a knave\". Logan said that Amelia is a knight and Logan is a knight. So who is a knight and who is a knave?", "names": ["Mia", "Owen", "Jackson", "Amelia", "Samuel", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "Mia is a knight, Owen is a knight, Jackson is a knight, Amelia is a knight, Samuel is a knave, and Logan is a knave.", "solution_text_format": "(1) Mia is a knight\n(2) Owen is a knight\n(3) Jackson is a knight\n(4) Amelia is a knight\n(5) Samuel is a knave\n(6) 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 Mia is a knight. No contradiction is found in their claim that Amelia is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of Amelia that Logan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Amelia is a knight and Logan is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Jackson is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that If Samuel is a knight then Logan is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that Owen is a knight if and only if Amelia is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Owen is a knight if and only if Amelia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 3), ('telling-truth', 2), ('->', ('telling-truth', 4), ('lying', 5)), ('lying', 5), ('<=>', ('telling-truth', 1), ('lying', 3)), ('and', ('telling-truth', 3), ('telling-truth', 5)))", "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 6 inhabitants: Samuel, James, Harper, Scarlett, Logan, and Charlotte. \"Logan is a knight or Logan is a knave,\" Samuel mentioned. James said that Charlotte is a knight if and only if Charlotte is a knave. Harper said that If Samuel is a knave then Charlotte is a knight. Scarlett stated, \"Logan is a knave or Scarlett is a knight\". Logan commented, \"Charlotte is a knave\". \"Harper is a knight and Scarlett is a knave,\" Charlotte mentioned. So who is a knight and who is a knave?", "names": ["Samuel", "James", "Harper", "Scarlett", "Logan", "Charlotte"], "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], "solution_text": "Samuel is a knight, James is a knave, Harper is a knight, Scarlett is a knight, Logan is a knight, and Charlotte is a knave.", "solution_text_format": "(1) Samuel is a knight\n(2) James is a knave\n(3) Harper is a knight\n(4) Scarlett is a knight\n(5) Logan is a knight\n(6) Charlotte is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that Logan is a knight or Logan is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Logan that Charlotte is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Harper is a knight and Scarlett is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that If Samuel is a knave then Charlotte is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Logan is a knave or Scarlett is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Charlotte is a knight if and only if Charlotte is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Charlotte is a knight if and only if Charlotte is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('lying', 4)), ('<=>', ('telling-truth', 5), ('lying', 5)), ('->', ('lying', 0), ('telling-truth', 5)), ('or', ('lying', 4), ('telling-truth', 3)), ('lying', 5), ('and', ('telling-truth', 2), ('lying', 3)))", "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 6 inhabitants: Matthew, Ella, Jackson, Mason, Scarlett, and Luke. Matthew noted, \"Mason is a knave\". \"Matthew is a knight or Luke is a knight\" - Ella. Jackson told you that Mason is not a knave. Mason asserted: \"Ella is a knight or Luke is a knave\". In a statement by Scarlett: \"If Matthew is a knave then Mason is a knight\". According to Luke, \"If Scarlett is a knave then Mason is a knight\". So who is a knight and who is a knave?", "names": ["Matthew", "Ella", "Jackson", "Mason", "Scarlett", "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], "solution_text": "Matthew is a knave, Ella is a knight, Jackson is a knight, Mason is a knight, Scarlett is a knight, and Luke is a knight.", "solution_text_format": "(1) Matthew is a knave\n(2) Ella is a knight\n(3) Jackson is a knight\n(4) Mason is a knight\n(5) Scarlett is a knight\n(6) Luke is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of Matthew that Mason is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Ella is a knight or Luke is a knave.", "Ella cannot be a knight, because this would contradict the false claim of Mason that Ella is a knight or Luke is a knave.", "Ella cannot be a knave, because this would contradict the false claim of their own that Matthew is a knight or Luke is a knight.", "We have exhausted all possibilities for Ella and Mason, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Mason is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Ella is a knight or Luke is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Matthew is a knight or Luke is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that If Scarlett is a knave then Mason is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Matthew is a knave then Mason is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Mason is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('or', ('telling-truth', 0), ('telling-truth', 5)), ('not', ('lying', 3)), ('or', ('telling-truth', 1), ('lying', 5)), ('->', ('lying', 0), ('telling-truth', 3)), ('->', ('lying', 4), ('telling-truth', 3)))", "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 6 inhabitants: Avery, Emma, Amelia, Zoey, Oliver, and Grace. In a statement by Avery: \"Zoey is a knight if and only if Avery is a knight\". Emma said that If Zoey is a knight then Oliver is a knave. \"Grace is a knave or Emma is a knight\" - Amelia. Zoey expressed that Oliver is a knave or Avery is a knave. \"Avery is a knight\" - Oliver. Grace noted, \"Oliver is a knave if and only if Emma is a knave\". So who is a knight and who is a knave?", "names": ["Avery", "Emma", "Amelia", "Zoey", "Oliver", "Grace"], "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], "solution_text": "Avery is a knave, Emma is a knight, Amelia is a knight, Zoey is a knight, Oliver is a knave, and Grace is a knave.", "solution_text_format": "(1) Avery is a knave\n(2) Emma is a knight\n(3) Amelia is a knight\n(4) Zoey is a knight\n(5) Oliver is a knave\n(6) Grace is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Zoey is a knight if and only if Avery is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Oliver is a knave or Avery is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Zoey that Oliver is a knave or Avery is a knave.", "Oliver cannot be a knave, because this would contradict the false claim of their own that Avery is a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Zoey.", "Zoey cannot be a knave, because this would contradict the claim of Avery that Zoey is a knight if and only if Avery is a knight.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Zoey is a knight if and only if Avery is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Oliver is a knave or Avery is a knave.", "Oliver cannot be a knight, because this would contradict the claim of their own that Avery is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Avery is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If Zoey is a knight then Oliver is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Grace is a knave or Emma is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Oliver is a knave if and only if Emma is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Oliver is a knave if and only if Emma is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 3), ('telling-truth', 0)), ('->', ('telling-truth', 3), ('lying', 4)), ('or', ('lying', 5), ('telling-truth', 1)), ('or', ('lying', 4), ('lying', 0)), ('telling-truth', 0), ('<=>', ('lying', 4), ('lying', 1)))", "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 6 inhabitants: Liam, Sofia, Sebastian, Aurora, David, and Oliver. Liam remarked, \"If Sebastian is a knave then Sofia is a knave\". Sofia was heard saying, \"Aurora is not a knave\". \"Aurora is a knight or Sebastian is a knight,\" Sebastian mentioned. Aurora said, \"Oliver is a knave if and only if Liam is a knave.\" In David's words: \"Aurora is a knight if and only if Sebastian is a knave\". \"If Sofia is a knight then David is a knave\" - Oliver. So who is a knight and who is a knave?", "names": ["Liam", "Sofia", "Sebastian", "Aurora", "David", "Oliver"], "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], "solution_text": "Liam is a knight, Sofia is a knight, Sebastian is a knight, Aurora is a knight, David is a knave, and Oliver is a knight.", "solution_text_format": "(1) Liam is a knight\n(2) Sofia is a knight\n(3) Sebastian is a knight\n(4) Aurora is a knight\n(5) David is a knave\n(6) 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 Liam is a knight. No contradiction is found in their claim that If Sebastian is a knave then Sofia is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Aurora is a knight or Sebastian is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Oliver is a knave if and only if Liam is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that If Sofia is a knight then David is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Aurora is not a knave.", "David cannot be a knight, because this would contradict the claim of their own that Aurora is a knight if and only if Sebastian is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Aurora is a knight if and only if Sebastian is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 2), ('lying', 1)), ('not', ('lying', 3)), ('or', ('telling-truth', 3), ('telling-truth', 2)), ('<=>', ('lying', 5), ('lying', 0)), ('<=>', ('telling-truth', 3), ('lying', 2)), ('->', ('telling-truth', 1), ('lying', 4)))", "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 6 inhabitants: Scarlett, Jacob, Benjamin, Charlotte, David, and Zoey. In Scarlett's words: \"Jacob is a knight or Charlotte is a knight\". \"If Charlotte is a knight then Zoey is a knave,\" Jacob claimed. Benjamin remarked, \"Jacob is a knave if and only if David is a knave\". In Charlotte's words: \"Jacob is a knight and David is a knave\". David told you that If Jacob is a knight then Zoey is a knave. As Zoey put it, \"Jacob is not a knight\". So who is a knight and who is a knave?", "names": ["Scarlett", "Jacob", "Benjamin", "Charlotte", "David", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false], "solution_text": "Scarlett is a knight, Jacob is a knight, Benjamin is a knight, Charlotte is a knave, David is a knight, and Zoey is a knave.", "solution_text_format": "(1) Scarlett is a knight\n(2) Jacob is a knight\n(3) Benjamin is a knight\n(4) Charlotte is a knave\n(5) David is a knight\n(6) Zoey is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Jacob is a knight or Charlotte is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that If Charlotte is a knight then Zoey is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Jacob is a knight and David is a knave.", "David cannot be a knight, because this would contradict the claim of Charlotte that Jacob is a knight and David is a knave.", "Assume David is a knave. No contradiction is found in their false claim that If Jacob is a knight then Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Jacob that If Charlotte is a knight then Zoey is a knave.", "Zoey cannot be a knave, because this would contradict the false claim of David that If Jacob is a knight then Zoey is a knave.", "We have exhausted all possibilities for Zoey and David, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Jacob is a knight and David is a knave.", "Assume David is a knight. No contradiction is found in their claim that If Jacob is a knight then Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of David that If Jacob is a knight then Zoey is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Jacob is not a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Jacob is a knave if and only if David is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('telling-truth', 3)), ('->', ('telling-truth', 3), ('lying', 5)), ('<=>', ('lying', 1), ('lying', 4)), ('and', ('telling-truth', 1), ('lying', 4)), ('->', ('telling-truth', 1), ('lying', 5)), ('not', ('telling-truth', 1)))", "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 6 inhabitants: Oliver, Henry, Luke, Ella, Benjamin, and Liam. \"Benjamin is a knave if and only if Ella is a knight\" - Oliver. As Henry put it, \"Oliver is a knave if and only if Benjamin is a knave\". Luke told you that Benjamin is a knave and Ella is a knave. Ella expressed that Henry is a knight and Benjamin is a knight. Benjamin remarked, \"Benjamin is a knight or Liam is a knight\". Liam remarked, \"Benjamin is a knave and Henry is a knave\". So who is a knight and who is a knave?", "names": ["Oliver", "Henry", "Luke", "Ella", "Benjamin", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false], "solution_text": "Oliver is a knave, Henry is a knight, Luke is a knight, Ella is a knave, Benjamin is a knave, and Liam is a knave.", "solution_text_format": "(1) Oliver is a knave\n(2) Henry is a knight\n(3) Luke is a knight\n(4) Ella is a knave\n(5) Benjamin is a knave\n(6) 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 Oliver is a knight. No contradiction is found in their claim that Benjamin is a knave if and only if Ella is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Benjamin is a knight or Liam is a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave and Henry is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Benjamin is a knave and Henry is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Oliver is a knave if and only if Benjamin is a knave.", "Ella cannot be a knight, because this would contradict the claim of Oliver that Benjamin is a knave if and only if Ella is a knight.", "Ella cannot be a knave, because this would contradict the false claim of their own that Henry is a knight and Benjamin is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the false claim of their own that Oliver is a knave if and only if Benjamin is a knave.", "We have exhausted all possibilities for Henry and Liam, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Benjamin is a knight or Liam is a knight.", "Liam cannot be a knight, because this would contradict the false claim of Benjamin that Benjamin is a knight or Liam is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Benjamin is a knave and Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of their own that Oliver is a knave if and only if Benjamin is a knave.", "Henry cannot be a knave, because this would contradict the false claim of Liam that Benjamin is a knave and Henry is a knave.", "We have exhausted all possibilities for Henry, Liam, and Benjamin, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Benjamin is a knave if and only if Ella is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Benjamin is a knight or Liam is a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave and Henry is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Benjamin is a knave and Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of their own that Oliver is a knave if and only if Benjamin is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Oliver is a knave if and only if Benjamin is a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Henry is a knight and Benjamin is a knight.", "Ella cannot be a knave, because this would contradict the false claim of Oliver that Benjamin is a knave if and only if Ella is a knight.", "We have exhausted all possibilities for Ella, Henry, and Liam, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Benjamin is a knight or Liam is a knight.", "Liam cannot be a knight, because this would contradict the false claim of Benjamin that Benjamin is a knight or Liam is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Benjamin is a knave and Henry is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Oliver is a knave if and only if Benjamin is a knave.", "Ella cannot be a knight, because this would contradict the false claim of Oliver that Benjamin is a knave if and only if Ella is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Henry is a knight and Benjamin is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Benjamin is a knave and Ella is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 4), ('telling-truth', 3)), ('<=>', ('lying', 0), ('lying', 4)), ('and', ('lying', 4), ('lying', 3)), ('and', ('telling-truth', 1), ('telling-truth', 4)), ('or', ('telling-truth', 4), ('telling-truth', 5)), ('and', ('lying', 4), ('lying', 1)))", "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 6 inhabitants: David, Charlotte, Aria, Amelia, Grace, and Jackson. David told you that Charlotte is a knight and Amelia is a knave. Charlotte expressed that Jackson is a knave if and only if David is a knight. In Aria's words: \"Amelia is a knight\". Amelia stated, \"David is a knave\". Grace commented, \"Jackson is a knight\". In Jackson's words: \"If Amelia is a knave then Aria is a knave\". So who is a knight and who is a knave?", "names": ["David", "Charlotte", "Aria", "Amelia", "Grace", "Jackson"], "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], "solution_text": "David is a knave, Charlotte is a knight, Aria is a knight, Amelia is a knight, Grace is a knight, and Jackson is a knight.", "solution_text_format": "(1) David is a knave\n(2) Charlotte is a knight\n(3) Aria is a knight\n(4) Amelia is a knight\n(5) Grace is a knight\n(6) Jackson is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Charlotte is a knight and Amelia is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Jackson is a knave if and only if David is a knight.", "Jackson cannot be a knight, because this would contradict the claim of Charlotte that Jackson is a knave if and only if David is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that If Amelia is a knave then Aria is a knave.", "Amelia cannot be a knight, because this would contradict the claim of David that Charlotte is a knight and Amelia is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that David is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Amelia is a knight.", "Aria cannot be a knave, because this would contradict the false claim of Jackson that If Amelia is a knave then Aria is a knave.", "We have exhausted all possibilities for Aria, Amelia, and Jackson, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the claim of David that Charlotte is a knight and Amelia is a knave.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Charlotte is a knight and Amelia is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Jackson is a knave if and only if David is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that If Amelia is a knave then Aria is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that David is a knave.", "Assume Aria 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 Jackson is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('lying', 3)), ('<=>', ('lying', 5), ('telling-truth', 0)), ('telling-truth', 3), ('lying', 0), ('telling-truth', 5), ('->', ('lying', 3), ('lying', 2)))", "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 6 inhabitants: Luke, Michael, Elizabeth, Samuel, Charlotte, and Aurora. In a statement by Luke: \"If Elizabeth is a knave then Samuel is a knave\". Michael noted, \"If Samuel is a knight then Luke is a knight\". Elizabeth told you that Samuel is a knave. Samuel asserted: \"Aurora is a knight or Luke is a knave\". Charlotte said that Aurora is a knight if and only if Elizabeth is a knight. Aurora was heard saying, \"If Elizabeth is a knight then Samuel is a knave\". So who is a knight and who is a knave?", "names": ["Luke", "Michael", "Elizabeth", "Samuel", "Charlotte", "Aurora"], "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], "solution_text": "Luke is a knave, Michael is a knave, Elizabeth is a knave, Samuel is a knight, Charlotte is a knave, and Aurora is a knight.", "solution_text_format": "(1) Luke is a knave\n(2) Michael is a knave\n(3) Elizabeth is a knave\n(4) Samuel is a knight\n(5) Charlotte is a knave\n(6) 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 Luke is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Samuel is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Elizabeth that Samuel is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Aurora is a knight or Luke is a knave.", "Aurora cannot be a knight, because this would contradict the false claim of Samuel that Aurora is a knight or Luke is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of their own that If Elizabeth is a knight then Samuel is a knave.", "We have exhausted all possibilities for Aurora and Samuel, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Luke that If Elizabeth is a knave then Samuel is a knave.", "Samuel cannot be a knave, because this would contradict the false claim of Elizabeth that Samuel is a knave.", "We have exhausted all possibilities for Samuel and Elizabeth, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that If Elizabeth is a knave then Samuel is a knave.", "Elizabeth cannot be a knight, because this would contradict the false claim of Luke that If Elizabeth is a knave then Samuel is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Samuel is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Aurora is a knight or Luke is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that If Elizabeth is a knight then Samuel is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that If Samuel is a knight then Luke is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that If Samuel is a knight then Luke is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Aurora is a knight if and only if Elizabeth is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Aurora is a knight if and only if Elizabeth is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 2), ('lying', 3)), ('->', ('telling-truth', 3), ('telling-truth', 0)), ('lying', 3), ('or', ('telling-truth', 5), ('lying', 0)), ('<=>', ('telling-truth', 5), ('telling-truth', 2)), ('->', ('telling-truth', 2), ('lying', 3)))", "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 6 inhabitants: Jackson, Olivia, Isabella, Sebastian, Jacob, and Daniel. \"Jacob is a knave if and only if Olivia is a knave,\" Jackson mentioned. Olivia said, \"Isabella is not a knave.\" \"Daniel is a knight or Sebastian is a knight\" - Isabella. As Sebastian put it, \"Daniel is a knight if and only if Jacob is a knave\". In Jacob's words: \"Isabella is a knight and Sebastian is a knight\". \"Isabella is a knight and Olivia is a knight,\" Daniel mentioned. So who is a knight and who is a knave?", "names": ["Jackson", "Olivia", "Isabella", "Sebastian", "Jacob", "Daniel"], "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], "solution_text": "Jackson is a knight, Olivia is a knave, Isabella is a knave, Sebastian is a knave, Jacob is a knave, and Daniel is a knave.", "solution_text_format": "(1) Jackson is a knight\n(2) Olivia is a knave\n(3) Isabella is a knave\n(4) Sebastian is a knave\n(5) Jacob is a knave\n(6) 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 Jackson is a knight. No contradiction is found in their claim that Jacob is a knave if and only if Olivia is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Isabella is a knight and Sebastian is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Daniel is a knight or Sebastian is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Isabella is a knight and Olivia is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Isabella is not a knave.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Daniel is a knight if and only if Jacob is a knave.", "Sebastian cannot be a knave, because this would contradict the claim of Jacob that Isabella is a knight and Sebastian is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the claim of Jackson that Jacob is a knave if and only if Olivia is a knave.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Isabella is a knight and Olivia is a knight.", "Olivia cannot be a knight, because this would contradict the false claim of Daniel that Isabella is a knight and Olivia is a knight.", "Olivia cannot be a knave, because this would contradict the claim of Jackson that Jacob is a knave if and only if Olivia is a knave.", "We have exhausted all possibilities for Olivia and Daniel, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the claim of Jacob that Isabella is a knight and Sebastian is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Isabella is a knight and Sebastian is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Daniel is a knight or Sebastian is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Isabella is a knight and Olivia is a knight.", "Olivia cannot be a knight, because this would contradict the claim of Jackson that Jacob is a knave if and only if Olivia is a knave.", "Olivia cannot be a knave, because this would contradict the false claim of their own that Isabella is not a knave.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Isabella is a knight and Olivia is a knight.", "Olivia cannot be a knight, because this would contradict the claim of Jackson that Jacob is a knave if and only if Olivia is a knave.", "Olivia cannot be a knave, because this would contradict the false claim of their own that Isabella is not a knave.", "We have exhausted all possibilities for Olivia and Daniel, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Daniel is a knight or Sebastian is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of Isabella that Daniel is a knight or Sebastian is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Isabella is a knight and Olivia is a knight.", "Olivia cannot be a knight, because this would contradict the claim of Jackson that Jacob is a knave if and only if Olivia is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Isabella is not a knave.", "Sebastian cannot be a knight, because this would contradict the false claim of Isabella that Daniel is a knight or Sebastian is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Daniel is a knight if and only if Jacob is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 4), ('lying', 1)), ('not', ('lying', 2)), ('or', ('telling-truth', 5), ('telling-truth', 3)), ('<=>', ('telling-truth', 5), ('lying', 4)), ('and', ('telling-truth', 2), ('telling-truth', 3)), ('and', ('telling-truth', 2), ('telling-truth', 1)))", "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 6 inhabitants: Ethan, Oliver, Amelia, Charlotte, Michael, and David. Ethan said that Oliver is a knave and David is a knight. Oliver told you that David is a knave or Amelia is a knight. Amelia said that David is a knight. Charlotte said that Amelia is a knight or Oliver is a knave. Michael was heard saying, \"David is not a knave\". David expressed that Amelia is a knight if and only if Charlotte is a knight. So who is a knight and who is a knave?", "names": ["Ethan", "Oliver", "Amelia", "Charlotte", "Michael", "David"], "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], "solution_text": "Ethan is a knave, Oliver is a knight, Amelia is a knight, Charlotte is a knight, Michael is a knight, and David is a knight.", "solution_text_format": "(1) Ethan is a knave\n(2) Oliver is a knight\n(3) Amelia is a knight\n(4) Charlotte is a knight\n(5) Michael is a knight\n(6) 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 Ethan is a knight. No contradiction is found in their claim that Oliver is a knave and David is a knight.", "Oliver cannot be a knight, because this would contradict the claim of Ethan that Oliver is a knave and David is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that David is a knave or Amelia is a knight.", "Assume David is a knight. No contradiction is found in their claim that Amelia is a knight if and only if Charlotte is a knight.", "Amelia cannot be a knight, because this would contradict the false claim of Oliver that David is a knave or Amelia is a knight.", "Amelia cannot be a knave, because this would contradict the false claim of their own that David is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the claim of Ethan that Oliver is a knave and David is a knight.", "We have exhausted all possibilities for David and Oliver, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Oliver is a knave and David is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that David is a knave or Amelia is a knight.", "Assume David is a knight. No contradiction is found in their claim that Amelia is a knight if and only if Charlotte is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that David is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Amelia is a knight or Oliver is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that David is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 1), ('telling-truth', 5)), ('or', ('lying', 5), ('telling-truth', 2)), ('telling-truth', 5), ('or', ('telling-truth', 2), ('lying', 1)), ('not', ('lying', 5)), ('<=>', ('telling-truth', 2), ('telling-truth', 3)))", "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 6 inhabitants: Amelia, Liam, Oliver, Michael, William, and Ava. Amelia noted, \"Ava is a knave or Michael is a knave\". \"William is a knight\" - Liam. \"Ava is a knave and Michael is a knave,\" Oliver claimed. As Michael put it, \"Amelia is not a knave\". William told you that Oliver is a knight and Michael is a knave. Ava remarked, \"Oliver is a knight or Amelia is a knave\". So who is a knight and who is a knave?", "names": ["Amelia", "Liam", "Oliver", "Michael", "William", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, false], "solution_text": "Amelia is a knight, Liam is a knave, Oliver is a knave, Michael is a knight, William is a knave, and Ava is a knave.", "solution_text_format": "(1) Amelia is a knight\n(2) Liam is a knave\n(3) Oliver is a knave\n(4) Michael is a knight\n(5) William is a knave\n(6) 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 Amelia is a knight. No contradiction is found in their claim that Ava is a knave or Michael is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Oliver is a knight or Amelia is a knave.", "Oliver cannot be a knight, because this would contradict the claim of their own that Ava is a knave and Michael is a knave.", "Oliver cannot be a knave, because this would contradict the claim of Ava that Oliver is a knight or Amelia is a knave.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Oliver is a knight or Amelia is a knave.", "Oliver cannot be a knight, because this would contradict the false claim of Ava that Oliver is a knight or Amelia is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Ava is a knave and Michael is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Amelia is not a knave.", "Assume Liam is a knight. No contradiction is found in their claim that William is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Oliver is a knight and Michael is a knave.", "William cannot be a knave, because this would contradict the claim of Liam that William is a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that William is a knight.", "William cannot be a knight, because this would contradict the false claim of Liam that William is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Oliver is a knight and Michael is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 5), ('lying', 3)), ('telling-truth', 4), ('and', ('lying', 5), ('lying', 3)), ('not', ('lying', 0)), ('and', ('telling-truth', 2), ('lying', 3)), ('or', ('telling-truth', 2), ('lying', 0)))", "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 6 inhabitants: Jack, Emma, Avery, Ethan, James, and Lucas. Jack said that If James is a knave then Emma is a knave. Emma commented, \"James is a knave\". According to Avery, \"Lucas is a knave or Jack is a knight\". \"Jack is a knight\" - Ethan. James said, \"Ethan is a knight or Emma is a knight.\" Lucas said that Avery is a knave or Ethan is a knave. So who is a knight and who is a knave?", "names": ["Jack", "Emma", "Avery", "Ethan", "James", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false], "solution_text": "Jack is a knight, Emma is a knave, Avery is a knight, Ethan is a knight, James is a knight, and Lucas is a knave.", "solution_text_format": "(1) Jack is a knight\n(2) Emma is a knave\n(3) Avery is a knight\n(4) Ethan is a knight\n(5) James is a knight\n(6) Lucas is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that If James is a knave then Emma is a knave.", "Assume James is a knight. No contradiction is found in their claim that Ethan is a knight or Emma is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Jack is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that James is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that James is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Lucas is a knave or Jack is a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Avery is a knave or Ethan is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Avery is a knave or Ethan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 4), ('lying', 1)), ('lying', 4), ('or', ('lying', 5), ('telling-truth', 0)), ('telling-truth', 0), ('or', ('telling-truth', 3), ('telling-truth', 1)), ('or', ('lying', 2), ('lying', 3)))", "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 6 inhabitants: Emma, Abigail, Victoria, Evelyn, Avery, and Ella. Emma told you that Avery is a knave. Abigail noted, \"Avery is a knave if and only if Evelyn is a knave\". In Victoria's words: \"Ella is a knave if and only if Avery is a knight\". Evelyn was heard saying, \"Avery is a knave and Avery is a knight\". Avery remarked, \"Victoria is a knave\". As Ella put it, \"Avery is a knave\". So who is a knight and who is a knave?", "names": ["Emma", "Abigail", "Victoria", "Evelyn", "Avery", "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], "solution_text": "Emma is a knight, Abigail is a knight, Victoria is a knight, Evelyn is a knave, Avery is a knave, and Ella is a knight.", "solution_text_format": "(1) Emma is a knight\n(2) Abigail is a knight\n(3) Victoria is a knight\n(4) Evelyn is a knave\n(5) Avery is a knave\n(6) 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 Emma 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 Emma that Avery is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Ella is a knave if and only if Avery is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Avery is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Avery is a knave if and only if Evelyn is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of Abigail that Avery is a knave if and only if Evelyn is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Avery is a knave and Avery is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('<=>', ('lying', 4), ('lying', 3)), ('<=>', ('lying', 5), ('telling-truth', 4)), ('and', ('lying', 4), ('telling-truth', 4)), ('lying', 2), ('lying', 4))", "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 6 inhabitants: Daniel, Emma, Michael, Owen, Liam, and Avery. Daniel commented, \"Michael is a knave and Liam is a knave\". \"Daniel is a knave or Michael is a knight,\" Emma declared. \"Daniel is a knave and Michael is a knight,\" Michael claimed. Owen asserted: \"Daniel is not a knave\". Liam asserted: \"Daniel is a knight\". \"Liam is a knight and Owen is a knave\" - Avery. So who is a knight and who is a knave?", "names": ["Daniel", "Emma", "Michael", "Owen", "Liam", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false], "solution_text": "Daniel is a knave, Emma is a knight, Michael is a knight, Owen is a knave, Liam is a knave, and Avery is a knave.", "solution_text_format": "(1) Daniel is a knave\n(2) Emma is a knight\n(3) Michael is a knight\n(4) Owen is a knave\n(5) Liam is a knave\n(6) 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 Daniel is a knight. No contradiction is found in their claim that Michael is a knave and Liam is a knave.", "Michael cannot be a knight, because this would contradict the claim of Daniel that Michael is a knave and Liam is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Daniel is a knave and Michael is a knight.", "Liam cannot be a knight, because this would contradict the claim of Daniel that Michael is a knave and Liam is a knave.", "Liam cannot be a knave, because this would contradict the false claim of their own that Daniel is a knight.", "We have exhausted all possibilities for Liam and Michael, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Michael is a knave and Liam is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Daniel is a knave and Michael is a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that Daniel is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Daniel is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Daniel is a knave or Michael is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Daniel is not a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Daniel is not a knave.", "Avery cannot be a knight, because this would contradict the claim of their own that Liam is a knight and Owen is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Liam is a knight and Owen is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('lying', 4)), ('or', ('lying', 0), ('telling-truth', 2)), ('and', ('lying', 0), ('telling-truth', 2)), ('not', ('lying', 0)), ('telling-truth', 0), ('and', ('telling-truth', 4), ('lying', 3)))", "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 6 inhabitants: Matthew, David, Lucas, Owen, Amelia, and Joseph. According to Matthew, \"Matthew is a knight if and only if Joseph is a knave\". David stated, \"Joseph is a knave if and only if Amelia is a knave\". Lucas stated, \"Owen is a knight or Amelia is a knave\". \"If Matthew is a knight then Amelia is a knave,\" Owen mentioned. \"Matthew is a knight and Owen is a knight,\" Amelia mentioned. Joseph said that Lucas is a knave or Amelia is a knight. So who is a knight and who is a knave?", "names": ["Matthew", "David", "Lucas", "Owen", "Amelia", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false], "solution_text": "Matthew is a knave, David is a knight, Lucas is a knight, Owen is a knight, Amelia is a knave, and Joseph is a knave.", "solution_text_format": "(1) Matthew is a knave\n(2) David is a knight\n(3) Lucas is a knight\n(4) Owen is a knight\n(5) Amelia is a knave\n(6) 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 Matthew is a knight. No contradiction is found in their claim that Matthew is a knight if and only if Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Matthew that Matthew is a knight if and only if Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Lucas is a knave or Amelia is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Owen is a knight or Amelia is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that If Matthew is a knight then Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Owen that If Matthew is a knight then Amelia is a knave.", "Amelia cannot be a knave, because this would contradict the false claim of their own that Matthew is a knight and Owen is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that If Matthew is a knight then Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Lucas that Owen is a knight or Amelia is a knave.", "Amelia cannot be a knave, because this would contradict the false claim of Owen that If Matthew is a knight then Amelia is a knave.", "We have exhausted all possibilities for Amelia and Owen, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the false claim of Joseph that Lucas is a knave or Amelia is a knight.", "We have exhausted all possibilities for Lucas and Joseph, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Matthew is a knight if and only if Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the false claim of Matthew that Matthew is a knight if and only if Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Lucas is a knave or Amelia is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Owen is a knight or Amelia is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that If Matthew is a knight then Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Matthew is a knight and Owen is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Matthew is a knight and Owen is a knight.", "Assume David is a knight. No contradiction is found in their claim that Joseph is a knave if and only if Amelia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 0), ('lying', 5)), ('<=>', ('lying', 5), ('lying', 4)), ('or', ('telling-truth', 3), ('lying', 4)), ('->', ('telling-truth', 0), ('lying', 4)), ('and', ('telling-truth', 0), ('telling-truth', 3)), ('or', ('lying', 2), ('telling-truth', 4)))", "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 6 inhabitants: Emily, Chloe, Luke, Penelope, Joseph, and Mason. Emily commented, \"Luke is not a knight\". Chloe remarked, \"Penelope is a knave if and only if Penelope is a knight\". Luke said that Luke is a knight if and only if Emily is a knave. In Penelope's words: \"Mason is a knight if and only if Emily is a knight\". \"Emily is a knave,\" Joseph declared. According to Mason, \"Joseph is not a knave\". So who is a knight and who is a knave?", "names": ["Emily", "Chloe", "Luke", "Penelope", "Joseph", "Mason"], "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], "solution_text": "Emily is a knave, Chloe is a knave, Luke is a knight, Penelope is a knave, Joseph is a knight, and Mason is a knight.", "solution_text_format": "(1) Emily is a knave\n(2) Chloe is a knave\n(3) Luke is a knight\n(4) Penelope is a knave\n(5) Joseph is a knight\n(6) 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 Emily 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 Emily that Luke is not a knight.", "Luke cannot be a knave, because this would contradict the false claim of their own that Luke is a knight if and only if Emily is a knave.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Luke is not a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Luke is a knight if and only if Emily is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Penelope is a knave if and only if Penelope is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Penelope is a knave if and only if Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Mason is a knight if and only if Emily is a knight.", "Mason cannot be a knight, because this would contradict the claim of Penelope that Mason is a knight if and only if Emily is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Joseph is not a knave.", "Joseph cannot be a knight, because this would contradict the false claim of Mason that Joseph is not a knave.", "Joseph cannot be a knave, because this would contradict the false claim of their own that Emily is a knave.", "We have exhausted all possibilities for Joseph and 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 if and only if Emily is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Joseph is not a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Emily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('<=>', ('lying', 3), ('telling-truth', 3)), ('<=>', ('telling-truth', 2), ('lying', 0)), ('<=>', ('telling-truth', 5), ('telling-truth', 0)), ('lying', 0), ('not', ('lying', 4)))", "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 6 inhabitants: Victoria, Sofia, Harper, Jack, Riley, and Daniel. Victoria told you that If Harper is a knave then Sofia is a knight. Sofia remarked, \"Victoria is a knave\". \"Daniel is a knave or Jack is a knave,\" Harper claimed. Jack asserted: \"Harper is a knave if and only if Sofia is a knave\". Riley told you that Victoria is a knave if and only if Sofia is a knave. \"Jack is a knave or Harper is a knave,\" Daniel claimed. So who is a knight and who is a knave?", "names": ["Victoria", "Sofia", "Harper", "Jack", "Riley", "Daniel"], "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], "solution_text": "Victoria is a knight, Sofia is a knave, Harper is a knight, Jack is a knave, Riley is a knave, and Daniel is a knight.", "solution_text_format": "(1) Victoria is a knight\n(2) Sofia is a knave\n(3) Harper is a knight\n(4) Jack is a knave\n(5) Riley is a knave\n(6) 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 Victoria is a knight. No contradiction is found in their claim that If Harper is a knave then Sofia is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Daniel is a knave or Jack is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Jack is a knave or Harper is a knave.", "Jack cannot be a knight, because this would contradict the claim of Harper that Daniel is a knave or Jack is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Harper is a knave if and only if Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Victoria is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Victoria is a knave.", "Riley cannot be a knight, because this would contradict the claim of their own that Victoria is a knave if and only if Sofia is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Victoria is a knave if and only if Sofia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 2), ('telling-truth', 1)), ('lying', 0), ('or', ('lying', 5), ('lying', 3)), ('<=>', ('lying', 2), ('lying', 1)), ('<=>', ('lying', 0), ('lying', 1)), ('or', ('lying', 3), ('lying', 2)))", "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 6 inhabitants: Isabella, Victoria, Aurora, David, Oliver, and Lily. \"Lily is a knave and Aurora is a knight,\" Isabella claimed. \"Isabella is not a knight,\" Victoria declared. As Aurora put it, \"David is a knave and Lily is a knight\". \"Lily is not a knight,\" David claimed. Oliver noted, \"Lily is a knight if and only if David is a knight\". Lily was heard saying, \"Oliver is not a knight\". So who is a knight and who is a knave?", "names": ["Isabella", "Victoria", "Aurora", "David", "Oliver", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true], "solution_text": "Isabella is a knave, Victoria is a knight, Aurora is a knight, David is a knave, Oliver is a knave, and Lily is a knight.", "solution_text_format": "(1) Isabella is a knave\n(2) Victoria is a knight\n(3) Aurora is a knight\n(4) David is a knave\n(5) Oliver is a knave\n(6) 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 Isabella is a knight. No contradiction is found in their claim that Lily is a knave and Aurora is a knight.", "Lily cannot be a knight, because this would contradict the claim of Isabella that Lily is a knave and Aurora is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Oliver is not a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Lily is a knight if and only if David is a knight.", "David cannot be a knight, because this would contradict the claim of Oliver that Lily is a knight if and only if David is a knight.", "David cannot be a knave, because this would contradict the false claim of their own that Lily is not a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the false claim of Lily that Oliver is not a knight.", "We have exhausted all possibilities for Oliver and Lily, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Lily is a knave and Aurora is a knight.", "Assume Lily 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 Lily that Oliver is not a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Lily is a knight if and only if David is a knight.", "David cannot be a knight, because this would contradict the claim of their own that Lily is not a knight.", "Assume David is a knave. No contradiction is found in their false claim that Lily is not a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that David is a knave and Lily is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Isabella is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 5), ('telling-truth', 2)), ('not', ('telling-truth', 0)), ('and', ('lying', 3), ('telling-truth', 5)), ('not', ('telling-truth', 5)), ('<=>', ('telling-truth', 5), ('telling-truth', 3)), ('not', ('telling-truth', 4)))", "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 6 inhabitants: Harper, Michael, Olivia, Emily, Alexander, and Isabella. Harper was heard saying, \"Alexander is a knave if and only if Michael is a knight\". Michael stated, \"Isabella is a knight\". Olivia said, \"Emily is a knave if and only if Emily is a knight.\" Emily asserted: \"Michael is not a knave\". In Alexander's words: \"Michael is not a knight\". Isabella commented, \"If Michael is a knave then Alexander is a knight\". So who is a knight and who is a knave?", "names": ["Harper", "Michael", "Olivia", "Emily", "Alexander", "Isabella"], "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], "solution_text": "Harper is a knight, Michael is a knight, Olivia is a knave, Emily is a knight, Alexander is a knave, and Isabella is a knight.", "solution_text_format": "(1) Harper is a knight\n(2) Michael is a knight\n(3) Olivia is a knave\n(4) Emily is a knight\n(5) Alexander is a knave\n(6) 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 Harper is a knight. No contradiction is found in their claim that Alexander is a knave if and only if Michael is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Michael is not a knight.", "Michael cannot be a knight, because this would contradict the claim of Harper that Alexander is a knave if and only if Michael is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Isabella is a knight.", "Isabella cannot be a knight, because this would contradict the false claim of Michael that Isabella is a knight.", "Isabella cannot be a knave, because this would contradict the false claim of their own that If Michael is a knave then Alexander is a knight.", "We have exhausted all possibilities for Isabella and Michael, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Michael is not a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Isabella is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that If Michael is a knave then Alexander is a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that Emily is a knave if and only if Emily is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Emily is a knave if and only if Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Michael is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 4), ('telling-truth', 1)), ('telling-truth', 5), ('<=>', ('lying', 3), ('telling-truth', 3)), ('not', ('lying', 1)), ('not', ('telling-truth', 1)), ('->', ('lying', 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 6 inhabitants: Samuel, Benjamin, Jack, David, Grace, and Ella. Samuel told you that Ella is a knight if and only if Benjamin is a knave. As Benjamin put it, \"Benjamin is a knight\". According to Jack, \"Grace is a knight if and only if Samuel is a knave\". David remarked, \"Samuel is a knight and Jack is a knave\". \"Benjamin is not a knave,\" Grace mentioned. In Ella's words: \"Benjamin is a knave or Samuel is a knight\". So who is a knight and who is a knave?", "names": ["Samuel", "Benjamin", "Jack", "David", "Grace", "Ella"], "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], "solution_text": "Samuel is a knight, Benjamin is a knave, Jack is a knight, David is a knave, Grace is a knave, and Ella is a knight.", "solution_text_format": "(1) Samuel is a knight\n(2) Benjamin is a knave\n(3) Jack is a knight\n(4) David is a knave\n(5) Grace is a knave\n(6) 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 Samuel is a knight. No contradiction is found in their claim that Ella is a knight if and only if Benjamin is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Benjamin is a knave or Samuel is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of Samuel that Ella is a knight if and only if Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Benjamin is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Grace is a knight if and only if Samuel is a knave.", "Grace cannot be a knight, because this would contradict the claim of Jack that Grace is a knight if and only if Samuel is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Benjamin is not a knave.", "David cannot be a knight, because this would contradict the claim of their own that Samuel is a knight and Jack is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Samuel is a knight and Jack is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 5), ('lying', 1)), ('telling-truth', 1), ('<=>', ('telling-truth', 4), ('lying', 0)), ('and', ('telling-truth', 0), ('lying', 2)), ('not', ('lying', 1)), ('or', ('lying', 1), ('telling-truth', 0)))", "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 6 inhabitants: Emma, Logan, Olivia, Evelyn, Ethan, and Owen. In a statement by Emma: \"Logan is a knight or Olivia is a knave\". According to Logan, \"Ethan is a knave or Owen is a knave\". Olivia expressed that Owen is a knave or Logan is a knave. Evelyn stated, \"Logan is a knight\". \"If Olivia is a knave then Owen is a knave,\" Ethan claimed. \"If Olivia is a knave then Emma is a knave,\" Owen declared. So who is a knight and who is a knave?", "names": ["Emma", "Logan", "Olivia", "Evelyn", "Ethan", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true], "solution_text": "Emma is a knave, Logan is a knave, Olivia is a knight, Evelyn is a knave, Ethan is a knight, and Owen is a knight.", "solution_text_format": "(1) Emma is a knave\n(2) Logan is a knave\n(3) Olivia is a knight\n(4) Evelyn is a knave\n(5) Ethan is a knight\n(6) Owen is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Logan is a knight or Olivia is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Ethan is a knave or Owen is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that If Olivia is a knave then Owen is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Owen is a knave or Logan is a knave.", "Owen cannot be a knight, because this would contradict the claim of Logan that Ethan is a knave or Owen is a knave.", "Owen cannot be a knave, because this would contradict the false claim of their own that If Olivia is a knave then Emma is a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Owen is a knave or Logan is a knave.", "Owen cannot be a knight, because this would contradict the claim of Logan that Ethan is a knave or Owen is a knave.", "Owen cannot be a knave, because this would contradict the false claim of Olivia that Owen is a knave or Logan is a knave.", "We have exhausted all possibilities for Owen and Olivia, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that If Olivia is a knave then Owen is a knave.", "Olivia cannot be a knight, because this would contradict the false claim of Ethan that If Olivia is a knave then Owen is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Owen is a knave or Logan is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that If Olivia is a knave then Emma is a knave.", "Owen cannot be a knave, because this would contradict the false claim of Olivia that Owen is a knave or Logan is a knave.", "We have exhausted all possibilities for Owen, Olivia, and Ethan, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Ethan is a knave or Owen is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that If Olivia is a knave then Owen is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Emma that Logan is a knight or Olivia is a knave.", "Olivia cannot be a knave, because this would contradict the false claim of their own that Owen is a knave or Logan is a knave.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the false claim of Logan that Ethan is a knave or Owen is a knave.", "We have exhausted all possibilities for Ethan and Logan, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Logan is a knight or Olivia is a knave.", "Logan cannot be a knight, because this would contradict the false claim of Emma that Logan is a knight or Olivia is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Ethan is a knave or Owen is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that If Olivia is a knave then Owen is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Owen is a knave or Logan is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that If Olivia is a knave then Emma is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Logan is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Logan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('lying', 2)), ('or', ('lying', 4), ('lying', 5)), ('or', ('lying', 5), ('lying', 1)), ('telling-truth', 1), ('->', ('lying', 2), ('lying', 5)), ('->', ('lying', 2), ('lying', 0)))", "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 6 inhabitants: Isabella, Chloe, Sebastian, Owen, Joseph, and Amelia. Isabella told you that Owen is a knave if and only if Chloe is a knight. Chloe asserted: \"Amelia is a knight or Sebastian is a knight\". Sebastian expressed that Amelia is a knave and Chloe is a knave. Owen expressed that Isabella is a knave if and only if Joseph is a knave. Joseph was heard saying, \"Chloe is a knight if and only if Chloe is a knave\". Amelia commented, \"Joseph is a knight if and only if Owen is a knight\". So who is a knight and who is a knave?", "names": ["Isabella", "Chloe", "Sebastian", "Owen", "Joseph", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, true], "solution_text": "Isabella is a knight, Chloe is a knight, Sebastian is a knave, Owen is a knave, Joseph is a knave, and Amelia is a knight.", "solution_text_format": "(1) Isabella is a knight\n(2) Chloe is a knight\n(3) Sebastian is a knave\n(4) Owen is a knave\n(5) Joseph is a knave\n(6) 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 Isabella is a knight. No contradiction is found in their claim that Owen is a knave if and only if Chloe is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Isabella is a knave if and only if Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of their own that Chloe is a knight if and only if Chloe is a knave.", "Joseph cannot be a knave, because this would contradict the claim of Owen that Isabella is a knave if and only if Joseph is a knave.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Isabella is a knave if and only if Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the false claim of Owen that Isabella is a knave if and only if Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Chloe is a knight if and only if Chloe is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Amelia is a knight or Sebastian is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Joseph is a knight if and only if Owen is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Amelia is a knave and Chloe is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Amelia is a knave and Chloe is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('telling-truth', 1)), ('or', ('telling-truth', 5), ('telling-truth', 2)), ('and', ('lying', 5), ('lying', 1)), ('<=>', ('lying', 0), ('lying', 4)), ('<=>', ('telling-truth', 1), ('lying', 1)), ('<=>', ('telling-truth', 4), ('telling-truth', 3)))", "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 6 inhabitants: Michael, Lily, Charlotte, Aria, Penelope, and Evelyn. In Michael's words: \"If Charlotte is a knight then Lily is a knave\". Lily expressed that Charlotte is a knave and Aria is a knight. According to Charlotte, \"Evelyn is a knight\". \"Charlotte is a knight if and only if Evelyn is a knight,\" Aria declared. As Penelope put it, \"Charlotte is a knave\". Evelyn said, \"Michael is a knave and Lily is a knave.\" So who is a knight and who is a knave?", "names": ["Michael", "Lily", "Charlotte", "Aria", "Penelope", "Evelyn"], "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], "solution_text": "Michael is a knight, Lily is a knight, Charlotte is a knave, Aria is a knight, Penelope is a knight, and Evelyn is a knave.", "solution_text_format": "(1) Michael is a knight\n(2) Lily is a knight\n(3) Charlotte is a knave\n(4) Aria is a knight\n(5) Penelope is a knight\n(6) 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 Michael is a knight. No contradiction is found in their claim that If Charlotte is a knight then Lily is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Evelyn is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Lily is a knave.", "Evelyn cannot be a knave, because this would contradict the claim of Charlotte that Evelyn is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Evelyn is a knight.", "Evelyn cannot be a knight, because this would contradict the false claim of Charlotte that Evelyn is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Michael is a knave and Lily is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Charlotte is a knave and Aria is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Charlotte is a knight if and only if Evelyn is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Charlotte is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('lying', 1)), ('and', ('lying', 2), ('telling-truth', 3)), ('telling-truth', 5), ('<=>', ('telling-truth', 2), ('telling-truth', 5)), ('lying', 2), ('and', ('lying', 0), ('lying', 1)))", "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 6 inhabitants: Noah, Isabella, Riley, Sebastian, Alexander, and Lily. Noah remarked, \"Alexander is a knave and Isabella is a knave\". Isabella commented, \"If Noah is a knight then Noah is a knave\". Riley expressed that Alexander is not a knight. Sebastian said, \"Lily is a knight.\" Alexander stated, \"Isabella is a knave\". Lily said that Sebastian is a knight and Sebastian is a knave. So who is a knight and who is a knave?", "names": ["Noah", "Isabella", "Riley", "Sebastian", "Alexander", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false], "solution_text": "Noah is a knave, Isabella is a knight, Riley is a knight, Sebastian is a knave, Alexander is a knave, and Lily is a knave.", "solution_text_format": "(1) Noah is a knave\n(2) Isabella is a knight\n(3) Riley is a knight\n(4) Sebastian is a knave\n(5) Alexander is a knave\n(6) 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 Noah is a knight. No contradiction is found in their claim that Alexander is a knave and Isabella is a knave.", "Alexander cannot be a knight, because this would contradict the claim of Noah that Alexander is a knave and Isabella is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Isabella is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Noah that Alexander is a knave and Isabella is a knave.", "Isabella cannot be a knave, because this would contradict the false claim of Alexander that Isabella is a knave.", "We have exhausted all possibilities for Isabella and Alexander, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Alexander is a knave and Isabella is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Isabella is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Alexander that Isabella is a knave.", "Isabella cannot be a knave, because this would contradict the false claim of their own that If Noah is a knight then Noah is a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Isabella is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that If Noah is a knight then Noah is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Lily is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight and Sebastian is a knave.", "Lily cannot be a knave, because this would contradict the claim of Sebastian that Lily is a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Lily is a knight.", "Lily cannot be a knight, because this would contradict the false claim of Sebastian that Lily is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Sebastian is a knight and Sebastian is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('lying', 1)), ('->', ('telling-truth', 0), ('lying', 0)), ('not', ('telling-truth', 4)), ('telling-truth', 5), ('lying', 1), ('and', ('telling-truth', 3), ('lying', 3)))", "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 6 inhabitants: Jackson, Aiden, Aria, Logan, Charlotte, and Harper. Jackson said, \"If Logan is a knave then Charlotte is a knight.\" According to Aiden, \"Logan is a knight or Jackson is a knave\". \"Jackson is a knight if and only if Aiden is a knave,\" Aria declared. As Logan put it, \"Jackson is a knave and Aiden is a knight\". In Charlotte's words: \"Aria is a knight if and only if Jackson is a knight\". Harper expressed that Aria is a knave if and only if Jackson is a knave. So who is a knight and who is a knave?", "names": ["Jackson", "Aiden", "Aria", "Logan", "Charlotte", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true], "solution_text": "Jackson is a knight, Aiden is a knave, Aria is a knight, Logan is a knave, Charlotte is a knight, and Harper is a knight.", "solution_text_format": "(1) Jackson is a knight\n(2) Aiden is a knave\n(3) Aria is a knight\n(4) Logan is a knave\n(5) Charlotte is a knight\n(6) Harper is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that If Logan is a knave then Charlotte is a knight.", "Logan cannot be a knight, because this would contradict the claim of their own that Jackson is a knave and Aiden is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Jackson is a knave and Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Logan is a knight or Jackson is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Logan is a knight or Jackson is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Aria is a knight if and only if Jackson is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Aiden is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Aria is a knave if and only if Jackson is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('telling-truth', 4)), ('or', ('telling-truth', 3), ('lying', 0)), ('<=>', ('telling-truth', 0), ('lying', 1)), ('and', ('lying', 0), ('telling-truth', 1)), ('<=>', ('telling-truth', 2), ('telling-truth', 0)), ('<=>', ('lying', 2), ('lying', 0)))", "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 6 inhabitants: Emily, Lucas, Aiden, David, Luke, and Daniel. Emily was heard saying, \"David is a knave if and only if Aiden is a knight\". Lucas expressed that If Aiden is a knave then Luke is a knight. Aiden told you that Aiden is a knight or Emily is a knave. David told you that David is a knight if and only if Luke is a knight. \"David is a knave,\" Luke mentioned. \"David is a knave if and only if Lucas is a knight,\" Daniel claimed. So who is a knight and who is a knave?", "names": ["Emily", "Lucas", "Aiden", "David", "Luke", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true], "solution_text": "Emily is a knight, Lucas is a knight, Aiden is a knight, David is a knave, Luke is a knight, and Daniel is a knight.", "solution_text_format": "(1) Emily is a knight\n(2) Lucas is a knight\n(3) Aiden is a knight\n(4) David is a knave\n(5) Luke is a knight\n(6) 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 Emily is a knight. No contradiction is found in their claim that David is a knave if and only if Aiden is a knight.", "Assume David is a knight. No contradiction is found in their claim that David is a knight if and only if Luke is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that David is a knave.", "Luke cannot be a knave, because this would contradict the claim of David that David is a knight if and only if Luke is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that David is a knight if and only if Luke is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that David is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Aiden is a knight or Emily is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that If Aiden is a knave then Luke is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that David is a knave if and only if Lucas is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('telling-truth', 2)), ('->', ('lying', 2), ('telling-truth', 4)), ('or', ('telling-truth', 2), ('lying', 0)), ('<=>', ('telling-truth', 3), ('telling-truth', 4)), ('lying', 3), ('<=>', ('lying', 3), ('telling-truth', 1)))", "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 6 inhabitants: Scarlett, Grace, Mason, Mia, Charlotte, and Riley. Scarlett stated, \"Mia is a knight if and only if Charlotte is a knave\". Grace noted, \"Charlotte is a knave and Scarlett is a knight\". In a statement by Mason: \"Mia is not a knight\". Mia said, \"Charlotte is a knight or Mason is a knave.\" Charlotte commented, \"Mia is a knight and Scarlett is a knight\". According to Riley, \"Mia is a knave or Mason is a knight\". So who is a knight and who is a knave?", "names": ["Scarlett", "Grace", "Mason", "Mia", "Charlotte", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, true], "solution_text": "Scarlett is a knave, Grace is a knave, Mason is a knight, Mia is a knave, Charlotte is a knave, and Riley is a knight.", "solution_text_format": "(1) Scarlett is a knave\n(2) Grace is a knave\n(3) Mason is a knight\n(4) Mia is a knave\n(5) Charlotte is a knave\n(6) 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 Scarlett is a knight. No contradiction is found in their claim that Mia is a knight if and only if Charlotte is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Charlotte is a knight or Mason is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Scarlett that Mia is a knight if and only if Charlotte is a knave.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that Mia is a knight and Scarlett is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Charlotte is a knight or Mason is a knave.", "Charlotte cannot be a knight, because this would contradict the false claim of Mia that Charlotte is a knight or Mason is a knave.", "Charlotte cannot be a knave, because this would contradict the claim of Scarlett that Mia is a knight if and only if Charlotte is a knave.", "We have exhausted all possibilities for Charlotte and Mia, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Mia is a knight if and only if Charlotte is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Charlotte is a knight or Mason is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Mia is a knight and Scarlett is a knight.", "Charlotte cannot be a knave, because this would contradict the false claim of Scarlett that Mia is a knight if and only if Charlotte is a knave.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Charlotte is a knight or Mason is a knave.", "Charlotte cannot be a knight, because this would contradict the false claim of Scarlett that Mia 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 Mia is a knight and Scarlett is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Mia is not a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Charlotte is a knave and Scarlett is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Charlotte is a knave and Scarlett is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Mia is a knave or Mason is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 3), ('lying', 4)), ('and', ('lying', 4), ('telling-truth', 0)), ('not', ('telling-truth', 3)), ('or', ('telling-truth', 4), ('lying', 2)), ('and', ('telling-truth', 3), ('telling-truth', 0)), ('or', ('lying', 3), ('telling-truth', 2)))", "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 6 inhabitants: Oliver, Logan, Elizabeth, Mia, Michael, and Ethan. Oliver stated, \"Elizabeth is a knave if and only if Mia is a knave\". In Logan's words: \"Mia is a knave and Michael is a knight\". According to Elizabeth, \"Logan is a knight or Michael is a knave\". Mia commented, \"Elizabeth is a knave\". According to Michael, \"If Michael is a knight then Logan is a knave\". Ethan expressed that If Elizabeth is a knight then Michael is a knave. So who is a knight and who is a knave?", "names": ["Oliver", "Logan", "Elizabeth", "Mia", "Michael", "Ethan"], "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], "solution_text": "Oliver is a knave, Logan is a knave, Elizabeth is a knave, Mia is a knight, Michael is a knight, and Ethan is a knight.", "solution_text_format": "(1) Oliver is a knave\n(2) Logan is a knave\n(3) Elizabeth is a knave\n(4) Mia is a knight\n(5) Michael is a knight\n(6) 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 Oliver is a knight. No contradiction is found in their claim that Elizabeth is a knave if and only if Mia is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Logan is a knight or Michael is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Mia is a knave and Michael is a knight.", "Mia cannot be a knight, because this would contradict the claim of Logan that Mia is a knave and Michael is a knight.", "Mia cannot be a knave, because this would contradict the claim of Oliver that Elizabeth is a knave if and only if Mia is a knave.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Mia is a knave and Michael is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave.", "Mia cannot be a knave, because this would contradict the claim of Oliver that Elizabeth is a knave if and only if Mia is a knave.", "We have exhausted all possibilities for Mia and Logan, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Logan is a knight or Michael is a knave.", "Logan cannot be a knight, because this would contradict the false claim of Elizabeth that Logan is a knight or Michael is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Mia is a knave and Michael is a knight.", "Mia cannot be a knight, because this would contradict the claim of Oliver that Elizabeth is a knave if and only if Mia is a knave.", "Mia cannot be a knave, because this would contradict the false claim of their own that Elizabeth is a knave.", "We have exhausted all possibilities for Mia, Logan, and Elizabeth, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Elizabeth is a knave if and only if Mia is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Logan is a knight or Michael is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Mia is a knave and Michael is a knight.", "Mia cannot be a knight, because this would contradict the false claim of Oliver that Elizabeth is a knave if and only if Mia is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Elizabeth is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that If Michael is a knight then Logan is a knave.", "Michael cannot be a knave, because this would contradict the claim of Logan that Mia is a knave and Michael is a knight.", "We have exhausted all possibilities for Michael and Mia, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Mia is a knave and Michael is a knight.", "Mia cannot be a knight, because this would contradict the false claim of Oliver that Elizabeth is a knave if and only if Mia is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Elizabeth is a knave.", "Michael cannot be a knight, because this would contradict the false claim of Logan that Mia is a knave and Michael is a knight.", "Michael cannot be a knave, because this would contradict the false claim of their own that If Michael is a knight then Logan is a knave.", "We have exhausted all possibilities for Michael, Mia, and Logan, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Logan is a knight or Michael is a knave.", "Logan cannot be a knight, because this would contradict the false claim of Elizabeth that Logan is a knight or Michael is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Mia is a knave and Michael is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Elizabeth is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that If Michael is a knight then Logan is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that If Elizabeth is a knight then Michael is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('lying', 3)), ('and', ('lying', 3), ('telling-truth', 4)), ('or', ('telling-truth', 1), ('lying', 4)), ('lying', 2), ('->', ('telling-truth', 4), ('lying', 1)), ('->', ('telling-truth', 2), ('lying', 4)))", "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 6 inhabitants: Noah, Harper, Jackson, Aria, Luke, and Penelope. In Noah's words: \"Luke is a knight and Noah is a knight\". Harper noted, \"Luke is a knave if and only if Penelope is a knave\". Jackson told you that If Harper is a knave then Luke is a knave. As Aria put it, \"If Harper is a knave then Jackson is a knight\". \"Penelope is a knave if and only if Jackson is a knight,\" Luke claimed. In Penelope's words: \"Aria is a knight if and only if Harper is a knave\". So who is a knight and who is a knave?", "names": ["Noah", "Harper", "Jackson", "Aria", "Luke", "Penelope"], "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], "solution_text": "Noah is a knave, Harper is a knave, Jackson is a knight, Aria is a knight, Luke is a knave, and Penelope is a knight.", "solution_text_format": "(1) Noah is a knave\n(2) Harper is a knave\n(3) Jackson is a knight\n(4) Aria is a knight\n(5) Luke is a knave\n(6) 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 Noah is a knight. No contradiction is found in their claim that Luke is a knight and Noah is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Penelope is a knave if and only if Jackson is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Aria is a knight if and only if Harper is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that If Harper is a knave then Jackson is a knight.", "Harper cannot be a knight, because this would contradict the claim of Penelope that Aria is a knight if and only if Harper is a knave.", "Harper cannot be a knave, because this would contradict the false claim of their own that Luke is a knave if and only if Penelope is a knave.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that If Harper is a knave then Jackson is a knight.", "Harper cannot be a knight, because this would contradict the false claim of Aria that If Harper is a knave then Jackson is a knight.", "Harper cannot be a knave, because this would contradict the false claim of their own that Luke is a knave if and only if Penelope is a knave.", "We have exhausted all possibilities for Harper and Aria, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Aria is a knight if and only if Harper is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that If Harper is a knave then Jackson is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that Luke is a knave if and only if Penelope is a knave.", "Harper cannot be a knave, because this would contradict the false claim of Penelope that Aria is a knight if and only if Harper is a knave.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that If Harper is a knave then Jackson is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that Luke is a knave if and only if Penelope is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Luke is a knave if and only if Penelope is a knave.", "Jackson cannot be a knight, because this would contradict the claim of their own that If Harper is a knave then Luke is a knave.", "Jackson cannot be a knave, because this would contradict the claim of Luke that Penelope is a knave if and only if Jackson is a knight.", "We have exhausted all possibilities for Jackson, Harper, Aria, and Penelope, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the claim of Noah that Luke is a knight and Noah is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Luke is a knight and Noah is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Penelope is a knave if and only if Jackson is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Aria is a knight if and only if Harper is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that If Harper is a knave then Jackson is a knight.", "Harper cannot be a knight, because this would contradict the claim of Penelope that Aria is a knight if and only if Harper is a knave.", "Harper cannot be a knave, because this would contradict the false claim of their own that Luke is a knave if and only if Penelope is a knave.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that If Harper is a knave then Jackson is a knight.", "Harper cannot be a knight, because this would contradict the false claim of Aria that If Harper is a knave then Jackson is a knight.", "Harper cannot be a knave, because this would contradict the false claim of their own that Luke is a knave if and only if Penelope is a knave.", "We have exhausted all possibilities for Harper and Aria, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Aria is a knight if and only if Harper is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that If Harper is a knave then Jackson is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that Luke is a knave if and only if Penelope is a knave.", "Harper cannot be a knave, because this would contradict the false claim of Penelope that Aria is a knight if and only if Harper is a knave.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that If Harper is a knave then Jackson is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that Luke is a knave if and only if Penelope is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Luke is a knave if and only if Penelope is a knave.", "Jackson cannot be a knight, because this would contradict the claim of their own that If Harper is a knave then Luke is a knave.", "Jackson cannot be a knave, because this would contradict the claim of Luke that Penelope is a knave if and only if Jackson is a knight.", "We have exhausted all possibilities for Jackson, Harper, Aria, and Penelope, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Penelope is a knave if and only if Jackson is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Aria is a knight if and only if Harper is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that If Harper is a knave then Jackson is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that Luke is a knave if and only if Penelope is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Luke is a knave if and only if Penelope is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that If Harper is a knave then Luke is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 4), ('telling-truth', 0)), ('<=>', ('lying', 4), ('lying', 5)), ('->', ('lying', 1), ('lying', 4)), ('->', ('lying', 1), ('telling-truth', 2)), ('<=>', ('lying', 5), ('telling-truth', 2)), ('<=>', ('telling-truth', 3), ('lying', 1)))", "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 6 inhabitants: Jack, Penelope, Daniel, Alexander, Ava, and Mason. In a statement by Jack: \"Daniel is a knave or Mason is a knight\". Penelope stated, \"Alexander is a knave if and only if Penelope is a knight\". Daniel was heard saying, \"Mason is a knave and Ava is a knight\". Alexander noted, \"Penelope is a knight or Jack is a knave\". As Ava put it, \"Alexander is a knight and Penelope is a knight\". Mason said that Ava is a knight or Jack is a knave. So who is a knight and who is a knave?", "names": ["Jack", "Penelope", "Daniel", "Alexander", "Ava", "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, false], "solution_text": "Jack is a knight, Penelope is a knave, Daniel is a knave, Alexander is a knave, Ava is a knave, and Mason is a knave.", "solution_text_format": "(1) Jack is a knight\n(2) Penelope is a knave\n(3) Daniel is a knave\n(4) Alexander is a knave\n(5) Ava is a knave\n(6) Mason is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Daniel is a knave or Mason is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Mason is a knave and Ava is a knight.", "Mason cannot be a knight, because this would contradict the claim of Daniel that Mason is a knave and Ava is a knight.", "Mason cannot be a knave, because this would contradict the claim of Jack that Daniel is a knave or Mason is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Mason is a knave and Ava is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Ava is a knight or Jack is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Alexander is a knight and Penelope is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Penelope is a knight or Jack is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Alexander 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 Alexander is a knave if and only if Penelope is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Alexander.", "Alexander cannot be a knave, because this would contradict the claim of Ava that Alexander is a knight and Penelope is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the claim of Mason that Ava is a knight or Jack is a knave.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Ava is a knight or Jack is a knave.", "Ava cannot be a knight, because this would contradict the false claim of Daniel that Mason is a knave and Ava is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Alexander is a knight and Penelope is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Penelope is a knight or Jack is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Alexander 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 Alexander is a knave if and only if Penelope is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Penelope is a knight or Jack is a knave.", "Penelope cannot be a knight, because this would contradict the false claim of Alexander that Penelope is a knight or Jack is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Alexander is a knave if and only if Penelope is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('telling-truth', 5)), ('<=>', ('lying', 3), ('telling-truth', 1)), ('and', ('lying', 5), ('telling-truth', 4)), ('or', ('telling-truth', 1), ('lying', 0)), ('and', ('telling-truth', 3), ('telling-truth', 1)), ('or', ('telling-truth', 4), ('lying', 0)))", "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 6 inhabitants: James, Grace, Owen, Evelyn, David, and Charlotte. In a statement by James: \"Charlotte is a knave\". In Grace's words: \"Owen is a knight or David is a knight\". Owen commented, \"If Evelyn is a knave then James is a knave\". Evelyn asserted: \"Evelyn is a knight and James is a knave\". David expressed that Charlotte is a knight. Charlotte noted, \"Grace is a knight if and only if Owen is a knave\". So who is a knight and who is a knave?", "names": ["James", "Grace", "Owen", "Evelyn", "David", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, false], "solution_text": "James is a knight, Grace is a knave, Owen is a knave, Evelyn is a knave, David is a knave, and Charlotte is a knave.", "solution_text_format": "(1) James is a knight\n(2) Grace is a knave\n(3) Owen is a knave\n(4) Evelyn is a knave\n(5) David is a knave\n(6) Charlotte is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of James that Charlotte is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Grace is a knight if and only if Owen is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Owen is a knight or David is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that If Evelyn is a knave then James is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Evelyn is a knight and James is a knave.", "Evelyn cannot be a knave, because this would contradict the claim of Owen that If Evelyn is a knave then James is a knave.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the false claim of Charlotte that Grace is a knight if and only if Owen is a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Owen is a knight or David is a knight.", "Owen cannot be a knight, because this would contradict the false claim of Grace that Owen is a knight or David is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that If Evelyn is a knave then James is a knave.", "Evelyn cannot be a knight, because this would contradict the false claim of Owen that If Evelyn is a knave then James is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Evelyn is a knight and James is a knave.", "David cannot be a knight, because this would contradict the false claim of Grace that Owen is a knight or David is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Charlotte is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 5), ('or', ('telling-truth', 2), ('telling-truth', 4)), ('->', ('lying', 3), ('lying', 0)), ('and', ('telling-truth', 3), ('lying', 0)), ('telling-truth', 5), ('<=>', ('telling-truth', 1), ('lying', 2)))", "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 6 inhabitants: Elizabeth, Harper, Emma, Sebastian, Luke, and Sofia. Elizabeth commented, \"Luke is a knave\". In a statement by Harper: \"Luke is not a knight\". Emma asserted: \"Harper is a knave or Sebastian is a knave\". \"Emma is a knave and Sebastian is a knight,\" Sebastian claimed. In a statement by Luke: \"Elizabeth is a knave or Sofia is a knave\". In a statement by Sofia: \"Elizabeth is a knight if and only if Elizabeth is a knave\". So who is a knight and who is a knave?", "names": ["Elizabeth", "Harper", "Emma", "Sebastian", "Luke", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, false], "solution_text": "Elizabeth is a knave, Harper is a knave, Emma is a knight, Sebastian is a knave, Luke is a knight, and Sofia is a knave.", "solution_text_format": "(1) Elizabeth is a knave\n(2) Harper is a knave\n(3) Emma is a knight\n(4) Sebastian is a knave\n(5) Luke is a knight\n(6) Sofia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Luke is a knave.", "Luke cannot be a knight, because this would contradict the claim of Elizabeth that Luke is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Elizabeth is a knave or Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight if and only if Elizabeth is a knave.", "Sofia cannot be a knave, because this would contradict the false claim of Luke that Elizabeth is a knave or Sofia is a knave.", "We have exhausted all possibilities for Sofia and Luke, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Luke is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Elizabeth is a knave or Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight if and only if Elizabeth is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Elizabeth is a knight if and only if Elizabeth is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Luke is not a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Luke is not a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Harper is a knave or Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Emma is a knave and Sebastian is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Emma is a knave and Sebastian is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('not', ('telling-truth', 4)), ('or', ('lying', 1), ('lying', 3)), ('and', ('lying', 2), ('telling-truth', 3)), ('or', ('lying', 0), ('lying', 5)), ('<=>', ('telling-truth', 0), ('lying', 0)))", "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 6 inhabitants: Aria, Penelope, Ella, Lily, Ethan, and Grace. Aria asserted: \"If Grace is a knight then Lily is a knight\". \"If Aria is a knave then Ella is a knight,\" Penelope mentioned. Ella remarked, \"Grace is a knight if and only if Ethan is a knave\". Lily was heard saying, \"If Ella is a knave then Aria is a knight\". \"Lily is not a knight,\" Ethan claimed. Grace was heard saying, \"If Aria is a knave then Ella is a knight\". So who is a knight and who is a knave?", "names": ["Aria", "Penelope", "Ella", "Lily", "Ethan", "Grace"], "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], "solution_text": "Aria is a knight, Penelope is a knight, Ella is a knight, Lily is a knight, Ethan is a knave, and Grace is a knight.", "solution_text_format": "(1) Aria is a knight\n(2) Penelope is a knight\n(3) Ella is a knight\n(4) Lily is a knight\n(5) Ethan is a knave\n(6) Grace is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that If Grace is a knight then Lily is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that If Aria is a knave then Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Grace is a knight if and only if Ethan is a knave.", "Ethan cannot be a knight, because this would contradict the claim of Ella that Grace is a knight if and only if Ethan is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Lily is not a knight.", "Assume Lily is a knight. No contradiction is found in their claim that If Ella is a knave then Aria is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that If Aria is a knave then Ella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 5), ('telling-truth', 3)), ('->', ('lying', 0), ('telling-truth', 2)), ('<=>', ('telling-truth', 5), ('lying', 4)), ('->', ('lying', 2), ('telling-truth', 0)), ('not', ('telling-truth', 3)), ('->', ('lying', 0), ('telling-truth', 2)))", "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 6 inhabitants: Samuel, Lily, Sebastian, Penelope, Chloe, and David. Samuel commented, \"Lily is a knight\". Lily said that Penelope is not a knight. \"David is a knight,\" Sebastian claimed. Penelope noted, \"David is a knight and Chloe is a knave\". Chloe remarked, \"If Penelope is a knave then David is a knight\". David noted, \"Penelope is a knave\". So who is a knight and who is a knave?", "names": ["Samuel", "Lily", "Sebastian", "Penelope", "Chloe", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true], "solution_text": "Samuel is a knight, Lily is a knight, Sebastian is a knight, Penelope is a knave, Chloe is a knight, and David is a knight.", "solution_text_format": "(1) Samuel is a knight\n(2) Lily is a knight\n(3) Sebastian is a knight\n(4) Penelope is a knave\n(5) Chloe is a knight\n(6) 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 Samuel is a knight. No contradiction is found in their claim that Lily is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Penelope cannot be a knight, because this would contradict the claim of Lily that Penelope is not a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that David is a knight and Chloe is a knave.", "Assume David is a knight. No contradiction is found in their claim that Penelope is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that If Penelope is a knave then David is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that David is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('not', ('telling-truth', 3)), ('telling-truth', 5), ('and', ('telling-truth', 5), ('lying', 4)), ('->', ('lying', 3), ('telling-truth', 5)), ('lying', 3))", "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 6 inhabitants: Noah, Charlotte, Lily, Samuel, Owen, and Grace. Noah expressed that Lily is a knight or Charlotte is a knave. Charlotte expressed that If Lily is a knight then Noah is a knight. \"If Samuel is a knight then Lily is a knight,\" Lily claimed. Samuel said, \"Lily is a knight.\" Owen told you that Samuel is a knave or Charlotte is a knave. Grace commented, \"Lily is a knight and Samuel is a knave\". So who is a knight and who is a knave?", "names": ["Noah", "Charlotte", "Lily", "Samuel", "Owen", "Grace"], "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], "solution_text": "Noah is a knight, Charlotte is a knight, Lily is a knight, Samuel is a knight, Owen is a knave, and Grace is a knave.", "solution_text_format": "(1) Noah is a knight\n(2) Charlotte is a knight\n(3) Lily is a knight\n(4) Samuel is a knight\n(5) Owen is a knave\n(6) Grace is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Noah is a knight. No contradiction is found in their claim that Lily is a knight or Charlotte is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that If Samuel is a knight then Lily is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Lily is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Lily is a knight then Noah is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Samuel is a knave or Charlotte is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Samuel is a knave or Charlotte is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Lily is a knight and Samuel is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Lily is a knight and Samuel is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('lying', 1)), ('->', ('telling-truth', 2), ('telling-truth', 0)), ('->', ('telling-truth', 3), ('telling-truth', 2)), ('telling-truth', 2), ('or', ('lying', 3), ('lying', 1)), ('and', ('telling-truth', 2), ('lying', 3)))", "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 6 inhabitants: Grace, Aiden, Alexander, Harper, Zoey, and Henry. According to Grace, \"Henry is a knave and Alexander is a knave\". Aiden expressed that Zoey is a knave if and only if Grace is a knight. \"Grace is a knight and Zoey is a knight\" - Alexander. Harper commented, \"Henry is a knight if and only if Aiden is a knight\". According to Zoey, \"Henry is not a knight\". Henry commented, \"Aiden is a knave\". So who is a knight and who is a knave?", "names": ["Grace", "Aiden", "Alexander", "Harper", "Zoey", "Henry"], "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], "solution_text": "Grace is a knave, Aiden is a knave, Alexander is a knave, Harper is a knave, Zoey is a knave, and Henry is a knight.", "solution_text_format": "(1) Grace is a knave\n(2) Aiden is a knave\n(3) Alexander is a knave\n(4) Harper is a knave\n(5) Zoey is a knave\n(6) Henry is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Henry is a knave and Alexander is a knave.", "Henry cannot be a knight, because this would contradict the claim of Grace that Henry is a knave and Alexander is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Aiden is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Zoey is a knave if and only if Grace is a knight.", "Zoey cannot be a knight, because this would contradict the claim of Aiden that Zoey is a knave if and only if Grace is a knight.", "Zoey cannot be a knave, because this would contradict the false claim of their own that Henry is not a knight.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the false claim of Henry that Aiden is a knave.", "We have exhausted all possibilities for Aiden and Henry, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Henry is a knave and Alexander is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Aiden is a knave.", "Aiden cannot be a knight, because this would contradict the claim of Henry that Aiden is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Zoey is a knave if and only if Grace is a knight.", "Zoey cannot be a knight, because this would contradict the false claim of Aiden that Zoey is a knave if and only if Grace is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Henry is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that Grace is a knight and Zoey is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Grace is a knight and Zoey is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that Henry is a knight if and only if Aiden is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Henry is a knight if and only if Aiden is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 5), ('lying', 2)), ('<=>', ('lying', 4), ('telling-truth', 0)), ('and', ('telling-truth', 0), ('telling-truth', 4)), ('<=>', ('telling-truth', 5), ('telling-truth', 1)), ('not', ('telling-truth', 5)), ('lying', 1))", "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 6 inhabitants: Mia, Lucas, Aiden, Liam, Samuel, and Sofia. In a statement by Mia: \"Samuel is a knave or Aiden is a knave\". Lucas told you that Aiden is a knight and Aiden is a knave. In Aiden's words: \"Aiden is a knight or Mia is a knight\". In a statement by Liam: \"Sofia is a knave or Lucas is a knave\". Samuel remarked, \"Sofia is a knight\". According to Sofia, \"Liam is a knave\". So who is a knight and who is a knave?", "names": ["Mia", "Lucas", "Aiden", "Liam", "Samuel", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, false], "solution_text": "Mia is a knight, Lucas is a knave, Aiden is a knight, Liam is a knight, Samuel is a knave, and Sofia is a knave.", "solution_text_format": "(1) Mia is a knight\n(2) Lucas is a knave\n(3) Aiden is a knight\n(4) Liam is a knight\n(5) Samuel is a knave\n(6) Sofia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Samuel is a knave or Aiden is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Sofia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of Sofia that Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Sofia is a knave or Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Aiden is a knight and Aiden is a knave.", "Lucas cannot be a knave, because this would contradict the false claim of Liam that Sofia is a knave or Lucas is a knave.", "We have exhausted all possibilities for Lucas and Liam, so let us go back and reconsider Sofia.", "Sofia cannot be a knave, because this would contradict the claim of Samuel that Sofia is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Sofia is a knight.", "Sofia cannot be a knight, because this would contradict the false claim of Samuel that Sofia is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Liam is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Sofia is a knave or Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Aiden is a knight and Aiden is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Aiden is a knight and Aiden is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Aiden is a knight or Mia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 4), ('lying', 2)), ('and', ('telling-truth', 2), ('lying', 2)), ('or', ('telling-truth', 2), ('telling-truth', 0)), ('or', ('lying', 5), ('lying', 1)), ('telling-truth', 5), ('lying', 3))", "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 6 inhabitants: James, Alexander, Benjamin, Mia, Sophia, and Oliver. \"Sophia is a knave or Alexander is a knight\" - James. Alexander noted, \"James is a knave and Mia is a knight\". Benjamin told you that Alexander is not a knight. \"Sophia is a knave or Alexander is a knight,\" Mia mentioned. In Sophia's words: \"If Benjamin is a knight then Oliver is a knave\". Oliver asserted: \"Benjamin is a knave and Mia is a knave\". So who is a knight and who is a knave?", "names": ["James", "Alexander", "Benjamin", "Mia", "Sophia", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, false], "solution_text": "James is a knave, Alexander is a knave, Benjamin is a knight, Mia is a knave, Sophia is a knight, and Oliver is a knave.", "solution_text_format": "(1) James is a knave\n(2) Alexander is a knave\n(3) Benjamin is a knight\n(4) Mia is a knave\n(5) Sophia is a knight\n(6) Oliver is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Sophia is a knave or Alexander is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that If Benjamin is a knight then Oliver is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that James is a knave and Mia is a knight.", "Alexander cannot be a knave, because this would contradict the claim of James that Sophia is a knave or Alexander is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that James is a knave and Mia is a knight.", "Alexander cannot be a knave, because this would contradict the claim of James that Sophia is a knave or Alexander is a knight.", "We have exhausted all possibilities for Alexander and Benjamin, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that If Benjamin is a knight then Oliver is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that James is a knave and Mia is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that James is a knave and Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Sophia is a knave or Alexander is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave and Mia is a knave.", "Oliver cannot be a knave, because this would contradict the false claim of Sophia that If Benjamin is a knight then Oliver is a knave.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the false claim of their own that Sophia is a knave or Alexander is a knight.", "We have exhausted all possibilities for Mia and Alexander, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the false claim of Sophia that If Benjamin is a knight then Oliver is a knave.", "We have exhausted all possibilities for Benjamin and Sophia, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Sophia is a knave or Alexander is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that If Benjamin is a knight then Oliver is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the false claim of James that Sophia is a knave or Alexander is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that James is a knave and Mia is a knight.", "Mia cannot be a knight, because this would contradict the false claim of Alexander that James is a knave and Mia is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Sophia is a knave or Alexander is a knight.", "Oliver cannot be a knight, because this would contradict the claim of Sophia that If Benjamin is a knight then Oliver is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Benjamin is a knave and Mia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 4), ('telling-truth', 1)), ('and', ('lying', 0), ('telling-truth', 3)), ('not', ('telling-truth', 1)), ('or', ('lying', 4), ('telling-truth', 1)), ('->', ('telling-truth', 2), ('lying', 5)), ('and', ('lying', 2), ('lying', 3)))", "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 6 inhabitants: Ava, Liam, Jacob, James, Noah, and Joseph. Ava said that Noah is a knave. \"Jacob is a knave if and only if Joseph is a knight,\" Liam mentioned. In Jacob's words: \"James is a knight or Joseph is a knight\". James stated, \"If Noah is a knave then Jacob is a knight\". Noah told you that Jacob is a knight or Jacob is a knave. Joseph remarked, \"Noah is not a knight\". So who is a knight and who is a knave?", "names": ["Ava", "Liam", "Jacob", "James", "Noah", "Joseph"], "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], "solution_text": "Ava is a knave, Liam is a knight, Jacob is a knight, James is a knight, Noah is a knight, and Joseph is a knave.", "solution_text_format": "(1) Ava is a knave\n(2) Liam is a knight\n(3) Jacob is a knight\n(4) James is a knight\n(5) Noah is a knight\n(6) 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 Ava is a knight. No contradiction is found in their claim that Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of Ava that Noah is a knave.", "Noah cannot be a knave, because this would contradict the false claim of their own that Jacob is a knight or Jacob is a knave.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Noah is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Jacob is a knight or Jacob is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that James is a knight or Joseph is a knight.", "Assume James is a knight. No contradiction is found in their claim that If Noah is a knave then Jacob is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Noah is not a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Noah is not a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Jacob is a knave if and only if Joseph is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('<=>', ('lying', 2), ('telling-truth', 5)), ('or', ('telling-truth', 3), ('telling-truth', 5)), ('->', ('lying', 4), ('telling-truth', 2)), ('or', ('telling-truth', 2), ('lying', 2)), ('not', ('telling-truth', 4)))", "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 6 inhabitants: Emily, Noah, Sophia, Olivia, Avery, and Grace. In a statement by Emily: \"If Avery is a knave then Noah is a knight\". As Noah put it, \"If Avery is a knave then Emily is a knave\". Sophia told you that Grace is a knave and Olivia is a knight. \"Noah is not a knight\" - Olivia. Avery told you that Grace is not a knight. Grace told you that If Olivia is a knave then Avery is a knave. So who is a knight and who is a knave?", "names": ["Emily", "Noah", "Sophia", "Olivia", "Avery", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, false], "solution_text": "Emily is a knight, Noah is a knight, Sophia is a knave, Olivia is a knave, Avery is a knight, and Grace is a knave.", "solution_text_format": "(1) Emily is a knight\n(2) Noah is a knight\n(3) Sophia is a knave\n(4) Olivia is a knave\n(5) Avery is a knight\n(6) Grace is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that If Avery is a knave then Noah is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Grace is not a knight.", "Grace cannot be a knight, because this would contradict the claim of Avery that Grace is not a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that If Olivia is a knave then Avery is a knave.", "Olivia cannot be a knight, because this would contradict the false claim of Grace that If Olivia is a knave then Avery is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Noah is not a knight.", "Assume Noah is a knight. No contradiction is found in their claim that If Avery is a knave then Emily is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that Grace is a knave and Olivia is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Grace is a knave and Olivia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 4), ('telling-truth', 1)), ('->', ('lying', 4), ('lying', 0)), ('and', ('lying', 5), ('telling-truth', 3)), ('not', ('telling-truth', 1)), ('not', ('telling-truth', 5)), ('->', ('lying', 3), ('lying', 4)))", "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 6 inhabitants: Elizabeth, Chloe, Avery, Liam, Isabella, and Grace. Elizabeth stated, \"If Avery is a knight then Liam is a knave\". Chloe expressed that Avery is a knight and Elizabeth is a knight. In a statement by Avery: \"Chloe is a knight if and only if Liam is a knight\". Liam said, \"Chloe is a knave if and only if Isabella is a knave.\" According to Isabella, \"Grace is a knave and Elizabeth is a knight\". As Grace put it, \"Chloe is a knave or Isabella is a knave\". So who is a knight and who is a knave?", "names": ["Elizabeth", "Chloe", "Avery", "Liam", "Isabella", "Grace"], "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], "solution_text": "Elizabeth is a knight, Chloe is a knave, Avery is a knave, Liam is a knight, Isabella is a knave, and Grace is a knight.", "solution_text_format": "(1) Elizabeth is a knight\n(2) Chloe is a knave\n(3) Avery is a knave\n(4) Liam is a knight\n(5) Isabella is a knave\n(6) Grace is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that If Avery is a knight then Liam is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Chloe is a knight if and only if Liam is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Avery is a knight and Elizabeth is a knight.", "Liam cannot be a knight, because this would contradict the claim of Elizabeth that If Avery is a knight then Liam is a knave.", "Liam cannot be a knave, because this would contradict the claim of Avery that Chloe 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 Chloe.", "Chloe cannot be a knave, because this would contradict the false claim of their own that Avery is a knight and Elizabeth is a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Chloe is a knight if and only if Liam is a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Avery is a knight and Elizabeth is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Avery is a knight and Elizabeth is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Chloe is a knave if and only if Isabella is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Liam that Chloe is a knave if and only if Isabella is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Grace is a knave and Elizabeth is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Chloe is a knave or Isabella is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('lying', 3)), ('and', ('telling-truth', 2), ('telling-truth', 0)), ('<=>', ('telling-truth', 1), ('telling-truth', 3)), ('<=>', ('lying', 1), ('lying', 4)), ('and', ('lying', 5), ('telling-truth', 0)), ('or', ('lying', 1), ('lying', 4)))", "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 6 inhabitants: Daniel, Harper, Sophia, Liam, Logan, and Oliver. Daniel was heard saying, \"Oliver is a knight or Sophia is a knave\". According to Harper, \"Logan is a knave and Daniel is a knight\". Sophia remarked, \"Daniel is a knight and Harper is a knight\". Liam expressed that Oliver is not a knight. Logan expressed that If Oliver is a knave then Harper is a knave. Oliver noted, \"Sophia is a knight\". So who is a knight and who is a knave?", "names": ["Daniel", "Harper", "Sophia", "Liam", "Logan", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false], "solution_text": "Daniel is a knight, Harper is a knave, Sophia is a knave, Liam is a knight, Logan is a knight, and Oliver is a knave.", "solution_text_format": "(1) Daniel is a knight\n(2) Harper is a knave\n(3) Sophia is a knave\n(4) Liam is a knight\n(5) Logan is a knight\n(6) Oliver is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that Oliver is a knight or Sophia is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Sophia is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Daniel is a knight and Harper is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Logan is a knave and Daniel is a knight.", "Logan cannot be a knight, because this would contradict the claim of Harper that Logan is a knave and Daniel is a knight.", "Logan cannot be a knave, because this would contradict the false claim of their own that If Oliver is a knave then Harper is a knave.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the claim of Sophia that Daniel is a knight and Harper is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the claim of Oliver that Sophia is a knight.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Sophia is a knight.", "Sophia cannot be a knight, because this would contradict the claim of Daniel that Oliver is a knight or Sophia is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Daniel is a knight and Harper is a knight.", "Harper cannot be a knight, because this would contradict the false claim of Sophia that Daniel is a knight and Harper is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Logan is a knave and Daniel is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that If Oliver is a knave then Harper is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Oliver is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('lying', 2)), ('and', ('lying', 4), ('telling-truth', 0)), ('and', ('telling-truth', 0), ('telling-truth', 1)), ('not', ('telling-truth', 5)), ('->', ('lying', 5), ('lying', 1)), ('telling-truth', 2))", "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 6 inhabitants: Olivia, Joseph, Abigail, Sophia, Liam, and Owen. Olivia noted, \"If Owen is a knight then Sophia is a knight\". Joseph expressed that Joseph is a knight or Abigail is a knave. Abigail commented, \"Olivia is a knave and Sophia is a knave\". In Sophia's words: \"Joseph is a knight or Olivia is a knave\". Liam told you that Abigail is not a knight. \"Liam is a knight\" - Owen. So who is a knight and who is a knave?", "names": ["Olivia", "Joseph", "Abigail", "Sophia", "Liam", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true], "solution_text": "Olivia is a knight, Joseph is a knight, Abigail is a knave, Sophia is a knight, Liam is a knight, and Owen is a knight.", "solution_text_format": "(1) Olivia is a knight\n(2) Joseph is a knight\n(3) Abigail is a knave\n(4) Sophia is a knight\n(5) Liam is a knight\n(6) Owen is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that If Owen is a knight then Sophia is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Liam is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Abigail is not a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Olivia is a knave and Sophia is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Olivia is a knave and Sophia is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Joseph is a knight or Olivia is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Joseph is a knight or Abigail is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 5), ('telling-truth', 3)), ('or', ('telling-truth', 1), ('lying', 2)), ('and', ('lying', 0), ('lying', 3)), ('or', ('telling-truth', 1), ('lying', 0)), ('not', ('telling-truth', 2)), ('telling-truth', 4))", "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 6 inhabitants: Sofia, Samuel, Zoey, Jackson, Isabella, and Emily. Sofia noted, \"Isabella is a knight if and only if Emily is a knight\". Samuel told you that Jackson is a knight. \"If Isabella is a knight then Sofia is a knave,\" Zoey claimed. Jackson told you that Sofia is a knight or Isabella is a knave. Isabella was heard saying, \"Jackson is a knight\". Emily expressed that Isabella is not a knave. So who is a knight and who is a knave?", "names": ["Sofia", "Samuel", "Zoey", "Jackson", "Isabella", "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, true], "solution_text": "Sofia is a knight, Samuel is a knight, Zoey is a knave, Jackson is a knight, Isabella is a knight, and Emily is a knight.", "solution_text_format": "(1) Sofia is a knight\n(2) Samuel is a knight\n(3) Zoey is a knave\n(4) Jackson is a knight\n(5) Isabella is a knight\n(6) Emily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Emily is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Jackson is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Sofia is a knight or Isabella is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Isabella is not a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Jackson is a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that If Isabella is a knight then Sofia is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that If Isabella is a knight then Sofia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 4), ('telling-truth', 5)), ('telling-truth', 3), ('->', ('telling-truth', 4), ('lying', 0)), ('or', ('telling-truth', 0), ('lying', 4)), ('telling-truth', 3), ('not', ('lying', 4)))", "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 6 inhabitants: Avery, Benjamin, Aurora, Samuel, James, and Logan. Avery was heard saying, \"Samuel is not a knave\". \"If James is a knave then Logan is a knave,\" Benjamin claimed. \"If James is a knave then James is a knight,\" Aurora claimed. Samuel commented, \"Avery is a knave or Logan is a knave\". James was heard saying, \"Samuel is a knight or Avery is a knight\". Logan commented, \"James is a knight and Samuel is a knave\". So who is a knight and who is a knave?", "names": ["Avery", "Benjamin", "Aurora", "Samuel", "James", "Logan"], "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], "solution_text": "Avery is a knight, Benjamin is a knight, Aurora is a knight, Samuel is a knight, James is a knight, and Logan is a knave.", "solution_text_format": "(1) Avery is a knight\n(2) Benjamin is a knight\n(3) Aurora is a knight\n(4) Samuel is a knight\n(5) James is a knight\n(6) 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 Avery is a knight. No contradiction is found in their claim that Samuel is not a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Avery is a knave or Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of Samuel that Avery is a knave or Logan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that James is a knight and Samuel is a knave.", "Assume James is a knight. No contradiction is found in their claim that Samuel is a knight or Avery is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that If James is a knave then Logan is a knave.", "Assume Aurora 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)), ('->', ('lying', 4), ('lying', 5)), ('->', ('lying', 4), ('telling-truth', 4)), ('or', ('lying', 0), ('lying', 5)), ('or', ('telling-truth', 3), ('telling-truth', 0)), ('and', ('telling-truth', 4), ('lying', 3)))", "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 6 inhabitants: Olivia, Isabella, Jackson, Elizabeth, Grace, and Chloe. \"Grace is a knave or Isabella is a knave,\" Olivia claimed. Isabella said that Olivia is a knave and Isabella is a knight. \"Isabella is a knave or Chloe is a knight,\" Jackson claimed. \"Grace is a knight\" - Elizabeth. Grace noted, \"Chloe is a knight\". Chloe commented, \"Jackson is a knave and Elizabeth is a knight\". So who is a knight and who is a knave?", "names": ["Olivia", "Isabella", "Jackson", "Elizabeth", "Grace", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, false], "solution_text": "Olivia is a knight, Isabella is a knave, Jackson is a knight, Elizabeth is a knave, Grace is a knave, and Chloe is a knave.", "solution_text_format": "(1) Olivia is a knight\n(2) Isabella is a knave\n(3) Jackson is a knight\n(4) Elizabeth is a knave\n(5) Grace is a knave\n(6) Chloe is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Grace is a knave or Isabella is a knave.", "Assume Grace 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 Jackson is a knave and Elizabeth is a knight.", "Jackson cannot be a knight, because this would contradict the claim of Chloe that Jackson is a knave and Elizabeth is a knight.", "Jackson cannot be a knave, because this would contradict the false claim of their own that Isabella is a knave or Chloe is a knight.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the claim of Grace that Chloe is a knight.", "We have exhausted all possibilities for 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 knight.", "Chloe cannot be a knight, because this would contradict the false claim of Grace that Chloe is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Jackson is a knave and Elizabeth is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Isabella is a knave or Chloe is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Olivia is a knave and Isabella is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Olivia is a knave and Isabella is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Grace is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Grace is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 4), ('lying', 1)), ('and', ('lying', 0), ('telling-truth', 1)), ('or', ('lying', 1), ('telling-truth', 5)), ('telling-truth', 4), ('telling-truth', 5), ('and', ('lying', 2), ('telling-truth', 3)))", "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 6 inhabitants: James, Isabella, Henry, Riley, Aurora, and Luke. According to James, \"Riley is a knight if and only if Riley is a knave\". In a statement by Isabella: \"Aurora is a knight if and only if Aurora is a knave\". Henry was heard saying, \"Isabella is not a knave\". Riley asserted: \"Henry is a knave or Aurora is a knight\". Aurora commented, \"James is a knave or Luke is a knight\". Luke asserted: \"If Aurora is a knight then Riley is a knave\". So who is a knight and who is a knave?", "names": ["James", "Isabella", "Henry", "Riley", "Aurora", "Luke"], "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], "solution_text": "James is a knave, Isabella is a knave, Henry is a knave, Riley is a knight, Aurora is a knight, and Luke is a knave.", "solution_text_format": "(1) James is a knave\n(2) Isabella is a knave\n(3) Henry is a knave\n(4) Riley is a knight\n(5) Aurora is a knight\n(6) 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": ["James cannot be a knight, because this would contradict the claim of their own that Riley is a knight if and only if Riley is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Riley is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Henry is a knave or Aurora is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Isabella is not a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that Aurora is a knight if and only if Aurora is a knave.", "Isabella cannot be a knave, because this would contradict the claim of Henry that Isabella is not a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Isabella is not a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that Aurora is a knight if and only if Aurora is a knave.", "Assume Isabella 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 James is a knave or Luke is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that If Aurora is a knight then Riley is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that If Aurora is a knight then Riley is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 3), ('lying', 3)), ('<=>', ('telling-truth', 4), ('lying', 4)), ('not', ('lying', 1)), ('or', ('lying', 2), ('telling-truth', 4)), ('or', ('lying', 0), ('telling-truth', 5)), ('->', ('telling-truth', 4), ('lying', 3)))", "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 6 inhabitants: Jackson, Sebastian, Mason, Abigail, Lucas, and Emma. Jackson said, \"Lucas is not a knave.\" \"Mason is a knave if and only if Lucas is a knave,\" Sebastian claimed. In a statement by Mason: \"Jackson is a knight and Emma is a knave\". \"Lucas is a knave if and only if Jackson is a knight\" - Abigail. \"If Emma is a knave then Abigail is a knight,\" Lucas declared. As Emma put it, \"Sebastian is a knight or Abigail is a knave\". So who is a knight and who is a knave?", "names": ["Jackson", "Sebastian", "Mason", "Abigail", "Lucas", "Emma"], "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], "solution_text": "Jackson is a knight, Sebastian is a knave, Mason is a knave, Abigail is a knave, Lucas is a knight, and Emma is a knight.", "solution_text_format": "(1) Jackson is a knight\n(2) Sebastian is a knave\n(3) Mason is a knave\n(4) Abigail is a knave\n(5) Lucas is a knight\n(6) Emma is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Lucas is not a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that If Emma is a knave then Abigail is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Sebastian is a knight or Abigail is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Mason is a knave if and only if Lucas is a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Jackson is a knight and Emma is a knave.", "Mason cannot be a knave, because this would contradict the claim of Sebastian that Mason is a knave if and only if Lucas is a knave.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Mason is a knave if and only if Lucas is a knave.", "Mason cannot be a knight, because this would contradict the false claim of Sebastian that Mason is a knave if and only if Lucas is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Jackson is a knight and Emma is a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Lucas is a knave if and only if Jackson is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Lucas is a knave if and only if Jackson is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('<=>', ('lying', 2), ('lying', 4)), ('and', ('telling-truth', 0), ('lying', 5)), ('<=>', ('lying', 4), ('telling-truth', 0)), ('->', ('lying', 5), ('telling-truth', 3)), ('or', ('telling-truth', 1), ('lying', 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 6 inhabitants: Ethan, Jacob, Penelope, Daniel, Charlotte, and Jack. Ethan was heard saying, \"Jacob is not a knight\". Jacob said that Penelope is a knight and Charlotte is a knave. Penelope expressed that Ethan is not a knight. Daniel expressed that Ethan is a knight or Charlotte is a knave. Charlotte asserted: \"Jack is not a knave\". Jack told you that If Daniel is a knave then Ethan is a knight. So who is a knight and who is a knave?", "names": ["Ethan", "Jacob", "Penelope", "Daniel", "Charlotte", "Jack"], "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], "solution_text": "Ethan is a knight, Jacob is a knave, Penelope is a knave, Daniel is a knight, Charlotte is a knight, and Jack is a knight.", "solution_text_format": "(1) Ethan is a knight\n(2) Jacob is a knave\n(3) Penelope is a knave\n(4) Daniel is a knight\n(5) Charlotte is a knight\n(6) 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 Jacob is not a knight.", "Jacob cannot be a knight, because this would contradict the claim of Ethan that Jacob is not a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Penelope is a knight and Charlotte is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Ethan is not a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Ethan is not a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Jack is not a knave.", "Assume Jack is a knight. No contradiction is found in their claim that If Daniel is a knave then Ethan is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Ethan is a knight or Charlotte is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 1)), ('and', ('telling-truth', 2), ('lying', 4)), ('not', ('telling-truth', 0)), ('or', ('telling-truth', 0), ('lying', 4)), ('not', ('lying', 5)), ('->', ('lying', 3), ('telling-truth', 0)))", "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 6 inhabitants: Lucas, Ella, James, Oliver, Sofia, and Jacob. \"Ella is not a knight,\" Lucas declared. \"Ella is a knight if and only if Jacob is a knave,\" Ella claimed. James remarked, \"Sofia is a knave if and only if Oliver is a knight\". Oliver commented, \"James is a knight\". In Sofia's words: \"If Jacob is a knave then Lucas is a knight\". Jacob noted, \"James is a knight if and only if Ella is a knave\". So who is a knight and who is a knave?", "names": ["Lucas", "Ella", "James", "Oliver", "Sofia", "Jacob"], "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], "solution_text": "Lucas is a knave, Ella is a knight, James is a knight, Oliver is a knight, Sofia is a knave, and Jacob is a knave.", "solution_text_format": "(1) Lucas is a knave\n(2) Ella is a knight\n(3) James is a knight\n(4) Oliver is a knight\n(5) Sofia is a knave\n(6) 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 Lucas is a knight. No contradiction is found in their claim that Ella is not a knight.", "Ella cannot be a knight, because this would contradict the claim of Lucas that Ella is not a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Ella is a knight if and only if Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the false claim of Ella that Ella is a knight if and only if Jacob is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that James is a knight if and only if Ella is a knave.", "James cannot be a knight, because this would contradict the false claim of Jacob that James is a knight if and only if Ella is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Sofia is a knave if and only if Oliver is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that If Jacob is a knave then Lucas is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that James is a knight.", "Oliver cannot be a knave, because this would contradict the false claim of James that Sofia is a knave if and only if Oliver is a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Sofia.", "Sofia cannot be a knave, because this would contradict the false claim of their own that If Jacob is a knave then Lucas is a knight.", "We have exhausted all possibilities for Sofia, James, Jacob, and Ella, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Ella is not a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Ella is a knight if and only if Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Ella that Ella is a knight if and only if Jacob is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that James is a knight if and only if Ella is a knave.", "Assume James is a knight. No contradiction is found in their claim that Sofia is a knave if and only if Oliver is a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that If Jacob is a knave then Lucas is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that If Jacob is a knave then Lucas is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that James is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 1)), ('<=>', ('telling-truth', 1), ('lying', 5)), ('<=>', ('lying', 4), ('telling-truth', 3)), ('telling-truth', 2), ('->', ('lying', 5), ('telling-truth', 0)), ('<=>', ('telling-truth', 2), ('lying', 1)))", "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 6 inhabitants: Emily, Amelia, Ella, Owen, Michael, and Noah. In a statement by Emily: \"Owen is a knight and Ella is a knave\". Amelia was heard saying, \"Emily is a knight or Michael is a knave\". As Ella put it, \"Michael is a knave if and only if Owen is a knight\". Owen asserted: \"Amelia is a knight and Ella is a knight\". Michael said, \"Owen is a knight or Owen is a knave.\" Noah remarked, \"Amelia is a knight and Owen is a knave\". So who is a knight and who is a knave?", "names": ["Emily", "Amelia", "Ella", "Owen", "Michael", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, false], "solution_text": "Emily is a knave, Amelia is a knave, Ella is a knight, Owen is a knave, Michael is a knight, and Noah is a knave.", "solution_text_format": "(1) Emily is a knave\n(2) Amelia is a knave\n(3) Ella is a knight\n(4) Owen is a knave\n(5) Michael is a knight\n(6) Noah is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Owen is a knight and Ella is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Amelia is a knight and Ella is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Emily is a knight or Michael is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Owen is a knight or Owen is a knave.", "Ella cannot be a knight, because this would contradict the claim of Emily that Owen is a knight and Ella is a knave.", "Ella cannot be a knave, because this would contradict the claim of Owen that Amelia is a knight and Ella is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Michael.", "Michael 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 Michael, so let us go back and reconsider Amelia.", "Amelia cannot be a knave, because this would contradict the false claim of their own that Emily is a knight or Michael is a knave.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the claim of Emily that Owen is a knight and Ella is a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Owen is a knight and Ella is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Amelia is a knight and Ella is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Emily is a knight or Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of Amelia that Emily is a knight or Michael is a knave.", "Michael 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 Michael, so let us go back and reconsider Amelia.", "Amelia cannot be a knave, because this would contradict the claim of Owen that Amelia is a knight and Ella is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Amelia is a knight and Ella is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Emily is a knight or Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of Amelia that Emily is a knight or Michael is a knave.", "Michael 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 Michael, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Emily is a knight or Michael is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Owen is a knight or Owen is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Michael is a knave if and only if Owen is a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that Amelia is a knight and Owen is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Amelia is a knight and Owen is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('lying', 2)), ('or', ('telling-truth', 0), ('lying', 4)), ('<=>', ('lying', 4), ('telling-truth', 3)), ('and', ('telling-truth', 1), ('telling-truth', 2)), ('or', ('telling-truth', 3), ('lying', 3)), ('and', ('telling-truth', 1), ('lying', 3)))", "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 6 inhabitants: Sofia, James, Henry, Jacob, Scarlett, and Amelia. \"Scarlett is a knave and Amelia is a knave,\" Sofia mentioned. According to James, \"Sofia is a knight and Amelia is a knave\". In a statement by Henry: \"James is a knave and Amelia is a knave\". Jacob said, \"Amelia is not a knave.\" \"If Sofia is a knight then Henry is a knave,\" Scarlett declared. According to Amelia, \"Sofia is not a knave\". So who is a knight and who is a knave?", "names": ["Sofia", "James", "Henry", "Jacob", "Scarlett", "Amelia"], "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], "solution_text": "Sofia is a knave, James is a knave, Henry is a knight, Jacob is a knave, Scarlett is a knight, and Amelia is a knave.", "solution_text_format": "(1) Sofia is a knave\n(2) James is a knave\n(3) Henry is a knight\n(4) Jacob is a knave\n(5) Scarlett is a knight\n(6) Amelia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Scarlett is a knave and Amelia is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Sofia that Scarlett is a knave and Amelia is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that If Sofia is a knight then Henry is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that James is a knave and Amelia is a knave.", "James cannot be a knight, because this would contradict the claim of Henry that James is a knave and Amelia is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Sofia is a knight and Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Sofia that Scarlett is a knave and Amelia is a knave.", "Amelia cannot be a knave, because this would contradict the false claim of James that Sofia is a knight and Amelia is a knave.", "We have exhausted all possibilities for Amelia and James, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the false claim of Scarlett that If Sofia is a knight then Henry is a knave.", "We have exhausted all possibilities for Henry and Scarlett, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Scarlett is a knave and Amelia is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Sofia is a knight then Henry is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that James is a knave and Amelia is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Sofia is a knight and Amelia is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Sofia is a knight and Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Henry that James is a knave and Amelia is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Sofia is not a knave.", "Jacob cannot be a knight, because this would contradict the claim of their own that Amelia is not a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Amelia is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('lying', 5)), ('and', ('telling-truth', 0), ('lying', 5)), ('and', ('lying', 1), ('lying', 5)), ('not', ('lying', 5)), ('->', ('telling-truth', 0), ('lying', 2)), ('not', ('lying', 0)))", "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 6 inhabitants: David, Noah, Abigail, Harper, Alexander, and Sebastian. \"Sebastian is a knave or David is a knight,\" David declared. Noah remarked, \"If David is a knight then Alexander is a knight\". Abigail was heard saying, \"Noah is a knave if and only if David is a knight\". Harper noted, \"If Harper is a knight then Alexander is a knave\". Alexander said, \"Sebastian is not a knight.\" Sebastian noted, \"Harper is a knight and David is a knave\". So who is a knight and who is a knave?", "names": ["David", "Noah", "Abigail", "Harper", "Alexander", "Sebastian"], "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], "solution_text": "David is a knave, Noah is a knight, Abigail is a knight, Harper is a knight, Alexander is a knave, and Sebastian is a knight.", "solution_text_format": "(1) David is a knave\n(2) Noah is a knight\n(3) Abigail is a knight\n(4) Harper is a knight\n(5) Alexander is a knave\n(6) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Sebastian is a knave or David is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Harper is a knight and David is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Harper is a knight and David is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that If Harper is a knight then Alexander is a knave.", "Alexander cannot be a knight, because this would contradict the claim of Harper that If Harper is a knight then Alexander is a knave.", "Alexander cannot be a knave, because this would contradict the false claim of their own that Sebastian is not a knight.", "We have exhausted all possibilities for Alexander, 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 Harper is a knight then Alexander is a knave.", "We have exhausted all possibilities for Harper and Sebastian, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Sebastian is a knave or David is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Harper is a knight and David is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that If Harper is a knight then Alexander is a knave.", "Alexander cannot be a knight, because this would contradict the claim of Harper that If Harper is a knight then Alexander is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Sebastian is not a knight.", "Assume Noah is a knight. No contradiction is found in their claim that If David is a knight then Alexander is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Noah is a knave if and only if David is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 5), ('telling-truth', 0)), ('->', ('telling-truth', 0), ('telling-truth', 4)), ('<=>', ('lying', 1), ('telling-truth', 0)), ('->', ('telling-truth', 3), ('lying', 4)), ('not', ('telling-truth', 5)), ('and', ('telling-truth', 3), ('lying', 0)))", "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 6 inhabitants: Elizabeth, Ava, Aurora, Logan, Daniel, and Joseph. Elizabeth was heard saying, \"Ava is a knight and Daniel is a knight\". \"Daniel is a knave and Elizabeth is a knave,\" Ava declared. \"If Joseph is a knave then Aurora is a knight,\" Aurora claimed. \"If Aurora is a knight then Elizabeth is a knave,\" Logan mentioned. According to Daniel, \"If Elizabeth is a knave then Aurora is a knave\". Joseph told you that Aurora is a knight if and only if Ava is a knight. So who is a knight and who is a knave?", "names": ["Elizabeth", "Ava", "Aurora", "Logan", "Daniel", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true], "solution_text": "Elizabeth is a knave, Ava is a knight, Aurora is a knight, Logan is a knight, Daniel is a knave, and Joseph is a knight.", "solution_text_format": "(1) Elizabeth is a knave\n(2) Ava is a knight\n(3) Aurora is a knight\n(4) Logan is a knight\n(5) Daniel is a knave\n(6) Joseph is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Ava is a knight and Daniel is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Daniel is a knave and Elizabeth is a knave.", "Ava cannot be a knave, because this would contradict the claim of Elizabeth that Ava is a knight and Daniel is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Ava is a knight and Daniel is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Daniel is a knave and Elizabeth is a knave.", "Daniel cannot be a knight, because this would contradict the false claim of Elizabeth that Ava is a knight and Daniel is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that If Elizabeth is a knave then Aurora is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that If Joseph is a knave then Aurora is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Aurora is a knight if and only if Ava is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that If Aurora is a knight then Elizabeth is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('telling-truth', 4)), ('and', ('lying', 4), ('lying', 0)), ('->', ('lying', 5), ('telling-truth', 2)), ('->', ('telling-truth', 2), ('lying', 0)), ('->', ('lying', 0), ('lying', 2)), ('<=>', ('telling-truth', 2), ('telling-truth', 1)))", "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 6 inhabitants: Matthew, Liam, Jackson, James, William, and Ava. Matthew noted, \"Ava is a knave if and only if William is a knight\". As Liam put it, \"Matthew is a knight or Ava is a knave\". In a statement by Jackson: \"Ava is not a knave\". James commented, \"William is a knave or James is a knight\". William commented, \"Ava is not a knight\". \"Matthew is a knight or Liam is a knave,\" Ava claimed. So who is a knight and who is a knave?", "names": ["Matthew", "Liam", "Jackson", "James", "William", "Ava"], "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], "solution_text": "Matthew is a knight, Liam is a knight, Jackson is a knight, James is a knight, William is a knave, and Ava is a knight.", "solution_text_format": "(1) Matthew is a knight\n(2) Liam is a knight\n(3) Jackson is a knight\n(4) James is a knight\n(5) William is a knave\n(6) 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 Matthew is a knight. No contradiction is found in their claim that Ava is a knave if and only if William is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Matthew is a knight or Liam is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Matthew is a knight or Ava is a knave.", "William cannot be a knight, because this would contradict the claim of Matthew that Ava is a knave if and only if William is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Ava is not a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Ava is not a knave.", "Assume James is a knight. No contradiction is found in their claim that William is a knave or James is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 5), ('telling-truth', 4)), ('or', ('telling-truth', 0), ('lying', 5)), ('not', ('lying', 5)), ('or', ('lying', 4), ('telling-truth', 3)), ('not', ('telling-truth', 5)), ('or', ('telling-truth', 0), ('lying', 1)))", "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 6 inhabitants: Jack, Emily, Ava, Daniel, Lily, and James. According to Jack, \"James is a knight if and only if Emily is a knight\". \"Ava is a knave\" - Emily. Ava said, \"Daniel is not a knight.\" As Daniel put it, \"If Lily is a knight then Jack is a knight\". Lily said, \"Daniel is a knave and Ava is a knight.\" James remarked, \"Daniel is a knave and Jack is a knight\". So who is a knight and who is a knave?", "names": ["Jack", "Emily", "Ava", "Daniel", "Lily", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, false], "solution_text": "Jack is a knave, Emily is a knight, Ava is a knave, Daniel is a knight, Lily is a knave, and James is a knave.", "solution_text_format": "(1) Jack is a knave\n(2) Emily is a knight\n(3) Ava is a knave\n(4) Daniel is a knight\n(5) Lily is a knave\n(6) 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 Jack is a knight. No contradiction is found in their claim that James is a knight if and only if Emily is a knight.", "Assume James is a knight. No contradiction is found in their claim that Daniel is a knave and Jack is a knight.", "Daniel cannot be a knight, because this would contradict the claim of James that Daniel is a knave and Jack is a knight.", "Daniel cannot be a knave, because this would contradict the false claim of their own that If Lily is a knight then Jack is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Daniel is a knave and Jack is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that If Lily is a knight then Jack is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Daniel is a knave and Ava is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Daniel is a knave and Ava is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Daniel is not a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Daniel is not a knight.", "Emily cannot be a knight, because this would contradict the claim of Jack that James is a knight if and only if Emily is a knight.", "Emily cannot be a knave, because this would contradict the false claim of their own that Ava is a knave.", "We have exhausted all possibilities for Emily, Ava, and Lily, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the false claim of their own that If Lily is a knight then Jack is a knight.", "We have exhausted all possibilities for Daniel and James, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that James is a knight if and only if Emily is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Daniel is a knave and Jack is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Daniel is a knave and Jack is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that If Lily is a knight then Jack is a knight.", "Lily cannot be a knight, because this would contradict the claim of Daniel that If Lily is a knight then Jack is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Daniel is a knave and Ava is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Daniel is not a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Daniel is not a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Ava is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 5), ('telling-truth', 1)), ('lying', 2), ('not', ('telling-truth', 3)), ('->', ('telling-truth', 4), ('telling-truth', 0)), ('and', ('lying', 3), ('telling-truth', 2)), ('and', ('lying', 3), ('telling-truth', 0)))", "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 6 inhabitants: Ava, Chloe, Sophia, Scarlett, Sebastian, and Sofia. \"Sofia is a knight if and only if Scarlett is a knight\" - Ava. \"Sofia is a knave and Chloe is a knight\" - Chloe. Sophia remarked, \"Sofia is a knave and Scarlett is a knave\". \"If Sebastian is a knight then Chloe is a knave,\" Scarlett declared. Sebastian was heard saying, \"Chloe is a knight\". As Sofia put it, \"Sebastian is a knight\". So who is a knight and who is a knave?", "names": ["Ava", "Chloe", "Sophia", "Scarlett", "Sebastian", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, false], "solution_text": "Ava is a knave, Chloe is a knave, Sophia is a knave, Scarlett is a knight, Sebastian is a knave, and Sofia is a knave.", "solution_text_format": "(1) Ava is a knave\n(2) Chloe is a knave\n(3) Sophia is a knave\n(4) Scarlett is a knight\n(5) Sebastian is a knave\n(6) Sofia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Sofia is a knight if and only if Scarlett is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Chloe is a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Sofia is a knave and Chloe is a knight.", "Chloe cannot be a knave, because this would contradict the claim of Sebastian that Chloe is a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the claim of Sofia that Sebastian is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Sebastian is a knight.", "Sebastian cannot be a knight, because this would contradict the false claim of Sofia that Sebastian is a knight.", "Assume Sebastian 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 Sebastian that Chloe is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Sofia is a knave and Chloe is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of Ava that Sofia is a knight if and only if Scarlett is a knight.", "Scarlett cannot be a knave, because this would contradict the false claim of their own that If Sebastian is a knight then Chloe is a knave.", "We have exhausted all possibilities for Scarlett, Chloe, Sebastian, and Sofia, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Sofia is a knight if and only if Scarlett is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Chloe is a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Sofia is a knave and Chloe is a knight.", "Chloe cannot be a knave, because this would contradict the claim of Sebastian that Chloe is a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the claim of Sofia that Sebastian is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Sebastian is a knight.", "Sebastian cannot be a knight, because this would contradict the false claim of Sofia that Sebastian is a knight.", "Assume Sebastian 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 Sebastian that Chloe is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Sofia is a knave and Chloe is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Sebastian is a knight then Chloe is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that Sofia is a knave and Scarlett is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Sofia is a knave and Scarlett is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 5), ('telling-truth', 3)), ('and', ('lying', 5), ('telling-truth', 1)), ('and', ('lying', 5), ('lying', 3)), ('->', ('telling-truth', 4), ('lying', 1)), ('telling-truth', 1), ('telling-truth', 4))", "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 6 inhabitants: Emily, Mia, Aiden, Zoey, Luke, and Victoria. Emily noted, \"Aiden is not a knight\". \"Aiden is a knave\" - Mia. \"Zoey is a knave or Victoria is a knave,\" Aiden mentioned. \"Luke is a knight or Luke is a knave,\" Zoey declared. \"If Emily is a knave then Aiden is a knave,\" Luke claimed. Victoria said, \"Zoey is not a knight.\" So who is a knight and who is a knave?", "names": ["Emily", "Mia", "Aiden", "Zoey", "Luke", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false], "solution_text": "Emily is a knave, Mia is a knave, Aiden is a knight, Zoey is a knight, Luke is a knave, and Victoria is a knave.", "solution_text_format": "(1) Emily is a knave\n(2) Mia is a knave\n(3) Aiden is a knight\n(4) Zoey is a knight\n(5) Luke is a knave\n(6) Victoria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Aiden is not a knight.", "Aiden cannot be a knight, because this would contradict the claim of Emily that Aiden is not a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Zoey is a knave or Victoria is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Luke is a knight or Luke is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that If Emily is a knave then Aiden is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that Zoey is not a knight.", "Victoria cannot be a knave, because this would contradict the false claim of Aiden that Zoey is a knave or Victoria is a knave.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the false claim of their own that If Emily is a knave then Aiden is a knave.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Zoey.", "Zoey cannot be a knave, because this would contradict the false claim of Aiden that Zoey is a knave or Victoria is a knave.", "We have exhausted all possibilities for Zoey and Aiden, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Aiden is not a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Zoey is a knave or Victoria is a knave.", "Assume Zoey 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 If Emily is a knave then Aiden is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that If Emily is a knave then Aiden is a knave.", "Victoria cannot be a knight, because this would contradict the claim of Aiden that Zoey is a knave or Victoria is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Zoey is not a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that Aiden is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Aiden is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('lying', 2), ('or', ('lying', 3), ('lying', 5)), ('or', ('telling-truth', 4), ('lying', 4)), ('->', ('lying', 0), ('lying', 2)), ('not', ('telling-truth', 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 6 inhabitants: Charlotte, Benjamin, Aurora, Aria, David, and Logan. According to Charlotte, \"Benjamin is a knight if and only if Aurora is a knight\". As Benjamin put it, \"Charlotte is not a knave\". According to Aurora, \"If Aria is a knight then Aria is a knave\". As Aria put it, \"Charlotte is a knave or David is a knight\". \"Benjamin is not a knight,\" David mentioned. \"Aria is a knave and Charlotte is a knight,\" Logan declared. So who is a knight and who is a knave?", "names": ["Charlotte", "Benjamin", "Aurora", "Aria", "David", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true], "solution_text": "Charlotte is a knight, Benjamin is a knight, Aurora is a knight, Aria is a knave, David is a knave, and Logan is a knight.", "solution_text_format": "(1) Charlotte is a knight\n(2) Benjamin is a knight\n(3) Aurora is a knight\n(4) Aria is a knave\n(5) David is a knave\n(6) Logan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that Benjamin is a knight if and only if Aurora is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Charlotte is not a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that If Aria is a knight then Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of Aurora that If Aria is a knight then Aria is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Charlotte is a knave or David is a knight.", "David cannot be a knight, because this would contradict the false claim of Aria that Charlotte is a knave or David is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Benjamin is not a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Aria is a knave and Charlotte is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('telling-truth', 2)), ('not', ('lying', 0)), ('->', ('telling-truth', 3), ('lying', 3)), ('or', ('lying', 0), ('telling-truth', 4)), ('not', ('telling-truth', 1)), ('and', ('lying', 3), ('telling-truth', 0)))", "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 6 inhabitants: Joseph, Luke, Riley, Avery, James, and Ava. Joseph said that Avery is a knight or James is a knight. Luke told you that James is a knight if and only if Avery is a knight. \"Ava is a knight,\" Riley claimed. Avery commented, \"Joseph is a knave\". James stated, \"If Ava is a knight then Avery is a knight\". \"Luke is a knight if and only if Luke is a knave\" - Ava. So who is a knight and who is a knave?", "names": ["Joseph", "Luke", "Riley", "Avery", "James", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, false], "solution_text": "Joseph is a knight, Luke is a knave, Riley is a knave, Avery is a knave, James is a knight, and Ava is a knave.", "solution_text_format": "(1) Joseph is a knight\n(2) Luke is a knave\n(3) Riley is a knave\n(4) Avery is a knave\n(5) James is a knight\n(6) 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 Joseph is a knight. No contradiction is found in their claim that Avery is a knight or James is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Joseph is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Joseph is a knave.", "Assume James is a knight. No contradiction is found in their claim that If Ava is a knight then Avery is a knight.", "Ava cannot be a knight, because this would contradict the claim of James that If Ava is a knight then Avery is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Luke is a knight if and only if Luke is a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that James is a knight if and only if Avery is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that James is a knight if and only if Avery is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Ava is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Ava is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('telling-truth', 4)), ('<=>', ('telling-truth', 4), ('telling-truth', 3)), ('telling-truth', 5), ('lying', 0), ('->', ('telling-truth', 5), ('telling-truth', 3)), ('<=>', ('telling-truth', 1), ('lying', 1)))", "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 6 inhabitants: Elizabeth, Isabella, Grace, Zoey, Emily, and Aiden. Elizabeth commented, \"Emily is a knave if and only if Zoey is a knave\". Isabella remarked, \"Grace is a knave or Aiden is a knight\". \"Zoey is not a knave,\" Grace mentioned. \"Grace is a knight and Isabella is a knave,\" Zoey mentioned. \"If Elizabeth is a knight then Zoey is a knave,\" Emily claimed. Aiden asserted: \"Grace is a knight\". So who is a knight and who is a knave?", "names": ["Elizabeth", "Isabella", "Grace", "Zoey", "Emily", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, false], "solution_text": "Elizabeth is a knave, Isabella is a knight, Grace is a knave, Zoey is a knave, Emily is a knight, and Aiden is a knave.", "solution_text_format": "(1) Elizabeth is a knave\n(2) Isabella is a knight\n(3) Grace is a knave\n(4) Zoey is a knave\n(5) Emily is a knight\n(6) 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 Elizabeth is a knight. No contradiction is found in their claim that Emily is a knave if and only if Zoey is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that If Elizabeth is a knight then Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Emily that If Elizabeth is a knight then Zoey is a knave.", "Zoey cannot be a knave, because this would contradict the claim of Elizabeth that Emily is a knave if and only if Zoey is a knave.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that If Elizabeth is a knight then Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Elizabeth that Emily is a knave if and only if Zoey is a knave.", "Zoey cannot be a knave, because this would contradict the false claim of Emily that If Elizabeth is a knight then Zoey is a knave.", "We have exhausted all possibilities for Zoey and Emily, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Emily is a knave if and only if Zoey is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that If Elizabeth is a knight then Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the false claim of Elizabeth that Emily is a knave if and only if Zoey is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Grace is a knight and Isabella is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Zoey is not a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Zoey is not a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Grace is a knave or Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Grace is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Grace is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 4), ('lying', 3)), ('or', ('lying', 2), ('telling-truth', 5)), ('not', ('lying', 3)), ('and', ('telling-truth', 2), ('lying', 1)), ('->', ('telling-truth', 0), ('lying', 3)), ('telling-truth', 2))", "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 6 inhabitants: Penelope, Emma, Matthew, Logan, Samuel, and Aria. Penelope told you that Aria is a knave and Matthew is a knight. Emma asserted: \"Samuel is a knight\". Matthew told you that If Aria is a knight then Penelope is a knave. Logan remarked, \"Emma is a knave or Logan is a knight\". \"Logan is a knave and Aria is a knave,\" Samuel claimed. \"If Logan is a knave then Emma is a knight,\" Aria claimed. So who is a knight and who is a knave?", "names": ["Penelope", "Emma", "Matthew", "Logan", "Samuel", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, true], "solution_text": "Penelope is a knave, Emma is a knave, Matthew is a knight, Logan is a knight, Samuel is a knave, and Aria is a knight.", "solution_text_format": "(1) Penelope is a knave\n(2) Emma is a knave\n(3) Matthew is a knight\n(4) Logan is a knight\n(5) Samuel is a knave\n(6) Aria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that Aria is a knave and Matthew is a knight.", "Aria cannot be a knight, because this would contradict the claim of Penelope that Aria is a knave and Matthew is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that If Logan is a knave then Emma is a knight.", "Logan cannot be a knight, because this would contradict the false claim of Aria that If Logan is a knave then Emma is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Emma is a knave or Logan is a knight.", "Emma cannot be a knight, because this would contradict the false claim of Aria that If Logan is a knave then Emma is a knight.", "Emma cannot be a knave, because this would contradict the false claim of Logan that Emma is a knave or Logan is a knight.", "We have exhausted all possibilities for Emma, Logan, and Aria, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Aria is a knave and Matthew is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that If Logan is a knave then Emma is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Emma is a knave or Logan is a knight.", "Assume Emma 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 Logan is a knave and Aria is a knave.", "Samuel cannot be a knave, because this would contradict the claim of Emma that Samuel is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Samuel is a knight.", "Samuel cannot be a knight, because this would contradict the false claim of Emma that Samuel is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Logan is a knave and Aria is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that If Aria is a knight then Penelope is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 5), ('telling-truth', 2)), ('telling-truth', 4), ('->', ('telling-truth', 5), ('lying', 0)), ('or', ('lying', 1), ('telling-truth', 3)), ('and', ('lying', 3), ('lying', 5)), ('->', ('lying', 3), ('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 6 inhabitants: Penelope, James, Matthew, Lucas, Sebastian, and Sophia. According to Penelope, \"Sebastian is a knight or Sebastian is a knave\". As James put it, \"If Matthew is a knight then Penelope is a knight\". Matthew noted, \"If Matthew is a knight then Lucas is a knight\". \"If Matthew is a knave then Penelope is a knave,\" Lucas claimed. Sebastian told you that If Sophia is a knave then Matthew is a knave. Sophia said that James is not a knave. So who is a knight and who is a knave?", "names": ["Penelope", "James", "Matthew", "Lucas", "Sebastian", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true], "solution_text": "Penelope is a knight, James is a knight, Matthew is a knight, Lucas is a knight, Sebastian is a knight, and Sophia is a knight.", "solution_text_format": "(1) Penelope is a knight\n(2) James is a knight\n(3) Matthew is a knight\n(4) Lucas is a knight\n(5) Sebastian is a knight\n(6) Sophia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that Sebastian is a knight or Sebastian is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Sophia is a knave then Matthew is a knave.", "Assume Sophia 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 Matthew is a knight then Penelope is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that If Matthew is a knight then Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that If Matthew is a knave then Penelope is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('lying', 4)), ('->', ('telling-truth', 2), ('telling-truth', 0)), ('->', ('telling-truth', 2), ('telling-truth', 3)), ('->', ('lying', 2), ('lying', 0)), ('->', ('lying', 5), ('lying', 2)), ('not', ('lying', 1)))", "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 6 inhabitants: Isabella, Noah, Emily, Riley, James, and Alexander. In Isabella's words: \"Emily is a knave\". Noah expressed that James is a knight or Isabella is a knave. Emily said, \"Noah is not a knight.\" Riley stated, \"Alexander is not a knight\". James told you that Emily is not a knight. \"If Isabella is a knave then Riley is a knight,\" Alexander mentioned. So who is a knight and who is a knave?", "names": ["Isabella", "Noah", "Emily", "Riley", "James", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true], "solution_text": "Isabella is a knight, Noah is a knight, Emily is a knave, Riley is a knave, James is a knight, and Alexander is a knight.", "solution_text_format": "(1) Isabella is a knight\n(2) Noah is a knight\n(3) Emily is a knave\n(4) Riley is a knave\n(5) James is a knight\n(6) 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 Isabella is a knight. No contradiction is found in their claim that Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of Isabella that Emily is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Noah is not a knight.", "Assume Noah is a knight. No contradiction is found in their claim that James is a knight or Isabella is a knave.", "Assume James is a knight. No contradiction is found in their claim that Emily is not a knight.", "Assume Riley 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 Riley that Alexander is not a knight.", "Alexander cannot be a knave, because this would contradict the false claim of their own that If Isabella is a knave then Riley is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Riley.", "Assume Riley 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 Isabella is a knave then Riley is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('or', ('telling-truth', 4), ('lying', 0)), ('not', ('telling-truth', 1)), ('not', ('telling-truth', 5)), ('not', ('telling-truth', 2)), ('->', ('lying', 0), ('telling-truth', 3)))", "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 6 inhabitants: Grace, James, Jackson, Luke, Liam, and Henry. \"If James is a knight then Jackson is a knight,\" Grace declared. James said, \"Luke is a knight or Liam is a knight.\" Jackson asserted: \"Grace is a knave and Jackson is a knight\". \"Grace is not a knight\" - Luke. \"Grace is a knight or James is a knight,\" Liam claimed. Henry noted, \"Liam is not a knight\". So who is a knight and who is a knave?", "names": ["Grace", "James", "Jackson", "Luke", "Liam", "Henry"], "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], "solution_text": "Grace is a knave, James is a knight, Jackson is a knave, Luke is a knight, Liam is a knight, and Henry is a knave.", "solution_text_format": "(1) Grace is a knave\n(2) James is a knight\n(3) Jackson is a knave\n(4) Luke is a knight\n(5) Liam is a knight\n(6) Henry is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that If James is a knight then Jackson is a knight.", "Assume James is a knight. No contradiction is found in their claim that Luke is a knight or Liam is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Grace is not a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Grace is not a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Grace is a knight or James is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Grace is a knave and Jackson is a knight.", "Jackson cannot be a knave, because this would contradict the claim of Grace that If James is a knight then Jackson is a knight.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the claim of James that Luke is a knight or Liam is a knight.", "We have exhausted all possibilities for Liam and Luke, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Luke is a knight or Liam is a knight.", "Luke cannot be a knight, because this would contradict the false claim of James that Luke is a knight or Liam is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Grace is not a knight.", "Liam cannot be a knight, because this would contradict the false claim of James that Luke is a knight or Liam is a knight.", "Liam cannot be a knave, because this would contradict the false claim of their own that Grace is a knight or James is a knight.", "We have exhausted all possibilities for Liam, Luke, and James, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that If James is a knight then Jackson is a knight.", "Assume James is a knight. No contradiction is found in their claim that Luke is a knight or Liam is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Grace is not a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Grace is a knight or James is a knight.", "Jackson cannot be a knight, because this would contradict the false claim of Grace that If James is a knight then Jackson is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Grace is a knave and Jackson is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Liam is not a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Liam is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 1), ('telling-truth', 2)), ('or', ('telling-truth', 3), ('telling-truth', 4)), ('and', ('lying', 0), ('telling-truth', 2)), ('not', ('telling-truth', 0)), ('or', ('telling-truth', 0), ('telling-truth', 1)), ('not', ('telling-truth', 4)))", "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 6 inhabitants: Emma, Isabella, Samuel, Luke, Liam, and Mason. In a statement by Emma: \"Luke is a knight and Mason is a knave\". Isabella said, \"Luke is not a knave.\" Samuel commented, \"Isabella is a knave and Liam is a knight\". Luke said that Emma is a knight and Isabella is a knave. \"Mason is a knave and Luke is a knight,\" Liam mentioned. According to Mason, \"If Luke is a knight then Liam is a knave\". So who is a knight and who is a knave?", "names": ["Emma", "Isabella", "Samuel", "Luke", "Liam", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, true], "solution_text": "Emma is a knave, Isabella is a knave, Samuel is a knave, Luke is a knave, Liam is a knave, and Mason is a knight.", "solution_text_format": "(1) Emma is a knave\n(2) Isabella is a knave\n(3) Samuel is a knave\n(4) Luke is a knave\n(5) Liam is a knave\n(6) 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 Emma is a knight. No contradiction is found in their claim that Luke is a knight and Mason is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Emma is a knight and Isabella is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Luke that Emma is a knight and Isabella is a knave.", "Isabella cannot be a knave, because this would contradict the false claim of their own that Luke is not a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the claim of Emma that Luke is a knight and Mason is a knave.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Luke is a knight and Mason is a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that Emma is a knight and Isabella is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Emma is a knight and Isabella is a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that Luke is not a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Luke is not a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Luke is a knight then Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Mason is a knave and Luke is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Mason is a knave and Luke is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Isabella is a knave and Liam is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Isabella is a knave and Liam is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('lying', 5)), ('not', ('lying', 3)), ('and', ('lying', 1), ('telling-truth', 4)), ('and', ('telling-truth', 0), ('lying', 1)), ('and', ('lying', 5), ('telling-truth', 3)), ('->', ('telling-truth', 3), ('lying', 4)))", "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 6 inhabitants: Logan, Ella, Aurora, James, Emma, and Lucas. Logan asserted: \"If Emma is a knave then Lucas is a knave\". Ella told you that If Logan is a knave then Aurora is a knave. In Aurora's words: \"Lucas is a knight and Lucas is a knave\". In a statement by James: \"Logan is a knight and Lucas is a knave\". Emma remarked, \"James is a knight or Lucas is a knight\". Lucas said that Lucas is a knight or James is a knight. So who is a knight and who is a knave?", "names": ["Logan", "Ella", "Aurora", "James", "Emma", "Lucas"], "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], "solution_text": "Logan is a knight, Ella is a knight, Aurora is a knave, James is a knave, Emma is a knight, and Lucas is a knight.", "solution_text_format": "(1) Logan is a knight\n(2) Ella is a knight\n(3) Aurora is a knave\n(4) James is a knave\n(5) Emma is a knight\n(6) Lucas is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that If Emma is a knave then Lucas is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that James is a knight or Lucas is a knight.", "Assume James is a knight. No contradiction is found in their claim that Logan is a knight and Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the claim of James that Logan is a knight and Lucas is a knave.", "Lucas cannot be a knave, because this would contradict the false claim of their own that Lucas is a knight or James is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Logan is a knight and Lucas is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Lucas is a knight or James is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that If Logan is a knave then Aurora is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Lucas is a knight and Lucas is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Lucas is a knight and Lucas is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 4), ('lying', 5)), ('->', ('lying', 0), ('lying', 2)), ('and', ('telling-truth', 5), ('lying', 5)), ('and', ('telling-truth', 0), ('lying', 5)), ('or', ('telling-truth', 3), ('telling-truth', 5)), ('or', ('telling-truth', 5), ('telling-truth', 3)))", "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 6 inhabitants: Olivia, Joseph, Matthew, Penelope, Charlotte, and Liam. Olivia told you that Olivia is a knight or Charlotte is a knave. Joseph said, \"Penelope is a knave and Liam is a knave.\" Matthew commented, \"Penelope is not a knave\". \"If Joseph is a knave then Liam is a knight\" - Penelope. Charlotte noted, \"Matthew is a knight if and only if Olivia is a knave\". Liam was heard saying, \"Penelope is a knave or Olivia is a knave\". So who is a knight and who is a knave?", "names": ["Olivia", "Joseph", "Matthew", "Penelope", "Charlotte", "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], "solution_text": "Olivia is a knave, Joseph is a knave, Matthew is a knight, Penelope is a knight, Charlotte is a knight, and Liam is a knight.", "solution_text_format": "(1) Olivia is a knave\n(2) Joseph is a knave\n(3) Matthew is a knight\n(4) Penelope is a knight\n(5) Charlotte is a knight\n(6) Liam is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Olivia is a knight or Charlotte is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Matthew is a knight if and only if Olivia is a knave.", "Matthew cannot be a knight, because this would contradict the claim of Charlotte that Matthew is a knight if and only if Olivia is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Penelope is not a knave.", "Penelope cannot be a knight, because this would contradict the false claim of Matthew that Penelope is not a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that If Joseph is a knave then Liam is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of Penelope that If Joseph is a knave then Liam is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Penelope is a knave and Liam is a knave.", "Liam cannot be a knight, because this would contradict the false claim of Penelope that If Joseph is a knave then Liam is a knight.", "Liam cannot be a knave, because this would contradict the false claim of Joseph that Penelope is a knave and Liam is a knave.", "We have exhausted all possibilities for Liam, Joseph, Penelope, and Matthew, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Matthew is a knight if and only if Olivia is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Penelope is not a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that If Joseph is a knave then Liam is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Penelope is a knave and Liam is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Penelope is a knave and Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Penelope is a knave or Olivia is a knave.", "Liam cannot be a knave, because this would contradict the claim of Penelope that If Joseph is a knave then Liam is a knight.", "We have exhausted all possibilities for Liam and Joseph, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the claim of Matthew that Penelope is not a knave.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the false claim of Charlotte that Matthew is a knight if and only if Olivia is a knave.", "We have exhausted all possibilities for Matthew and Charlotte, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Olivia is a knight or Charlotte is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Matthew is a knight if and only if Olivia is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Penelope is not a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that If Joseph is a knave then Liam is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Penelope is a knave and Liam is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Penelope is a knave and Liam is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Penelope is a knave or Olivia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 0), ('lying', 4)), ('and', ('lying', 3), ('lying', 5)), ('not', ('lying', 3)), ('->', ('lying', 1), ('telling-truth', 5)), ('<=>', ('telling-truth', 2), ('lying', 0)), ('or', ('lying', 3), ('lying', 0)))", "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 6 inhabitants: Joseph, Scarlett, Aiden, Riley, Emma, and Henry. Joseph told you that Riley is a knight or Emma is a knight. Scarlett commented, \"Aiden is a knight and Joseph is a knave\". Aiden noted, \"If Emma is a knave then Henry is a knight\". \"Henry is a knight if and only if Aiden is a knave,\" Riley declared. According to Emma, \"Scarlett is not a knave\". Henry noted, \"Emma is not a knave\". So who is a knight and who is a knave?", "names": ["Joseph", "Scarlett", "Aiden", "Riley", "Emma", "Henry"], "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], "solution_text": "Joseph is a knave, Scarlett is a knave, Aiden is a knave, Riley is a knave, Emma is a knave, and Henry is a knave.", "solution_text_format": "(1) Joseph is a knave\n(2) Scarlett is a knave\n(3) Aiden is a knave\n(4) Riley is a knave\n(5) Emma is a knave\n(6) Henry is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that Riley is a knight or Emma is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Henry is a knight if and only if Aiden is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Emma is not a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Aiden is a knight and Joseph is a knave.", "Scarlett cannot be a knave, because this would contradict the claim of Emma that Scarlett is not a knave.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Emma.", "Emma cannot be a knave, because this would contradict the claim of Henry that Emma is not a knave.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Henry.", "Assume Henry 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 Henry that Emma is not a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Scarlett is not a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Aiden is a knight and Joseph is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Aiden is a knight and Joseph is a knave.", "Aiden cannot be a knight, because this would contradict the claim of their own that If Emma is a knave then Henry is a knight.", "Aiden cannot be a knave, because this would contradict the claim of Riley that Henry is a knight if and only if Aiden is a knave.", "We have exhausted all possibilities for Aiden, Scarlett, Emma, and Henry, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Henry is a knight if and only if Aiden is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Emma is not a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Aiden is a knight and Joseph is a knave.", "Scarlett cannot be a knave, because this would contradict the claim of Emma that Scarlett is not a knave.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Emma.", "Emma cannot be a knave, because this would contradict the claim of Joseph that Riley is a knight or Emma is a knight.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Henry.", "Assume Henry 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 Henry that Emma is not a knave.", "Emma cannot be a knave, because this would contradict the claim of Joseph that Riley is a knight or Emma is a knight.", "We have exhausted all possibilities for Emma, Henry, and Riley, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Riley is a knight or Emma is a knight.", "Riley cannot be a knight, because this would contradict the false claim of Joseph that Riley is a knight or Emma is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Henry is a knight if and only if Aiden is a knave.", "Assume Henry 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 false claim of Joseph that Riley is a knight or Emma is a knight.", "Emma cannot be a knave, because this would contradict the claim of Henry that Emma is not a knave.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Henry.", "Assume Henry 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 Joseph that Riley is a knight or Emma is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Scarlett is not a knave.", "Scarlett cannot be a knight, because this would contradict the false claim of Emma that Scarlett is not a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Aiden is a knight and Joseph is a knave.", "Aiden cannot be a knight, because this would contradict the false claim of Scarlett that Aiden is a knight and Joseph is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that If Emma is a knave then Henry is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('telling-truth', 4)), ('and', ('telling-truth', 2), ('lying', 0)), ('->', ('lying', 4), ('telling-truth', 5)), ('<=>', ('telling-truth', 5), ('lying', 2)), ('not', ('lying', 1)), ('not', ('lying', 4)))", "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 6 inhabitants: Chloe, Henry, Emma, Elizabeth, Jacob, and Ella. Chloe stated, \"Ella is a knave and Elizabeth is a knight\". \"If Elizabeth is a knave then Chloe is a knave\" - Henry. \"If Elizabeth is a knave then Henry is a knave,\" Emma claimed. Elizabeth commented, \"Ella is a knight\". Jacob stated, \"Emma is not a knight\". Ella asserted: \"Jacob is a knave or Elizabeth is a knave\". So who is a knight and who is a knave?", "names": ["Chloe", "Henry", "Emma", "Elizabeth", "Jacob", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true], "solution_text": "Chloe is a knave, Henry is a knight, Emma is a knight, Elizabeth is a knight, Jacob is a knave, and Ella is a knight.", "solution_text_format": "(1) Chloe is a knave\n(2) Henry is a knight\n(3) Emma is a knight\n(4) Elizabeth is a knight\n(5) Jacob is a knave\n(6) 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 Chloe is a knight. No contradiction is found in their claim that Ella is a knave and Elizabeth is a knight.", "Ella cannot be a knight, because this would contradict the claim of Chloe that Ella is a knave and Elizabeth is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Jacob is a knave or Elizabeth is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Emma is not a knight.", "Emma cannot be a knight, because this would contradict the claim of Jacob that Emma is not a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that If Elizabeth is a knave then Henry is a knave.", "Elizabeth cannot be a knight, because this would contradict the false claim of Emma that If Elizabeth is a knave then Henry is a knave.", "Elizabeth cannot be a knave, because this would contradict the claim of Chloe that Ella is a knave and Elizabeth is a knight.", "We have exhausted all possibilities for Elizabeth and Emma, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the false claim of Ella that Jacob is a knave or Elizabeth is a knave.", "We have exhausted all possibilities for Jacob and Ella, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Ella is a knave and Elizabeth is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Jacob is a knave or Elizabeth is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Emma is not a knight.", "Emma cannot be a knight, because this would contradict the claim of Jacob that Emma is not a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that If Elizabeth is a knave then Henry is a knave.", "Elizabeth cannot be a knight, because this would contradict the false claim of Emma that If Elizabeth is a knave then Henry is a knave.", "Elizabeth cannot be a knave, because this would contradict the false claim of their own that Ella is a knight.", "We have exhausted all possibilities for Elizabeth and Emma, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Emma is not a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Henry is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Ella is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Chloe is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 5), ('telling-truth', 3)), ('->', ('lying', 3), ('lying', 0)), ('->', ('lying', 3), ('lying', 1)), ('telling-truth', 5), ('not', ('telling-truth', 2)), ('or', ('lying', 4), ('lying', 3)))", "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 6 inhabitants: Joseph, Jacob, Avery, Scarlett, Sofia, and Noah. Joseph expressed that Avery is a knave or Noah is a knave. As Jacob put it, \"Noah is not a knight\". In a statement by Avery: \"Scarlett is a knight or Sofia is a knight\". Scarlett remarked, \"Noah is a knave and Avery is a knave\". In a statement by Sofia: \"Noah is a knave if and only if Sofia is a knight\". Noah noted, \"Jacob is a knave if and only if Sofia is a knight\". So who is a knight and who is a knave?", "names": ["Joseph", "Jacob", "Avery", "Scarlett", "Sofia", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false], "solution_text": "Joseph is a knight, Jacob is a knight, Avery is a knight, Scarlett is a knave, Sofia is a knight, and Noah is a knave.", "solution_text_format": "(1) Joseph is a knight\n(2) Jacob is a knight\n(3) Avery is a knight\n(4) Scarlett is a knave\n(5) Sofia is a knight\n(6) Noah is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that Avery is a knave or Noah is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Scarlett is a knight or Sofia is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Noah is a knave and Avery is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Noah is a knave and Avery is a knave.", "Noah cannot be a knight, because this would contradict the claim of Joseph that Avery is a knave or Noah is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Jacob is a knave if and only if Sofia is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Noah is not a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Noah is a knave if and only if Sofia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('lying', 5)), ('not', ('telling-truth', 5)), ('or', ('telling-truth', 3), ('telling-truth', 4)), ('and', ('lying', 5), ('lying', 2)), ('<=>', ('lying', 5), ('telling-truth', 4)), ('<=>', ('lying', 1), ('telling-truth', 4)))", "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 6 inhabitants: Michael, Jacob, Sofia, Isabella, Emily, and Joseph. As Michael put it, \"If Emily is a knight then Michael is a knight\". Jacob remarked, \"Sofia is a knight or Isabella is a knave\". In a statement by Sofia: \"Isabella is a knave and Isabella is a knight\". In Isabella's words: \"Michael is a knave or Joseph is a knave\". \"Jacob is a knave and Emily is a knight\" - Emily. Joseph expressed that Joseph is a knight if and only if Jacob is a knight. So who is a knight and who is a knave?", "names": ["Michael", "Jacob", "Sofia", "Isabella", "Emily", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, true], "solution_text": "Michael is a knight, Jacob is a knight, Sofia is a knave, Isabella is a knave, Emily is a knave, and Joseph is a knight.", "solution_text_format": "(1) Michael is a knight\n(2) Jacob is a knight\n(3) Sofia is a knave\n(4) Isabella is a knave\n(5) Emily is a knave\n(6) Joseph is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that If Emily is a knight then Michael is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Jacob is a knave and Emily is a knight.", "Jacob cannot be a knight, because this would contradict the claim of Emily that Jacob is a knave and Emily is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Sofia is a knight or Isabella is a knave.", "Sofia cannot be a knight, because this would contradict the false claim of Jacob that Sofia is a knight or Isabella is a knave.", "Assume Sofia 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 Michael is a knave or Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Isabella that Michael is a knave or Joseph is a knave.", "Joseph cannot be a knave, because this would contradict the false claim of their own that Joseph is a knight if and only if Jacob is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the false claim of Jacob that Sofia is a knight or Isabella is a knave.", "We have exhausted all possibilities for Isabella, Sofia, and Jacob, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Jacob is a knave and Emily is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Sofia is a knight or Isabella is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Isabella is a knave and Isabella is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Isabella is a knave and Isabella is a knight.", "Isabella cannot be a knight, because this would contradict the claim of Jacob that Sofia is a knight or Isabella is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Michael is a knave or Joseph is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Joseph is a knight if and only if Jacob is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 4), ('telling-truth', 0)), ('or', ('telling-truth', 2), ('lying', 3)), ('and', ('lying', 3), ('telling-truth', 3)), ('or', ('lying', 0), ('lying', 5)), ('and', ('lying', 1), ('telling-truth', 4)), ('<=>', ('telling-truth', 5), ('telling-truth', 1)))", "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 6 inhabitants: David, Ava, Riley, Aiden, Sebastian, and Abigail. In David's words: \"Riley is not a knave\". Ava said that Sebastian is a knight and Abigail is a knight. Riley expressed that David is a knave and Aiden is a knight. Aiden noted, \"David is a knight and Sebastian is a knight\". Sebastian asserted: \"David is a knight\". Abigail asserted: \"Riley is a knight or Sebastian is a knight\". So who is a knight and who is a knave?", "names": ["David", "Ava", "Riley", "Aiden", "Sebastian", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, false], "solution_text": "David is a knave, Ava is a knave, Riley is a knave, Aiden is a knave, Sebastian is a knave, and Abigail is a knave.", "solution_text_format": "(1) David is a knave\n(2) Ava is a knave\n(3) Riley is a knave\n(4) Aiden is a knave\n(5) Sebastian is a knave\n(6) Abigail is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Riley is not a knave.", "Riley cannot be a knight, because this would contradict the claim of their own that David is a knave and Aiden is a knight.", "Riley cannot be a knave, because this would contradict the claim of David that Riley is not a knave.", "We have exhausted all possibilities for Riley, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Riley is not a knave.", "Riley cannot be a knight, because this would contradict the false claim of David that Riley is not a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that David is a knave and Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the false claim of Riley that David is a knave and Aiden is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that David is a knight and Sebastian is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that David is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that David is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight and Abigail is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Sebastian is a knight and Abigail is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Riley is a knight or Sebastian is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Riley is a knight or Sebastian is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('and', ('telling-truth', 4), ('telling-truth', 5)), ('and', ('lying', 0), ('telling-truth', 3)), ('and', ('telling-truth', 0), ('telling-truth', 4)), ('telling-truth', 0), ('or', ('telling-truth', 2), ('telling-truth', 4)))", "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 6 inhabitants: Riley, Charlotte, Oliver, Abigail, Scarlett, and Joseph. Riley said, \"Riley is a knight if and only if Charlotte is a knave.\" Charlotte was heard saying, \"Oliver is a knave or Abigail is a knave\". Oliver noted, \"Joseph is a knight\". \"If Scarlett is a knave then Riley is a knave,\" Abigail mentioned. Scarlett stated, \"Charlotte is not a knave\". \"If Charlotte is a knight then Abigail is a knight,\" Joseph claimed. So who is a knight and who is a knave?", "names": ["Riley", "Charlotte", "Oliver", "Abigail", "Scarlett", "Joseph"], "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], "solution_text": "Riley is a knave, Charlotte is a knave, Oliver is a knight, Abigail is a knight, Scarlett is a knave, and Joseph is a knight.", "solution_text_format": "(1) Riley is a knave\n(2) Charlotte is a knave\n(3) Oliver is a knight\n(4) Abigail is a knight\n(5) Scarlett is a knave\n(6) Joseph is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Riley is a knight if and only if Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Riley that Riley 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 Oliver is a knave or Abigail is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Charlotte is a knight then Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If Scarlett is a knave then Riley is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Charlotte is not a knave.", "Scarlett cannot be a knave, because this would contradict the claim of Abigail that If Scarlett is a knave then Riley is a knave.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the false claim of Charlotte that Oliver is a knave or Abigail is a knave.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of Oliver that Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the false claim of Charlotte that Oliver is a knave or Abigail is a knave.", "We have exhausted all possibilities for Oliver and Charlotte, 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 if and only if Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the false claim of Riley that Riley 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 Oliver is a knave or Abigail is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Charlotte is a knight then Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If Scarlett is a knave then Riley is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Charlotte is not a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Charlotte is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 0), ('lying', 1)), ('or', ('lying', 2), ('lying', 3)), ('telling-truth', 5), ('->', ('lying', 4), ('lying', 0)), ('not', ('lying', 1)), ('->', ('telling-truth', 1), ('telling-truth', 3)))", "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 6 inhabitants: Aiden, Daniel, Aurora, Penelope, Abigail, and Matthew. In Aiden's words: \"Penelope is a knight or Aurora is a knight\". According to Daniel, \"Penelope is not a knave\". Aurora stated, \"Aiden is a knight or Aiden is a knave\". \"Aurora is a knight,\" Penelope mentioned. \"Aurora is a knave,\" Abigail claimed. Matthew stated, \"Aurora is not a knave\". So who is a knight and who is a knave?", "names": ["Aiden", "Daniel", "Aurora", "Penelope", "Abigail", "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, true], "solution_text": "Aiden is a knight, Daniel is a knight, Aurora is a knight, Penelope is a knight, Abigail is a knave, and Matthew is a knight.", "solution_text_format": "(1) Aiden is a knight\n(2) Daniel is a knight\n(3) Aurora is a knight\n(4) Penelope is a knight\n(5) Abigail is a knave\n(6) 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 Aiden is a knight. No contradiction is found in their claim that Penelope is a knight or Aurora is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Aurora is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Aiden is a knight or Aiden is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Penelope is not a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Aurora is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Aurora is a knave.", "Assume Matthew 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', 3), ('telling-truth', 2)), ('not', ('lying', 3)), ('or', ('telling-truth', 0), ('lying', 0)), ('telling-truth', 2), ('lying', 2), ('not', ('lying', 2)))", "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 6 inhabitants: Owen, Samuel, Abigail, Daniel, Benjamin, and Zoey. Owen said that If Daniel is a knight then Samuel is a knight. Samuel stated, \"Daniel is a knave or Zoey is a knight\". Abigail remarked, \"Daniel is a knight\". In Daniel's words: \"If Zoey is a knave then Samuel is a knight\". \"Abigail is a knave,\" Benjamin declared. Zoey said, \"Zoey is a knight.\" So who is a knight and who is a knave?", "names": ["Owen", "Samuel", "Abigail", "Daniel", "Benjamin", "Zoey"], "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], "solution_text": "Owen is a knight, Samuel is a knight, Abigail is a knight, Daniel is a knight, Benjamin is a knave, and Zoey is a knight.", "solution_text_format": "(1) Owen is a knight\n(2) Samuel is a knight\n(3) Abigail is a knight\n(4) Daniel is a knight\n(5) Benjamin is a knave\n(6) Zoey is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that If Daniel is a knight then Samuel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that If Zoey is a knave then Samuel is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Zoey is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Daniel is a knave or Zoey is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Daniel is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Abigail is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Abigail is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('telling-truth', 1)), ('or', ('lying', 3), ('telling-truth', 5)), ('telling-truth', 3), ('->', ('lying', 5), ('telling-truth', 1)), ('lying', 2), ('telling-truth', 5))", "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 6 inhabitants: Lily, Emma, Victoria, Alexander, Zoey, and Scarlett. In a statement by Lily: \"If Alexander is a knave then Zoey is a knave\". Emma commented, \"Victoria is a knight if and only if Alexander is a knave\". Victoria said, \"Scarlett is not a knight.\" In Alexander's words: \"Zoey is a knight\". In a statement by Zoey: \"Scarlett is a knave\". \"Victoria is a knight and Alexander is a knave,\" Scarlett declared. So who is a knight and who is a knave?", "names": ["Lily", "Emma", "Victoria", "Alexander", "Zoey", "Scarlett"], "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], "solution_text": "Lily is a knight, Emma is a knave, Victoria is a knight, Alexander is a knight, Zoey is a knight, and Scarlett is a knave.", "solution_text_format": "(1) Lily is a knight\n(2) Emma is a knave\n(3) Victoria is a knight\n(4) Alexander is a knight\n(5) Zoey is a knight\n(6) Scarlett is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that If Alexander is a knave then Zoey is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Zoey that Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Victoria is a knight and Alexander is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Scarlett is not a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Victoria is a knight if and only if Alexander is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Victoria is a knight if and only if Alexander is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('lying', 4)), ('<=>', ('telling-truth', 2), ('lying', 3)), ('not', ('telling-truth', 5)), ('telling-truth', 4), ('lying', 5), ('and', ('telling-truth', 2), ('lying', 3)))", "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 6 inhabitants: Avery, Elizabeth, Mia, Olivia, Mason, and Ava. Avery commented, \"If Mason is a knight then Ava is a knight\". Elizabeth told you that Mason is a knave or Mia is a knave. \"Elizabeth is a knave or Ava is a knight,\" Mia mentioned. Olivia said that Ava is a knight. Mason expressed that If Ava is a knave then Olivia is a knave. According to Ava, \"Mason is not a knave\". So who is a knight and who is a knave?", "names": ["Avery", "Elizabeth", "Mia", "Olivia", "Mason", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true], "solution_text": "Avery is a knight, Elizabeth is a knave, Mia is a knight, Olivia is a knight, Mason is a knight, and Ava is a knight.", "solution_text_format": "(1) Avery is a knight\n(2) Elizabeth is a knave\n(3) Mia is a knight\n(4) Olivia is a knight\n(5) Mason is a knight\n(6) 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 Avery is a knight. No contradiction is found in their claim that If Mason is a knight then Ava is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that If Ava is a knave then Olivia is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Mason is not a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Ava is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Mason is a knave or Mia is a knave.", "Mia cannot be a knight, because this would contradict the claim of Elizabeth that Mason is a knave or Mia is a knave.", "Mia cannot be a knave, because this would contradict the false claim of their own that Elizabeth is a knave or Ava is a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Mason is a knave or Mia is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Elizabeth is a knave or Ava is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 4), ('telling-truth', 5)), ('or', ('lying', 4), ('lying', 2)), ('or', ('lying', 1), ('telling-truth', 5)), ('telling-truth', 5), ('->', ('lying', 5), ('lying', 3)), ('not', ('lying', 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 6 inhabitants: Aiden, Benjamin, Olivia, Sofia, Aurora, and Harper. Aiden told you that Aiden is a knight or Olivia is a knave. Benjamin told you that Aurora is a knave or Sofia is a knave. In Olivia's words: \"Aurora is not a knave\". Sofia said that Aurora is a knight. In Aurora's words: \"Sofia is a knave if and only if Aurora is a knight\". Harper asserted: \"Sofia is a knight and Aiden is a knight\". So who is a knight and who is a knave?", "names": ["Aiden", "Benjamin", "Olivia", "Sofia", "Aurora", "Harper"], "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], "solution_text": "Aiden is a knight, Benjamin is a knight, Olivia is a knave, Sofia is a knave, Aurora is a knave, and Harper is a knave.", "solution_text_format": "(1) Aiden is a knight\n(2) Benjamin is a knight\n(3) Olivia is a knave\n(4) Sofia is a knave\n(5) Aurora is a knave\n(6) Harper is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Aiden is a knight or Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Aurora is not a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Sofia is a knave if and only if Aurora is a knight.", "Sofia cannot be a knight, because this would contradict the claim of Aurora that Sofia is a knave if and only if Aurora is a knight.", "Sofia cannot be a knave, because this would contradict the false claim of their own that Aurora is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the claim of Olivia that Aurora is not a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Aurora is not a knave.", "Aurora cannot be a knight, because this would contradict the false claim of Olivia that Aurora is not a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Sofia is a knave if and only if Aurora is a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that Aurora is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Aurora is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Aurora is a knave or Sofia is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Sofia is a knight and Aiden is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Sofia is a knight and Aiden is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 0), ('lying', 2)), ('or', ('lying', 4), ('lying', 3)), ('not', ('lying', 4)), ('telling-truth', 4), ('<=>', ('lying', 3), ('telling-truth', 4)), ('and', ('telling-truth', 3), ('telling-truth', 0)))", "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 6 inhabitants: Sophia, Logan, Abigail, Lily, Victoria, and Aiden. \"Logan is a knight and Lily is a knave,\" Sophia declared. \"Logan is a knight if and only if Lily is a knave,\" Logan declared. Abigail said that Aiden is not a knave. Lily stated, \"Sophia is a knave and Victoria is a knight\". According to Victoria, \"Sophia is not a knight\". \"Victoria is a knight,\" Aiden declared. So who is a knight and who is a knave?", "names": ["Sophia", "Logan", "Abigail", "Lily", "Victoria", "Aiden"], "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], "solution_text": "Sophia is a knight, Logan is a knight, Abigail is a knave, Lily is a knave, Victoria is a knave, and Aiden is a knave.", "solution_text_format": "(1) Sophia is a knight\n(2) Logan is a knight\n(3) Abigail is a knave\n(4) Lily is a knave\n(5) Victoria is a knave\n(6) Aiden is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Logan is a knight and Lily is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Logan is a knight if and only if Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of Sophia that Logan is a knight and Lily is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Sophia is a knave and Victoria is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Sophia is not a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Sophia is not a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Aiden is not a knave.", "Aiden cannot be a knight, because this would contradict the claim of their own that Victoria is a knight.", "Aiden cannot be a knave, because this would contradict the claim of Abigail that Aiden is not a knave.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Aiden is not a knave.", "Aiden cannot be a knight, because this would contradict the false claim of Abigail that Aiden is not a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Victoria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('lying', 3)), ('<=>', ('telling-truth', 1), ('lying', 3)), ('not', ('lying', 5)), ('and', ('lying', 0), ('telling-truth', 4)), ('not', ('telling-truth', 0)), ('telling-truth', 4))", "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 6 inhabitants: Avery, Amelia, Liam, Emily, Olivia, and Jack. \"Avery is a knight or Jack is a knight,\" Avery mentioned. \"Emily is a knight if and only if Olivia is a knave,\" Amelia claimed. \"Avery is a knave,\" Liam mentioned. Emily remarked, \"Liam is a knave or Olivia is a knave\". Olivia commented, \"Avery is a knight and Avery is a knave\". Jack told you that If Olivia is a knave then Amelia is a knight. So who is a knight and who is a knave?", "names": ["Avery", "Amelia", "Liam", "Emily", "Olivia", "Jack"], "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], "solution_text": "Avery is a knight, Amelia is a knight, Liam is a knave, Emily is a knight, Olivia is a knave, and Jack is a knight.", "solution_text_format": "(1) Avery is a knight\n(2) Amelia is a knight\n(3) Liam is a knave\n(4) Emily is a knight\n(5) Olivia is a knave\n(6) Jack is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Avery is a knight or Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that If Olivia is a knave then Amelia is a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that Avery is a knight and Avery is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Avery is a knight and Avery is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Emily is a knight if and only if Olivia is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Liam is a knave or Olivia is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Avery is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Avery is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 0), ('telling-truth', 5)), ('<=>', ('telling-truth', 3), ('lying', 4)), ('lying', 0), ('or', ('lying', 2), ('lying', 4)), ('and', ('telling-truth', 0), ('lying', 0)), ('->', ('lying', 4), ('telling-truth', 1)))", "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 6 inhabitants: Sofia, Liam, Owen, Riley, Aurora, and Alexander. \"Aurora is not a knave,\" Sofia declared. \"Sofia is a knave\" - Liam. Owen said that If Sofia is a knight then Aurora is a knave. Riley expressed that Sofia is a knave and Aurora is a knight. Aurora commented, \"Riley is not a knave\". Alexander asserted: \"Sofia is a knight and Aurora is a knave\". So who is a knight and who is a knave?", "names": ["Sofia", "Liam", "Owen", "Riley", "Aurora", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false], "solution_text": "Sofia is a knave, Liam is a knight, Owen is a knight, Riley is a knave, Aurora is a knave, and Alexander is a knave.", "solution_text_format": "(1) Sofia is a knave\n(2) Liam is a knight\n(3) Owen is a knight\n(4) Riley is a knave\n(5) Aurora is a knave\n(6) Alexander is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Aurora is not a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Riley is not a knave.", "Riley cannot be a knight, because this would contradict the claim of their own that Sofia is a knave and Aurora is a knight.", "Riley cannot be a knave, because this would contradict the claim of Aurora that Riley is not a knave.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the claim of Sofia that Aurora is not a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Aurora is not a knave.", "Aurora cannot be a knight, because this would contradict the false claim of Sofia that Aurora is not a knave.", "Assume Aurora 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 claim of their own that Sofia is a knave and Aurora is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Sofia is a knave and Aurora is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Sofia is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that If Sofia is a knight then Aurora is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that Sofia is a knight and Aurora is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Sofia is a knight and Aurora is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('lying', 0), ('->', ('telling-truth', 0), ('lying', 4)), ('and', ('lying', 0), ('telling-truth', 4)), ('not', ('lying', 3)), ('and', ('telling-truth', 0), ('lying', 4)))", "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 6 inhabitants: Aiden, Evelyn, Ella, Avery, James, and Emma. \"Emma is a knight and Evelyn is a knight,\" Aiden declared. Evelyn told you that If Aiden is a knave then Ella is a knight. As Ella put it, \"James is a knave\". Avery told you that Ella is a knight. James commented, \"Emma is a knight\". Emma commented, \"Emma is a knight and James is a knave\". So who is a knight and who is a knave?", "names": ["Aiden", "Evelyn", "Ella", "Avery", "James", "Emma"], "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], "solution_text": "Aiden is a knave, Evelyn is a knight, Ella is a knight, Avery is a knight, James is a knave, and Emma is a knave.", "solution_text_format": "(1) Aiden is a knave\n(2) Evelyn is a knight\n(3) Ella is a knight\n(4) Avery is a knight\n(5) James is a knave\n(6) Emma is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Emma is a knight and Evelyn is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Emma is a knight and James is a knave.", "James cannot be a knight, because this would contradict the claim of Emma that Emma is a knight and James is a knave.", "James cannot be a knave, because this would contradict the false claim of their own that Emma is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Emma.", "Emma cannot be a knave, because this would contradict the claim of Aiden that Emma is a knight and Evelyn is a knight.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Emma is a knight and Evelyn is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Emma is a knight and James is a knave.", "James cannot be a knight, because this would contradict the claim of Emma that Emma is a knight and James is a knave.", "James cannot be a knave, because this would contradict the false claim of their own that Emma is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Emma is a knight and James is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Emma is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Emma is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Aiden is a knave then Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that James is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Ella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('telling-truth', 1)), ('->', ('lying', 0), ('telling-truth', 2)), ('lying', 4), ('telling-truth', 2), ('telling-truth', 5), ('and', ('telling-truth', 5), ('lying', 4)))", "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 6 inhabitants: Mason, Riley, Jacob, Zoey, Ava, and Amelia. \"If Mason is a knight then Zoey is a knight,\" Mason declared. Riley said, \"Mason is a knave or Mason is a knight.\" \"If Zoey is a knight then Mason is a knave,\" Jacob claimed. According to Zoey, \"Jacob is a knave\". Ava asserted: \"Mason is not a knave\". Amelia stated, \"Mason is a knight and Ava is a knight\". So who is a knight and who is a knave?", "names": ["Mason", "Riley", "Jacob", "Zoey", "Ava", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true], "solution_text": "Mason is a knight, Riley is a knight, Jacob is a knave, Zoey is a knight, Ava is a knight, and Amelia is a knight.", "solution_text_format": "(1) Mason is a knight\n(2) Riley is a knight\n(3) Jacob is a knave\n(4) Zoey is a knight\n(5) Ava is a knight\n(6) 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 Mason is a knight. No contradiction is found in their claim that If Mason is a knight then Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of their own that If Zoey is a knight then Mason is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that If Zoey is a knight then Mason is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Mason is a knave or Mason is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Mason is not a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Mason is a knight and Ava is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 0), ('telling-truth', 3)), ('or', ('lying', 0), ('telling-truth', 0)), ('->', ('telling-truth', 3), ('lying', 0)), ('lying', 2), ('not', ('lying', 0)), ('and', ('telling-truth', 0), ('telling-truth', 4)))", "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 6 inhabitants: Amelia, Liam, Sebastian, Scarlett, Ava, and Oliver. Amelia stated, \"Ava is not a knight\". Liam said, \"Oliver is not a knave.\" In a statement by Sebastian: \"Oliver is a knave\". \"If Oliver is a knave then Ava is a knight,\" Scarlett claimed. Ava commented, \"If Sebastian is a knave then Sebastian is a knight\". As Oliver put it, \"Liam is a knave if and only if Sebastian is a knave\". So who is a knight and who is a knave?", "names": ["Amelia", "Liam", "Sebastian", "Scarlett", "Ava", "Oliver"], "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], "solution_text": "Amelia is a knave, Liam is a knave, Sebastian is a knight, Scarlett is a knight, Ava is a knight, and Oliver is a knave.", "solution_text_format": "(1) Amelia is a knave\n(2) Liam is a knave\n(3) Sebastian is a knight\n(4) Scarlett is a knight\n(5) Ava is a knight\n(6) Oliver is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Amelia is a knight. No contradiction is found in their claim that Ava is not a knight.", "Ava cannot be a knight, because this would contradict the claim of Amelia that Ava is not a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that If Sebastian is a knave then Sebastian is a knight.", "Sebastian cannot be a knight, because this would contradict the false claim of Ava that If Sebastian is a knave then Sebastian is a knight.", "Assume Sebastian 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 Liam is a knave if and only if Sebastian is a knave.", "Liam cannot be a knight, because this would contradict the claim of Oliver that Liam is a knave if and only if Sebastian is a knave.", "Liam cannot be a knave, because this would contradict the false claim of their own that Oliver is not a knave.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the false claim of Sebastian that Oliver is a knave.", "We have exhausted all possibilities for Oliver, Sebastian, and Ava, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Ava is not a knight.", "Assume Ava is a knight. No contradiction is found in their claim that If Sebastian is a knave then Sebastian is a knight.", "Assume Sebastian 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 Sebastian that Oliver is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Liam is a knave if and only if Sebastian is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Oliver is not a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Oliver is not a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Oliver is a knave then Ava is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 4)), ('not', ('lying', 5)), ('lying', 5), ('->', ('lying', 5), ('telling-truth', 4)), ('->', ('lying', 2), ('telling-truth', 2)), ('<=>', ('lying', 1), ('lying', 2)))", "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 6 inhabitants: Sebastian, Owen, Mason, Lily, Evelyn, and William. \"Owen is a knight,\" Sebastian claimed. According to Owen, \"Evelyn is not a knight\". As Mason put it, \"William is not a knight\". Lily said, \"Mason is a knight and William is a knave.\" \"Sebastian is a knave if and only if Evelyn is a knight,\" Evelyn declared. In William's words: \"If Mason is a knave then Evelyn is a knight\". So who is a knight and who is a knave?", "names": ["Sebastian", "Owen", "Mason", "Lily", "Evelyn", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, true], "solution_text": "Sebastian is a knave, Owen is a knave, Mason is a knave, Lily is a knave, Evelyn is a knight, and William is a knight.", "solution_text_format": "(1) Sebastian is a knave\n(2) Owen is a knave\n(3) Mason is a knave\n(4) Lily is a knave\n(5) Evelyn is a knight\n(6) 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 Sebastian is a knight. No contradiction is found in their claim that Owen is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Evelyn is not a knight.", "Evelyn cannot be a knight, because this would contradict the claim of Owen that Evelyn is not a knight.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that Sebastian is a knave if and only if Evelyn is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the claim of Sebastian that Owen is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Owen is a knight.", "Owen cannot be a knight, because this would contradict the false claim of Sebastian that Owen is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Evelyn is not a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Sebastian is a knave if and only if Evelyn is a knight.", "Assume Mason 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 Mason that William is not a knight.", "William cannot be a knave, because this would contradict the false claim of their own that If Mason is a knave then Evelyn is a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that William is not a knight.", "Assume William is a knight. No contradiction is found in their claim that If Mason is a knave then Evelyn is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Mason is a knight and William is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Mason is a knight and William is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('not', ('telling-truth', 4)), ('not', ('telling-truth', 5)), ('and', ('telling-truth', 2), ('lying', 5)), ('<=>', ('lying', 0), ('telling-truth', 4)), ('->', ('lying', 2), ('telling-truth', 4)))", "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 6 inhabitants: Charlotte, Lily, Jackson, Alexander, Emma, and Lucas. \"Lucas is a knight and Charlotte is a knight\" - Charlotte. Lily was heard saying, \"Alexander is a knave if and only if Lucas is a knight\". Jackson expressed that Charlotte is not a knight. Alexander remarked, \"Charlotte is a knave\". \"Jackson is a knave and Lily is a knave,\" Emma claimed. Lucas said, \"Emma is not a knave.\" So who is a knight and who is a knave?", "names": ["Charlotte", "Lily", "Jackson", "Alexander", "Emma", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false], "solution_text": "Charlotte is a knave, Lily is a knight, Jackson is a knight, Alexander is a knight, Emma is a knave, and Lucas is a knave.", "solution_text_format": "(1) Charlotte is a knave\n(2) Lily is a knight\n(3) Jackson is a knight\n(4) Alexander is a knight\n(5) Emma is a knave\n(6) Lucas is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that Lucas is a knight and Charlotte is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Emma is not a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Jackson is a knave and Lily is a knave.", "Jackson cannot be a knight, because this would contradict the claim of their own that Charlotte is not a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Charlotte is not a knight.", "Lily cannot be a knight, because this would contradict the claim of Emma that Jackson is a knave and Lily is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Alexander is a knave if and only if Lucas is a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that Charlotte is a knave.", "Alexander cannot be a knave, because this would contradict the false claim of Lily that Alexander is a knave if and only if Lucas is a knight.", "We have exhausted all possibilities for Alexander, Lily, and Jackson, so let us go back and reconsider Emma.", "Emma cannot be a knave, because this would contradict the claim of Lucas that Emma is not a knave.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the claim of Charlotte that Lucas is a knight and Charlotte is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Lucas is a knight and Charlotte is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Emma is not a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Jackson is a knave and Lily is a knave.", "Jackson cannot be a knight, because this would contradict the claim of Emma that Jackson is a knave and Lily is a knave.", "Jackson 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 Jackson, so let us go back and reconsider Emma.", "Emma cannot be a knave, because this would contradict the claim of Lucas that Emma is not a knave.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Lucas.", "Assume Lucas 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 Lucas that Emma is not a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Jackson is a knave and Lily is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Charlotte is not a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Alexander is a knave if and only if Lucas is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Charlotte is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('telling-truth', 0)), ('<=>', ('lying', 3), ('telling-truth', 5)), ('not', ('telling-truth', 0)), ('lying', 0), ('and', ('lying', 2), ('lying', 1)), ('not', ('lying', 4)))", "index": 99}