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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 7 inhabitants: Evelyn, Isabella, Oliver, Aurora, Ethan, Lily, and Luke. According to Evelyn, \"Aurora is a knave\". Isabella commented, \"Luke is a knight\". In Oliver's words: \"Aurora is a knave and Isabella is a knight\". Aurora commented, \"Isabella is not a knight\". \"If Lily is a knave then Luke is a knave,\" Ethan claimed. \"Luke is a knave and Luke is a knight,\" Lily claimed. According to Luke, \"Lily is a knight and Aurora is a knave\". So who is a knight and who is a knave?", "names": ["Evelyn", "Isabella", "Oliver", "Aurora", "Ethan", "Lily", "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, false], "solution_text": "Evelyn is a knave, Isabella is a knave, Oliver is a knave, Aurora is a knight, Ethan is a knight, Lily is a knave, and Luke is a knave.", "solution_text_format": "(1) Evelyn is a knave\n(2) Isabella is a knave\n(3) Oliver is a knave\n(4) Aurora is a knight\n(5) Ethan is a knight\n(6) Lily is a knave\n(7) Luke is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Aurora is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Evelyn that Aurora is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Isabella is not a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Luke is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Lily is a knight and Aurora is a knave.", "Lily cannot be a knight, because this would contradict the claim of their own that Luke is a knave and Luke is a knight.", "Lily cannot be a knave, because this would contradict the claim of Luke that Lily is a knight and Aurora is a knave.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the claim of Isabella that Luke is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the false claim of Aurora that Isabella is not a knight.", "We have exhausted all possibilities for Isabella and Aurora, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Aurora is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Isabella is not a knight.", "Isabella cannot be a knight, because this would contradict the claim of Aurora that Isabella is not a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Luke is a knight.", "Luke cannot be a knight, because this would contradict the false claim of Isabella that Luke is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Lily is a knight and Aurora is a knave.", "Lily cannot be a knight, because this would contradict the claim of their own that Luke is a knave and Luke is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Luke is a knave and Luke is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Aurora is a knave and Isabella is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Aurora is a knave and Isabella is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If Lily is a knave then Luke is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('telling-truth', 6), ('and', ('lying', 3), ('telling-truth', 1)), ('not', ('telling-truth', 1)), ('->', ('lying', 5), ('lying', 6)), ('and', ('lying', 6), ('telling-truth', 6)), ('and', ('telling-truth', 5), ('lying', 3)))", "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 7 inhabitants: Isabella, Mason, Ella, Harper, Daniel, David, and Michael. According to Isabella, \"David is a knight\". \"Daniel is not a knight,\" Mason mentioned. \"Mason is not a knave\" - Ella. In Harper's words: \"David is a knave\". Daniel said that David is a knight or David is a knave. David said, \"Ella is a knight if and only if Daniel is a knave.\" As Michael put it, \"If Harper is a knight then Daniel is a knave\". So who is a knight and who is a knave?", "names": ["Isabella", "Mason", "Ella", "Harper", "Daniel", "David", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true, true], "solution_text": "Isabella is a knight, Mason is a knave, Ella is a knave, Harper is a knave, Daniel is a knight, David is a knight, and Michael is a knight.", "solution_text_format": "(1) Isabella is a knight\n(2) Mason is a knave\n(3) Ella is a knave\n(4) Harper is a knave\n(5) Daniel is a knight\n(6) David is a knight\n(7) Michael is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that David is a knight.", "Assume David is a knight. No contradiction is found in their claim that Ella is a knight if and only if Daniel is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Mason is not a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Daniel is not a knight.", "Daniel cannot be a knight, because this would contradict the claim of Mason that Daniel is not a knight.", "Daniel cannot be a knave, because this would contradict the false claim of their own that David is a knight or David is a knave.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Mason.", "Mason cannot be a knave, because this would contradict the claim of Ella that Mason is not a knave.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Mason is not a knave.", "Mason cannot be a knight, because this would contradict the false claim of Ella that Mason is not a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Daniel is not a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that David is a knight or David is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that David is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that David is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that If Harper is a knight then Daniel is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 5), ('not', ('telling-truth', 4)), ('not', ('lying', 1)), ('lying', 5), ('or', ('telling-truth', 5), ('lying', 5)), ('<=>', ('telling-truth', 2), ('lying', 4)), ('->', ('telling-truth', 3), ('lying', 4)))", "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 7 inhabitants: Sebastian, Mia, Benjamin, Aria, Aurora, Jack, and Avery. Sebastian said, \"Jack is a knight.\" Mia noted, \"If Avery is a knight then Avery is a knave\". \"Sebastian is a knave or Benjamin is a knight,\" Benjamin mentioned. \"Aurora is a knave and Jack is a knave,\" Aria mentioned. Aurora asserted: \"Sebastian is not a knight\". Jack told you that Aurora is a knight or Benjamin is a knight. Avery said, \"Mia is a knave and Mia is a knight.\" So who is a knight and who is a knave?", "names": ["Sebastian", "Mia", "Benjamin", "Aria", "Aurora", "Jack", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true, false], "solution_text": "Sebastian is a knight, Mia is a knight, Benjamin is a knight, Aria is a knave, Aurora is a knave, Jack is a knight, and Avery is a knave.", "solution_text_format": "(1) Sebastian is a knight\n(2) Mia is a knight\n(3) Benjamin is a knight\n(4) Aria is a knave\n(5) Aurora is a knave\n(6) Jack is a knight\n(7) 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 Sebastian is a knight. No contradiction is found in their claim that Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Aurora is a knight or Benjamin is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Sebastian is not a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Sebastian is not a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Sebastian is a knave or Benjamin is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that If Avery is a knight then Avery is a knave.", "Avery cannot be a knight, because this would contradict the claim of Mia that If Avery is a knight then Avery is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Mia is a knave and Mia is a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that Aurora is a knave and Jack is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Aurora is a knave and Jack is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 5), ('->', ('telling-truth', 6), ('lying', 6)), ('or', ('lying', 0), ('telling-truth', 2)), ('and', ('lying', 4), ('lying', 5)), ('not', ('telling-truth', 0)), ('or', ('telling-truth', 4), ('telling-truth', 2)), ('and', ('lying', 1), ('telling-truth', 1)))", "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 7 inhabitants: James, Sebastian, Noah, Olivia, Daniel, Aurora, and Joseph. In James's words: \"Daniel is a knave if and only if Joseph is a knight\". As Sebastian put it, \"Joseph is a knight\". Noah expressed that Aurora is a knave or Olivia is a knight. Olivia said, \"Olivia is a knight if and only if Noah is a knave.\" Daniel commented, \"Aurora is not a knave\". Aurora stated, \"James is a knight if and only if Olivia is a knave\". Joseph told you that James is not a knight. So who is a knight and who is a knave?", "names": ["James", "Sebastian", "Noah", "Olivia", "Daniel", "Aurora", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true, false], "solution_text": "James is a knight, Sebastian is a knave, Noah is a knave, Olivia is a knave, Daniel is a knight, Aurora is a knight, and Joseph is a knave.", "solution_text_format": "(1) James is a knight\n(2) Sebastian is a knave\n(3) Noah is a knave\n(4) Olivia is a knave\n(5) Daniel is a knight\n(6) Aurora is a knight\n(7) 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 James is a knight. No contradiction is found in their claim that Daniel is a knave if and only if Joseph is a knight.", "Assume Daniel 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 James is a knight if and only if Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Aurora that James is a knight if and only if Olivia is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Olivia is a knight if and only if Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of their own that Aurora is a knave or Olivia is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Aurora is a knave or Olivia is a knight.", "Joseph cannot be a knight, because this would contradict the claim of James that Daniel is a knave if and only if Joseph is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that James is not a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Joseph is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Joseph is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 4), ('telling-truth', 6)), ('telling-truth', 6), ('or', ('lying', 5), ('telling-truth', 3)), ('<=>', ('telling-truth', 3), ('lying', 2)), ('not', ('lying', 5)), ('<=>', ('telling-truth', 0), ('lying', 3)), ('not', ('telling-truth', 0)))", "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 7 inhabitants: Aiden, Sofia, William, Victoria, Aria, Ethan, and Liam. Aiden was heard saying, \"William is a knight\". Sofia commented, \"Liam is a knight or Victoria is a knight\". As William put it, \"Liam is not a knave\". As Victoria put it, \"Ethan is a knight if and only if Aiden is a knave\". Aria told you that If Ethan is a knight then Liam is a knight. Ethan asserted: \"Victoria is a knave\". According to Liam, \"Ethan is a knight if and only if Aria is a knave\". So who is a knight and who is a knave?", "names": ["Aiden", "Sofia", "William", "Victoria", "Aria", "Ethan", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false, true], "solution_text": "Aiden is a knight, Sofia is a knight, William is a knight, Victoria is a knight, Aria is a knight, Ethan is a knave, and Liam is a knight.", "solution_text_format": "(1) Aiden is a knight\n(2) Sofia is a knight\n(3) William is a knight\n(4) Victoria is a knight\n(5) Aria is a knight\n(6) Ethan is a knave\n(7) 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 Aiden is a knight. No contradiction is found in their claim that William is a knight.", "Assume William is a knight. No contradiction is found in their claim that Liam is not a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Ethan is a knight if and only if Aria is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Victoria is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that Ethan is a knight if and only if Aiden is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Ethan is a knight if and only if Aiden is a knave.", "Aria cannot be a knight, because this would contradict the claim of Liam that Ethan is a knight if and only if Aria is a knave.", "Aria cannot be a knave, because this would contradict the false claim of their own that If Ethan is a knight then Liam is a knight.", "We have exhausted all possibilities for Aria and Victoria, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Ethan is a knight if and only if Aiden is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that If Ethan is a knight then Liam is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Liam is a knight or Victoria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('or', ('telling-truth', 6), ('telling-truth', 3)), ('not', ('lying', 6)), ('<=>', ('telling-truth', 5), ('lying', 0)), ('->', ('telling-truth', 5), ('telling-truth', 6)), ('lying', 3), ('<=>', ('telling-truth', 5), ('lying', 4)))", "index": 4}
-{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Jackson, Daniel, Aurora, Sofia, Grace, David, and Chloe. Jackson was heard saying, \"If Grace is a knave then Chloe is a knight\". Daniel said that David is not a knight. According to Aurora, \"Chloe is a knight or Aurora is a knight\". Sofia said, \"Aurora is a knight.\" Grace said, \"Jackson is a knave or Aurora is a knight.\" David said, \"Aurora is a knave if and only if Jackson is a knight.\" Chloe told you that Jackson is a knave or Grace is a knave. So who is a knight and who is a knave?", "names": ["Jackson", "Daniel", "Aurora", "Sofia", "Grace", "David", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false, false], "solution_text": "Jackson is a knight, Daniel is a knight, Aurora is a knight, Sofia is a knight, Grace is a knight, David is a knave, and Chloe is a knave.", "solution_text_format": "(1) Jackson is a knight\n(2) Daniel is a knight\n(3) Aurora is a knight\n(4) Sofia is a knight\n(5) Grace is a knight\n(6) David is a knave\n(7) Chloe is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that If Grace is a knave then Chloe is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Jackson is a knave or Aurora is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Chloe is a knight or Aurora is a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Jackson is a knave or Grace is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Jackson is a knave or Grace is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that David is not a knight.", "David cannot be a knight, because this would contradict the claim of Daniel that David is not a knight.", "Assume David is a knave. No contradiction is found in their false claim that Aurora is a knave if and only if Jackson is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Aurora is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 4), ('telling-truth', 6)), ('not', ('telling-truth', 5)), ('or', ('telling-truth', 6), ('telling-truth', 2)), ('telling-truth', 2), ('or', ('lying', 0), ('telling-truth', 2)), ('<=>', ('lying', 2), ('telling-truth', 0)), ('or', ('lying', 0), ('lying', 4)))", "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 7 inhabitants: Sophia, Avery, Luke, Logan, Mia, Benjamin, and Olivia. Sophia stated, \"Mia is a knight if and only if Avery is a knight\". \"Mia is not a knave,\" Avery mentioned. Luke said, \"Benjamin is a knight and Avery is a knight.\" \"Logan is a knight,\" Logan mentioned. \"If Luke is a knight then Sophia is a knave,\" Mia declared. In Benjamin's words: \"Logan is a knave or Luke is a knight\". \"Luke is not a knight,\" Olivia declared. So who is a knight and who is a knave?", "names": ["Sophia", "Avery", "Luke", "Logan", "Mia", "Benjamin", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false, true], "solution_text": "Sophia is a knight, Avery is a knight, Luke is a knave, Logan is a knight, Mia is a knight, Benjamin is a knave, and Olivia is a knight.", "solution_text_format": "(1) Sophia is a knight\n(2) Avery is a knight\n(3) Luke is a knave\n(4) Logan is a knight\n(5) Mia is a knight\n(6) Benjamin is a knave\n(7) Olivia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Mia is a knight if and only if Avery is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that If Luke is a knight then Sophia is a knave.", "Luke cannot be a knight, because this would contradict the claim of Mia that If Luke is a knight then Sophia is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Benjamin is a knight and Avery is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Logan is a knave or Luke is a knight.", "Logan cannot be a knight, because this would contradict the claim of Benjamin that Logan is a knave or Luke is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Logan is a knight.", "Avery cannot be a knight, because this would contradict the false claim of Luke that Benjamin is a knight and Avery is a knight.", "Avery cannot be a knave, because this would contradict the claim of Sophia that Mia is a knight if and only if Avery is a knight.", "We have exhausted all possibilities for Avery and Logan, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Logan is a knave or Luke is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Logan is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Mia is not a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Luke is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 4), ('telling-truth', 1)), ('not', ('lying', 4)), ('and', ('telling-truth', 5), ('telling-truth', 1)), ('telling-truth', 3), ('->', ('telling-truth', 2), ('lying', 0)), ('or', ('lying', 3), ('telling-truth', 2)), ('not', ('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 7 inhabitants: Evelyn, Lily, Liam, Grace, David, Jack, and Daniel. \"Lily is a knight or Grace is a knight,\" Evelyn mentioned. In a statement by Lily: \"Evelyn is a knight or David is a knight\". Liam said, \"David is a knave or Lily is a knight.\" Grace noted, \"Liam is a knight\". David told you that Grace is a knight and Grace is a knave. Jack told you that Grace is a knave or Evelyn is a knight. Daniel asserted: \"Grace is a knight and David is a knight\". So who is a knight and who is a knave?", "names": ["Evelyn", "Lily", "Liam", "Grace", "David", "Jack", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true, false], "solution_text": "Evelyn is a knight, Lily is a knight, Liam is a knight, Grace is a knight, David is a knave, Jack is a knight, and Daniel is a knave.", "solution_text_format": "(1) Evelyn is a knight\n(2) Lily is a knight\n(3) Liam is a knight\n(4) Grace is a knight\n(5) David is a knave\n(6) Jack is a knight\n(7) 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 Evelyn is a knight. No contradiction is found in their claim that Lily is a knight or Grace is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Evelyn is a knight or David is a knight.", "David cannot be a knight, because this would contradict the claim of their own that Grace is a knight and Grace is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Grace is a knight and Grace is a knave.", "Assume Grace 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 David is a knave or Lily is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Grace is a knave or Evelyn is a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that Grace is a knight and David is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Grace is a knight and David is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('telling-truth', 3)), ('or', ('telling-truth', 0), ('telling-truth', 4)), ('or', ('lying', 4), ('telling-truth', 1)), ('telling-truth', 2), ('and', ('telling-truth', 3), ('lying', 3)), ('or', ('lying', 3), ('telling-truth', 0)), ('and', ('telling-truth', 3), ('telling-truth', 4)))", "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 7 inhabitants: Mia, Emily, Logan, Amelia, Michael, William, and Ethan. As Mia put it, \"Amelia is a knight or Michael is a knave\". Emily noted, \"William is a knave and Amelia is a knight\". Logan expressed that Michael is a knave and Ethan is a knight. \"Mia is not a knight,\" Amelia claimed. Michael was heard saying, \"Mia is a knight and William is a knight\". William stated, \"Emily is a knight and Ethan is a knave\". Ethan stated, \"Emily is a knave\". So who is a knight and who is a knave?", "names": ["Mia", "Emily", "Logan", "Amelia", "Michael", "William", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, false, true], "solution_text": "Mia is a knight, Emily is a knave, Logan is a knight, Amelia is a knave, Michael is a knave, William is a knave, and Ethan is a knight.", "solution_text_format": "(1) Mia is a knight\n(2) Emily is a knave\n(3) Logan is a knight\n(4) Amelia is a knave\n(5) Michael is a knave\n(6) William is a knave\n(7) 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 Mia is a knight. No contradiction is found in their claim that Amelia is a knight or Michael is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Mia is not a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Mia is not a knight.", "Michael cannot be a knight, because this would contradict the claim of Mia that Amelia is a knight or Michael is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Mia is a knight and William is a knight.", "William cannot be a knight, because this would contradict the false claim of Michael that Mia is a knight and William is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Emily is a knight and Ethan is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that William is a knave and Amelia is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that William is a knave and Amelia is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Emily is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Michael is a knave and Ethan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('lying', 4)), ('and', ('lying', 5), ('telling-truth', 3)), ('and', ('lying', 4), ('telling-truth', 6)), ('not', ('telling-truth', 0)), ('and', ('telling-truth', 0), ('telling-truth', 5)), ('and', ('telling-truth', 1), ('lying', 6)), ('lying', 1))", "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 7 inhabitants: Penelope, Mason, William, Mia, Jackson, Logan, and Sophia. In Penelope's words: \"Logan is a knight or Sophia is a knave\". Mason expressed that Jackson is not a knight. \"Logan is a knave if and only if William is a knight\" - William. \"Mason is not a knave\" - Mia. Jackson noted, \"William is a knave\". As Logan put it, \"Sophia is not a knave\". As Sophia put it, \"Mia is not a knave\". So who is a knight and who is a knave?", "names": ["Penelope", "Mason", "William", "Mia", "Jackson", "Logan", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, false, false], "solution_text": "Penelope is a knight, Mason is a knave, William is a knave, Mia is a knave, Jackson is a knight, Logan is a knave, and Sophia is a knave.", "solution_text_format": "(1) Penelope is a knight\n(2) Mason is a knave\n(3) William is a knave\n(4) Mia is a knave\n(5) Jackson is a knight\n(6) Logan is a knave\n(7) Sophia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that Logan is a knight or Sophia is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Sophia is not a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Mia is not a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Mason is not a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Jackson is not a knight.", "Jackson cannot be a knight, because this would contradict the claim of Mason that Jackson is not a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that William is a knave.", "William cannot be a knight, because this would contradict the claim of their own that Logan is a knave if and only if William is a knight.", "William cannot be a knave, because this would contradict the false claim of their own that Logan is a knave if and only if William is a knight.", "We have exhausted all possibilities for William and Jackson, so let us go back and reconsider Mason.", "Mason cannot be a knave, because this would contradict the claim of Mia that Mason is not a knave.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the claim of Sophia that Mia is not a knave.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the claim of Logan that Sophia is not a knave.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Sophia is not a knave.", "Sophia cannot be a knight, because this would contradict the claim of Penelope that Logan is a knight or Sophia is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Mia is not a knave.", "Mia cannot be a knight, because this would contradict the false claim of Sophia that Mia is not a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Mason is not a knave.", "Mason cannot be a knight, because this would contradict the false claim of Mia that Mason is not a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Jackson is not a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that William is a knave.", "William cannot be a knight, because this would contradict the claim of Jackson that William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Logan is a knave if and only if William is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('lying', 6)), ('not', ('telling-truth', 4)), ('<=>', ('lying', 5), ('telling-truth', 2)), ('not', ('lying', 1)), ('lying', 2), ('not', ('lying', 6)), ('not', ('lying', 3)))", "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 7 inhabitants: Benjamin, Luke, Amelia, Noah, Mia, Emily, and Samuel. \"If Emily is a knight then Amelia is a knave,\" Benjamin claimed. Luke asserted: \"If Emily is a knight then Noah is a knight\". \"Emily is not a knight,\" Amelia claimed. Noah expressed that Mia is a knight if and only if Benjamin is a knave. As Mia put it, \"Emily is a knight or Noah is a knight\". Emily said that Amelia is not a knight. \"If Benjamin is a knight then Amelia is a knave,\" Samuel claimed. So who is a knight and who is a knave?", "names": ["Benjamin", "Luke", "Amelia", "Noah", "Mia", "Emily", "Samuel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true, true], "solution_text": "Benjamin is a knight, Luke is a knave, Amelia is a knave, Noah is a knave, Mia is a knight, Emily is a knight, and Samuel is a knight.", "solution_text_format": "(1) Benjamin is a knight\n(2) Luke is a knave\n(3) Amelia is a knave\n(4) Noah is a knave\n(5) Mia is a knight\n(6) Emily is a knight\n(7) Samuel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that If Emily is a knight then Amelia is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Amelia is not a knight.", "Amelia cannot be a knight, because this would contradict the claim of Benjamin that If Emily is a knight then Amelia is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Emily is not a knight.", "Assume Luke is a knight. No contradiction is found in their claim that If Emily is a knight then Noah is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Mia is a knight if and only if Benjamin is a knave.", "Mia cannot be a knight, because this would contradict the claim of Noah that Mia is a knight if and only if Benjamin is a knave.", "Mia cannot be a knave, because this would contradict the false claim of their own that Emily is a knight or Noah is a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the claim of Luke that If Emily is a knight then Noah is a knight.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that If Emily is a knight then Noah is a knight.", "Noah cannot be a knight, because this would contradict the false claim of Luke that If Emily is a knight then Noah is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Mia is a knight if and only if Benjamin is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Emily is a knight or Noah is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that If Benjamin is a knight then Amelia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 5), ('lying', 2)), ('->', ('telling-truth', 5), ('telling-truth', 3)), ('not', ('telling-truth', 5)), ('<=>', ('telling-truth', 4), ('lying', 0)), ('or', ('telling-truth', 5), ('telling-truth', 3)), ('not', ('telling-truth', 2)), ('->', ('telling-truth', 0), ('lying', 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 7 inhabitants: Aria, Emily, Luke, Chloe, Owen, David, and Ethan. Aria stated, \"Ethan is a knight if and only if Luke is a knave\". \"If Owen is a knave then Luke is a knave\" - Emily. Luke commented, \"Owen is not a knight\". According to Chloe, \"Owen is a knight or Owen is a knave\". Owen told you that Ethan is not a knight. As David put it, \"David is a knight and Ethan is a knave\". Ethan said, \"David is a knight and Aria is a knave.\" So who is a knight and who is a knave?", "names": ["Aria", "Emily", "Luke", "Chloe", "Owen", "David", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false, false], "solution_text": "Aria is a knave, Emily is a knight, Luke is a knave, Chloe is a knight, Owen is a knight, David is a knave, and Ethan is a knave.", "solution_text_format": "(1) Aria is a knave\n(2) Emily is a knight\n(3) Luke is a knave\n(4) Chloe is a knight\n(5) Owen is a knight\n(6) David is a knave\n(7) Ethan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that Ethan is a knight if and only if Luke is a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that David is a knight and Aria is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that David is a knight and Aria is a knave.", "Assume David is a knight. No contradiction is found in their claim that David is a knight and Ethan is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Owen is not a knight.", "Owen cannot be a knight, because this would contradict the claim of Luke that Owen is not a knight.", "Owen cannot be a knave, because this would contradict the false claim of their own that Ethan is not a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the claim of Aria that Ethan is a knight if and only if Luke is a knave.", "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 and Ethan is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Owen is not a knight.", "Owen cannot be a knight, because this would contradict the claim of Luke that Owen is not a knight.", "Owen cannot be a knave, because this would contradict the false claim of their own that Ethan is not a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the claim of Aria that Ethan is a knight if and only if Luke is a knave.", "We have exhausted all possibilities for Luke, David, and Ethan, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Ethan is a knight if and only if Luke is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that David is a knight and Aria is a knave.", "David cannot be a knight, because this would contradict the claim of their own that David is a knight and Ethan is a knave.", "David cannot be a knave, because this would contradict the claim of Ethan that David is a knight and Aria is a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that David is a knight and Aria is a knave.", "David cannot be a knight, because this would contradict the false claim of Ethan that David is a knight and Aria is a knave.", "Assume David is a knave. No contradiction is found in their false claim that David is a knight and Ethan is a knave.", "Luke cannot be a knight, because this would contradict the false claim of Aria that Ethan 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 Owen is not a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Ethan is not a knight.", "Assume Emily is a knight. No contradiction is found in their claim that If Owen is a knave then Luke is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Owen is a knight or Owen is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 6), ('lying', 2)), ('->', ('lying', 4), ('lying', 2)), ('not', ('telling-truth', 4)), ('or', ('telling-truth', 4), ('lying', 4)), ('not', ('telling-truth', 6)), ('and', ('telling-truth', 5), ('lying', 6)), ('and', ('telling-truth', 5), ('lying', 0)))", "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 7 inhabitants: Benjamin, Avery, Sofia, Owen, Mia, Penelope, and Victoria. \"Sofia is a knight or Owen is a knave,\" Benjamin declared. \"Penelope is a knave and Sofia is a knave\" - Avery. Sofia was heard saying, \"Mia is a knave or Penelope is a knave\". Owen said that Benjamin is a knave and Benjamin is a knight. Mia stated, \"Owen is a knave and Owen is a knight\". In a statement by Penelope: \"Avery is a knave if and only if Owen is a knight\". Victoria asserted: \"Penelope is a knave if and only if Mia is a knight\". So who is a knight and who is a knave?", "names": ["Benjamin", "Avery", "Sofia", "Owen", "Mia", "Penelope", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, false, false], "solution_text": "Benjamin is a knight, Avery is a knave, Sofia is a knight, Owen is a knave, Mia is a knave, Penelope is a knave, and Victoria is a knave.", "solution_text_format": "(1) Benjamin is a knight\n(2) Avery is a knave\n(3) Sofia is a knight\n(4) Owen is a knave\n(5) Mia is a knave\n(6) Penelope is a knave\n(7) 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 Benjamin is a knight. No contradiction is found in their claim that Sofia is a knight or Owen is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Mia is a knave or Penelope is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Owen is a knave and Owen is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Owen is a knave and Owen is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave and Benjamin is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Benjamin is a knave and Benjamin is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Avery is a knave if and only if Owen is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Penelope is a knave and Sofia is a knave.", "Avery cannot be a knave, because this would contradict the claim of Penelope that Avery is a knave if and only if Owen is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Avery is a knave if and only if Owen is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Penelope is a knave and Sofia is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Penelope is a knave and Sofia is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that Penelope is a knave if and only if Mia is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Penelope is a knave if and only if Mia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('lying', 3)), ('and', ('lying', 5), ('lying', 2)), ('or', ('lying', 4), ('lying', 5)), ('and', ('lying', 0), ('telling-truth', 0)), ('and', ('lying', 3), ('telling-truth', 3)), ('<=>', ('lying', 1), ('telling-truth', 3)), ('<=>', ('lying', 5), ('telling-truth', 4)))", "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 7 inhabitants: James, Victoria, Sebastian, David, Lucas, Sofia, and Harper. James said that James is a knight or Sofia is a knight. Victoria stated, \"David is not a knight\". Sebastian commented, \"Sofia is a knave or Lucas is a knight\". \"David is a knight and Lucas is a knight,\" David mentioned. Lucas was heard saying, \"Sofia is a knave or Harper is a knave\". Sofia remarked, \"If David is a knave then Lucas is a knight\". Harper expressed that David is a knight. So who is a knight and who is a knave?", "names": ["James", "Victoria", "Sebastian", "David", "Lucas", "Sofia", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true, false], "solution_text": "James is a knight, Victoria is a knight, Sebastian is a knight, David is a knave, Lucas is a knight, Sofia is a knight, and Harper is a knave.", "solution_text_format": "(1) James is a knight\n(2) Victoria is a knight\n(3) Sebastian is a knight\n(4) David is a knave\n(5) Lucas is a knight\n(6) Sofia is a knight\n(7) Harper is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that James is a knight or Sofia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that If David is a knave then Lucas is a knight.", "Assume David is a knight. No contradiction is found in their claim that David is a knight and Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Sofia is a knave or Harper is a knave.", "Harper cannot be a knight, because this would contradict the claim of Lucas that Sofia is a knave or Harper is a knave.", "Harper 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 Harper, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the claim of David that David is a knight and Lucas is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that David is a knight and Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Sofia is a knave or Harper is a knave.", "Harper cannot be a knight, because this would contradict the claim of Lucas that Sofia is a knave or Harper is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that David is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that David is not a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Sofia is a knave or Lucas is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 0), ('telling-truth', 5)), ('not', ('telling-truth', 3)), ('or', ('lying', 5), ('telling-truth', 4)), ('and', ('telling-truth', 3), ('telling-truth', 4)), ('or', ('lying', 5), ('lying', 6)), ('->', ('lying', 3), ('telling-truth', 4)), ('telling-truth', 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 7 inhabitants: Sebastian, Sophia, Lily, Ella, Jackson, Riley, and Penelope. Sebastian told you that Penelope is a knight. Sophia asserted: \"Sebastian is a knight or Sophia is a knight\". In a statement by Lily: \"Riley is a knight if and only if Ella is a knight\". According to Ella, \"Sebastian is a knight\". Jackson stated, \"Sophia is a knight\". \"Sebastian is not a knave\" - Riley. \"Lily is a knight or Ella is a knave,\" Penelope claimed. So who is a knight and who is a knave?", "names": ["Sebastian", "Sophia", "Lily", "Ella", "Jackson", "Riley", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true, true], "solution_text": "Sebastian is a knight, Sophia is a knight, Lily is a knight, Ella is a knight, Jackson is a knight, Riley is a knight, and Penelope is a knight.", "solution_text_format": "(1) Sebastian is a knight\n(2) Sophia is a knight\n(3) Lily is a knight\n(4) Ella is a knight\n(5) Jackson is a knight\n(6) Riley is a knight\n(7) 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 Sebastian is a knight. No contradiction is found in their claim that Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Lily is a knight or Ella is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Riley is a knight if and only if Ella is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Sebastian is not a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Sebastian is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Sebastian is a knight or Sophia is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Sophia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 6), ('or', ('telling-truth', 0), ('telling-truth', 1)), ('<=>', ('telling-truth', 5), ('telling-truth', 3)), ('telling-truth', 0), ('telling-truth', 1), ('not', ('lying', 0)), ('or', ('telling-truth', 2), ('lying', 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 7 inhabitants: Emma, Zoey, David, Jack, Amelia, Logan, and Abigail. \"David is not a knight\" - Emma. Zoey expressed that If Abigail is a knight then Jack is a knave. \"If Jack is a knave then Jack is a knight\" - David. Jack noted, \"If Zoey is a knave then David is a knave\". Amelia stated, \"Abigail is a knave if and only if Zoey is a knave\". In Logan's words: \"Jack is a knight if and only if Amelia is a knight\". According to Abigail, \"David is a knight and Abigail is a knight\". So who is a knight and who is a knave?", "names": ["Emma", "Zoey", "David", "Jack", "Amelia", "Logan", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false, false], "solution_text": "Emma is a knave, Zoey is a knight, David is a knight, Jack is a knight, Amelia is a knave, Logan is a knave, and Abigail is a knave.", "solution_text_format": "(1) Emma is a knave\n(2) Zoey is a knight\n(3) David is a knight\n(4) Jack is a knight\n(5) Amelia is a knave\n(6) Logan is a knave\n(7) 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 Emma is a knight. No contradiction is found in their claim that David is not a knight.", "David cannot be a knight, because this would contradict the claim of Emma that David is not a knight.", "Assume David is a knave. No contradiction is found in their false claim that If Jack is a knave then Jack is a knight.", "Jack cannot be a knight, because this would contradict the false claim of David that If Jack is a knave then Jack is a knight.", "Jack cannot be a knave, because this would contradict the false claim of their own that If Zoey is a knave then David is a knave.", "We have exhausted all possibilities for Jack and David, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that David is not a knight.", "Assume David is a knight. No contradiction is found in their claim that If Jack is a knave then Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that If Zoey is a knave then David is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that If Abigail is a knight then Jack is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Zoey that If Abigail is a knight then Jack is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that David is a knight and Abigail is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Abigail is a knave if and only if Zoey is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Abigail is a knave if and only if Zoey is a knave.", "Logan cannot be a knight, because this would contradict the claim of their own that Jack is a knight if and only if Amelia is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Jack is a knight if and only if Amelia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('->', ('telling-truth', 6), ('lying', 3)), ('->', ('lying', 3), ('telling-truth', 3)), ('->', ('lying', 1), ('lying', 2)), ('<=>', ('lying', 6), ('lying', 1)), ('<=>', ('telling-truth', 3), ('telling-truth', 4)), ('and', ('telling-truth', 2), ('telling-truth', 6)))", "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 7 inhabitants: Aiden, Sofia, Liam, Sebastian, Luke, Aurora, and Ella. \"Liam is a knave if and only if Ella is a knave,\" Aiden mentioned. Sofia said, \"Sebastian is a knave or Luke is a knave.\" In Liam's words: \"If Sofia is a knave then Ella is a knight\". \"Ella is not a knave\" - Sebastian. Luke remarked, \"Aiden is a knight if and only if Luke is a knight\". Aurora said, \"If Liam is a knave then Liam is a knight.\" \"Sofia is a knave and Luke is a knight,\" Ella declared. So who is a knight and who is a knave?", "names": ["Aiden", "Sofia", "Liam", "Sebastian", "Luke", "Aurora", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true, true], "solution_text": "Aiden is a knight, Sofia is a knave, Liam is a knight, Sebastian is a knight, Luke is a knight, Aurora is a knight, and Ella is a knight.", "solution_text_format": "(1) Aiden is a knight\n(2) Sofia is a knave\n(3) Liam is a knight\n(4) Sebastian is a knight\n(5) Luke is a knight\n(6) Aurora is a knight\n(7) 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 Aiden is a knight. No contradiction is found in their claim that Liam is a knave if and only if Ella is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that If Sofia is a knave then Ella is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Sebastian is a knave or Luke is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Ella is not a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Sofia is a knave and Luke is a knight.", "Ella cannot be a knave, because this would contradict the claim of Aiden that Liam is a knave if and only if Ella is a knave.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Ella is not a knave.", "Ella cannot be a knight, because this would contradict the false claim of Sebastian that Ella is not a knave.", "Ella cannot be a knave, because this would contradict the claim of Aiden that Liam is a knave if and only if Ella is a knave.", "We have exhausted all possibilities for Ella and Sebastian, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Sebastian is a knave or Luke is a knave.", "Assume Sebastian 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 Sofia is a knave and Luke is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Aiden is a knight if and only if Luke is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that If Liam is a knave then Liam is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('lying', 6)), ('or', ('lying', 3), ('lying', 4)), ('->', ('lying', 1), ('telling-truth', 6)), ('not', ('lying', 6)), ('<=>', ('telling-truth', 0), ('telling-truth', 4)), ('->', ('lying', 2), ('telling-truth', 2)), ('and', ('lying', 1), ('telling-truth', 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 7 inhabitants: Penelope, Benjamin, Scarlett, Jacob, Sebastian, Charlotte, and Aurora. Penelope remarked, \"Sebastian is a knight\". In Benjamin's words: \"If Jacob is a knave then Charlotte is a knave\". Scarlett told you that If Sebastian is a knight then Scarlett is a knight. As Jacob put it, \"Scarlett is not a knave\". \"Charlotte is a knave if and only if Aurora is a knave,\" Sebastian declared. As Charlotte put it, \"Jacob is not a knight\". Aurora remarked, \"Benjamin is a knight\". So who is a knight and who is a knave?", "names": ["Penelope", "Benjamin", "Scarlett", "Jacob", "Sebastian", "Charlotte", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false, true], "solution_text": "Penelope is a knave, Benjamin is a knight, Scarlett is a knight, Jacob is a knight, Sebastian is a knave, Charlotte is a knave, and Aurora is a knight.", "solution_text_format": "(1) Penelope is a knave\n(2) Benjamin is a knight\n(3) Scarlett is a knight\n(4) Jacob is a knight\n(5) Sebastian is a knave\n(6) Charlotte is a knave\n(7) 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 Penelope 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 Charlotte is a knave if and only if Aurora is a knave.", "Assume Charlotte 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 Charlotte that Jacob is not a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Scarlett is not a knave.", "Scarlett cannot be a knight, because this would contradict the false claim of Jacob that Scarlett is not a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that If Sebastian is a knight then Scarlett is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Benjamin is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that If Jacob is a knave then Charlotte is a knave.", "Benjamin cannot be a knave, because this would contradict the claim of Aurora that Benjamin is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the claim of Sebastian that Charlotte is a knave if and only if Aurora is a knave.", "We have exhausted all possibilities for Aurora, Scarlett, and Jacob, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Jacob is not a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Sebastian is a knight then Scarlett is a knight.", "Aurora cannot be a knight, because this would contradict the claim of Sebastian that Charlotte is a knave if and only if Aurora is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Benjamin is a knight.", "Benjamin cannot be a knight, because this would contradict the false claim of Aurora that Benjamin is a knight.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that If Jacob is a knave then Charlotte is a knave.", "We have exhausted all possibilities for Benjamin and Aurora, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the claim of Jacob that Scarlett is not a knave.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the false claim of Charlotte that Jacob is not a knight.", "We have exhausted all possibilities for Jacob and Charlotte, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the claim of Penelope that Sebastian is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Sebastian is a knight.", "Sebastian cannot be a knight, because this would contradict the false claim of Penelope that Sebastian is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Charlotte is a knave if and only if Aurora is a knave.", "Assume Charlotte 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 Charlotte that Jacob is not a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Scarlett is not a knave.", "Scarlett cannot be a knight, because this would contradict the false claim of Jacob that Scarlett is not a knave.", "Scarlett cannot be a knave, because this would contradict the false claim of their own that If Sebastian is a knight then Scarlett is a knight.", "We have exhausted all possibilities for Scarlett and Jacob, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Jacob is not a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Sebastian is a knight then Scarlett is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Benjamin is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Jacob is a knave then Charlotte is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('->', ('lying', 3), ('lying', 5)), ('->', ('telling-truth', 4), ('telling-truth', 2)), ('not', ('lying', 2)), ('<=>', ('lying', 5), ('lying', 6)), ('not', ('telling-truth', 3)), ('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 7 inhabitants: Ella, Lily, Zoey, Charlotte, Harper, Isabella, and Liam. Ella told you that Charlotte is a knight or Zoey is a knight. Lily expressed that Harper is a knave if and only if Liam is a knave. Zoey remarked, \"If Harper is a knave then Harper is a knight\". Charlotte remarked, \"Harper is not a knight\". Harper stated, \"Isabella is a knight or Ella is a knave\". Isabella asserted: \"Charlotte is a knight if and only if Zoey is a knave\". In Liam's words: \"Lily is a knave if and only if Liam is a knight\". So who is a knight and who is a knave?", "names": ["Ella", "Lily", "Zoey", "Charlotte", "Harper", "Isabella", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true, false], "solution_text": "Ella is a knight, Lily is a knave, Zoey is a knight, Charlotte is a knave, Harper is a knight, Isabella is a knight, and Liam is a knave.", "solution_text_format": "(1) Ella is a knight\n(2) Lily is a knave\n(3) Zoey is a knight\n(4) Charlotte is a knave\n(5) Harper is a knight\n(6) Isabella is a knight\n(7) 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 Ella is a knight. No contradiction is found in their claim that Charlotte is a knight or Zoey is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Harper is not a knight.", "Harper cannot be a knight, because this would contradict the claim of Charlotte that Harper is not a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Isabella is a knight or Ella is a knave.", "Isabella cannot be a knight, because this would contradict the false claim of Harper that Isabella is a knight or Ella is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Charlotte is a knight if and only if Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that If Harper is a knave then Harper is a knight.", "Zoey cannot be a knave, because this would contradict the false claim of Isabella that Charlotte is a knight if and only if Zoey is a knave.", "We have exhausted all possibilities for Zoey, Isabella, and Harper, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Harper is not a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Isabella is a knight or Ella is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Charlotte is a knight if and only if Zoey is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that If Harper is a knave then Harper is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Harper is a knave if and only if Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Lily is a knave if and only if Liam is a knight.", "Liam cannot be a knave, because this would contradict the claim of Lily that Harper is a knave if and only if Liam is a knave.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Harper is a knave if and only if Liam is a knave.", "Liam cannot be a knight, because this would contradict the false claim of Lily that Harper is a knave if and only if Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Lily is a knave if and only if Liam is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('telling-truth', 2)), ('<=>', ('lying', 4), ('lying', 6)), ('->', ('lying', 4), ('telling-truth', 4)), ('not', ('telling-truth', 4)), ('or', ('telling-truth', 5), ('lying', 0)), ('<=>', ('telling-truth', 3), ('lying', 2)), ('<=>', ('lying', 1), ('telling-truth', 6)))", "index": 18}
-{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Amelia, Avery, James, Luke, Aurora, Matthew, and Jack. In Amelia's words: \"Luke is a knave\". Avery stated, \"Amelia is a knight or Jack is a knight\". James commented, \"Avery is not a knight\". In Luke's words: \"Avery is a knight or Jack is a knave\". Aurora said, \"If Amelia is a knave then Luke is a knight.\" Matthew commented, \"If Avery is a knave then Amelia is a knave\". Jack told you that Matthew is a knight. So who is a knight and who is a knave?", "names": ["Amelia", "Avery", "James", "Luke", "Aurora", "Matthew", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true, true], "solution_text": "Amelia is a knave, Avery is a knight, James is a knave, Luke is a knight, Aurora is a knight, Matthew is a knight, and Jack is a knight.", "solution_text_format": "(1) Amelia is a knave\n(2) Avery is a knight\n(3) James is a knave\n(4) Luke is a knight\n(5) Aurora is a knight\n(6) Matthew is a knight\n(7) 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 Amelia 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 Amelia that Luke is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Avery is a knight or Jack is a knave.", "Avery cannot be a knight, because this would contradict the false claim of Luke that Avery is a knight or Jack is a knave.", "Avery cannot be a knave, because this would contradict the false claim of their own that Amelia is a knight or Jack is a knight.", "We have exhausted all possibilities for Avery and Luke, so let us go back and reconsider Amelia.", "Assume Amelia 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 Avery is a knight or Jack is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Amelia is a knight or Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that If Avery is a knave then Amelia is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Avery is not a knight.", "Assume James is a knave. No contradiction is found in their false claim that Avery is not a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that If Amelia is a knave then Luke is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('or', ('telling-truth', 0), ('telling-truth', 6)), ('not', ('telling-truth', 1)), ('or', ('telling-truth', 1), ('lying', 6)), ('->', ('lying', 0), ('telling-truth', 3)), ('->', ('lying', 1), ('lying', 0)), ('telling-truth', 5))", "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 7 inhabitants: Luke, Lily, David, Elizabeth, Charlotte, Michael, and Victoria. Luke told you that David is a knight if and only if Victoria is a knave. Lily asserted: \"Charlotte is a knave and David is a knave\". David said that Victoria is a knave and Michael is a knight. Elizabeth was heard saying, \"Luke is a knight and Charlotte is a knave\". Charlotte said, \"Victoria is a knave.\" Michael commented, \"Luke is not a knave\". Victoria said that Charlotte is a knave if and only if David is a knight. So who is a knight and who is a knave?", "names": ["Luke", "Lily", "David", "Elizabeth", "Charlotte", "Michael", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true, false], "solution_text": "Luke is a knight, Lily is a knave, David is a knight, Elizabeth is a knave, Charlotte is a knight, Michael is a knight, and Victoria is a knave.", "solution_text_format": "(1) Luke is a knight\n(2) Lily is a knave\n(3) David is a knight\n(4) Elizabeth is a knave\n(5) Charlotte is a knight\n(6) Michael is a knight\n(7) 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 Luke is a knight. No contradiction is found in their claim that David is a knight if and only if Victoria is a knave.", "Assume David is a knight. No contradiction is found in their claim that Victoria is a knave and Michael is a knight.", "Victoria cannot be a knight, because this would contradict the claim of Luke that David is a knight if and only if Victoria is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Charlotte is a knave if and only if David is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Victoria is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Luke is not a knave.", "Lily cannot be a knight, because this would contradict the claim of their own that Charlotte is a knave and David is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Charlotte is a knave and David is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Luke is a knight and Charlotte is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Luke is a knight and Charlotte is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('lying', 6)), ('and', ('lying', 4), ('lying', 2)), ('and', ('lying', 6), ('telling-truth', 5)), ('and', ('telling-truth', 0), ('lying', 4)), ('lying', 6), ('not', ('lying', 0)), ('<=>', ('lying', 4), ('telling-truth', 2)))", "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 7 inhabitants: Olivia, Penelope, Mason, Ella, Emily, Avery, and Elizabeth. \"Ella is a knave\" - Olivia. As Penelope put it, \"If Mason is a knave then Avery is a knave\". In Mason's words: \"If Ella is a knave then Penelope is a knight\". \"Ella is a knight or Emily is a knight,\" Ella mentioned. \"Mason is a knight or Olivia is a knave,\" Emily mentioned. Avery said, \"Elizabeth is a knight.\" Elizabeth said that Emily is a knight and Emily is a knave. So who is a knight and who is a knave?", "names": ["Olivia", "Penelope", "Mason", "Ella", "Emily", "Avery", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false, false], "solution_text": "Olivia is a knave, Penelope is a knight, Mason is a knight, Ella is a knight, Emily is a knight, Avery is a knave, and Elizabeth is a knave.", "solution_text_format": "(1) Olivia is a knave\n(2) Penelope is a knight\n(3) Mason is a knight\n(4) Ella is a knight\n(5) Emily is a knight\n(6) Avery is a knave\n(7) Elizabeth is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of Olivia that Ella is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Ella is a knight or Emily is a knight.", "Emily cannot be a knight, because this would contradict the false claim of Ella that Ella is a knight or Emily is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Mason is a knight or Olivia is a knave.", "Mason cannot be a knight, because this would contradict the false claim of Emily that Mason is a knight or Olivia is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that If Ella is a knave then Penelope is a knight.", "Penelope cannot be a knight, because this would contradict the false claim of Mason that If Ella is a knave then Penelope is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that If Mason is a knave then Avery is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Emily is a knight and Emily is a knave.", "Elizabeth cannot be a knave, because this would contradict the claim of Avery that Elizabeth is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Avery.", "Avery cannot be a knave, because this would contradict the false claim of Penelope that If Mason is a knave then Avery is a knave.", "We have exhausted all possibilities for Avery, Penelope, Mason, Emily, and Ella, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Ella is a knight or Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Mason is a knight or Olivia is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Ella is a knave then Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that If Mason is a knave then Avery is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Emily is a knight and Emily is a knave.", "Elizabeth cannot be a knave, because this would contradict the claim of Avery that Elizabeth is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the false claim of Avery that Elizabeth is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Emily is a knight and Emily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('->', ('lying', 2), ('lying', 5)), ('->', ('lying', 3), ('telling-truth', 1)), ('or', ('telling-truth', 3), ('telling-truth', 4)), ('or', ('telling-truth', 2), ('lying', 0)), ('telling-truth', 6), ('and', ('telling-truth', 4), ('lying', 4)))", "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 7 inhabitants: Amelia, Aurora, Abigail, Daniel, Charlotte, Ethan, and Michael. Amelia said that Aurora is not a knave. Aurora said that Michael is a knave if and only if Charlotte is a knight. Abigail was heard saying, \"Charlotte is a knave and Daniel is a knight\". Daniel expressed that Aurora is not a knave. Charlotte noted, \"Ethan is not a knight\". Ethan expressed that Michael is not a knight. In a statement by Michael: \"Amelia is a knave\". So who is a knight and who is a knave?", "names": ["Amelia", "Aurora", "Abigail", "Daniel", "Charlotte", "Ethan", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, false, true], "solution_text": "Amelia is a knave, Aurora is a knave, Abigail is a knave, Daniel is a knave, Charlotte is a knight, Ethan is a knave, and Michael is a knight.", "solution_text_format": "(1) Amelia is a knave\n(2) Aurora is a knave\n(3) Abigail is a knave\n(4) Daniel is a knave\n(5) Charlotte is a knight\n(6) Ethan is a knave\n(7) Michael is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Amelia is a knight. No contradiction is found in their claim that Aurora is not a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Michael is a knave if and only if Charlotte is a knight.", "Michael cannot be a knight, because this would contradict the claim of their own that Amelia is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Amelia is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Ethan is not a knight.", "Ethan cannot be a knight, because this would contradict the claim of Charlotte that Ethan is not a knight.", "Ethan cannot be a knave, because this would contradict the false claim of their own that Michael is not a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the claim of Aurora that Michael is a knave if and only if Charlotte is a knight.", "We have exhausted all possibilities for Charlotte and Michael, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the claim of Amelia that Aurora is not a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Amelia.", "Assume Amelia 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 Amelia that Aurora is not a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Michael is a knave if and only if Charlotte is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Amelia is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Ethan is not a knight.", "Ethan cannot be a knight, because this would contradict the claim of Charlotte that Ethan is not a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Michael is not a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Charlotte is a knave and Daniel is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Charlotte is a knave and Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that Aurora is not a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Aurora is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('<=>', ('lying', 6), ('telling-truth', 4)), ('and', ('lying', 4), ('telling-truth', 3)), ('not', ('lying', 1)), ('not', ('telling-truth', 5)), ('not', ('telling-truth', 6)), ('lying', 0))", "index": 22}
-{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Ava, Liam, Abigail, William, Amelia, Olivia, and Zoey. \"William is not a knave,\" Ava claimed. As Liam put it, \"William is a knave if and only if Ava is a knight\". Abigail told you that Zoey is a knave if and only if Zoey is a knight. William remarked, \"Abigail is not a knave\". In a statement by Amelia: \"Abigail is a knave if and only if Liam is a knight\". Olivia said, \"Liam is a knave if and only if Abigail is a knave.\" In a statement by Zoey: \"Zoey is a knight and Liam is a knight\". So who is a knight and who is a knave?", "names": ["Ava", "Liam", "Abigail", "William", "Amelia", "Olivia", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, true, false], "solution_text": "Ava is a knave, Liam is a knave, Abigail is a knave, William is a knave, Amelia is a knave, Olivia is a knight, and Zoey is a knave.", "solution_text_format": "(1) Ava is a knave\n(2) Liam is a knave\n(3) Abigail is a knave\n(4) William is a knave\n(5) Amelia is a knave\n(6) Olivia is a knight\n(7) 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 Ava is a knight. No contradiction is found in their claim that William is not a knave.", "Assume William is a knight. No contradiction is found in their claim that Abigail is not a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Zoey is a knave if and only if Zoey is a knight.", "Abigail cannot be a knave, because this would contradict the claim of William that Abigail is not a knave.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the claim of Ava that William is not a knave.", "We have exhausted all possibilities for William, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that William is not a knave.", "William cannot be a knight, because this would contradict the false claim of Ava that William is not a knave.", "Assume William is a knave. No contradiction is found in their false claim that Abigail is not a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Zoey is a knave if and only if Zoey is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Zoey is a knave if and only if Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Zoey is a knight and Liam is a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that William is a knave if and only if Ava is a knight.", "Liam cannot be a knave, because this would contradict the claim of Zoey that Zoey is a knight and Liam is a knight.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Zoey is a knight and Liam is a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that William is a knave if and only if Ava is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that William is a knave if and only if Ava is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Abigail is a knave if and only if Liam is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Abigail is a knave if and only if Liam is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Liam is a knave if and only if Abigail is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 3)), ('<=>', ('lying', 3), ('telling-truth', 0)), ('<=>', ('lying', 6), ('telling-truth', 6)), ('not', ('lying', 2)), ('<=>', ('lying', 2), ('telling-truth', 1)), ('<=>', ('lying', 1), ('lying', 2)), ('and', ('telling-truth', 6), ('telling-truth', 1)))", "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 7 inhabitants: Amelia, Jack, Avery, Emma, James, Jacob, and Ethan. According to Amelia, \"If Jacob is a knave then Avery is a knave\". \"Avery is a knight or James is a knight\" - Jack. Avery said, \"Amelia is a knave.\" Emma said that Jacob is a knight or Jacob is a knave. James noted, \"Jack is not a knight\". According to Jacob, \"If James is a knave then Avery is a knave\". \"James is a knave or Emma is a knave,\" Ethan claimed. So who is a knight and who is a knave?", "names": ["Amelia", "Jack", "Avery", "Emma", "James", "Jacob", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false, true], "solution_text": "Amelia is a knave, Jack is a knight, Avery is a knight, Emma is a knight, James is a knave, Jacob is a knave, and Ethan is a knight.", "solution_text_format": "(1) Amelia is a knave\n(2) Jack is a knight\n(3) Avery is a knight\n(4) Emma is a knight\n(5) James is a knave\n(6) Jacob is a knave\n(7) 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 Amelia is a knight. No contradiction is found in their claim that If Jacob is a knave then Avery is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that If James is a knave then Avery is a knave.", "Assume James is a knight. No contradiction is found in their claim that Jack is not a knight.", "Jack cannot be a knight, because this would contradict the claim of James that Jack is not a knight.", "Jack cannot be a knave, because this would contradict the false claim of their own that Avery is a knight or James is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Jack is not a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Avery is a knight or James is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Amelia is a knave.", "Avery cannot be a knave, because this would contradict the claim of Jack that Avery is a knight or James is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the false claim of James that Jack is not a knight.", "We have exhausted all possibilities for Jack and James, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that If James is a knave then Avery is a knave.", "James cannot be a knight, because this would contradict the false claim of Jacob that If James is a knave then Avery is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Jack is not a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Avery is a knight or James is a knight.", "Avery cannot be a knight, because this would contradict the claim of Amelia that If Jacob is a knave then Avery is a knave.", "Avery cannot be a knave, because this would contradict the claim of Jack that Avery is a knight or James is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the false claim of James that Jack is not a knight.", "We have exhausted all possibilities for Jack, James, and Jacob, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that If Jacob is a knave then Avery is a knave.", "Jacob cannot be a knight, because this would contradict the false claim of Amelia that If Jacob is a knave then Avery is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that If James is a knave then Avery is a knave.", "James cannot be a knight, because this would contradict the false claim of Jacob that If James is a knave then Avery is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Jack is not a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Avery is a knight or James is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Amelia is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Jacob is a knight or Jacob is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that James is a knave or Emma is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('lying', 2)), ('or', ('telling-truth', 2), ('telling-truth', 4)), ('lying', 0), ('or', ('telling-truth', 5), ('lying', 5)), ('not', ('telling-truth', 1)), ('->', ('lying', 4), ('lying', 2)), ('or', ('lying', 4), ('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 7 inhabitants: Avery, Mason, Abigail, Evelyn, Ella, Emma, and Owen. In Avery's words: \"Mason is a knave\". Mason was heard saying, \"Abigail is a knave\". Abigail remarked, \"Emma is a knight or Mason is a knave\". As Evelyn put it, \"Abigail is a knight\". \"Mason is a knight or Evelyn is a knave,\" Ella claimed. In Emma's words: \"Ella is a knave or Owen is a knight\". In a statement by Owen: \"Evelyn is a knave or Mason is a knight\". So who is a knight and who is a knave?", "names": ["Avery", "Mason", "Abigail", "Evelyn", "Ella", "Emma", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true, false], "solution_text": "Avery is a knight, Mason is a knave, Abigail is a knight, Evelyn is a knight, Ella is a knave, Emma is a knight, and Owen is a knave.", "solution_text_format": "(1) Avery is a knight\n(2) Mason is a knave\n(3) Abigail is a knight\n(4) Evelyn is a knight\n(5) Ella is a knave\n(6) Emma is a knight\n(7) Owen is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of Avery that Mason is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Abigail is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Emma is a knight or Mason is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Ella is a knave or Owen is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Mason is a knight or Evelyn is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of Ella that Mason is a knight or Evelyn is a knave.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that Abigail is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Mason is a knight or Evelyn is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Abigail is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave or Mason is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Evelyn is a knave or Mason is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 1), ('lying', 2), ('or', ('telling-truth', 5), ('lying', 1)), ('telling-truth', 2), ('or', ('telling-truth', 1), ('lying', 3)), ('or', ('lying', 4), ('telling-truth', 6)), ('or', ('lying', 3), ('telling-truth', 1)))", "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 7 inhabitants: Abigail, Logan, Mason, Liam, Owen, Daniel, and Emma. \"Liam is a knave,\" Abigail claimed. Logan asserted: \"Emma is not a knight\". Mason asserted: \"Liam is not a knave\". \"Abigail is a knave if and only if Logan is a knave\" - Liam. Owen said, \"Emma is a knave.\" According to Daniel, \"Mason is a knave if and only if Owen is a knave\". Emma was heard saying, \"Abigail is a knave if and only if Owen is a knave\". So who is a knight and who is a knave?", "names": ["Abigail", "Logan", "Mason", "Liam", "Owen", "Daniel", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false, true], "solution_text": "Abigail is a knave, Logan is a knave, Mason is a knight, Liam is a knight, Owen is a knave, Daniel is a knave, and Emma is a knight.", "solution_text_format": "(1) Abigail is a knave\n(2) Logan is a knave\n(3) Mason is a knight\n(4) Liam is a knight\n(5) Owen is a knave\n(6) Daniel is a knave\n(7) 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 Abigail is a knight. No contradiction is found in their claim that Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of Abigail that Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Abigail is a knave if and only if Logan is a knave.", "Logan cannot be a knight, because this would contradict the false claim of Liam that Abigail is a knave if and only if Logan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Emma is not a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Abigail is a knave if and only if Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Emma is a knave.", "Owen cannot be a knave, because this would contradict the claim of Emma that Abigail is a knave if and only if Owen is a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Emma.", "Emma cannot be a knave, because this would contradict the false claim of Logan that Emma is not a knight.", "We have exhausted all possibilities for Emma, Logan, and Liam, so let us go back and reconsider Abigail.", "Assume Abigail 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 Abigail is a knave if and only if Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of Liam that Abigail is a knave if and only if Logan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Emma is not a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Abigail is a knave if and only if Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Emma is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Emma is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Liam is not a knave.", "Daniel cannot be a knight, because this would contradict the claim of their own that Mason is a knave if and only if Owen is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Mason is a knave if and only if Owen is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('not', ('telling-truth', 6)), ('not', ('lying', 3)), ('<=>', ('lying', 0), ('lying', 1)), ('lying', 6), ('<=>', ('lying', 2), ('lying', 4)), ('<=>', ('lying', 0), ('lying', 4)))", "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 7 inhabitants: Aiden, Aurora, Lucas, Aria, Riley, Chloe, and Amelia. Aiden stated, \"Aria is a knave or Chloe is a knight\". \"Aria is not a knight,\" Aurora mentioned. \"Aiden is a knave if and only if Aiden is a knight,\" Lucas mentioned. Aria said that Riley is not a knight. \"Lucas is a knave,\" Riley claimed. In a statement by Chloe: \"If Aiden is a knave then Aiden is a knight\". Amelia noted, \"If Aurora is a knight then Aiden is a knave\". So who is a knight and who is a knave?", "names": ["Aiden", "Aurora", "Lucas", "Aria", "Riley", "Chloe", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true, false], "solution_text": "Aiden is a knight, Aurora is a knight, Lucas is a knave, Aria is a knave, Riley is a knight, Chloe is a knight, and Amelia is a knave.", "solution_text_format": "(1) Aiden is a knight\n(2) Aurora is a knight\n(3) Lucas is a knave\n(4) Aria is a knave\n(5) Riley is a knight\n(6) Chloe is a knight\n(7) 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 Aiden is a knight. No contradiction is found in their claim that Aria is a knave or Chloe is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Riley is not a knight.", "Riley cannot be a knight, because this would contradict the claim of Aria that Riley is not a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Aiden is a knave if and only if Aiden is a knight.", "Lucas cannot be a knave, because this would contradict the false claim of Riley that Lucas is a knave.", "We have exhausted all possibilities for Lucas and Riley, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Riley is not a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Aiden is a knave if and only if Aiden is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if Aiden is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that If Aiden is a knave then Aiden is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Aria is not a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that If Aurora is a knight then Aiden is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that If Aurora is a knight then Aiden is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('telling-truth', 5)), ('not', ('telling-truth', 3)), ('<=>', ('lying', 0), ('telling-truth', 0)), ('not', ('telling-truth', 4)), ('lying', 2), ('->', ('lying', 0), ('telling-truth', 0)), ('->', ('telling-truth', 1), ('lying', 0)))", "index": 27}
-{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Aria, Aiden, Emily, Lily, Mason, Sophia, and Sebastian. Aria said that Lily is not a knave. In Aiden's words: \"Lily is a knight or Aria is a knight\". \"Lily is a knight and Aria is a knave,\" Emily declared. According to Lily, \"Sophia is a knight or Sebastian is a knight\". In Mason's words: \"Emily is a knight and Sophia is a knight\". \"Sebastian is not a knight,\" Sophia declared. As Sebastian put it, \"If Sophia is a knave then Aria is a knight\". So who is a knight and who is a knave?", "names": ["Aria", "Aiden", "Emily", "Lily", "Mason", "Sophia", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false, true], "solution_text": "Aria is a knight, Aiden is a knight, Emily is a knave, Lily is a knight, Mason is a knave, Sophia is a knave, and Sebastian is a knight.", "solution_text_format": "(1) Aria is a knight\n(2) Aiden is a knight\n(3) Emily is a knave\n(4) Lily is a knight\n(5) Mason is a knave\n(6) Sophia is a knave\n(7) 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 Aria is a knight. No contradiction is found in their claim that Lily is not a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Sophia is a knight or Sebastian is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Sebastian is not a knight.", "Sebastian cannot be a knight, because this would contradict the claim of Sophia that Sebastian is not a knight.", "Sebastian cannot be a knave, because this would contradict the false claim of their own that If Sophia is a knave then Aria is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Sebastian is not a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Sophia is a knave then Aria is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Lily is a knight or Aria is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Lily is a knight and Aria is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Lily is a knight and Aria is a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Emily is a knight and Sophia is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Emily is a knight and Sophia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 3)), ('or', ('telling-truth', 3), ('telling-truth', 0)), ('and', ('telling-truth', 3), ('lying', 0)), ('or', ('telling-truth', 5), ('telling-truth', 6)), ('and', ('telling-truth', 2), ('telling-truth', 5)), ('not', ('telling-truth', 6)), ('->', ('lying', 5), ('telling-truth', 0)))", "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 7 inhabitants: Emily, Scarlett, Sofia, Harper, Owen, Samuel, and Penelope. \"Sofia is a knave and Owen is a knave,\" Emily claimed. Scarlett asserted: \"Scarlett is a knight and Owen is a knave\". Sofia told you that Penelope is a knight and Scarlett is a knave. \"If Sofia is a knave then Owen is a knight,\" Harper claimed. \"Sofia is a knave or Emily is a knave,\" Owen claimed. \"Scarlett is a knave and Harper is a knave,\" Samuel declared. Penelope was heard saying, \"Samuel is not a knight\". So who is a knight and who is a knave?", "names": ["Emily", "Scarlett", "Sofia", "Harper", "Owen", "Samuel", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false, true], "solution_text": "Emily is a knave, Scarlett is a knave, Sofia is a knight, Harper is a knight, Owen is a knight, Samuel is a knave, and Penelope is a knight.", "solution_text_format": "(1) Emily is a knave\n(2) Scarlett is a knave\n(3) Sofia is a knight\n(4) Harper is a knight\n(5) Owen is a knight\n(6) Samuel is a knave\n(7) 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 Emily is a knight. No contradiction is found in their claim that Sofia is a knave and Owen is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Emily that Sofia is a knave and Owen is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Penelope is a knight and Scarlett is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Samuel is not a knight.", "Samuel cannot be a knight, because this would contradict the claim of Penelope that Samuel is not a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Scarlett is a knave and Harper is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Scarlett is a knight and Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of Emily that Sofia is a knave and Owen is a knave.", "Owen cannot be a knave, because this would contradict the false claim of their own that Sofia is a knave or Emily is a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the false claim of Sofia that Penelope is a knight and Scarlett is a knave.", "We have exhausted all possibilities for Scarlett and Samuel, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Samuel is not a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Scarlett is a knave and Harper is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Samuel that Scarlett is a knave and Harper is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Scarlett is a knight and Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of Emily that Sofia is a knave and Owen is a knave.", "Owen cannot be a knave, because this would contradict the false claim of their own that Sofia is a knave or Emily is a knave.", "We have exhausted all possibilities for Owen and Scarlett, so let us go back and reconsider Samuel.", "Samuel cannot be a knave, because this would contradict the false claim of Penelope that Samuel is not a knight.", "We have exhausted all possibilities for Samuel, Penelope, and Sofia, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Sofia is a knave and Owen is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Penelope is a knight and Scarlett is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Samuel is not a knight.", "Samuel cannot be a knight, because this would contradict the claim of Penelope that Samuel is not a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Scarlett is a knave and Harper is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Sofia that Penelope is a knight and Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Scarlett is a knight and Owen is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Sofia is a knave or Emily is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that If Sofia is a knave then Owen is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('lying', 4)), ('and', ('telling-truth', 1), ('lying', 4)), ('and', ('telling-truth', 6), ('lying', 1)), ('->', ('lying', 2), ('telling-truth', 4)), ('or', ('lying', 2), ('lying', 0)), ('and', ('lying', 1), ('lying', 3)), ('not', ('telling-truth', 5)))", "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 7 inhabitants: Luke, Isabella, Owen, Joseph, Aurora, Zoey, and Ava. As Luke put it, \"Owen is not a knight\". \"If Luke is a knave then Aurora is a knight,\" Isabella claimed. Owen noted, \"If Owen is a knight then Ava is a knave\". Joseph was heard saying, \"Ava is a knight if and only if Ava is a knave\". In a statement by Aurora: \"Luke is a knave or Owen is a knight\". According to Zoey, \"Joseph is not a knave\". Ava stated, \"Owen is a knight and Owen is a knave\". So who is a knight and who is a knave?", "names": ["Luke", "Isabella", "Owen", "Joseph", "Aurora", "Zoey", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, false, false], "solution_text": "Luke is a knave, Isabella is a knight, Owen is a knight, Joseph is a knave, Aurora is a knight, Zoey is a knave, and Ava is a knave.", "solution_text_format": "(1) Luke is a knave\n(2) Isabella is a knight\n(3) Owen is a knight\n(4) Joseph is a knave\n(5) Aurora is a knight\n(6) Zoey is a knave\n(7) 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 Luke is a knight. No contradiction is found in their claim that Owen is not a knight.", "Owen cannot be a knight, because this would contradict the claim of Luke that Owen is not a knight.", "Owen cannot be a knave, because this would contradict the false claim of their own that If Owen is a knight then Ava is a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Owen is not a knight.", "Assume Owen is a knight. No contradiction is found in their claim that If Owen is a knight then Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of Owen that If Owen is a knight then Ava is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Owen is a knight and Owen is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that If Luke is a knave then Aurora is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Luke is a knave or Owen is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Ava is a knight if and only if Ava is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Ava is a knight if and only if Ava is a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that Joseph is not a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Joseph is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('->', ('lying', 0), ('telling-truth', 4)), ('->', ('telling-truth', 2), ('lying', 6)), ('<=>', ('telling-truth', 6), ('lying', 6)), ('or', ('lying', 0), ('telling-truth', 2)), ('not', ('lying', 3)), ('and', ('telling-truth', 2), ('lying', 2)))", "index": 30}
-{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Isabella, Harper, Michael, Grace, Alexander, Olivia, and Oliver. Isabella said, \"Grace is a knight and Alexander is a knave.\" Harper asserted: \"If Alexander is a knave then Harper is a knight\". In Michael's words: \"Alexander is a knave if and only if Alexander is a knight\". Grace commented, \"If Harper is a knight then Michael is a knave\". In Alexander's words: \"Michael is a knave\". Olivia stated, \"Harper is a knight if and only if Isabella is a knight\". According to Oliver, \"Alexander is a knave or Olivia is a knave\". So who is a knight and who is a knave?", "names": ["Isabella", "Harper", "Michael", "Grace", "Alexander", "Olivia", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false, true], "solution_text": "Isabella is a knave, Harper is a knight, Michael is a knave, Grace is a knight, Alexander is a knight, Olivia is a knave, and Oliver is a knight.", "solution_text_format": "(1) Isabella is a knave\n(2) Harper is a knight\n(3) Michael is a knave\n(4) Grace is a knight\n(5) Alexander is a knight\n(6) Olivia is a knave\n(7) 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 Isabella is a knight. No contradiction is found in their claim that Grace is a knight and Alexander is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that If Harper is a knight then Michael is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that If Alexander is a knave then Harper is a knight.", "Alexander cannot be a knight, because this would contradict the claim of Isabella that Grace is a knight and Alexander is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Alexander is a knave if and only if Alexander is a knight.", "Michael cannot be a knave, because this would contradict the false claim of Alexander that Michael is a knave.", "We have exhausted all possibilities for Michael and Alexander, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that If Alexander is a knave then Harper is a knight.", "Alexander cannot be a knight, because this would contradict the claim of Isabella that Grace is a knight and Alexander is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Alexander is a knave if and only if Alexander is a knight.", "Michael cannot be a knave, because this would contradict the false claim of Alexander that Michael is a knave.", "We have exhausted all possibilities for Michael, Alexander, and Harper, so let us go back and reconsider Grace.", "Grace cannot be a knave, because this would contradict the claim of Isabella that Grace is a knight and Alexander is a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Grace is a knight and Alexander is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that If Harper is a knight then Michael is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that If Alexander is a knave then Harper is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Alexander is a knave if and only if Alexander is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Alexander is a knave if and only if Alexander is a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that Harper is a knight if and only if Isabella is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Harper is a knight if and only if Isabella is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Alexander is a knave or Olivia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('lying', 4)), ('->', ('lying', 4), ('telling-truth', 1)), ('<=>', ('lying', 4), ('telling-truth', 4)), ('->', ('telling-truth', 1), ('lying', 2)), ('lying', 2), ('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('or', ('lying', 4), ('lying', 5)))", "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 7 inhabitants: Benjamin, Henry, Jack, Aurora, Jackson, Victoria, and Scarlett. According to Benjamin, \"Scarlett is not a knight\". Henry remarked, \"If Jackson is a knave then Victoria is a knight\". \"Victoria is not a knight,\" Jack mentioned. In Aurora's words: \"Jack is a knight and Benjamin is a knight\". Jackson asserted: \"Jack is a knave\". In Victoria's words: \"Jack is a knave or Henry is a knave\". Scarlett asserted: \"Aurora is a knave and Henry is a knave\". So who is a knight and who is a knave?", "names": ["Benjamin", "Henry", "Jack", "Aurora", "Jackson", "Victoria", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true, false], "solution_text": "Benjamin is a knight, Henry is a knight, Jack is a knave, Aurora is a knave, Jackson is a knight, Victoria is a knight, and Scarlett is a knave.", "solution_text_format": "(1) Benjamin is a knight\n(2) Henry is a knight\n(3) Jack is a knave\n(4) Aurora is a knave\n(5) Jackson is a knight\n(6) Victoria is a knight\n(7) 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 Benjamin is a knight. No contradiction is found in their claim that Scarlett is not a knight.", "Scarlett cannot be a knight, because this would contradict the claim of Benjamin that Scarlett is not a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Aurora is a knave and Henry is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Jack is a knight and Benjamin is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Victoria is not a knight.", "Victoria cannot be a knight, because this would contradict the claim of Jack that Victoria is not a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Jack is a knave or Henry is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Jackson is a knave then Victoria is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Jack is a knave.", "Jackson cannot be a knave, because this would contradict the claim of Henry that If Jackson is a knave then Victoria is a knight.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the false claim of Victoria that Jack is a knave or Henry is a knave.", "We have exhausted all possibilities for Henry and Victoria, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the claim of Aurora that Jack is a knight and Benjamin is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Jack is a knight and Benjamin is a knight.", "Jack cannot be a knight, because this would contradict the false claim of Aurora that Jack is a knight and Benjamin is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Victoria is not a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Jack is a knave or Henry is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Jackson is a knave then Victoria is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Jack is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 6)), ('->', ('lying', 4), ('telling-truth', 5)), ('not', ('telling-truth', 5)), ('and', ('telling-truth', 2), ('telling-truth', 0)), ('lying', 2), ('or', ('lying', 2), ('lying', 1)), ('and', ('lying', 3), ('lying', 1)))", "index": 32}
-{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Olivia, Owen, Ethan, Logan, Evelyn, Scarlett, and Emma. Olivia expressed that Scarlett is a knave and Scarlett is a knight. Owen stated, \"Logan is a knight if and only if Logan is a knave\". \"If Evelyn is a knave then Evelyn is a knight,\" Ethan claimed. \"Evelyn is a knave and Evelyn is a knight,\" Logan declared. \"Owen is a knight,\" Evelyn mentioned. \"Ethan is a knight or Olivia is a knave\" - Scarlett. In a statement by Emma: \"Evelyn is a knave if and only if Scarlett is a knight\". So who is a knight and who is a knave?", "names": ["Olivia", "Owen", "Ethan", "Logan", "Evelyn", "Scarlett", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, true, true], "solution_text": "Olivia is a knave, Owen is a knave, Ethan is a knave, Logan is a knave, Evelyn is a knave, Scarlett is a knight, and Emma is a knight.", "solution_text_format": "(1) Olivia is a knave\n(2) Owen is a knave\n(3) Ethan is a knave\n(4) Logan is a knave\n(5) Evelyn is a knave\n(6) Scarlett is a knight\n(7) 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": ["Olivia cannot be a knight, because this would contradict the claim of their own that Scarlett is a knave and Scarlett is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Scarlett is a knave and Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Ethan is a knight or Olivia is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that If Evelyn is a knave then Evelyn is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Owen is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Logan is a knight if and only if Logan is a knave.", "Owen cannot be a knave, because this would contradict the claim of Evelyn that Owen is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the claim of Ethan that If Evelyn is a knave then Evelyn is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that If Evelyn is a knave then Evelyn is a knight.", "Evelyn cannot be a knight, because this would contradict the false claim of Ethan that If Evelyn is a knave then Evelyn is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Owen is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Logan is a knight if and only if Logan is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Logan is a knight if and only if Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave and Evelyn is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Evelyn is a knave and Evelyn is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Evelyn is a knave if and only if Scarlett is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 5), ('telling-truth', 5)), ('<=>', ('telling-truth', 3), ('lying', 3)), ('->', ('lying', 4), ('telling-truth', 4)), ('and', ('lying', 4), ('telling-truth', 4)), ('telling-truth', 1), ('or', ('telling-truth', 2), ('lying', 0)), ('<=>', ('lying', 4), ('telling-truth', 5)))", "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 7 inhabitants: Benjamin, Mason, Sebastian, Aiden, Daniel, Chloe, and Aria. Benjamin expressed that Aria is a knave or Aiden is a knave. Mason expressed that Sebastian is a knight if and only if Daniel is a knave. Sebastian was heard saying, \"Daniel is a knave and Daniel is a knight\". Aiden commented, \"Aria is a knight and Benjamin is a knave\". Daniel told you that Aria is a knight or Aria is a knave. \"If Aiden is a knight then Sebastian is a knave,\" Chloe mentioned. \"Aiden is a knave and Sebastian is a knight,\" Aria mentioned. So who is a knight and who is a knave?", "names": ["Benjamin", "Mason", "Sebastian", "Aiden", "Daniel", "Chloe", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true, false], "solution_text": "Benjamin is a knight, Mason is a knight, Sebastian is a knave, Aiden is a knave, Daniel is a knight, Chloe is a knight, and Aria is a knave.", "solution_text_format": "(1) Benjamin is a knight\n(2) Mason is a knight\n(3) Sebastian is a knave\n(4) Aiden is a knave\n(5) Daniel is a knight\n(6) Chloe is a knight\n(7) 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 Benjamin is a knight. No contradiction is found in their claim that Aria is a knave or Aiden is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Aiden is a knave and Sebastian is a knight.", "Aiden cannot be a knight, because this would contradict the claim of Benjamin that Aria is a knave or Aiden is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Aria is a knight and Benjamin is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Daniel is a knave and Daniel is a knight.", "Sebastian cannot be a knave, because this would contradict the claim of Aria that Aiden is a knave and Sebastian is a knight.", "We have exhausted all possibilities for Sebastian and Aiden, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Aiden is a knave and Sebastian is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Aria is a knight and Benjamin is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Aria is a knight and Benjamin is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Daniel is a knave and Daniel is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Daniel is a knave and Daniel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Aria is a knight or Aria is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Sebastian is a knight if and only if Daniel is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that If Aiden is a knight then Sebastian is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 6), ('lying', 3)), ('<=>', ('telling-truth', 2), ('lying', 4)), ('and', ('lying', 4), ('telling-truth', 4)), ('and', ('telling-truth', 6), ('lying', 0)), ('or', ('telling-truth', 6), ('lying', 6)), ('->', ('telling-truth', 3), ('lying', 2)), ('and', ('lying', 3), ('telling-truth', 2)))", "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 7 inhabitants: Lucas, Matthew, Charlotte, Joseph, James, Evelyn, and Michael. According to Lucas, \"If Evelyn is a knave then Charlotte is a knave\". \"Evelyn is a knight,\" Matthew declared. As Charlotte put it, \"Joseph is a knight and James is a knave\". Joseph said, \"Michael is a knight if and only if Lucas is a knave.\" \"Evelyn is not a knave,\" James declared. In Evelyn's words: \"Evelyn is a knight or Joseph is a knight\". Michael remarked, \"James is a knight\". So who is a knight and who is a knave?", "names": ["Lucas", "Matthew", "Charlotte", "Joseph", "James", "Evelyn", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true, true], "solution_text": "Lucas is a knight, Matthew is a knight, Charlotte is a knave, Joseph is a knave, James is a knight, Evelyn is a knight, and Michael is a knight.", "solution_text_format": "(1) Lucas is a knight\n(2) Matthew is a knight\n(3) Charlotte is a knave\n(4) Joseph is a knave\n(5) James is a knight\n(6) Evelyn is a knight\n(7) Michael is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that If Evelyn is a knave then Charlotte is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Evelyn is a knight or Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Michael is a knight if and only if Lucas is a knave.", "Michael cannot be a knight, because this would contradict the claim of Joseph that Michael is a knight if and only if Lucas is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that James is a knight.", "James cannot be a knight, because this would contradict the false claim of Michael that James is a knight.", "James cannot be a knave, because this would contradict the false claim of their own that Evelyn is not a knave.", "We have exhausted all possibilities for James and Michael, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Michael is a knight if and only if Lucas is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that James is a knight.", "Assume James is a knight. No contradiction is found in their claim that Evelyn is not a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Joseph is a knight and James is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Joseph is a knight and James is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Evelyn is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('lying', 2)), ('telling-truth', 5), ('and', ('telling-truth', 3), ('lying', 4)), ('<=>', ('telling-truth', 6), ('lying', 0)), ('not', ('lying', 5)), ('or', ('telling-truth', 5), ('telling-truth', 3)), ('telling-truth', 4))", "index": 35}
-{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Isabella, Noah, Samuel, Alexander, Ella, Joseph, and William. Isabella expressed that William is a knave. Noah said, \"If Isabella is a knave then Samuel is a knight.\" Samuel stated, \"Noah is a knave or Noah is a knight\". Alexander said that William is not a knight. Ella remarked, \"Noah is a knave\". Joseph commented, \"Noah is a knave or Isabella is a knight\". William told you that Ella is a knight or Noah is a knave. So who is a knight and who is a knave?", "names": ["Isabella", "Noah", "Samuel", "Alexander", "Ella", "Joseph", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true, false], "solution_text": "Isabella is a knight, Noah is a knight, Samuel is a knight, Alexander is a knight, Ella is a knave, Joseph is a knight, and William is a knave.", "solution_text_format": "(1) Isabella is a knight\n(2) Noah is a knight\n(3) Samuel is a knight\n(4) Alexander is a knight\n(5) Ella is a knave\n(6) Joseph is a knight\n(7) William is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that William is a knave.", "William cannot be a knight, because this would contradict the claim of Isabella that William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Ella is a knight or Noah is a knave.", "Ella cannot be a knight, because this would contradict the false claim of William that Ella is a knight or Noah is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Noah is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that If Isabella is a knave then Samuel is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Noah is a knave or Noah is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that William is not a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Noah is a knave or Isabella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 6), ('->', ('lying', 0), ('telling-truth', 2)), ('or', ('lying', 1), ('telling-truth', 1)), ('not', ('telling-truth', 6)), ('lying', 1), ('or', ('lying', 1), ('telling-truth', 0)), ('or', ('telling-truth', 4), ('lying', 1)))", "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 7 inhabitants: Matthew, Sofia, Ava, Jackson, Grace, Charlotte, and Harper. \"Grace is a knave,\" Matthew declared. As Sofia put it, \"Matthew is a knight if and only if Harper is a knight\". In Ava's words: \"Grace is a knight if and only if Sofia is a knight\". Jackson expressed that Ava is not a knight. Grace said that Jackson is a knave and Harper is a knight. Charlotte noted, \"Matthew is a knave if and only if Ava is a knave\". As Harper put it, \"Charlotte is a knave if and only if Ava is a knight\". So who is a knight and who is a knave?", "names": ["Matthew", "Sofia", "Ava", "Jackson", "Grace", "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, false, true, false], "solution_text": "Matthew is a knight, Sofia is a knave, Ava is a knight, Jackson is a knave, Grace is a knave, Charlotte is a knight, and Harper is a knave.", "solution_text_format": "(1) Matthew is a knight\n(2) Sofia is a knave\n(3) Ava is a knight\n(4) Jackson is a knave\n(5) Grace is a knave\n(6) Charlotte is a knight\n(7) 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 Matthew is a knight. No contradiction is found in their claim that Grace is a knave.", "Grace cannot be a knight, because this would contradict the claim of Matthew that Grace is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Jackson is a knave and Harper is a knight.", "Assume Jackson 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 Jackson that Ava is not a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Grace is a knight if and only if Sofia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Matthew is a knight if and only if Harper is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Charlotte is a knave if and only if Ava is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Matthew is a knave if and only if Ava is a knave.", "Charlotte cannot be a knave, because this would contradict the claim of Harper that Charlotte is a knave if and only if Ava is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the claim of Sofia that Matthew is a knight if and only if Harper is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Sofia.", "Sofia cannot be a knave, because this would contradict the false claim of Ava that Grace is a knight if and only if Sofia is a knight.", "We have exhausted all possibilities for Sofia and Ava, so let us go back and reconsider Jackson.", "Assume Jackson 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 Grace is a knight if and only if Sofia is a knight.", "Sofia cannot be a knight, because this would contradict the claim of Ava that Grace is a knight if and only if Sofia is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Matthew is a knight if and only if Harper is a knight.", "Harper cannot be a knight, because this would contradict the false claim of Sofia that Matthew is a knight if and only if Harper is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Charlotte is a knave if and only if Ava is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Matthew is a knave if and only if Ava is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('<=>', ('telling-truth', 0), ('telling-truth', 6)), ('<=>', ('telling-truth', 4), ('telling-truth', 1)), ('not', ('telling-truth', 2)), ('and', ('lying', 3), ('telling-truth', 6)), ('<=>', ('lying', 0), ('lying', 2)), ('<=>', ('lying', 5), ('telling-truth', 2)))", "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 7 inhabitants: Aurora, Lucas, Mia, Emily, Grace, Lily, and Daniel. Aurora told you that Grace is a knave if and only if Lily is a knave. Lucas told you that Aurora is not a knight. \"Emily is a knave if and only if Lucas is a knight,\" Mia mentioned. \"Lucas is a knight,\" Emily claimed. Grace said that If Aurora is a knight then Daniel is a knight. In a statement by Lily: \"Lucas is not a knight\". Daniel stated, \"Emily is not a knave\". So who is a knight and who is a knave?", "names": ["Aurora", "Lucas", "Mia", "Emily", "Grace", "Lily", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false, true], "solution_text": "Aurora is a knave, Lucas is a knight, Mia is a knave, Emily is a knight, Grace is a knight, Lily is a knave, and Daniel is a knight.", "solution_text_format": "(1) Aurora is a knave\n(2) Lucas is a knight\n(3) Mia is a knave\n(4) Emily is a knight\n(5) Grace is a knight\n(6) Lily is a knave\n(7) Daniel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that Grace is a knave if and only if Lily is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that If Aurora is a knight then Daniel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Emily is not a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Aurora is not a knight.", "Lucas cannot be a knave, because this would contradict the claim of Emily that Lucas is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the claim of Daniel that Emily is not a knave.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the claim of Grace that If Aurora is a knight then Daniel is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that If Aurora is a knight then Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of Grace that If Aurora is a knight then Daniel is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Emily is not a knave.", "Emily cannot be a knight, because this would contradict the false claim of Daniel that Emily is not a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Aurora is not a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Aurora is not a knight.", "Lily cannot be a knight, because this would contradict the claim of Aurora that Grace is a knave if and only if Lily is a knave.", "Lily cannot be a knave, because this would contradict the false claim of their own that Lucas is not a knight.", "We have exhausted all possibilities for Lily, Lucas, Emily, Daniel, and Grace, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Grace is a knave if and only if Lily is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that If Aurora is a knight then Daniel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Emily is not a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Aurora is not a knight.", "Lily cannot be a knight, because this would contradict the false claim of Aurora that Grace is a knave if and only if Lily is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Lucas is not a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that Emily is a knave if and only if Lucas is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Emily is a knave if and only if Lucas is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 4), ('lying', 5)), ('not', ('telling-truth', 0)), ('<=>', ('lying', 3), ('telling-truth', 1)), ('telling-truth', 1), ('->', ('telling-truth', 0), ('telling-truth', 6)), ('not', ('telling-truth', 1)), ('not', ('lying', 3)))", "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 7 inhabitants: Sophia, Sebastian, Mia, Charlotte, Grace, Emma, and Riley. In a statement by Sophia: \"Emma is not a knight\". Sebastian said, \"Riley is a knight if and only if Riley is a knave.\" Mia commented, \"Riley is not a knight\". According to Charlotte, \"If Charlotte is a knight then Emma is a knave\". Grace remarked, \"Sophia is a knave\". As Emma put it, \"Sebastian is a knight and Riley is a knight\". Riley expressed that If Grace is a knight then Sebastian is a knight. So who is a knight and who is a knave?", "names": ["Sophia", "Sebastian", "Mia", "Charlotte", "Grace", "Emma", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, false, true], "solution_text": "Sophia is a knight, Sebastian is a knave, Mia is a knave, Charlotte is a knight, Grace is a knave, Emma is a knave, and Riley is a knight.", "solution_text_format": "(1) Sophia is a knight\n(2) Sebastian is a knave\n(3) Mia is a knave\n(4) Charlotte is a knight\n(5) Grace is a knave\n(6) Emma is a knave\n(7) 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 Sophia 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 Sophia that Emma is not a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Sebastian is a knight and Riley is a knight.", "Sebastian 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 Sebastian is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Riley is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that If Grace is a knight then Sebastian is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Sophia is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Sophia is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Riley is not a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Riley is not a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Charlotte is a knight then Emma is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 5)), ('<=>', ('telling-truth', 6), ('lying', 6)), ('not', ('telling-truth', 6)), ('->', ('telling-truth', 3), ('lying', 5)), ('lying', 0), ('and', ('telling-truth', 1), ('telling-truth', 6)), ('->', ('telling-truth', 4), ('telling-truth', 1)))", "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 7 inhabitants: Daniel, Ethan, Sofia, Mia, Penelope, William, and Abigail. According to Daniel, \"Mia is a knave and Daniel is a knight\". Ethan commented, \"Mia is a knave if and only if William is a knave\". According to Sofia, \"If Mia is a knight then Ethan is a knave\". Mia expressed that Penelope is a knight. According to Penelope, \"Daniel is a knight if and only if Abigail is a knight\". William said that Penelope is not a knight. \"If Abigail is a knight then Penelope is a knave,\" Abigail claimed. So who is a knight and who is a knave?", "names": ["Daniel", "Ethan", "Sofia", "Mia", "Penelope", "William", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, true, true], "solution_text": "Daniel is a knave, Ethan is a knave, Sofia is a knight, Mia is a knave, Penelope is a knave, William is a knight, and Abigail is a knight.", "solution_text_format": "(1) Daniel is a knave\n(2) Ethan is a knave\n(3) Sofia is a knight\n(4) Mia is a knave\n(5) Penelope is a knave\n(6) William is a knight\n(7) Abigail is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that Mia is a knave and Daniel is a knight.", "Mia cannot be a knight, because this would contradict the claim of Daniel that Mia is a knave and Daniel is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Penelope is a knight.", "Penelope cannot be a knight, because this would contradict the false claim of Mia that Penelope is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Daniel is a knight if and only if Abigail is a knight.", "Abigail cannot be a knight, because this would contradict the false claim of Penelope that Daniel is a knight if and only if Abigail is a knight.", "Abigail cannot be a knave, because this would contradict the false claim of their own that If Abigail is a knight then Penelope is a knave.", "We have exhausted all possibilities for Abigail, Penelope, and Mia, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Mia is a knave and Daniel is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Daniel is a knight if and only if Abigail is a knight.", "Abigail cannot be a knight, because this would contradict the claim of Penelope that Daniel is a knight if and only if Abigail is a knight.", "Abigail cannot be a knave, because this would contradict the false claim of their own that If Abigail is a knight then Penelope is a knave.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the claim of Mia that Penelope is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Penelope is a knight.", "Penelope cannot be a knight, because this would contradict the false claim of Mia that Penelope is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Daniel is a knight if and only if Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If Abigail is a knight then Penelope is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Mia is a knave if and only if William is a knave.", "William cannot be a knight, because this would contradict the claim of Ethan that Mia is a knave if and only if William is a knave.", "William cannot be a knave, because this would contradict the false claim of their own that Penelope is not a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Mia is a knave if and only if William is a knave.", "Assume William is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that If Mia is a knight then Ethan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('telling-truth', 0)), ('<=>', ('lying', 3), ('lying', 5)), ('->', ('telling-truth', 3), ('lying', 1)), ('telling-truth', 4), ('<=>', ('telling-truth', 0), ('telling-truth', 6)), ('not', ('telling-truth', 4)), ('->', ('telling-truth', 6), ('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 7 inhabitants: Matthew, Noah, Avery, Harper, Lucas, Lily, and Penelope. Matthew told you that If Lily is a knight then Lucas is a knight. As Noah put it, \"If Avery is a knave then Matthew is a knave\". \"Penelope is a knave or Matthew is a knight,\" Avery claimed. In Harper's words: \"If Noah is a knight then Lucas is a knight\". Lucas said that Noah is a knave if and only if Penelope is a knight. Lily stated, \"Lucas is a knight and Avery is a knight\". Penelope expressed that If Noah is a knave then Harper is a knight. So who is a knight and who is a knave?", "names": ["Matthew", "Noah", "Avery", "Harper", "Lucas", "Lily", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false, true], "solution_text": "Matthew is a knight, Noah is a knight, Avery is a knight, Harper is a knave, Lucas is a knave, Lily is a knave, and Penelope is a knight.", "solution_text_format": "(1) Matthew is a knight\n(2) Noah is a knight\n(3) Avery is a knight\n(4) Harper is a knave\n(5) Lucas is a knave\n(6) Lily is a knave\n(7) 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 Matthew is a knight. No contradiction is found in their claim that If Lily is a knight then Lucas is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Lucas is a knight and Avery is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Noah is a knave if and only if Penelope is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that If Avery is a knave then Matthew is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Penelope is a knave or Matthew is a knight.", "Penelope cannot be a knight, because this would contradict the claim of Lucas that Noah 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 If Noah is a knave then Harper is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Avery.", "Avery cannot be a knave, because this would contradict the claim of Noah that If Avery is a knave then Matthew is a knave.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that If Avery is a knave then Matthew is a knave.", "Avery cannot be a knight, because this would contradict the false claim of Noah that If Avery is a knave then Matthew is a knave.", "Avery cannot be a knave, because this would contradict the false claim of their own that Penelope is a knave or Matthew is a knight.", "We have exhausted all possibilities for Avery and Noah, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the claim of Matthew that If Lily is a knight then Lucas is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Lucas is a knight and Avery is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Noah is a knave if and only if Penelope is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that If Avery is a knave then Matthew is a knave.", "Avery cannot be a knight, because this would contradict the false claim of Lily that Lucas is a knight and Avery is a knight.", "Avery cannot be a knave, because this would contradict the claim of Noah that If Avery is a knave then Matthew is a knave.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that If Avery is a knave then Matthew is a knave.", "Avery cannot be a knight, because this would contradict the false claim of Noah that If Avery is a knave then Matthew is a knave.", "Avery cannot be a knave, because this would contradict the false claim of their own that Penelope is a knave or Matthew is a knight.", "We have exhausted all possibilities for Avery and Noah, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Noah is a knave if and only if Penelope is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that If Avery is a knave then Matthew is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Penelope is a knave or Matthew is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that If Noah is a knave then Harper is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that If Noah is a knight then Lucas is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that If Noah is a knight then Lucas is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 5), ('telling-truth', 4)), ('->', ('lying', 2), ('lying', 0)), ('or', ('lying', 6), ('telling-truth', 0)), ('->', ('telling-truth', 1), ('telling-truth', 4)), ('<=>', ('lying', 1), ('telling-truth', 6)), ('and', ('telling-truth', 4), ('telling-truth', 2)), ('->', ('lying', 1), ('telling-truth', 3)))", "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 7 inhabitants: Oliver, Mason, Jackson, Emily, Ava, Jack, and Alexander. Oliver was heard saying, \"Ava is a knave\". Mason noted, \"Jackson is a knight and Mason is a knight\". As Jackson put it, \"Ava is a knight or Oliver is a knave\". Emily said that Jackson is a knave. Ava expressed that Alexander is not a knave. \"Jackson is a knight if and only if Mason is a knight,\" Jack mentioned. According to Alexander, \"If Mason is a knave then Jackson is a knave\". So who is a knight and who is a knave?", "names": ["Oliver", "Mason", "Jackson", "Emily", "Ava", "Jack", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true, true], "solution_text": "Oliver is a knave, Mason is a knight, Jackson is a knight, Emily is a knave, Ava is a knight, Jack is a knight, and Alexander is a knight.", "solution_text_format": "(1) Oliver is a knave\n(2) Mason is a knight\n(3) Jackson is a knight\n(4) Emily is a knave\n(5) Ava is a knight\n(6) Jack is a knight\n(7) 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 Oliver is a knight. No contradiction is found in their claim that Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of Oliver that Ava is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Alexander is not a knave.", "Alexander cannot be a knight, because this would contradict the false claim of Ava that Alexander is not a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that If Mason is a knave then Jackson is a knave.", "Mason cannot be a knight, because this would contradict the false claim of Alexander that If Mason is a knave then Jackson is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Jackson is a knight and Mason is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Ava is a knight or Oliver is a knave.", "Jackson cannot be a knave, because this would contradict the false claim of Alexander that If Mason is a knave then Jackson is a knave.", "We have exhausted all possibilities for Jackson, Mason, Alexander, and Ava, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Ava is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Alexander is not a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that If Mason is a knave then Jackson is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Jackson is a knight and Mason is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Ava is a knight or Oliver is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Jackson is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Jackson is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Mason is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('and', ('telling-truth', 2), ('telling-truth', 1)), ('or', ('telling-truth', 4), ('lying', 0)), ('lying', 2), ('not', ('lying', 6)), ('<=>', ('telling-truth', 2), ('telling-truth', 1)), ('->', ('lying', 1), ('lying', 2)))", "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 7 inhabitants: James, Charlotte, Evelyn, Jack, David, Owen, and Aria. James commented, \"James is a knight if and only if Owen is a knave\". Charlotte asserted: \"Jack is not a knave\". Evelyn expressed that David is a knight if and only if Jack is a knight. Jack noted, \"James is a knight and Evelyn is a knight\". David asserted: \"Jack is a knight\". Owen said, \"David is a knave if and only if Aria is a knave.\" \"If David is a knave then Owen is a knave,\" Aria declared. So who is a knight and who is a knave?", "names": ["James", "Charlotte", "Evelyn", "Jack", "David", "Owen", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, false, true], "solution_text": "James is a knave, Charlotte is a knave, Evelyn is a knight, Jack is a knave, David is a knave, Owen is a knave, and Aria is a knight.", "solution_text_format": "(1) James is a knave\n(2) Charlotte is a knave\n(3) Evelyn is a knight\n(4) Jack is a knave\n(5) David is a knave\n(6) Owen is a knave\n(7) 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 James is a knight. No contradiction is found in their claim that James is a knight if and only if Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of James that James is a knight if and only if Owen is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that David is a knave if and only if Aria is a knave.", "Assume David is a knight. No contradiction is found in their claim that Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that James is a knight and Evelyn is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that David is a knight if and only if Jack is a knight.", "Aria cannot be a knight, because this would contradict the false claim of Owen that David is a knave if and only if Aria is a knave.", "Aria cannot be a knave, because this would contradict the false claim of their own that If David is a knave then Owen is a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that David is a knight if and only if Jack is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the claim of David that Jack is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Jack is a knight.", "Jack cannot be a knight, because this would contradict the false claim of David that Jack is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that James is a knight and Evelyn is a knight.", "Evelyn cannot be a knight, because this would contradict the false claim of Jack that James is a knight and Evelyn is a knight.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that David is a knight if and only if Jack is a knight.", "We have exhausted all possibilities for Evelyn, Jack, David, and Owen, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that James is a knight if and only if Owen is a knave.", "Owen cannot be a knight, because this would contradict the false claim of James that James is a knight if and only if Owen is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that David is a knave if and only if Aria is a knave.", "Assume David is a knight. No contradiction is found in their claim that Jack is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that James is a knight and Evelyn is a knight.", "Jack cannot be a knave, because this would contradict the claim of David that Jack is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Jack is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that James is a knight and Evelyn is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that James is a knight and Evelyn is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that David is a knight if and only if Jack is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that If David is a knave then Owen is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Jack is not a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Jack is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 0), ('lying', 5)), ('not', ('lying', 3)), ('<=>', ('telling-truth', 4), ('telling-truth', 3)), ('and', ('telling-truth', 0), ('telling-truth', 2)), ('telling-truth', 3), ('<=>', ('lying', 4), ('lying', 6)), ('->', ('lying', 4), ('lying', 5)))", "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 7 inhabitants: Lily, Harper, Emma, Elizabeth, Ella, Sofia, and Charlotte. Lily asserted: \"Sofia is a knight\". \"Lily is a knave or Charlotte is a knave,\" Harper claimed. In a statement by Emma: \"Ella is a knight or Lily is a knight\". In a statement by Elizabeth: \"If Charlotte is a knight then Harper is a knave\". Ella asserted: \"Charlotte is a knight\". As Sofia put it, \"Harper is a knave or Emma is a knave\". Charlotte stated, \"If Lily is a knave then Ella is a knave\". So who is a knight and who is a knave?", "names": ["Lily", "Harper", "Emma", "Elizabeth", "Ella", "Sofia", "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, true, true], "solution_text": "Lily is a knight, Harper is a knave, Emma is a knight, Elizabeth is a knight, Ella is a knight, Sofia is a knight, and Charlotte is a knight.", "solution_text_format": "(1) Lily is a knight\n(2) Harper is a knave\n(3) Emma is a knight\n(4) Elizabeth is a knight\n(5) Ella is a knight\n(6) Sofia is a knight\n(7) Charlotte is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily 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 Harper is a knave or Emma is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Lily is a knave or Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Harper that Lily is a knave or Charlotte is a knave.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that If Lily is a knave then Ella is a knave.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Lily is a knave or Charlotte is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Lily is a knave then Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Charlotte is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Ella is a knight or Lily is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Charlotte is a knight then Harper is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 5), ('or', ('lying', 0), ('lying', 6)), ('or', ('telling-truth', 4), ('telling-truth', 0)), ('->', ('telling-truth', 6), ('lying', 1)), ('telling-truth', 6), ('or', ('lying', 1), ('lying', 2)), ('->', ('lying', 0), ('lying', 4)))", "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 7 inhabitants: Oliver, Amelia, Jackson, Matthew, Joseph, Ava, and Jack. Oliver remarked, \"Joseph is a knight or Oliver is a knight\". Amelia was heard saying, \"Jack is a knight or Jackson is a knight\". \"Jack is a knave or Oliver is a knight,\" Jackson claimed. Matthew was heard saying, \"Jack is not a knave\". \"Matthew is not a knight,\" Joseph declared. \"Jack is a knave,\" Ava claimed. \"Matthew is a knave if and only if Jack is a knight,\" Jack declared. So who is a knight and who is a knave?", "names": ["Oliver", "Amelia", "Jackson", "Matthew", "Joseph", "Ava", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true, false], "solution_text": "Oliver is a knight, Amelia is a knight, Jackson is a knight, Matthew is a knave, Joseph is a knight, Ava is a knight, and Jack is a knave.", "solution_text_format": "(1) Oliver is a knight\n(2) Amelia is a knight\n(3) Jackson is a knight\n(4) Matthew is a knave\n(5) Joseph is a knight\n(6) Ava is a knight\n(7) 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 Oliver is a knight. No contradiction is found in their claim that Joseph is a knight or Oliver is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Matthew is not a knight.", "Matthew cannot be a knight, because this would contradict the claim of Joseph that Matthew is not a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Jack is not a knave.", "Jack cannot be a knight, because this would contradict the false claim of Matthew that Jack is not a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Matthew is a knave if and only if Jack is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Jack is a knight or Jackson is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Jack is a knave or Oliver is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Jack is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('telling-truth', 0)), ('or', ('telling-truth', 6), ('telling-truth', 2)), ('or', ('lying', 6), ('telling-truth', 0)), ('not', ('lying', 6)), ('not', ('telling-truth', 3)), ('lying', 6), ('<=>', ('lying', 3), ('telling-truth', 6)))", "index": 45}
-{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Samuel, Sebastian, Aiden, Victoria, Joseph, Grace, and Aurora. \"Aiden is not a knave,\" Samuel claimed. Sebastian noted, \"Victoria is a knight if and only if Samuel is a knight\". Aiden remarked, \"If Victoria is a knight then Aurora is a knight\". Victoria noted, \"Aiden is a knight if and only if Grace is a knave\". Joseph noted, \"If Samuel is a knight then Samuel is a knave\". \"Samuel is not a knave,\" Grace mentioned. Aurora expressed that Grace is a knave if and only if Sebastian is a knave. So who is a knight and who is a knave?", "names": ["Samuel", "Sebastian", "Aiden", "Victoria", "Joseph", "Grace", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true, false], "solution_text": "Samuel is a knight, Sebastian is a knave, Aiden is a knight, Victoria is a knave, Joseph is a knave, Grace is a knight, and Aurora is a knave.", "solution_text_format": "(1) Samuel is a knight\n(2) Sebastian is a knave\n(3) Aiden is a knight\n(4) Victoria is a knave\n(5) Joseph is a knave\n(6) Grace is a knight\n(7) 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 Samuel is a knight. No contradiction is found in their claim that Aiden is not a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Victoria is a knight then Aurora is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Aiden is a knight if and only if Grace is a knave.", "Grace cannot be a knight, because this would contradict the claim of Victoria that Aiden is a knight if and only if Grace is a knave.", "Grace cannot be a knave, because this would contradict the false claim of their own that Samuel is not a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Aiden is a knight if and only if Grace is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Samuel is not a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Grace is a knave if and only if Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Victoria is a knight if and only if Samuel is a knight.", "Sebastian cannot be a knave, because this would contradict the claim of Aurora that Grace is a knave if and only if Sebastian is a knave.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Grace is a knave if and only if Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Victoria is a knight if and only if Samuel is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Victoria is a knight if and only if Samuel is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that If Samuel is a knight then Samuel is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that If Samuel is a knight then Samuel is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('<=>', ('telling-truth', 3), ('telling-truth', 0)), ('->', ('telling-truth', 3), ('telling-truth', 6)), ('<=>', ('telling-truth', 2), ('lying', 5)), ('->', ('telling-truth', 0), ('lying', 0)), ('not', ('lying', 0)), ('<=>', ('lying', 5), ('lying', 1)))", "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 7 inhabitants: Noah, Alexander, Victoria, Charlotte, Chloe, Jack, and Joseph. \"Chloe is a knight and Charlotte is a knave,\" Noah claimed. Alexander said, \"Chloe is a knave.\" Victoria told you that Joseph is a knight and Jack is a knight. Charlotte commented, \"Joseph is a knave or Chloe is a knight\". Chloe noted, \"Joseph is not a knight\". Jack remarked, \"If Charlotte is a knight then Chloe is a knight\". As Joseph put it, \"If Joseph is a knight then Alexander is a knight\". So who is a knight and who is a knave?", "names": ["Noah", "Alexander", "Victoria", "Charlotte", "Chloe", "Jack", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true, true], "solution_text": "Noah is a knave, Alexander is a knight, Victoria is a knight, Charlotte is a knave, Chloe is a knave, Jack is a knight, and Joseph is a knight.", "solution_text_format": "(1) Noah is a knave\n(2) Alexander is a knight\n(3) Victoria is a knight\n(4) Charlotte is a knave\n(5) Chloe is a knave\n(6) Jack is a knight\n(7) Joseph is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Noah is a knight. No contradiction is found in their claim that Chloe is a knight and Charlotte is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Joseph is not a knight.", "Joseph cannot be a knight, because this would contradict the claim of Chloe that Joseph is not a knight.", "Joseph cannot be a knave, because this would contradict the false claim of their own that If Joseph is a knight then Alexander is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the claim of Noah that Chloe is a knight and Charlotte is a knave.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Chloe is a knight and Charlotte is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Joseph is not a knight.", "Joseph cannot be a knight, because this would contradict the claim of Chloe that Joseph is not a knight.", "Joseph cannot be a knave, because this would contradict the false claim of their own that If Joseph is a knight then Alexander is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Joseph is not a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Joseph is a knight then Alexander is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Chloe is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Joseph is a knave or Chloe is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Joseph is a knave or Chloe is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Joseph is a knight and Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that If Charlotte is a knight then Chloe is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 4), ('lying', 3)), ('lying', 4), ('and', ('telling-truth', 6), ('telling-truth', 5)), ('or', ('lying', 6), ('telling-truth', 4)), ('not', ('telling-truth', 6)), ('->', ('telling-truth', 3), ('telling-truth', 4)), ('->', ('telling-truth', 6), ('telling-truth', 1)))", "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 7 inhabitants: Evelyn, David, Henry, Jack, Harper, Olivia, and Grace. \"Grace is a knight or Jack is a knave\" - Evelyn. David commented, \"Jack is a knave\". According to Henry, \"Jack is a knave and Olivia is a knave\". Jack commented, \"If Olivia is a knight then David is a knight\". Harper was heard saying, \"If Olivia is a knave then Henry is a knight\". In a statement by Olivia: \"Henry is a knight and David is a knight\". In Grace's words: \"Olivia is a knight\". So who is a knight and who is a knave?", "names": ["Evelyn", "David", "Henry", "Jack", "Harper", "Olivia", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, false, false], "solution_text": "Evelyn is a knave, David is a knave, Henry is a knave, Jack is a knight, Harper is a knave, Olivia is a knave, and Grace is a knave.", "solution_text_format": "(1) Evelyn is a knave\n(2) David is a knave\n(3) Henry is a knave\n(4) Jack is a knight\n(5) Harper is a knave\n(6) Olivia is a knave\n(7) 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 Evelyn is a knight. No contradiction is found in their claim that Grace is a knight or Jack is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Olivia is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Henry is a knight and David is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Jack is a knave and Olivia is a knave.", "Henry cannot be a knave, because this would contradict the claim of Olivia that Henry is a knight and David is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the claim of Grace that Olivia is a knight.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Olivia is a knight.", "Olivia cannot be a knight, because this would contradict the false claim of Grace that Olivia is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Henry is a knight and David is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Jack is a knave and Olivia is a knave.", "Jack cannot be a knight, because this would contradict the claim of Evelyn that Grace is a knight or Jack is a knave.", "Jack cannot be a knave, because this would contradict the false claim of their own that If Olivia is a knight then David is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Jack is a knave and Olivia is a knave.", "Jack cannot be a knight, because this would contradict the claim of Evelyn that Grace is a knight or Jack is a knave.", "Jack cannot be a knave, because this would contradict the false claim of Henry that Jack is a knave and Olivia is a knave.", "We have exhausted all possibilities for Jack, Henry, Olivia, and Grace, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Grace is a knight or Jack is a knave.", "Grace cannot be a knight, because this would contradict the false claim of Evelyn that Grace is a knight or Jack is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Olivia is a knight.", "Olivia cannot be a knight, because this would contradict the false claim of Grace that Olivia is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Henry is a knight and David is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Jack is a knave and Olivia is a knave.", "Jack cannot be a knight, because this would contradict the claim of Henry that Jack is a knave and Olivia is a knave.", "Jack cannot be a knave, because this would contradict the false claim of Evelyn that Grace is a knight or Jack is a knave.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Jack is a knave and Olivia is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that If Olivia is a knight then David is a knight.", "David cannot be a knight, because this would contradict the claim of their own that Jack is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Jack is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that If Olivia is a knave then Henry is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that If Olivia is a knave then Henry is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 6), ('lying', 3)), ('lying', 3), ('and', ('lying', 3), ('lying', 5)), ('->', ('telling-truth', 5), ('telling-truth', 1)), ('->', ('lying', 5), ('telling-truth', 2)), ('and', ('telling-truth', 2), ('telling-truth', 1)), ('telling-truth', 5))", "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 7 inhabitants: Liam, Isabella, Mia, Lucas, Aiden, Sofia, and Victoria. In Liam's words: \"Aiden is not a knight\". In a statement by Isabella: \"Sofia is a knave if and only if Liam is a knave\". Mia remarked, \"Liam is a knight\". According to Lucas, \"Lucas is a knight or Aiden is a knave\". Aiden said that Isabella is not a knave. Sofia remarked, \"Lucas is a knight\". \"Liam is a knave and Lucas is a knight,\" Victoria claimed. So who is a knight and who is a knave?", "names": ["Liam", "Isabella", "Mia", "Lucas", "Aiden", "Sofia", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, false, false], "solution_text": "Liam is a knave, Isabella is a knight, Mia is a knave, Lucas is a knave, Aiden is a knight, Sofia is a knave, and Victoria is a knave.", "solution_text_format": "(1) Liam is a knave\n(2) Isabella is a knight\n(3) Mia is a knave\n(4) Lucas is a knave\n(5) Aiden is a knight\n(6) Sofia is a knave\n(7) 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 Liam 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 Liam that Aiden is not a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Isabella is not a knave.", "Isabella cannot be a knight, because this would contradict the false claim of Aiden that Isabella is not a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Sofia is a knave if and only if Liam is a knave.", "Sofia cannot be a knight, because this would contradict the false claim of Isabella that Sofia is a knave if and only if Liam is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of Sofia that Lucas is a knight.", "Lucas cannot be a knave, because this would contradict the false claim of their own that Lucas is a knight or Aiden is a knave.", "We have exhausted all possibilities for Lucas, Sofia, Isabella, and Aiden, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Aiden is not a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Isabella is not a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Sofia is a knave if and only if Liam is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Isabella that Sofia is a knave if and only if Liam is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of Sofia that Lucas is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Lucas is a knight or Aiden is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Liam is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Liam is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Liam is a knave and Lucas is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Liam is a knave and Lucas is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 4)), ('<=>', ('lying', 5), ('lying', 0)), ('telling-truth', 0), ('or', ('telling-truth', 3), ('lying', 4)), ('not', ('lying', 1)), ('telling-truth', 3), ('and', ('lying', 0), ('telling-truth', 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 7 inhabitants: Benjamin, Zoey, William, Samuel, Alexander, Mia, and Sophia. Benjamin told you that Samuel is not a knight. \"Mia is not a knave,\" Zoey mentioned. In William's words: \"If Samuel is a knight then Zoey is a knave\". Samuel asserted: \"Mia is not a knight\". According to Alexander, \"Zoey is a knight if and only if Samuel is a knight\". Mia expressed that If Mia is a knight then Benjamin is a knight. \"Alexander is a knave,\" Sophia claimed. So who is a knight and who is a knave?", "names": ["Benjamin", "Zoey", "William", "Samuel", "Alexander", "Mia", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true, true], "solution_text": "Benjamin is a knight, Zoey is a knight, William is a knight, Samuel is a knave, Alexander is a knave, Mia is a knight, and Sophia is a knight.", "solution_text_format": "(1) Benjamin is a knight\n(2) Zoey is a knight\n(3) William is a knight\n(4) Samuel is a knave\n(5) Alexander is a knave\n(6) Mia is a knight\n(7) 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 Benjamin is a knight. No contradiction is found in their claim that Samuel is not a knight.", "Samuel cannot be a knight, because this would contradict the claim of Benjamin that Samuel is not a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Mia is not a knight.", "Assume Mia is a knight. No contradiction is found in their claim that If Mia is a knight then Benjamin is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Mia is not a knave.", "Assume William is a knight. No contradiction is found in their claim that If Samuel is a knight then Zoey is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that Zoey is a knight if and only if Samuel is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Zoey is a knight if and only if Samuel is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Alexander is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 3)), ('not', ('lying', 5)), ('->', ('telling-truth', 3), ('lying', 1)), ('not', ('telling-truth', 5)), ('<=>', ('telling-truth', 1), ('telling-truth', 3)), ('->', ('telling-truth', 5), ('telling-truth', 0)), ('lying', 4))", "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 7 inhabitants: Liam, Elizabeth, Emily, James, Ava, Joseph, and Noah. In Liam's words: \"Emily is a knave\". Elizabeth stated, \"Noah is a knight and Joseph is a knave\". Emily told you that Joseph is not a knight. James remarked, \"Liam is a knave\". Ava said, \"Elizabeth is not a knave.\" Joseph was heard saying, \"Noah is a knight if and only if James is a knight\". In Noah's words: \"Emily is a knave or Joseph is a knight\". So who is a knight and who is a knave?", "names": ["Liam", "Elizabeth", "Emily", "James", "Ava", "Joseph", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false, false], "solution_text": "Liam is a knave, Elizabeth is a knave, Emily is a knight, James is a knight, Ava is a knave, Joseph is a knave, and Noah is a knave.", "solution_text_format": "(1) Liam is a knave\n(2) Elizabeth is a knave\n(3) Emily is a knight\n(4) James is a knight\n(5) Ava is a knave\n(6) Joseph is a knave\n(7) 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 Liam 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 Liam that Emily is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Joseph is not a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Noah is a knight if and only if James is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Emily is a knave or Joseph is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Liam is a knave.", "James cannot be a knave, because this would contradict the claim of Joseph that Noah is a knight if and only if James is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the false claim of their own that Emily is a knave or Joseph is a knight.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the false claim of Emily that Joseph is not a knight.", "We have exhausted all possibilities for Joseph and Emily, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Joseph is not a knight.", "Joseph cannot be a knight, because this would contradict the claim of Emily that Joseph is not a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Noah is a knight if and only if James is a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that Emily is a knave or Joseph is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Emily is a knave or Joseph is a knight.", "Assume James is a knight. No contradiction is found in their claim that Liam is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Noah is a knight and Joseph is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Noah is a knight and Joseph is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Elizabeth is not a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Elizabeth is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('and', ('telling-truth', 6), ('lying', 5)), ('not', ('telling-truth', 5)), ('lying', 0), ('not', ('lying', 1)), ('<=>', ('telling-truth', 6), ('telling-truth', 3)), ('or', ('lying', 2), ('telling-truth', 5)))", "index": 51}
-{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Emily, Sophia, Avery, Olivia, Grace, Noah, and Michael. Emily told you that Avery is a knight and Grace is a knight. \"Emily is not a knave\" - Sophia. Avery told you that Sophia is a knight or Olivia is a knight. Olivia told you that Avery is a knave or Avery is a knight. As Grace put it, \"Olivia is a knave\". In Noah's words: \"Sophia is not a knave\". \"If Olivia is a knight then Emily is a knight,\" Michael mentioned. So who is a knight and who is a knave?", "names": ["Emily", "Sophia", "Avery", "Olivia", "Grace", "Noah", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false, false], "solution_text": "Emily is a knave, Sophia is a knave, Avery is a knight, Olivia is a knight, Grace is a knave, Noah is a knave, and Michael is a knave.", "solution_text_format": "(1) Emily is a knave\n(2) Sophia is a knave\n(3) Avery is a knight\n(4) Olivia is a knight\n(5) Grace is a knave\n(6) Noah is a knave\n(7) Michael is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Avery is a knight and Grace is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Sophia is a knight or Olivia is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Emily is not a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Avery is a knave or Avery is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Olivia is a knave.", "Grace cannot be a knave, because this would contradict the claim of Emily that Avery is a knight and Grace is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the false claim of their own that Avery is a knave or Avery is a knight.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the false claim of their own that Emily is not a knave.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Avery.", "Avery cannot be a knave, because this would contradict the claim of Emily that Avery is a knight and Grace is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Avery is a knight and Grace is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Sophia is a knight or Olivia is a knight.", "Sophia cannot be a knight, because this would contradict the claim of their own that Emily is not a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Emily is not a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Avery is a knave or Avery is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Emily that Avery is a knight and Grace is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Olivia is a knave.", "Noah cannot be a knight, because this would contradict the claim of their own that Sophia is not a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Sophia is not a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that If Olivia is a knight then Emily is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that If Olivia is a knight then Emily is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 2), ('telling-truth', 4)), ('not', ('lying', 0)), ('or', ('telling-truth', 1), ('telling-truth', 3)), ('or', ('lying', 2), ('telling-truth', 2)), ('lying', 3), ('not', ('lying', 1)), ('->', ('telling-truth', 3), ('telling-truth', 0)))", "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 7 inhabitants: Aiden, Daniel, Luke, Liam, Avery, Grace, and Isabella. In a statement by Aiden: \"Daniel is a knight\". Daniel said, \"Avery is a knave or Grace is a knave.\" According to Luke, \"Liam is a knight and Avery is a knave\". As Liam put it, \"Grace is a knight\". Avery asserted: \"If Liam is a knave then Isabella is a knave\". Grace commented, \"If Avery is a knight then Daniel is a knave\". According to Isabella, \"Liam is not a knight\". So who is a knight and who is a knave?", "names": ["Aiden", "Daniel", "Luke", "Liam", "Avery", "Grace", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true, false], "solution_text": "Aiden is a knave, Daniel is a knave, Luke is a knave, Liam is a knight, Avery is a knight, Grace is a knight, and Isabella is a knave.", "solution_text_format": "(1) Aiden is a knave\n(2) Daniel is a knave\n(3) Luke is a knave\n(4) Liam is a knight\n(5) Avery is a knight\n(6) Grace is a knight\n(7) Isabella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Daniel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Avery is a knave or Grace is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that If Liam is a knave then Isabella is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Grace is a knight.", "Grace cannot be a knight, because this would contradict the claim of Daniel that Avery is a knave or Grace is a knave.", "Grace cannot be a knave, because this would contradict the claim of Liam that Grace is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Grace is a knight.", "Grace cannot be a knight, because this would contradict the claim of Daniel that Avery is a knave or Grace is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that If Avery is a knight then Daniel is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Avery that If Liam is a knave then Isabella is a knave.", "Isabella cannot be a knave, because this would contradict the false claim of their own that Liam is not a knight.", "We have exhausted all possibilities for Isabella, Grace, and Liam, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that If Liam is a knave then Isabella is a knave.", "Liam cannot be a knight, because this would contradict the false claim of Avery that If Liam is a knave then Isabella is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Grace is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Liam that Grace is a knight.", "Grace cannot be a knave, because this would contradict the false claim of their own that If Avery is a knight then Daniel is a knave.", "We have exhausted all possibilities for Grace, Liam, and Avery, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the claim of Aiden that Daniel is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of Aiden that Daniel is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Avery is a knave or Grace is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that If Liam is a knave then Isabella is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that If Avery is a knight then Daniel is a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that Liam is not a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Liam is not a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Liam is a knight and Avery is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Liam is a knight and Avery is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('or', ('lying', 4), ('lying', 5)), ('and', ('telling-truth', 3), ('lying', 4)), ('telling-truth', 5), ('->', ('lying', 3), ('lying', 6)), ('->', ('telling-truth', 4), ('lying', 1)), ('not', ('telling-truth', 3)))", "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 7 inhabitants: Logan, Zoey, Harper, Matthew, Daniel, Liam, and Ethan. Logan remarked, \"Liam is a knight\". Zoey expressed that Ethan is a knave. Harper expressed that Zoey is a knave or Ethan is a knave. Matthew noted, \"Zoey is a knave if and only if Liam is a knight\". Daniel noted, \"Logan is a knight or Logan is a knave\". Liam said, \"Liam is a knight if and only if Matthew is a knave.\" Ethan told you that If Logan is a knave then Zoey is a knave. So who is a knight and who is a knave?", "names": ["Logan", "Zoey", "Harper", "Matthew", "Daniel", "Liam", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, false, true], "solution_text": "Logan is a knave, Zoey is a knave, Harper is a knight, Matthew is a knave, Daniel is a knight, Liam is a knave, and Ethan is a knight.", "solution_text_format": "(1) Logan is a knave\n(2) Zoey is a knave\n(3) Harper is a knight\n(4) Matthew is a knave\n(5) Daniel is a knight\n(6) Liam is a knave\n(7) 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 Logan 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 Liam is a knight if and only if Matthew is a knave.", "Matthew cannot be a knight, because this would contradict the claim of Liam that Liam is a knight if and only if Matthew is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Zoey is a knave if and only if Liam is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Ethan is a knave.", "Ethan cannot be a knight, because this would contradict the claim of Zoey that Ethan is a knave.", "Ethan cannot be a knave, because this would contradict the false claim of their own that If Logan is a knave then Zoey is a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Zoey.", "Zoey cannot be a knave, because this would contradict the false claim of Matthew that Zoey is a knave if and only if Liam is a knight.", "We have exhausted all possibilities for Zoey and Matthew, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the claim of Logan that Liam is a knight.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Liam is a knight.", "Liam cannot be a knight, because this would contradict the false claim of Logan that Liam is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Liam is a knight if and only if Matthew is a knave.", "Matthew cannot be a knight, because this would contradict the false claim of Liam that Liam is a knight if and only if Matthew is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Zoey is a knave if and only if Liam is a knight.", "Zoey cannot be a knight, because this would contradict the false claim of Matthew that Zoey is a knave if and only if Liam is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Ethan is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that If Logan is a knave then Zoey is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Zoey is a knave or Ethan is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Logan is a knight or Logan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 5), ('lying', 6), ('or', ('lying', 1), ('lying', 6)), ('<=>', ('lying', 1), ('telling-truth', 5)), ('or', ('telling-truth', 0), ('lying', 0)), ('<=>', ('telling-truth', 5), ('lying', 3)), ('->', ('lying', 0), ('lying', 1)))", "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 7 inhabitants: Chloe, Sophia, Samuel, Olivia, Alexander, Liam, and Aria. Chloe commented, \"If Aria is a knave then Samuel is a knave\". In Sophia's words: \"Olivia is a knight\". Samuel told you that Sophia is not a knave. \"Aria is a knave if and only if Sophia is a knave\" - Olivia. Alexander expressed that Sophia is not a knight. \"Chloe is a knave,\" Liam declared. Aria told you that Sophia is not a knave. So who is a knight and who is a knave?", "names": ["Chloe", "Sophia", "Samuel", "Olivia", "Alexander", "Liam", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false, true], "solution_text": "Chloe is a knight, Sophia is a knight, Samuel is a knight, Olivia is a knight, Alexander is a knave, Liam is a knave, and Aria is a knight.", "solution_text_format": "(1) Chloe is a knight\n(2) Sophia is a knight\n(3) Samuel is a knight\n(4) Olivia is a knight\n(5) Alexander is a knave\n(6) Liam is a knave\n(7) 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 Chloe is a knight. No contradiction is found in their claim that If Aria is a knave then Samuel is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Sophia is not a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Olivia is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Aria is a knave if and only if Sophia is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Sophia is not a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that Sophia is not a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Sophia is not a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that Chloe is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Chloe is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 6), ('lying', 2)), ('telling-truth', 3), ('not', ('lying', 1)), ('<=>', ('lying', 6), ('lying', 1)), ('not', ('telling-truth', 1)), ('lying', 0), ('not', ('lying', 1)))", "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 7 inhabitants: Jackson, Sofia, Avery, Victoria, David, Isabella, and Emily. \"Emily is a knave,\" Jackson claimed. Sofia told you that David is not a knight. Avery was heard saying, \"Emily is a knave or Emily is a knight\". Victoria expressed that Avery is a knight. David told you that Avery is a knight. Isabella told you that Emily is a knave or Jackson is a knave. Emily stated, \"David is not a knave\". So who is a knight and who is a knave?", "names": ["Jackson", "Sofia", "Avery", "Victoria", "David", "Isabella", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true, true], "solution_text": "Jackson is a knave, Sofia is a knave, Avery is a knight, Victoria is a knight, David is a knight, Isabella is a knight, and Emily is a knight.", "solution_text_format": "(1) Jackson is a knave\n(2) Sofia is a knave\n(3) Avery is a knight\n(4) Victoria is a knight\n(5) David is a knight\n(6) Isabella is a knight\n(7) 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 Jackson 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 Jackson that Emily is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that David is not a knave.", "David cannot be a knight, because this would contradict the false claim of Emily that David is not a knave.", "Assume David is a knave. No contradiction is found in their false claim that Avery is a knight.", "Avery cannot be a knight, because this would contradict the false claim of David that Avery is a knight.", "Avery cannot be a knave, because this would contradict the false claim of their own that Emily is a knave or Emily is a knight.", "We have exhausted all possibilities for Avery, David, and Emily, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that David is not a knave.", "Assume David is a knight. No contradiction is found in their claim that Avery is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Emily is a knave or Emily is a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that David is not a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that David is not a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Avery is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Emily is a knave or Jackson is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 6), ('not', ('telling-truth', 4)), ('or', ('lying', 6), ('telling-truth', 6)), ('telling-truth', 2), ('telling-truth', 2), ('or', ('lying', 6), ('lying', 0)), ('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 7 inhabitants: Victoria, James, Luke, Charlotte, Sebastian, Logan, and Sofia. \"Luke is a knight,\" Victoria claimed. James commented, \"Charlotte is a knight and Sebastian is a knight\". Luke was heard saying, \"James is a knight if and only if Luke is a knight\". Charlotte commented, \"If Sebastian is a knight then Victoria is a knight\". Sebastian noted, \"If Logan is a knight then Charlotte is a knight\". In a statement by Logan: \"Sebastian is a knave or Victoria is a knave\". Sofia was heard saying, \"Luke is a knave if and only if James is a knight\". So who is a knight and who is a knave?", "names": ["Victoria", "James", "Luke", "Charlotte", "Sebastian", "Logan", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false, false], "solution_text": "Victoria is a knight, James is a knight, Luke is a knight, Charlotte is a knight, Sebastian is a knight, Logan is a knave, and Sofia is a knave.", "solution_text_format": "(1) Victoria is a knight\n(2) James is a knight\n(3) Luke is a knight\n(4) Charlotte is a knight\n(5) Sebastian is a knight\n(6) Logan is a knave\n(7) 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 Victoria is a knight. No contradiction is found in their claim that Luke is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that James is a knight if and only if Luke is a knight.", "Assume James is a knight. No contradiction is found in their claim that Charlotte is a knight and Sebastian is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Sebastian is a knight then Victoria is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Logan is a knight then Charlotte is a knight.", "Logan cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave or Victoria is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Sebastian is a knave or Victoria is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Luke is a knave if and only if James is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Luke is a knave if and only if James is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('and', ('telling-truth', 3), ('telling-truth', 4)), ('<=>', ('telling-truth', 1), ('telling-truth', 2)), ('->', ('telling-truth', 4), ('telling-truth', 0)), ('->', ('telling-truth', 5), ('telling-truth', 3)), ('or', ('lying', 4), ('lying', 0)), ('<=>', ('lying', 2), ('telling-truth', 1)))", "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 7 inhabitants: Jack, Aiden, Isabella, Elizabeth, Avery, Penelope, and Olivia. \"If Olivia is a knight then Isabella is a knight,\" Jack claimed. \"If Jack is a knave then Olivia is a knave\" - Aiden. Isabella noted, \"Olivia is not a knight\". Elizabeth commented, \"Olivia is a knave or Elizabeth is a knight\". Avery expressed that Penelope is a knight and Olivia is a knight. Penelope remarked, \"Isabella is not a knight\". \"Penelope is a knight if and only if Elizabeth is a knave\" - Olivia. So who is a knight and who is a knave?", "names": ["Jack", "Aiden", "Isabella", "Elizabeth", "Avery", "Penelope", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, true, true], "solution_text": "Jack is a knave, Aiden is a knave, Isabella is a knave, Elizabeth is a knave, Avery is a knight, Penelope is a knight, and Olivia is a knight.", "solution_text_format": "(1) Jack is a knave\n(2) Aiden is a knave\n(3) Isabella is a knave\n(4) Elizabeth is a knave\n(5) Avery is a knight\n(6) Penelope is a knight\n(7) Olivia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that If Olivia is a knight then Isabella is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Penelope is a knight if and only if Elizabeth is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Isabella is not a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Olivia is not a knight.", "Isabella cannot be a knave, because this would contradict the claim of Jack that If Olivia is a knight then Isabella is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Isabella is not a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Olivia is not a knight.", "Isabella cannot be a knave, because this would contradict the claim of Jack that If Olivia is a knight then Isabella is a knight.", "We have exhausted all possibilities for Isabella and Penelope, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Penelope is a knight if and only if Elizabeth is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Isabella is not a knight.", "Isabella cannot be a knight, because this would contradict the claim of Penelope that Isabella is not a knight.", "Isabella cannot be a knave, because this would contradict the false claim of their own that Olivia is not a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Isabella is not a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Olivia is not a knight.", "Elizabeth cannot be a knight, because this would contradict the false claim of Olivia that Penelope is a knight if and only if Elizabeth is a knave.", "Elizabeth cannot be a knave, because this would contradict the false claim of their own that Olivia is a knave or Elizabeth is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the false claim of their own that Olivia is not a knight.", "We have exhausted all possibilities for Isabella, Penelope, and Olivia, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that If Olivia is a knight then Isabella is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Penelope is a knight if and only if Elizabeth is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Isabella is not a knight.", "Isabella cannot be a knight, because this would contradict the false claim of Jack that If Olivia is a knight then Isabella is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Olivia is not a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Olivia that Penelope is a knight if and only if Elizabeth is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Olivia is a knave or Elizabeth is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that If Jack is a knave then Olivia is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that If Jack is a knave then Olivia is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Penelope is a knight and Olivia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 6), ('telling-truth', 2)), ('->', ('lying', 0), ('lying', 6)), ('not', ('telling-truth', 6)), ('or', ('lying', 6), ('telling-truth', 3)), ('and', ('telling-truth', 5), ('telling-truth', 6)), ('not', ('telling-truth', 2)), ('<=>', ('telling-truth', 5), ('lying', 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 7 inhabitants: Mason, Mia, Lily, Riley, Henry, Aria, and Luke. Mason was heard saying, \"Riley is a knave if and only if Luke is a knave\". Mia asserted: \"Mason is a knight or Riley is a knight\". Lily commented, \"Mason is a knight if and only if Riley is a knave\". Riley asserted: \"Riley is a knight\". As Henry put it, \"Luke is a knave and Riley is a knave\". \"If Aria is a knight then Mia is a knave,\" Aria claimed. \"Riley is a knight if and only if Henry is a knight,\" Luke mentioned. So who is a knight and who is a knave?", "names": ["Mason", "Mia", "Lily", "Riley", "Henry", "Aria", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, true, true], "solution_text": "Mason is a knave, Mia is a knave, Lily is a knave, Riley is a knave, Henry is a knave, Aria is a knight, and Luke is a knight.", "solution_text_format": "(1) Mason is a knave\n(2) Mia is a knave\n(3) Lily is a knave\n(4) Riley is a knave\n(5) Henry is a knave\n(6) Aria is a knight\n(7) Luke is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Riley is a knave if and only if Luke is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Riley is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Riley is a knight if and only if Henry is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Luke is a knave and Riley is a knave.", "Henry cannot be a knave, because this would contradict the claim of Luke that Riley is a knight if and only if Henry is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the claim of Mason that Riley is a knave if and only if Luke is a knave.", "We have exhausted all possibilities for Luke, 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.", "Luke cannot be a knight, because this would contradict the claim of Mason that Riley is a knave if and only if Luke is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Henry is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Luke is a knave and Riley is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Mason is a knight or Riley is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Mason is a knight if and only if Riley is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that If Aria is a knight then Mia is a knave.", "Aria cannot be a knave, because this would contradict the false claim of their own that If Aria is a knight then Mia is a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the false claim of their own that Mason is a knight if and only if Riley is a knave.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the false claim of their own that Mason is a knight or Riley is a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the false claim of their own that Luke is a knave and Riley is a knave.", "We have exhausted all possibilities for Henry, Luke, and Riley, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Riley is a knave if and only if Luke is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Riley is a knight.", "Luke cannot be a knight, because this would contradict the false claim of Mason that Riley is a knave if and only if Luke is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Henry is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Luke is a knave and Riley is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Luke is a knave and Riley is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Mason is a knight or Riley is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Mason is a knight if and only if Riley is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that If Aria is a knight then Mia is a knave.", "Aria cannot be a knave, because this would contradict the false claim of their own that If Aria is a knight then Mia is a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the false claim of their own that Mason is a knight if and only if Riley is a knave.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the false claim of their own that Mason is a knight or Riley is a knight.", "We have exhausted all possibilities for Mia, Henry, and Luke, 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.", "Assume Luke is a knight. No contradiction is found in their claim that Riley is a knight if and only if Henry is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Luke is a knave and Riley is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Luke is a knave and Riley is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Mason is a knight or Riley is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Mason is a knight or Riley is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Mason is a knight if and only if Riley is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Mason is a knight if and only if Riley is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that If Aria is a knight then Mia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('lying', 6)), ('or', ('telling-truth', 0), ('telling-truth', 3)), ('<=>', ('telling-truth', 0), ('lying', 3)), ('telling-truth', 3), ('and', ('lying', 6), ('lying', 3)), ('->', ('telling-truth', 5), ('lying', 1)), ('<=>', ('telling-truth', 3), ('telling-truth', 4)))", "index": 59}
-{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Alexander, Avery, Mason, Amelia, Emma, Sebastian, and Charlotte. In a statement by Alexander: \"If Emma is a knave then Avery is a knight\". \"Sebastian is a knight or Sebastian is a knave\" - Avery. \"If Amelia is a knight then Avery is a knight,\" Mason declared. As Amelia put it, \"Alexander is a knave\". Emma told you that If Amelia is a knave then Avery is a knave. Sebastian remarked, \"If Charlotte is a knave then Amelia is a knave\". Charlotte was heard saying, \"Mason is not a knave\". So who is a knight and who is a knave?", "names": ["Alexander", "Avery", "Mason", "Amelia", "Emma", "Sebastian", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true, true], "solution_text": "Alexander is a knight, Avery is a knight, Mason is a knight, Amelia is a knave, Emma is a knave, Sebastian is a knight, and Charlotte is a knight.", "solution_text_format": "(1) Alexander is a knight\n(2) Avery is a knight\n(3) Mason is a knight\n(4) Amelia is a knave\n(5) Emma is a knave\n(6) Sebastian is a knight\n(7) Charlotte is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that If Emma is a knave then Avery is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If Amelia is a knave then Avery is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Alexander is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Alexander is a knave.", "Avery cannot be a knight, because this would contradict the claim of Emma that If Amelia is a knave then Avery is a knave.", "Avery cannot be a knave, because this would contradict the false claim of their own that Sebastian is a knight or Sebastian is a knave.", "We have exhausted all possibilities for Avery and Amelia, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that If Amelia is a knave then Avery is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Alexander is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Alexander is a knave.", "Assume Avery 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 Charlotte is a knave then Amelia is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Mason is not a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Amelia is a knight then Avery is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 4), ('telling-truth', 1)), ('or', ('telling-truth', 5), ('lying', 5)), ('->', ('telling-truth', 3), ('telling-truth', 1)), ('lying', 0), ('->', ('lying', 3), ('lying', 1)), ('->', ('lying', 6), ('lying', 3)), ('not', ('lying', 2)))", "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 7 inhabitants: Jack, Ethan, Penelope, Oliver, Emily, Jacob, and James. Jack expressed that Emily is a knave and Jacob is a knight. Ethan expressed that Oliver is a knight. Penelope asserted: \"Penelope is a knight if and only if Ethan is a knight\". Oliver told you that Ethan is a knight and James is a knave. In a statement by Emily: \"Oliver is a knave and Penelope is a knave\". \"Oliver is not a knight,\" Jacob claimed. James told you that Penelope is a knight if and only if Emily is a knight. So who is a knight and who is a knave?", "names": ["Jack", "Ethan", "Penelope", "Oliver", "Emily", "Jacob", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false, false], "solution_text": "Jack is a knave, Ethan is a knight, Penelope is a knight, Oliver is a knight, Emily is a knave, Jacob is a knave, and James is a knave.", "solution_text_format": "(1) Jack is a knave\n(2) Ethan is a knight\n(3) Penelope is a knight\n(4) Oliver is a knight\n(5) Emily is a knave\n(6) Jacob is a knave\n(7) 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 Emily is a knave and Jacob is a knight.", "Emily cannot be a knight, because this would contradict the claim of Jack that Emily is a knave and Jacob is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Oliver is a knave and Penelope is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Ethan is a knight and James is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Oliver is a knight.", "James cannot be a knight, because this would contradict the claim of Oliver that Ethan is a knight and James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Penelope is a knight if and only if Emily is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Penelope is a knight if and only if Ethan is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Oliver is not a knight.", "Jacob cannot be a knave, because this would contradict the claim of Jack that Emily is a knave and Jacob is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the false claim of James that Penelope is a knight if and only if Emily is a knight.", "We have exhausted all possibilities for Penelope and James, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the false claim of their own that Oliver is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Ethan is a knight and James is a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Oliver is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Oliver is a knight.", "Assume James is a knight. No contradiction is found in their claim that Penelope is a knight if and only if Emily is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Penelope is a knight if and only if Ethan is a knight.", "Penelope cannot be a knave, because this would contradict the false claim of their own that Penelope is a knight if and only if Ethan is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Penelope is a knight if and only if Emily is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Penelope is a knight if and only if Ethan is a knight.", "Penelope cannot be a knave, because this would contradict the false claim of their own that Penelope is a knight if and only if Ethan is a knight.", "We have exhausted all possibilities for Penelope, James, Ethan, Oliver, and Emily, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Emily is a knave and Jacob is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Oliver is a knave and Penelope is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Emily that Oliver is a knave and Penelope is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Ethan is a knight and James is a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Oliver is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Oliver is a knight.", "Assume James is a knight. No contradiction is found in their claim that Penelope is a knight if and only if Emily is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Penelope is a knight if and only if Ethan is a knight.", "Penelope cannot be a knave, because this would contradict the false claim of their own that Penelope is a knight if and only if Ethan is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Penelope is a knight if and only if Emily is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Penelope is a knight if and only if Ethan is a knight.", "Penelope cannot be a knave, because this would contradict the false claim of their own that Penelope is a knight if and only if Ethan is a knight.", "We have exhausted all possibilities for Penelope, James, Ethan, and Oliver, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Oliver is a knave and Penelope is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Ethan is a knight and James is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Oliver is a knight.", "James cannot be a knight, because this would contradict the claim of Oliver that Ethan is a knight and James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Penelope is a knight if and only if Emily is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Penelope is a knight if and only if Ethan is a knight.", "Jacob cannot be a knight, because this would contradict the false claim of Jack that Emily is a knave and Jacob is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Oliver is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('telling-truth', 5)), ('telling-truth', 3), ('<=>', ('telling-truth', 2), ('telling-truth', 1)), ('and', ('telling-truth', 1), ('lying', 6)), ('and', ('lying', 3), ('lying', 2)), ('not', ('telling-truth', 3)), ('<=>', ('telling-truth', 2), ('telling-truth', 4)))", "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 7 inhabitants: Lucas, Sofia, Zoey, Jackson, Mia, Ella, and Elizabeth. Lucas remarked, \"If Zoey is a knave then Lucas is a knight\". Sofia commented, \"If Mia is a knave then Elizabeth is a knight\". In Zoey's words: \"Lucas is a knight if and only if Elizabeth is a knight\". Jackson noted, \"Sofia is a knave and Mia is a knave\". In Mia's words: \"Elizabeth is a knight or Jackson is a knight\". Ella said that Lucas is a knave or Mia is a knight. \"Ella is a knight and Zoey is a knave\" - Elizabeth. So who is a knight and who is a knave?", "names": ["Lucas", "Sofia", "Zoey", "Jackson", "Mia", "Ella", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true, true], "solution_text": "Lucas is a knave, Sofia is a knight, Zoey is a knave, Jackson is a knave, Mia is a knight, Ella is a knight, and Elizabeth is a knight.", "solution_text_format": "(1) Lucas is a knave\n(2) Sofia is a knight\n(3) Zoey is a knave\n(4) Jackson is a knave\n(5) Mia is a knight\n(6) Ella is a knight\n(7) 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 Lucas is a knight. No contradiction is found in their claim that If Zoey is a knave then Lucas is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Lucas is a knight if and only if Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Ella is a knight and Zoey is a knave.", "Elizabeth cannot be a knave, because this would contradict the claim of Zoey that Lucas is a knight if and only if Elizabeth is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Lucas is a knight if and only if Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the false claim of Zoey that Lucas is a knight if and only if Elizabeth is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Ella is a knight and Zoey is a knave.", "Ella cannot be a knight, because this would contradict the false claim of Elizabeth that Ella is a knight and Zoey is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Lucas is a knave or Mia is a knight.", "Mia cannot be a knight, because this would contradict the false claim of Ella that Lucas is a knave or Mia is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Elizabeth is a knight or Jackson is a knight.", "Jackson cannot be a knight, because this would contradict the false claim of Mia that Elizabeth is a knight or Jackson is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Sofia is a knave and Mia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that If Mia is a knave then Elizabeth is a knight.", "Sofia cannot be a knave, because this would contradict the false claim of Jackson that Sofia is a knave and Mia is a knave.", "We have exhausted all possibilities for Sofia, Jackson, Mia, Ella, Elizabeth, and Zoey, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that If Zoey is a knave then Lucas is a knight.", "Zoey cannot be a knight, because this would contradict the false claim of Lucas that If Zoey is a knave then Lucas is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Lucas is a knight if and only if Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Ella is a knight and Zoey is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Lucas is a knave or Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Elizabeth is a knight or Jackson is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Sofia is a knave and Mia is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Sofia is a knave and Mia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that If Mia is a knave then Elizabeth is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 2), ('telling-truth', 0)), ('->', ('lying', 4), ('telling-truth', 6)), ('<=>', ('telling-truth', 0), ('telling-truth', 6)), ('and', ('lying', 1), ('lying', 4)), ('or', ('telling-truth', 6), ('telling-truth', 3)), ('or', ('lying', 0), ('telling-truth', 4)), ('and', ('telling-truth', 5), ('lying', 2)))", "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 7 inhabitants: Chloe, Amelia, Noah, Emily, Abigail, Henry, and Jackson. As Chloe put it, \"Emily is not a knight\". Amelia asserted: \"Abigail is not a knight\". Noah said, \"If Chloe is a knave then Emily is a knave.\" Emily remarked, \"If Henry is a knight then Emily is a knight\". \"Henry is not a knight\" - Abigail. \"Chloe is a knave and Noah is a knight,\" Henry declared. In Jackson's words: \"Abigail is not a knight\". So who is a knight and who is a knave?", "names": ["Chloe", "Amelia", "Noah", "Emily", "Abigail", "Henry", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, false, false], "solution_text": "Chloe is a knave, Amelia is a knave, Noah is a knave, Emily is a knight, Abigail is a knight, Henry is a knave, and Jackson is a knave.", "solution_text_format": "(1) Chloe is a knave\n(2) Amelia is a knave\n(3) Noah is a knave\n(4) Emily is a knight\n(5) Abigail is a knight\n(6) Henry is a knave\n(7) Jackson is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Emily is not a knight.", "Emily cannot be a knight, because this would contradict the claim of Chloe that Emily is not a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that If Henry is a knight then Emily is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Chloe is a knave and Noah is a knight.", "Henry cannot be a knave, because this would contradict the false claim of Emily that If Henry is a knight then Emily is a knight.", "We have exhausted all possibilities for Henry and Emily, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Emily is not a knight.", "Assume Emily is a knight. No contradiction is found in their claim that If Henry is a knight then Emily is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Chloe is a knave and Noah is a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that If Chloe is a knave then Emily is a knave.", "Noah cannot be a knave, because this would contradict the claim of Henry that Chloe is a knave and Noah is a knight.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Chloe is a knave and Noah is a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that If Chloe is a knave then Emily is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that If Chloe is a knave then Emily is a knave.", "Assume Amelia 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 Amelia that Abigail is not a knight.", "Abigail 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 Abigail, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Abigail is not a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Henry is not a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Abigail is not a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Abigail is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 3)), ('not', ('telling-truth', 4)), ('->', ('lying', 0), ('lying', 3)), ('->', ('telling-truth', 5), ('telling-truth', 3)), ('not', ('telling-truth', 5)), ('and', ('lying', 0), ('telling-truth', 2)), ('not', ('telling-truth', 4)))", "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 7 inhabitants: Penelope, Elizabeth, Amelia, Sofia, James, Sebastian, and Harper. In a statement by Penelope: \"Elizabeth is a knave\". Elizabeth said, \"Sebastian is a knave and Sofia is a knight.\" \"Sofia is a knight if and only if Sebastian is a knight,\" Amelia declared. According to Sofia, \"Penelope is a knight or Sofia is a knight\". James asserted: \"Sebastian is not a knave\". In a statement by Sebastian: \"Sebastian is a knight and Sofia is a knave\". Harper asserted: \"Elizabeth is a knight and Amelia is a knight\". So who is a knight and who is a knave?", "names": ["Penelope", "Elizabeth", "Amelia", "Sofia", "James", "Sebastian", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, false, false], "solution_text": "Penelope is a knave, Elizabeth is a knight, Amelia is a knave, Sofia is a knight, James is a knave, Sebastian is a knave, and Harper is a knave.", "solution_text_format": "(1) Penelope is a knave\n(2) Elizabeth is a knight\n(3) Amelia is a knave\n(4) Sofia is a knight\n(5) James is a knave\n(6) Sebastian is a knave\n(7) Harper is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that Elizabeth is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of Penelope that Elizabeth is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Sebastian is a knave and Sofia is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Sebastian is a knight and Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Sebastian that Sebastian is a knight and Sofia is a knave.", "Sofia cannot be a knave, because this would contradict the false claim of their own that Penelope is a knight or Sofia is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Sebastian is a knight and Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the false claim of Elizabeth that Sebastian is a knave and Sofia is a knight.", "Sofia cannot be a knave, because this would contradict the false claim of their own that Penelope is a knight or Sofia is a knight.", "We have exhausted all possibilities for Sofia, Sebastian, and Elizabeth, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Elizabeth is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Sebastian is a knave and Sofia is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of Elizabeth that Sebastian is a knave and Sofia is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Sebastian is a knight and Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Penelope is a knight or Sofia is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Sofia is a knight if and only if Sebastian is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Sofia is a knight if and only if Sebastian is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Sebastian is not a knave.", "Assume James is a knave. No contradiction is found in their false claim that Sebastian is not a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight and Amelia is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Elizabeth is a knight and Amelia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 1), ('and', ('lying', 5), ('telling-truth', 3)), ('<=>', ('telling-truth', 3), ('telling-truth', 5)), ('or', ('telling-truth', 0), ('telling-truth', 3)), ('not', ('lying', 5)), ('and', ('telling-truth', 5), ('lying', 3)), ('and', ('telling-truth', 1), ('telling-truth', 2)))", "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 7 inhabitants: Oliver, Riley, Harper, Noah, Sebastian, Alexander, and Aurora. Oliver was heard saying, \"Sebastian is a knave or Alexander is a knave\". Riley noted, \"Harper is a knight or Aurora is a knave\". Harper said, \"Riley is a knight or Noah is a knave.\" Noah noted, \"Aurora is a knave and Harper is a knight\". In a statement by Sebastian: \"Oliver is a knave if and only if Alexander is a knight\". According to Alexander, \"Sebastian is a knight and Aurora is a knight\". Aurora noted, \"Harper is not a knight\". So who is a knight and who is a knave?", "names": ["Oliver", "Riley", "Harper", "Noah", "Sebastian", "Alexander", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false, false], "solution_text": "Oliver is a knight, Riley is a knight, Harper is a knight, Noah is a knight, Sebastian is a knight, Alexander is a knave, and Aurora is a knave.", "solution_text_format": "(1) Oliver is a knight\n(2) Riley is a knight\n(3) Harper is a knight\n(4) Noah is a knight\n(5) Sebastian is a knight\n(6) Alexander is a knave\n(7) 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 Oliver is a knight. No contradiction is found in their claim that Sebastian is a knave or Alexander is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Oliver is a knave if and only if Alexander is a knight.", "Alexander cannot be a knight, because this would contradict the claim of Oliver that Sebastian is a knave or Alexander is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Sebastian is a knight and Aurora is a knight.", "Aurora cannot be a knight, because this would contradict the false claim of Alexander that Sebastian is a knight and Aurora is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Harper is not a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Riley is a knight or Noah is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Harper is a knight or Aurora is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Aurora is a knave and Harper is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 4), ('lying', 5)), ('or', ('telling-truth', 2), ('lying', 6)), ('or', ('telling-truth', 1), ('lying', 3)), ('and', ('lying', 6), ('telling-truth', 2)), ('<=>', ('lying', 0), ('telling-truth', 5)), ('and', ('telling-truth', 4), ('telling-truth', 6)), ('not', ('telling-truth', 2)))", "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 7 inhabitants: Sofia, Amelia, Aria, Elizabeth, Luke, Ava, and Emily. \"Emily is a knave,\" Sofia claimed. \"If Aria is a knave then Elizabeth is a knave,\" Amelia mentioned. According to Aria, \"If Ava is a knave then Emily is a knave\". Elizabeth told you that Ava is not a knave. Luke expressed that Sofia is a knave and Luke is a knight. Ava expressed that Elizabeth is a knave and Sofia is a knight. \"If Luke is a knave then Elizabeth is a knight\" - Emily. So who is a knight and who is a knave?", "names": ["Sofia", "Amelia", "Aria", "Elizabeth", "Luke", "Ava", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, false, true], "solution_text": "Sofia is a knave, Amelia is a knight, Aria is a knave, Elizabeth is a knave, Luke is a knight, Ava is a knave, and Emily is a knight.", "solution_text_format": "(1) Sofia is a knave\n(2) Amelia is a knight\n(3) Aria is a knave\n(4) Elizabeth is a knave\n(5) Luke is a knight\n(6) Ava is a knave\n(7) 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 Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of Sofia that Emily is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that If Luke is a knave then Elizabeth is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Sofia is a knave and Luke is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Sofia is a knave and Luke is a knight.", "Elizabeth cannot be a knight, because this would contradict the false claim of Emily that If Luke is a knave then Elizabeth is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Ava is not a knave.", "Ava cannot be a knight, because this would contradict the false claim of Elizabeth that Ava is not a knave.", "Ava cannot be a knave, because this would contradict the false claim of their own that Elizabeth is a knave and Sofia is a knight.", "We have exhausted all possibilities for Ava, Elizabeth, Luke, and Emily, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that If Luke is a knave then Elizabeth is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Sofia is a knave and Luke is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Ava is not a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave and Sofia is a knight.", "Ava cannot be a knave, because this would contradict the claim of Elizabeth that Ava is not a knave.", "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 not a knave.", "Ava cannot be a knight, because this would contradict the false claim of Elizabeth that Ava is not a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Elizabeth is a knave and Sofia is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that If Aria is a knave then Elizabeth is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that If Ava is a knave then Emily is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that If Ava is a knave then Emily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 6), ('->', ('lying', 2), ('lying', 3)), ('->', ('lying', 5), ('lying', 6)), ('not', ('lying', 5)), ('and', ('lying', 0), ('telling-truth', 4)), ('and', ('lying', 3), ('telling-truth', 0)), ('->', ('lying', 4), ('telling-truth', 3)))", "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 7 inhabitants: Avery, Liam, William, James, Isabella, Riley, and Ava. In a statement by Avery: \"William is not a knave\". Liam commented, \"Avery is a knight or Isabella is a knave\". William commented, \"James is a knave and Ava is a knave\". \"Liam is not a knave,\" James claimed. In Isabella's words: \"Liam is a knight if and only if Liam is a knave\". Riley stated, \"Isabella is a knight\". Ava told you that Liam is a knave or Isabella is a knight. So who is a knight and who is a knave?", "names": ["Avery", "Liam", "William", "James", "Isabella", "Riley", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, false, false], "solution_text": "Avery is a knave, Liam is a knight, William is a knave, James is a knight, Isabella is a knave, Riley is a knave, and Ava is a knave.", "solution_text_format": "(1) Avery is a knave\n(2) Liam is a knight\n(3) William is a knave\n(4) James is a knight\n(5) Isabella is a knave\n(6) Riley is a knave\n(7) 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 Avery is a knight. No contradiction is found in their claim that William is not a knave.", "Assume William is a knight. No contradiction is found in their claim that James is a knave and Ava is a knave.", "James cannot be a knight, because this would contradict the claim of William that James is a knave and Ava is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Liam is not a knave.", "Liam cannot be a knight, because this would contradict the false claim of James that Liam is not a knave.", "Liam cannot be a knave, because this would contradict the false claim of their own that Avery is a knight or Isabella is a knave.", "We have exhausted all possibilities for Liam and James, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the claim of Avery that William is not a knave.", "We have exhausted all possibilities for William, so let us go back and reconsider Avery.", "Assume Avery 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 Avery that William is not a knave.", "Assume William is a knave. No contradiction is found in their false claim that James is a knave and Ava is a knave.", "Assume James is a knight. No contradiction is found in their claim that Liam is not a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Avery is a knight or Isabella is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Liam that Avery is a knight or Isabella is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Liam is a knight if and only if Liam is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Liam is a knave or Isabella is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Liam is a knave or Isabella is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Isabella is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Isabella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('or', ('telling-truth', 0), ('lying', 4)), ('and', ('lying', 3), ('lying', 6)), ('not', ('lying', 1)), ('<=>', ('telling-truth', 1), ('lying', 1)), ('telling-truth', 4), ('or', ('lying', 1), ('telling-truth', 4)))", "index": 67}
-{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: James, Ava, Emily, Daniel, Luke, Joseph, and Scarlett. James said, \"Daniel is a knave or Joseph is a knave.\" As Ava put it, \"Emily is a knave if and only if Daniel is a knight\". Emily said, \"Luke is not a knight.\" Daniel remarked, \"Ava is a knave if and only if Scarlett is a knave\". Luke told you that Scarlett is a knave and Scarlett is a knight. According to Joseph, \"Emily is a knight if and only if Ava is a knave\". In Scarlett's words: \"Joseph is not a knave\". So who is a knight and who is a knave?", "names": ["James", "Ava", "Emily", "Daniel", "Luke", "Joseph", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false, false], "solution_text": "James is a knight, Ava is a knight, Emily is a knight, Daniel is a knave, Luke is a knave, Joseph is a knave, and Scarlett is a knave.", "solution_text_format": "(1) James is a knight\n(2) Ava is a knight\n(3) Emily is a knight\n(4) Daniel is a knave\n(5) Luke is a knave\n(6) Joseph is a knave\n(7) Scarlett is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Daniel is a knave or Joseph is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Ava is a knave if and only if Scarlett is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Emily is a knave if and only if Daniel is a knight.", "Emily cannot be a knight, because this would contradict the claim of Ava that Emily is a knave if and only if Daniel is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Luke is not a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Scarlett is a knave and Scarlett is a knight.", "Luke cannot be a knave, because this would contradict the false claim of Emily that Luke is not a knight.", "We have exhausted all possibilities for Luke and Emily, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Emily is a knave if and only if Daniel is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Luke is not a knight.", "Luke cannot be a knight, because this would contradict the claim of Emily that Luke is not a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Scarlett is a knave and Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of Daniel that Ava is a knave if and only if Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Joseph is not a knave.", "Joseph cannot be a knight, because this would contradict the claim of James that Daniel is a knave or Joseph is a knave.", "Joseph cannot be a knave, because this would contradict the false claim of their own that Emily is a knight if and only if Ava is a knave.", "We have exhausted all possibilities for Joseph, Scarlett, and Luke, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the false claim of Ava that Emily is a knave if and only if Daniel is a knight.", "We have exhausted all possibilities for Emily and Ava, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Ava is a knave if and only if Scarlett is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Emily is a knave if and only if Daniel is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Luke is not a knight.", "Luke cannot be a knight, because this would contradict the claim of Emily that Luke is not a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Scarlett is a knave and Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the false claim of Daniel that Ava is a knave if and only if Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Joseph is not a knave.", "Joseph cannot be a knight, because this would contradict the claim of their own that Emily is a knight if and only if Ava is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Emily is a knight if and only if Ava is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('lying', 5)), ('<=>', ('lying', 2), ('telling-truth', 3)), ('not', ('telling-truth', 4)), ('<=>', ('lying', 1), ('lying', 6)), ('and', ('lying', 6), ('telling-truth', 6)), ('<=>', ('telling-truth', 2), ('lying', 1)), ('not', ('lying', 5)))", "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 7 inhabitants: Jacob, Sebastian, Isabella, Sophia, Ava, Aiden, and Ella. Jacob remarked, \"Aiden is not a knight\". \"If Jacob is a knave then Sophia is a knight,\" Sebastian declared. Isabella was heard saying, \"Ava is a knave or Jacob is a knave\". As Sophia put it, \"If Aiden is a knave then Ava is a knave\". Ava remarked, \"If Isabella is a knave then Sophia is a knave\". \"If Ella is a knight then Ava is a knight,\" Aiden claimed. Ella said, \"Sebastian is not a knave.\" So who is a knight and who is a knave?", "names": ["Jacob", "Sebastian", "Isabella", "Sophia", "Ava", "Aiden", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true, true], "solution_text": "Jacob is a knave, Sebastian is a knight, Isabella is a knight, Sophia is a knight, Ava is a knight, Aiden is a knight, and Ella is a knight.", "solution_text_format": "(1) Jacob is a knave\n(2) Sebastian is a knight\n(3) Isabella is a knight\n(4) Sophia is a knight\n(5) Ava is a knight\n(6) Aiden is a knight\n(7) 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 Jacob 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 Jacob that Aiden is not a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that If Ella is a knight then Ava is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Sebastian is not a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Jacob is a knave then Sophia is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that If Aiden is a knave then Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of Sophia that If Aiden is a knave then Ava is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that If Isabella is a knave then Sophia is a knave.", "Isabella cannot be a knight, because this would contradict the false claim of Ava that If Isabella is a knave then Sophia is a knave.", "Isabella cannot be a knave, because this would contradict the false claim of their own that Ava is a knave or Jacob is a knave.", "We have exhausted all possibilities for Isabella and Ava, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that If Aiden is a knave then Ava is a knave.", "Ava cannot be a knight, because this would contradict the false claim of Aiden that If Ella is a knight then Ava is a knight.", "Ava cannot be a knave, because this would contradict the false claim of Sophia that If Aiden is a knave then Ava is a knave.", "We have exhausted all possibilities for Ava and Sophia, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the false claim of their own that If Jacob is a knave then Sophia is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the false claim of Aiden that If Ella is a knight then Ava is a knight.", "We have exhausted all possibilities for Ella and Aiden, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Aiden is not a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that If Ella is a knight then Ava is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Sebastian is not a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Jacob is a knave then Sophia is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that If Aiden is a knave then Ava is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that If Isabella is a knave then Sophia is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Ava is a knave or Jacob is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 5)), ('->', ('lying', 0), ('telling-truth', 3)), ('or', ('lying', 4), ('lying', 0)), ('->', ('lying', 5), ('lying', 4)), ('->', ('lying', 2), ('lying', 3)), ('->', ('telling-truth', 6), ('telling-truth', 4)), ('not', ('lying', 1)))", "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 7 inhabitants: Penelope, Mia, David, Aiden, Emily, Owen, and Lily. \"Lily is not a knight,\" Penelope mentioned. \"Penelope is a knight and Owen is a knight,\" Mia declared. \"Penelope is a knight,\" David claimed. Aiden said, \"If Aiden is a knight then David is a knave.\" In a statement by Emily: \"Lily is a knave and Penelope is a knight\". Owen stated, \"Emily is a knight if and only if Lily is a knight\". \"Owen is a knave or Emily is a knave,\" Lily mentioned. So who is a knight and who is a knave?", "names": ["Penelope", "Mia", "David", "Aiden", "Emily", "Owen", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, false, true], "solution_text": "Penelope is a knave, Mia is a knave, David is a knave, Aiden is a knight, Emily is a knave, Owen is a knave, and Lily is a knight.", "solution_text_format": "(1) Penelope is a knave\n(2) Mia is a knave\n(3) David is a knave\n(4) Aiden is a knight\n(5) Emily is a knave\n(6) Owen is a knave\n(7) 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 Penelope 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 Penelope that Lily is not a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Owen is a knave or Emily is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Emily is a knight if and only if Lily is a knight.", "Emily cannot be a knight, because this would contradict the claim of Owen that Emily is a knight if and only if Lily is a knight.", "Emily cannot be a knave, because this would contradict the false claim of their own that Lily is a knave and Penelope is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the false claim of Lily that Owen is a knave or Emily is a knave.", "We have exhausted all possibilities for Owen and Lily, so let us go back and reconsider Penelope.", "Assume Penelope 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 Owen is a knave or Emily is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Emily is a knight if and only if Lily is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Lily is a knave and Penelope is a knight.", "Emily cannot be a knave, because this would contradict the claim of Owen that Emily is a knight if and only if Lily is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Emily is a knight if and only if Lily is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Lily is a knave and Penelope is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Lily is a knave and Penelope is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that Penelope is a knight and Owen is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Penelope is a knight and Owen is a knight.", "David cannot be a knight, because this would contradict the claim of their own that Penelope is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Penelope is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that If Aiden is a knight then David is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 6)), ('and', ('telling-truth', 0), ('telling-truth', 5)), ('telling-truth', 0), ('->', ('telling-truth', 3), ('lying', 2)), ('and', ('lying', 6), ('telling-truth', 0)), ('<=>', ('telling-truth', 4), ('telling-truth', 6)), ('or', ('lying', 5), ('lying', 4)))", "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 7 inhabitants: Noah, Charlotte, Matthew, Logan, Luke, Benjamin, and Aurora. According to Noah, \"Luke is not a knave\". As Charlotte put it, \"If Logan is a knave then Benjamin is a knight\". \"Benjamin is not a knave,\" Matthew mentioned. \"Matthew is a knight and Luke is a knight,\" Logan declared. Luke said, \"Benjamin is not a knight.\" Benjamin noted, \"Logan is a knight and Luke is a knight\". Aurora stated, \"If Logan is a knight then Luke is a knave\". So who is a knight and who is a knave?", "names": ["Noah", "Charlotte", "Matthew", "Logan", "Luke", "Benjamin", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, false, true], "solution_text": "Noah is a knight, Charlotte is a knave, Matthew is a knave, Logan is a knave, Luke is a knight, Benjamin is a knave, and Aurora is a knight.", "solution_text_format": "(1) Noah is a knight\n(2) Charlotte is a knave\n(3) Matthew is a knave\n(4) Logan is a knave\n(5) Luke is a knight\n(6) Benjamin is a knave\n(7) 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 Noah is a knight. No contradiction is found in their claim that Luke is not a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Benjamin is not a knight.", "Benjamin cannot be a knight, because this would contradict the claim of Luke that Benjamin is not a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Logan is a knight and Luke is a knight.", "Logan cannot be a knight, because this would contradict the false claim of Benjamin that Logan is a knight and Luke is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Matthew is a knight and Luke is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Benjamin is not a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Benjamin is not a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that If Logan is a knave then Benjamin is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that If Logan is a knave then Benjamin is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that If Logan is a knight then Luke is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('->', ('lying', 3), ('telling-truth', 5)), ('not', ('lying', 5)), ('and', ('telling-truth', 2), ('telling-truth', 4)), ('not', ('telling-truth', 5)), ('and', ('telling-truth', 3), ('telling-truth', 4)), ('->', ('telling-truth', 3), ('lying', 4)))", "index": 71}
-{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Harper, Aria, Lily, Logan, James, Ava, and Samuel. \"Harper is a knight and Logan is a knave,\" Harper claimed. Aria commented, \"Lily is a knight\". Lily stated, \"If Ava is a knight then Logan is a knight\". \"Lily is a knight if and only if James is a knave\" - Logan. James remarked, \"Aria is a knight if and only if Lily is a knave\". Ava expressed that Aria is a knave and Samuel is a knave. Samuel commented, \"Logan is a knave\". So who is a knight and who is a knave?", "names": ["Harper", "Aria", "Lily", "Logan", "James", "Ava", "Samuel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false, false], "solution_text": "Harper is a knave, Aria is a knight, Lily is a knight, Logan is a knight, James is a knave, Ava is a knave, and Samuel is a knave.", "solution_text_format": "(1) Harper is a knave\n(2) Aria is a knight\n(3) Lily is a knight\n(4) Logan is a knight\n(5) James is a knave\n(6) Ava is a knave\n(7) Samuel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that Harper is a knight and Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of Harper that Harper is a knight and Logan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Lily is a knight if and only if James is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that If Ava is a knight then Logan is a knight.", "Ava cannot be a knight, because this would contradict the claim of Lily that If Ava is a knight then Logan is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Aria is a knave and Samuel is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Lily is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Logan is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Aria is a knight if and only if Lily is a knave.", "James cannot be a knave, because this would contradict the false claim of Logan that Lily is a knight if and only if James is a knave.", "We have exhausted all possibilities for James, so let us go back and reconsider Samuel.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Logan is a knave.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Aria.", "Aria cannot be a knave, because this would contradict the false claim of their own that Lily is a knight.", "We have exhausted all possibilities for Aria and Ava, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that If Ava is a knight then Logan is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Aria is a knave and Samuel is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Lily is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Lily is a knight.", "Samuel cannot be a knight, because this would contradict the claim of Ava that Aria is a knave and Samuel is a knave.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Logan is a knave.", "We have exhausted all possibilities for Samuel and Aria, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the false claim of Lily that If Ava is a knight then Logan is a knight.", "We have exhausted all possibilities for Ava, Lily, and Logan, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Harper is a knight and Logan is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Lily is a knight if and only if James is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that If Ava is a knight then Logan is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Aria is a knave and Samuel is a knave.", "Aria cannot be a knight, because this would contradict the claim of Ava that Aria is a knave and Samuel is a knave.", "Aria cannot be a knave, because this would contradict the false claim of their own that Lily is a knight.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Aria is a knave and Samuel is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Lily is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Logan is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Logan is a knave.", "James cannot be a knight, because this would contradict the claim of Logan that Lily is a knight if and only if James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Aria is a knight if and only if Lily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 0), ('lying', 3)), ('telling-truth', 2), ('->', ('telling-truth', 5), ('telling-truth', 3)), ('<=>', ('telling-truth', 2), ('lying', 4)), ('<=>', ('telling-truth', 1), ('lying', 2)), ('and', ('lying', 1), ('lying', 6)), ('lying', 3))", "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 7 inhabitants: Jack, Grace, Sofia, Mason, Elizabeth, Michael, and David. \"Jack is a knight if and only if Elizabeth is a knight,\" Jack mentioned. \"David is a knight or Mason is a knight,\" Grace mentioned. \"David is not a knave,\" Sofia claimed. Mason asserted: \"David is a knave or Elizabeth is a knave\". Elizabeth was heard saying, \"David is a knave\". In a statement by Michael: \"Sofia is a knight if and only if Jack is a knave\". \"Michael is a knight if and only if Sofia is a knight,\" David claimed. So who is a knight and who is a knave?", "names": ["Jack", "Grace", "Sofia", "Mason", "Elizabeth", "Michael", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true, false], "solution_text": "Jack is a knight, Grace is a knight, Sofia is a knave, Mason is a knight, Elizabeth is a knight, Michael is a knight, and David is a knave.", "solution_text_format": "(1) Jack is a knight\n(2) Grace is a knight\n(3) Sofia is a knave\n(4) Mason is a knight\n(5) Elizabeth is a knight\n(6) Michael is a knight\n(7) David is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Jack is a knight if and only if Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that David is a knave.", "David cannot be a knight, because this would contradict the claim of Elizabeth that David is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Michael is a knight if and only if Sofia is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Sofia is a knight if and only if Jack is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that David is not a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that David is not a knave.", "Assume Grace is a knight. No contradiction is found in their claim that David is a knight or Mason is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that David is a knave or Elizabeth is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 0), ('telling-truth', 4)), ('or', ('telling-truth', 6), ('telling-truth', 3)), ('not', ('lying', 6)), ('or', ('lying', 6), ('lying', 4)), ('lying', 6), ('<=>', ('telling-truth', 2), ('lying', 0)), ('<=>', ('telling-truth', 5), ('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 7 inhabitants: Victoria, Penelope, Logan, Matthew, Oliver, Riley, and Emma. Victoria told you that If Matthew is a knight then Logan is a knave. Penelope remarked, \"Logan is a knight if and only if Oliver is a knave\". \"If Victoria is a knave then Riley is a knave,\" Logan claimed. \"Victoria is a knave and Logan is a knave,\" Matthew claimed. \"Logan is a knave or Victoria is a knave,\" Oliver mentioned. Riley was heard saying, \"If Penelope is a knight then Oliver is a knave\". As Emma put it, \"Victoria is a knave and Victoria is a knight\". So who is a knight and who is a knave?", "names": ["Victoria", "Penelope", "Logan", "Matthew", "Oliver", "Riley", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true, false], "solution_text": "Victoria is a knight, Penelope is a knight, Logan is a knight, Matthew is a knave, Oliver is a knave, Riley is a knight, and Emma is a knave.", "solution_text_format": "(1) Victoria is a knight\n(2) Penelope is a knight\n(3) Logan is a knight\n(4) Matthew is a knave\n(5) Oliver is a knave\n(6) Riley is a knight\n(7) 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 Victoria is a knight. No contradiction is found in their claim that If Matthew is a knight then Logan is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Victoria is a knave and Logan is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Victoria is a knave and Logan is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that If Victoria is a knave then Riley is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that If Penelope is a knight then Oliver is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Logan is a knight if and only if Oliver is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Penelope that Logan is a knight if and only if Oliver is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Logan is a knave or Victoria is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Victoria is a knave and Victoria is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Victoria is a knave and Victoria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('lying', 2)), ('<=>', ('telling-truth', 2), ('lying', 4)), ('->', ('lying', 0), ('lying', 5)), ('and', ('lying', 0), ('lying', 2)), ('or', ('lying', 2), ('lying', 0)), ('->', ('telling-truth', 1), ('lying', 4)), ('and', ('lying', 0), ('telling-truth', 0)))", "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 7 inhabitants: Lucas, Penelope, James, Ella, Oliver, Riley, and Sophia. Lucas noted, \"Ella is not a knight\". \"Riley is a knave or Penelope is a knight,\" Penelope claimed. James told you that Oliver is a knight if and only if Penelope is a knight. Ella said that Lucas is a knight or Penelope is a knave. In Oliver's words: \"If Riley is a knave then Lucas is a knight\". In Riley's words: \"Ella is not a knave\". Sophia stated, \"James is a knave\". So who is a knight and who is a knave?", "names": ["Lucas", "Penelope", "James", "Ella", "Oliver", "Riley", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true, true], "solution_text": "Lucas is a knave, Penelope is a knave, James is a knave, Ella is a knight, Oliver is a knight, Riley is a knight, and Sophia is a knight.", "solution_text_format": "(1) Lucas is a knave\n(2) Penelope is a knave\n(3) James is a knave\n(4) Ella is a knight\n(5) Oliver is a knight\n(6) Riley is a knight\n(7) 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 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.", "Ella cannot be a knave, because this would contradict the false claim of their own that Lucas is a knight or Penelope is a knave.", "We have exhausted all possibilities for 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 Lucas is a knight or Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the claim of Ella that Lucas is a knight or Penelope is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Riley is a knave or Penelope is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Ella is not a knave.", "Assume James is a knight. No contradiction is found in their claim that Oliver is a knight if and only if Penelope is a knight.", "Oliver cannot be a knight, because this would contradict the claim of James that Oliver is a knight if and only if Penelope is a knight.", "Oliver cannot be a knave, because this would contradict the false claim of their own that If Riley is a knave then Lucas is a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Oliver is a knight if and only if Penelope is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that If Riley is a knave then Lucas is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that James is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 3)), ('or', ('lying', 5), ('telling-truth', 1)), ('<=>', ('telling-truth', 4), ('telling-truth', 1)), ('or', ('telling-truth', 0), ('lying', 1)), ('->', ('lying', 5), ('telling-truth', 0)), ('not', ('lying', 3)), ('lying', 2))", "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 7 inhabitants: Noah, Mason, Samuel, Evelyn, Emily, James, and Owen. Noah said, \"Samuel is a knight.\" Mason stated, \"Noah is a knight or James is a knave\". Samuel told you that Owen is a knight and Samuel is a knight. \"Noah is not a knight,\" Evelyn mentioned. \"Noah is a knave or Emily is a knight\" - Emily. James told you that Evelyn is a knave if and only if Noah is a knave. Owen stated, \"Evelyn is a knight\". So who is a knight and who is a knave?", "names": ["Noah", "Mason", "Samuel", "Evelyn", "Emily", "James", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false, true], "solution_text": "Noah is a knave, Mason is a knight, Samuel is a knave, Evelyn is a knight, Emily is a knight, James is a knave, and Owen is a knight.", "solution_text_format": "(1) Noah is a knave\n(2) Mason is a knight\n(3) Samuel is a knave\n(4) Evelyn is a knight\n(5) Emily is a knight\n(6) James is a knave\n(7) 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 Noah is a knight. No contradiction is found in their claim that Samuel is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Owen is a knight and Samuel is a knight.", "Assume Owen 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 Noah is not a knight.", "Evelyn cannot be a knave, because this would contradict the claim of Owen that 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 Samuel that Owen is a knight and Samuel is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Samuel.", "Samuel cannot be a knave, because this would contradict the claim of Noah that Samuel is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Samuel is a knight.", "Samuel cannot be a knight, because this would contradict the false claim of Noah that Samuel is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Owen is a knight and Samuel is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Evelyn is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Noah is not a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Noah is a knight or James is a knave.", "James cannot be a knight, because this would contradict the claim of Mason that Noah is a knight or James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Evelyn is a knave if and only if Noah is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Noah is a knave or Emily is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('or', ('telling-truth', 0), ('lying', 5)), ('and', ('telling-truth', 6), ('telling-truth', 2)), ('not', ('telling-truth', 0)), ('or', ('lying', 0), ('telling-truth', 4)), ('<=>', ('lying', 3), ('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 7 inhabitants: James, Jackson, Jack, Liam, Henry, Lily, and Oliver. James asserted: \"If Oliver is a knight then Jack is a knight\". \"Jackson is a knight if and only if Liam is a knave\" - Jackson. \"Lily is a knave,\" Jack claimed. Liam noted, \"If Oliver is a knave then Jack is a knave\". Henry noted, \"If Jack is a knave then Lily is a knave\". Lily told you that Jack is a knave if and only if Jackson is a knight. Oliver remarked, \"Lily is not a knave\". So who is a knight and who is a knave?", "names": ["James", "Jackson", "Jack", "Liam", "Henry", "Lily", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false, false], "solution_text": "James is a knight, Jackson is a knight, Jack is a knight, Liam is a knave, Henry is a knight, Lily is a knave, and Oliver is a knave.", "solution_text_format": "(1) James is a knight\n(2) Jackson is a knight\n(3) Jack is a knight\n(4) Liam is a knave\n(5) Henry is a knight\n(6) Lily is a knave\n(7) 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 If Oliver is a knight then Jack is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Lily is not a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Jack is a knave if and only if Jackson is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Lily is a knave.", "Jack cannot be a knave, because this would contradict the claim of James that If Oliver is a knight then Jack is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the claim of Oliver that Lily is not a knave.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Lily is not a knave.", "Lily cannot be a knight, because this would contradict the false claim of Oliver that Lily is not a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Jack is a knave if and only if Jackson is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Lily is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of Jackson that Jackson is a knight if and only if Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that If Oliver is a knave then Jack is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Jack is a knave then Lily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 6), ('telling-truth', 2)), ('<=>', ('telling-truth', 1), ('lying', 3)), ('lying', 5), ('->', ('lying', 6), ('lying', 2)), ('->', ('lying', 2), ('lying', 5)), ('<=>', ('lying', 2), ('telling-truth', 1)), ('not', ('lying', 5)))", "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 7 inhabitants: Isabella, Emma, Mason, Lily, Evelyn, Liam, and Victoria. Isabella commented, \"Evelyn is a knight and Emma is a knave\". Emma said that If Evelyn is a knave then Mason is a knight. \"If Liam is a knight then Victoria is a knave,\" Mason mentioned. According to Lily, \"Liam is a knight or Mason is a knight\". Evelyn said that Isabella is a knight or Mason is a knight. Liam asserted: \"Mason is a knight if and only if Emma is a knave\". Victoria asserted: \"Emma is a knight if and only if Evelyn is a knave\". So who is a knight and who is a knave?", "names": ["Isabella", "Emma", "Mason", "Lily", "Evelyn", "Liam", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false, false], "solution_text": "Isabella is a knave, Emma is a knight, Mason is a knight, Lily is a knight, Evelyn is a knight, Liam is a knave, and Victoria is a knave.", "solution_text_format": "(1) Isabella is a knave\n(2) Emma is a knight\n(3) Mason is a knight\n(4) Lily is a knight\n(5) Evelyn is a knight\n(6) Liam is a knave\n(7) 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 Isabella is a knight. No contradiction is found in their claim that Evelyn is a knight and Emma is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Isabella is a knight or Mason is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that If Liam is a knight then Victoria is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Mason is a knight if and only if Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of Isabella that Evelyn is a knight and Emma is a knave.", "Emma cannot be a knave, because this would contradict the false claim of their own that If Evelyn is a knave then Mason is a knight.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Mason is a knight if and only if Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of Isabella that Evelyn is a knight and Emma is a knave.", "Emma cannot be a knave, because this would contradict the false claim of their own that If Evelyn is a knave then Mason is a knight.", "We have exhausted all possibilities for Emma and Liam, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that If Liam is a knight then Victoria is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Mason is a knight if and only if Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of Isabella that Evelyn is a knight and Emma is a knave.", "Emma cannot be a knave, because this would contradict the false claim of their own that If Evelyn is a knave then Mason is a knight.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the false claim of Mason that If Liam is a knight then Victoria is a knave.", "We have exhausted all possibilities for Liam and Mason, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the claim of Isabella that Evelyn is a knight and Emma is a knave.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Evelyn is a knight and Emma is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Isabella is a knight or Mason is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that If Liam is a knight then Victoria is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Mason is a knight if and only if Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of Liam that Mason is a knight if and only if Emma is a knave.", "Emma cannot be a knave, because this would contradict the false claim of Isabella that Evelyn is a knight and Emma is a knave.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Mason is a knight if and only if Emma is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that If Evelyn is a knave then Mason is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Emma is a knight if and only if Evelyn is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Emma is a knight if and only if Evelyn is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Liam is a knight or Mason is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 4), ('lying', 1)), ('->', ('lying', 4), ('telling-truth', 2)), ('->', ('telling-truth', 5), ('lying', 6)), ('or', ('telling-truth', 5), ('telling-truth', 2)), ('or', ('telling-truth', 0), ('telling-truth', 2)), ('<=>', ('telling-truth', 2), ('lying', 1)), ('<=>', ('telling-truth', 1), ('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 7 inhabitants: Lucas, Isabella, James, Ella, Emma, Luke, and Sofia. In Lucas's words: \"James is a knave if and only if Luke is a knave\". In a statement by Isabella: \"Luke is a knave and Luke is a knight\". James remarked, \"If Sofia is a knave then Lucas is a knave\". Ella said that Lucas is a knave or Luke is a knave. Emma said, \"Lucas is a knave and Luke is a knight.\" Luke asserted: \"Lucas is a knight\". As Sofia put it, \"Ella is a knave if and only if Lucas is a knave\". So who is a knight and who is a knave?", "names": ["Lucas", "Isabella", "James", "Ella", "Emma", "Luke", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false, false], "solution_text": "Lucas is a knave, Isabella is a knave, James is a knight, Ella is a knight, Emma is a knave, Luke is a knave, and Sofia is a knave.", "solution_text_format": "(1) Lucas is a knave\n(2) Isabella is a knave\n(3) James is a knight\n(4) Ella is a knight\n(5) Emma is a knave\n(6) Luke is a knave\n(7) 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 Lucas is a knight. No contradiction is found in their claim that James is a knave if and only if Luke is a knave.", "Assume James is a knight. No contradiction is found in their claim that If Sofia is a knave then Lucas is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Ella is a knave if and only if Lucas is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Lucas is a knave or Luke is a knave.", "Luke cannot be a knight, because this would contradict the claim of Ella that Lucas is a knave or Luke is a knave.", "Luke cannot be a knave, because this would contradict the claim of Lucas that James is a knave if and only if Luke is a knave.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the claim of Sofia that Ella is a knave if and only if Lucas is a knave.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Sofia.", "Sofia cannot be a knave, because this would contradict the claim of James that If Sofia is a knave then Lucas is a knave.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that If Sofia is a knave then Lucas is a knave.", "Sofia cannot be a knight, because this would contradict the false claim of James that If Sofia is a knave then Lucas is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Ella is a knave if and only if Lucas is a knave.", "Ella cannot be a knight, because this would contradict the false claim of Sofia that Ella is a knave if and only if Lucas is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Lucas is a knave or Luke is a knave.", "Luke cannot be a knight, because this would contradict the claim of Lucas that James is a knave if and only if Luke is a knave.", "Luke cannot be a knave, because this would contradict the false claim of Ella that Lucas is a knave or Luke is a knave.", "We have exhausted all possibilities for Luke, Ella, Sofia, and James, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that James is a knave if and only if Luke is a knave.", "Assume James is a knight. No contradiction is found in their claim that If Sofia is a knave then Lucas is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Ella is a knave if and only if Lucas is a knave.", "Ella cannot be a knight, because this would contradict the claim of Sofia that Ella is a knave if and only if Lucas is a knave.", "Ella cannot be a knave, because this would contradict the false claim of their own that Lucas is a knave or Luke is a knave.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Ella is a knave if and only if Lucas is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Lucas is a knave or Luke is a knave.", "Luke cannot be a knight, because this would contradict the false claim of Lucas that James is a knave if and only if Luke is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Lucas is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Luke is a knave and Luke is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Luke is a knave and Luke is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Lucas is a knave and Luke is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Lucas is a knave and Luke is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('lying', 5)), ('and', ('lying', 5), ('telling-truth', 5)), ('->', ('lying', 6), ('lying', 0)), ('or', ('lying', 0), ('lying', 5)), ('and', ('lying', 0), ('telling-truth', 5)), ('telling-truth', 0), ('<=>', ('lying', 3), ('lying', 0)))", "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 7 inhabitants: Charlotte, Evelyn, Olivia, Oliver, Riley, Aria, and Liam. Charlotte commented, \"If Olivia is a knave then Oliver is a knave\". \"Liam is a knave\" - Evelyn. Olivia noted, \"Liam is not a knight\". Oliver was heard saying, \"Oliver is a knight and Evelyn is a knight\". Riley asserted: \"Charlotte is a knave if and only if Olivia is a knave\". \"Riley is not a knave,\" Aria declared. In Liam's words: \"Liam is a knight or Riley is a knight\". So who is a knight and who is a knave?", "names": ["Charlotte", "Evelyn", "Olivia", "Oliver", "Riley", "Aria", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, false, true], "solution_text": "Charlotte is a knight, Evelyn is a knave, Olivia is a knave, Oliver is a knave, Riley is a knave, Aria is a knave, and Liam is a knight.", "solution_text_format": "(1) Charlotte is a knight\n(2) Evelyn is a knave\n(3) Olivia is a knave\n(4) Oliver is a knave\n(5) Riley is a knave\n(6) Aria is a knave\n(7) 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 Charlotte is a knight. No contradiction is found in their claim that If Olivia is a knave then Oliver is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Liam is not a knight.", "Liam cannot be a knight, because this would contradict the claim of Olivia that Liam is not a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Liam is a knight or Riley is a knight.", "Riley cannot be a knight, because this would contradict the false claim of Liam that Liam is a knight or Riley is a knight.", "Riley cannot be a knave, because this would contradict the false claim of their own that Charlotte is a knave if and only if Olivia is a knave.", "We have exhausted all possibilities for Riley and Liam, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Liam is not a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Liam is a knight or Riley is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Charlotte is a knave if and only if Olivia is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Charlotte is a knave if and only if Olivia is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Charlotte that If Olivia is a knave then Oliver is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Oliver is a knight and Evelyn is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Liam is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Liam is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Riley is not a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Riley is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 2), ('lying', 3)), ('lying', 6), ('not', ('telling-truth', 6)), ('and', ('telling-truth', 3), ('telling-truth', 1)), ('<=>', ('lying', 0), ('lying', 2)), ('not', ('lying', 4)), ('or', ('telling-truth', 6), ('telling-truth', 4)))", "index": 80}
-{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Emma, Samuel, Harper, Aria, Grace, Sophia, and Sebastian. Emma noted, \"Samuel is a knave if and only if Sophia is a knave\". \"Sophia is a knave and Grace is a knight,\" Samuel declared. According to Harper, \"Aria is a knave if and only if Sophia is a knave\". Aria noted, \"Grace is a knave if and only if Sophia is a knave\". \"Emma is a knight and Emma is a knave,\" Grace mentioned. \"Aria is a knight or Sebastian is a knight,\" Sophia declared. Sebastian asserted: \"Grace is a knave\". So who is a knight and who is a knave?", "names": ["Emma", "Samuel", "Harper", "Aria", "Grace", "Sophia", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, true, true], "solution_text": "Emma is a knave, Samuel is a knave, Harper is a knave, Aria is a knave, Grace is a knave, Sophia is a knight, and Sebastian is a knight.", "solution_text_format": "(1) Emma is a knave\n(2) Samuel is a knave\n(3) Harper is a knave\n(4) Aria is a knave\n(5) Grace is a knave\n(6) Sophia is a knight\n(7) 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 Emma is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Sophia is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Sophia is a knave and Grace is a knight.", "Sophia cannot be a knight, because this would contradict the claim of Samuel that Sophia is a knave and Grace is a knight.", "Sophia cannot be a knave, because this would contradict the claim of Emma that Samuel is a knave if and only if Sophia is a knave.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Sophia is a knave and Grace is a knight.", "Sophia cannot be a knight, because this would contradict the claim of Emma that Samuel is a knave if and only if Sophia is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Aria is a knight or Sebastian is a knight.", "Aria cannot be a knight, because this would contradict the false claim of Sophia that Aria is a knight or Sebastian is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Grace is a knave if and only if Sophia is a knave.", "Grace cannot be a knight, because this would contradict the false claim of Samuel that Sophia is a knave and Grace is a knight.", "Grace cannot be a knave, because this would contradict the false claim of Aria that Grace is a knave if and only if Sophia is a knave.", "We have exhausted all possibilities for Grace, Aria, Sophia, and 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 knave if and only if Sophia is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Sophia is a knave and Grace is a knight.", "Sophia cannot be a knight, because this would contradict the false claim of Emma that Samuel is a knave if and only if Sophia is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Aria is a knight or Sebastian is a knight.", "Aria cannot be a knight, because this would contradict the false claim of Sophia that Aria is a knight or Sebastian is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Grace is a knave if and only if Sophia is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Emma is a knight and Emma is a knave.", "Grace cannot be a knave, because this would contradict the claim of Samuel that Sophia is a knave and Grace is a knight.", "We have exhausted all possibilities for Grace, Aria, and Sophia, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Sophia is a knave and Grace is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Aria is a knight or Sebastian is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Grace is a knave if and only if Sophia is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Emma is a knight and Emma is a knave.", "Grace cannot be a knave, because this would contradict the claim of Aria that Grace is a knave if and only if Sophia is a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Grace is a knave if and only if Sophia is a knave.", "Grace cannot be a knight, because this would contradict the false claim of Aria that Grace is a knave if and only if Sophia is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Emma is a knight and Emma is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Grace is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Aria is a knave if and only if Sophia is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Aria is a knave if and only if Sophia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('lying', 5)), ('and', ('lying', 5), ('telling-truth', 4)), ('<=>', ('lying', 3), ('lying', 5)), ('<=>', ('lying', 4), ('lying', 5)), ('and', ('telling-truth', 0), ('lying', 0)), ('or', ('telling-truth', 3), ('telling-truth', 6)), ('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 7 inhabitants: Emma, Daniel, Aiden, Henry, Ella, Scarlett, and Elizabeth. \"If Aiden is a knight then Ella is a knight,\" Emma claimed. Daniel commented, \"Daniel is a knight if and only if Henry is a knight\". Aiden stated, \"If Daniel is a knight then Scarlett is a knave\". Henry asserted: \"Emma is a knave or Daniel is a knave\". Ella stated, \"If Aiden is a knave then Henry is a knave\". \"Ella is a knave if and only if Daniel is a knight,\" Scarlett declared. Elizabeth stated, \"Henry is a knight\". So who is a knight and who is a knave?", "names": ["Emma", "Daniel", "Aiden", "Henry", "Ella", "Scarlett", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true, true], "solution_text": "Emma is a knight, Daniel is a knave, Aiden is a knight, Henry is a knight, Ella is a knight, Scarlett is a knight, and Elizabeth is a knight.", "solution_text_format": "(1) Emma is a knight\n(2) Daniel is a knave\n(3) Aiden is a knight\n(4) Henry is a knight\n(5) Ella is a knight\n(6) Scarlett is a knight\n(7) 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 Emma is a knight. No contradiction is found in their claim that If Aiden is a knight then Ella is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that If Daniel is a knight then Scarlett is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Daniel is a knight if and only if Henry is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Emma is a knave or Daniel is a knave.", "Henry cannot be a knave, because this would contradict the claim of Daniel that Daniel is a knight if and only if Henry is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Daniel is a knight if and only if Henry is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Emma is a knave or Daniel is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Ella is a knave if and only if Daniel is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that If Aiden is a knave then Henry is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Henry is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('telling-truth', 4)), ('<=>', ('telling-truth', 1), ('telling-truth', 3)), ('->', ('telling-truth', 1), ('lying', 5)), ('or', ('lying', 0), ('lying', 1)), ('->', ('lying', 2), ('lying', 3)), ('<=>', ('lying', 4), ('telling-truth', 1)), ('telling-truth', 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 7 inhabitants: Aria, Avery, Penelope, Noah, Sebastian, Jacob, and Luke. In a statement by Aria: \"Avery is a knave if and only if Penelope is a knave\". Avery remarked, \"Penelope is a knight\". In a statement by Penelope: \"Jacob is not a knight\". Noah noted, \"Luke is not a knave\". In Sebastian's words: \"Noah is a knight and Luke is a knave\". Jacob noted, \"Aria is a knave if and only if Sebastian is a knight\". Luke noted, \"If Noah is a knave then Jacob is a knight\". So who is a knight and who is a knave?", "names": ["Aria", "Avery", "Penelope", "Noah", "Sebastian", "Jacob", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, true, true], "solution_text": "Aria is a knight, Avery is a knave, Penelope is a knave, Noah is a knight, Sebastian is a knave, Jacob is a knight, and Luke is a knight.", "solution_text_format": "(1) Aria is a knight\n(2) Avery is a knave\n(3) Penelope is a knave\n(4) Noah is a knight\n(5) Sebastian is a knave\n(6) Jacob is a knight\n(7) 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 Aria is a knight. No contradiction is found in their claim that Avery is a knave if and only if Penelope is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Jacob is not a knight.", "Jacob cannot be a knight, because this would contradict the claim of Penelope that Jacob is not a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Aria is a knave if and only if Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Noah is a knight and Luke is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Luke is not a knave.", "Luke cannot be a knight, because this would contradict the claim of Sebastian that Noah is a knight and Luke is a knave.", "Luke cannot be a knave, because this would contradict the claim of Noah that Luke is not a knave.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the claim of Sebastian that Noah is a knight and Luke is a knave.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the false claim of Jacob that Aria is a knave if and only if Sebastian is a knight.", "We have exhausted all possibilities for Sebastian and Jacob, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the claim of Aria that Avery is a knave if and only if Penelope is a knave.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Penelope is a knight.", "Penelope cannot be a knight, because this would contradict the claim of Aria that Avery is a knave if and only if Penelope is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Jacob is not a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Aria is a knave if and only if Sebastian is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of Jacob that Aria is a knave if and only if Sebastian is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Noah is a knight and Luke is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Luke is not a knave.", "Assume Luke is a knight. No contradiction is found in their claim that If Noah is a knave then Jacob is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('lying', 2)), ('telling-truth', 2), ('not', ('telling-truth', 5)), ('not', ('lying', 6)), ('and', ('telling-truth', 3), ('lying', 6)), ('<=>', ('lying', 0), ('telling-truth', 4)), ('->', ('lying', 3), ('telling-truth', 5)))", "index": 83}
-{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Michael, Elizabeth, Mia, Emily, Aria, Isabella, and Jacob. In a statement by Michael: \"Aria is a knight or Isabella is a knight\". In Elizabeth's words: \"Michael is a knight and Emily is a knight\". \"Aria is a knight\" - Mia. Emily expressed that Isabella is a knave. \"If Jacob is a knave then Isabella is a knight,\" Aria mentioned. \"Aria is a knight or Elizabeth is a knave,\" Isabella claimed. Jacob stated, \"If Aria is a knave then Michael is a knight\". So who is a knight and who is a knave?", "names": ["Michael", "Elizabeth", "Mia", "Emily", "Aria", "Isabella", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true, true], "solution_text": "Michael is a knight, Elizabeth is a knave, Mia is a knight, Emily is a knave, Aria is a knight, Isabella is a knight, and Jacob is a knight.", "solution_text_format": "(1) Michael is a knight\n(2) Elizabeth is a knave\n(3) Mia is a knight\n(4) Emily is a knave\n(5) Aria is a knight\n(6) Isabella is a knight\n(7) Jacob is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Aria is a knight or Isabella is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that If Jacob is a knave then Isabella is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that If Aria is a knave then Michael is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Aria is a knight or Elizabeth is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Michael is a knight and Emily is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Isabella is a knave.", "Emily cannot be a knave, because this would contradict the claim of Elizabeth that Michael is a knight and Emily is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Michael is a knight and Emily is a knight.", "Emily cannot be a knight, because this would contradict the false claim of Elizabeth that Michael is a knight and Emily is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Isabella is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Aria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('telling-truth', 5)), ('and', ('telling-truth', 0), ('telling-truth', 3)), ('telling-truth', 4), ('lying', 5), ('->', ('lying', 6), ('telling-truth', 5)), ('or', ('telling-truth', 4), ('lying', 1)), ('->', ('lying', 4), ('telling-truth', 0)))", "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 7 inhabitants: Grace, Sebastian, Noah, Aurora, Abigail, Ava, and Riley. Grace expressed that Sebastian is a knave or Grace is a knight. Sebastian noted, \"Aurora is not a knight\". Noah asserted: \"Abigail is not a knave\". Aurora asserted: \"Riley is a knave or Riley is a knight\". Abigail said that Aurora is a knight. \"Grace is not a knave,\" Ava mentioned. Riley said, \"Grace is a knave or Ava is a knight.\" So who is a knight and who is a knave?", "names": ["Grace", "Sebastian", "Noah", "Aurora", "Abigail", "Ava", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true, true], "solution_text": "Grace is a knight, Sebastian is a knave, Noah is a knight, Aurora is a knight, Abigail is a knight, Ava is a knight, and Riley is a knight.", "solution_text_format": "(1) Grace is a knight\n(2) Sebastian is a knave\n(3) Noah is a knight\n(4) Aurora is a knight\n(5) Abigail is a knight\n(6) Ava is a knight\n(7) 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 Grace is a knight. No contradiction is found in their claim that Sebastian is a knave or Grace is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Aurora is not a knight.", "Aurora cannot be a knight, because this would contradict the claim of Sebastian that Aurora is not a knight.", "Aurora cannot be a knave, because this would contradict the false claim of their own that Riley is a knave or Riley is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Aurora is not a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Riley is a knave or Riley is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Grace is a knave or Ava is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Grace is not a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Abigail is not a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Aurora is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('telling-truth', 0)), ('not', ('telling-truth', 3)), ('not', ('lying', 4)), ('or', ('lying', 6), ('telling-truth', 6)), ('telling-truth', 3), ('not', ('lying', 0)), ('or', ('lying', 0), ('telling-truth', 5)))", "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 7 inhabitants: Charlotte, Aria, Zoey, Sebastian, Abigail, Alexander, and Samuel. Charlotte noted, \"Sebastian is a knave and Abigail is a knight\". \"Alexander is a knight if and only if Sebastian is a knave,\" Aria mentioned. Zoey stated, \"Abigail is not a knight\". \"Abigail is not a knight,\" Sebastian claimed. \"Alexander is a knight if and only if Samuel is a knight,\" Abigail declared. Alexander asserted: \"Zoey is a knight or Samuel is a knave\". Samuel commented, \"Charlotte is a knave if and only if Zoey is a knave\". So who is a knight and who is a knave?", "names": ["Charlotte", "Aria", "Zoey", "Sebastian", "Abigail", "Alexander", "Samuel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, true, false], "solution_text": "Charlotte is a knave, Aria is a knave, Zoey is a knight, Sebastian is a knight, Abigail is a knave, Alexander is a knight, and Samuel is a knave.", "solution_text_format": "(1) Charlotte is a knave\n(2) Aria is a knave\n(3) Zoey is a knight\n(4) Sebastian is a knight\n(5) Abigail is a knave\n(6) Alexander is a knight\n(7) Samuel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that Sebastian is a knave and Abigail is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of Charlotte that Sebastian is a knave and Abigail is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Abigail is not a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Alexander is a knight if and only if Samuel is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Zoey is a knight or Samuel is a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that Abigail is not a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Abigail is not a knight.", "Samuel cannot be a knight, because this would contradict the claim of Alexander that Zoey is a knight or Samuel is a knave.", "Samuel cannot be a knave, because this would contradict the claim of Abigail that Alexander is a knight if and only if Samuel is a knight.", "We have exhausted all possibilities for Samuel and Zoey, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Zoey is a knight or Samuel is a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that Abigail is not a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Abigail is not a knight.", "Samuel cannot be a knight, because this would contradict the claim of Abigail that Alexander is a knight if and only if Samuel is a knight.", "Samuel cannot be a knave, because this would contradict the false claim of Alexander that Zoey is a knight or Samuel is a knave.", "We have exhausted all possibilities for Samuel, Zoey, and Alexander, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the claim of Charlotte that Sebastian is a knave and Abigail is a knight.", "We have exhausted all possibilities for Abigail and Sebastian, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Sebastian is a knave and Abigail is a knight.", "Assume Sebastian 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 Sebastian that Abigail is not a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Alexander is a knight if and only if Samuel is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Zoey is a knight or Samuel is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Abigail is not a knight.", "Samuel cannot be a knight, because this would contradict the false claim of Abigail that Alexander is a knight if and only if Samuel is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Charlotte is a knave if and only if Zoey is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Alexander is a knight if and only if Sebastian is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Alexander is a knight if and only if Sebastian is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('telling-truth', 4)), ('<=>', ('telling-truth', 5), ('lying', 3)), ('not', ('telling-truth', 4)), ('not', ('telling-truth', 4)), ('<=>', ('telling-truth', 5), ('telling-truth', 6)), ('or', ('telling-truth', 2), ('lying', 6)), ('<=>', ('lying', 0), ('lying', 2)))", "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 7 inhabitants: Emily, Alexander, Amelia, Riley, Luke, Grace, and Abigail. Emily stated, \"Emily is a knight or Abigail is a knave\". \"Riley is a knave or Amelia is a knight,\" Alexander mentioned. \"Riley is a knave,\" Amelia claimed. Riley stated, \"Emily is a knight or Amelia is a knave\". In Luke's words: \"Abigail is not a knight\". Grace remarked, \"Grace is a knight and Luke is a knight\". Abigail was heard saying, \"If Grace is a knave then Grace is a knight\". So who is a knight and who is a knave?", "names": ["Emily", "Alexander", "Amelia", "Riley", "Luke", "Grace", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false, false], "solution_text": "Emily is a knight, Alexander is a knave, Amelia is a knave, Riley is a knight, Luke is a knight, Grace is a knave, and Abigail is a knave.", "solution_text_format": "(1) Emily is a knight\n(2) Alexander is a knave\n(3) Amelia is a knave\n(4) Riley is a knight\n(5) Luke is a knight\n(6) Grace is a knave\n(7) 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 Emily is a knight. No contradiction is found in their claim that Emily is a knight or Abigail is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that If Grace is a knave then Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Grace is a knight and Luke is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Abigail is not a knight.", "Luke cannot be a knave, because this would contradict the claim of Grace that Grace is a knight and Luke is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Grace.", "Grace cannot be a knave, because this would contradict the claim of Abigail that If Grace is a knave then Grace is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that If Grace is a knave then Grace is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Abigail that If Grace is a knave then Grace is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Grace is a knight and Luke is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Abigail is not a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Riley is a knave or Amelia is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Emily is a knight or Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Riley is a knave.", "Amelia cannot be a knave, because this would contradict the claim of Alexander that Riley is a knave or Amelia is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Riley.", "Riley cannot be a knave, because this would contradict the false claim of their own that Emily is a knight or Amelia is a knave.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Riley is a knave or Amelia is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Emily is a knight or Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the false claim of Alexander that Riley is a knave or Amelia is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Riley is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 0), ('lying', 6)), ('or', ('lying', 3), ('telling-truth', 2)), ('lying', 3), ('or', ('telling-truth', 0), ('lying', 2)), ('not', ('telling-truth', 6)), ('and', ('telling-truth', 5), ('telling-truth', 4)), ('->', ('lying', 5), ('telling-truth', 5)))", "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 7 inhabitants: Abigail, David, Oliver, Victoria, Emily, Chloe, and Benjamin. Abigail remarked, \"David is a knight\". In David's words: \"David is a knight if and only if Emily is a knave\". \"Abigail is a knave,\" Oliver declared. Victoria said, \"Oliver is a knight if and only if Emily is a knave.\" Emily told you that Emily is a knight or Benjamin is a knave. Chloe asserted: \"Oliver is a knight if and only if Emily is a knave\". Benjamin expressed that Emily is a knave if and only if Abigail is a knight. So who is a knight and who is a knave?", "names": ["Abigail", "David", "Oliver", "Victoria", "Emily", "Chloe", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, false, true], "solution_text": "Abigail is a knight, David is a knight, Oliver is a knave, Victoria is a knave, Emily is a knave, Chloe is a knave, and Benjamin is a knight.", "solution_text_format": "(1) Abigail is a knight\n(2) David is a knight\n(3) Oliver is a knave\n(4) Victoria is a knave\n(5) Emily is a knave\n(6) Chloe is a knave\n(7) Benjamin is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that David is a knight.", "Assume David is a knight. No contradiction is found in their claim that David is a knight if and only if Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of David that David is a knight if and only if Emily is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Emily is a knight or Benjamin is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Emily is a knave if and only if Abigail is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Abigail is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Abigail is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that Oliver is a knight if and only if Emily is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Oliver 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 Oliver is a knight if and only if Emily is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Oliver is a knight if and only if Emily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('<=>', ('telling-truth', 1), ('lying', 4)), ('lying', 0), ('<=>', ('telling-truth', 2), ('lying', 4)), ('or', ('telling-truth', 4), ('lying', 6)), ('<=>', ('telling-truth', 2), ('lying', 4)), ('<=>', ('lying', 4), ('telling-truth', 0)))", "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 7 inhabitants: Owen, Benjamin, Evelyn, Emma, David, Joseph, and Sebastian. Owen said, \"David is a knave if and only if Sebastian is a knave.\" In Benjamin's words: \"Sebastian is a knight and Emma is a knight\". In a statement by Evelyn: \"Owen is a knight or Joseph is a knave\". \"Owen is a knight or Joseph is a knight,\" Emma declared. David told you that Sebastian is a knight if and only if Benjamin is a knight. According to Joseph, \"Owen is not a knight\". As Sebastian put it, \"If Benjamin is a knave then Joseph is a knight\". So who is a knight and who is a knave?", "names": ["Owen", "Benjamin", "Evelyn", "Emma", "David", "Joseph", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false, true], "solution_text": "Owen is a knight, Benjamin is a knight, Evelyn is a knight, Emma is a knight, David is a knight, Joseph is a knave, and Sebastian is a knight.", "solution_text_format": "(1) Owen is a knight\n(2) Benjamin is a knight\n(3) Evelyn is a knight\n(4) Emma is a knight\n(5) David is a knight\n(6) Joseph is a knave\n(7) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that David is a knave if and only if Sebastian is a knave.", "Assume David is a knight. No contradiction is found in their claim that Sebastian is a knight if and only if Benjamin is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Benjamin is a knave then Joseph is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Sebastian is a knight and Emma is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Owen is a knight or Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Owen is not a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Owen is not a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Owen is a knight or Joseph is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 4), ('lying', 6)), ('and', ('telling-truth', 6), ('telling-truth', 3)), ('or', ('telling-truth', 0), ('lying', 5)), ('or', ('telling-truth', 0), ('telling-truth', 5)), ('<=>', ('telling-truth', 6), ('telling-truth', 1)), ('not', ('telling-truth', 0)), ('->', ('lying', 1), ('telling-truth', 5)))", "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 7 inhabitants: Noah, Mason, Joseph, Liam, Logan, Mia, and Elizabeth. \"Joseph is a knight and Elizabeth is a knight,\" Noah mentioned. Mason said that Noah is a knave and Mia is a knave. Joseph expressed that Elizabeth is a knave and Logan is a knight. According to Liam, \"Mia is a knight\". Logan said that Elizabeth is a knight. Mia said that Noah is a knave if and only if Logan is a knight. According to Elizabeth, \"Liam is a knave and Mia is a knight\". So who is a knight and who is a knave?", "names": ["Noah", "Mason", "Joseph", "Liam", "Logan", "Mia", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, false, false], "solution_text": "Noah is a knave, Mason is a knight, Joseph is a knave, Liam is a knave, Logan is a knave, Mia is a knave, and Elizabeth is a knave.", "solution_text_format": "(1) Noah is a knave\n(2) Mason is a knight\n(3) Joseph is a knave\n(4) Liam is a knave\n(5) Logan is a knave\n(6) Mia is a knave\n(7) Elizabeth is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Noah is a knight. No contradiction is found in their claim that Joseph is a knight and Elizabeth is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Elizabeth is a knave and Logan is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Joseph that Elizabeth is a knave and Logan is a knight.", "Elizabeth cannot be a knave, because this would contradict the claim of Noah that Joseph is a knight and Elizabeth is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of Noah that Joseph is a knight and Elizabeth is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Joseph is a knight and Elizabeth is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Elizabeth is a knave and Logan is a knight.", "Elizabeth cannot be a knight, because this would contradict the false claim of Noah that Joseph is a knight and Elizabeth is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Liam is a knave and Mia is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Noah is a knave if and only if Logan is a knight.", "Logan cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight.", "Logan cannot be a knave, because this would contradict the claim of Joseph that Elizabeth is a knave and Logan is a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the claim of Liam that Mia is a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Mia is a knight.", "Mia cannot be a knight, because this would contradict the false claim of Liam that Mia is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Noah is a knave if and only if Logan is a knight.", "Logan cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight.", "Logan cannot be a knave, because this would contradict the claim of Joseph that Elizabeth is a knave and Logan is a knight.", "We have exhausted all possibilities for Logan, Mia, Liam, and Elizabeth, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Elizabeth is a knave and Logan is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Liam is a knave and Mia is a knight.", "Liam cannot be a knight, because this would contradict the claim of Elizabeth that Liam is a knave and Mia is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Mia is a knight.", "Mia cannot be a knight, because this would contradict the false claim of Liam that Mia is a knight.", "Mia cannot be a knave, because this would contradict the claim of Elizabeth that Liam is a knave and Mia is a knight.", "We have exhausted all possibilities for Mia and Liam, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Liam is a knave and Mia is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Noah is a knave if and only if Logan is a knight.", "Logan cannot be a knight, because this would contradict the false claim of Joseph that Elizabeth is a knave and Logan is a knight.", "Logan cannot be a knave, because this would contradict the claim of Mia that Noah is a knave if and only if Logan is a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the claim of Liam that Mia is a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Mia is a knight.", "Mia cannot be a knight, because this would contradict the false claim of Liam that Mia is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Noah is a knave if and only if Logan is a knight.", "Logan cannot be a knight, because this would contradict the false claim of Joseph that Elizabeth is a knave and Logan is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Elizabeth is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Noah is a knave and Mia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 2), ('telling-truth', 6)), ('and', ('lying', 0), ('lying', 5)), ('and', ('lying', 6), ('telling-truth', 4)), ('telling-truth', 5), ('telling-truth', 6), ('<=>', ('lying', 0), ('telling-truth', 4)), ('and', ('lying', 3), ('telling-truth', 5)))", "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 7 inhabitants: Olivia, Charlotte, Aiden, Avery, Luke, Harper, and Sofia. In Olivia's words: \"If Luke is a knight then Aiden is a knave\". Charlotte said that Sofia is a knave and Harper is a knave. In Aiden's words: \"If Sofia is a knight then Charlotte is a knight\". Avery asserted: \"Olivia is not a knight\". According to Luke, \"Harper is a knight\". Harper said that Avery is a knight or Aiden is a knight. Sofia said that Harper is a knave and Avery is a knight. So who is a knight and who is a knave?", "names": ["Olivia", "Charlotte", "Aiden", "Avery", "Luke", "Harper", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true, false], "solution_text": "Olivia is a knave, Charlotte is a knave, Aiden is a knight, Avery is a knight, Luke is a knight, Harper is a knight, and Sofia is a knave.", "solution_text_format": "(1) Olivia is a knave\n(2) Charlotte is a knave\n(3) Aiden is a knight\n(4) Avery is a knight\n(5) Luke is a knight\n(6) Harper is a knight\n(7) 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 Olivia is a knight. No contradiction is found in their claim that If Luke is a knight then Aiden is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Harper is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Avery is a knight or Aiden is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Olivia is not a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Olivia is not a knight.", "Aiden cannot be a knight, because this would contradict the claim of Olivia that If Luke is a knight then Aiden is a knave.", "Aiden cannot be a knave, because this would contradict the claim of Harper that Avery is a knight or Aiden is a knight.", "We have exhausted all possibilities for Aiden and Avery, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the claim of Luke that Harper is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Harper is a knight.", "Harper cannot be a knight, because this would contradict the false claim of Luke that Harper is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Avery is a knight or Aiden is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Olivia is not a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Olivia is not a knight.", "Aiden cannot be a knight, because this would contradict the false claim of Harper that Avery is a knight or Aiden is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that If Sofia is a knight then Charlotte is a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that Harper is a knave and Avery is a knight.", "Sofia cannot be a knave, because this would contradict the false claim of Aiden that If Sofia is a knight then Charlotte is a knight.", "We have exhausted all possibilities for Sofia, Aiden, Avery, Harper, and Luke, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that If Luke is a knight then Aiden is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Harper is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Avery is a knight or Aiden is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Olivia is not a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that If Sofia is a knight then Charlotte is a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that Harper is a knave and Avery is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Harper is a knave and Avery is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Sofia is a knave and Harper is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Sofia is a knave and Harper is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 4), ('lying', 2)), ('and', ('lying', 6), ('lying', 5)), ('->', ('telling-truth', 6), ('telling-truth', 1)), ('not', ('telling-truth', 0)), ('telling-truth', 5), ('or', ('telling-truth', 3), ('telling-truth', 2)), ('and', ('lying', 5), ('telling-truth', 3)))", "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 7 inhabitants: Abigail, Sophia, Logan, Owen, Joseph, Aiden, and Matthew. Abigail said that Matthew is a knave or Logan is a knight. Sophia stated, \"Owen is a knave if and only if Joseph is a knave\". According to Logan, \"Abigail is a knave and Matthew is a knight\". \"If Aiden is a knight then Matthew is a knight,\" Owen declared. Joseph said that Abigail is not a knight. Aiden was heard saying, \"Owen is a knave\". According to Matthew, \"Joseph is a knave if and only if Sophia is a knight\". So who is a knight and who is a knave?", "names": ["Abigail", "Sophia", "Logan", "Owen", "Joseph", "Aiden", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, false, false], "solution_text": "Abigail is a knight, Sophia is a knave, Logan is a knave, Owen is a knight, Joseph is a knave, Aiden is a knave, and Matthew is a knave.", "solution_text_format": "(1) Abigail is a knight\n(2) Sophia is a knave\n(3) Logan is a knave\n(4) Owen is a knight\n(5) Joseph is a knave\n(6) Aiden is a knave\n(7) Matthew is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Matthew is a knave or Logan is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Joseph is a knave if and only if Sophia is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Abigail is not a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Abigail is not a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Owen is a knave if and only if Joseph is a knave.", "Owen cannot be a knight, because this would contradict the claim of Sophia that Owen is a knave if and only if Joseph is a knave.", "Owen cannot be a knave, because this would contradict the false claim of their own that If Aiden is a knight then Matthew is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the claim of Matthew that Joseph is a knave if and only if Sophia is a knight.", "We have exhausted all possibilities for Sophia and Joseph, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Joseph is a knave if and only if Sophia is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Abigail is not a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Abigail is not a knight.", "Sophia cannot be a knight, because this would contradict the false claim of Matthew that Joseph is a knave if and only if Sophia is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Owen is a knave if and only if Joseph is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that If Aiden is a knight then Matthew is a knight.", "Aiden cannot be a knight, because this would contradict the claim of Owen that If Aiden is a knight then Matthew is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Owen is a knave.", "Logan cannot be a knight, because this would contradict the claim of their own that Abigail is a knave and Matthew is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Abigail is a knave and Matthew is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 6), ('telling-truth', 2)), ('<=>', ('lying', 3), ('lying', 4)), ('and', ('lying', 0), ('telling-truth', 6)), ('->', ('telling-truth', 5), ('telling-truth', 6)), ('not', ('telling-truth', 0)), ('lying', 3), ('<=>', ('lying', 4), ('telling-truth', 1)))", "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 7 inhabitants: Avery, Olivia, Liam, Jack, Penelope, Emily, and Benjamin. \"If Olivia is a knave then Emily is a knight,\" Avery mentioned. Olivia remarked, \"Liam is not a knave\". Liam commented, \"Olivia is a knight and Jack is a knight\". Jack told you that Benjamin is a knight and Liam is a knave. Penelope stated, \"Jack is not a knight\". Emily noted, \"Avery is a knave or Liam is a knave\". \"If Liam is a knave then Olivia is a knight,\" Benjamin mentioned. So who is a knight and who is a knave?", "names": ["Avery", "Olivia", "Liam", "Jack", "Penelope", "Emily", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true, false], "solution_text": "Avery is a knight, Olivia is a knave, Liam is a knave, Jack is a knave, Penelope is a knight, Emily is a knight, and Benjamin is a knave.", "solution_text_format": "(1) Avery is a knight\n(2) Olivia is a knave\n(3) Liam is a knave\n(4) Jack is a knave\n(5) Penelope is a knight\n(6) Emily is a knight\n(7) Benjamin is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that If Olivia is a knave then Emily is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Liam is not a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Olivia is a knight and Jack is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight and Liam is a knave.", "Jack cannot be a knave, because this would contradict the claim of Liam that Olivia is a knight and Jack is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the claim of Olivia that Liam is not a knave.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Liam is not a knave.", "Liam cannot be a knight, because this would contradict the false claim of Olivia that Liam is not a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Olivia is a knight and Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Benjamin is a knight and Liam is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that If Liam is a knave then Olivia is a knight.", "Benjamin cannot be a knave, because this would contradict the claim of Jack that Benjamin is a knight and Liam is a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Benjamin is a knight and Liam is a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Jack that Benjamin is a knight and Liam is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that If Liam is a knave then Olivia is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Avery is a knave or Liam is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Jack is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 1), ('telling-truth', 5)), ('not', ('lying', 2)), ('and', ('telling-truth', 1), ('telling-truth', 3)), ('and', ('telling-truth', 6), ('lying', 2)), ('not', ('telling-truth', 3)), ('or', ('lying', 0), ('lying', 2)), ('->', ('lying', 2), ('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 7 inhabitants: Luke, Lucas, Evelyn, Samuel, Chloe, Jacob, and Liam. Luke said that Chloe is a knight and Samuel is a knave. Lucas expressed that Chloe is a knave. Evelyn commented, \"Jacob is a knave or Jacob is a knight\". Samuel asserted: \"If Chloe is a knight then Evelyn is a knight\". Chloe remarked, \"Luke is a knight\". According to Jacob, \"Samuel is a knave and Samuel is a knight\". \"Chloe is a knave and Chloe is a knight,\" Liam declared. So who is a knight and who is a knave?", "names": ["Luke", "Lucas", "Evelyn", "Samuel", "Chloe", "Jacob", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false, false], "solution_text": "Luke is a knave, Lucas is a knight, Evelyn is a knight, Samuel is a knight, Chloe is a knave, Jacob is a knave, and Liam is a knave.", "solution_text_format": "(1) Luke is a knave\n(2) Lucas is a knight\n(3) Evelyn is a knight\n(4) Samuel is a knight\n(5) Chloe is a knave\n(6) Jacob is a knave\n(7) 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 Luke is a knight. No contradiction is found in their claim that Chloe is a knight and Samuel is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Luke is a knight.", "Samuel cannot be a knight, because this would contradict the claim of Luke that Chloe is a knight and Samuel is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that If Chloe is a knight then Evelyn is a knight.", "Evelyn cannot be a knight, because this would contradict the false claim of Samuel that If Chloe is a knight then Evelyn is a knight.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that Jacob is a knave or Jacob is a knight.", "We have exhausted all possibilities for Evelyn and Samuel, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the claim of Luke that Chloe is a knight and Samuel is a knave.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Chloe is a knight and Samuel is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Luke is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Luke is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that If Chloe is a knight then Evelyn is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Jacob is a knave or Jacob is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Samuel is a knave and Samuel is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Samuel is a knave and Samuel is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Chloe is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Chloe is a knave and Chloe is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Chloe is a knave and Chloe is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 4), ('lying', 3)), ('lying', 4), ('or', ('lying', 5), ('telling-truth', 5)), ('->', ('telling-truth', 4), ('telling-truth', 2)), ('telling-truth', 0), ('and', ('lying', 3), ('telling-truth', 3)), ('and', ('lying', 4), ('telling-truth', 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 7 inhabitants: Avery, Evelyn, James, Lucas, Jackson, Grace, and Emma. As Avery put it, \"Evelyn is not a knave\". Evelyn told you that Jackson is a knave if and only if Jackson is a knight. James commented, \"Avery is a knave if and only if Jackson is a knight\". Lucas commented, \"Jackson is not a knight\". Jackson was heard saying, \"Emma is a knave\". \"Emma is a knave or Avery is a knave,\" Grace mentioned. Emma remarked, \"Avery is a knave and Grace is a knight\". So who is a knight and who is a knave?", "names": ["Avery", "Evelyn", "James", "Lucas", "Jackson", "Grace", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, true, true], "solution_text": "Avery is a knave, Evelyn is a knave, James is a knave, Lucas is a knight, Jackson is a knave, Grace is a knight, and Emma is a knight.", "solution_text_format": "(1) Avery is a knave\n(2) Evelyn is a knave\n(3) James is a knave\n(4) Lucas is a knight\n(5) Jackson is a knave\n(6) Grace is a knight\n(7) 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 Avery is a knight. No contradiction is found in their claim that Evelyn is not a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Jackson is a knave if and only if Jackson is a knight.", "Evelyn cannot be a knave, because this would contradict the claim of Avery that Evelyn is not a knave.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Evelyn is not a knave.", "Evelyn cannot be a knight, because this would contradict the false claim of Avery that Evelyn is not a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Jackson is a knave if and only if Jackson is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of Jackson that Emma is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Avery is a knave and Grace is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Emma that Avery is a knave and Grace is a knight.", "Grace cannot be a knave, because this would contradict the false claim of their own that Emma is a knave or Avery is a knave.", "We have exhausted all possibilities for Grace and Emma, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Emma is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Avery is a knave and Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Emma is a knave or Avery is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Avery is a knave if and only if Jackson is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Avery is a knave if and only if Jackson is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Jackson is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('<=>', ('lying', 4), ('telling-truth', 4)), ('<=>', ('lying', 0), ('telling-truth', 4)), ('not', ('telling-truth', 4)), ('lying', 6), ('or', ('lying', 6), ('lying', 0)), ('and', ('lying', 0), ('telling-truth', 5)))", "index": 95}
-{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Benjamin, Ava, Samuel, Alexander, Amelia, Mason, and Jacob. \"Amelia is a knave,\" Benjamin claimed. According to Ava, \"Alexander is a knave if and only if Samuel is a knight\". Samuel asserted: \"If Ava is a knave then Mason is a knight\". Alexander stated, \"Samuel is not a knight\". As Amelia put it, \"Jacob is a knave and Samuel is a knave\". According to Mason, \"If Amelia is a knave then Benjamin is a knave\". \"If Mason is a knight then Samuel is a knight,\" Jacob claimed. So who is a knight and who is a knave?", "names": ["Benjamin", "Ava", "Samuel", "Alexander", "Amelia", "Mason", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false, true], "solution_text": "Benjamin is a knight, Ava is a knight, Samuel is a knight, Alexander is a knave, Amelia is a knave, Mason is a knave, and Jacob is a knight.", "solution_text_format": "(1) Benjamin is a knight\n(2) Ava is a knight\n(3) Samuel is a knight\n(4) Alexander is a knave\n(5) Amelia is a knave\n(6) Mason is a knave\n(7) Jacob is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Benjamin that Amelia is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Jacob is a knave and Samuel is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that If Mason is a knight then Samuel is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that If Amelia is a knave then Benjamin is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that If Amelia is a knave then Benjamin is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that If Ava is a knave then Mason is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Alexander is a knave if and only if Samuel is a knight.", "Alexander cannot be a knight, because this would contradict the claim of Ava that Alexander is a knave if and only if Samuel is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Samuel is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('<=>', ('lying', 3), ('telling-truth', 2)), ('->', ('lying', 1), ('telling-truth', 5)), ('not', ('telling-truth', 2)), ('and', ('lying', 6), ('lying', 2)), ('->', ('lying', 4), ('lying', 0)), ('->', ('telling-truth', 5), ('telling-truth', 2)))", "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 7 inhabitants: Sebastian, Ella, Amelia, Zoey, Samuel, Ava, and Liam. In a statement by Sebastian: \"Ella is a knave\". \"If Ava is a knave then Liam is a knave,\" Ella claimed. Amelia commented, \"Sebastian is a knight or Ella is a knave\". As Zoey put it, \"Sebastian is a knight\". Samuel remarked, \"Ava is a knave if and only if Liam is a knave\". Ava commented, \"Sebastian is a knave\". \"Sebastian is not a knight,\" Liam declared. So who is a knight and who is a knave?", "names": ["Sebastian", "Ella", "Amelia", "Zoey", "Samuel", "Ava", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true, true], "solution_text": "Sebastian is a knave, Ella is a knight, Amelia is a knave, Zoey is a knave, Samuel is a knight, Ava is a knight, and Liam is a knight.", "solution_text_format": "(1) Sebastian is a knave\n(2) Ella is a knight\n(3) Amelia is a knave\n(4) Zoey is a knave\n(5) Samuel is a knight\n(6) Ava is a knight\n(7) 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 Sebastian is a knight. No contradiction is found in their claim that Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of Sebastian that Ella is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that If Ava is a knave then Liam is a knave.", "Ava cannot be a knight, because this would contradict the false claim of Ella that If Ava is a knave then Liam is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Sebastian is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Sebastian is not a knight.", "Liam cannot be a knave, because this would contradict the false claim of Ella that If Ava is a knave then Liam is a knave.", "We have exhausted all possibilities for Liam, Ava, and Ella, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that If Ava is a knave then Liam is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Sebastian is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Sebastian is not a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight or Ella is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Sebastian is a knight or Ella is a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Sebastian is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Ava is a knave if and only if Liam is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 1), ('->', ('lying', 5), ('lying', 6)), ('or', ('telling-truth', 0), ('lying', 1)), ('telling-truth', 0), ('<=>', ('lying', 5), ('lying', 6)), ('lying', 0), ('not', ('telling-truth', 0)))", "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 7 inhabitants: Sebastian, Evelyn, William, Chloe, Mason, Joseph, and Elizabeth. As Sebastian put it, \"Joseph is a knight and William is a knave\". Evelyn said, \"Chloe is a knave or Chloe is a knight.\" \"Mason is not a knave,\" William declared. In Chloe's words: \"Sebastian is not a knight\". Mason remarked, \"Elizabeth is a knight\". Joseph expressed that Elizabeth is a knight and William is a knight. \"Mason is a knight if and only if William is a knave,\" Elizabeth declared. So who is a knight and who is a knave?", "names": ["Sebastian", "Evelyn", "William", "Chloe", "Mason", "Joseph", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, false, false], "solution_text": "Sebastian is a knave, Evelyn is a knight, William is a knave, Chloe is a knight, Mason is a knave, Joseph is a knave, and Elizabeth is a knave.", "solution_text_format": "(1) Sebastian is a knave\n(2) Evelyn is a knight\n(3) William is a knave\n(4) Chloe is a knight\n(5) Mason is a knave\n(6) Joseph is a knave\n(7) Elizabeth is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that Joseph is a knight and William is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Elizabeth is a knight and William is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Mason is a knight if and only if William is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "William cannot be a knight, because this would contradict the claim of Sebastian that Joseph is a knight and William is a knave.", "William cannot be a knave, because this would contradict the false claim of their own that Mason is not a knave.", "We have exhausted all possibilities for William, so let us go back and reconsider Mason.", "Mason cannot be a knave, because this would contradict the false claim of their own that Elizabeth is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Elizabeth.", "Elizabeth cannot be a knave, because this would contradict the claim of Joseph that Elizabeth is a knight and William is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of Sebastian that Joseph is a knight and William is a knave.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Joseph is a knight and William is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Elizabeth is a knight and William is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Mason is a knight if and only if William is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "William cannot be a knight, because this would contradict the claim of Elizabeth that Mason is a knight if and only if William is a knave.", "William cannot be a knave, because this would contradict the false claim of Sebastian that Joseph is a knight and William is a knave.", "We have exhausted all possibilities for William, so let us go back and reconsider Mason.", "Mason cannot be a knave, because this would contradict the false claim of their own that Elizabeth is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Elizabeth.", "Elizabeth cannot be a knave, because this would contradict the claim of Joseph that Elizabeth is a knight and William is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Elizabeth is a knight and William is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Mason is a knight if and only if William is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "William cannot be a knight, because this would contradict the false claim of Joseph that Elizabeth is a knight and William is a knight.", "William cannot be a knave, because this would contradict the false claim of their own that Mason is not a knave.", "We have exhausted all possibilities for William, so let us go back and reconsider Mason.", "Mason cannot be a knave, because this would contradict the false claim of their own that Elizabeth is a knight.", "We have exhausted all possibilities for Mason, 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 knight if and only if William is a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Elizabeth is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Mason is not a knave.", "Assume William is a knave. No contradiction is found in their false claim that Mason is not a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Chloe is a knave or Chloe is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Sebastian is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('lying', 2)), ('or', ('lying', 3), ('telling-truth', 3)), ('not', ('lying', 4)), ('not', ('telling-truth', 0)), ('telling-truth', 6), ('and', ('telling-truth', 6), ('telling-truth', 2)), ('<=>', ('telling-truth', 4), ('lying', 2)))", "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 7 inhabitants: Avery, Mason, Evelyn, Charlotte, Emma, Joseph, and Lucas. Avery expressed that Evelyn is not a knight. Mason remarked, \"Avery is a knave\". \"Charlotte is a knight and Mason is a knave,\" Evelyn claimed. Charlotte said, \"Mason is not a knave.\" \"Lucas is a knight or Charlotte is a knight,\" Emma mentioned. As Joseph put it, \"Emma is a knight\". Lucas remarked, \"Charlotte is a knight if and only if Charlotte is a knave\". So who is a knight and who is a knave?", "names": ["Avery", "Mason", "Evelyn", "Charlotte", "Emma", "Joseph", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, false, false], "solution_text": "Avery is a knight, Mason is a knave, Evelyn is a knave, Charlotte is a knave, Emma is a knave, Joseph is a knave, and Lucas is a knave.", "solution_text_format": "(1) Avery is a knight\n(2) Mason is a knave\n(3) Evelyn is a knave\n(4) Charlotte is a knave\n(5) Emma is a knave\n(6) Joseph is a knave\n(7) 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 Avery is a knight. No contradiction is found in their claim that Evelyn is not a knight.", "Evelyn cannot be a knight, because this would contradict the claim of Avery that Evelyn is not a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Charlotte is a knight and Mason is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Mason is not a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Avery is a knave.", "Mason cannot be a knave, because this would contradict the false claim of Evelyn that Charlotte is a knight and Mason is a knave.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Mason is not a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Avery is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Avery is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Lucas is a knight or Charlotte is a knight.", "Lucas 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.", "Lucas cannot be a knave, because this would contradict the claim of Emma that Lucas is a knight or Charlotte is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Lucas is a knight or Charlotte is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of Emma that Lucas is a knight or Charlotte is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Charlotte is a knight if and only if Charlotte is a knave.", "Joseph cannot be a knight, because this would contradict the claim of their own that Emma is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Emma is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('lying', 0), ('and', ('telling-truth', 3), ('lying', 1)), ('not', ('lying', 1)), ('or', ('telling-truth', 6), ('telling-truth', 3)), ('telling-truth', 4), ('<=>', ('telling-truth', 3), ('lying', 3)))", "index": 99}