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stringclasses 1
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listlengths 1
1
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sequencelengths 9
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stringlengths 769
1.19k
| answer
stringlengths 463
7.99k
| ability
stringclasses 1
value | reward_model
dict | extra_info
dict |
|---|---|---|---|---|---|---|---|
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Lily, Ethan, and Liam. Lily told you that Liam is a knave. \"Lily is a knave or Liam is a knight,\" Ethan mentioned. As Liam put it, \"Lily is a knight and Ethan is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Lily is a knight. ",
"No contradiction is found in their claim that Liam is a knave.\n",
"Liam cannot be a knight, because this would contradict the claim of Lily that Liam is a knave.\n",
"Assume Liam is a knave. ",
"No contradiction is found in their false claim that Lily is a knight and Ethan is a knight.\n",
"Ethan cannot be a knight, because this would contradict the claim of their own that Lily is a knave or Liam is a knight.\n",
"Assume Ethan is a knave. ",
"No contradiction is found in their false claim that Lily is a knave or Liam is a knight.\n",
"Therefore, (1) Lily is a knight\n",
"(2) Ethan is a knave\n",
"(3) Liam is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Lily, Ethan, and Liam. Lily told you that Liam is a knave. "Lily is a knave or Liam is a knight," Ethan mentioned. As Liam put it, "Lily is a knight and Ethan is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Lily 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 Lily that Liam is a knave.
Assume Liam is a knave. No contradiction is found in their false claim that Lily is a knight and Ethan is a knight.
Ethan cannot be a knight, because this would contradict the claim of their own that Lily is a knave or Liam is a knight.
Assume Ethan is a knave. No contradiction is found in their false claim that Lily is a knave or Liam is a knight.
Therefore, (1) Lily is a knight
(2) Ethan is a knave
(3) Liam is a knave </think>
<answer> (1) Lily is a knight
(2) Ethan is a knave
(3) Liam is a knave </answer> | math | {
"ground_truth": {
"names": [
"Lily",
"Ethan",
"Liam"
],
"solution": [
true,
false,
false
],
"solution_text_format": "(1) Lily is a knight\n(2) Ethan is a knave\n(3) Liam is a knave",
"statements": "(('lying', 2), ('or', ('lying', 0), ('telling-truth', 2)), ('and', ('telling-truth', 0), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 200,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Matthew, Aiden, and Oliver. \"Aiden is a knave and Aiden is a knight\" - Matthew. \"Oliver is a knave if and only if Oliver is a knight,\" Aiden claimed. Oliver was heard saying, \"Aiden is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Matthew cannot be a knight, because this would contradict the claim of their own that Aiden is a knave and Aiden is a knight.\n",
"Assume Matthew is a knave. ",
"No contradiction is found in their false claim that Aiden is a knave and Aiden is a knight.\n",
"Aiden cannot be a knight, because this would contradict the claim of their own that Oliver is a knave if and only if Oliver is a knight.\n",
"Assume Aiden is a knave. ",
"No contradiction is found in their false claim that Oliver is a knave if and only if Oliver is a knight.\n",
"Oliver cannot be a knight, because this would contradict the claim of their own that Aiden is a knight.\n",
"Assume Oliver is a knave. ",
"No contradiction is found in their false claim that Aiden is a knight.\n",
"Therefore, (1) Matthew is a knave\n",
"(2) Aiden is a knave\n",
"(3) Oliver is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Matthew, Aiden, and Oliver. "Aiden is a knave and Aiden is a knight" - Matthew. "Oliver is a knave if and only if Oliver is a knight," Aiden claimed. Oliver was heard saying, "Aiden is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Matthew cannot be a knight, because this would contradict the claim of their own that Aiden is a knave and Aiden is a knight.
Assume Matthew is a knave. No contradiction is found in their false claim that Aiden is a knave and Aiden is a knight.
Aiden cannot be a knight, because this would contradict the claim of their own that Oliver is a knave if and only if Oliver is a knight.
Assume Aiden is a knave. No contradiction is found in their false claim that Oliver is a knave if and only if Oliver is a knight.
Oliver cannot be a knight, because this would contradict the claim of their own that Aiden is a knight.
Assume Oliver is a knave. No contradiction is found in their false claim that Aiden is a knight.
Therefore, (1) Matthew is a knave
(2) Aiden is a knave
(3) Oliver is a knave </think>
<answer> (1) Matthew is a knave
(2) Aiden is a knave
(3) Oliver is a knave </answer> | math | {
"ground_truth": {
"names": [
"Matthew",
"Aiden",
"Oliver"
],
"solution": [
false,
false,
false
],
"solution_text_format": "(1) Matthew is a knave\n(2) Aiden is a knave\n(3) Oliver is a knave",
"statements": "(('and', ('lying', 1), ('telling-truth', 1)), ('<=>', ('lying', 2), ('telling-truth', 2)), ('telling-truth', 1))"
},
"style": "rule"
} | {
"index": 201,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Benjamin, Grace, and Daniel. In Benjamin's words: \"Daniel is a knave or Grace is a knave\". Grace remarked, \"Grace is a knight if and only if Daniel is a knight\". \"If Grace is a knight then Benjamin is a knight,\" Daniel claimed. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Benjamin is a knight. ",
"No contradiction is found in their claim that Daniel is a knave or Grace is a knave.\n",
"Assume Daniel is a knight. ",
"No contradiction is found in their claim that If Grace is a knight then Benjamin is a knight.\n",
"Grace cannot be a knight, because this would contradict the claim of Benjamin that Daniel is a knave or Grace is a knave.\n",
"Assume Grace is a knave. ",
"No contradiction is found in their false claim that Grace is a knight if and only if Daniel is a knight.\n",
"Therefore, (1) Benjamin is a knight\n",
"(2) Grace is a knave\n",
"(3) Daniel is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Benjamin, Grace, and Daniel. In Benjamin's words: "Daniel is a knave or Grace is a knave". Grace remarked, "Grace is a knight if and only if Daniel is a knight". "If Grace is a knight then Benjamin is a knight," Daniel claimed. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Benjamin is a knight. No contradiction is found in their claim that Daniel is a knave or Grace is a knave.
Assume Daniel is a knight. No contradiction is found in their claim that If Grace is a knight then Benjamin is a knight.
Grace cannot be a knight, because this would contradict the claim of Benjamin that Daniel is a knave or Grace is a knave.
Assume Grace is a knave. No contradiction is found in their false claim that Grace is a knight if and only if Daniel is a knight.
Therefore, (1) Benjamin is a knight
(2) Grace is a knave
(3) Daniel is a knight </think>
<answer> (1) Benjamin is a knight
(2) Grace is a knave
(3) Daniel is a knight </answer> | math | {
"ground_truth": {
"names": [
"Benjamin",
"Grace",
"Daniel"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Benjamin is a knight\n(2) Grace is a knave\n(3) Daniel is a knight",
"statements": "(('or', ('lying', 2), ('lying', 1)), ('<=>', ('telling-truth', 1), ('telling-truth', 2)), ('->', ('telling-truth', 1), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 202,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Samuel, Olivia, and Charlotte. Samuel asserted: \"If Charlotte is a knight then Samuel is a knight\". In a statement by Olivia: \"Charlotte is not a knave\". As Charlotte put it, \"If Samuel is a knave then Samuel is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Samuel is a knight. ",
"No contradiction is found in their claim that If Charlotte is a knight then Samuel is a knight.\n",
"Assume Charlotte is a knight. ",
"No contradiction is found in their claim that If Samuel is a knave then Samuel is a knight.\n",
"Assume Olivia is a knight. ",
"No contradiction is found in their claim that Charlotte is not a knave.\n",
"Therefore, (1) Samuel is a knight\n",
"(2) Olivia is a knight\n",
"(3) Charlotte is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Samuel, Olivia, and Charlotte. Samuel asserted: "If Charlotte is a knight then Samuel is a knight". In a statement by Olivia: "Charlotte is not a knave". As Charlotte put it, "If Samuel is a knave then Samuel is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Samuel is a knight. No contradiction is found in their claim that If Charlotte is a knight then Samuel is a knight.
Assume Charlotte is a knight. No contradiction is found in their claim that If Samuel is a knave then Samuel is a knight.
Assume Olivia is a knight. No contradiction is found in their claim that Charlotte is not a knave.
Therefore, (1) Samuel is a knight
(2) Olivia is a knight
(3) Charlotte is a knight </think>
<answer> (1) Samuel is a knight
(2) Olivia is a knight
(3) Charlotte is a knight </answer> | math | {
"ground_truth": {
"names": [
"Samuel",
"Olivia",
"Charlotte"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Samuel is a knight\n(2) Olivia is a knight\n(3) Charlotte is a knight",
"statements": "(('->', ('telling-truth', 2), ('telling-truth', 0)), ('not', ('lying', 2)), ('->', ('lying', 0), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 203,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Daniel, James, and Liam. According to Daniel, \"James is not a knave\". \"Daniel is a knave if and only if Liam is a knave\" - James. According to Liam, \"Daniel is a knight or James is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Daniel is a knight. ",
"No contradiction is found in their claim that James is not a knave.\n",
"Assume James is a knight. ",
"No contradiction is found in their claim that Daniel is a knave if and only if Liam is a knave.\n",
"Assume Liam is a knight. ",
"No contradiction is found in their claim that Daniel is a knight or James is a knight.\n",
"Therefore, (1) Daniel is a knight\n",
"(2) James is a knight\n",
"(3) Liam is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Daniel, James, and Liam. According to Daniel, "James is not a knave". "Daniel is a knave if and only if Liam is a knave" - James. According to Liam, "Daniel is a knight or James is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Daniel is a knight. No contradiction is found in their claim that James is not a knave.
Assume James is a knight. No contradiction is found in their claim that Daniel is a knave if and only if Liam is a knave.
Assume Liam is a knight. No contradiction is found in their claim that Daniel is a knight or James is a knight.
Therefore, (1) Daniel is a knight
(2) James is a knight
(3) Liam is a knight </think>
<answer> (1) Daniel is a knight
(2) James is a knight
(3) Liam is a knight </answer> | math | {
"ground_truth": {
"names": [
"Daniel",
"James",
"Liam"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Daniel is a knight\n(2) James is a knight\n(3) Liam is a knight",
"statements": "(('not', ('lying', 1)), ('<=>', ('lying', 0), ('lying', 2)), ('or', ('telling-truth', 0), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 204,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Victoria, Matthew, and Abigail. Victoria remarked, \"Abigail is not a knave\". Matthew expressed that If Matthew is a knight then Abigail is a knave. In a statement by Abigail: \"Victoria is a knight and Matthew is a knave\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Victoria is a knight. ",
"No contradiction is found in their claim that Abigail is not a knave.\n",
"Assume Abigail is a knight. ",
"No contradiction is found in their claim that Victoria is a knight and Matthew is a knave.\n",
"Matthew cannot be a knight, because this would contradict the claim of their own that If Matthew is a knight then Abigail is a knave.\n",
"Matthew cannot be a knave, because this would contradict the false claim of their own that If Matthew is a knight then Abigail is a knave.\n",
"We have exhausted all possibilities for Matthew, so let us go back and reconsider Abigail.\n",
"Abigail cannot be a knave, because this would contradict the claim of Victoria that Abigail is not a knave.\n",
"We have exhausted all possibilities for Abigail, so let us go back and reconsider Victoria.\n",
"Assume Victoria is a knave. ",
"No contradiction is found in their false claim that Abigail is not a knave.\n",
"Abigail cannot be a knight, because this would contradict the false claim of Victoria that Abigail is not a knave.\n",
"Assume Abigail is a knave. ",
"No contradiction is found in their false claim that Victoria is a knight and Matthew is a knave.\n",
"Assume Matthew is a knight. ",
"No contradiction is found in their claim that If Matthew is a knight then Abigail is a knave.\n",
"Therefore, (1) Victoria is a knave\n",
"(2) Matthew is a knight\n",
"(3) Abigail is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Victoria, Matthew, and Abigail. Victoria remarked, "Abigail is not a knave". Matthew expressed that If Matthew is a knight then Abigail is a knave. In a statement by Abigail: "Victoria is a knight and Matthew is a knave". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Victoria 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 Victoria is a knight and Matthew is a knave.
Matthew cannot be a knight, because this would contradict the claim of their own that If Matthew is a knight then Abigail is a knave.
Matthew cannot be a knave, because this would contradict the false claim of their own that If Matthew is a knight then Abigail is a knave.
We have exhausted all possibilities for Matthew, so let us go back and reconsider Abigail.
Abigail cannot be a knave, because this would contradict the claim of Victoria that Abigail is not a knave.
We have exhausted all possibilities for Abigail, so let us go back and reconsider Victoria.
Assume Victoria is a knave. No contradiction is found in their false claim that Abigail is not a knave.
Abigail cannot be a knight, because this would contradict the false claim of Victoria that Abigail is not a knave.
Assume Abigail is a knave. No contradiction is found in their false claim that Victoria is a knight and Matthew is a knave.
Assume Matthew is a knight. No contradiction is found in their claim that If Matthew is a knight then Abigail is a knave.
Therefore, (1) Victoria is a knave
(2) Matthew is a knight
(3) Abigail is a knave </think>
<answer> (1) Victoria is a knave
(2) Matthew is a knight
(3) Abigail is a knave </answer> | math | {
"ground_truth": {
"names": [
"Victoria",
"Matthew",
"Abigail"
],
"solution": [
false,
true,
false
],
"solution_text_format": "(1) Victoria is a knave\n(2) Matthew is a knight\n(3) Abigail is a knave",
"statements": "(('not', ('lying', 2)), ('->', ('telling-truth', 1), ('lying', 2)), ('and', ('telling-truth', 0), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 205,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Amelia, Benjamin, and Michael. Amelia said, \"Michael is a knave and Benjamin is a knave.\" \"Benjamin is a knight or Michael is a knave,\" Benjamin declared. Michael remarked, \"Amelia is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Amelia is a knight. ",
"No contradiction is found in their claim that Michael is a knave and Benjamin is a knave.\n",
"Michael cannot be a knight, because this would contradict the claim of Amelia that Michael is a knave and Benjamin is a knave.\n",
"Michael cannot be a knave, because this would contradict the false claim of their own that Amelia is a knight.\n",
"We have exhausted all possibilities for Michael, so let us go back and reconsider Amelia.\n",
"Assume Amelia is a knave. ",
"No contradiction is found in their false claim that Michael is a knave and Benjamin is a knave.\n",
"Michael cannot be a knight, because this would contradict the claim of their own that Amelia is a knight.\n",
"Assume Michael is a knave. ",
"No contradiction is found in their false claim that Amelia is a knight.\n",
"Assume Benjamin is a knight. ",
"No contradiction is found in their claim that Benjamin is a knight or Michael is a knave.\n",
"Therefore, (1) Amelia is a knave\n",
"(2) Benjamin is a knight\n",
"(3) Michael is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Amelia, Benjamin, and Michael. Amelia said, "Michael is a knave and Benjamin is a knave." "Benjamin is a knight or Michael is a knave," Benjamin declared. Michael remarked, "Amelia is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Amelia is a knight. No contradiction is found in their claim that Michael is a knave and Benjamin is a knave.
Michael cannot be a knight, because this would contradict the claim of Amelia that Michael is a knave and Benjamin is a knave.
Michael cannot be a knave, because this would contradict the false claim of their own that Amelia is a knight.
We have exhausted all possibilities for Michael, so let us go back and reconsider Amelia.
Assume Amelia is a knave. No contradiction is found in their false claim that Michael is a knave and Benjamin is a knave.
Michael cannot be a knight, because this would contradict the claim of their own that Amelia is a knight.
Assume Michael is a knave. No contradiction is found in their false claim that Amelia is a knight.
Assume Benjamin is a knight. No contradiction is found in their claim that Benjamin is a knight or Michael is a knave.
Therefore, (1) Amelia is a knave
(2) Benjamin is a knight
(3) Michael is a knave </think>
<answer> (1) Amelia is a knave
(2) Benjamin is a knight
(3) Michael is a knave </answer> | math | {
"ground_truth": {
"names": [
"Amelia",
"Benjamin",
"Michael"
],
"solution": [
false,
true,
false
],
"solution_text_format": "(1) Amelia is a knave\n(2) Benjamin is a knight\n(3) Michael is a knave",
"statements": "(('and', ('lying', 2), ('lying', 1)), ('or', ('telling-truth', 1), ('lying', 2)), ('telling-truth', 0))"
},
"style": "rule"
} | {
"index": 206,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Emma, Zoey, and Aurora. \"Zoey is a knight,\" Emma declared. \"Emma is a knight,\" Zoey mentioned. Aurora was heard saying, \"If Aurora is a knight then Emma is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Emma is a knight. ",
"No contradiction is found in their claim that Zoey is a knight.\n",
"Assume Zoey is a knight. ",
"No contradiction is found in their claim that Emma is a knight.\n",
"Assume Aurora is a knight. ",
"No contradiction is found in their claim that If Aurora is a knight then Emma is a knight.\n",
"Therefore, (1) Emma is a knight\n",
"(2) Zoey is a knight\n",
"(3) Aurora is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Emma, Zoey, and Aurora. "Zoey is a knight," Emma declared. "Emma is a knight," Zoey mentioned. Aurora was heard saying, "If Aurora is a knight then Emma is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Emma is a knight. No contradiction is found in their claim that Zoey is a knight.
Assume Zoey is a knight. No contradiction is found in their claim that Emma is a knight.
Assume Aurora is a knight. No contradiction is found in their claim that If Aurora is a knight then Emma is a knight.
Therefore, (1) Emma is a knight
(2) Zoey is a knight
(3) Aurora is a knight </think>
<answer> (1) Emma is a knight
(2) Zoey is a knight
(3) Aurora is a knight </answer> | math | {
"ground_truth": {
"names": [
"Emma",
"Zoey",
"Aurora"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Emma is a knight\n(2) Zoey is a knight\n(3) Aurora is a knight",
"statements": "(('telling-truth', 1), ('telling-truth', 0), ('->', ('telling-truth', 2), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 207,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Olivia, Aiden, and Daniel. In Olivia's words: \"If Daniel is a knight then Aiden is a knave\". Aiden remarked, \"Olivia is a knight\". \"Daniel is a knight and Aiden is a knight,\" Daniel mentioned. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Olivia is a knight. ",
"No contradiction is found in their claim that If Daniel is a knight then Aiden is a knave.\n",
"Assume Daniel is a knight. ",
"No contradiction is found in their claim that Daniel is a knight and Aiden is a knight.\n",
"Aiden cannot be a knight, because this would contradict the claim of Olivia that If Daniel is a knight then Aiden is a knave.\n",
"Aiden cannot be a knave, because this would contradict the false claim of their own that Olivia is a knight.\n",
"We have exhausted all possibilities for Aiden, so let us go back and reconsider Daniel.\n",
"Assume Daniel is a knave. ",
"No contradiction is found in their false claim that Daniel is a knight and Aiden is a knight.\n",
"Assume Aiden is a knight. ",
"No contradiction is found in their claim that Olivia is a knight.\n",
"Therefore, (1) Olivia is a knight\n",
"(2) Aiden is a knight\n",
"(3) Daniel is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Olivia, Aiden, and Daniel. In Olivia's words: "If Daniel is a knight then Aiden is a knave". Aiden remarked, "Olivia is a knight". "Daniel is a knight and Aiden is a knight," Daniel mentioned. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Olivia is a knight. No contradiction is found in their claim that If Daniel is a knight then Aiden is a knave.
Assume Daniel is a knight. No contradiction is found in their claim that Daniel is a knight and Aiden is a knight.
Aiden cannot be a knight, because this would contradict the claim of Olivia that If Daniel is a knight then Aiden is a knave.
Aiden cannot be a knave, because this would contradict the false claim of their own that Olivia is a knight.
We have exhausted all possibilities for Aiden, so let us go back and reconsider Daniel.
Assume Daniel is a knave. No contradiction is found in their false claim that Daniel is a knight and Aiden is a knight.
Assume Aiden is a knight. No contradiction is found in their claim that Olivia is a knight.
Therefore, (1) Olivia is a knight
(2) Aiden is a knight
(3) Daniel is a knave </think>
<answer> (1) Olivia is a knight
(2) Aiden is a knight
(3) Daniel is a knave </answer> | math | {
"ground_truth": {
"names": [
"Olivia",
"Aiden",
"Daniel"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Olivia is a knight\n(2) Aiden is a knight\n(3) Daniel is a knave",
"statements": "(('->', ('telling-truth', 2), ('lying', 1)), ('telling-truth', 0), ('and', ('telling-truth', 2), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 208,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Samuel, Chloe, and Victoria. As Samuel put it, \"If Victoria is a knight then Chloe is a knight\". Chloe told you that Victoria is a knight if and only if Samuel is a knave. Victoria noted, \"Chloe is a knave and Victoria is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Samuel is a knight. ",
"No contradiction is found in their claim that If Victoria is a knight then Chloe is a knight.\n",
"Assume Victoria is a knight. ",
"No contradiction is found in their claim that Chloe is a knave and Victoria is a knight.\n",
"Chloe 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 knave.\n",
"Chloe cannot be a knave, because this would contradict the claim of Samuel that If Victoria is a knight then Chloe is a knight.\n",
"We have exhausted all possibilities for Chloe, so let us go back and reconsider Victoria.\n",
"Assume Victoria is a knave. ",
"No contradiction is found in their false claim that Chloe is a knave and Victoria is a knight.\n",
"Assume Chloe is a knight. ",
"No contradiction is found in their claim that Victoria is a knight if and only if Samuel is a knave.\n",
"Therefore, (1) Samuel is a knight\n",
"(2) Chloe is a knight\n",
"(3) Victoria is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Samuel, Chloe, and Victoria. As Samuel put it, "If Victoria is a knight then Chloe is a knight". Chloe told you that Victoria is a knight if and only if Samuel is a knave. Victoria noted, "Chloe is a knave and Victoria is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Samuel is a knight. No contradiction is found in their claim that If Victoria is a knight then Chloe is a knight.
Assume Victoria is a knight. No contradiction is found in their claim that Chloe is a knave and Victoria is a knight.
Chloe 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 knave.
Chloe cannot be a knave, because this would contradict the claim of Samuel that If Victoria is a knight then Chloe is a knight.
We have exhausted all possibilities for Chloe, so let us go back and reconsider Victoria.
Assume Victoria is a knave. No contradiction is found in their false claim that Chloe is a knave and Victoria is a knight.
Assume Chloe is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Samuel is a knave.
Therefore, (1) Samuel is a knight
(2) Chloe is a knight
(3) Victoria is a knave </think>
<answer> (1) Samuel is a knight
(2) Chloe is a knight
(3) Victoria is a knave </answer> | math | {
"ground_truth": {
"names": [
"Samuel",
"Chloe",
"Victoria"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Samuel is a knight\n(2) Chloe is a knight\n(3) Victoria is a knave",
"statements": "(('->', ('telling-truth', 2), ('telling-truth', 1)), ('<=>', ('telling-truth', 2), ('lying', 0)), ('and', ('lying', 1), ('telling-truth', 2)))"
},
"style": "rule"
} | {
"index": 209,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Mia, Emily, and Aiden. Mia stated, \"If Aiden is a knave then Mia is a knight\". As Emily put it, \"Mia is not a knight\". Aiden expressed that Mia is a knave or Emily is a knight. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Mia is a knight. ",
"No contradiction is found in their claim that If Aiden is a knave then Mia is a knight.\n",
"Assume Aiden is a knight. ",
"No contradiction is found in their claim that Mia is a knave or Emily is a knight.\n",
"Emily cannot be a knight, because this would contradict the claim of their own that Mia is not a knight.\n",
"Emily cannot be a knave, because this would contradict the claim of Aiden that Mia is a knave or Emily is a knight.\n",
"We have exhausted all possibilities for Emily, so let us go back and reconsider Aiden.\n",
"Assume Aiden is a knave. ",
"No contradiction is found in their false claim that Mia is a knave or Emily is a knight.\n",
"Emily cannot be a knight, because this would contradict the claim of their own that Mia is not a knight.\n",
"Assume Emily is a knave. ",
"No contradiction is found in their false claim that Mia is not a knight.\n",
"Therefore, (1) Mia is a knight\n",
"(2) Emily is a knave\n",
"(3) Aiden is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Mia, Emily, and Aiden. Mia stated, "If Aiden is a knave then Mia is a knight". As Emily put it, "Mia is not a knight". Aiden expressed that Mia is a knave or Emily is a knight. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Mia is a knight. No contradiction is found in their claim that If Aiden is a knave then Mia is a knight.
Assume Aiden is a knight. No contradiction is found in their claim that Mia is a knave or Emily is a knight.
Emily cannot be a knight, because this would contradict the claim of their own that Mia is not a knight.
Emily cannot be a knave, because this would contradict the claim of Aiden that Mia is a knave or Emily is a knight.
We have exhausted all possibilities for Emily, so let us go back and reconsider Aiden.
Assume Aiden is a knave. No contradiction is found in their false claim that Mia is a knave or Emily is a knight.
Emily cannot be a knight, because this would contradict the claim of their own that Mia is not a knight.
Assume Emily is a knave. No contradiction is found in their false claim that Mia is not a knight.
Therefore, (1) Mia is a knight
(2) Emily is a knave
(3) Aiden is a knave </think>
<answer> (1) Mia is a knight
(2) Emily is a knave
(3) Aiden is a knave </answer> | math | {
"ground_truth": {
"names": [
"Mia",
"Emily",
"Aiden"
],
"solution": [
true,
false,
false
],
"solution_text_format": "(1) Mia is a knight\n(2) Emily is a knave\n(3) Aiden is a knave",
"statements": "(('->', ('lying', 2), ('telling-truth', 0)), ('not', ('telling-truth', 0)), ('or', ('lying', 0), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 210,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Evelyn, James, and Mason. \"If Mason is a knave then Evelyn is a knight,\" Evelyn claimed. James said that Evelyn is a knight or Mason is a knight. \"Evelyn is a knave or Evelyn is a knight\" - Mason. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Evelyn is a knight. ",
"No contradiction is found in their claim that If Mason is a knave then Evelyn is a knight.\n",
"Assume Mason is a knight. ",
"No contradiction is found in their claim that Evelyn is a knave or Evelyn is a knight.\n",
"Assume James is a knight. ",
"No contradiction is found in their claim that Evelyn is a knight or Mason is a knight.\n",
"Therefore, (1) Evelyn is a knight\n",
"(2) James is a knight\n",
"(3) Mason is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Evelyn, James, and Mason. "If Mason is a knave then Evelyn is a knight," Evelyn claimed. James said that Evelyn is a knight or Mason is a knight. "Evelyn is a knave or Evelyn is a knight" - Mason. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Evelyn is a knight. No contradiction is found in their claim that If Mason is a knave then Evelyn is a knight.
Assume Mason is a knight. No contradiction is found in their claim that Evelyn is a knave or Evelyn is a knight.
Assume James is a knight. No contradiction is found in their claim that Evelyn is a knight or Mason is a knight.
Therefore, (1) Evelyn is a knight
(2) James is a knight
(3) Mason is a knight </think>
<answer> (1) Evelyn is a knight
(2) James is a knight
(3) Mason is a knight </answer> | math | {
"ground_truth": {
"names": [
"Evelyn",
"James",
"Mason"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Evelyn is a knight\n(2) James is a knight\n(3) Mason is a knight",
"statements": "(('->', ('lying', 2), ('telling-truth', 0)), ('or', ('telling-truth', 0), ('telling-truth', 2)), ('or', ('lying', 0), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 211,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Jackson, Benjamin, and Sofia. In Jackson's words: \"Sofia is a knave\". In Benjamin's words: \"Sofia is a knave\". Sofia commented, \"Jackson is a knave if and only if Benjamin is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Jackson is a knight. ",
"No contradiction is found in their claim that Sofia is a knave.\n",
"Sofia cannot be a knight, because this would contradict the claim of Jackson that Sofia is a knave.\n",
"Assume Sofia is a knave. ",
"No contradiction is found in their false claim that Jackson is a knave if and only if Benjamin is a knight.\n",
"Assume Benjamin is a knight. ",
"No contradiction is found in their claim that Sofia is a knave.\n",
"Therefore, (1) Jackson is a knight\n",
"(2) Benjamin is a knight\n",
"(3) Sofia is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Jackson, Benjamin, and Sofia. In Jackson's words: "Sofia is a knave". In Benjamin's words: "Sofia is a knave". Sofia commented, "Jackson is a knave if and only if Benjamin is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Jackson is a knight. No contradiction is found in their claim that Sofia is a knave.
Sofia cannot be a knight, because this would contradict the claim of Jackson that Sofia is a knave.
Assume Sofia is a knave. No contradiction is found in their false claim that Jackson is a knave if and only if Benjamin is a knight.
Assume Benjamin is a knight. No contradiction is found in their claim that Sofia is a knave.
Therefore, (1) Jackson is a knight
(2) Benjamin is a knight
(3) Sofia is a knave </think>
<answer> (1) Jackson is a knight
(2) Benjamin is a knight
(3) Sofia is a knave </answer> | math | {
"ground_truth": {
"names": [
"Jackson",
"Benjamin",
"Sofia"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Jackson is a knight\n(2) Benjamin is a knight\n(3) Sofia is a knave",
"statements": "(('lying', 2), ('lying', 2), ('<=>', ('lying', 0), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 212,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Grace, Emma, and Matthew. Grace asserted: \"If Emma is a knight then Matthew is a knight\". Emma remarked, \"Matthew is a knave if and only if Emma is a knight\". Matthew was heard saying, \"If Emma is a knave then Grace is a knave\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Grace is a knight. ",
"No contradiction is found in their claim that If Emma is a knight then Matthew is a knight.\n",
"Assume Emma is a knight. ",
"No contradiction is found in their claim that Matthew is a knave if and only if Emma is a knight.\n",
"Matthew cannot be a knight, because this would contradict the claim of Emma that Matthew is a knave if and only if Emma is a knight.\n",
"Matthew cannot be a knave, because this would contradict the claim of Grace that If Emma is a knight then Matthew is a knight.\n",
"We have exhausted all possibilities for Matthew, so let us go back and reconsider Emma.\n",
"Assume Emma is a knave. ",
"No contradiction is found in their false claim that Matthew is a knave if and only if Emma is a knight.\n",
"Matthew cannot be a knight, because this would contradict the false claim of Emma that Matthew is a knave if and only if Emma is a knight.\n",
"Assume Matthew is a knave. ",
"No contradiction is found in their false claim that If Emma is a knave then Grace is a knave.\n",
"Therefore, (1) Grace is a knight\n",
"(2) Emma is a knave\n",
"(3) Matthew is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Grace, Emma, and Matthew. Grace asserted: "If Emma is a knight then Matthew is a knight". Emma remarked, "Matthew is a knave if and only if Emma is a knight". Matthew was heard saying, "If Emma is a knave then Grace is a knave". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Grace is a knight. No contradiction is found in their claim that If Emma is a knight then Matthew is a knight.
Assume Emma is a knight. No contradiction is found in their claim that Matthew is a knave if and only if Emma is a knight.
Matthew cannot be a knight, because this would contradict the claim of Emma that Matthew is a knave if and only if Emma is a knight.
Matthew cannot be a knave, because this would contradict the claim of Grace that If Emma is a knight then Matthew is a knight.
We have exhausted all possibilities for Matthew, so let us go back and reconsider Emma.
Assume Emma is a knave. No contradiction is found in their false claim that Matthew is a knave if and only if Emma is a knight.
Matthew cannot be a knight, because this would contradict the false claim of Emma that Matthew is a knave if and only if Emma is a knight.
Assume Matthew is a knave. No contradiction is found in their false claim that If Emma is a knave then Grace is a knave.
Therefore, (1) Grace is a knight
(2) Emma is a knave
(3) Matthew is a knave </think>
<answer> (1) Grace is a knight
(2) Emma is a knave
(3) Matthew is a knave </answer> | math | {
"ground_truth": {
"names": [
"Grace",
"Emma",
"Matthew"
],
"solution": [
true,
false,
false
],
"solution_text_format": "(1) Grace is a knight\n(2) Emma is a knave\n(3) Matthew is a knave",
"statements": "(('->', ('telling-truth', 1), ('telling-truth', 2)), ('<=>', ('lying', 2), ('telling-truth', 1)), ('->', ('lying', 1), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 213,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Isabella, Lily, and Joseph. \"Lily is a knave and Lily is a knight\" - Isabella. Lily said that Isabella is a knave and Joseph is a knave. Joseph said, \"If Joseph is a knight then Lily is a knave.\" So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Isabella cannot be a knight, because this would contradict the claim of their own that Lily is a knave and Lily is a knight.\n",
"Assume Isabella is a knave. ",
"No contradiction is found in their false claim that Lily is a knave and Lily is a knight.\n",
"Assume Lily is a knight. ",
"No contradiction is found in their claim that Isabella is a knave and Joseph is a knave.\n",
"Joseph cannot be a knight, because this would contradict the claim of Lily that Isabella is a knave and Joseph is a knave.\n",
"Joseph cannot be a knave, because this would contradict the false claim of their own that If Joseph is a knight then Lily is a knave.\n",
"We have exhausted all possibilities for Joseph, so let us go back and reconsider Lily.\n",
"Assume Lily is a knave. ",
"No contradiction is found in their false claim that Isabella is a knave and Joseph is a knave.\n",
"Assume Joseph is a knight. ",
"No contradiction is found in their claim that If Joseph is a knight then Lily is a knave.\n",
"Therefore, (1) Isabella is a knave\n",
"(2) Lily is a knave\n",
"(3) Joseph is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Isabella, Lily, and Joseph. "Lily is a knave and Lily is a knight" - Isabella. Lily said that Isabella is a knave and Joseph is a knave. Joseph said, "If Joseph is a knight then Lily is a knave." So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Isabella cannot be a knight, because this would contradict the claim of their own that Lily is a knave and Lily is a knight.
Assume Isabella is a knave. No contradiction is found in their false claim that Lily is a knave and Lily is a knight.
Assume Lily is a knight. No contradiction is found in their claim that Isabella is a knave and Joseph is a knave.
Joseph cannot be a knight, because this would contradict the claim of Lily that Isabella is a knave and Joseph is a knave.
Joseph cannot be a knave, because this would contradict the false claim of their own that If Joseph is a knight then Lily is a knave.
We have exhausted all possibilities for Joseph, so let us go back and reconsider Lily.
Assume Lily is a knave. No contradiction is found in their false claim that Isabella is a knave and Joseph is a knave.
Assume Joseph is a knight. No contradiction is found in their claim that If Joseph is a knight then Lily is a knave.
Therefore, (1) Isabella is a knave
(2) Lily is a knave
(3) Joseph is a knight </think>
<answer> (1) Isabella is a knave
(2) Lily is a knave
(3) Joseph is a knight </answer> | math | {
"ground_truth": {
"names": [
"Isabella",
"Lily",
"Joseph"
],
"solution": [
false,
false,
true
],
"solution_text_format": "(1) Isabella is a knave\n(2) Lily is a knave\n(3) Joseph is a knight",
"statements": "(('and', ('lying', 1), ('telling-truth', 1)), ('and', ('lying', 0), ('lying', 2)), ('->', ('telling-truth', 2), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 214,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Jack, Benjamin, and Chloe. In a statement by Jack: \"Benjamin is a knight\". Benjamin said, \"If Chloe is a knight then Benjamin is a knight.\" Chloe said that Benjamin is a knight. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Jack is a knight. ",
"No contradiction is found in their claim that Benjamin is a knight.\n",
"Assume Benjamin is a knight. ",
"No contradiction is found in their claim that If Chloe is a knight then Benjamin is a knight.\n",
"Assume Chloe is a knight. ",
"No contradiction is found in their claim that Benjamin is a knight.\n",
"Therefore, (1) Jack is a knight\n",
"(2) Benjamin is a knight\n",
"(3) Chloe is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Jack, Benjamin, and Chloe. In a statement by Jack: "Benjamin is a knight". Benjamin said, "If Chloe is a knight then Benjamin is a knight." Chloe said that Benjamin is a knight. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Jack 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 Chloe is a knight then Benjamin is a knight.
Assume Chloe is a knight. No contradiction is found in their claim that Benjamin is a knight.
Therefore, (1) Jack is a knight
(2) Benjamin is a knight
(3) Chloe is a knight </think>
<answer> (1) Jack is a knight
(2) Benjamin is a knight
(3) Chloe is a knight </answer> | math | {
"ground_truth": {
"names": [
"Jack",
"Benjamin",
"Chloe"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Jack is a knight\n(2) Benjamin is a knight\n(3) Chloe is a knight",
"statements": "(('telling-truth', 1), ('->', ('telling-truth', 2), ('telling-truth', 1)), ('telling-truth', 1))"
},
"style": "rule"
} | {
"index": 215,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Samuel, Aria, and Zoey. \"Aria is a knave,\" Samuel declared. \"If Aria is a knight then Zoey is a knight\" - Aria. In a statement by Zoey: \"Aria is a knight or Aria is a knave\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Samuel is a knight. ",
"No contradiction is found in their claim that Aria is a knave.\n",
"Aria cannot be a knight, because this would contradict the claim of Samuel that Aria is a knave.\n",
"Aria cannot be a knave, because this would contradict the false claim of their own that If Aria is a knight then Zoey is a knight.\n",
"We have exhausted all possibilities for Aria, so let us go back and reconsider Samuel.\n",
"Assume Samuel is a knave. ",
"No contradiction is found in their false claim that Aria is a knave.\n",
"Assume Aria is a knight. ",
"No contradiction is found in their claim that If Aria is a knight then Zoey is a knight.\n",
"Assume Zoey is a knight. ",
"No contradiction is found in their claim that Aria is a knight or Aria is a knave.\n",
"Therefore, (1) Samuel is a knave\n",
"(2) Aria is a knight\n",
"(3) Zoey is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Samuel, Aria, and Zoey. "Aria is a knave," Samuel declared. "If Aria is a knight then Zoey is a knight" - Aria. In a statement by Zoey: "Aria is a knight or Aria is a knave". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Samuel is a knight. No contradiction is found in their claim that Aria is a knave.
Aria cannot be a knight, because this would contradict the claim of Samuel that Aria is a knave.
Aria cannot be a knave, because this would contradict the false claim of their own that If Aria is a knight then Zoey is a knight.
We have exhausted all possibilities for Aria, so let us go back and reconsider Samuel.
Assume Samuel is a knave. No contradiction is found in their false claim that Aria is a knave.
Assume Aria is a knight. No contradiction is found in their claim that If Aria is a knight then Zoey is a knight.
Assume Zoey is a knight. No contradiction is found in their claim that Aria is a knight or Aria is a knave.
Therefore, (1) Samuel is a knave
(2) Aria is a knight
(3) Zoey is a knight </think>
<answer> (1) Samuel is a knave
(2) Aria is a knight
(3) Zoey is a knight </answer> | math | {
"ground_truth": {
"names": [
"Samuel",
"Aria",
"Zoey"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Samuel is a knave\n(2) Aria is a knight\n(3) Zoey is a knight",
"statements": "(('lying', 1), ('->', ('telling-truth', 1), ('telling-truth', 2)), ('or', ('telling-truth', 1), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 216,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Aurora, Sofia, and Zoey. Aurora said, \"Zoey is a knight if and only if Sofia is a knight.\" Sofia told you that Zoey is a knave if and only if Sofia is a knight. \"Sofia is a knave if and only if Zoey is a knight,\" Zoey mentioned. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Aurora is a knight. ",
"No contradiction is found in their claim that Zoey is a knight if and only if Sofia is a knight.\n",
"Assume Zoey is a knight. ",
"No contradiction is found in their claim that Sofia is a knave if and only if Zoey is a knight.\n",
"Sofia cannot be a knight, because this would contradict the claim of their own that Zoey is a knave if and only if Sofia is a knight.\n",
"Sofia cannot be a knave, because this would contradict the claim of Aurora that Zoey is a knight if and only if Sofia is a knight.\n",
"We have exhausted all possibilities for Sofia, so let us go back and reconsider Zoey.\n",
"Assume Zoey is a knave. ",
"No contradiction is found in their false claim that Sofia is a knave if and only if Zoey is a knight.\n",
"Sofia cannot be a knight, because this would contradict the claim of Aurora that Zoey is a knight if and only if Sofia is a knight.\n",
"Assume Sofia is a knave. ",
"No contradiction is found in their false claim that Zoey is a knave if and only if Sofia is a knight.\n",
"Therefore, (1) Aurora is a knight\n",
"(2) Sofia is a knave\n",
"(3) Zoey is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Aurora, Sofia, and Zoey. Aurora said, "Zoey is a knight if and only if Sofia is a knight." Sofia told you that Zoey is a knave if and only if Sofia is a knight. "Sofia is a knave if and only if Zoey is a knight," Zoey mentioned. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Aurora is a knight. No contradiction is found in their claim that Zoey is a knight if and only if Sofia is a knight.
Assume Zoey is a knight. No contradiction is found in their claim that Sofia is a knave if and only if Zoey is a knight.
Sofia cannot be a knight, because this would contradict the claim of their own that Zoey is a knave if and only if Sofia is a knight.
Sofia cannot be a knave, because this would contradict the claim of Aurora that Zoey is a knight if and only if Sofia is a knight.
We have exhausted all possibilities for Sofia, so let us go back and reconsider Zoey.
Assume Zoey is a knave. No contradiction is found in their false claim that Sofia is a knave if and only if Zoey is a knight.
Sofia cannot be a knight, because this would contradict the claim of Aurora that Zoey 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 Zoey is a knave if and only if Sofia is a knight.
Therefore, (1) Aurora is a knight
(2) Sofia is a knave
(3) Zoey is a knave </think>
<answer> (1) Aurora is a knight
(2) Sofia is a knave
(3) Zoey is a knave </answer> | math | {
"ground_truth": {
"names": [
"Aurora",
"Sofia",
"Zoey"
],
"solution": [
true,
false,
false
],
"solution_text_format": "(1) Aurora is a knight\n(2) Sofia is a knave\n(3) Zoey is a knave",
"statements": "(('<=>', ('telling-truth', 2), ('telling-truth', 1)), ('<=>', ('lying', 2), ('telling-truth', 1)), ('<=>', ('lying', 1), ('telling-truth', 2)))"
},
"style": "rule"
} | {
"index": 217,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Matthew, Ava, and Logan. Matthew said, \"If Matthew is a knight then Logan is a knight.\" According to Ava, \"Matthew is a knave\". \"Logan is a knight if and only if Matthew is a knight,\" Logan claimed. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Matthew is a knight. ",
"No contradiction is found in their claim that If Matthew is a knight then Logan is a knight.\n",
"Assume Logan is a knight. ",
"No contradiction is found in their claim that Logan is a knight if and only if Matthew is a knight.\n",
"Ava cannot be a knight, because this would contradict the claim of their own that Matthew is a knave.\n",
"Assume Ava is a knave. ",
"No contradiction is found in their false claim that Matthew is a knave.\n",
"Therefore, (1) Matthew is a knight\n",
"(2) Ava is a knave\n",
"(3) Logan is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Matthew, Ava, and Logan. Matthew said, "If Matthew is a knight then Logan is a knight." According to Ava, "Matthew is a knave". "Logan is a knight if and only if Matthew is a knight," Logan claimed. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Matthew is a knight. No contradiction is found in their claim that If Matthew is a knight then Logan is a knight.
Assume Logan is a knight. No contradiction is found in their claim that Logan is a knight if and only if Matthew is a knight.
Ava cannot be a knight, because this would contradict the claim of their own that Matthew is a knave.
Assume Ava is a knave. No contradiction is found in their false claim that Matthew is a knave.
Therefore, (1) Matthew is a knight
(2) Ava is a knave
(3) Logan is a knight </think>
<answer> (1) Matthew is a knight
(2) Ava is a knave
(3) Logan is a knight </answer> | math | {
"ground_truth": {
"names": [
"Matthew",
"Ava",
"Logan"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Matthew is a knight\n(2) Ava is a knave\n(3) Logan is a knight",
"statements": "(('->', ('telling-truth', 0), ('telling-truth', 2)), ('lying', 0), ('<=>', ('telling-truth', 2), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 218,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Jackson, Ethan, and Emma. Jackson expressed that Emma is a knight if and only if Ethan is a knight. In Ethan's words: \"If Jackson is a knave then Emma is a knave\". Emma said, \"Ethan is a knight and Ethan is a knave.\" So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Jackson is a knight. ",
"No contradiction is found in their claim that Emma is a knight if and only if Ethan is a knight.\n",
"Emma cannot be a knight, because this would contradict the claim of their own that Ethan is a knight and Ethan is a knave.\n",
"Assume Emma is a knave. ",
"No contradiction is found in their false claim that Ethan is a knight and Ethan is a knave.\n",
"Ethan cannot be a knight, because this would contradict the claim of Jackson that Emma is a knight if and only if Ethan is a knight.\n",
"Ethan cannot be a knave, because this would contradict the false claim of their own that If Jackson is a knave then Emma is a knave.\n",
"We have exhausted all possibilities for Ethan and Emma, so let us go back and reconsider Jackson.\n",
"Assume Jackson is a knave. ",
"No contradiction is found in their false claim that Emma is a knight if and only if Ethan is a knight.\n",
"Emma cannot be a knight, because this would contradict the claim of their own that Ethan is a knight and Ethan is a knave.\n",
"Assume Emma is a knave. ",
"No contradiction is found in their false claim that Ethan is a knight and Ethan is a knave.\n",
"Assume Ethan is a knight. ",
"No contradiction is found in their claim that If Jackson is a knave then Emma is a knave.\n",
"Therefore, (1) Jackson is a knave\n",
"(2) Ethan is a knight\n",
"(3) Emma is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Jackson, Ethan, and Emma. Jackson expressed that Emma is a knight if and only if Ethan is a knight. In Ethan's words: "If Jackson is a knave then Emma is a knave". Emma said, "Ethan is a knight and Ethan is a knave." So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Jackson is a knight. No contradiction is found in their claim that Emma is a knight if and only if Ethan is a knight.
Emma cannot be a knight, because this would contradict the claim of their own that Ethan is a knight and Ethan is a knave.
Assume Emma is a knave. No contradiction is found in their false claim that Ethan is a knight and Ethan is a knave.
Ethan cannot be a knight, because this would contradict the claim of Jackson that Emma is a knight if and only if Ethan is a knight.
Ethan cannot be a knave, because this would contradict the false claim of their own that If Jackson is a knave then Emma is a knave.
We have exhausted all possibilities for Ethan 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 knight if and only if Ethan is a knight.
Emma cannot be a knight, because this would contradict the claim of their own that Ethan is a knight and Ethan is a knave.
Assume Emma is a knave. No contradiction is found in their false claim that Ethan is a knight and Ethan is a knave.
Assume Ethan is a knight. No contradiction is found in their claim that If Jackson is a knave then Emma is a knave.
Therefore, (1) Jackson is a knave
(2) Ethan is a knight
(3) Emma is a knave </think>
<answer> (1) Jackson is a knave
(2) Ethan is a knight
(3) Emma is a knave </answer> | math | {
"ground_truth": {
"names": [
"Jackson",
"Ethan",
"Emma"
],
"solution": [
false,
true,
false
],
"solution_text_format": "(1) Jackson is a knave\n(2) Ethan is a knight\n(3) Emma is a knave",
"statements": "(('<=>', ('telling-truth', 2), ('telling-truth', 1)), ('->', ('lying', 0), ('lying', 2)), ('and', ('telling-truth', 1), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 219,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Grace, Amelia, and Zoey. Grace stated, \"Zoey is a knave\". Amelia stated, \"If Zoey is a knight then Grace is a knave\". As Zoey put it, \"Amelia is a knight or Amelia is a knave\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Grace is a knight. ",
"No contradiction is found in their claim that Zoey is a knave.\n",
"Zoey cannot be a knight, because this would contradict the claim of Grace that Zoey is a knave.\n",
"Zoey cannot be a knave, because this would contradict the false claim of their own that Amelia is a knight or Amelia is a knave.\n",
"We have exhausted all possibilities for Zoey, so let us go back and reconsider Grace.\n",
"Assume Grace is a knave. ",
"No contradiction is found in their false claim that Zoey is a knave.\n",
"Assume Zoey is a knight. ",
"No contradiction is found in their claim that Amelia is a knight or Amelia is a knave.\n",
"Assume Amelia is a knight. ",
"No contradiction is found in their claim that If Zoey is a knight then Grace is a knave.\n",
"Therefore, (1) Grace is a knave\n",
"(2) Amelia is a knight\n",
"(3) Zoey is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Grace, Amelia, and Zoey. Grace stated, "Zoey is a knave". Amelia stated, "If Zoey is a knight then Grace is a knave". As Zoey put it, "Amelia is a knight or Amelia is a knave". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Grace is a knight. No contradiction is found in their claim that Zoey is a knave.
Zoey cannot be a knight, because this would contradict the claim of Grace that Zoey is a knave.
Zoey cannot be a knave, because this would contradict the false claim of their own that Amelia is a knight or Amelia is a knave.
We have exhausted all possibilities for Zoey, so let us go back and reconsider Grace.
Assume Grace is a knave. No contradiction is found in their false claim that Zoey is a knave.
Assume Zoey is a knight. No contradiction is found in their claim that Amelia is a knight or Amelia is a knave.
Assume Amelia is a knight. No contradiction is found in their claim that If Zoey is a knight then Grace is a knave.
Therefore, (1) Grace is a knave
(2) Amelia is a knight
(3) Zoey is a knight </think>
<answer> (1) Grace is a knave
(2) Amelia is a knight
(3) Zoey is a knight </answer> | math | {
"ground_truth": {
"names": [
"Grace",
"Amelia",
"Zoey"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Grace is a knave\n(2) Amelia is a knight\n(3) Zoey is a knight",
"statements": "(('lying', 2), ('->', ('telling-truth', 2), ('lying', 0)), ('or', ('telling-truth', 1), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 220,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Chloe, David, and Sebastian. Chloe said that David is not a knight. \"Sebastian is a knave if and only if Chloe is a knight\" - David. Sebastian stated, \"Chloe is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Chloe is a knight. ",
"No contradiction is found in their claim that David is not a knight.\n",
"David cannot be a knight, because this would contradict the claim of Chloe that David is not a knight.\n",
"Assume David is a knave. ",
"No contradiction is found in their false claim that Sebastian is a knave if and only if Chloe is a knight.\n",
"Assume Sebastian is a knight. ",
"No contradiction is found in their claim that Chloe is a knight.\n",
"Therefore, (1) Chloe is a knight\n",
"(2) David is a knave\n",
"(3) Sebastian is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Chloe, David, and Sebastian. Chloe said that David is not a knight. "Sebastian is a knave if and only if Chloe is a knight" - David. Sebastian stated, "Chloe is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Chloe 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 Chloe that David is not a knight.
Assume David is a knave. No contradiction is found in their false claim that Sebastian is a knave if and only if Chloe is a knight.
Assume Sebastian is a knight. No contradiction is found in their claim that Chloe is a knight.
Therefore, (1) Chloe is a knight
(2) David is a knave
(3) Sebastian is a knight </think>
<answer> (1) Chloe is a knight
(2) David is a knave
(3) Sebastian is a knight </answer> | math | {
"ground_truth": {
"names": [
"Chloe",
"David",
"Sebastian"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Chloe is a knight\n(2) David is a knave\n(3) Sebastian is a knight",
"statements": "(('not', ('telling-truth', 1)), ('<=>', ('lying', 2), ('telling-truth', 0)), ('telling-truth', 0))"
},
"style": "rule"
} | {
"index": 221,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: James, Aiden, and Avery. James stated, \"Avery is a knight and James is a knight\". As Aiden put it, \"James is a knave\". Avery expressed that Aiden is a knight if and only if James is a knight. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume James is a knight. ",
"No contradiction is found in their claim that Avery is a knight and James is a knight.\n",
"Assume Avery is a knight. ",
"No contradiction is found in their claim that Aiden is a knight if and only if James is a knight.\n",
"Aiden cannot be a knight, because this would contradict the claim of their own that James is a knave.\n",
"Aiden cannot be a knave, because this would contradict the claim of Avery that Aiden is a knight if and only if James is a knight.\n",
"We have exhausted all possibilities for Aiden, so let us go back and reconsider Avery.\n",
"Avery cannot be a knave, because this would contradict the claim of James that Avery is a knight and James is a knight.\n",
"We have exhausted all possibilities for Avery, so let us go back and reconsider James.\n",
"Assume James is a knave. ",
"No contradiction is found in their false claim that Avery is a knight and James is a knight.\n",
"Assume Avery is a knight. ",
"No contradiction is found in their claim that Aiden is a knight if and only if James is a knight.\n",
"Aiden cannot be a knight, because this would contradict the claim of Avery that Aiden is a knight if and only if James is a knight.\n",
"Aiden cannot be a knave, because this would contradict the false claim of their own that James is a knave.\n",
"We have exhausted all possibilities for Aiden, so let us go back and reconsider Avery.\n",
"Assume Avery is a knave. ",
"No contradiction is found in their false claim that Aiden is a knight if and only if James is a knight.\n",
"Assume Aiden is a knight. ",
"No contradiction is found in their claim that James is a knave.\n",
"Therefore, (1) James is a knave\n",
"(2) Aiden is a knight\n",
"(3) Avery is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: James, Aiden, and Avery. James stated, "Avery is a knight and James is a knight". As Aiden put it, "James is a knave". Avery expressed that Aiden is a knight if and only if James is a knight. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume James is a knight. No contradiction is found in their claim that Avery is a knight and James is a knight.
Assume Avery is a knight. No contradiction is found in their claim that Aiden is a knight if and only if James is a knight.
Aiden cannot be a knight, because this would contradict the claim of their own that James is a knave.
Aiden cannot be a knave, because this would contradict the claim of Avery that Aiden is a knight if and only if James is a knight.
We have exhausted all possibilities for Aiden, so let us go back and reconsider Avery.
Avery cannot be a knave, because this would contradict the claim of James that Avery is a knight and James is a knight.
We have exhausted all possibilities for Avery, so let us go back and reconsider James.
Assume James is a knave. No contradiction is found in their false claim that Avery is a knight and James is a knight.
Assume Avery is a knight. No contradiction is found in their claim that Aiden is a knight if and only if James is a knight.
Aiden cannot be a knight, because this would contradict the claim of Avery that Aiden is a knight if and only if James is a knight.
Aiden cannot be a knave, because this would contradict the false claim of their own that James is a knave.
We have exhausted all possibilities for Aiden, so let us go back and reconsider Avery.
Assume Avery is a knave. No contradiction is found in their false claim that Aiden is a knight if and only if James is a knight.
Assume Aiden is a knight. No contradiction is found in their claim that James is a knave.
Therefore, (1) James is a knave
(2) Aiden is a knight
(3) Avery is a knave </think>
<answer> (1) James is a knave
(2) Aiden is a knight
(3) Avery is a knave </answer> | math | {
"ground_truth": {
"names": [
"James",
"Aiden",
"Avery"
],
"solution": [
false,
true,
false
],
"solution_text_format": "(1) James is a knave\n(2) Aiden is a knight\n(3) Avery is a knave",
"statements": "(('and', ('telling-truth', 2), ('telling-truth', 0)), ('lying', 0), ('<=>', ('telling-truth', 1), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 222,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Abigail, Zoey, and Isabella. Abigail asserted: \"Zoey is a knave if and only if Abigail is a knight\". Zoey remarked, \"Abigail is not a knave\". Isabella asserted: \"Zoey is a knave\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Abigail is a knight. ",
"No contradiction is found in their claim that Zoey is a knave if and only if Abigail is a knight.\n",
"Zoey cannot be a knight, because this would contradict the claim of Abigail that Zoey is a knave if and only if Abigail is a knight.\n",
"Zoey cannot be a knave, because this would contradict the false claim of their own that Abigail is not a knave.\n",
"We have exhausted all possibilities for Zoey, so let us go back and reconsider Abigail.\n",
"Assume Abigail is a knave. ",
"No contradiction is found in their false claim that Zoey is a knave if and only if Abigail is a knight.\n",
"Zoey cannot be a knight, because this would contradict the false claim of Abigail that Zoey is a knave if and only if Abigail is a knight.\n",
"Assume Zoey is a knave. ",
"No contradiction is found in their false claim that Abigail is not a knave.\n",
"Assume Isabella is a knight. ",
"No contradiction is found in their claim that Zoey is a knave.\n",
"Therefore, (1) Abigail is a knave\n",
"(2) Zoey is a knave\n",
"(3) Isabella is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Abigail, Zoey, and Isabella. Abigail asserted: "Zoey is a knave if and only if Abigail is a knight". Zoey remarked, "Abigail is not a knave". Isabella asserted: "Zoey is a knave". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Abigail is a knight. No contradiction is found in their claim that Zoey is a knave if and only if Abigail is a knight.
Zoey cannot be a knight, because this would contradict the claim of Abigail that Zoey is a knave if and only if Abigail is a knight.
Zoey cannot be a knave, because this would contradict the false claim of their own that Abigail is not a knave.
We have exhausted all possibilities for Zoey, so let us go back and reconsider Abigail.
Assume Abigail is a knave. No contradiction is found in their false claim that Zoey is a knave if and only if Abigail is a knight.
Zoey cannot be a knight, because this would contradict the false claim of Abigail that Zoey is a knave if and only if Abigail is a knight.
Assume Zoey is a knave. No contradiction is found in their false claim that Abigail is not a knave.
Assume Isabella is a knight. No contradiction is found in their claim that Zoey is a knave.
Therefore, (1) Abigail is a knave
(2) Zoey is a knave
(3) Isabella is a knight </think>
<answer> (1) Abigail is a knave
(2) Zoey is a knave
(3) Isabella is a knight </answer> | math | {
"ground_truth": {
"names": [
"Abigail",
"Zoey",
"Isabella"
],
"solution": [
false,
false,
true
],
"solution_text_format": "(1) Abigail is a knave\n(2) Zoey is a knave\n(3) Isabella is a knight",
"statements": "(('<=>', ('lying', 1), ('telling-truth', 0)), ('not', ('lying', 0)), ('lying', 1))"
},
"style": "rule"
} | {
"index": 223,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Emily, Amelia, and Michael. Emily noted, \"Amelia is a knight\". Amelia expressed that Emily is a knave or Emily is a knight. Michael was heard saying, \"Emily is a knave or Emily is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Emily is a knight. ",
"No contradiction is found in their claim that Amelia is a knight.\n",
"Assume Amelia is a knight. ",
"No contradiction is found in their claim that Emily is a knave or Emily is a knight.\n",
"Assume Michael is a knight. ",
"No contradiction is found in their claim that Emily is a knave or Emily is a knight.\n",
"Therefore, (1) Emily is a knight\n",
"(2) Amelia is a knight\n",
"(3) Michael is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Emily, Amelia, and Michael. Emily noted, "Amelia is a knight". Amelia expressed that Emily is a knave or Emily is a knight. Michael was heard saying, "Emily is a knave or Emily is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Emily is a knight. No contradiction is found in their claim that Amelia is a knight.
Assume Amelia is a knight. No contradiction is found in their claim that Emily is a knave or Emily is a knight.
Assume Michael is a knight. No contradiction is found in their claim that Emily is a knave or Emily is a knight.
Therefore, (1) Emily is a knight
(2) Amelia is a knight
(3) Michael is a knight </think>
<answer> (1) Emily is a knight
(2) Amelia is a knight
(3) Michael is a knight </answer> | math | {
"ground_truth": {
"names": [
"Emily",
"Amelia",
"Michael"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Emily is a knight\n(2) Amelia is a knight\n(3) Michael is a knight",
"statements": "(('telling-truth', 1), ('or', ('lying', 0), ('telling-truth', 0)), ('or', ('lying', 0), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 224,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Grace, Amelia, and Lucas. Grace told you that Lucas is a knight or Amelia is a knave. Amelia told you that Grace is a knave or Lucas is a knave. According to Lucas, \"Amelia is a knight or Lucas is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Grace is a knight. ",
"No contradiction is found in their claim that Lucas is a knight or Amelia is a knave.\n",
"Assume Lucas is a knight. ",
"No contradiction is found in their claim that Amelia is a knight or Lucas is a knight.\n",
"Amelia cannot be a knight, because this would contradict the claim of their own that Grace is a knave or Lucas is a knave.\n",
"Assume Amelia is a knave. ",
"No contradiction is found in their false claim that Grace is a knave or Lucas is a knave.\n",
"Therefore, (1) Grace is a knight\n",
"(2) Amelia is a knave\n",
"(3) Lucas is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Grace, Amelia, and Lucas. Grace told you that Lucas is a knight or Amelia is a knave. Amelia told you that Grace is a knave or Lucas is a knave. According to Lucas, "Amelia is a knight or Lucas is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Grace is a knight. No contradiction is found in their claim that Lucas is a knight or Amelia is a knave.
Assume Lucas is a knight. No contradiction is found in their claim that Amelia is a knight or Lucas is a knight.
Amelia cannot be a knight, because this would contradict the claim of their own that Grace is a knave or Lucas is a knave.
Assume Amelia is a knave. No contradiction is found in their false claim that Grace is a knave or Lucas is a knave.
Therefore, (1) Grace is a knight
(2) Amelia is a knave
(3) Lucas is a knight </think>
<answer> (1) Grace is a knight
(2) Amelia is a knave
(3) Lucas is a knight </answer> | math | {
"ground_truth": {
"names": [
"Grace",
"Amelia",
"Lucas"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Grace is a knight\n(2) Amelia is a knave\n(3) Lucas is a knight",
"statements": "(('or', ('telling-truth', 2), ('lying', 1)), ('or', ('lying', 0), ('lying', 2)), ('or', ('telling-truth', 1), ('telling-truth', 2)))"
},
"style": "rule"
} | {
"index": 225,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Scarlett, Matthew, and Evelyn. Scarlett stated, \"Matthew is not a knight\". \"Evelyn is a knight or Scarlett is a knave,\" Matthew declared. Evelyn expressed that Matthew is a knave. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Scarlett is a knight. ",
"No contradiction is found in their claim that Matthew is not a knight.\n",
"Matthew cannot be a knight, because this would contradict the claim of Scarlett that Matthew is not a knight.\n",
"Assume Matthew is a knave. ",
"No contradiction is found in their false claim that Evelyn is a knight or Scarlett is a knave.\n",
"Evelyn cannot be a knight, because this would contradict the false claim of Matthew that Evelyn is a knight or Scarlett is a knave.\n",
"Evelyn cannot be a knave, because this would contradict the false claim of their own that Matthew is a knave.\n",
"We have exhausted all possibilities for Evelyn and Matthew, so let us go back and reconsider Scarlett.\n",
"Assume Scarlett is a knave. ",
"No contradiction is found in their false claim that Matthew is not a knight.\n",
"Assume Matthew is a knight. ",
"No contradiction is found in their claim that Evelyn is a knight or Scarlett is a knave.\n",
"Evelyn cannot be a knight, because this would contradict the claim of their own that Matthew is a knave.\n",
"Assume Evelyn is a knave. ",
"No contradiction is found in their false claim that Matthew is a knave.\n",
"Therefore, (1) Scarlett is a knave\n",
"(2) Matthew is a knight\n",
"(3) Evelyn is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Scarlett, Matthew, and Evelyn. Scarlett stated, "Matthew is not a knight". "Evelyn is a knight or Scarlett is a knave," Matthew declared. Evelyn expressed that Matthew is a knave. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Scarlett 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 Scarlett that Matthew is not a knight.
Assume Matthew is a knave. No contradiction is found in their false claim that Evelyn is a knight or Scarlett is a knave.
Evelyn cannot be a knight, because this would contradict the false claim of Matthew that Evelyn is a knight or Scarlett is a knave.
Evelyn cannot be a knave, because this would contradict the false claim of their own that Matthew is a knave.
We have exhausted all possibilities for Evelyn and Matthew, so let us go back and reconsider Scarlett.
Assume Scarlett is a knave. No contradiction is found in their false claim that Matthew is not a knight.
Assume Matthew is a knight. No contradiction is found in their claim that Evelyn is a knight or Scarlett is a knave.
Evelyn cannot be a knight, because this would contradict the claim of their own that Matthew is a knave.
Assume Evelyn is a knave. No contradiction is found in their false claim that Matthew is a knave.
Therefore, (1) Scarlett is a knave
(2) Matthew is a knight
(3) Evelyn is a knave </think>
<answer> (1) Scarlett is a knave
(2) Matthew is a knight
(3) Evelyn is a knave </answer> | math | {
"ground_truth": {
"names": [
"Scarlett",
"Matthew",
"Evelyn"
],
"solution": [
false,
true,
false
],
"solution_text_format": "(1) Scarlett is a knave\n(2) Matthew is a knight\n(3) Evelyn is a knave",
"statements": "(('not', ('telling-truth', 1)), ('or', ('telling-truth', 2), ('lying', 0)), ('lying', 1))"
},
"style": "rule"
} | {
"index": 226,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Victoria, Daniel, and Mia. Victoria asserted: \"Mia is a knight and Mia is a knave\". Daniel was heard saying, \"Mia is not a knight\". \"Victoria is a knave,\" Mia declared. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Victoria cannot be a knight, because this would contradict the claim of their own that Mia is a knight and Mia is a knave.\n",
"Assume Victoria is a knave. ",
"No contradiction is found in their false claim that Mia is a knight and Mia is a knave.\n",
"Assume Mia is a knight. ",
"No contradiction is found in their claim that Victoria is a knave.\n",
"Daniel cannot be a knight, because this would contradict the claim of their own that Mia is not a knight.\n",
"Assume Daniel is a knave. ",
"No contradiction is found in their false claim that Mia is not a knight.\n",
"Therefore, (1) Victoria is a knave\n",
"(2) Daniel is a knave\n",
"(3) Mia is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Victoria, Daniel, and Mia. Victoria asserted: "Mia is a knight and Mia is a knave". Daniel was heard saying, "Mia is not a knight". "Victoria is a knave," Mia declared. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Victoria cannot be a knight, because this would contradict the claim of their own that Mia is a knight and Mia is a knave.
Assume Victoria is a knave. No contradiction is found in their false claim that Mia is a knight and Mia is a knave.
Assume Mia is a knight. No contradiction is found in their claim that Victoria is a knave.
Daniel cannot be a knight, because this would contradict the claim of their own that Mia is not a knight.
Assume Daniel is a knave. No contradiction is found in their false claim that Mia is not a knight.
Therefore, (1) Victoria is a knave
(2) Daniel is a knave
(3) Mia is a knight </think>
<answer> (1) Victoria is a knave
(2) Daniel is a knave
(3) Mia is a knight </answer> | math | {
"ground_truth": {
"names": [
"Victoria",
"Daniel",
"Mia"
],
"solution": [
false,
false,
true
],
"solution_text_format": "(1) Victoria is a knave\n(2) Daniel is a knave\n(3) Mia is a knight",
"statements": "(('and', ('telling-truth', 2), ('lying', 2)), ('not', ('telling-truth', 2)), ('lying', 0))"
},
"style": "rule"
} | {
"index": 227,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Alexander, Noah, and Ava. According to Alexander, \"Alexander is a knight and Noah is a knight\". Noah said, \"Alexander is a knave.\" \"Alexander is a knight if and only if Alexander is a knave\" - Ava. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Alexander is a knight. ",
"No contradiction is found in their claim that Alexander is a knight and Noah is a knight.\n",
"Noah cannot be a knight, because this would contradict the claim of their own that Alexander is a knave.\n",
"Noah cannot be a knave, because this would contradict the claim of Alexander that Alexander is a knight and Noah is a knight.\n",
"We have exhausted all possibilities for Noah, so let us go back and reconsider Alexander.\n",
"Assume Alexander is a knave. ",
"No contradiction is found in their false claim that Alexander is a knight and Noah is a knight.\n",
"Assume Noah is a knight. ",
"No contradiction is found in their claim that Alexander is a knave.\n",
"Ava cannot be a knight, because this would contradict the claim of their own that Alexander is a knight if and only if Alexander is a knave.\n",
"Assume Ava is a knave. ",
"No contradiction is found in their false claim that Alexander is a knight if and only if Alexander is a knave.\n",
"Therefore, (1) Alexander is a knave\n",
"(2) Noah is a knight\n",
"(3) Ava is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Alexander, Noah, and Ava. According to Alexander, "Alexander is a knight and Noah is a knight". Noah said, "Alexander is a knave." "Alexander is a knight if and only if Alexander is a knave" - Ava. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Alexander is a knight. No contradiction is found in their claim that Alexander is a knight and Noah is a knight.
Noah cannot be a knight, because this would contradict the claim of their own that Alexander is a knave.
Noah cannot be a knave, because this would contradict the claim of Alexander that Alexander is a knight and Noah is a knight.
We have exhausted all possibilities for Noah, so let us go back and reconsider Alexander.
Assume Alexander is a knave. No contradiction is found in their false claim that Alexander is a knight and Noah is a knight.
Assume Noah is a knight. No contradiction is found in their claim that Alexander is a knave.
Ava cannot be a knight, because this would contradict the claim of their own that Alexander is a knight if and only if Alexander is a knave.
Assume Ava is a knave. No contradiction is found in their false claim that Alexander is a knight if and only if Alexander is a knave.
Therefore, (1) Alexander is a knave
(2) Noah is a knight
(3) Ava is a knave </think>
<answer> (1) Alexander is a knave
(2) Noah is a knight
(3) Ava is a knave </answer> | math | {
"ground_truth": {
"names": [
"Alexander",
"Noah",
"Ava"
],
"solution": [
false,
true,
false
],
"solution_text_format": "(1) Alexander is a knave\n(2) Noah is a knight\n(3) Ava is a knave",
"statements": "(('and', ('telling-truth', 0), ('telling-truth', 1)), ('lying', 0), ('<=>', ('telling-truth', 0), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 228,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Aria, Evelyn, and Logan. According to Aria, \"Aria is a knight and Evelyn is a knave\". Evelyn said that If Evelyn is a knight then Logan is a knight. According to Logan, \"Logan is a knight or Evelyn is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Aria is a knight. ",
"No contradiction is found in their claim that Aria is a knight and Evelyn is a knave.\n",
"Evelyn cannot be a knight, because this would contradict the claim of Aria that Aria is a knight and Evelyn is a knave.\n",
"Evelyn cannot be a knave, because this would contradict the false claim of their own that If Evelyn is a knight then Logan is a knight.\n",
"We have exhausted all possibilities for Evelyn, so let us go back and reconsider Aria.\n",
"Assume Aria is a knave. ",
"No contradiction is found in their false claim that Aria is a knight and Evelyn is a knave.\n",
"Assume Evelyn is a knight. ",
"No contradiction is found in their claim that If Evelyn is a knight then Logan is a knight.\n",
"Assume Logan is a knight. ",
"No contradiction is found in their claim that Logan is a knight or Evelyn is a knight.\n",
"Therefore, (1) Aria is a knave\n",
"(2) Evelyn is a knight\n",
"(3) Logan is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Aria, Evelyn, and Logan. According to Aria, "Aria is a knight and Evelyn is a knave". Evelyn said that If Evelyn is a knight then Logan is a knight. According to Logan, "Logan is a knight or Evelyn is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Aria is a knight. No contradiction is found in their claim that Aria is a knight and Evelyn is a knave.
Evelyn cannot be a knight, because this would contradict the claim of Aria that Aria is a knight and Evelyn is a knave.
Evelyn cannot be a knave, because this would contradict the false claim of their own that If Evelyn is a knight then Logan is a knight.
We have exhausted all possibilities for Evelyn, so let us go back and reconsider Aria.
Assume Aria is a knave. No contradiction is found in their false claim that Aria is a knight and Evelyn is a knave.
Assume Evelyn is a knight. No contradiction is found in their claim that If Evelyn is a knight then Logan is a knight.
Assume Logan is a knight. No contradiction is found in their claim that Logan is a knight or Evelyn is a knight.
Therefore, (1) Aria is a knave
(2) Evelyn is a knight
(3) Logan is a knight </think>
<answer> (1) Aria is a knave
(2) Evelyn is a knight
(3) Logan is a knight </answer> | math | {
"ground_truth": {
"names": [
"Aria",
"Evelyn",
"Logan"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Aria is a knave\n(2) Evelyn is a knight\n(3) Logan is a knight",
"statements": "(('and', ('telling-truth', 0), ('lying', 1)), ('->', ('telling-truth', 1), ('telling-truth', 2)), ('or', ('telling-truth', 2), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 229,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Joseph, Benjamin, and Isabella. Joseph remarked, \"Isabella is a knight if and only if Benjamin is a knight\". \"Isabella is a knave or Joseph is a knave\" - Benjamin. Isabella asserted: \"If Joseph is a knave then Isabella is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Joseph is a knight. ",
"No contradiction is found in their claim that Isabella is a knight if and only if Benjamin is a knight.\n",
"Assume Isabella is a knight. ",
"No contradiction is found in their claim that If Joseph is a knave then Isabella is a knight.\n",
"Benjamin cannot be a knight, because this would contradict the claim of their own that Isabella is a knave or Joseph is a knave.\n",
"Benjamin cannot be a knave, because this would contradict the claim of Joseph that Isabella is a knight if and only if Benjamin is a knight.\n",
"We have exhausted all possibilities for Benjamin, so let us go back and reconsider Isabella.\n",
"Isabella cannot be a knave, because this would contradict the false claim of their own that If Joseph is a knave then Isabella is a knight.\n",
"We have exhausted all possibilities for Isabella, so let us go back and reconsider Joseph.\n",
"Assume Joseph is a knave. ",
"No contradiction is found in their false claim that Isabella is a knight if and only if Benjamin is a knight.\n",
"Assume Isabella is a knight. ",
"No contradiction is found in their claim that If Joseph is a knave then Isabella is a knight.\n",
"Benjamin cannot be a knight, because this would contradict the false claim of Joseph that Isabella is a knight if and only if Benjamin is a knight.\n",
"Benjamin cannot be a knave, because this would contradict the false claim of their own that Isabella is a knave or Joseph is a knave.\n",
"We have exhausted all possibilities for Benjamin, so let us go back and reconsider Isabella.\n",
"Assume Isabella is a knave. ",
"No contradiction is found in their false claim that If Joseph is a knave then Isabella is a knight.\n",
"Assume Benjamin is a knight. ",
"No contradiction is found in their claim that Isabella is a knave or Joseph is a knave.\n",
"Therefore, (1) Joseph is a knave\n",
"(2) Benjamin is a knight\n",
"(3) Isabella is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Joseph, Benjamin, and Isabella. Joseph remarked, "Isabella is a knight if and only if Benjamin is a knight". "Isabella is a knave or Joseph is a knave" - Benjamin. Isabella asserted: "If Joseph is a knave then Isabella is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Joseph is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Benjamin is a knight.
Assume Isabella is a knight. No contradiction is found in their claim that If Joseph is a knave then Isabella is a knight.
Benjamin cannot be a knight, because this would contradict the claim of their own that Isabella is a knave or Joseph is a knave.
Benjamin cannot be a knave, because this would contradict the claim of Joseph that Isabella is a knight if and only if Benjamin is a knight.
We have exhausted all possibilities for Benjamin, so let us go back and reconsider Isabella.
Isabella cannot be a knave, because this would contradict the false claim of their own that If Joseph is a knave then Isabella is a knight.
We have exhausted all possibilities for Isabella, so let us go back and reconsider Joseph.
Assume Joseph is a knave. No contradiction is found in their false claim that Isabella is a knight if and only if Benjamin is a knight.
Assume Isabella is a knight. No contradiction is found in their claim that If Joseph is a knave then Isabella is a knight.
Benjamin cannot be a knight, because this would contradict the false claim of Joseph that Isabella is a knight if and only if Benjamin is a knight.
Benjamin cannot be a knave, because this would contradict the false claim of their own that Isabella is a knave or Joseph is a knave.
We have exhausted all possibilities for Benjamin, so let us go back and reconsider Isabella.
Assume Isabella is a knave. No contradiction is found in their false claim that If Joseph is a knave then Isabella is a knight.
Assume Benjamin is a knight. No contradiction is found in their claim that Isabella is a knave or Joseph is a knave.
Therefore, (1) Joseph is a knave
(2) Benjamin is a knight
(3) Isabella is a knave </think>
<answer> (1) Joseph is a knave
(2) Benjamin is a knight
(3) Isabella is a knave </answer> | math | {
"ground_truth": {
"names": [
"Joseph",
"Benjamin",
"Isabella"
],
"solution": [
false,
true,
false
],
"solution_text_format": "(1) Joseph is a knave\n(2) Benjamin is a knight\n(3) Isabella is a knave",
"statements": "(('<=>', ('telling-truth', 2), ('telling-truth', 1)), ('or', ('lying', 2), ('lying', 0)), ('->', ('lying', 0), ('telling-truth', 2)))"
},
"style": "rule"
} | {
"index": 230,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Emily, Mia, and Victoria. Emily was heard saying, \"Mia is a knave\". In a statement by Mia: \"Victoria is a knight if and only if Mia is a knight\". As Victoria put it, \"If Emily is a knave then Mia is a knave\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Emily is a knight. ",
"No contradiction is found in their claim that Mia is a knave.\n",
"Mia cannot be a knight, because this would contradict the claim of Emily that Mia is a knave.\n",
"Assume Mia is a knave. ",
"No contradiction is found in their false claim that Victoria is a knight if and only if Mia is a knight.\n",
"Assume Victoria is a knight. ",
"No contradiction is found in their claim that If Emily is a knave then Mia is a knave.\n",
"Therefore, (1) Emily is a knight\n",
"(2) Mia is a knave\n",
"(3) Victoria is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Emily, Mia, and Victoria. Emily was heard saying, "Mia is a knave". In a statement by Mia: "Victoria is a knight if and only if Mia is a knight". As Victoria put it, "If Emily is a knave then Mia is a knave". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Emily is a knight. No contradiction is found in their claim that Mia is a knave.
Mia cannot be a knight, because this would contradict the claim of Emily that Mia is a knave.
Assume Mia is a knave. No contradiction is found in their false claim that Victoria is a knight if and only if Mia is a knight.
Assume Victoria is a knight. No contradiction is found in their claim that If Emily is a knave then Mia is a knave.
Therefore, (1) Emily is a knight
(2) Mia is a knave
(3) Victoria is a knight </think>
<answer> (1) Emily is a knight
(2) Mia is a knave
(3) Victoria is a knight </answer> | math | {
"ground_truth": {
"names": [
"Emily",
"Mia",
"Victoria"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Emily is a knight\n(2) Mia is a knave\n(3) Victoria is a knight",
"statements": "(('lying', 1), ('<=>', ('telling-truth', 2), ('telling-truth', 1)), ('->', ('lying', 0), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 231,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Daniel, Isabella, and Samuel. In Daniel's words: \"Isabella is not a knave\". \"Isabella is a knight or Daniel is a knave,\" Isabella mentioned. \"Isabella is a knave if and only if Daniel is a knight\" - Samuel. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Daniel is a knight. ",
"No contradiction is found in their claim that Isabella is not a knave.\n",
"Assume Isabella is a knight. ",
"No contradiction is found in their claim that Isabella is a knight or Daniel is a knave.\n",
"Samuel cannot be a knight, because this would contradict the claim of their own that Isabella is a knave if and only if Daniel is a knight.\n",
"Assume Samuel is a knave. ",
"No contradiction is found in their false claim that Isabella is a knave if and only if Daniel is a knight.\n",
"Therefore, (1) Daniel is a knight\n",
"(2) Isabella is a knight\n",
"(3) Samuel is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Daniel, Isabella, and Samuel. In Daniel's words: "Isabella is not a knave". "Isabella is a knight or Daniel is a knave," Isabella mentioned. "Isabella is a knave if and only if Daniel is a knight" - Samuel. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Daniel 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 Isabella is a knight or Daniel is a knave.
Samuel cannot be a knight, because this would contradict the claim of their own that Isabella is a knave if and only if Daniel is a knight.
Assume Samuel is a knave. No contradiction is found in their false claim that Isabella is a knave if and only if Daniel is a knight.
Therefore, (1) Daniel is a knight
(2) Isabella is a knight
(3) Samuel is a knave </think>
<answer> (1) Daniel is a knight
(2) Isabella is a knight
(3) Samuel is a knave </answer> | math | {
"ground_truth": {
"names": [
"Daniel",
"Isabella",
"Samuel"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Daniel is a knight\n(2) Isabella is a knight\n(3) Samuel is a knave",
"statements": "(('not', ('lying', 1)), ('or', ('telling-truth', 1), ('lying', 0)), ('<=>', ('lying', 1), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 232,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Jacob, Sophia, and Aiden. \"Sophia is a knight if and only if Sophia is a knave,\" Jacob declared. Sophia expressed that Jacob is not a knight. Aiden stated, \"Jacob is a knave\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Jacob cannot be a knight, because this would contradict the claim of their own that Sophia is a knight if and only if Sophia is a knave.\n",
"Assume Jacob is a knave. ",
"No contradiction is found in their false claim that Sophia is a knight if and only if Sophia is a knave.\n",
"Assume Sophia is a knight. ",
"No contradiction is found in their claim that Jacob is not a knight.\n",
"Assume Aiden is a knight. ",
"No contradiction is found in their claim that Jacob is a knave.\n",
"Therefore, (1) Jacob is a knave\n",
"(2) Sophia is a knight\n",
"(3) Aiden is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Jacob, Sophia, and Aiden. "Sophia is a knight if and only if Sophia is a knave," Jacob declared. Sophia expressed that Jacob is not a knight. Aiden stated, "Jacob is a knave". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Jacob cannot be a knight, because this would contradict the claim of their own that Sophia is a knight if and only if Sophia is a knave.
Assume Jacob is a knave. No contradiction is found in their false claim that Sophia is a knight if and only if Sophia is a knave.
Assume Sophia is a knight. No contradiction is found in their claim that Jacob is not a knight.
Assume Aiden is a knight. No contradiction is found in their claim that Jacob is a knave.
Therefore, (1) Jacob is a knave
(2) Sophia is a knight
(3) Aiden is a knight </think>
<answer> (1) Jacob is a knave
(2) Sophia is a knight
(3) Aiden is a knight </answer> | math | {
"ground_truth": {
"names": [
"Jacob",
"Sophia",
"Aiden"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Jacob is a knave\n(2) Sophia is a knight\n(3) Aiden is a knight",
"statements": "(('<=>', ('telling-truth', 1), ('lying', 1)), ('not', ('telling-truth', 0)), ('lying', 0))"
},
"style": "rule"
} | {
"index": 233,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Elizabeth, Henry, and Charlotte. \"Henry is a knight if and only if Elizabeth is a knight,\" Elizabeth declared. Henry asserted: \"If Elizabeth is a knight then Elizabeth is a knave\". Charlotte asserted: \"Henry is a knight or Elizabeth is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Elizabeth is a knight. ",
"No contradiction is found in their claim that Henry is a knight if and only if Elizabeth is a knight.\n",
"Henry cannot be a knight, because this would contradict the claim of their own that If Elizabeth is a knight then Elizabeth is a knave.\n",
"Henry cannot be a knave, because this would contradict the claim of Elizabeth that Henry is a knight if and only if Elizabeth is a knight.\n",
"We have exhausted all possibilities for Henry, so let us go back and reconsider Elizabeth.\n",
"Assume Elizabeth is a knave. ",
"No contradiction is found in their false claim that Henry is a knight if and only if Elizabeth is a knight.\n",
"Assume Henry is a knight. ",
"No contradiction is found in their claim that If Elizabeth is a knight then Elizabeth is a knave.\n",
"Assume Charlotte is a knight. ",
"No contradiction is found in their claim that Henry is a knight or Elizabeth is a knight.\n",
"Therefore, (1) Elizabeth is a knave\n",
"(2) Henry is a knight\n",
"(3) Charlotte is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Elizabeth, Henry, and Charlotte. "Henry is a knight if and only if Elizabeth is a knight," Elizabeth declared. Henry asserted: "If Elizabeth is a knight then Elizabeth is a knave". Charlotte asserted: "Henry is a knight or Elizabeth is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Elizabeth is a knight. No contradiction is found in their claim that Henry is a knight if and only if Elizabeth is a knight.
Henry cannot be a knight, because this would contradict the claim of their own that If Elizabeth is a knight then Elizabeth is a knave.
Henry cannot be a knave, because this would contradict the claim of Elizabeth that Henry is a knight if and only if Elizabeth is a knight.
We have exhausted all possibilities for Henry, so let us go back and reconsider Elizabeth.
Assume Elizabeth is a knave. No contradiction is found in their false claim that Henry is a knight if and only if Elizabeth is a knight.
Assume Henry is a knight. No contradiction is found in their claim that If Elizabeth is a knight then Elizabeth is a knave.
Assume Charlotte is a knight. No contradiction is found in their claim that Henry is a knight or Elizabeth is a knight.
Therefore, (1) Elizabeth is a knave
(2) Henry is a knight
(3) Charlotte is a knight </think>
<answer> (1) Elizabeth is a knave
(2) Henry is a knight
(3) Charlotte is a knight </answer> | math | {
"ground_truth": {
"names": [
"Elizabeth",
"Henry",
"Charlotte"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Elizabeth is a knave\n(2) Henry is a knight\n(3) Charlotte is a knight",
"statements": "(('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('->', ('telling-truth', 0), ('lying', 0)), ('or', ('telling-truth', 1), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 234,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Matthew, Charlotte, and Sebastian. Matthew expressed that Sebastian is a knight or Sebastian is a knave. \"Matthew is not a knave,\" Charlotte declared. Sebastian stated, \"If Charlotte is a knight then Charlotte is a knave\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Matthew is a knight. ",
"No contradiction is found in their claim that Sebastian is a knight or Sebastian is a knave.\n",
"Assume Sebastian is a knight. ",
"No contradiction is found in their claim that If Charlotte is a knight then Charlotte is a knave.\n",
"Charlotte cannot be a knight, because this would contradict the claim of Sebastian that If Charlotte is a knight then Charlotte is a knave.\n",
"Charlotte cannot be a knave, because this would contradict the false claim of their own that Matthew is not a knave.\n",
"We have exhausted all possibilities for Charlotte, so let us go back and reconsider Sebastian.\n",
"Assume Sebastian is a knave. ",
"No contradiction is found in their false claim that If Charlotte is a knight then Charlotte is a knave.\n",
"Assume Charlotte is a knight. ",
"No contradiction is found in their claim that Matthew is not a knave.\n",
"Therefore, (1) Matthew is a knight\n",
"(2) Charlotte is a knight\n",
"(3) Sebastian is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Matthew, Charlotte, and Sebastian. Matthew expressed that Sebastian is a knight or Sebastian is a knave. "Matthew is not a knave," Charlotte declared. Sebastian stated, "If Charlotte is a knight then Charlotte is a knave". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Matthew 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 knight then Charlotte is a knave.
Charlotte cannot be a knight, because this would contradict the claim of Sebastian that If Charlotte is a knight then Charlotte is a knave.
Charlotte cannot be a knave, because this would contradict the false claim of their own that Matthew is not a knave.
We have exhausted all possibilities for Charlotte, so let us go back and reconsider Sebastian.
Assume Sebastian is a knave. No contradiction is found in their false claim that If Charlotte is a knight then Charlotte is a knave.
Assume Charlotte is a knight. No contradiction is found in their claim that Matthew is not a knave.
Therefore, (1) Matthew is a knight
(2) Charlotte is a knight
(3) Sebastian is a knave </think>
<answer> (1) Matthew is a knight
(2) Charlotte is a knight
(3) Sebastian is a knave </answer> | math | {
"ground_truth": {
"names": [
"Matthew",
"Charlotte",
"Sebastian"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Matthew is a knight\n(2) Charlotte is a knight\n(3) Sebastian is a knave",
"statements": "(('or', ('telling-truth', 2), ('lying', 2)), ('not', ('lying', 0)), ('->', ('telling-truth', 1), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 235,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Isabella, Evelyn, and Victoria. \"Evelyn is a knave and Victoria is a knave,\" Isabella declared. \"Victoria is a knave and Isabella is a knave,\" Evelyn declared. Victoria stated, \"Isabella is not a knave\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Isabella is a knight. ",
"No contradiction is found in their claim that Evelyn is a knave and Victoria is a knave.\n",
"Evelyn cannot be a knight, because this would contradict the claim of Isabella that Evelyn is a knave and Victoria is a knave.\n",
"Assume Evelyn is a knave. ",
"No contradiction is found in their false claim that Victoria is a knave and Isabella is a knave.\n",
"Victoria cannot be a knight, because this would contradict the claim of Isabella that Evelyn is a knave and Victoria is a knave.\n",
"Victoria cannot be a knave, because this would contradict the false claim of their own that Isabella is not a knave.\n",
"We have exhausted all possibilities for Victoria and Evelyn, so let us go back and reconsider Isabella.\n",
"Assume Isabella is a knave. ",
"No contradiction is found in their false claim that Evelyn is a knave and Victoria is a knave.\n",
"Assume Evelyn is a knight. ",
"No contradiction is found in their claim that Victoria is a knave and Isabella is a knave.\n",
"Victoria cannot be a knight, because this would contradict the claim of Evelyn that Victoria is a knave and Isabella is a knave.\n",
"Assume Victoria is a knave. ",
"No contradiction is found in their false claim that Isabella is not a knave.\n",
"Therefore, (1) Isabella is a knave\n",
"(2) Evelyn is a knight\n",
"(3) Victoria is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Isabella, Evelyn, and Victoria. "Evelyn is a knave and Victoria is a knave," Isabella declared. "Victoria is a knave and Isabella is a knave," Evelyn declared. Victoria stated, "Isabella is not a knave". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Isabella is a knight. No contradiction is found in their claim that Evelyn is a knave and Victoria is a knave.
Evelyn cannot be a knight, because this would contradict the claim of Isabella that Evelyn is a knave and Victoria is a knave.
Assume Evelyn is a knave. No contradiction is found in their false claim that Victoria is a knave and Isabella is a knave.
Victoria cannot be a knight, because this would contradict the claim of Isabella that Evelyn is a knave and Victoria is a knave.
Victoria cannot be a knave, because this would contradict the false claim of their own that Isabella is not a knave.
We have exhausted all possibilities for Victoria and 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 knave and Victoria is a knave.
Assume Evelyn is a knight. No contradiction is found in their claim that Victoria is a knave and Isabella is a knave.
Victoria cannot be a knight, because this would contradict the claim of Evelyn that Victoria is a knave and Isabella is a knave.
Assume Victoria is a knave. No contradiction is found in their false claim that Isabella is not a knave.
Therefore, (1) Isabella is a knave
(2) Evelyn is a knight
(3) Victoria is a knave </think>
<answer> (1) Isabella is a knave
(2) Evelyn is a knight
(3) Victoria is a knave </answer> | math | {
"ground_truth": {
"names": [
"Isabella",
"Evelyn",
"Victoria"
],
"solution": [
false,
true,
false
],
"solution_text_format": "(1) Isabella is a knave\n(2) Evelyn is a knight\n(3) Victoria is a knave",
"statements": "(('and', ('lying', 1), ('lying', 2)), ('and', ('lying', 2), ('lying', 0)), ('not', ('lying', 0)))"
},
"style": "rule"
} | {
"index": 236,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Aurora, Evelyn, and Emily. Aurora asserted: \"Evelyn is a knave and Evelyn is a knight\". In a statement by Evelyn: \"If Emily is a knight then Aurora is a knave\". In Emily's words: \"If Evelyn is a knave then Aurora is a knave\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Aurora cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave and Evelyn is a knight.\n",
"Assume Aurora is a knave. ",
"No contradiction is found in their false claim that Evelyn is a knave and Evelyn is a knight.\n",
"Assume Evelyn is a knight. ",
"No contradiction is found in their claim that If Emily is a knight then Aurora is a knave.\n",
"Assume Emily is a knight. ",
"No contradiction is found in their claim that If Evelyn is a knave then Aurora is a knave.\n",
"Therefore, (1) Aurora is a knave\n",
"(2) Evelyn is a knight\n",
"(3) Emily is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Aurora, Evelyn, and Emily. Aurora asserted: "Evelyn is a knave and Evelyn is a knight". In a statement by Evelyn: "If Emily is a knight then Aurora is a knave". In Emily's words: "If Evelyn is a knave then Aurora is a knave". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Aurora cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave and Evelyn is a knight.
Assume Aurora is a knave. No contradiction is found in their false claim that Evelyn is a knave and Evelyn is a knight.
Assume Evelyn is a knight. No contradiction is found in their claim that If Emily is a knight then Aurora is a knave.
Assume Emily is a knight. No contradiction is found in their claim that If Evelyn is a knave then Aurora is a knave.
Therefore, (1) Aurora is a knave
(2) Evelyn is a knight
(3) Emily is a knight </think>
<answer> (1) Aurora is a knave
(2) Evelyn is a knight
(3) Emily is a knight </answer> | math | {
"ground_truth": {
"names": [
"Aurora",
"Evelyn",
"Emily"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Aurora is a knave\n(2) Evelyn is a knight\n(3) Emily is a knight",
"statements": "(('and', ('lying', 1), ('telling-truth', 1)), ('->', ('telling-truth', 2), ('lying', 0)), ('->', ('lying', 1), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 237,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Mia, Lucas, and Scarlett. Mia noted, \"Lucas is a knave or Scarlett is a knight\". Lucas asserted: \"Scarlett is a knight and Scarlett is a knave\". Scarlett commented, \"Mia is a knave and Mia is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Mia is a knight. ",
"No contradiction is found in their claim that Lucas is a knave or Scarlett is a knight.\n",
"Lucas cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight and Scarlett is a knave.\n",
"Assume Lucas is a knave. ",
"No contradiction is found in their false claim that Scarlett is a knight and Scarlett is a knave.\n",
"Scarlett cannot be a knight, because this would contradict the claim of their own that Mia is a knave and Mia is a knight.\n",
"Assume Scarlett is a knave. ",
"No contradiction is found in their false claim that Mia is a knave and Mia is a knight.\n",
"Therefore, (1) Mia is a knight\n",
"(2) Lucas is a knave\n",
"(3) Scarlett is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Mia, Lucas, and Scarlett. Mia noted, "Lucas is a knave or Scarlett is a knight". Lucas asserted: "Scarlett is a knight and Scarlett is a knave". Scarlett commented, "Mia is a knave and Mia is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Mia is a knight. No contradiction is found in their claim that Lucas is a knave or Scarlett is a knight.
Lucas cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight and Scarlett is a knave.
Assume Lucas is a knave. No contradiction is found in their false claim that Scarlett is a knight and Scarlett is a knave.
Scarlett cannot be a knight, because this would contradict the claim of their own that Mia is a knave and Mia is a knight.
Assume Scarlett is a knave. No contradiction is found in their false claim that Mia is a knave and Mia is a knight.
Therefore, (1) Mia is a knight
(2) Lucas is a knave
(3) Scarlett is a knave </think>
<answer> (1) Mia is a knight
(2) Lucas is a knave
(3) Scarlett is a knave </answer> | math | {
"ground_truth": {
"names": [
"Mia",
"Lucas",
"Scarlett"
],
"solution": [
true,
false,
false
],
"solution_text_format": "(1) Mia is a knight\n(2) Lucas is a knave\n(3) Scarlett is a knave",
"statements": "(('or', ('lying', 1), ('telling-truth', 2)), ('and', ('telling-truth', 2), ('lying', 2)), ('and', ('lying', 0), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 238,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Sofia, Aria, and Riley. Sofia said, \"Riley is a knight if and only if Aria is a knave.\" Aria said that Sofia is a knave. Riley expressed that Aria is a knight. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Sofia is a knight. ",
"No contradiction is found in their claim that Riley is a knight if and only if Aria is a knave.\n",
"Assume Riley is a knight. ",
"No contradiction is found in their claim that Aria is a knight.\n",
"Aria cannot be a knight, because this would contradict the claim of Sofia that Riley is a knight if and only if Aria is a knave.\n",
"Aria cannot be a knave, because this would contradict the claim of Riley that Aria is a knight.\n",
"We have exhausted all possibilities for Aria, so let us go back and reconsider Riley.\n",
"Assume Riley is a knave. ",
"No contradiction is found in their false claim that Aria is a knight.\n",
"Aria cannot be a knight, because this would contradict the claim of their own that Sofia is a knave.\n",
"Aria cannot be a knave, because this would contradict the claim of Sofia that Riley is a knight if and only if Aria is a knave.\n",
"We have exhausted all possibilities for Aria and Riley, so let us go back and reconsider Sofia.\n",
"Assume Sofia is a knave. ",
"No contradiction is found in their false claim that Riley is a knight if and only if Aria is a knave.\n",
"Assume Riley is a knight. ",
"No contradiction is found in their claim that Aria is a knight.\n",
"Assume Aria is a knight. ",
"No contradiction is found in their claim that Sofia is a knave.\n",
"Therefore, (1) Sofia is a knave\n",
"(2) Aria is a knight\n",
"(3) Riley is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Sofia, Aria, and Riley. Sofia said, "Riley is a knight if and only if Aria is a knave." Aria said that Sofia is a knave. Riley expressed that Aria is a knight. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Sofia is a knight. No contradiction is found in their claim that Riley is a knight if and only if Aria is a knave.
Assume Riley is a knight. No contradiction is found in their claim that Aria is a knight.
Aria cannot be a knight, because this would contradict the claim of Sofia that Riley is a knight if and only if Aria is a knave.
Aria cannot be a knave, because this would contradict the claim of Riley that Aria is a knight.
We have exhausted all possibilities for Aria, so let us go back and reconsider Riley.
Assume Riley is a knave. No contradiction is found in their false claim that Aria is a knight.
Aria cannot be a knight, because this would contradict the claim of their own that Sofia is a knave.
Aria cannot be a knave, because this would contradict the claim of Sofia that Riley is a knight if and only if Aria is a knave.
We have exhausted all possibilities for Aria and Riley, so let us go back and reconsider Sofia.
Assume Sofia is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Aria is a knave.
Assume Riley is a knight. No contradiction is found in their claim that Aria is a knight.
Assume Aria is a knight. No contradiction is found in their claim that Sofia is a knave.
Therefore, (1) Sofia is a knave
(2) Aria is a knight
(3) Riley is a knight </think>
<answer> (1) Sofia is a knave
(2) Aria is a knight
(3) Riley is a knight </answer> | math | {
"ground_truth": {
"names": [
"Sofia",
"Aria",
"Riley"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Sofia is a knave\n(2) Aria is a knight\n(3) Riley is a knight",
"statements": "(('<=>', ('telling-truth', 2), ('lying', 1)), ('lying', 0), ('telling-truth', 1))"
},
"style": "rule"
} | {
"index": 239,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Harper, Isabella, and Elizabeth. Harper commented, \"Isabella is a knave and Harper is a knight\". In Isabella's words: \"Harper is a knight if and only if Isabella is a knight\". \"Isabella is not a knight\" - Elizabeth. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Harper is a knight. ",
"No contradiction is found in their claim that Isabella is a knave and Harper is a knight.\n",
"Isabella cannot be a knight, because this would contradict the claim of Harper that Isabella is a knave and Harper is a knight.\n",
"Assume Isabella is a knave. ",
"No contradiction is found in their false claim that Harper is a knight if and only if Isabella is a knight.\n",
"Assume Elizabeth is a knight. ",
"No contradiction is found in their claim that Isabella is not a knight.\n",
"Therefore, (1) Harper is a knight\n",
"(2) Isabella is a knave\n",
"(3) Elizabeth is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Harper, Isabella, and Elizabeth. Harper commented, "Isabella is a knave and Harper is a knight". In Isabella's words: "Harper is a knight if and only if Isabella is a knight". "Isabella is not a knight" - Elizabeth. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Harper is a knight. No contradiction is found in their claim that Isabella is a knave and Harper is a knight.
Isabella cannot be a knight, because this would contradict the claim of Harper that Isabella is a knave and Harper is a knight.
Assume Isabella 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 Elizabeth is a knight. No contradiction is found in their claim that Isabella is not a knight.
Therefore, (1) Harper is a knight
(2) Isabella is a knave
(3) Elizabeth is a knight </think>
<answer> (1) Harper is a knight
(2) Isabella is a knave
(3) Elizabeth is a knight </answer> | math | {
"ground_truth": {
"names": [
"Harper",
"Isabella",
"Elizabeth"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Harper is a knight\n(2) Isabella is a knave\n(3) Elizabeth is a knight",
"statements": "(('and', ('lying', 1), ('telling-truth', 0)), ('<=>', ('telling-truth', 0), ('telling-truth', 1)), ('not', ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 240,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Mason, Emma, and Alexander. \"Alexander is a knight or Alexander is a knave,\" Mason mentioned. As Emma put it, \"Alexander is a knight or Mason is a knave\". \"Mason is a knave if and only if Mason is a knight,\" Alexander declared. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Mason is a knight. ",
"No contradiction is found in their claim that Alexander is a knight or Alexander is a knave.\n",
"Alexander cannot be a knight, because this would contradict the claim of their own that Mason is a knave if and only if Mason is a knight.\n",
"Assume Alexander is a knave. ",
"No contradiction is found in their false claim that Mason is a knave if and only if Mason is a knight.\n",
"Emma cannot be a knight, because this would contradict the claim of their own that Alexander is a knight or Mason is a knave.\n",
"Assume Emma is a knave. ",
"No contradiction is found in their false claim that Alexander is a knight or Mason is a knave.\n",
"Therefore, (1) Mason is a knight\n",
"(2) Emma is a knave\n",
"(3) Alexander is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Mason, Emma, and Alexander. "Alexander is a knight or Alexander is a knave," Mason mentioned. As Emma put it, "Alexander is a knight or Mason is a knave". "Mason is a knave if and only if Mason is a knight," Alexander declared. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Mason is a knight. No contradiction is found in their claim that Alexander is a knight or Alexander is a knave.
Alexander cannot be a knight, because this would contradict the claim of their own that Mason is a knave if and only if Mason is a knight.
Assume Alexander is a knave. No contradiction is found in their false claim that Mason is a knave if and only if Mason is a knight.
Emma cannot be a knight, because this would contradict the claim of their own that Alexander is a knight or Mason is a knave.
Assume Emma is a knave. No contradiction is found in their false claim that Alexander is a knight or Mason is a knave.
Therefore, (1) Mason is a knight
(2) Emma is a knave
(3) Alexander is a knave </think>
<answer> (1) Mason is a knight
(2) Emma is a knave
(3) Alexander is a knave </answer> | math | {
"ground_truth": {
"names": [
"Mason",
"Emma",
"Alexander"
],
"solution": [
true,
false,
false
],
"solution_text_format": "(1) Mason is a knight\n(2) Emma is a knave\n(3) Alexander is a knave",
"statements": "(('or', ('telling-truth', 2), ('lying', 2)), ('or', ('telling-truth', 2), ('lying', 0)), ('<=>', ('lying', 0), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 241,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Scarlett, Riley, and Zoey. According to Scarlett, \"Riley is a knave or Zoey is a knave\". According to Riley, \"Scarlett is a knave if and only if Riley is a knight\". \"Riley is a knave or Zoey is a knight,\" Zoey claimed. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Scarlett is a knight. ",
"No contradiction is found in their claim that Riley is a knave or Zoey is a knave.\n",
"Riley cannot be a knight, because this would contradict the claim of their own that Scarlett is a knave if and only if Riley is a knight.\n",
"Riley cannot be a knave, because this would contradict the false claim of their own that Scarlett is a knave if and only if Riley is a knight.\n",
"We have exhausted all possibilities for Riley, so let us go back and reconsider Scarlett.\n",
"Assume Scarlett is a knave. ",
"No contradiction is found in their false claim that Riley is a knave or Zoey is a knave.\n",
"Assume Riley is a knight. ",
"No contradiction is found in their claim that Scarlett is a knave if and only if Riley is a knight.\n",
"Assume Zoey is a knight. ",
"No contradiction is found in their claim that Riley is a knave or Zoey is a knight.\n",
"Therefore, (1) Scarlett is a knave\n",
"(2) Riley is a knight\n",
"(3) Zoey is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Scarlett, Riley, and Zoey. According to Scarlett, "Riley is a knave or Zoey is a knave". According to Riley, "Scarlett is a knave if and only if Riley is a knight". "Riley is a knave or Zoey is a knight," Zoey claimed. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Scarlett is a knight. No contradiction is found in their claim that Riley is a knave or Zoey is a knave.
Riley cannot be a knight, because this would contradict the claim of their own that Scarlett is a knave if and only if Riley is a knight.
Riley cannot be a knave, because this would contradict the false claim of their own that Scarlett is a knave if and only if Riley is a knight.
We have exhausted all possibilities for Riley, so let us go back and reconsider Scarlett.
Assume Scarlett is a knave. No contradiction is found in their false claim that Riley is a knave or Zoey is a knave.
Assume Riley is a knight. No contradiction is found in their claim that Scarlett is a knave if and only if Riley is a knight.
Assume Zoey is a knight. No contradiction is found in their claim that Riley is a knave or Zoey is a knight.
Therefore, (1) Scarlett is a knave
(2) Riley is a knight
(3) Zoey is a knight </think>
<answer> (1) Scarlett is a knave
(2) Riley is a knight
(3) Zoey is a knight </answer> | math | {
"ground_truth": {
"names": [
"Scarlett",
"Riley",
"Zoey"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Scarlett is a knave\n(2) Riley is a knight\n(3) Zoey is a knight",
"statements": "(('or', ('lying', 1), ('lying', 2)), ('<=>', ('lying', 0), ('telling-truth', 1)), ('or', ('lying', 1), ('telling-truth', 2)))"
},
"style": "rule"
} | {
"index": 242,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: James, Evelyn, and Noah. \"Evelyn is a knave if and only if Noah is a knave,\" James mentioned. Evelyn asserted: \"James is a knight or Noah is a knave\". \"Evelyn is not a knave,\" Noah declared. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume James is a knight. ",
"No contradiction is found in their claim that Evelyn is a knave if and only if Noah is a knave.\n",
"Assume Evelyn is a knight. ",
"No contradiction is found in their claim that James is a knight or Noah is a knave.\n",
"Assume Noah is a knight. ",
"No contradiction is found in their claim that Evelyn is not a knave.\n",
"Therefore, (1) James is a knight\n",
"(2) Evelyn is a knight\n",
"(3) Noah is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: James, Evelyn, and Noah. "Evelyn is a knave if and only if Noah is a knave," James mentioned. Evelyn asserted: "James is a knight or Noah is a knave". "Evelyn is not a knave," Noah declared. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume James is a knight. No contradiction is found in their claim that Evelyn is a knave if and only if Noah is a knave.
Assume Evelyn is a knight. No contradiction is found in their claim that James is a knight or Noah is a knave.
Assume Noah is a knight. No contradiction is found in their claim that Evelyn is not a knave.
Therefore, (1) James is a knight
(2) Evelyn is a knight
(3) Noah is a knight </think>
<answer> (1) James is a knight
(2) Evelyn is a knight
(3) Noah is a knight </answer> | math | {
"ground_truth": {
"names": [
"James",
"Evelyn",
"Noah"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) James is a knight\n(2) Evelyn is a knight\n(3) Noah is a knight",
"statements": "(('<=>', ('lying', 1), ('lying', 2)), ('or', ('telling-truth', 0), ('lying', 2)), ('not', ('lying', 1)))"
},
"style": "rule"
} | {
"index": 243,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Aurora, Benjamin, and Mason. Aurora remarked, \"If Mason is a knave then Mason is a knight\". Benjamin told you that Aurora is a knight. Mason noted, \"If Benjamin is a knave then Aurora is a knave\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Aurora is a knight. ",
"No contradiction is found in their claim that If Mason is a knave then Mason is a knight.\n",
"Assume Mason is a knight. ",
"No contradiction is found in their claim that If Benjamin is a knave then Aurora is a knave.\n",
"Assume Benjamin is a knight. ",
"No contradiction is found in their claim that Aurora is a knight.\n",
"Therefore, (1) Aurora is a knight\n",
"(2) Benjamin is a knight\n",
"(3) Mason is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Aurora, Benjamin, and Mason. Aurora remarked, "If Mason is a knave then Mason is a knight". Benjamin told you that Aurora is a knight. Mason noted, "If Benjamin is a knave then Aurora is a knave". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Aurora is a knight. No contradiction is found in their claim that If Mason is a knave then Mason is a knight.
Assume Mason is a knight. No contradiction is found in their claim that If Benjamin is a knave then Aurora is a knave.
Assume Benjamin is a knight. No contradiction is found in their claim that Aurora is a knight.
Therefore, (1) Aurora is a knight
(2) Benjamin is a knight
(3) Mason is a knight </think>
<answer> (1) Aurora is a knight
(2) Benjamin is a knight
(3) Mason is a knight </answer> | math | {
"ground_truth": {
"names": [
"Aurora",
"Benjamin",
"Mason"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Aurora is a knight\n(2) Benjamin is a knight\n(3) Mason is a knight",
"statements": "(('->', ('lying', 2), ('telling-truth', 2)), ('telling-truth', 0), ('->', ('lying', 1), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 244,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Sophia, Alexander, and Amelia. Sophia was heard saying, \"If Amelia is a knave then Alexander is a knave\". In a statement by Alexander: \"Amelia is not a knave\". \"If Amelia is a knight then Alexander is a knight,\" Amelia mentioned. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Sophia is a knight. ",
"No contradiction is found in their claim that If Amelia is a knave then Alexander is a knave.\n",
"Assume Amelia is a knight. ",
"No contradiction is found in their claim that If Amelia is a knight then Alexander is a knight.\n",
"Assume Alexander is a knight. ",
"No contradiction is found in their claim that Amelia is not a knave.\n",
"Therefore, (1) Sophia is a knight\n",
"(2) Alexander is a knight\n",
"(3) Amelia is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Sophia, Alexander, and Amelia. Sophia was heard saying, "If Amelia is a knave then Alexander is a knave". In a statement by Alexander: "Amelia is not a knave". "If Amelia is a knight then Alexander is a knight," Amelia mentioned. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Sophia is a knight. No contradiction is found in their claim that If Amelia is a knave then Alexander is a knave.
Assume Amelia is a knight. No contradiction is found in their claim that If Amelia is a knight then Alexander is a knight.
Assume Alexander is a knight. No contradiction is found in their claim that Amelia is not a knave.
Therefore, (1) Sophia is a knight
(2) Alexander is a knight
(3) Amelia is a knight </think>
<answer> (1) Sophia is a knight
(2) Alexander is a knight
(3) Amelia is a knight </answer> | math | {
"ground_truth": {
"names": [
"Sophia",
"Alexander",
"Amelia"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Sophia is a knight\n(2) Alexander is a knight\n(3) Amelia is a knight",
"statements": "(('->', ('lying', 2), ('lying', 1)), ('not', ('lying', 2)), ('->', ('telling-truth', 2), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 245,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Mason, Jacob, and Jack. Mason said that Jack is a knave and Mason is a knight. Jacob remarked, \"Jacob is a knight and Jack is a knight\". In a statement by Jack: \"Mason is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Mason is a knight. ",
"No contradiction is found in their claim that Jack is a knave and Mason is a knight.\n",
"Jack cannot be a knight, because this would contradict the claim of Mason that Jack is a knave and Mason is a knight.\n",
"Jack cannot be a knave, because this would contradict the false claim of their own that Mason is a knight.\n",
"We have exhausted all possibilities for Jack, so let us go back and reconsider Mason.\n",
"Assume Mason is a knave. ",
"No contradiction is found in their false claim that Jack is a knave and Mason is a knight.\n",
"Jack cannot be a knight, because this would contradict the claim of their own that Mason is a knight.\n",
"Assume Jack is a knave. ",
"No contradiction is found in their false claim that Mason is a knight.\n",
"Jacob cannot be a knight, because this would contradict the claim of their own that Jacob is a knight and Jack is a knight.\n",
"Assume Jacob is a knave. ",
"No contradiction is found in their false claim that Jacob is a knight and Jack is a knight.\n",
"Therefore, (1) Mason is a knave\n",
"(2) Jacob is a knave\n",
"(3) Jack is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Mason, Jacob, and Jack. Mason said that Jack is a knave and Mason is a knight. Jacob remarked, "Jacob is a knight and Jack is a knight". In a statement by Jack: "Mason is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Mason is a knight. No contradiction is found in their claim that Jack is a knave and Mason is a knight.
Jack cannot be a knight, because this would contradict the claim of Mason that Jack is a knave and Mason is a knight.
Jack cannot be a knave, because this would contradict the false claim of their own that Mason is a knight.
We have exhausted all possibilities for Jack, so let us go back and reconsider Mason.
Assume Mason is a knave. No contradiction is found in their false claim that Jack is a knave and Mason is a knight.
Jack cannot be a knight, because this would contradict the claim of their own that Mason is a knight.
Assume Jack is a knave. No contradiction is found in their false claim that Mason is a knight.
Jacob cannot be a knight, because this would contradict the claim of their own that Jacob is a knight and Jack is a knight.
Assume Jacob is a knave. No contradiction is found in their false claim that Jacob is a knight and Jack is a knight.
Therefore, (1) Mason is a knave
(2) Jacob is a knave
(3) Jack is a knave </think>
<answer> (1) Mason is a knave
(2) Jacob is a knave
(3) Jack is a knave </answer> | math | {
"ground_truth": {
"names": [
"Mason",
"Jacob",
"Jack"
],
"solution": [
false,
false,
false
],
"solution_text_format": "(1) Mason is a knave\n(2) Jacob is a knave\n(3) Jack is a knave",
"statements": "(('and', ('lying', 2), ('telling-truth', 0)), ('and', ('telling-truth', 1), ('telling-truth', 2)), ('telling-truth', 0))"
},
"style": "rule"
} | {
"index": 246,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Lucas, Penelope, and Emily. In Lucas's words: \"Penelope is a knave\". Penelope noted, \"Lucas is a knight and Penelope is a knight\". \"If Penelope is a knave then Lucas is a knight,\" Emily declared. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Lucas is a knight. ",
"No contradiction is found in their claim that Penelope is a knave.\n",
"Penelope cannot be a knight, because this would contradict the claim of Lucas that Penelope is a knave.\n",
"Assume Penelope is a knave. ",
"No contradiction is found in their false claim that Lucas is a knight and Penelope is a knight.\n",
"Assume Emily is a knight. ",
"No contradiction is found in their claim that If Penelope is a knave then Lucas is a knight.\n",
"Therefore, (1) Lucas is a knight\n",
"(2) Penelope is a knave\n",
"(3) Emily is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Lucas, Penelope, and Emily. In Lucas's words: "Penelope is a knave". Penelope noted, "Lucas is a knight and Penelope is a knight". "If Penelope is a knave then Lucas is a knight," Emily declared. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Lucas is a knight. No contradiction is found in their claim that Penelope is a knave.
Penelope cannot be a knight, because this would contradict the claim of Lucas that Penelope is a knave.
Assume Penelope is a knave. No contradiction is found in their false claim that Lucas is a knight and Penelope is a knight.
Assume Emily is a knight. No contradiction is found in their claim that If Penelope is a knave then Lucas is a knight.
Therefore, (1) Lucas is a knight
(2) Penelope is a knave
(3) Emily is a knight </think>
<answer> (1) Lucas is a knight
(2) Penelope is a knave
(3) Emily is a knight </answer> | math | {
"ground_truth": {
"names": [
"Lucas",
"Penelope",
"Emily"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Lucas is a knight\n(2) Penelope is a knave\n(3) Emily is a knight",
"statements": "(('lying', 1), ('and', ('telling-truth', 0), ('telling-truth', 1)), ('->', ('lying', 1), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 247,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Samuel, Emily, and Mia. Samuel noted, \"Emily is a knight if and only if Mia is a knave\". Emily commented, \"Samuel is not a knight\". Mia noted, \"If Samuel is a knight then Emily is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Samuel is a knight. ",
"No contradiction is found in their claim that Emily is a knight if and only if Mia is a knave.\n",
"Emily cannot be a knight, because this would contradict the claim of their own that Samuel is not a knight.\n",
"Assume Emily is a knave. ",
"No contradiction is found in their false claim that Samuel is not a knight.\n",
"Mia cannot be a knight, because this would contradict the claim of their own that If Samuel is a knight then Emily is a knight.\n",
"Mia cannot be a knave, because this would contradict the claim of Samuel that Emily is a knight if and only if Mia is a knave.\n",
"We have exhausted all possibilities for Mia and Emily, so let us go back and reconsider Samuel.\n",
"Assume Samuel is a knave. ",
"No contradiction is found in their false claim that Emily is a knight if and only if Mia is a knave.\n",
"Assume Emily is a knight. ",
"No contradiction is found in their claim that Samuel is not a knight.\n",
"Assume Mia is a knight. ",
"No contradiction is found in their claim that If Samuel is a knight then Emily is a knight.\n",
"Therefore, (1) Samuel is a knave\n",
"(2) Emily is a knight\n",
"(3) Mia is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Samuel, Emily, and Mia. Samuel noted, "Emily is a knight if and only if Mia is a knave". Emily commented, "Samuel is not a knight". Mia noted, "If Samuel is a knight then Emily is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Samuel is a knight. No contradiction is found in their claim that Emily is a knight if and only if Mia is a knave.
Emily cannot be a knight, because this would contradict the claim of their own that Samuel is not a knight.
Assume Emily is a knave. No contradiction is found in their false claim that Samuel is not a knight.
Mia cannot be a knight, because this would contradict the claim of their own that If Samuel is a knight then Emily is a knight.
Mia cannot be a knave, because this would contradict the claim of Samuel that Emily is a knight if and only if Mia is a knave.
We have exhausted all possibilities for Mia and Emily, so let us go back and reconsider Samuel.
Assume Samuel is a knave. No contradiction is found in their false claim that Emily is a knight if and only if Mia is a knave.
Assume Emily is a knight. No contradiction is found in their claim that Samuel is not a knight.
Assume Mia is a knight. No contradiction is found in their claim that If Samuel is a knight then Emily is a knight.
Therefore, (1) Samuel is a knave
(2) Emily is a knight
(3) Mia is a knight </think>
<answer> (1) Samuel is a knave
(2) Emily is a knight
(3) Mia is a knight </answer> | math | {
"ground_truth": {
"names": [
"Samuel",
"Emily",
"Mia"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Samuel is a knave\n(2) Emily is a knight\n(3) Mia is a knight",
"statements": "(('<=>', ('telling-truth', 1), ('lying', 2)), ('not', ('telling-truth', 0)), ('->', ('telling-truth', 0), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 248,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Owen, Mason, and James. \"Mason is a knight,\" Owen claimed. \"If Owen is a knave then James is a knight,\" Mason claimed. James commented, \"Owen is a knave or Mason is a knave\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Owen is a knight. ",
"No contradiction is found in their claim that Mason is a knight.\n",
"Assume Mason is a knight. ",
"No contradiction is found in their claim that If Owen is a knave then James is a knight.\n",
"James cannot be a knight, because this would contradict the claim of their own that Owen is a knave or Mason is a knave.\n",
"Assume James is a knave. ",
"No contradiction is found in their false claim that Owen is a knave or Mason is a knave.\n",
"Therefore, (1) Owen is a knight\n",
"(2) Mason is a knight\n",
"(3) James is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Owen, Mason, and James. "Mason is a knight," Owen claimed. "If Owen is a knave then James is a knight," Mason claimed. James commented, "Owen is a knave or Mason is a knave". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Owen is a knight. No contradiction is found in their claim that Mason is a knight.
Assume Mason is a knight. No contradiction is found in their claim that If Owen is a knave then James is a knight.
James cannot be a knight, because this would contradict the claim of their own that Owen is a knave or Mason is a knave.
Assume James is a knave. No contradiction is found in their false claim that Owen is a knave or Mason is a knave.
Therefore, (1) Owen is a knight
(2) Mason is a knight
(3) James is a knave </think>
<answer> (1) Owen is a knight
(2) Mason is a knight
(3) James is a knave </answer> | math | {
"ground_truth": {
"names": [
"Owen",
"Mason",
"James"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Owen is a knight\n(2) Mason is a knight\n(3) James is a knave",
"statements": "(('telling-truth', 1), ('->', ('lying', 0), ('telling-truth', 2)), ('or', ('lying', 0), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 249,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Elizabeth, Matthew, and Owen. According to Elizabeth, \"If Matthew is a knave then Elizabeth is a knight\". Matthew was heard saying, \"Owen is a knight if and only if Elizabeth is a knight\". \"Elizabeth is a knave if and only if Owen is a knight,\" Owen mentioned. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Elizabeth is a knight. ",
"No contradiction is found in their claim that If Matthew is a knave then Elizabeth is a knight.\n",
"Assume Matthew is a knight. ",
"No contradiction is found in their claim that Owen is a knight if and only if Elizabeth is a knight.\n",
"Owen cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave if and only if Owen is a knight.\n",
"Owen cannot be a knave, because this would contradict the claim of Matthew that Owen is a knight if and only if Elizabeth is a knight.\n",
"We have exhausted all possibilities for Owen, so let us go back and reconsider Matthew.\n",
"Assume Matthew is a knave. ",
"No contradiction is found in their false claim that Owen is a knight if and only if Elizabeth is a knight.\n",
"Owen cannot be a knight, because this would contradict the false claim of Matthew that Owen is a knight if and only if Elizabeth is a knight.\n",
"Owen cannot be a knave, because this would contradict the false claim of their own that Elizabeth is a knave if and only if Owen is a knight.\n",
"We have exhausted all possibilities for Owen and Matthew, so let us go back and reconsider Elizabeth.\n",
"Assume Elizabeth is a knave. ",
"No contradiction is found in their false claim that If Matthew is a knave then Elizabeth is a knight.\n",
"Matthew cannot be a knight, because this would contradict the false claim of Elizabeth that If Matthew is a knave then Elizabeth is a knight.\n",
"Assume Matthew is a knave. ",
"No contradiction is found in their false claim that Owen is a knight if and only if Elizabeth is a knight.\n",
"Assume Owen is a knight. ",
"No contradiction is found in their claim that Elizabeth is a knave if and only if Owen is a knight.\n",
"Therefore, (1) Elizabeth is a knave\n",
"(2) Matthew is a knave\n",
"(3) Owen is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Elizabeth, Matthew, and Owen. According to Elizabeth, "If Matthew is a knave then Elizabeth is a knight". Matthew was heard saying, "Owen is a knight if and only if Elizabeth is a knight". "Elizabeth is a knave if and only if Owen is a knight," Owen mentioned. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Elizabeth is a knight. No contradiction is found in their claim that If Matthew is a knave then Elizabeth is a knight.
Assume Matthew is a knight. No contradiction is found in their claim that Owen is a knight if and only if Elizabeth is a knight.
Owen cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave if and only if Owen is a knight.
Owen cannot be a knave, because this would contradict the claim of Matthew that Owen is a knight if and only if Elizabeth is a knight.
We have exhausted all possibilities for Owen, so let us go back and reconsider Matthew.
Assume Matthew is a knave. No contradiction is found in their false claim that Owen is a knight if and only if Elizabeth is a knight.
Owen cannot be a knight, because this would contradict the false claim of Matthew that Owen is a knight if and only if Elizabeth is a knight.
Owen cannot be a knave, because this would contradict the false claim of their own that Elizabeth is a knave if and only if Owen is a knight.
We have exhausted all possibilities for Owen and Matthew, so let us go back and reconsider Elizabeth.
Assume Elizabeth is a knave. No contradiction is found in their false claim that If Matthew is a knave then Elizabeth is a knight.
Matthew cannot be a knight, because this would contradict the false claim of Elizabeth that If Matthew is a knave then Elizabeth is a knight.
Assume Matthew is a knave. No contradiction is found in their false claim that Owen is a knight if and only if Elizabeth is a knight.
Assume Owen is a knight. No contradiction is found in their claim that Elizabeth is a knave if and only if Owen is a knight.
Therefore, (1) Elizabeth is a knave
(2) Matthew is a knave
(3) Owen is a knight </think>
<answer> (1) Elizabeth is a knave
(2) Matthew is a knave
(3) Owen is a knight </answer> | math | {
"ground_truth": {
"names": [
"Elizabeth",
"Matthew",
"Owen"
],
"solution": [
false,
false,
true
],
"solution_text_format": "(1) Elizabeth is a knave\n(2) Matthew is a knave\n(3) Owen is a knight",
"statements": "(('->', ('lying', 1), ('telling-truth', 0)), ('<=>', ('telling-truth', 2), ('telling-truth', 0)), ('<=>', ('lying', 0), ('telling-truth', 2)))"
},
"style": "rule"
} | {
"index": 250,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Henry, Jack, and Michael. Henry commented, \"If Henry is a knight then Michael is a knave\". Jack told you that Jack is a knight. In Michael's words: \"Jack is a knight if and only if Henry is a knave\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Henry is a knight. ",
"No contradiction is found in their claim that If Henry is a knight then Michael is a knave.\n",
"Michael cannot be a knight, because this would contradict the claim of Henry that If Henry is a knight then Michael is a knave.\n",
"Assume Michael is a knave. ",
"No contradiction is found in their false claim that Jack is a knight if and only if Henry is a knave.\n",
"Assume Jack is a knight. ",
"No contradiction is found in their claim that Jack is a knight.\n",
"Therefore, (1) Henry is a knight\n",
"(2) Jack is a knight\n",
"(3) Michael is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Henry, Jack, and Michael. Henry commented, "If Henry is a knight then Michael is a knave". Jack told you that Jack is a knight. In Michael's words: "Jack is a knight if and only if Henry is a knave". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Henry is a knight. No contradiction is found in their claim that If Henry is a knight then Michael is a knave.
Michael cannot be a knight, because this would contradict the claim of Henry that If Henry is a knight then Michael is a knave.
Assume Michael is a knave. No contradiction is found in their false claim that Jack is a knight if and only if Henry is a knave.
Assume Jack is a knight. No contradiction is found in their claim that Jack is a knight.
Therefore, (1) Henry is a knight
(2) Jack is a knight
(3) Michael is a knave </think>
<answer> (1) Henry is a knight
(2) Jack is a knight
(3) Michael is a knave </answer> | math | {
"ground_truth": {
"names": [
"Henry",
"Jack",
"Michael"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Henry is a knight\n(2) Jack is a knight\n(3) Michael is a knave",
"statements": "(('->', ('telling-truth', 0), ('lying', 2)), ('telling-truth', 1), ('<=>', ('telling-truth', 1), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 251,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Ava, Avery, and Zoey. \"Zoey is a knave and Avery is a knave,\" Ava declared. \"Zoey is a knave,\" Avery mentioned. \"Zoey is a knight if and only if Avery is a knight,\" Zoey mentioned. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Ava is a knight. ",
"No contradiction is found in their claim that Zoey is a knave and Avery is a knave.\n",
"Zoey cannot be a knight, because this would contradict the claim of Ava that Zoey is a knave and Avery is a knave.\n",
"Assume Zoey is a knave. ",
"No contradiction is found in their false claim that Zoey is a knight if and only if Avery is a knight.\n",
"Avery cannot be a knight, because this would contradict the claim of Ava that Zoey is a knave and Avery is a knave.\n",
"Avery cannot be a knave, because this would contradict the false claim of their own that Zoey is a knave.\n",
"We have exhausted all possibilities for Avery and Zoey, so let us go back and reconsider Ava.\n",
"Assume Ava is a knave. ",
"No contradiction is found in their false claim that Zoey is a knave and Avery is a knave.\n",
"Assume Zoey is a knight. ",
"No contradiction is found in their claim that Zoey is a knight if and only if Avery is a knight.\n",
"Avery cannot be a knight, because this would contradict the claim of their own that Zoey is a knave.\n",
"Avery cannot be a knave, because this would contradict the claim of Zoey that Zoey is a knight if and only if Avery is a knight.\n",
"We have exhausted all possibilities for Avery, so let us go back and reconsider Zoey.\n",
"Assume Zoey is a knave. ",
"No contradiction is found in their false claim that Zoey is a knight if and only if Avery is a knight.\n",
"Assume Avery is a knight. ",
"No contradiction is found in their claim that Zoey is a knave.\n",
"Therefore, (1) Ava is a knave\n",
"(2) Avery is a knight\n",
"(3) Zoey is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Ava, Avery, and Zoey. "Zoey is a knave and Avery is a knave," Ava declared. "Zoey is a knave," Avery mentioned. "Zoey is a knight if and only if Avery is a knight," Zoey mentioned. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Ava is a knight. No contradiction is found in their claim that Zoey is a knave and Avery is a knave.
Zoey cannot be a knight, because this would contradict the claim of Ava that Zoey is a knave and Avery is a knave.
Assume Zoey is a knave. No contradiction is found in their false claim that Zoey is a knight if and only if Avery is a knight.
Avery cannot be a knight, because this would contradict the claim of Ava that Zoey is a knave and Avery is a knave.
Avery cannot be a knave, because this would contradict the false claim of their own that Zoey is a knave.
We have exhausted all possibilities for Avery and Zoey, so let us go back and reconsider Ava.
Assume Ava is a knave. No contradiction is found in their false claim that Zoey is a knave and Avery is a knave.
Assume Zoey is a knight. No contradiction is found in their claim that Zoey is a knight if and only if Avery is a knight.
Avery cannot be a knight, because this would contradict the claim of their own that Zoey is a knave.
Avery cannot be a knave, because this would contradict the claim of Zoey that Zoey is a knight if and only if Avery is a knight.
We have exhausted all possibilities for Avery, 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 if and only if Avery is a knight.
Assume Avery is a knight. No contradiction is found in their claim that Zoey is a knave.
Therefore, (1) Ava is a knave
(2) Avery is a knight
(3) Zoey is a knave </think>
<answer> (1) Ava is a knave
(2) Avery is a knight
(3) Zoey is a knave </answer> | math | {
"ground_truth": {
"names": [
"Ava",
"Avery",
"Zoey"
],
"solution": [
false,
true,
false
],
"solution_text_format": "(1) Ava is a knave\n(2) Avery is a knight\n(3) Zoey is a knave",
"statements": "(('and', ('lying', 2), ('lying', 1)), ('lying', 2), ('<=>', ('telling-truth', 2), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 252,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Owen, Penelope, and Oliver. Owen commented, \"If Owen is a knight then Penelope is a knave\". Penelope was heard saying, \"Penelope is a knight and Oliver is a knight\". \"Penelope is a knave,\" Oliver claimed. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Owen is a knight. ",
"No contradiction is found in their claim that If Owen is a knight then Penelope is a knave.\n",
"Penelope cannot be a knight, because this would contradict the claim of Owen that If Owen is a knight then Penelope is a knave.\n",
"Assume Penelope is a knave. ",
"No contradiction is found in their false claim that Penelope is a knight and Oliver is a knight.\n",
"Assume Oliver is a knight. ",
"No contradiction is found in their claim that Penelope is a knave.\n",
"Therefore, (1) Owen is a knight\n",
"(2) Penelope is a knave\n",
"(3) Oliver is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Owen, Penelope, and Oliver. Owen commented, "If Owen is a knight then Penelope is a knave". Penelope was heard saying, "Penelope is a knight and Oliver is a knight". "Penelope is a knave," Oliver claimed. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Owen is a knight. No contradiction is found in their claim that If Owen is a knight then Penelope is a knave.
Penelope cannot be a knight, because this would contradict the claim of Owen that If Owen is a knight then Penelope is a knave.
Assume Penelope is a knave. No contradiction is found in their false claim that Penelope is a knight and Oliver is a knight.
Assume Oliver is a knight. No contradiction is found in their claim that Penelope is a knave.
Therefore, (1) Owen is a knight
(2) Penelope is a knave
(3) Oliver is a knight </think>
<answer> (1) Owen is a knight
(2) Penelope is a knave
(3) Oliver is a knight </answer> | math | {
"ground_truth": {
"names": [
"Owen",
"Penelope",
"Oliver"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Owen is a knight\n(2) Penelope is a knave\n(3) Oliver is a knight",
"statements": "(('->', ('telling-truth', 0), ('lying', 1)), ('and', ('telling-truth', 1), ('telling-truth', 2)), ('lying', 1))"
},
"style": "rule"
} | {
"index": 253,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Daniel, Luke, and Penelope. As Daniel put it, \"Penelope is a knight and Daniel is a knight\". \"Penelope is a knight if and only if Daniel is a knight\" - Luke. \"Luke is not a knave,\" Penelope claimed. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Daniel is a knight. ",
"No contradiction is found in their claim that Penelope is a knight and Daniel is a knight.\n",
"Assume Penelope is a knight. ",
"No contradiction is found in their claim that Luke is not a knave.\n",
"Assume Luke is a knight. ",
"No contradiction is found in their claim that Penelope is a knight if and only if Daniel is a knight.\n",
"Therefore, (1) Daniel is a knight\n",
"(2) Luke is a knight\n",
"(3) Penelope is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Daniel, Luke, and Penelope. As Daniel put it, "Penelope is a knight and Daniel is a knight". "Penelope is a knight if and only if Daniel is a knight" - Luke. "Luke is not a knave," Penelope claimed. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Daniel is a knight. No contradiction is found in their claim that Penelope is a knight and Daniel is a knight.
Assume Penelope 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 Penelope is a knight if and only if Daniel is a knight.
Therefore, (1) Daniel is a knight
(2) Luke is a knight
(3) Penelope is a knight </think>
<answer> (1) Daniel is a knight
(2) Luke is a knight
(3) Penelope is a knight </answer> | math | {
"ground_truth": {
"names": [
"Daniel",
"Luke",
"Penelope"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Daniel is a knight\n(2) Luke is a knight\n(3) Penelope is a knight",
"statements": "(('and', ('telling-truth', 2), ('telling-truth', 0)), ('<=>', ('telling-truth', 2), ('telling-truth', 0)), ('not', ('lying', 1)))"
},
"style": "rule"
} | {
"index": 254,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Samuel, Chloe, and Daniel. \"Chloe is a knight and Chloe is a knave,\" Samuel mentioned. In a statement by Chloe: \"If Daniel is a knight then Daniel is a knave\". Daniel said, \"Samuel is a knave.\" So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Samuel cannot be a knight, because this would contradict the claim of their own that Chloe is a knight and Chloe is a knave.\n",
"Assume Samuel is a knave. ",
"No contradiction is found in their false claim that Chloe is a knight and Chloe is a knave.\n",
"Assume Chloe is a knight. ",
"No contradiction is found in their claim that If Daniel is a knight then Daniel is a knave.\n",
"Daniel cannot be a knight, because this would contradict the claim of Chloe that If Daniel is a knight then Daniel is a knave.\n",
"Daniel cannot be a knave, because this would contradict the false claim of their own that Samuel is a knave.\n",
"We have exhausted all possibilities for Daniel, so let us go back and reconsider Chloe.\n",
"Assume Chloe is a knave. ",
"No contradiction is found in their false claim that If Daniel is a knight then Daniel is a knave.\n",
"Assume Daniel is a knight. ",
"No contradiction is found in their claim that Samuel is a knave.\n",
"Therefore, (1) Samuel is a knave\n",
"(2) Chloe is a knave\n",
"(3) Daniel is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Samuel, Chloe, and Daniel. "Chloe is a knight and Chloe is a knave," Samuel mentioned. In a statement by Chloe: "If Daniel is a knight then Daniel is a knave". Daniel said, "Samuel is a knave." So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Samuel cannot be a knight, because this would contradict the claim of their own that Chloe is a knight and Chloe is a knave.
Assume Samuel is a knave. No contradiction is found in their false claim that Chloe is a knight and Chloe is a knave.
Assume Chloe is a knight. No contradiction is found in their claim that If Daniel is a knight then Daniel is a knave.
Daniel cannot be a knight, because this would contradict the claim of Chloe that If Daniel is a knight then Daniel is a knave.
Daniel cannot be a knave, because this would contradict the false claim of their own that Samuel is a knave.
We have exhausted all possibilities for Daniel, so let us go back and reconsider Chloe.
Assume Chloe is a knave. No contradiction is found in their false claim that If Daniel is a knight then Daniel is a knave.
Assume Daniel is a knight. No contradiction is found in their claim that Samuel is a knave.
Therefore, (1) Samuel is a knave
(2) Chloe is a knave
(3) Daniel is a knight </think>
<answer> (1) Samuel is a knave
(2) Chloe is a knave
(3) Daniel is a knight </answer> | math | {
"ground_truth": {
"names": [
"Samuel",
"Chloe",
"Daniel"
],
"solution": [
false,
false,
true
],
"solution_text_format": "(1) Samuel is a knave\n(2) Chloe is a knave\n(3) Daniel is a knight",
"statements": "(('and', ('telling-truth', 1), ('lying', 1)), ('->', ('telling-truth', 2), ('lying', 2)), ('lying', 0))"
},
"style": "rule"
} | {
"index": 255,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Ella, Emily, and Evelyn. As Ella put it, \"If Ella is a knight then Emily is a knight\". Emily asserted: \"Emily is a knight\". \"Emily is a knight\" - Evelyn. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Ella is a knight. ",
"No contradiction is found in their claim that If Ella is a knight then Emily is a knight.\n",
"Assume Emily is a knight. ",
"No contradiction is found in their claim that Emily is a knight.\n",
"Assume Evelyn is a knight. ",
"No contradiction is found in their claim that Emily is a knight.\n",
"Therefore, (1) Ella is a knight\n",
"(2) Emily is a knight\n",
"(3) Evelyn is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Ella, Emily, and Evelyn. As Ella put it, "If Ella is a knight then Emily is a knight". Emily asserted: "Emily is a knight". "Emily is a knight" - Evelyn. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Ella is a knight. No contradiction is found in their claim that If Ella is a knight then Emily is a knight.
Assume Emily is a knight. No contradiction is found in their claim that Emily is a knight.
Assume Evelyn is a knight. No contradiction is found in their claim that Emily is a knight.
Therefore, (1) Ella is a knight
(2) Emily is a knight
(3) Evelyn is a knight </think>
<answer> (1) Ella is a knight
(2) Emily is a knight
(3) Evelyn is a knight </answer> | math | {
"ground_truth": {
"names": [
"Ella",
"Emily",
"Evelyn"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Ella is a knight\n(2) Emily is a knight\n(3) Evelyn is a knight",
"statements": "(('->', ('telling-truth', 0), ('telling-truth', 1)), ('telling-truth', 1), ('telling-truth', 1))"
},
"style": "rule"
} | {
"index": 256,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Isabella, Zoey, and Riley. Isabella commented, \"Riley is a knight\". Zoey commented, \"Zoey is a knight and Isabella is a knight\". Riley stated, \"If Isabella is a knight then Zoey is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Isabella is a knight. ",
"No contradiction is found in their claim that Riley is a knight.\n",
"Assume Riley is a knight. ",
"No contradiction is found in their claim that If Isabella is a knight then Zoey is a knight.\n",
"Assume Zoey is a knight. ",
"No contradiction is found in their claim that Zoey is a knight and Isabella is a knight.\n",
"Therefore, (1) Isabella is a knight\n",
"(2) Zoey is a knight\n",
"(3) Riley is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Isabella, Zoey, and Riley. Isabella commented, "Riley is a knight". Zoey commented, "Zoey is a knight and Isabella is a knight". Riley stated, "If Isabella is a knight then Zoey is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Isabella is a knight. No contradiction is found in their claim that Riley is a knight.
Assume Riley is a knight. No contradiction is found in their claim that If Isabella is a knight then Zoey is a knight.
Assume Zoey is a knight. No contradiction is found in their claim that Zoey is a knight and Isabella is a knight.
Therefore, (1) Isabella is a knight
(2) Zoey is a knight
(3) Riley is a knight </think>
<answer> (1) Isabella is a knight
(2) Zoey is a knight
(3) Riley is a knight </answer> | math | {
"ground_truth": {
"names": [
"Isabella",
"Zoey",
"Riley"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Isabella is a knight\n(2) Zoey is a knight\n(3) Riley is a knight",
"statements": "(('telling-truth', 2), ('and', ('telling-truth', 1), ('telling-truth', 0)), ('->', ('telling-truth', 0), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 257,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Liam, Penelope, and Elizabeth. According to Liam, \"Penelope is a knight and Elizabeth is a knave\". Penelope commented, \"Liam is not a knight\". Elizabeth expressed that If Penelope is a knave then Penelope is a knight. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Liam is a knight. ",
"No contradiction is found in their claim that Penelope is a knight and Elizabeth is a knave.\n",
"Penelope cannot be a knight, because this would contradict the claim of their own that Liam is not a knight.\n",
"Penelope cannot be a knave, because this would contradict the claim of Liam that Penelope is a knight and Elizabeth is a knave.\n",
"We have exhausted all possibilities for Penelope, so let us go back and reconsider Liam.\n",
"Assume Liam is a knave. ",
"No contradiction is found in their false claim that Penelope is a knight and Elizabeth is a knave.\n",
"Assume Penelope is a knight. ",
"No contradiction is found in their claim that Liam is not a knight.\n",
"Assume Elizabeth is a knight. ",
"No contradiction is found in their claim that If Penelope is a knave then Penelope is a knight.\n",
"Therefore, (1) Liam is a knave\n",
"(2) Penelope is a knight\n",
"(3) Elizabeth is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Liam, Penelope, and Elizabeth. According to Liam, "Penelope is a knight and Elizabeth is a knave". Penelope commented, "Liam is not a knight". Elizabeth expressed that If Penelope is a knave then Penelope is a knight. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Liam is a knight. No contradiction is found in their claim that Penelope is a knight and Elizabeth is a knave.
Penelope cannot be a knight, because this would contradict the claim of their own that Liam is not a knight.
Penelope cannot be a knave, because this would contradict the claim of Liam that Penelope is a knight and Elizabeth is a knave.
We have exhausted all possibilities for Penelope, so let us go back and reconsider Liam.
Assume Liam is a knave. No contradiction is found in their false claim that Penelope is a knight and Elizabeth is a knave.
Assume Penelope is a knight. No contradiction is found in their claim that Liam is not a knight.
Assume Elizabeth is a knight. No contradiction is found in their claim that If Penelope is a knave then Penelope is a knight.
Therefore, (1) Liam is a knave
(2) Penelope is a knight
(3) Elizabeth is a knight </think>
<answer> (1) Liam is a knave
(2) Penelope is a knight
(3) Elizabeth is a knight </answer> | math | {
"ground_truth": {
"names": [
"Liam",
"Penelope",
"Elizabeth"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Liam is a knave\n(2) Penelope is a knight\n(3) Elizabeth is a knight",
"statements": "(('and', ('telling-truth', 1), ('lying', 2)), ('not', ('telling-truth', 0)), ('->', ('lying', 1), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 258,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Owen, Aria, and Liam. Owen said that Aria is a knight and Owen is a knight. Aria asserted: \"Owen is a knave\". Liam expressed that Owen is not a knight. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Owen is a knight. ",
"No contradiction is found in their claim that Aria is a knight and Owen is a knight.\n",
"Aria cannot be a knight, because this would contradict the claim of their own that Owen is a knave.\n",
"Aria cannot be a knave, because this would contradict the claim of Owen that Aria is a knight and Owen is a knight.\n",
"We have exhausted all possibilities for Aria, so let us go back and reconsider Owen.\n",
"Assume Owen is a knave. ",
"No contradiction is found in their false claim that Aria is a knight and Owen is a knight.\n",
"Assume Aria is a knight. ",
"No contradiction is found in their claim that Owen is a knave.\n",
"Assume Liam is a knight. ",
"No contradiction is found in their claim that Owen is not a knight.\n",
"Therefore, (1) Owen is a knave\n",
"(2) Aria is a knight\n",
"(3) Liam is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Owen, Aria, and Liam. Owen said that Aria is a knight and Owen is a knight. Aria asserted: "Owen is a knave". Liam expressed that Owen is not a knight. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Owen is a knight. No contradiction is found in their claim that Aria is a knight and Owen is a knight.
Aria cannot be a knight, because this would contradict the claim of their own that Owen is a knave.
Aria cannot be a knave, because this would contradict the claim of Owen that Aria is a knight and Owen is a knight.
We have exhausted all possibilities for Aria, so let us go back and reconsider Owen.
Assume Owen is a knave. No contradiction is found in their false claim that Aria is a knight and Owen is a knight.
Assume Aria is a knight. No contradiction is found in their claim that Owen is a knave.
Assume Liam is a knight. No contradiction is found in their claim that Owen is not a knight.
Therefore, (1) Owen is a knave
(2) Aria is a knight
(3) Liam is a knight </think>
<answer> (1) Owen is a knave
(2) Aria is a knight
(3) Liam is a knight </answer> | math | {
"ground_truth": {
"names": [
"Owen",
"Aria",
"Liam"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Owen is a knave\n(2) Aria is a knight\n(3) Liam is a knight",
"statements": "(('and', ('telling-truth', 1), ('telling-truth', 0)), ('lying', 0), ('not', ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 259,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Owen, Aria, and Oliver. Owen commented, \"Owen is a knight and Oliver is a knight\". Aria was heard saying, \"Oliver is a knave or Oliver is a knight\". Oliver told you that Aria is a knave if and only if Aria is a knight. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Owen is a knight. ",
"No contradiction is found in their claim that Owen is a knight and Oliver is a knight.\n",
"Oliver cannot be a knight, because this would contradict the claim of their own that Aria is a knave if and only if Aria is a knight.\n",
"Oliver cannot be a knave, because this would contradict the claim of Owen that Owen is a knight and Oliver is a knight.\n",
"We have exhausted all possibilities for Oliver, so let us go back and reconsider Owen.\n",
"Assume Owen is a knave. ",
"No contradiction is found in their false claim that Owen is a knight and Oliver is a knight.\n",
"Oliver cannot be a knight, because this would contradict the claim of their own that Aria is a knave if and only if Aria is a knight.\n",
"Assume Oliver is a knave. ",
"No contradiction is found in their false claim that Aria is a knave if and only if Aria is a knight.\n",
"Assume Aria is a knight. ",
"No contradiction is found in their claim that Oliver is a knave or Oliver is a knight.\n",
"Therefore, (1) Owen is a knave\n",
"(2) Aria is a knight\n",
"(3) Oliver is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Owen, Aria, and Oliver. Owen commented, "Owen is a knight and Oliver is a knight". Aria was heard saying, "Oliver is a knave or Oliver is a knight". Oliver told you that Aria is a knave if and only if Aria is a knight. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Owen is a knight. No contradiction is found in their claim that Owen is a knight and Oliver is a knight.
Oliver cannot be a knight, because this would contradict the claim of their own that Aria is a knave if and only if Aria is a knight.
Oliver cannot be a knave, because this would contradict the claim of Owen that Owen is a knight and Oliver is a knight.
We have exhausted all possibilities for Oliver, so let us go back and reconsider Owen.
Assume Owen is a knave. No contradiction is found in their false claim that Owen is a knight and Oliver is a knight.
Oliver cannot be a knight, because this would contradict the claim of their own that Aria is a knave if and only if Aria is a knight.
Assume Oliver is a knave. No contradiction is found in their false claim that Aria is a knave if and only if Aria is a knight.
Assume Aria is a knight. No contradiction is found in their claim that Oliver is a knave or Oliver is a knight.
Therefore, (1) Owen is a knave
(2) Aria is a knight
(3) Oliver is a knave </think>
<answer> (1) Owen is a knave
(2) Aria is a knight
(3) Oliver is a knave </answer> | math | {
"ground_truth": {
"names": [
"Owen",
"Aria",
"Oliver"
],
"solution": [
false,
true,
false
],
"solution_text_format": "(1) Owen is a knave\n(2) Aria is a knight\n(3) Oliver is a knave",
"statements": "(('and', ('telling-truth', 0), ('telling-truth', 2)), ('or', ('lying', 2), ('telling-truth', 2)), ('<=>', ('lying', 1), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 260,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Riley, Emily, and Daniel. In Riley's words: \"Daniel is a knight or Daniel is a knave\". \"If Daniel is a knight then Emily is a knight,\" Emily mentioned. Daniel said that Daniel is a knight if and only if Emily is a knave. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Riley is a knight. ",
"No contradiction is found in their claim that Daniel is a knight or Daniel is a knave.\n",
"Assume Daniel is a knight. ",
"No contradiction is found in their claim that Daniel is a knight if and only if Emily is a knave.\n",
"Emily cannot be a knight, because this would contradict the claim of Daniel that Daniel is a knight if and only if Emily is a knave.\n",
"Assume Emily is a knave. ",
"No contradiction is found in their false claim that If Daniel is a knight then Emily is a knight.\n",
"Therefore, (1) Riley is a knight\n",
"(2) Emily is a knave\n",
"(3) Daniel is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Riley, Emily, and Daniel. In Riley's words: "Daniel is a knight or Daniel is a knave". "If Daniel is a knight then Emily is a knight," Emily mentioned. Daniel said that Daniel is a knight if and only if Emily is a knave. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Riley is a knight. No contradiction is found in their claim that Daniel is a knight or Daniel is a knave.
Assume Daniel is a knight. No contradiction is found in their claim that Daniel is a knight if and only if Emily is a knave.
Emily cannot be a knight, because this would contradict the claim of Daniel that Daniel 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 If Daniel is a knight then Emily is a knight.
Therefore, (1) Riley is a knight
(2) Emily is a knave
(3) Daniel is a knight </think>
<answer> (1) Riley is a knight
(2) Emily is a knave
(3) Daniel is a knight </answer> | math | {
"ground_truth": {
"names": [
"Riley",
"Emily",
"Daniel"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Riley is a knight\n(2) Emily is a knave\n(3) Daniel is a knight",
"statements": "(('or', ('telling-truth', 2), ('lying', 2)), ('->', ('telling-truth', 2), ('telling-truth', 1)), ('<=>', ('telling-truth', 2), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 261,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Mason, Zoey, and Owen. Mason commented, \"Mason is a knight\". In a statement by Zoey: \"If Zoey is a knight then Owen is a knave\". \"Mason is a knave or Owen is a knight,\" Owen mentioned. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Mason is a knight. ",
"No contradiction is found in their claim that Mason is a knight.\n",
"Assume Zoey is a knight. ",
"No contradiction is found in their claim that If Zoey is a knight then Owen is a knave.\n",
"Owen cannot be a knight, because this would contradict the claim of Zoey that If Zoey is a knight then Owen is a knave.\n",
"Assume Owen is a knave. ",
"No contradiction is found in their false claim that Mason is a knave or Owen is a knight.\n",
"Therefore, (1) Mason is a knight\n",
"(2) Zoey is a knight\n",
"(3) Owen is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Mason, Zoey, and Owen. Mason commented, "Mason is a knight". In a statement by Zoey: "If Zoey is a knight then Owen is a knave". "Mason is a knave or Owen is a knight," Owen mentioned. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Mason is a knight. No contradiction is found in their claim that Mason is a knight.
Assume Zoey is a knight. No contradiction is found in their claim that If Zoey is a knight then Owen is a knave.
Owen cannot be a knight, because this would contradict the claim of Zoey that If Zoey is a knight then Owen is a knave.
Assume Owen is a knave. No contradiction is found in their false claim that Mason is a knave or Owen is a knight.
Therefore, (1) Mason is a knight
(2) Zoey is a knight
(3) Owen is a knave </think>
<answer> (1) Mason is a knight
(2) Zoey is a knight
(3) Owen is a knave </answer> | math | {
"ground_truth": {
"names": [
"Mason",
"Zoey",
"Owen"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Mason is a knight\n(2) Zoey is a knight\n(3) Owen is a knave",
"statements": "(('telling-truth', 0), ('->', ('telling-truth', 1), ('lying', 2)), ('or', ('lying', 0), ('telling-truth', 2)))"
},
"style": "rule"
} | {
"index": 262,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Logan, Elizabeth, and Harper. Logan asserted: \"Harper is a knight and Harper is a knave\". Elizabeth remarked, \"Harper is a knave and Logan is a knave\". In a statement by Harper: \"Logan is not a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Logan cannot be a knight, because this would contradict the claim of their own that Harper is a knight and Harper is a knave.\n",
"Assume Logan is a knave. ",
"No contradiction is found in their false claim that Harper is a knight and Harper is a knave.\n",
"Assume Harper is a knight. ",
"No contradiction is found in their claim that Logan is not a knight.\n",
"Elizabeth cannot be a knight, because this would contradict the claim of their own that Harper is a knave and Logan is a knave.\n",
"Assume Elizabeth is a knave. ",
"No contradiction is found in their false claim that Harper is a knave and Logan is a knave.\n",
"Therefore, (1) Logan is a knave\n",
"(2) Elizabeth is a knave\n",
"(3) Harper is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Logan, Elizabeth, and Harper. Logan asserted: "Harper is a knight and Harper is a knave". Elizabeth remarked, "Harper is a knave and Logan is a knave". In a statement by Harper: "Logan is not a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Logan cannot be a knight, because this would contradict the claim of their own that Harper is a knight and Harper is a knave.
Assume Logan is a knave. No contradiction is found in their false claim that Harper is a knight and Harper is a knave.
Assume Harper is a knight. No contradiction is found in their claim that Logan is not a knight.
Elizabeth cannot be a knight, because this would contradict the claim of their own that Harper is a knave and Logan is a knave.
Assume Elizabeth is a knave. No contradiction is found in their false claim that Harper is a knave and Logan is a knave.
Therefore, (1) Logan is a knave
(2) Elizabeth is a knave
(3) Harper is a knight </think>
<answer> (1) Logan is a knave
(2) Elizabeth is a knave
(3) Harper is a knight </answer> | math | {
"ground_truth": {
"names": [
"Logan",
"Elizabeth",
"Harper"
],
"solution": [
false,
false,
true
],
"solution_text_format": "(1) Logan is a knave\n(2) Elizabeth is a knave\n(3) Harper is a knight",
"statements": "(('and', ('telling-truth', 2), ('lying', 2)), ('and', ('lying', 2), ('lying', 0)), ('not', ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 263,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Lily, Chloe, and Aurora. Lily was heard saying, \"Aurora is a knave and Chloe is a knave\". In Chloe's words: \"Chloe is a knight if and only if Lily is a knight\". Aurora was heard saying, \"Lily is not a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Lily is a knight. ",
"No contradiction is found in their claim that Aurora is a knave and Chloe is a knave.\n",
"Aurora cannot be a knight, because this would contradict the claim of Lily that Aurora is a knave and Chloe is a knave.\n",
"Assume Aurora is a knave. ",
"No contradiction is found in their false claim that Lily is not a knight.\n",
"Chloe cannot be a knight, because this would contradict the claim of Lily that Aurora is a knave and Chloe is a knave.\n",
"Assume Chloe is a knave. ",
"No contradiction is found in their false claim that Chloe is a knight if and only if Lily is a knight.\n",
"Therefore, (1) Lily is a knight\n",
"(2) Chloe is a knave\n",
"(3) Aurora is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Lily, Chloe, and Aurora. Lily was heard saying, "Aurora is a knave and Chloe is a knave". In Chloe's words: "Chloe is a knight if and only if Lily is a knight". Aurora was heard saying, "Lily is not a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Lily is a knight. No contradiction is found in their claim that Aurora is a knave and Chloe is a knave.
Aurora cannot be a knight, because this would contradict the claim of Lily that Aurora is a knave and Chloe is a knave.
Assume Aurora is a knave. No contradiction is found in their false claim that Lily is not a knight.
Chloe cannot be a knight, because this would contradict the claim of Lily that Aurora is a knave and Chloe is a knave.
Assume Chloe is a knave. No contradiction is found in their false claim that Chloe is a knight if and only if Lily is a knight.
Therefore, (1) Lily is a knight
(2) Chloe is a knave
(3) Aurora is a knave </think>
<answer> (1) Lily is a knight
(2) Chloe is a knave
(3) Aurora is a knave </answer> | math | {
"ground_truth": {
"names": [
"Lily",
"Chloe",
"Aurora"
],
"solution": [
true,
false,
false
],
"solution_text_format": "(1) Lily is a knight\n(2) Chloe is a knave\n(3) Aurora is a knave",
"statements": "(('and', ('lying', 2), ('lying', 1)), ('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('not', ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 264,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Luke, Michael, and Elizabeth. Luke commented, \"If Elizabeth is a knight then Luke is a knight\". Michael said, \"Elizabeth is a knave and Elizabeth is a knight.\" \"Michael is a knave if and only if Luke is a knight\" - Elizabeth. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Luke is a knight. ",
"No contradiction is found in their claim that If Elizabeth is a knight then Luke is a knight.\n",
"Assume Elizabeth is a knight. ",
"No contradiction is found in their claim that Michael is a knave if and only if Luke is a knight.\n",
"Michael cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave and Elizabeth is a knight.\n",
"Assume Michael is a knave. ",
"No contradiction is found in their false claim that Elizabeth is a knave and Elizabeth is a knight.\n",
"Therefore, (1) Luke is a knight\n",
"(2) Michael is a knave\n",
"(3) Elizabeth is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Luke, Michael, and Elizabeth. Luke commented, "If Elizabeth is a knight then Luke is a knight". Michael said, "Elizabeth is a knave and Elizabeth is a knight." "Michael is a knave if and only if Luke is a knight" - Elizabeth. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Luke is a knight. No contradiction is found in their claim that If Elizabeth is a knight then Luke is a knight.
Assume Elizabeth is a knight. No contradiction is found in their claim that Michael is a knave if and only if Luke is a knight.
Michael cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave and Elizabeth is a knight.
Assume Michael is a knave. No contradiction is found in their false claim that Elizabeth is a knave and Elizabeth is a knight.
Therefore, (1) Luke is a knight
(2) Michael is a knave
(3) Elizabeth is a knight </think>
<answer> (1) Luke is a knight
(2) Michael is a knave
(3) Elizabeth is a knight </answer> | math | {
"ground_truth": {
"names": [
"Luke",
"Michael",
"Elizabeth"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Luke is a knight\n(2) Michael is a knave\n(3) Elizabeth is a knight",
"statements": "(('->', ('telling-truth', 2), ('telling-truth', 0)), ('and', ('lying', 2), ('telling-truth', 2)), ('<=>', ('lying', 1), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 265,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Abigail, Harper, and Olivia. In Abigail's words: \"Harper is a knight or Harper is a knave\". As Harper put it, \"Olivia is a knave or Harper is a knight\". According to Olivia, \"Harper is not a knave\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Abigail is a knight. ",
"No contradiction is found in their claim that Harper is a knight or Harper is a knave.\n",
"Assume Harper is a knight. ",
"No contradiction is found in their claim that Olivia is a knave or Harper is a knight.\n",
"Assume Olivia is a knight. ",
"No contradiction is found in their claim that Harper is not a knave.\n",
"Therefore, (1) Abigail is a knight\n",
"(2) Harper is a knight\n",
"(3) Olivia is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Abigail, Harper, and Olivia. In Abigail's words: "Harper is a knight or Harper is a knave". As Harper put it, "Olivia is a knave or Harper is a knight". According to Olivia, "Harper is not a knave". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Abigail is a knight. No contradiction is found in their claim that Harper is a knight or Harper is a knave.
Assume Harper is a knight. No contradiction is found in their claim that Olivia is a knave or Harper is a knight.
Assume Olivia is a knight. No contradiction is found in their claim that Harper is not a knave.
Therefore, (1) Abigail is a knight
(2) Harper is a knight
(3) Olivia is a knight </think>
<answer> (1) Abigail is a knight
(2) Harper is a knight
(3) Olivia is a knight </answer> | math | {
"ground_truth": {
"names": [
"Abigail",
"Harper",
"Olivia"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Abigail is a knight\n(2) Harper is a knight\n(3) Olivia is a knight",
"statements": "(('or', ('telling-truth', 1), ('lying', 1)), ('or', ('lying', 2), ('telling-truth', 1)), ('not', ('lying', 1)))"
},
"style": "rule"
} | {
"index": 266,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: James, Benjamin, and Emma. \"Benjamin is not a knave,\" James mentioned. Benjamin commented, \"Emma is a knave and Benjamin is a knight\". \"James is a knave or Benjamin is a knight\" - Emma. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume James is a knight. ",
"No contradiction is found in their claim that Benjamin is not a knave.\n",
"Assume Benjamin is a knight. ",
"No contradiction is found in their claim that Emma is a knave and Benjamin is a knight.\n",
"Emma cannot be a knight, because this would contradict the claim of Benjamin that Emma is a knave and Benjamin is a knight.\n",
"Emma cannot be a knave, because this would contradict the false claim of their own that James is a knave or Benjamin is a knight.\n",
"We have exhausted all possibilities for Emma, so let us go back and reconsider Benjamin.\n",
"Benjamin cannot be a knave, because this would contradict the claim of James that Benjamin is not a knave.\n",
"We have exhausted all possibilities for Benjamin, so let us go back and reconsider James.\n",
"Assume James is a knave. ",
"No contradiction is found in their false claim that Benjamin is not a knave.\n",
"Benjamin cannot be a knight, because this would contradict the false claim of James that Benjamin is not a knave.\n",
"Assume Benjamin is a knave. ",
"No contradiction is found in their false claim that Emma is a knave and Benjamin is a knight.\n",
"Assume Emma is a knight. ",
"No contradiction is found in their claim that James is a knave or Benjamin is a knight.\n",
"Therefore, (1) James is a knave\n",
"(2) Benjamin is a knave\n",
"(3) Emma is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: James, Benjamin, and Emma. "Benjamin is not a knave," James mentioned. Benjamin commented, "Emma is a knave and Benjamin is a knight". "James is a knave or Benjamin is a knight" - Emma. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume James is a knight. No contradiction is found in their claim that Benjamin is not a knave.
Assume Benjamin is a knight. No contradiction is found in their claim that Emma is a knave and Benjamin is a knight.
Emma cannot be a knight, because this would contradict the claim of Benjamin that Emma is a knave and Benjamin is a knight.
Emma cannot be a knave, because this would contradict the false claim of their own that James is a knave or Benjamin is a knight.
We have exhausted all possibilities for Emma, so let us go back and reconsider Benjamin.
Benjamin cannot be a knave, because this would contradict the claim of James that Benjamin is not a knave.
We have exhausted all possibilities for Benjamin, so let us go back and reconsider James.
Assume James is a knave. No contradiction is found in their false claim that Benjamin is not a knave.
Benjamin cannot be a knight, because this would contradict the false claim of James that Benjamin is not a knave.
Assume Benjamin is a knave. No contradiction is found in their false claim that Emma is a knave and Benjamin is a knight.
Assume Emma is a knight. No contradiction is found in their claim that James is a knave or Benjamin is a knight.
Therefore, (1) James is a knave
(2) Benjamin is a knave
(3) Emma is a knight </think>
<answer> (1) James is a knave
(2) Benjamin is a knave
(3) Emma is a knight </answer> | math | {
"ground_truth": {
"names": [
"James",
"Benjamin",
"Emma"
],
"solution": [
false,
false,
true
],
"solution_text_format": "(1) James is a knave\n(2) Benjamin is a knave\n(3) Emma is a knight",
"statements": "(('not', ('lying', 1)), ('and', ('lying', 2), ('telling-truth', 1)), ('or', ('lying', 0), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 267,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Owen, Oliver, and Abigail. Owen commented, \"Abigail is not a knight\". Oliver asserted: \"If Abigail is a knave then Owen is a knave\". Abigail said, \"Abigail is a knight and Oliver is a knave.\" So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Owen is a knight. ",
"No contradiction is found in their claim that Abigail is not a knight.\n",
"Abigail cannot be a knight, because this would contradict the claim of Owen that Abigail is not a knight.\n",
"Assume Abigail is a knave. ",
"No contradiction is found in their false claim that Abigail is a knight and Oliver is a knave.\n",
"Oliver cannot be a knight, because this would contradict the claim of their own that If Abigail is a knave then Owen is a knave.\n",
"Assume Oliver is a knave. ",
"No contradiction is found in their false claim that If Abigail is a knave then Owen is a knave.\n",
"Therefore, (1) Owen is a knight\n",
"(2) Oliver is a knave\n",
"(3) Abigail is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Owen, Oliver, and Abigail. Owen commented, "Abigail is not a knight". Oliver asserted: "If Abigail is a knave then Owen is a knave". Abigail said, "Abigail is a knight and Oliver is a knave." So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Owen 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 Owen that Abigail is not a knight.
Assume Abigail is a knave. No contradiction is found in their false claim that Abigail is a knight and Oliver is a knave.
Oliver cannot be a knight, because this would contradict the claim of their own that If Abigail is a knave then Owen is a knave.
Assume Oliver is a knave. No contradiction is found in their false claim that If Abigail is a knave then Owen is a knave.
Therefore, (1) Owen is a knight
(2) Oliver is a knave
(3) Abigail is a knave </think>
<answer> (1) Owen is a knight
(2) Oliver is a knave
(3) Abigail is a knave </answer> | math | {
"ground_truth": {
"names": [
"Owen",
"Oliver",
"Abigail"
],
"solution": [
true,
false,
false
],
"solution_text_format": "(1) Owen is a knight\n(2) Oliver is a knave\n(3) Abigail is a knave",
"statements": "(('not', ('telling-truth', 2)), ('->', ('lying', 2), ('lying', 0)), ('and', ('telling-truth', 2), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 268,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Aurora, Ava, and Riley. Aurora commented, \"Ava is a knight or Aurora is a knight\". Ava expressed that If Aurora is a knave then Riley is a knight. \"If Aurora is a knight then Ava is a knight,\" Riley claimed. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Aurora is a knight. ",
"No contradiction is found in their claim that Ava is a knight or Aurora is a knight.\n",
"Assume Ava is a knight. ",
"No contradiction is found in their claim that If Aurora is a knave then Riley is a knight.\n",
"Assume Riley is a knight. ",
"No contradiction is found in their claim that If Aurora is a knight then Ava is a knight.\n",
"Therefore, (1) Aurora is a knight\n",
"(2) Ava is a knight\n",
"(3) Riley is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Aurora, Ava, and Riley. Aurora commented, "Ava is a knight or Aurora is a knight". Ava expressed that If Aurora is a knave then Riley is a knight. "If Aurora is a knight then Ava is a knight," Riley claimed. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Aurora is a knight. No contradiction is found in their claim that Ava is a knight or Aurora is a knight.
Assume Ava is a knight. No contradiction is found in their claim that If Aurora is a knave then Riley is a knight.
Assume Riley is a knight. No contradiction is found in their claim that If Aurora is a knight then Ava is a knight.
Therefore, (1) Aurora is a knight
(2) Ava is a knight
(3) Riley is a knight </think>
<answer> (1) Aurora is a knight
(2) Ava is a knight
(3) Riley is a knight </answer> | math | {
"ground_truth": {
"names": [
"Aurora",
"Ava",
"Riley"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Aurora is a knight\n(2) Ava is a knight\n(3) Riley is a knight",
"statements": "(('or', ('telling-truth', 1), ('telling-truth', 0)), ('->', ('lying', 0), ('telling-truth', 2)), ('->', ('telling-truth', 0), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 269,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Victoria, Aurora, and Ella. \"Aurora is a knave if and only if Victoria is a knight,\" Victoria declared. Aurora said, \"Ella is a knave.\" In a statement by Ella: \"Victoria is a knight if and only if Aurora is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Victoria is a knight. ",
"No contradiction is found in their claim that Aurora is a knave if and only if Victoria is a knight.\n",
"Aurora cannot be a knight, because this would contradict the claim of Victoria that Aurora is a knave if and only if Victoria is a knight.\n",
"Assume Aurora is a knave. ",
"No contradiction is found in their false claim that Ella is a knave.\n",
"Ella cannot be a knight, because this would contradict the claim of their own that Victoria is a knight if and only if Aurora is a knight.\n",
"Ella cannot be a knave, because this would contradict the false claim of Aurora that Ella is a knave.\n",
"We have exhausted all possibilities for Ella and Aurora, so let us go back and reconsider Victoria.\n",
"Assume Victoria is a knave. ",
"No contradiction is found in their false claim that Aurora is a knave if and only if Victoria is a knight.\n",
"Aurora cannot be a knight, because this would contradict the false claim of Victoria that Aurora is a knave if and only if Victoria is a knight.\n",
"Assume Aurora is a knave. ",
"No contradiction is found in their false claim that Ella is a knave.\n",
"Assume Ella is a knight. ",
"No contradiction is found in their claim that Victoria is a knight if and only if Aurora is a knight.\n",
"Therefore, (1) Victoria is a knave\n",
"(2) Aurora is a knave\n",
"(3) Ella is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Victoria, Aurora, and Ella. "Aurora is a knave if and only if Victoria is a knight," Victoria declared. Aurora said, "Ella is a knave." In a statement by Ella: "Victoria is a knight if and only if Aurora is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Victoria is a knight. No contradiction is found in their claim that Aurora is a knave if and only if Victoria is a knight.
Aurora cannot be a knight, because this would contradict the claim of Victoria that Aurora is a knave if and only if Victoria is a knight.
Assume Aurora is a knave. No contradiction is found in their false claim that Ella is a knave.
Ella cannot be a knight, because this would contradict the claim of their own that Victoria is a knight if and only if Aurora is a knight.
Ella cannot be a knave, because this would contradict the false claim of Aurora that Ella is a knave.
We have exhausted all possibilities for Ella and Aurora, so let us go back and reconsider Victoria.
Assume Victoria is a knave. No contradiction is found in their false claim that Aurora is a knave if and only if Victoria is a knight.
Aurora cannot be a knight, because this would contradict the false claim of Victoria that Aurora is a knave if and only if Victoria is a knight.
Assume Aurora 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 Victoria is a knight if and only if Aurora is a knight.
Therefore, (1) Victoria is a knave
(2) Aurora is a knave
(3) Ella is a knight </think>
<answer> (1) Victoria is a knave
(2) Aurora is a knave
(3) Ella is a knight </answer> | math | {
"ground_truth": {
"names": [
"Victoria",
"Aurora",
"Ella"
],
"solution": [
false,
false,
true
],
"solution_text_format": "(1) Victoria is a knave\n(2) Aurora is a knave\n(3) Ella is a knight",
"statements": "(('<=>', ('lying', 1), ('telling-truth', 0)), ('lying', 2), ('<=>', ('telling-truth', 0), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 270,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Avery, Aria, and Evelyn. Avery told you that Aria is a knave. \"Aria is a knight or Avery is a knight,\" Aria mentioned. Evelyn commented, \"Avery is a knight or Avery is a knave\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Avery is a knight. ",
"No contradiction is found in their claim that Aria is a knave.\n",
"Aria cannot be a knight, because this would contradict the claim of Avery that Aria is a knave.\n",
"Aria cannot be a knave, because this would contradict the false claim of their own that Aria is a knight or Avery is a knight.\n",
"We have exhausted all possibilities for Aria, so let us go back and reconsider Avery.\n",
"Assume Avery is a knave. ",
"No contradiction is found in their false claim that Aria is a knave.\n",
"Assume Aria is a knight. ",
"No contradiction is found in their claim that Aria is a knight or Avery is a knight.\n",
"Assume Evelyn is a knight. ",
"No contradiction is found in their claim that Avery is a knight or Avery is a knave.\n",
"Therefore, (1) Avery is a knave\n",
"(2) Aria is a knight\n",
"(3) Evelyn is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Avery, Aria, and Evelyn. Avery told you that Aria is a knave. "Aria is a knight or Avery is a knight," Aria mentioned. Evelyn commented, "Avery is a knight or Avery is a knave". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Avery is a knight. No contradiction is found in their claim that Aria is a knave.
Aria cannot be a knight, because this would contradict the claim of Avery that Aria is a knave.
Aria cannot be a knave, because this would contradict the false claim of their own that Aria is a knight or Avery is a knight.
We have exhausted all possibilities for Aria, so let us go back and reconsider Avery.
Assume Avery is a knave. No contradiction is found in their false claim that Aria is a knave.
Assume Aria is a knight. No contradiction is found in their claim that Aria is a knight or Avery is a knight.
Assume Evelyn is a knight. No contradiction is found in their claim that Avery is a knight or Avery is a knave.
Therefore, (1) Avery is a knave
(2) Aria is a knight
(3) Evelyn is a knight </think>
<answer> (1) Avery is a knave
(2) Aria is a knight
(3) Evelyn is a knight </answer> | math | {
"ground_truth": {
"names": [
"Avery",
"Aria",
"Evelyn"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Avery is a knave\n(2) Aria is a knight\n(3) Evelyn is a knight",
"statements": "(('lying', 1), ('or', ('telling-truth', 1), ('telling-truth', 0)), ('or', ('telling-truth', 0), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 271,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Ella, Jackson, and Sophia. According to Ella, \"Sophia is a knave if and only if Ella is a knight\". In Jackson's words: \"Ella is a knave and Ella is a knight\". Sophia expressed that If Ella is a knight then Ella is a knave. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Ella is a knight. ",
"No contradiction is found in their claim that Sophia is a knave if and only if Ella is a knight.\n",
"Sophia cannot be a knight, because this would contradict the claim of Ella that Sophia is a knave if and only if Ella is a knight.\n",
"Assume Sophia is a knave. ",
"No contradiction is found in their false claim that If Ella is a knight then Ella is a knave.\n",
"Jackson cannot be a knight, because this would contradict the claim of their own that Ella is a knave and Ella is a knight.\n",
"Assume Jackson is a knave. ",
"No contradiction is found in their false claim that Ella is a knave and Ella is a knight.\n",
"Therefore, (1) Ella is a knight\n",
"(2) Jackson is a knave\n",
"(3) Sophia is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Ella, Jackson, and Sophia. According to Ella, "Sophia is a knave if and only if Ella is a knight". In Jackson's words: "Ella is a knave and Ella is a knight". Sophia expressed that If Ella is a knight then Ella is a knave. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Ella is a knight. No contradiction is found in their claim that Sophia is a knave if and only if Ella is a knight.
Sophia cannot be a knight, because this would contradict the claim of Ella that Sophia is a knave if and only if Ella is a knight.
Assume Sophia is a knave. No contradiction is found in their false claim that If Ella is a knight then Ella is a knave.
Jackson cannot be a knight, because this would contradict the claim of their own that Ella is a knave and Ella is a knight.
Assume Jackson is a knave. No contradiction is found in their false claim that Ella is a knave and Ella is a knight.
Therefore, (1) Ella is a knight
(2) Jackson is a knave
(3) Sophia is a knave </think>
<answer> (1) Ella is a knight
(2) Jackson is a knave
(3) Sophia is a knave </answer> | math | {
"ground_truth": {
"names": [
"Ella",
"Jackson",
"Sophia"
],
"solution": [
true,
false,
false
],
"solution_text_format": "(1) Ella is a knight\n(2) Jackson is a knave\n(3) Sophia is a knave",
"statements": "(('<=>', ('lying', 2), ('telling-truth', 0)), ('and', ('lying', 0), ('telling-truth', 0)), ('->', ('telling-truth', 0), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 272,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Emma, Olivia, and Sofia. According to Emma, \"Olivia is not a knight\". \"Sofia is a knight if and only if Sofia is a knave\" - Olivia. As Sofia put it, \"Emma is a knight and Emma is a knave\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Emma is a knight. ",
"No contradiction is found in their claim that Olivia is not a knight.\n",
"Olivia cannot be a knight, because this would contradict the claim of Emma that Olivia is not a knight.\n",
"Assume Olivia is a knave. ",
"No contradiction is found in their false claim that Sofia is a knight if and only if Sofia is a knave.\n",
"Sofia cannot be a knight, because this would contradict the claim of their own that Emma is a knight and Emma is a knave.\n",
"Assume Sofia is a knave. ",
"No contradiction is found in their false claim that Emma is a knight and Emma is a knave.\n",
"Therefore, (1) Emma is a knight\n",
"(2) Olivia is a knave\n",
"(3) Sofia is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Emma, Olivia, and Sofia. According to Emma, "Olivia is not a knight". "Sofia is a knight if and only if Sofia is a knave" - Olivia. As Sofia put it, "Emma is a knight and Emma is a knave". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Emma is a knight. No contradiction is found in their claim that Olivia is not a knight.
Olivia cannot be a knight, because this would contradict the claim of Emma that Olivia is not a knight.
Assume Olivia is a knave. No contradiction is found in their false claim that Sofia is a knight if and only if Sofia is a knave.
Sofia cannot be a knight, because this would contradict the claim of their own that Emma is a knight and Emma is a knave.
Assume Sofia is a knave. No contradiction is found in their false claim that Emma is a knight and Emma is a knave.
Therefore, (1) Emma is a knight
(2) Olivia is a knave
(3) Sofia is a knave </think>
<answer> (1) Emma is a knight
(2) Olivia is a knave
(3) Sofia is a knave </answer> | math | {
"ground_truth": {
"names": [
"Emma",
"Olivia",
"Sofia"
],
"solution": [
true,
false,
false
],
"solution_text_format": "(1) Emma is a knight\n(2) Olivia is a knave\n(3) Sofia is a knave",
"statements": "(('not', ('telling-truth', 1)), ('<=>', ('telling-truth', 2), ('lying', 2)), ('and', ('telling-truth', 0), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 273,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: James, Harper, and Alexander. According to James, \"Alexander is a knight if and only if Alexander is a knave\". \"Alexander is a knight,\" Harper mentioned. According to Alexander, \"If James is a knight then Harper is a knave\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"James cannot be a knight, because this would contradict the claim of their own that Alexander is a knight if and only if Alexander is a knave.\n",
"Assume James is a knave. ",
"No contradiction is found in their false claim that Alexander is a knight if and only if Alexander is a knave.\n",
"Assume Alexander is a knight. ",
"No contradiction is found in their claim that If James is a knight then Harper is a knave.\n",
"Assume Harper is a knight. ",
"No contradiction is found in their claim that Alexander is a knight.\n",
"Therefore, (1) James is a knave\n",
"(2) Harper is a knight\n",
"(3) Alexander is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: James, Harper, and Alexander. According to James, "Alexander is a knight if and only if Alexander is a knave". "Alexander is a knight," Harper mentioned. According to Alexander, "If James is a knight then Harper is a knave". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | James cannot be a knight, because this would contradict the claim of their own that Alexander is a knight if and only if Alexander is a knave.
Assume James is a knave. No contradiction is found in their false claim that Alexander is a knight if and only if Alexander is a knave.
Assume Alexander is a knight. No contradiction is found in their claim that If James is a knight then Harper is a knave.
Assume Harper is a knight. No contradiction is found in their claim that Alexander is a knight.
Therefore, (1) James is a knave
(2) Harper is a knight
(3) Alexander is a knight </think>
<answer> (1) James is a knave
(2) Harper is a knight
(3) Alexander is a knight </answer> | math | {
"ground_truth": {
"names": [
"James",
"Harper",
"Alexander"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) James is a knave\n(2) Harper is a knight\n(3) Alexander is a knight",
"statements": "(('<=>', ('telling-truth', 2), ('lying', 2)), ('telling-truth', 2), ('->', ('telling-truth', 0), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 274,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Emily, Harper, and Jack. \"If Harper is a knave then Emily is a knight,\" Emily declared. Harper said, \"Jack is a knave.\" In Jack's words: \"Harper is a knave and Harper is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Emily is a knight. ",
"No contradiction is found in their claim that If Harper is a knave then Emily is a knight.\n",
"Assume Harper is a knight. ",
"No contradiction is found in their claim that Jack is a knave.\n",
"Jack cannot be a knight, because this would contradict the claim of Harper that Jack is a knave.\n",
"Assume Jack is a knave. ",
"No contradiction is found in their false claim that Harper is a knave and Harper is a knight.\n",
"Therefore, (1) Emily is a knight\n",
"(2) Harper is a knight\n",
"(3) Jack is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Emily, Harper, and Jack. "If Harper is a knave then Emily is a knight," Emily declared. Harper said, "Jack is a knave." In Jack's words: "Harper is a knave and Harper is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Emily is a knight. No contradiction is found in their claim that If Harper is a knave then Emily is a knight.
Assume Harper is a knight. No contradiction is found in their claim that Jack is a knave.
Jack cannot be a knight, because this would contradict the claim of Harper that Jack is a knave.
Assume Jack is a knave. No contradiction is found in their false claim that Harper is a knave and Harper is a knight.
Therefore, (1) Emily is a knight
(2) Harper is a knight
(3) Jack is a knave </think>
<answer> (1) Emily is a knight
(2) Harper is a knight
(3) Jack is a knave </answer> | math | {
"ground_truth": {
"names": [
"Emily",
"Harper",
"Jack"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Emily is a knight\n(2) Harper is a knight\n(3) Jack is a knave",
"statements": "(('->', ('lying', 1), ('telling-truth', 0)), ('lying', 2), ('and', ('lying', 1), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 275,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Penelope, Liam, and Charlotte. Penelope told you that Charlotte is a knight or Liam is a knight. Liam asserted: \"Penelope is a knave\". Charlotte asserted: \"If Penelope is a knave then Penelope is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Penelope is a knight. ",
"No contradiction is found in their claim that Charlotte is a knight or Liam is a knight.\n",
"Assume Charlotte is a knight. ",
"No contradiction is found in their claim that If Penelope is a knave then Penelope is a knight.\n",
"Liam cannot be a knight, because this would contradict the claim of their own that Penelope is a knave.\n",
"Assume Liam is a knave. ",
"No contradiction is found in their false claim that Penelope is a knave.\n",
"Therefore, (1) Penelope is a knight\n",
"(2) Liam is a knave\n",
"(3) Charlotte is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Penelope, Liam, and Charlotte. Penelope told you that Charlotte is a knight or Liam is a knight. Liam asserted: "Penelope is a knave". Charlotte asserted: "If Penelope is a knave then Penelope is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Penelope is a knight. No contradiction is found in their claim that Charlotte is a knight or Liam is a knight.
Assume Charlotte is a knight. No contradiction is found in their claim that If Penelope is a knave then Penelope is a knight.
Liam cannot be a knight, because this would contradict the claim of their own that Penelope is a knave.
Assume Liam is a knave. No contradiction is found in their false claim that Penelope is a knave.
Therefore, (1) Penelope is a knight
(2) Liam is a knave
(3) Charlotte is a knight </think>
<answer> (1) Penelope is a knight
(2) Liam is a knave
(3) Charlotte is a knight </answer> | math | {
"ground_truth": {
"names": [
"Penelope",
"Liam",
"Charlotte"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Penelope is a knight\n(2) Liam is a knave\n(3) Charlotte is a knight",
"statements": "(('or', ('telling-truth', 2), ('telling-truth', 1)), ('lying', 0), ('->', ('lying', 0), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 276,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Grace, Noah, and Penelope. Grace noted, \"Noah is not a knave\". Noah was heard saying, \"Grace is a knave and Penelope is a knight\". Penelope told you that Grace is a knight if and only if Noah is a knave. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Grace is a knight. ",
"No contradiction is found in their claim that Noah is not a knave.\n",
"Noah cannot be a knight, because this would contradict the claim of their own that Grace is a knave and Penelope is a knight.\n",
"Noah cannot be a knave, because this would contradict the claim of Grace that Noah is not a knave.\n",
"We have exhausted all possibilities for Noah, so let us go back and reconsider Grace.\n",
"Assume Grace is a knave. ",
"No contradiction is found in their false claim that Noah is not a knave.\n",
"Noah cannot be a knight, because this would contradict the false claim of Grace that Noah is not a knave.\n",
"Assume Noah is a knave. ",
"No contradiction is found in their false claim that Grace is a knave and Penelope is a knight.\n",
"Penelope cannot be a knight, because this would contradict the false claim of Noah that Grace is a knave and Penelope is a knight.\n",
"Assume Penelope is a knave. ",
"No contradiction is found in their false claim that Grace is a knight if and only if Noah is a knave.\n",
"Therefore, (1) Grace is a knave\n",
"(2) Noah is a knave\n",
"(3) Penelope is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Grace, Noah, and Penelope. Grace noted, "Noah is not a knave". Noah was heard saying, "Grace is a knave and Penelope is a knight". Penelope told you that Grace is a knight if and only if Noah is a knave. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Grace is a knight. No contradiction is found in their claim that Noah is not a knave.
Noah cannot be a knight, because this would contradict the claim of their own that Grace is a knave and Penelope is a knight.
Noah cannot be a knave, because this would contradict the claim of Grace that Noah is not a knave.
We have exhausted all possibilities for Noah, so let us go back and reconsider Grace.
Assume Grace is a knave. No contradiction is found in their false claim that Noah is not a knave.
Noah cannot be a knight, because this would contradict the false claim of Grace that Noah is not a knave.
Assume Noah is a knave. No contradiction is found in their false claim that Grace is a knave and Penelope is a knight.
Penelope cannot be a knight, because this would contradict the false claim of Noah that Grace is a knave and Penelope is a knight.
Assume Penelope is a knave. No contradiction is found in their false claim that Grace is a knight if and only if Noah is a knave.
Therefore, (1) Grace is a knave
(2) Noah is a knave
(3) Penelope is a knave </think>
<answer> (1) Grace is a knave
(2) Noah is a knave
(3) Penelope is a knave </answer> | math | {
"ground_truth": {
"names": [
"Grace",
"Noah",
"Penelope"
],
"solution": [
false,
false,
false
],
"solution_text_format": "(1) Grace is a knave\n(2) Noah is a knave\n(3) Penelope is a knave",
"statements": "(('not', ('lying', 1)), ('and', ('lying', 0), ('telling-truth', 2)), ('<=>', ('telling-truth', 0), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 277,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Charlotte, Emma, and Sophia. \"Sophia is not a knight\" - Charlotte. Emma stated, \"If Sophia is a knight then Charlotte is a knave\". Sophia said, \"Emma is a knave.\" So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Charlotte is a knight. ",
"No contradiction is found in their claim that Sophia is not a knight.\n",
"Sophia cannot be a knight, because this would contradict the claim of Charlotte that Sophia is not a knight.\n",
"Assume Sophia is a knave. ",
"No contradiction is found in their false claim that Emma is a knave.\n",
"Assume Emma is a knight. ",
"No contradiction is found in their claim that If Sophia is a knight then Charlotte is a knave.\n",
"Therefore, (1) Charlotte is a knight\n",
"(2) Emma is a knight\n",
"(3) Sophia is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Charlotte, Emma, and Sophia. "Sophia is not a knight" - Charlotte. Emma stated, "If Sophia is a knight then Charlotte is a knave". Sophia said, "Emma is a knave." So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Charlotte is a knight. No contradiction is found in their claim that Sophia is not a knight.
Sophia cannot be a knight, because this would contradict the claim of Charlotte that Sophia is not a knight.
Assume Sophia is a knave. No contradiction is found in their false claim that Emma is a knave.
Assume Emma is a knight. No contradiction is found in their claim that If Sophia is a knight then Charlotte is a knave.
Therefore, (1) Charlotte is a knight
(2) Emma is a knight
(3) Sophia is a knave </think>
<answer> (1) Charlotte is a knight
(2) Emma is a knight
(3) Sophia is a knave </answer> | math | {
"ground_truth": {
"names": [
"Charlotte",
"Emma",
"Sophia"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Charlotte is a knight\n(2) Emma is a knight\n(3) Sophia is a knave",
"statements": "(('not', ('telling-truth', 2)), ('->', ('telling-truth', 2), ('lying', 0)), ('lying', 1))"
},
"style": "rule"
} | {
"index": 278,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Jackson, Samuel, and Benjamin. Jackson stated, \"If Jackson is a knight then Samuel is a knave\". Samuel stated, \"Jackson is a knight if and only if Jackson is a knave\". \"If Samuel is a knight then Jackson is a knight,\" Benjamin declared. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Jackson is a knight. ",
"No contradiction is found in their claim that If Jackson is a knight then Samuel is a knave.\n",
"Samuel cannot be a knight, because this would contradict the claim of Jackson that If Jackson is a knight then Samuel is a knave.\n",
"Assume Samuel is a knave. ",
"No contradiction is found in their false claim that Jackson is a knight if and only if Jackson is a knave.\n",
"Assume Benjamin is a knight. ",
"No contradiction is found in their claim that If Samuel is a knight then Jackson is a knight.\n",
"Therefore, (1) Jackson is a knight\n",
"(2) Samuel is a knave\n",
"(3) Benjamin is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Jackson, Samuel, and Benjamin. Jackson stated, "If Jackson is a knight then Samuel is a knave". Samuel stated, "Jackson is a knight if and only if Jackson is a knave". "If Samuel is a knight then Jackson is a knight," Benjamin declared. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Jackson is a knight. No contradiction is found in their claim that If Jackson is a knight then Samuel is a knave.
Samuel cannot be a knight, because this would contradict the claim of Jackson that If Jackson is a knight then Samuel is a knave.
Assume Samuel is a knave. No contradiction is found in their false claim that Jackson is a knight if and only if Jackson is a knave.
Assume Benjamin is a knight. No contradiction is found in their claim that If Samuel is a knight then Jackson is a knight.
Therefore, (1) Jackson is a knight
(2) Samuel is a knave
(3) Benjamin is a knight </think>
<answer> (1) Jackson is a knight
(2) Samuel is a knave
(3) Benjamin is a knight </answer> | math | {
"ground_truth": {
"names": [
"Jackson",
"Samuel",
"Benjamin"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Jackson is a knight\n(2) Samuel is a knave\n(3) Benjamin is a knight",
"statements": "(('->', ('telling-truth', 0), ('lying', 1)), ('<=>', ('telling-truth', 0), ('lying', 0)), ('->', ('telling-truth', 1), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 279,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Henry, Avery, and Victoria. According to Henry, \"Victoria is a knave\". \"Victoria is a knave,\" Avery mentioned. Victoria asserted: \"Henry is a knight if and only if Avery is a knave\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Henry is a knight. ",
"No contradiction is found in their claim that Victoria is a knave.\n",
"Victoria cannot be a knight, because this would contradict the claim of Henry that Victoria is a knave.\n",
"Assume Victoria is a knave. ",
"No contradiction is found in their false claim that Henry is a knight if and only if Avery is a knave.\n",
"Assume Avery is a knight. ",
"No contradiction is found in their claim that Victoria is a knave.\n",
"Therefore, (1) Henry is a knight\n",
"(2) Avery is a knight\n",
"(3) Victoria is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Henry, Avery, and Victoria. According to Henry, "Victoria is a knave". "Victoria is a knave," Avery mentioned. Victoria asserted: "Henry is a knight if and only if Avery is a knave". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Henry 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 Henry that Victoria is a knave.
Assume Victoria is a knave. No contradiction is found in their false claim that Henry is a knight if and only if Avery is a knave.
Assume Avery is a knight. No contradiction is found in their claim that Victoria is a knave.
Therefore, (1) Henry is a knight
(2) Avery is a knight
(3) Victoria is a knave </think>
<answer> (1) Henry is a knight
(2) Avery is a knight
(3) Victoria is a knave </answer> | math | {
"ground_truth": {
"names": [
"Henry",
"Avery",
"Victoria"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Henry is a knight\n(2) Avery is a knight\n(3) Victoria is a knave",
"statements": "(('lying', 2), ('lying', 2), ('<=>', ('telling-truth', 0), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 280,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: David, Ella, and Isabella. David said, \"Ella is a knight.\" \"If Isabella is a knight then Ella is a knight,\" Ella mentioned. In a statement by Isabella: \"David is a knight and Ella is a knave\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume David is a knight. ",
"No contradiction is found in their claim that Ella is a knight.\n",
"Assume Ella is a knight. ",
"No contradiction is found in their claim that If Isabella is a knight then Ella is a knight.\n",
"Isabella cannot be a knight, because this would contradict the claim of their own that David is a knight and Ella is a knave.\n",
"Assume Isabella is a knave. ",
"No contradiction is found in their false claim that David is a knight and Ella is a knave.\n",
"Therefore, (1) David is a knight\n",
"(2) Ella is a knight\n",
"(3) Isabella is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: David, Ella, and Isabella. David said, "Ella is a knight." "If Isabella is a knight then Ella is a knight," Ella mentioned. In a statement by Isabella: "David is a knight and Ella is a knave". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume David is a knight. No contradiction is found in their claim that Ella is a knight.
Assume Ella is a knight. No contradiction is found in their claim that If Isabella is a knight then Ella is a knight.
Isabella cannot be a knight, because this would contradict the claim of their own that David is a knight and Ella is a knave.
Assume Isabella is a knave. No contradiction is found in their false claim that David is a knight and Ella is a knave.
Therefore, (1) David is a knight
(2) Ella is a knight
(3) Isabella is a knave </think>
<answer> (1) David is a knight
(2) Ella is a knight
(3) Isabella is a knave </answer> | math | {
"ground_truth": {
"names": [
"David",
"Ella",
"Isabella"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) David is a knight\n(2) Ella is a knight\n(3) Isabella is a knave",
"statements": "(('telling-truth', 1), ('->', ('telling-truth', 2), ('telling-truth', 1)), ('and', ('telling-truth', 0), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 281,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Abigail, Charlotte, and Aiden. Abigail expressed that Aiden is a knight. \"Aiden is a knave\" - Charlotte. \"Abigail is a knight if and only if Aiden is a knight,\" Aiden declared. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Abigail is a knight. ",
"No contradiction is found in their claim that Aiden is a knight.\n",
"Assume Aiden is a knight. ",
"No contradiction is found in their claim that Abigail is a knight if and only if Aiden is a knight.\n",
"Charlotte cannot be a knight, because this would contradict the claim of their own that Aiden is a knave.\n",
"Assume Charlotte is a knave. ",
"No contradiction is found in their false claim that Aiden is a knave.\n",
"Therefore, (1) Abigail is a knight\n",
"(2) Charlotte is a knave\n",
"(3) Aiden is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Abigail, Charlotte, and Aiden. Abigail expressed that Aiden is a knight. "Aiden is a knave" - Charlotte. "Abigail is a knight if and only if Aiden is a knight," Aiden declared. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Abigail is a knight. No contradiction is found in their claim that Aiden is a knight.
Assume Aiden is a knight. No contradiction is found in their claim that Abigail is a knight if and only if Aiden is a knight.
Charlotte cannot be a knight, because this would contradict the claim of their own that Aiden is a knave.
Assume Charlotte is a knave. No contradiction is found in their false claim that Aiden is a knave.
Therefore, (1) Abigail is a knight
(2) Charlotte is a knave
(3) Aiden is a knight </think>
<answer> (1) Abigail is a knight
(2) Charlotte is a knave
(3) Aiden is a knight </answer> | math | {
"ground_truth": {
"names": [
"Abigail",
"Charlotte",
"Aiden"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Abigail is a knight\n(2) Charlotte is a knave\n(3) Aiden is a knight",
"statements": "(('telling-truth', 2), ('lying', 2), ('<=>', ('telling-truth', 0), ('telling-truth', 2)))"
},
"style": "rule"
} | {
"index": 282,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Ethan, Elizabeth, and Sophia. Ethan asserted: \"Sophia is a knight and Elizabeth is a knight\". Elizabeth stated, \"Elizabeth is a knight\". Sophia said, \"Elizabeth is a knave or Ethan is a knave.\" So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Ethan is a knight. ",
"No contradiction is found in their claim that Sophia is a knight and Elizabeth is a knight.\n",
"Assume Sophia is a knight. ",
"No contradiction is found in their claim that Elizabeth is a knave or Ethan is a knave.\n",
"Elizabeth cannot be a knight, because this would contradict the claim of Sophia that Elizabeth is a knave or Ethan is a knave.\n",
"Elizabeth cannot be a knave, because this would contradict the claim of Ethan that Sophia is a knight and Elizabeth is a knight.\n",
"We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Sophia.\n",
"Sophia cannot be a knave, because this would contradict the claim of Ethan that Sophia is a knight and Elizabeth is a knight.\n",
"We have exhausted all possibilities for Sophia, so let us go back and reconsider Ethan.\n",
"Assume Ethan is a knave. ",
"No contradiction is found in their false claim that Sophia is a knight and Elizabeth is a knight.\n",
"Assume Sophia is a knight. ",
"No contradiction is found in their claim that Elizabeth is a knave or Ethan is a knave.\n",
"Elizabeth cannot be a knight, because this would contradict the false claim of Ethan that Sophia is a knight and Elizabeth is a knight.\n",
"Assume Elizabeth is a knave. ",
"No contradiction is found in their false claim that Elizabeth is a knight.\n",
"Therefore, (1) Ethan is a knave\n",
"(2) Elizabeth is a knave\n",
"(3) Sophia is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Ethan, Elizabeth, and Sophia. Ethan asserted: "Sophia is a knight and Elizabeth is a knight". Elizabeth stated, "Elizabeth is a knight". Sophia said, "Elizabeth is a knave or Ethan is a knave." So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Ethan is a knight. No contradiction is found in their claim that Sophia is a knight and Elizabeth is a knight.
Assume Sophia is a knight. No contradiction is found in their claim that Elizabeth is a knave or Ethan is a knave.
Elizabeth cannot be a knight, because this would contradict the claim of Sophia that Elizabeth is a knave or Ethan is a knave.
Elizabeth cannot be a knave, because this would contradict the claim of Ethan that Sophia is a knight and Elizabeth is a knight.
We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Sophia.
Sophia cannot be a knave, because this would contradict the claim of Ethan that Sophia is a knight and Elizabeth is a knight.
We have exhausted all possibilities for Sophia, so let us go back and reconsider Ethan.
Assume Ethan is a knave. No contradiction is found in their false claim that Sophia is a knight and Elizabeth is a knight.
Assume Sophia is a knight. No contradiction is found in their claim that Elizabeth is a knave or Ethan is a knave.
Elizabeth cannot be a knight, because this would contradict the false claim of Ethan that Sophia is a knight and Elizabeth is a knight.
Assume Elizabeth is a knave. No contradiction is found in their false claim that Elizabeth is a knight.
Therefore, (1) Ethan is a knave
(2) Elizabeth is a knave
(3) Sophia is a knight </think>
<answer> (1) Ethan is a knave
(2) Elizabeth is a knave
(3) Sophia is a knight </answer> | math | {
"ground_truth": {
"names": [
"Ethan",
"Elizabeth",
"Sophia"
],
"solution": [
false,
false,
true
],
"solution_text_format": "(1) Ethan is a knave\n(2) Elizabeth is a knave\n(3) Sophia is a knight",
"statements": "(('and', ('telling-truth', 2), ('telling-truth', 1)), ('telling-truth', 1), ('or', ('lying', 1), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 283,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Jackson, Luke, and Zoey. \"Zoey is a knave if and only if Zoey is a knight,\" Jackson mentioned. \"If Luke is a knight then Zoey is a knave,\" Luke declared. In a statement by Zoey: \"Jackson is a knight or Zoey is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Jackson 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.\n",
"Assume Jackson is a knave. ",
"No contradiction is found in their false claim that Zoey is a knave if and only if Zoey is a knight.\n",
"Assume Zoey is a knight. ",
"No contradiction is found in their claim that Jackson is a knight or Zoey is a knight.\n",
"Luke cannot be a knight, because this would contradict the claim of their own that If Luke is a knight then Zoey is a knave.\n",
"Luke cannot be a knave, because this would contradict the false claim of their own that If Luke is a knight then Zoey is a knave.\n",
"We have exhausted all possibilities for Luke, so let us go back and reconsider Zoey.\n",
"Assume Zoey is a knave. ",
"No contradiction is found in their false claim that Jackson is a knight or Zoey is a knight.\n",
"Assume Luke is a knight. ",
"No contradiction is found in their claim that If Luke is a knight then Zoey is a knave.\n",
"Therefore, (1) Jackson is a knave\n",
"(2) Luke is a knight\n",
"(3) Zoey is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Jackson, Luke, and Zoey. "Zoey is a knave if and only if Zoey is a knight," Jackson mentioned. "If Luke is a knight then Zoey is a knave," Luke declared. In a statement by Zoey: "Jackson is a knight or Zoey is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Jackson 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 Jackson 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 Jackson is a knight or Zoey is a knight.
Luke cannot be a knight, because this would contradict the claim of their own that If Luke is a knight then Zoey is a knave.
Luke cannot be a knave, because this would contradict the false claim of their own that If Luke is a knight then Zoey is a knave.
We have exhausted all possibilities for Luke, so let us go back and reconsider Zoey.
Assume Zoey is a knave. No contradiction is found in their false claim that Jackson is a knight or Zoey is a knight.
Assume Luke is a knight. No contradiction is found in their claim that If Luke is a knight then Zoey is a knave.
Therefore, (1) Jackson is a knave
(2) Luke is a knight
(3) Zoey is a knave </think>
<answer> (1) Jackson is a knave
(2) Luke is a knight
(3) Zoey is a knave </answer> | math | {
"ground_truth": {
"names": [
"Jackson",
"Luke",
"Zoey"
],
"solution": [
false,
true,
false
],
"solution_text_format": "(1) Jackson is a knave\n(2) Luke is a knight\n(3) Zoey is a knave",
"statements": "(('<=>', ('lying', 2), ('telling-truth', 2)), ('->', ('telling-truth', 1), ('lying', 2)), ('or', ('telling-truth', 0), ('telling-truth', 2)))"
},
"style": "rule"
} | {
"index": 284,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Mia, Luke, and Emma. Mia stated, \"Emma is a knave\". Luke expressed that Mia is a knight. Emma remarked, \"Luke is a knight and Mia is a knave\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Mia is a knight. ",
"No contradiction is found in their claim that Emma is a knave.\n",
"Emma cannot be a knight, because this would contradict the claim of Mia that Emma is a knave.\n",
"Assume Emma is a knave. ",
"No contradiction is found in their false claim that Luke is a knight and Mia is a knave.\n",
"Assume Luke is a knight. ",
"No contradiction is found in their claim that Mia is a knight.\n",
"Therefore, (1) Mia is a knight\n",
"(2) Luke is a knight\n",
"(3) Emma is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Mia, Luke, and Emma. Mia stated, "Emma is a knave". Luke expressed that Mia is a knight. Emma remarked, "Luke is a knight and Mia is a knave". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Mia 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 Mia that Emma is a knave.
Assume Emma is a knave. No contradiction is found in their false claim that Luke is a knight and Mia is a knave.
Assume Luke is a knight. No contradiction is found in their claim that Mia is a knight.
Therefore, (1) Mia is a knight
(2) Luke is a knight
(3) Emma is a knave </think>
<answer> (1) Mia is a knight
(2) Luke is a knight
(3) Emma is a knave </answer> | math | {
"ground_truth": {
"names": [
"Mia",
"Luke",
"Emma"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Mia is a knight\n(2) Luke is a knight\n(3) Emma is a knave",
"statements": "(('lying', 2), ('telling-truth', 0), ('and', ('telling-truth', 1), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 285,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Logan, Owen, and Isabella. Logan remarked, \"Isabella is a knight\". Owen stated, \"Isabella is a knight and Owen is a knight\". In a statement by Isabella: \"Logan is a knave and Logan is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Logan is a knight. ",
"No contradiction is found in their claim that Isabella is a knight.\n",
"Isabella cannot be a knight, because this would contradict the claim of their own that Logan is a knave and Logan is a knight.\n",
"Isabella cannot be a knave, because this would contradict the claim of Logan that Isabella is a knight.\n",
"We have exhausted all possibilities for Isabella, so let us go back and reconsider Logan.\n",
"Assume Logan is a knave. ",
"No contradiction is found in their false claim that Isabella is a knight.\n",
"Isabella cannot be a knight, because this would contradict the false claim of Logan that Isabella is a knight.\n",
"Assume Isabella is a knave. ",
"No contradiction is found in their false claim that Logan is a knave and Logan is a knight.\n",
"Owen cannot be a knight, because this would contradict the claim of their own that Isabella is a knight and Owen is a knight.\n",
"Assume Owen is a knave. ",
"No contradiction is found in their false claim that Isabella is a knight and Owen is a knight.\n",
"Therefore, (1) Logan is a knave\n",
"(2) Owen is a knave\n",
"(3) Isabella is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Logan, Owen, and Isabella. Logan remarked, "Isabella is a knight". Owen stated, "Isabella is a knight and Owen is a knight". In a statement by Isabella: "Logan is a knave and Logan is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Logan is a knight. No contradiction is found in their claim that Isabella is a knight.
Isabella cannot be a knight, because this would contradict the claim of their own that Logan is a knave and Logan is a knight.
Isabella cannot be a knave, because this would contradict the claim of Logan that Isabella is a knight.
We have exhausted all possibilities for Isabella, so let us go back and reconsider Logan.
Assume Logan is a knave. No contradiction is found in their false claim that Isabella is a knight.
Isabella cannot be a knight, because this would contradict the false claim of Logan that Isabella is a knight.
Assume Isabella is a knave. No contradiction is found in their false claim that Logan is a knave and Logan is a knight.
Owen cannot be a knight, because this would contradict the claim of their own that Isabella is a knight and Owen is a knight.
Assume Owen is a knave. No contradiction is found in their false claim that Isabella is a knight and Owen is a knight.
Therefore, (1) Logan is a knave
(2) Owen is a knave
(3) Isabella is a knave </think>
<answer> (1) Logan is a knave
(2) Owen is a knave
(3) Isabella is a knave </answer> | math | {
"ground_truth": {
"names": [
"Logan",
"Owen",
"Isabella"
],
"solution": [
false,
false,
false
],
"solution_text_format": "(1) Logan is a knave\n(2) Owen is a knave\n(3) Isabella is a knave",
"statements": "(('telling-truth', 2), ('and', ('telling-truth', 2), ('telling-truth', 1)), ('and', ('lying', 0), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 286,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Mason, William, and Luke. Mason remarked, \"If William is a knight then Luke is a knight\". In a statement by William: \"Luke is a knight if and only if Luke is a knave\". Luke said, \"William is a knave or Mason is a knight.\" So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Mason is a knight. ",
"No contradiction is found in their claim that If William is a knight then Luke is a knight.\n",
"William cannot be a knight, because this would contradict the claim of their own that Luke is a knight if and only if Luke is a knave.\n",
"Assume William is a knave. ",
"No contradiction is found in their false claim that Luke is a knight if and only if Luke is a knave.\n",
"Assume Luke is a knight. ",
"No contradiction is found in their claim that William is a knave or Mason is a knight.\n",
"Therefore, (1) Mason is a knight\n",
"(2) William is a knave\n",
"(3) Luke is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Mason, William, and Luke. Mason remarked, "If William is a knight then Luke is a knight". In a statement by William: "Luke is a knight if and only if Luke is a knave". Luke said, "William is a knave or Mason is a knight." So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Mason is a knight. No contradiction is found in their claim that If William is a knight then Luke is a knight.
William cannot be a knight, because this would contradict the claim of their own that Luke is a knight if and only if Luke is a knave.
Assume William is a knave. No contradiction is found in their false claim that Luke is a knight if and only if Luke is a knave.
Assume Luke is a knight. No contradiction is found in their claim that William is a knave or Mason is a knight.
Therefore, (1) Mason is a knight
(2) William is a knave
(3) Luke is a knight </think>
<answer> (1) Mason is a knight
(2) William is a knave
(3) Luke is a knight </answer> | math | {
"ground_truth": {
"names": [
"Mason",
"William",
"Luke"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Mason is a knight\n(2) William is a knave\n(3) Luke is a knight",
"statements": "(('->', ('telling-truth', 1), ('telling-truth', 2)), ('<=>', ('telling-truth', 2), ('lying', 2)), ('or', ('lying', 1), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 287,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Emma, Lily, and Michael. Emma was heard saying, \"Michael is a knave\". In Lily's words: \"Lily is a knight or Emma is a knight\". Michael said, \"Emma is a knight or Lily is a knave.\" So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Emma is a knight. ",
"No contradiction is found in their claim that Michael is a knave.\n",
"Michael cannot be a knight, because this would contradict the claim of Emma that Michael is a knave.\n",
"Michael cannot be a knave, because this would contradict the false claim of their own that Emma is a knight or Lily is a knave.\n",
"We have exhausted all possibilities for Michael, so let us go back and reconsider Emma.\n",
"Assume Emma is a knave. ",
"No contradiction is found in their false claim that Michael is a knave.\n",
"Assume Michael is a knight. ",
"No contradiction is found in their claim that Emma is a knight or Lily is a knave.\n",
"Lily cannot be a knight, because this would contradict the claim of Michael that Emma is a knight or Lily is a knave.\n",
"Assume Lily is a knave. ",
"No contradiction is found in their false claim that Lily is a knight or Emma is a knight.\n",
"Therefore, (1) Emma is a knave\n",
"(2) Lily is a knave\n",
"(3) Michael is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Emma, Lily, and Michael. Emma was heard saying, "Michael is a knave". In Lily's words: "Lily is a knight or Emma is a knight". Michael said, "Emma is a knight or Lily is a knave." So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Emma 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 Emma that Michael is a knave.
Michael cannot be a knave, because this would contradict the false claim of their own that Emma is a knight or Lily is a knave.
We have exhausted all possibilities for Michael, so let us go back and reconsider Emma.
Assume Emma is a knave. No contradiction is found in their false claim that Michael is a knave.
Assume Michael is a knight. No contradiction is found in their claim that Emma is a knight or Lily is a knave.
Lily cannot be a knight, because this would contradict the claim of Michael that Emma is a knight or Lily is a knave.
Assume Lily is a knave. No contradiction is found in their false claim that Lily is a knight or Emma is a knight.
Therefore, (1) Emma is a knave
(2) Lily is a knave
(3) Michael is a knight </think>
<answer> (1) Emma is a knave
(2) Lily is a knave
(3) Michael is a knight </answer> | math | {
"ground_truth": {
"names": [
"Emma",
"Lily",
"Michael"
],
"solution": [
false,
false,
true
],
"solution_text_format": "(1) Emma is a knave\n(2) Lily is a knave\n(3) Michael is a knight",
"statements": "(('lying', 2), ('or', ('telling-truth', 1), ('telling-truth', 0)), ('or', ('telling-truth', 0), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 288,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Matthew, Jack, and Scarlett. Matthew told you that Jack is a knave if and only if Matthew is a knight. Jack said that Matthew is a knave. Scarlett said, \"If Matthew is a knave then Jack is a knave.\" So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Matthew is a knight. ",
"No contradiction is found in their claim that Jack is a knave if and only if Matthew is a knight.\n",
"Jack cannot be a knight, because this would contradict the claim of Matthew that Jack is a knave if and only if Matthew is a knight.\n",
"Assume Jack is a knave. ",
"No contradiction is found in their false claim that Matthew is a knave.\n",
"Assume Scarlett is a knight. ",
"No contradiction is found in their claim that If Matthew is a knave then Jack is a knave.\n",
"Therefore, (1) Matthew is a knight\n",
"(2) Jack is a knave\n",
"(3) Scarlett is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Matthew, Jack, and Scarlett. Matthew told you that Jack is a knave if and only if Matthew is a knight. Jack said that Matthew is a knave. Scarlett said, "If Matthew is a knave then Jack is a knave." So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Matthew is a knight. No contradiction is found in their claim that Jack is a knave if and only if Matthew is a knight.
Jack cannot be a knight, because this would contradict the claim of Matthew that Jack is a knave if and only if Matthew is a knight.
Assume Jack is a knave. No contradiction is found in their false claim that Matthew is a knave.
Assume Scarlett is a knight. No contradiction is found in their claim that If Matthew is a knave then Jack is a knave.
Therefore, (1) Matthew is a knight
(2) Jack is a knave
(3) Scarlett is a knight </think>
<answer> (1) Matthew is a knight
(2) Jack is a knave
(3) Scarlett is a knight </answer> | math | {
"ground_truth": {
"names": [
"Matthew",
"Jack",
"Scarlett"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Matthew is a knight\n(2) Jack is a knave\n(3) Scarlett is a knight",
"statements": "(('<=>', ('lying', 1), ('telling-truth', 0)), ('lying', 0), ('->', ('lying', 0), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 289,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Benjamin, Henry, and Oliver. Benjamin told you that Oliver is a knave. Henry said, \"Oliver is a knave or Benjamin is a knight.\" Oliver told you that Oliver is a knight if and only if Benjamin is a knight. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Benjamin is a knight. ",
"No contradiction is found in their claim that Oliver is a knave.\n",
"Oliver cannot be a knight, because this would contradict the claim of Benjamin that Oliver is a knave.\n",
"Assume Oliver is a knave. ",
"No contradiction is found in their false claim that Oliver is a knight if and only if Benjamin is a knight.\n",
"Assume Henry is a knight. ",
"No contradiction is found in their claim that Oliver is a knave or Benjamin is a knight.\n",
"Therefore, (1) Benjamin is a knight\n",
"(2) Henry is a knight\n",
"(3) Oliver is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Benjamin, Henry, and Oliver. Benjamin told you that Oliver is a knave. Henry said, "Oliver is a knave or Benjamin is a knight." Oliver told you that Oliver is a knight if and only if Benjamin is a knight. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Benjamin is a knight. No contradiction is found in their claim that Oliver is a knave.
Oliver cannot be a knight, because this would contradict the claim of Benjamin that Oliver is a knave.
Assume Oliver is a knave. No contradiction is found in their false claim that Oliver is a knight if and only if Benjamin is a knight.
Assume Henry is a knight. No contradiction is found in their claim that Oliver is a knave or Benjamin is a knight.
Therefore, (1) Benjamin is a knight
(2) Henry is a knight
(3) Oliver is a knave </think>
<answer> (1) Benjamin is a knight
(2) Henry is a knight
(3) Oliver is a knave </answer> | math | {
"ground_truth": {
"names": [
"Benjamin",
"Henry",
"Oliver"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Benjamin is a knight\n(2) Henry is a knight\n(3) Oliver is a knave",
"statements": "(('lying', 2), ('or', ('lying', 2), ('telling-truth', 0)), ('<=>', ('telling-truth', 2), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 290,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Henry, Grace, and Lily. Henry was heard saying, \"Grace is a knave\". Grace stated, \"Lily is a knave and Lily is a knight\". Lily remarked, \"Henry is not a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Henry is a knight. ",
"No contradiction is found in their claim that Grace is a knave.\n",
"Grace cannot be a knight, because this would contradict the claim of Henry that Grace is a knave.\n",
"Assume Grace is a knave. ",
"No contradiction is found in their false claim that Lily is a knave and Lily is a knight.\n",
"Lily cannot be a knight, because this would contradict the claim of their own that Henry is not a knight.\n",
"Assume Lily is a knave. ",
"No contradiction is found in their false claim that Henry is not a knight.\n",
"Therefore, (1) Henry is a knight\n",
"(2) Grace is a knave\n",
"(3) Lily is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Henry, Grace, and Lily. Henry was heard saying, "Grace is a knave". Grace stated, "Lily is a knave and Lily is a knight". Lily remarked, "Henry is not a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Henry 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 Henry that Grace is a knave.
Assume Grace is a knave. No contradiction is found in their false claim that Lily is a knave and Lily is a knight.
Lily cannot be a knight, because this would contradict the claim of their own that Henry is not a knight.
Assume Lily is a knave. No contradiction is found in their false claim that Henry is not a knight.
Therefore, (1) Henry is a knight
(2) Grace is a knave
(3) Lily is a knave </think>
<answer> (1) Henry is a knight
(2) Grace is a knave
(3) Lily is a knave </answer> | math | {
"ground_truth": {
"names": [
"Henry",
"Grace",
"Lily"
],
"solution": [
true,
false,
false
],
"solution_text_format": "(1) Henry is a knight\n(2) Grace is a knave\n(3) Lily is a knave",
"statements": "(('lying', 1), ('and', ('lying', 2), ('telling-truth', 2)), ('not', ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 291,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Lucas, Daniel, and Benjamin. Lucas asserted: \"Daniel is a knight or Benjamin is a knight\". \"Lucas is a knight,\" Daniel mentioned. Benjamin said that Daniel is a knave. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Lucas is a knight. ",
"No contradiction is found in their claim that Daniel is a knight or Benjamin is a knight.\n",
"Assume Daniel is a knight. ",
"No contradiction is found in their claim that Lucas is a knight.\n",
"Benjamin cannot be a knight, because this would contradict the claim of their own that Daniel is a knave.\n",
"Assume Benjamin is a knave. ",
"No contradiction is found in their false claim that Daniel is a knave.\n",
"Therefore, (1) Lucas is a knight\n",
"(2) Daniel is a knight\n",
"(3) Benjamin is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Lucas, Daniel, and Benjamin. Lucas asserted: "Daniel is a knight or Benjamin is a knight". "Lucas is a knight," Daniel mentioned. Benjamin said that Daniel is a knave. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Lucas is a knight. No contradiction is found in their claim that Daniel is a knight or Benjamin is a knight.
Assume Daniel is a knight. No contradiction is found in their claim that Lucas is a knight.
Benjamin cannot be a knight, because this would contradict the claim of their own that Daniel is a knave.
Assume Benjamin is a knave. No contradiction is found in their false claim that Daniel is a knave.
Therefore, (1) Lucas is a knight
(2) Daniel is a knight
(3) Benjamin is a knave </think>
<answer> (1) Lucas is a knight
(2) Daniel is a knight
(3) Benjamin is a knave </answer> | math | {
"ground_truth": {
"names": [
"Lucas",
"Daniel",
"Benjamin"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Lucas is a knight\n(2) Daniel is a knight\n(3) Benjamin is a knave",
"statements": "(('or', ('telling-truth', 1), ('telling-truth', 2)), ('telling-truth', 0), ('lying', 1))"
},
"style": "rule"
} | {
"index": 292,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Avery, Oliver, and Alexander. \"If Avery is a knight then Oliver is a knight,\" Avery mentioned. Oliver told you that If Avery is a knight then Oliver is a knight. Alexander noted, \"Oliver is a knight if and only if Avery is a knave\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Avery is a knight. ",
"No contradiction is found in their claim that If Avery is a knight then Oliver is a knight.\n",
"Assume Oliver is a knight. ",
"No contradiction is found in their claim that If Avery is a knight then Oliver is a knight.\n",
"Alexander cannot be a knight, because this would contradict the claim of their own that Oliver is a knight if and only if Avery is a knave.\n",
"Assume Alexander is a knave. ",
"No contradiction is found in their false claim that Oliver is a knight if and only if Avery is a knave.\n",
"Therefore, (1) Avery is a knight\n",
"(2) Oliver is a knight\n",
"(3) Alexander is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Avery, Oliver, and Alexander. "If Avery is a knight then Oliver is a knight," Avery mentioned. Oliver told you that If Avery is a knight then Oliver is a knight. Alexander noted, "Oliver is a knight if and only if Avery is a knave". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Avery is a knight. No contradiction is found in their claim that If Avery is a knight then Oliver is a knight.
Assume Oliver is a knight. No contradiction is found in their claim that If Avery is a knight then Oliver is a knight.
Alexander cannot be a knight, because this would contradict the claim of their own that Oliver is a knight if and only if Avery is a knave.
Assume Alexander is a knave. No contradiction is found in their false claim that Oliver is a knight if and only if Avery is a knave.
Therefore, (1) Avery is a knight
(2) Oliver is a knight
(3) Alexander is a knave </think>
<answer> (1) Avery is a knight
(2) Oliver is a knight
(3) Alexander is a knave </answer> | math | {
"ground_truth": {
"names": [
"Avery",
"Oliver",
"Alexander"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Avery is a knight\n(2) Oliver is a knight\n(3) Alexander is a knave",
"statements": "(('->', ('telling-truth', 0), ('telling-truth', 1)), ('->', ('telling-truth', 0), ('telling-truth', 1)), ('<=>', ('telling-truth', 1), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 293,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Emma, Chloe, and Victoria. \"Victoria is a knight and Chloe is a knave,\" Emma mentioned. Chloe said, \"Victoria is a knight.\" Victoria told you that Chloe is a knave and Emma is a knight. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Emma is a knight. ",
"No contradiction is found in their claim that Victoria is a knight and Chloe is a knave.\n",
"Assume Victoria is a knight. ",
"No contradiction is found in their claim that Chloe is a knave and Emma is a knight.\n",
"Chloe cannot be a knight, because this would contradict the claim of Emma that Victoria is a knight and Chloe is a knave.\n",
"Chloe cannot be a knave, because this would contradict the false claim of their own that Victoria is a knight.\n",
"We have exhausted all possibilities for Chloe, so let us go back and reconsider Victoria.\n",
"Victoria cannot be a knave, because this would contradict the claim of Emma that Victoria is a knight and Chloe is a knave.\n",
"We have exhausted all possibilities for Victoria, so let us go back and reconsider Emma.\n",
"Assume Emma is a knave. ",
"No contradiction is found in their false claim that Victoria is a knight and Chloe is a knave.\n",
"Victoria cannot be a knight, because this would contradict the claim of their own that Chloe is a knave and Emma is a knight.\n",
"Assume Victoria is a knave. ",
"No contradiction is found in their false claim that Chloe is a knave and Emma is a knight.\n",
"Chloe cannot be a knight, because this would contradict the claim of their own that Victoria is a knight.\n",
"Assume Chloe is a knave. ",
"No contradiction is found in their false claim that Victoria is a knight.\n",
"Therefore, (1) Emma is a knave\n",
"(2) Chloe is a knave\n",
"(3) Victoria is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Emma, Chloe, and Victoria. "Victoria is a knight and Chloe is a knave," Emma mentioned. Chloe said, "Victoria is a knight." Victoria told you that Chloe is a knave and Emma is a knight. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Emma is a knight. No contradiction is found in their claim that Victoria is a knight and Chloe is a knave.
Assume Victoria is a knight. No contradiction is found in their claim that Chloe is a knave and Emma is a knight.
Chloe cannot be a knight, because this would contradict the claim of Emma that Victoria is a knight and Chloe is a knave.
Chloe cannot be a knave, because this would contradict the false claim of their own that Victoria is a knight.
We have exhausted all possibilities for Chloe, so let us go back and reconsider Victoria.
Victoria cannot be a knave, because this would contradict the claim of Emma that Victoria is a knight and Chloe is a knave.
We have exhausted all possibilities for Victoria, so let us go back and reconsider Emma.
Assume Emma is a knave. No contradiction is found in their false claim that Victoria is a knight and Chloe is a knave.
Victoria cannot be a knight, because this would contradict the claim of their own that Chloe is a knave and Emma is a knight.
Assume Victoria is a knave. No contradiction is found in their false claim that Chloe is a knave and Emma is a knight.
Chloe cannot be a knight, because this would contradict the claim of their own that Victoria is a knight.
Assume Chloe is a knave. No contradiction is found in their false claim that Victoria is a knight.
Therefore, (1) Emma is a knave
(2) Chloe is a knave
(3) Victoria is a knave </think>
<answer> (1) Emma is a knave
(2) Chloe is a knave
(3) Victoria is a knave </answer> | math | {
"ground_truth": {
"names": [
"Emma",
"Chloe",
"Victoria"
],
"solution": [
false,
false,
false
],
"solution_text_format": "(1) Emma is a knave\n(2) Chloe is a knave\n(3) Victoria is a knave",
"statements": "(('and', ('telling-truth', 2), ('lying', 1)), ('telling-truth', 2), ('and', ('lying', 1), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 294,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Olivia, Charlotte, and Owen. Olivia told you that If Charlotte is a knave then Owen is a knight. Charlotte commented, \"If Charlotte is a knight then Owen is a knave\". As Owen put it, \"Owen is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Olivia is a knight. ",
"No contradiction is found in their claim that If Charlotte is a knave then Owen is a knight.\n",
"Assume Charlotte is a knight. ",
"No contradiction is found in their claim that If Charlotte is a knight then Owen is a knave.\n",
"Owen cannot be a knight, because this would contradict the claim of Charlotte that If Charlotte is a knight then Owen is a knave.\n",
"Assume Owen is a knave. ",
"No contradiction is found in their false claim that Owen is a knight.\n",
"Therefore, (1) Olivia is a knight\n",
"(2) Charlotte is a knight\n",
"(3) Owen is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Olivia, Charlotte, and Owen. Olivia told you that If Charlotte is a knave then Owen is a knight. Charlotte commented, "If Charlotte is a knight then Owen is a knave". As Owen put it, "Owen is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Olivia is a knight. No contradiction is found in their claim that If Charlotte is a knave then Owen is a knight.
Assume Charlotte is a knight. No contradiction is found in their claim that If Charlotte is a knight then Owen is a knave.
Owen cannot be a knight, because this would contradict the claim of Charlotte that If Charlotte is a knight then Owen is a knave.
Assume Owen is a knave. No contradiction is found in their false claim that Owen is a knight.
Therefore, (1) Olivia is a knight
(2) Charlotte is a knight
(3) Owen is a knave </think>
<answer> (1) Olivia is a knight
(2) Charlotte is a knight
(3) Owen is a knave </answer> | math | {
"ground_truth": {
"names": [
"Olivia",
"Charlotte",
"Owen"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Olivia is a knight\n(2) Charlotte is a knight\n(3) Owen is a knave",
"statements": "(('->', ('lying', 1), ('telling-truth', 2)), ('->', ('telling-truth', 1), ('lying', 2)), ('telling-truth', 2))"
},
"style": "rule"
} | {
"index": 295,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Olivia, Victoria, and Joseph. \"Victoria is a knight and Joseph is a knave,\" Olivia mentioned. Victoria remarked, \"Olivia is a knight or Olivia is a knave\". In Joseph's words: \"Olivia is a knave if and only if Joseph is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Olivia is a knight. ",
"No contradiction is found in their claim that Victoria is a knight and Joseph is a knave.\n",
"Assume Victoria is a knight. ",
"No contradiction is found in their claim that Olivia is a knight or Olivia is a knave.\n",
"Joseph cannot be a knight, because this would contradict the claim of Olivia that Victoria is a knight and Joseph is a knave.\n",
"Joseph cannot be a knave, because this would contradict the false claim of their own that Olivia is a knave if and only if Joseph is a knight.\n",
"We have exhausted all possibilities for Joseph, so let us go back and reconsider Victoria.\n",
"Victoria cannot be a knave, because this would contradict the claim of Olivia that Victoria is a knight and Joseph is a knave.\n",
"We have exhausted all possibilities for Victoria, so let us go back and reconsider Olivia.\n",
"Assume Olivia is a knave. ",
"No contradiction is found in their false claim that Victoria is a knight and Joseph is a knave.\n",
"Assume Victoria is a knight. ",
"No contradiction is found in their claim that Olivia is a knight or Olivia is a knave.\n",
"Assume Joseph is a knight. ",
"No contradiction is found in their claim that Olivia is a knave if and only if Joseph is a knight.\n",
"Therefore, (1) Olivia is a knave\n",
"(2) Victoria is a knight\n",
"(3) Joseph is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Olivia, Victoria, and Joseph. "Victoria is a knight and Joseph is a knave," Olivia mentioned. Victoria remarked, "Olivia is a knight or Olivia is a knave". In Joseph's words: "Olivia is a knave if and only if Joseph is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Olivia is a knight. No contradiction is found in their claim that Victoria is a knight and Joseph is a knave.
Assume Victoria is a knight. No contradiction is found in their claim that Olivia is a knight or Olivia is a knave.
Joseph cannot be a knight, because this would contradict the claim of Olivia that Victoria is a knight and Joseph is a knave.
Joseph cannot be a knave, because this would contradict the false claim of their own that Olivia is a knave if and only if Joseph is a knight.
We have exhausted all possibilities for Joseph, so let us go back and reconsider Victoria.
Victoria cannot be a knave, because this would contradict the claim of Olivia that Victoria is a knight and Joseph is a knave.
We have exhausted all possibilities for Victoria, so let us go back and reconsider Olivia.
Assume Olivia is a knave. No contradiction is found in their false claim that Victoria is a knight and Joseph is a knave.
Assume Victoria is a knight. No contradiction is found in their claim that Olivia is a knight or Olivia is a knave.
Assume Joseph is a knight. No contradiction is found in their claim that Olivia is a knave if and only if Joseph is a knight.
Therefore, (1) Olivia is a knave
(2) Victoria is a knight
(3) Joseph is a knight </think>
<answer> (1) Olivia is a knave
(2) Victoria is a knight
(3) Joseph is a knight </answer> | math | {
"ground_truth": {
"names": [
"Olivia",
"Victoria",
"Joseph"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Olivia is a knave\n(2) Victoria is a knight\n(3) Joseph is a knight",
"statements": "(('and', ('telling-truth', 1), ('lying', 2)), ('or', ('telling-truth', 0), ('lying', 0)), ('<=>', ('lying', 0), ('telling-truth', 2)))"
},
"style": "rule"
} | {
"index": 296,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Michael, Samuel, and Liam. Michael expressed that Samuel is a knight or Samuel is a knave. As Samuel put it, \"If Liam is a knave then Michael is a knave\". Liam noted, \"If Samuel is a knight then Michael is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Michael is a knight. ",
"No contradiction is found in their claim that Samuel is a knight or Samuel is a knave.\n",
"Assume Samuel is a knight. ",
"No contradiction is found in their claim that If Liam is a knave then Michael is a knave.\n",
"Assume Liam is a knight. ",
"No contradiction is found in their claim that If Samuel is a knight then Michael is a knight.\n",
"Therefore, (1) Michael is a knight\n",
"(2) Samuel is a knight\n",
"(3) Liam is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Michael, Samuel, and Liam. Michael expressed that Samuel is a knight or Samuel is a knave. As Samuel put it, "If Liam is a knave then Michael is a knave". Liam noted, "If Samuel is a knight then Michael is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Michael is a knight. No contradiction is found in their claim that Samuel is a knight or Samuel is a knave.
Assume Samuel is a knight. No contradiction is found in their claim that If Liam is a knave then Michael is a knave.
Assume Liam is a knight. No contradiction is found in their claim that If Samuel is a knight then Michael is a knight.
Therefore, (1) Michael is a knight
(2) Samuel is a knight
(3) Liam is a knight </think>
<answer> (1) Michael is a knight
(2) Samuel is a knight
(3) Liam is a knight </answer> | math | {
"ground_truth": {
"names": [
"Michael",
"Samuel",
"Liam"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Michael is a knight\n(2) Samuel is a knight\n(3) Liam is a knight",
"statements": "(('or', ('telling-truth', 1), ('lying', 1)), ('->', ('lying', 2), ('lying', 0)), ('->', ('telling-truth', 1), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 297,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Alexander, Aiden, and Charlotte. \"If Aiden is a knight then Aiden is a knave,\" Alexander mentioned. Aiden remarked, \"Charlotte is a knave if and only if Alexander is a knave\". Charlotte said that Alexander is a knave or Aiden is a knight. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Alexander is a knight. ",
"No contradiction is found in their claim that If Aiden is a knight then Aiden is a knave.\n",
"Aiden cannot be a knight, because this would contradict the claim of Alexander that If Aiden is a knight then Aiden is a knave.\n",
"Assume Aiden is a knave. ",
"No contradiction is found in their false claim that Charlotte is a knave if and only if Alexander is a knave.\n",
"Charlotte cannot be a knight, because this would contradict the false claim of Aiden that Charlotte is a knave if and only if Alexander is a knave.\n",
"Assume Charlotte is a knave. ",
"No contradiction is found in their false claim that Alexander is a knave or Aiden is a knight.\n",
"Therefore, (1) Alexander is a knight\n",
"(2) Aiden is a knave\n",
"(3) Charlotte is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Alexander, Aiden, and Charlotte. "If Aiden is a knight then Aiden is a knave," Alexander mentioned. Aiden remarked, "Charlotte is a knave if and only if Alexander is a knave". Charlotte said that Alexander is a knave or Aiden is a knight. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Alexander is a knight. No contradiction is found in their claim that If Aiden is a knight then Aiden is a knave.
Aiden cannot be a knight, because this would contradict the claim of Alexander that If Aiden is a knight then Aiden is a knave.
Assume Aiden is a knave. No contradiction is found in their false claim that Charlotte is a knave if and only if Alexander is a knave.
Charlotte cannot be a knight, because this would contradict the false claim of Aiden that Charlotte is a knave if and only if Alexander is a knave.
Assume Charlotte is a knave. No contradiction is found in their false claim that Alexander is a knave or Aiden is a knight.
Therefore, (1) Alexander is a knight
(2) Aiden is a knave
(3) Charlotte is a knave </think>
<answer> (1) Alexander is a knight
(2) Aiden is a knave
(3) Charlotte is a knave </answer> | math | {
"ground_truth": {
"names": [
"Alexander",
"Aiden",
"Charlotte"
],
"solution": [
true,
false,
false
],
"solution_text_format": "(1) Alexander is a knight\n(2) Aiden is a knave\n(3) Charlotte is a knave",
"statements": "(('->', ('telling-truth', 1), ('lying', 1)), ('<=>', ('lying', 2), ('lying', 0)), ('or', ('lying', 0), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 298,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Emma, Noah, and Isabella. Emma stated, \"Isabella is a knight if and only if Emma is a knight\". \"If Isabella is a knave then Isabella is a knight,\" Noah claimed. Isabella remarked, \"Emma is a knave\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Emma is a knight. ",
"No contradiction is found in their claim that Isabella is a knight if and only if Emma is a knight.\n",
"Isabella cannot be a knight, because this would contradict the claim of their own that Emma is a knave.\n",
"Isabella cannot be a knave, because this would contradict the claim of Emma that Isabella is a knight if and only if Emma is a knight.\n",
"We have exhausted all possibilities for Isabella, so let us go back and reconsider Emma.\n",
"Assume Emma is a knave. ",
"No contradiction is found in their false claim that Isabella is a knight if and only if Emma is a knight.\n",
"Assume Isabella is a knight. ",
"No contradiction is found in their claim that Emma is a knave.\n",
"Assume Noah is a knight. ",
"No contradiction is found in their claim that If Isabella is a knave then Isabella is a knight.\n",
"Therefore, (1) Emma is a knave\n",
"(2) Noah is a knight\n",
"(3) Isabella is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Emma, Noah, and Isabella. Emma stated, "Isabella is a knight if and only if Emma is a knight". "If Isabella is a knave then Isabella is a knight," Noah claimed. Isabella remarked, "Emma is a knave". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Emma is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Emma is a knight.
Isabella cannot be a knight, because this would contradict the claim of their own that Emma is a knave.
Isabella cannot be a knave, because this would contradict the claim of Emma that Isabella is a knight if and only if Emma is a knight.
We have exhausted all possibilities for Isabella, so let us go back and reconsider Emma.
Assume Emma is a knave. No contradiction is found in their false claim that Isabella is a knight if and only if Emma is a knight.
Assume Isabella is a knight. No contradiction is found in their claim that Emma is a knave.
Assume Noah is a knight. No contradiction is found in their claim that If Isabella is a knave then Isabella is a knight.
Therefore, (1) Emma is a knave
(2) Noah is a knight
(3) Isabella is a knight </think>
<answer> (1) Emma is a knave
(2) Noah is a knight
(3) Isabella is a knight </answer> | math | {
"ground_truth": {
"names": [
"Emma",
"Noah",
"Isabella"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Emma is a knave\n(2) Noah is a knight\n(3) Isabella is a knight",
"statements": "(('<=>', ('telling-truth', 2), ('telling-truth', 0)), ('->', ('lying', 2), ('telling-truth', 2)), ('lying', 0))"
},
"style": "rule"
} | {
"index": 299,
"split": "train"
} |
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