UFT
Collection
UFT: Unifying Supervised and Reinforcement Fine-Tuning
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80 items
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Updated
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1
Dataset Viewer
data_source
stringclasses 1
value | prompt
listlengths 1
1
| hint
sequencelengths 9
107
| question
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: Michael, Zoey, and Ethan. Michael was heard saying, \"Ethan is a knight if and only if Michael is a knight\". \"Zoey is a knight or Ethan is a knight,\" Zoey mentioned. Ethan asserted: \"Michael is a knave if and only if 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 Michael is a knight. ",
"No contradiction is found in their claim that Ethan is a knight if and only if Michael is a knight.\n",
"Assume Ethan is a knight. ",
"No contradiction is found in their claim that Michael is a knave if and only if Zoey is a knave.\n",
"Assume Zoey is a knight. ",
"No contradiction is found in their claim that Zoey is a knight or Ethan is a knight.\n",
"Therefore, (1) Michael is a knight\n",
"(2) Zoey is a knight\n",
"(3) Ethan 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, Zoey, and Ethan. Michael was heard saying, "Ethan is a knight if and only if Michael is a knight". "Zoey is a knight or Ethan is a knight," Zoey mentioned. Ethan asserted: "Michael is a knave if and only if 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 Michael is a knight. No contradiction is found in their claim that Ethan is a knight if and only if Michael is a knight.
Assume Ethan is a knight. No contradiction is found in their claim that Michael is a knave if and only if Zoey is a knave.
Assume Zoey is a knight. No contradiction is found in their claim that Zoey is a knight or Ethan is a knight.
Therefore, (1) Michael is a knight
(2) Zoey is a knight
(3) Ethan is a knight </think>
<answer> (1) Michael is a knight
(2) Zoey is a knight
(3) Ethan is a knight </answer> | math | {
"ground_truth": {
"names": [
"Michael",
"Zoey",
"Ethan"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Michael is a knight\n(2) Zoey is a knight\n(3) Ethan is a knight",
"statements": "(('<=>', ('telling-truth', 2), ('telling-truth', 0)), ('or', ('telling-truth', 1), ('telling-truth', 2)), ('<=>', ('lying', 0), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 0,
"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, Mason, and Jacob. Michael commented, \"Mason is not a knight\". Mason commented, \"Michael is a knight and Jacob is a knave\". Jacob stated, \"If Michael is a knight then Jacob 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 Mason is not a knight.\n",
"Mason cannot be a knight, because this would contradict the claim of Michael that Mason is not a knight.\n",
"Assume Mason is a knave. ",
"No contradiction is found in their false claim that Michael is a knight and Jacob is a knave.\n",
"Assume Jacob is a knight. ",
"No contradiction is found in their claim that If Michael is a knight then Jacob is a knight.\n",
"Therefore, (1) Michael is a knight\n",
"(2) Mason is a knave\n",
"(3) Jacob 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, Mason, and Jacob. Michael commented, "Mason is not a knight". Mason commented, "Michael is a knight and Jacob is a knave". Jacob stated, "If Michael is a knight then Jacob 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 Mason is not a knight.
Mason cannot be a knight, because this would contradict the claim of Michael that Mason is not a knight.
Assume Mason is a knave. No contradiction is found in their false claim that Michael is a knight and Jacob is a knave.
Assume Jacob is a knight. No contradiction is found in their claim that If Michael is a knight then Jacob is a knight.
Therefore, (1) Michael is a knight
(2) Mason is a knave
(3) Jacob is a knight </think>
<answer> (1) Michael is a knight
(2) Mason is a knave
(3) Jacob is a knight </answer> | math | {
"ground_truth": {
"names": [
"Michael",
"Mason",
"Jacob"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Michael is a knight\n(2) Mason is a knave\n(3) Jacob is a knight",
"statements": "(('not', ('telling-truth', 1)), ('and', ('telling-truth', 0), ('lying', 2)), ('->', ('telling-truth', 0), ('telling-truth', 2)))"
},
"style": "rule"
} | {
"index": 1,
"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, Harper, and Amelia. Lucas expressed that Harper is not a knave. In a statement by Harper: \"Harper is a knight if and only if Amelia is a knave\". As Amelia put it, \"Harper 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 Lucas is a knight. ",
"No contradiction is found in their claim that Harper is not a knave.\n",
"Assume Harper is a knight. ",
"No contradiction is found in their claim that Harper is a knight if and only if Amelia is a knave.\n",
"Amelia cannot be a knight, because this would contradict the claim of Harper that Harper is a knight if and only if Amelia is a knave.\n",
"Assume Amelia is a knave. ",
"No contradiction is found in their false claim that Harper is not a knight.\n",
"Therefore, (1) Lucas is a knight\n",
"(2) Harper is a knight\n",
"(3) Amelia 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, Harper, and Amelia. Lucas expressed that Harper is not a knave. In a statement by Harper: "Harper is a knight if and only if Amelia is a knave". As Amelia put it, "Harper 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 Lucas is a knight. No contradiction is found in their claim that Harper is not a knave.
Assume Harper is a knight. No contradiction is found in their claim that Harper is a knight if and only if Amelia is a knave.
Amelia cannot be a knight, because this would contradict the claim of Harper that Harper is a knight if and only if Amelia is a knave.
Assume Amelia is a knave. No contradiction is found in their false claim that Harper is not a knight.
Therefore, (1) Lucas is a knight
(2) Harper is a knight
(3) Amelia is a knave </think>
<answer> (1) Lucas is a knight
(2) Harper is a knight
(3) Amelia is a knave </answer> | math | {
"ground_truth": {
"names": [
"Lucas",
"Harper",
"Amelia"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Lucas is a knight\n(2) Harper is a knight\n(3) Amelia is a knave",
"statements": "(('not', ('lying', 1)), ('<=>', ('telling-truth', 1), ('lying', 2)), ('not', ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 2,
"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, Joseph, and Sofia. Owen noted, \"Joseph is a knight or Sofia is a knight\". \"Owen is a knave if and only if Sofia is a knight,\" Joseph declared. \"If Joseph is a knave then Joseph is a knight,\" Sofia 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 Joseph is a knight or Sofia is a knight.\n",
"Assume Joseph is a knight. ",
"No contradiction is found in their claim that Owen is a knave if and only if Sofia is a knight.\n",
"Sofia cannot be a knight, because this would contradict the claim of Joseph that Owen is a knave if and only if Sofia is a knight.\n",
"Sofia cannot be a knave, because this would contradict the false claim of their own that If Joseph is a knave then Joseph is a knight.\n",
"We have exhausted all possibilities for Sofia, so let us go back and reconsider Joseph.\n",
"Assume Joseph is a knave. ",
"No contradiction is found in their false claim that Owen is a knave if and only if Sofia is a knight.\n",
"Sofia cannot be a knight, because this would contradict the claim of their own that If Joseph is a knave then Joseph is a knight.\n",
"Sofia cannot be a knave, because this would contradict the claim of Owen that Joseph is a knight or Sofia is a knight.\n",
"We have exhausted all possibilities for Sofia and Joseph, so let us go back and reconsider Owen.\n",
"Assume Owen is a knave. ",
"No contradiction is found in their false claim that Joseph is a knight or Sofia is a knight.\n",
"Joseph cannot be a knight, because this would contradict the false claim of Owen that Joseph is a knight or Sofia is a knight.\n",
"Assume Joseph is a knave. ",
"No contradiction is found in their false claim that Owen is a knave if and only if Sofia is a knight.\n",
"Sofia cannot be a knight, because this would contradict the false claim of Owen that Joseph is a knight or Sofia is a knight.\n",
"Assume Sofia is a knave. ",
"No contradiction is found in their false claim that If Joseph is a knave then Joseph is a knight.\n",
"Therefore, (1) Owen is a knave\n",
"(2) Joseph 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: Owen, Joseph, and Sofia. Owen noted, "Joseph is a knight or Sofia is a knight". "Owen is a knave if and only if Sofia is a knight," Joseph declared. "If Joseph is a knave then Joseph is a knight," Sofia 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 Joseph is a knight or Sofia is a knight.
Assume Joseph is a knight. No contradiction is found in their claim that Owen is a knave if and only if Sofia is a knight.
Sofia cannot be a knight, because this would contradict the claim of Joseph that Owen is a knave if and only if Sofia is a knight.
Sofia cannot be a knave, because this would contradict the false claim of their own that If Joseph is a knave then Joseph is a knight.
We have exhausted all possibilities for Sofia, so let us go back and reconsider Joseph.
Assume Joseph is a knave. No contradiction is found in their false claim that Owen is a knave if and only if Sofia is a knight.
Sofia cannot be a knight, because this would contradict the claim of their own that If Joseph is a knave then Joseph is a knight.
Sofia cannot be a knave, because this would contradict the claim of Owen that Joseph is a knight or Sofia is a knight.
We have exhausted all possibilities for Sofia and Joseph, so let us go back and reconsider Owen.
Assume Owen is a knave. No contradiction is found in their false claim that Joseph is a knight or Sofia is a knight.
Joseph cannot be a knight, because this would contradict the false claim of Owen that Joseph is a knight or Sofia is a knight.
Assume Joseph is a knave. No contradiction is found in their false claim that Owen is a knave if and only if Sofia is a knight.
Sofia cannot be a knight, because this would contradict the false claim of Owen that Joseph is a knight or Sofia is a knight.
Assume Sofia is a knave. No contradiction is found in their false claim that If Joseph is a knave then Joseph is a knight.
Therefore, (1) Owen is a knave
(2) Joseph is a knave
(3) Sofia is a knave </think>
<answer> (1) Owen is a knave
(2) Joseph is a knave
(3) Sofia is a knave </answer> | math | {
"ground_truth": {
"names": [
"Owen",
"Joseph",
"Sofia"
],
"solution": [
false,
false,
false
],
"solution_text_format": "(1) Owen is a knave\n(2) Joseph is a knave\n(3) Sofia is a knave",
"statements": "(('or', ('telling-truth', 1), ('telling-truth', 2)), ('<=>', ('lying', 0), ('telling-truth', 2)), ('->', ('lying', 1), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 3,
"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, Scarlett, and Evelyn. In Abigail's words: \"Abigail is a knight if and only if Evelyn is a knight\". Scarlett remarked, \"Abigail is a knight\". According to Evelyn, \"Scarlett 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 Abigail is a knight. ",
"No contradiction is found in their claim that Abigail is a knight if and only if Evelyn is a knight.\n",
"Assume Evelyn is a knight. ",
"No contradiction is found in their claim that Scarlett is not a knight.\n",
"Scarlett cannot be a knight, because this would contradict the claim of Evelyn that Scarlett is not a knight.\n",
"Scarlett cannot be a knave, because this would contradict the false claim of their own that Abigail is a knight.\n",
"We have exhausted all possibilities for Scarlett, so let us go back and reconsider Evelyn.\n",
"Evelyn cannot be a knave, because this would contradict the claim of Abigail that Abigail is a knight if and only if Evelyn is a knight.\n",
"We have exhausted all possibilities for Evelyn, so let us go back and reconsider Abigail.\n",
"Assume Abigail is a knave. ",
"No contradiction is found in their false claim that Abigail is a knight if and only if Evelyn is a knight.\n",
"Assume Evelyn is a knight. ",
"No contradiction is found in their claim that Scarlett is not a knight.\n",
"Scarlett cannot be a knight, because this would contradict the claim of their own that Abigail is a knight.\n",
"Assume Scarlett is a knave. ",
"No contradiction is found in their false claim that Abigail is a knight.\n",
"Therefore, (1) Abigail is a knave\n",
"(2) Scarlett is a knave\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: Abigail, Scarlett, and Evelyn. In Abigail's words: "Abigail is a knight if and only if Evelyn is a knight". Scarlett remarked, "Abigail is a knight". According to Evelyn, "Scarlett 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 Abigail is a knight. No contradiction is found in their claim that Abigail is a knight if and only if Evelyn is a knight.
Assume Evelyn is a knight. No contradiction is found in their claim that Scarlett is not a knight.
Scarlett cannot be a knight, because this would contradict the claim of Evelyn that Scarlett is not a knight.
Scarlett cannot be a knave, because this would contradict the false claim of their own that Abigail is a knight.
We have exhausted all possibilities for Scarlett, so let us go back and reconsider Evelyn.
Evelyn cannot be a knave, because this would contradict the claim of Abigail that Abigail is a knight if and only if Evelyn is a knight.
We have exhausted all possibilities for Evelyn, so let us go back and reconsider Abigail.
Assume Abigail is a knave. No contradiction is found in their false claim that Abigail is a knight if and only if Evelyn is a knight.
Assume Evelyn is a knight. No contradiction is found in their claim that Scarlett is not a knight.
Scarlett cannot be a knight, because this would contradict the claim of their own that Abigail is a knight.
Assume Scarlett is a knave. No contradiction is found in their false claim that Abigail is a knight.
Therefore, (1) Abigail is a knave
(2) Scarlett is a knave
(3) Evelyn is a knight </think>
<answer> (1) Abigail is a knave
(2) Scarlett is a knave
(3) Evelyn is a knight </answer> | math | {
"ground_truth": {
"names": [
"Abigail",
"Scarlett",
"Evelyn"
],
"solution": [
false,
false,
true
],
"solution_text_format": "(1) Abigail is a knave\n(2) Scarlett is a knave\n(3) Evelyn is a knight",
"statements": "(('<=>', ('telling-truth', 0), ('telling-truth', 2)), ('telling-truth', 0), ('not', ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 4,
"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, Matthew, and Victoria. \"Penelope is a knight and Matthew is a knight,\" Penelope claimed. Matthew was heard saying, \"Victoria is a knave and Victoria is a knight\". Victoria said that If Matthew is a knight then 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 Penelope is a knight. ",
"No contradiction is found in their claim that Penelope is a knight and Matthew is a knight.\n",
"Matthew cannot be a knight, because this would contradict the claim of their own that Victoria is a knave and Victoria is a knight.\n",
"Matthew cannot be a knave, because this would contradict the claim of Penelope that Penelope is a knight and Matthew is a knight.\n",
"We have exhausted all possibilities for Matthew, so let us go back and reconsider Penelope.\n",
"Assume Penelope is a knave. ",
"No contradiction is found in their false claim that Penelope is a knight and Matthew is a knight.\n",
"Matthew cannot be a knight, because this would contradict the claim of their own that Victoria is a knave and Victoria is a knight.\n",
"Assume Matthew is a knave. ",
"No contradiction is found in their false claim that Victoria is a knave and Victoria is a knight.\n",
"Assume Victoria is a knight. ",
"No contradiction is found in their claim that If Matthew is a knight then Matthew is a knave.\n",
"Therefore, (1) Penelope is a knave\n",
"(2) Matthew 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: Penelope, Matthew, and Victoria. "Penelope is a knight and Matthew is a knight," Penelope claimed. Matthew was heard saying, "Victoria is a knave and Victoria is a knight". Victoria said that If Matthew is a knight then 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 Penelope is a knight. No contradiction is found in their claim that Penelope is a knight and Matthew is a knight.
Matthew cannot be a knight, because this would contradict the claim of their own that Victoria is a knave and Victoria is a knight.
Matthew cannot be a knave, because this would contradict the claim of Penelope that Penelope is a knight and Matthew is a knight.
We have exhausted all possibilities for Matthew, so let us go back and reconsider Penelope.
Assume Penelope is a knave. No contradiction is found in their false claim that Penelope is a knight and Matthew is a knight.
Matthew cannot be a knight, because this would contradict the claim of their own that Victoria is a knave and Victoria is a knight.
Assume Matthew is a knave. No contradiction is found in their false claim that Victoria is a knave and Victoria is a knight.
Assume Victoria is a knight. No contradiction is found in their claim that If Matthew is a knight then Matthew is a knave.
Therefore, (1) Penelope is a knave
(2) Matthew is a knave
(3) Victoria is a knight </think>
<answer> (1) Penelope is a knave
(2) Matthew is a knave
(3) Victoria is a knight </answer> | math | {
"ground_truth": {
"names": [
"Penelope",
"Matthew",
"Victoria"
],
"solution": [
false,
false,
true
],
"solution_text_format": "(1) Penelope is a knave\n(2) Matthew is a knave\n(3) Victoria is a knight",
"statements": "(('and', ('telling-truth', 0), ('telling-truth', 1)), ('and', ('lying', 2), ('telling-truth', 2)), ('->', ('telling-truth', 1), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 5,
"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, Liam, and Elizabeth. According to Emily, \"Elizabeth is a knight or Elizabeth is a knave\". Liam told you that If Elizabeth is a knave then Emily is a knight. Elizabeth said, \"Liam 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 Elizabeth is a knight or Elizabeth is a knave.\n",
"Assume Elizabeth 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 Elizabeth that Liam is a knave.\n",
"Liam cannot be a knave, because this would contradict the false claim of their own that If Elizabeth is a knave then Emily is a knight.\n",
"We have exhausted all possibilities for Liam, so let us go back and reconsider Elizabeth.\n",
"Assume Elizabeth is a knave. ",
"No contradiction is found in their false claim that Liam is a knave.\n",
"Assume Liam is a knight. ",
"No contradiction is found in their claim that If Elizabeth is a knave then Emily is a knight.\n",
"Therefore, (1) Emily is a knight\n",
"(2) Liam is a knight\n",
"(3) Elizabeth 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, Liam, and Elizabeth. According to Emily, "Elizabeth is a knight or Elizabeth is a knave". Liam told you that If Elizabeth is a knave then Emily is a knight. Elizabeth said, "Liam 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 Elizabeth is a knight or Elizabeth is a knave.
Assume Elizabeth 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 Elizabeth that Liam is a knave.
Liam cannot be a knave, because this would contradict the false claim of their own that If Elizabeth is a knave then Emily is a knight.
We have exhausted all possibilities for Liam, so let us go back and reconsider Elizabeth.
Assume Elizabeth is a knave. No contradiction is found in their false claim that Liam is a knave.
Assume Liam is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Emily is a knight.
Therefore, (1) Emily is a knight
(2) Liam is a knight
(3) Elizabeth is a knave </think>
<answer> (1) Emily is a knight
(2) Liam is a knight
(3) Elizabeth is a knave </answer> | math | {
"ground_truth": {
"names": [
"Emily",
"Liam",
"Elizabeth"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Emily is a knight\n(2) Liam is a knight\n(3) Elizabeth is a knave",
"statements": "(('or', ('telling-truth', 2), ('lying', 2)), ('->', ('lying', 2), ('telling-truth', 0)), ('lying', 1))"
},
"style": "rule"
} | {
"index": 6,
"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, Ava, and Henry. As Michael put it, \"Ava is a knave or Ava is a knight\". \"Michael is not a knave,\" Ava mentioned. In Henry's words: \"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 Ava is a knave or Ava is a knight.\n",
"Assume Ava is a knight. ",
"No contradiction is found in their claim that Michael is not a knave.\n",
"Assume Henry is a knight. ",
"No contradiction is found in their claim that Michael is a knight.\n",
"Therefore, (1) Michael is a knight\n",
"(2) Ava is a knight\n",
"(3) Henry 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, Ava, and Henry. As Michael put it, "Ava is a knave or Ava is a knight". "Michael is not a knave," Ava mentioned. In Henry's words: "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 Ava is a knave or Ava is a knight.
Assume Ava is a knight. No contradiction is found in their claim that Michael is not a knave.
Assume Henry is a knight. No contradiction is found in their claim that Michael is a knight.
Therefore, (1) Michael is a knight
(2) Ava is a knight
(3) Henry is a knight </think>
<answer> (1) Michael is a knight
(2) Ava is a knight
(3) Henry is a knight </answer> | math | {
"ground_truth": {
"names": [
"Michael",
"Ava",
"Henry"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Michael is a knight\n(2) Ava is a knight\n(3) Henry is a knight",
"statements": "(('or', ('lying', 1), ('telling-truth', 1)), ('not', ('lying', 0)), ('telling-truth', 0))"
},
"style": "rule"
} | {
"index": 7,
"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: Oliver, Alexander, and Mason. \"Alexander is a knave or Alexander is a knight\" - Oliver. \"Mason is not a knave,\" Alexander mentioned. Mason noted, \"Mason is a knight or Oliver 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 Oliver is a knight. ",
"No contradiction is found in their claim that Alexander is a knave or Alexander is a knight.\n",
"Assume Alexander is a knight. ",
"No contradiction is found in their claim that Mason is not a knave.\n",
"Assume Mason is a knight. ",
"No contradiction is found in their claim that Mason is a knight or Oliver is a knight.\n",
"Therefore, (1) Oliver is a knight\n",
"(2) Alexander 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: Oliver, Alexander, and Mason. "Alexander is a knave or Alexander is a knight" - Oliver. "Mason is not a knave," Alexander mentioned. Mason noted, "Mason is a knight or Oliver 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 Oliver is a knight. No contradiction is found in their claim that Alexander is a knave or Alexander is a knight.
Assume Alexander is a knight. No contradiction is found in their claim that Mason is not a knave.
Assume Mason is a knight. No contradiction is found in their claim that Mason is a knight or Oliver is a knight.
Therefore, (1) Oliver is a knight
(2) Alexander is a knight
(3) Mason is a knight </think>
<answer> (1) Oliver is a knight
(2) Alexander is a knight
(3) Mason is a knight </answer> | math | {
"ground_truth": {
"names": [
"Oliver",
"Alexander",
"Mason"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Oliver is a knight\n(2) Alexander is a knight\n(3) Mason is a knight",
"statements": "(('or', ('lying', 1), ('telling-truth', 1)), ('not', ('lying', 2)), ('or', ('telling-truth', 2), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 8,
"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, Samuel, and Sophia. In a statement by Lily: \"Sophia is a knight or Samuel is a knight\". Samuel stated, \"Sophia is a knight or Lily is a knave\". As Sophia 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 Lily is a knight. ",
"No contradiction is found in their claim that Sophia is a knight or Samuel is a knight.\n",
"Assume Sophia is a knight. ",
"No contradiction is found in their claim that If Samuel is a knave then Samuel is a knight.\n",
"Assume Samuel is a knight. ",
"No contradiction is found in their claim that Sophia is a knight or Lily is a knave.\n",
"Therefore, (1) Lily is a knight\n",
"(2) Samuel is a knight\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: Lily, Samuel, and Sophia. In a statement by Lily: "Sophia is a knight or Samuel is a knight". Samuel stated, "Sophia is a knight or Lily is a knave". As Sophia 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 Lily is a knight. No contradiction is found in their claim that Sophia is a knight or Samuel is a knight.
Assume Sophia is a knight. No contradiction is found in their claim that If Samuel is a knave then Samuel is a knight.
Assume Samuel is a knight. No contradiction is found in their claim that Sophia is a knight or Lily is a knave.
Therefore, (1) Lily is a knight
(2) Samuel is a knight
(3) Sophia is a knight </think>
<answer> (1) Lily is a knight
(2) Samuel is a knight
(3) Sophia is a knight </answer> | math | {
"ground_truth": {
"names": [
"Lily",
"Samuel",
"Sophia"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Lily is a knight\n(2) Samuel is a knight\n(3) Sophia is a knight",
"statements": "(('or', ('telling-truth', 2), ('telling-truth', 1)), ('or', ('telling-truth', 2), ('lying', 0)), ('->', ('lying', 1), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 9,
"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, Luke, and Liam. Charlotte expressed that Luke is a knave if and only if Liam is a knave. In Luke's words: \"Charlotte is not a knight\". \"Charlotte is a knave,\" Liam 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 Charlotte is a knight. ",
"No contradiction is found in their claim that Luke is a knave if and only if Liam is a knave.\n",
"Luke cannot be a knight, because this would contradict the claim of their own that Charlotte is not a knight.\n",
"Assume Luke is a knave. ",
"No contradiction is found in their false claim that Charlotte is not a knight.\n",
"Liam cannot be a knight, because this would contradict the claim of Charlotte that Luke is a knave if and only if Liam is a knave.\n",
"Assume Liam is a knave. ",
"No contradiction is found in their false claim that Charlotte is a knave.\n",
"Therefore, (1) Charlotte is a knight\n",
"(2) Luke 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: Charlotte, Luke, and Liam. Charlotte expressed that Luke is a knave if and only if Liam is a knave. In Luke's words: "Charlotte is not a knight". "Charlotte is a knave," Liam 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 Charlotte is a knight. No contradiction is found in their claim that Luke is a knave if and only if Liam is a knave.
Luke cannot be a knight, because this would contradict the claim of their own that Charlotte is not a knight.
Assume Luke is a knave. No contradiction is found in their false claim that Charlotte is not a knight.
Liam cannot be a knight, because this would contradict the claim of Charlotte that Luke is a knave if and only if Liam is a knave.
Assume Liam is a knave. No contradiction is found in their false claim that Charlotte is a knave.
Therefore, (1) Charlotte is a knight
(2) Luke is a knave
(3) Liam is a knave </think>
<answer> (1) Charlotte is a knight
(2) Luke is a knave
(3) Liam is a knave </answer> | math | {
"ground_truth": {
"names": [
"Charlotte",
"Luke",
"Liam"
],
"solution": [
true,
false,
false
],
"solution_text_format": "(1) Charlotte is a knight\n(2) Luke is a knave\n(3) Liam is a knave",
"statements": "(('<=>', ('lying', 1), ('lying', 2)), ('not', ('telling-truth', 0)), ('lying', 0))"
},
"style": "rule"
} | {
"index": 10,
"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: Sebastian, Matthew, and Logan. Sebastian was heard saying, \"Logan is a knave or Sebastian is a knight\". As Matthew put it, \"If Logan is a knight then Sebastian is a knave\". As Logan put it, \"Matthew 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 Sebastian is a knight. ",
"No contradiction is found in their claim that Logan is a knave or Sebastian is a knight.\n",
"Assume Logan is a knight. ",
"No contradiction is found in their claim that Matthew is not a knave.\n",
"Matthew cannot be a knight, because this would contradict the claim of their own that If Logan is a knight then Sebastian is a knave.\n",
"Matthew cannot be a knave, because this would contradict the claim of Logan that Matthew is not a knave.\n",
"We have exhausted all possibilities for Matthew, so let us go back and reconsider Logan.\n",
"Assume Logan is a knave. ",
"No contradiction is found in their false claim that Matthew is not a knave.\n",
"Matthew cannot be a knight, because this would contradict the false claim of Logan that Matthew is not a knave.\n",
"Matthew cannot be a knave, because this would contradict the false claim of their own that If Logan is a knight then Sebastian is a knave.\n",
"We have exhausted all possibilities for Matthew and Logan, so let us go back and reconsider Sebastian.\n",
"Assume Sebastian is a knave. ",
"No contradiction is found in their false claim that Logan is a knave or Sebastian is a knight.\n",
"Assume Logan is a knight. ",
"No contradiction is found in their claim that Matthew is not a knave.\n",
"Assume Matthew is a knight. ",
"No contradiction is found in their claim that If Logan is a knight then Sebastian is a knave.\n",
"Therefore, (1) Sebastian is a knave\n",
"(2) Matthew 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: Sebastian, Matthew, and Logan. Sebastian was heard saying, "Logan is a knave or Sebastian is a knight". As Matthew put it, "If Logan is a knight then Sebastian is a knave". As Logan put it, "Matthew 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 Sebastian is a knight. No contradiction is found in their claim that Logan is a knave or Sebastian is a knight.
Assume Logan is a knight. No contradiction is found in their claim that Matthew is not a knave.
Matthew cannot be a knight, because this would contradict the claim of their own that If Logan is a knight then Sebastian is a knave.
Matthew cannot be a knave, because this would contradict the claim of Logan that Matthew is not a knave.
We have exhausted all possibilities for Matthew, so let us go back and reconsider Logan.
Assume Logan is a knave. No contradiction is found in their false claim that Matthew is not a knave.
Matthew cannot be a knight, because this would contradict the false claim of Logan that Matthew is not a knave.
Matthew cannot be a knave, because this would contradict the false claim of their own that If Logan is a knight then Sebastian is a knave.
We have exhausted all possibilities for Matthew and Logan, so let us go back and reconsider Sebastian.
Assume Sebastian is a knave. No contradiction is found in their false claim that Logan is a knave or Sebastian is a knight.
Assume Logan is a knight. No contradiction is found in their claim that Matthew is not a knave.
Assume Matthew is a knight. No contradiction is found in their claim that If Logan is a knight then Sebastian is a knave.
Therefore, (1) Sebastian is a knave
(2) Matthew is a knight
(3) Logan is a knight </think>
<answer> (1) Sebastian is a knave
(2) Matthew is a knight
(3) Logan is a knight </answer> | math | {
"ground_truth": {
"names": [
"Sebastian",
"Matthew",
"Logan"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Sebastian is a knave\n(2) Matthew is a knight\n(3) Logan is a knight",
"statements": "(('or', ('lying', 2), ('telling-truth', 0)), ('->', ('telling-truth', 2), ('lying', 0)), ('not', ('lying', 1)))"
},
"style": "rule"
} | {
"index": 11,
"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, Harper, and Luke. Lily was heard saying, \"Harper is a knave or Luke is a knight\". According to Harper, \"If Lily is a knave then Luke is a knave\". Luke said, \"Lily is a knight and 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 Lily is a knight. ",
"No contradiction is found in their claim that Harper is a knave or Luke is a knight.\n",
"Assume Harper is a knight. ",
"No contradiction is found in their claim that If Lily is a knave then Luke is a knave.\n",
"Luke cannot be a knight, because this would contradict the claim of their own that Lily is a knight and Lily is a knave.\n",
"Luke cannot be a knave, because this would contradict the claim of Lily that Harper is a knave or Luke is a knight.\n",
"We have exhausted all possibilities for Luke, so let us go back and reconsider Harper.\n",
"Harper cannot be a knave, because this would contradict the false claim of their own that If Lily is a knave then Luke is a knave.\n",
"We have exhausted all possibilities for Harper, so let us go back and reconsider Lily.\n",
"Assume Lily is a knave. ",
"No contradiction is found in their false claim that Harper is a knave or Luke is a knight.\n",
"Assume Harper is a knight. ",
"No contradiction is found in their claim that If Lily is a knave then Luke is a knave.\n",
"Luke cannot be a knight, because this would contradict the false claim of Lily that Harper is a knave or Luke is a knight.\n",
"Assume Luke is a knave. ",
"No contradiction is found in their false claim that Lily is a knight and Lily is a knave.\n",
"Therefore, (1) Lily is a knave\n",
"(2) Harper is a knight\n",
"(3) Luke 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, Harper, and Luke. Lily was heard saying, "Harper is a knave or Luke is a knight". According to Harper, "If Lily is a knave then Luke is a knave". Luke said, "Lily is a knight and 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 Lily is a knight. No contradiction is found in their claim that Harper is a knave or Luke is a knight.
Assume Harper is a knight. No contradiction is found in their claim that If Lily is a knave then Luke is a knave.
Luke cannot be a knight, because this would contradict the claim of their own that Lily is a knight and Lily is a knave.
Luke cannot be a knave, because this would contradict the claim of Lily that Harper is a knave or Luke is a knight.
We have exhausted all possibilities for Luke, so let us go back and reconsider Harper.
Harper cannot be a knave, because this would contradict the false claim of their own that If Lily is a knave then Luke is a knave.
We have exhausted all possibilities for Harper, so let us go back and reconsider Lily.
Assume Lily is a knave. No contradiction is found in their false claim that Harper is a knave or Luke is a knight.
Assume Harper is a knight. No contradiction is found in their claim that If Lily is a knave then Luke is a knave.
Luke cannot be a knight, because this would contradict the false claim of Lily that Harper is a knave or Luke is a knight.
Assume Luke is a knave. No contradiction is found in their false claim that Lily is a knight and Lily is a knave.
Therefore, (1) Lily is a knave
(2) Harper is a knight
(3) Luke is a knave </think>
<answer> (1) Lily is a knave
(2) Harper is a knight
(3) Luke is a knave </answer> | math | {
"ground_truth": {
"names": [
"Lily",
"Harper",
"Luke"
],
"solution": [
false,
true,
false
],
"solution_text_format": "(1) Lily is a knave\n(2) Harper is a knight\n(3) Luke is a knave",
"statements": "(('or', ('lying', 1), ('telling-truth', 2)), ('->', ('lying', 0), ('lying', 2)), ('and', ('telling-truth', 0), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 12,
"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, Abigail, and Ava. James noted, \"Abigail is a knight\". \"Abigail is a knight if and only if James is a knight,\" Abigail claimed. Ava expressed that Abigail 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 James is a knight. ",
"No contradiction is found in their claim that Abigail is a knight.\n",
"Assume Abigail is a knight. ",
"No contradiction is found in their claim that Abigail is a knight if and only if James is a knight.\n",
"Ava cannot be a knight, because this would contradict the claim of their own that Abigail is not a knight.\n",
"Assume Ava is a knave. ",
"No contradiction is found in their false claim that Abigail is not a knight.\n",
"Therefore, (1) James is a knight\n",
"(2) Abigail 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: James, Abigail, and Ava. James noted, "Abigail is a knight". "Abigail is a knight if and only if James is a knight," Abigail claimed. Ava expressed that Abigail 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 James is a knight. No contradiction is found in their claim that Abigail is a knight.
Assume Abigail is a knight. No contradiction is found in their claim that Abigail is a knight if and only if James is a knight.
Ava cannot be a knight, because this would contradict the claim of their own that Abigail is not a knight.
Assume Ava is a knave. No contradiction is found in their false claim that Abigail is not a knight.
Therefore, (1) James is a knight
(2) Abigail is a knight
(3) Ava is a knave </think>
<answer> (1) James is a knight
(2) Abigail is a knight
(3) Ava is a knave </answer> | math | {
"ground_truth": {
"names": [
"James",
"Abigail",
"Ava"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) James is a knight\n(2) Abigail is a knight\n(3) Ava is a knave",
"statements": "(('telling-truth', 1), ('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('not', ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 13,
"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, William, and Aria. Victoria noted, \"Aria is a knave or Aria is a knight\". William expressed that Victoria is a knave or Aria is a knave. \"William is a knight or William is a knave,\" Aria 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 Victoria is a knight. ",
"No contradiction is found in their claim that Aria is a knave or Aria is a knight.\n",
"Assume Aria is a knight. ",
"No contradiction is found in their claim that William is a knight or William is a knave.\n",
"William cannot be a knight, because this would contradict the claim of their own that Victoria is a knave or Aria is a knave.\n",
"Assume William is a knave. ",
"No contradiction is found in their false claim that Victoria is a knave or Aria is a knave.\n",
"Therefore, (1) Victoria is a knight\n",
"(2) William is a knave\n",
"(3) Aria 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, William, and Aria. Victoria noted, "Aria is a knave or Aria is a knight". William expressed that Victoria is a knave or Aria is a knave. "William is a knight or William is a knave," Aria 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 Victoria is a knight. No contradiction is found in their claim that Aria is a knave or Aria is a knight.
Assume Aria is a knight. No contradiction is found in their claim that William is a knight or William is a knave.
William cannot be a knight, because this would contradict the claim of their own that Victoria is a knave or Aria is a knave.
Assume William is a knave. No contradiction is found in their false claim that Victoria is a knave or Aria is a knave.
Therefore, (1) Victoria is a knight
(2) William is a knave
(3) Aria is a knight </think>
<answer> (1) Victoria is a knight
(2) William is a knave
(3) Aria is a knight </answer> | math | {
"ground_truth": {
"names": [
"Victoria",
"William",
"Aria"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Victoria is a knight\n(2) William is a knave\n(3) Aria is a knight",
"statements": "(('or', ('lying', 2), ('telling-truth', 2)), ('or', ('lying', 0), ('lying', 2)), ('or', ('telling-truth', 1), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 14,
"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: Sebastian, Charlotte, and Riley. Sebastian noted, \"Riley is a knave or Sebastian is a knight\". \"If Sebastian is a knight then Charlotte is a knight\" - Charlotte. In Riley's words: \"Sebastian is a knave if and only if Riley 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 Sebastian is a knight. ",
"No contradiction is found in their claim that Riley is a knave or Sebastian is a knight.\n",
"Riley cannot be a knight, because this would contradict the claim of their own that Sebastian 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 Sebastian 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 Sebastian.\n",
"Assume Sebastian is a knave. ",
"No contradiction is found in their false claim that Riley is a knave or Sebastian is a knight.\n",
"Assume Riley is a knight. ",
"No contradiction is found in their claim that Sebastian is a knave if and only if Riley is a knight.\n",
"Assume Charlotte is a knight. ",
"No contradiction is found in their claim that If Sebastian is a knight then Charlotte is a knight.\n",
"Therefore, (1) Sebastian is a knave\n",
"(2) Charlotte 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: Sebastian, Charlotte, and Riley. Sebastian noted, "Riley is a knave or Sebastian is a knight". "If Sebastian is a knight then Charlotte is a knight" - Charlotte. In Riley's words: "Sebastian is a knave if and only if Riley 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 Sebastian is a knight. No contradiction is found in their claim that Riley is a knave or Sebastian is a knight.
Riley cannot be a knight, because this would contradict the claim of their own that Sebastian 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 Sebastian 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 Sebastian.
Assume Sebastian is a knave. No contradiction is found in their false claim that Riley is a knave or Sebastian is a knight.
Assume Riley is a knight. No contradiction is found in their claim that Sebastian is a knave if and only if Riley is a knight.
Assume Charlotte is a knight. No contradiction is found in their claim that If Sebastian is a knight then Charlotte is a knight.
Therefore, (1) Sebastian is a knave
(2) Charlotte is a knight
(3) Riley is a knight </think>
<answer> (1) Sebastian is a knave
(2) Charlotte is a knight
(3) Riley is a knight </answer> | math | {
"ground_truth": {
"names": [
"Sebastian",
"Charlotte",
"Riley"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Sebastian is a knave\n(2) Charlotte is a knight\n(3) Riley is a knight",
"statements": "(('or', ('lying', 2), ('telling-truth', 0)), ('->', ('telling-truth', 0), ('telling-truth', 1)), ('<=>', ('lying', 0), ('telling-truth', 2)))"
},
"style": "rule"
} | {
"index": 15,
"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, Jacob, and Amelia. Owen said that Jacob is not a knight. Jacob said, \"If Amelia is a knave then Owen is a knight.\" Amelia commented, \"If Owen is a knight then Owen 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 Jacob is not a knight.\n",
"Jacob cannot be a knight, because this would contradict the claim of Owen that Jacob is not a knight.\n",
"Jacob cannot be a knave, because this would contradict the false claim of their own that If Amelia is a knave then Owen is a knight.\n",
"We have exhausted all possibilities for Jacob, so let us go back and reconsider Owen.\n",
"Assume Owen is a knave. ",
"No contradiction is found in their false claim that Jacob is not a knight.\n",
"Assume Jacob is a knight. ",
"No contradiction is found in their claim that If Amelia is a knave then Owen is a knight.\n",
"Assume Amelia is a knight. ",
"No contradiction is found in their claim that If Owen is a knight then Owen is a knave.\n",
"Therefore, (1) Owen is a knave\n",
"(2) Jacob 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: Owen, Jacob, and Amelia. Owen said that Jacob is not a knight. Jacob said, "If Amelia is a knave then Owen is a knight." Amelia commented, "If Owen is a knight then Owen 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 Jacob is not a knight.
Jacob cannot be a knight, because this would contradict the claim of Owen that Jacob is not a knight.
Jacob cannot be a knave, because this would contradict the false claim of their own that If Amelia is a knave then Owen is a knight.
We have exhausted all possibilities for Jacob, so let us go back and reconsider Owen.
Assume Owen is a knave. No contradiction is found in their false claim that Jacob is not a knight.
Assume Jacob is a knight. No contradiction is found in their claim that If Amelia is a knave then Owen is a knight.
Assume Amelia is a knight. No contradiction is found in their claim that If Owen is a knight then Owen is a knave.
Therefore, (1) Owen is a knave
(2) Jacob is a knight
(3) Amelia is a knight </think>
<answer> (1) Owen is a knave
(2) Jacob is a knight
(3) Amelia is a knight </answer> | math | {
"ground_truth": {
"names": [
"Owen",
"Jacob",
"Amelia"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Owen is a knave\n(2) Jacob is a knight\n(3) Amelia is a knight",
"statements": "(('not', ('telling-truth', 1)), ('->', ('lying', 2), ('telling-truth', 0)), ('->', ('telling-truth', 0), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 16,
"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, Lucas, and Daniel. \"Lucas is not a knave\" - Alexander. Lucas told you that Daniel is not a knave. \"Lucas is a knight if and only if Daniel is a knight\" - Daniel. 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 Lucas is not a knave.\n",
"Assume Lucas is a knight. ",
"No contradiction is found in their claim that Daniel is not a knave.\n",
"Assume Daniel is a knight. ",
"No contradiction is found in their claim that Lucas is a knight if and only if Daniel is a knight.\n",
"Therefore, (1) Alexander is a knight\n",
"(2) Lucas is a knight\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: Alexander, Lucas, and Daniel. "Lucas is not a knave" - Alexander. Lucas told you that Daniel is not a knave. "Lucas is a knight if and only if Daniel is a knight" - Daniel. 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 Lucas is not a knave.
Assume Lucas is a knight. No contradiction is found in their claim that Daniel is not a knave.
Assume Daniel is a knight. No contradiction is found in their claim that Lucas is a knight if and only if Daniel is a knight.
Therefore, (1) Alexander is a knight
(2) Lucas is a knight
(3) Daniel is a knight </think>
<answer> (1) Alexander is a knight
(2) Lucas is a knight
(3) Daniel is a knight </answer> | math | {
"ground_truth": {
"names": [
"Alexander",
"Lucas",
"Daniel"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Alexander is a knight\n(2) Lucas is a knight\n(3) Daniel is a knight",
"statements": "(('not', ('lying', 1)), ('not', ('lying', 2)), ('<=>', ('telling-truth', 1), ('telling-truth', 2)))"
},
"style": "rule"
} | {
"index": 17,
"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: Sebastian, Aria, and Benjamin. \"Aria is a knave or Sebastian is a knight,\" Sebastian claimed. Aria said, \"Sebastian is not a knave.\" \"Sebastian is a knight or Benjamin 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 Sebastian is a knight. ",
"No contradiction is found in their claim that Aria is a knave or Sebastian is a knight.\n",
"Assume Aria is a knight. ",
"No contradiction is found in their claim that Sebastian is not a knave.\n",
"Assume Benjamin is a knight. ",
"No contradiction is found in their claim that Sebastian is a knight or Benjamin is a knight.\n",
"Therefore, (1) Sebastian is a knight\n",
"(2) Aria is a knight\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: Sebastian, Aria, and Benjamin. "Aria is a knave or Sebastian is a knight," Sebastian claimed. Aria said, "Sebastian is not a knave." "Sebastian is a knight or Benjamin 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 Sebastian is a knight. No contradiction is found in their claim that Aria is a knave or Sebastian is a knight.
Assume Aria is a knight. No contradiction is found in their claim that Sebastian is not a knave.
Assume Benjamin is a knight. No contradiction is found in their claim that Sebastian is a knight or Benjamin is a knight.
Therefore, (1) Sebastian is a knight
(2) Aria is a knight
(3) Benjamin is a knight </think>
<answer> (1) Sebastian is a knight
(2) Aria is a knight
(3) Benjamin is a knight </answer> | math | {
"ground_truth": {
"names": [
"Sebastian",
"Aria",
"Benjamin"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Sebastian is a knight\n(2) Aria is a knight\n(3) Benjamin is a knight",
"statements": "(('or', ('lying', 1), ('telling-truth', 0)), ('not', ('lying', 0)), ('or', ('telling-truth', 0), ('telling-truth', 2)))"
},
"style": "rule"
} | {
"index": 18,
"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, Ethan, and Riley. Daniel told you that Ethan is a knave or Riley is a knave. Ethan told you that Daniel is a knight. \"Daniel is a knight if and only if Daniel is a knave\" - Riley. 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 Ethan is a knave or Riley is a knave.\n",
"Assume Ethan is a knight. ",
"No contradiction is found in their claim that Daniel is a knight.\n",
"Riley cannot be a knight, because this would contradict the claim of Daniel that Ethan is a knave or Riley is a knave.\n",
"Assume Riley is a knave. ",
"No contradiction is found in their false claim that Daniel is a knight if and only if Daniel is a knave.\n",
"Therefore, (1) Daniel is a knight\n",
"(2) Ethan is a knight\n",
"(3) Riley 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, Ethan, and Riley. Daniel told you that Ethan is a knave or Riley is a knave. Ethan told you that Daniel is a knight. "Daniel is a knight if and only if Daniel is a knave" - Riley. 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 Ethan is a knave or Riley is a knave.
Assume Ethan is a knight. No contradiction is found in their claim that Daniel is a knight.
Riley cannot be a knight, because this would contradict the claim of Daniel that Ethan is a knave or Riley is a knave.
Assume Riley is a knave. No contradiction is found in their false claim that Daniel is a knight if and only if Daniel is a knave.
Therefore, (1) Daniel is a knight
(2) Ethan is a knight
(3) Riley is a knave </think>
<answer> (1) Daniel is a knight
(2) Ethan is a knight
(3) Riley is a knave </answer> | math | {
"ground_truth": {
"names": [
"Daniel",
"Ethan",
"Riley"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Daniel is a knight\n(2) Ethan is a knight\n(3) Riley is a knave",
"statements": "(('or', ('lying', 1), ('lying', 2)), ('telling-truth', 0), ('<=>', ('telling-truth', 0), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 19,
"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, Zoey, and Mason. Elizabeth remarked, \"Mason is a knight or Zoey is a knight\". Zoey noted, \"Mason is a knave if and only if Mason is a knight\". \"Elizabeth is a knave or Elizabeth is a knight,\" Mason 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 Elizabeth is a knight. ",
"No contradiction is found in their claim that Mason is a knight or Zoey is a knight.\n",
"Assume Mason is a knight. ",
"No contradiction is found in their claim that Elizabeth is a knave or Elizabeth is a knight.\n",
"Zoey 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 Zoey 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",
"Therefore, (1) Elizabeth is a knight\n",
"(2) Zoey is a knave\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: Elizabeth, Zoey, and Mason. Elizabeth remarked, "Mason is a knight or Zoey is a knight". Zoey noted, "Mason is a knave if and only if Mason is a knight". "Elizabeth is a knave or Elizabeth is a knight," Mason 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 Elizabeth is a knight. No contradiction is found in their claim that Mason is a knight or Zoey is a knight.
Assume Mason is a knight. No contradiction is found in their claim that Elizabeth is a knave or Elizabeth is a knight.
Zoey 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 Zoey is a knave. No contradiction is found in their false claim that Mason is a knave if and only if Mason is a knight.
Therefore, (1) Elizabeth is a knight
(2) Zoey is a knave
(3) Mason is a knight </think>
<answer> (1) Elizabeth is a knight
(2) Zoey is a knave
(3) Mason is a knight </answer> | math | {
"ground_truth": {
"names": [
"Elizabeth",
"Zoey",
"Mason"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Elizabeth is a knight\n(2) Zoey is a knave\n(3) Mason is a knight",
"statements": "(('or', ('telling-truth', 2), ('telling-truth', 1)), ('<=>', ('lying', 2), ('telling-truth', 2)), ('or', ('lying', 0), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 20,
"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, Emily, and Abigail. Harper commented, \"Abigail is a knight and Emily is a knave\". Emily stated, \"Abigail is a knight\". Abigail was heard saying, \"Harper is a knave or Abigail 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 Harper is a knight. ",
"No contradiction is found in their claim that Abigail is a knight and Emily is a knave.\n",
"Assume Abigail is a knight. ",
"No contradiction is found in their claim that Harper is a knave or Abigail is a knight.\n",
"Emily cannot be a knight, because this would contradict the claim of Harper that Abigail is a knight and Emily is a knave.\n",
"Emily cannot be a knave, because this would contradict the false claim of their own that Abigail is a knight.\n",
"We have exhausted all possibilities for Emily, so let us go back and reconsider Abigail.\n",
"Abigail cannot be a knave, because this would contradict the claim of Harper that Abigail is a knight and Emily is a knave.\n",
"We have exhausted all possibilities for Abigail, so let us go back and reconsider Harper.\n",
"Assume Harper is a knave. ",
"No contradiction is found in their false claim that Abigail is a knight and Emily is a knave.\n",
"Assume Abigail is a knight. ",
"No contradiction is found in their claim that Harper is a knave or Abigail is a knight.\n",
"Assume Emily is a knight. ",
"No contradiction is found in their claim that Abigail is a knight.\n",
"Therefore, (1) Harper is a knave\n",
"(2) Emily is a knight\n",
"(3) Abigail 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, Emily, and Abigail. Harper commented, "Abigail is a knight and Emily is a knave". Emily stated, "Abigail is a knight". Abigail was heard saying, "Harper is a knave or Abigail 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 Harper is a knight. No contradiction is found in their claim that Abigail is a knight and Emily is a knave.
Assume Abigail is a knight. No contradiction is found in their claim that Harper is a knave or Abigail is a knight.
Emily cannot be a knight, because this would contradict the claim of Harper that Abigail is a knight and Emily is a knave.
Emily cannot be a knave, because this would contradict the false claim of their own that Abigail is a knight.
We have exhausted all possibilities for Emily, so let us go back and reconsider Abigail.
Abigail cannot be a knave, because this would contradict the claim of Harper that Abigail is a knight and Emily is a knave.
We have exhausted all possibilities for Abigail, so let us go back and reconsider Harper.
Assume Harper is a knave. No contradiction is found in their false claim that Abigail is a knight and Emily is a knave.
Assume Abigail is a knight. No contradiction is found in their claim that Harper is a knave or Abigail is a knight.
Assume Emily is a knight. No contradiction is found in their claim that Abigail is a knight.
Therefore, (1) Harper is a knave
(2) Emily is a knight
(3) Abigail is a knight </think>
<answer> (1) Harper is a knave
(2) Emily is a knight
(3) Abigail is a knight </answer> | math | {
"ground_truth": {
"names": [
"Harper",
"Emily",
"Abigail"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Harper is a knave\n(2) Emily is a knight\n(3) Abigail is a knight",
"statements": "(('and', ('telling-truth', 2), ('lying', 1)), ('telling-truth', 2), ('or', ('lying', 0), ('telling-truth', 2)))"
},
"style": "rule"
} | {
"index": 21,
"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, Lucas, and Sophia. Logan remarked, \"Sophia is a knight\". Lucas said that If Sophia is a knave then Logan is a knight. Sophia stated, \"Logan is a knave if and only if 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 Logan is a knight. ",
"No contradiction is found in their claim that Sophia is a knight.\n",
"Assume Sophia is a knight. ",
"No contradiction is found in their claim that Logan is a knave if and only if Lucas is a knight.\n",
"Lucas cannot be a knight, because this would contradict the claim of Sophia that Logan is a knave if and only if Lucas is a knight.\n",
"Lucas cannot be a knave, because this would contradict the false claim of their own that If Sophia is a knave then Logan is a knight.\n",
"We have exhausted all possibilities for Lucas, so let us go back and reconsider Sophia.\n",
"Sophia cannot be a knave, because this would contradict the claim of Logan that Sophia is a knight.\n",
"We have exhausted all possibilities for Sophia, so let us go back and reconsider Logan.\n",
"Assume Logan is a knave. ",
"No contradiction is found in their false claim that Sophia is a knight.\n",
"Sophia cannot be a knight, because this would contradict the false claim of Logan that Sophia is a knight.\n",
"Assume Sophia is a knave. ",
"No contradiction is found in their false claim that Logan is a knave if and only if Lucas is a knight.\n",
"Lucas cannot be a knight, because this would contradict the claim of their own that If Sophia is a knave then Logan is a knight.\n",
"Assume Lucas is a knave. ",
"No contradiction is found in their false claim that If Sophia is a knave then Logan is a knight.\n",
"Therefore, (1) Logan is a knave\n",
"(2) Lucas 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: Logan, Lucas, and Sophia. Logan remarked, "Sophia is a knight". Lucas said that If Sophia is a knave then Logan is a knight. Sophia stated, "Logan is a knave if and only if 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 Logan is a knight. No contradiction is found in their claim that Sophia is a knight.
Assume Sophia is a knight. No contradiction is found in their claim that Logan is a knave if and only if Lucas is a knight.
Lucas cannot be a knight, because this would contradict the claim of Sophia that Logan is a knave if and only if Lucas is a knight.
Lucas cannot be a knave, because this would contradict the false claim of their own that If Sophia is a knave then Logan is a knight.
We have exhausted all possibilities for Lucas, so let us go back and reconsider Sophia.
Sophia cannot be a knave, because this would contradict the claim of Logan that Sophia is a knight.
We have exhausted all possibilities for Sophia, so let us go back and reconsider Logan.
Assume Logan is a knave. No contradiction is found in their false claim that Sophia is a knight.
Sophia cannot be a knight, because this would contradict the false claim of Logan that Sophia is a knight.
Assume Sophia is a knave. No contradiction is found in their false claim that Logan is a knave if and only if Lucas is a knight.
Lucas cannot be a knight, because this would contradict the claim of their own that If Sophia is a knave then Logan is a knight.
Assume Lucas is a knave. No contradiction is found in their false claim that If Sophia is a knave then Logan is a knight.
Therefore, (1) Logan is a knave
(2) Lucas is a knave
(3) Sophia is a knave </think>
<answer> (1) Logan is a knave
(2) Lucas is a knave
(3) Sophia is a knave </answer> | math | {
"ground_truth": {
"names": [
"Logan",
"Lucas",
"Sophia"
],
"solution": [
false,
false,
false
],
"solution_text_format": "(1) Logan is a knave\n(2) Lucas is a knave\n(3) Sophia is a knave",
"statements": "(('telling-truth', 2), ('->', ('lying', 2), ('telling-truth', 0)), ('<=>', ('lying', 0), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 22,
"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, Mia, and Evelyn. Charlotte remarked, \"Evelyn is a knight or Mia is a knave\". According to Mia, \"Charlotte is a knight\". Evelyn remarked, \"Charlotte is a knave if and only if 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 Charlotte is a knight. ",
"No contradiction is found in their claim that Evelyn is a knight or Mia is a knave.\n",
"Assume Evelyn is a knight. ",
"No contradiction is found in their claim that Charlotte is a knave if and only if Mia is a knave.\n",
"Assume Mia is a knight. ",
"No contradiction is found in their claim that Charlotte is a knight.\n",
"Therefore, (1) Charlotte is a knight\n",
"(2) Mia 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: Charlotte, Mia, and Evelyn. Charlotte remarked, "Evelyn is a knight or Mia is a knave". According to Mia, "Charlotte is a knight". Evelyn remarked, "Charlotte is a knave if and only if 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 Charlotte is a knight. No contradiction is found in their claim that Evelyn is a knight or Mia is a knave.
Assume Evelyn is a knight. No contradiction is found in their claim that Charlotte is a knave if and only if Mia is a knave.
Assume Mia is a knight. No contradiction is found in their claim that Charlotte is a knight.
Therefore, (1) Charlotte is a knight
(2) Mia is a knight
(3) Evelyn is a knight </think>
<answer> (1) Charlotte is a knight
(2) Mia is a knight
(3) Evelyn is a knight </answer> | math | {
"ground_truth": {
"names": [
"Charlotte",
"Mia",
"Evelyn"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Charlotte is a knight\n(2) Mia is a knight\n(3) Evelyn is a knight",
"statements": "(('or', ('telling-truth', 2), ('lying', 1)), ('telling-truth', 0), ('<=>', ('lying', 0), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 23,
"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, Penelope, and Charlotte. \"If Penelope is a knight then Penelope is a knave,\" Grace claimed. In Penelope's words: \"Grace is a knave or Grace is a knight\". Charlotte asserted: \"Penelope 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 Penelope is a knight then Penelope is a knave.\n",
"Penelope cannot be a knight, because this would contradict the claim of Grace that If Penelope is a knight then Penelope is a knave.\n",
"Penelope cannot be a knave, because this would contradict the false claim of their own that Grace is a knave or Grace is a knight.\n",
"We have exhausted all possibilities for Penelope, so let us go back and reconsider Grace.\n",
"Assume Grace is a knave. ",
"No contradiction is found in their false claim that If Penelope is a knight then Penelope is a knave.\n",
"Assume Penelope is a knight. ",
"No contradiction is found in their claim that Grace is a knave or Grace is a knight.\n",
"Charlotte cannot be a knight, because this would contradict the claim of their own that Penelope is a knave.\n",
"Assume Charlotte is a knave. ",
"No contradiction is found in their false claim that Penelope is a knave.\n",
"Therefore, (1) Grace is a knave\n",
"(2) Penelope is a knight\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: Grace, Penelope, and Charlotte. "If Penelope is a knight then Penelope is a knave," Grace claimed. In Penelope's words: "Grace is a knave or Grace is a knight". Charlotte asserted: "Penelope 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 Penelope is a knight then Penelope is a knave.
Penelope cannot be a knight, because this would contradict the claim of Grace that If Penelope is a knight then Penelope is a knave.
Penelope cannot be a knave, because this would contradict the false claim of their own that Grace is a knave or Grace is a knight.
We have exhausted all possibilities for Penelope, so let us go back and reconsider Grace.
Assume Grace is a knave. No contradiction is found in their false claim that If Penelope is a knight then Penelope is a knave.
Assume Penelope is a knight. No contradiction is found in their claim that Grace is a knave or Grace is a knight.
Charlotte cannot be a knight, because this would contradict the claim of their own that Penelope is a knave.
Assume Charlotte is a knave. No contradiction is found in their false claim that Penelope is a knave.
Therefore, (1) Grace is a knave
(2) Penelope is a knight
(3) Charlotte is a knave </think>
<answer> (1) Grace is a knave
(2) Penelope is a knight
(3) Charlotte is a knave </answer> | math | {
"ground_truth": {
"names": [
"Grace",
"Penelope",
"Charlotte"
],
"solution": [
false,
true,
false
],
"solution_text_format": "(1) Grace is a knave\n(2) Penelope is a knight\n(3) Charlotte is a knave",
"statements": "(('->', ('telling-truth', 1), ('lying', 1)), ('or', ('lying', 0), ('telling-truth', 0)), ('lying', 1))"
},
"style": "rule"
} | {
"index": 24,
"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, Scarlett, and Charlotte. In a statement by Elizabeth: \"Charlotte is a knight\". Scarlett stated, \"Charlotte is a knave\". Charlotte commented, \"Elizabeth is a knight or Scarlett 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 Charlotte is a knight.\n",
"Assume Charlotte is a knight. ",
"No contradiction is found in their claim that Elizabeth is a knight or Scarlett is a knight.\n",
"Scarlett cannot be a knight, because this would contradict the claim of their own that Charlotte is a knave.\n",
"Assume Scarlett is a knave. ",
"No contradiction is found in their false claim that Charlotte is a knave.\n",
"Therefore, (1) Elizabeth is a knight\n",
"(2) Scarlett 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: Elizabeth, Scarlett, and Charlotte. In a statement by Elizabeth: "Charlotte is a knight". Scarlett stated, "Charlotte is a knave". Charlotte commented, "Elizabeth is a knight or Scarlett 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 Charlotte is a knight.
Assume Charlotte is a knight. No contradiction is found in their claim that Elizabeth is a knight or Scarlett is a knight.
Scarlett cannot be a knight, because this would contradict the claim of their own that Charlotte is a knave.
Assume Scarlett is a knave. No contradiction is found in their false claim that Charlotte is a knave.
Therefore, (1) Elizabeth is a knight
(2) Scarlett is a knave
(3) Charlotte is a knight </think>
<answer> (1) Elizabeth is a knight
(2) Scarlett is a knave
(3) Charlotte is a knight </answer> | math | {
"ground_truth": {
"names": [
"Elizabeth",
"Scarlett",
"Charlotte"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Elizabeth is a knight\n(2) Scarlett is a knave\n(3) Charlotte is a knight",
"statements": "(('telling-truth', 2), ('lying', 2), ('or', ('telling-truth', 0), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 25,
"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, Harper, and Ethan. Olivia said, \"Olivia is a knight or Harper is a knave.\" Harper stated, \"Ethan is a knave if and only if Olivia is a knight\". In a statement by Ethan: \"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 Olivia is a knight. ",
"No contradiction is found in their claim that Olivia is a knight or Harper is a knave.\n",
"Assume Harper is a knight. ",
"No contradiction is found in their claim that Ethan is a knave if and only if Olivia is a knight.\n",
"Ethan cannot be a knight, because this would contradict the claim of Harper that Ethan is a knave if and only if Olivia is a knight.\n",
"Ethan cannot be a knave, because this would contradict the false claim of their own that Harper is a knight.\n",
"We have exhausted all possibilities for Ethan, so let us go back and reconsider Harper.\n",
"Assume Harper is a knave. ",
"No contradiction is found in their false claim that Ethan is a knave if and only if Olivia is a knight.\n",
"Ethan cannot be a knight, because this would contradict the claim of their own that Harper is a knight.\n",
"Ethan cannot be a knave, because this would contradict the false claim of Harper that Ethan is a knave if and only if Olivia is a knight.\n",
"We have exhausted all possibilities for Ethan and Harper, so let us go back and reconsider Olivia.\n",
"Assume Olivia is a knave. ",
"No contradiction is found in their false claim that Olivia is a knight or Harper is a knave.\n",
"Assume Harper is a knight. ",
"No contradiction is found in their claim that Ethan is a knave if and only if Olivia is a knight.\n",
"Assume Ethan is a knight. ",
"No contradiction is found in their claim that Harper is a knight.\n",
"Therefore, (1) Olivia is a knave\n",
"(2) Harper is a knight\n",
"(3) Ethan 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, Harper, and Ethan. Olivia said, "Olivia is a knight or Harper is a knave." Harper stated, "Ethan is a knave if and only if Olivia is a knight". In a statement by Ethan: "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 Olivia is a knight. No contradiction is found in their claim that Olivia is a knight or Harper is a knave.
Assume Harper is a knight. No contradiction is found in their claim that Ethan is a knave if and only if Olivia is a knight.
Ethan cannot be a knight, because this would contradict the claim of Harper that Ethan is a knave if and only if Olivia is a knight.
Ethan cannot be a knave, because this would contradict the false claim of their own that Harper is a knight.
We have exhausted all possibilities for Ethan, so let us go back and reconsider Harper.
Assume Harper is a knave. No contradiction is found in their false claim that Ethan is a knave if and only if Olivia is a knight.
Ethan cannot be a knight, because this would contradict the claim of their own that Harper is a knight.
Ethan cannot be a knave, because this would contradict the false claim of Harper that Ethan is a knave if and only if Olivia is a knight.
We have exhausted all possibilities for Ethan and Harper, so let us go back and reconsider Olivia.
Assume Olivia is a knave. No contradiction is found in their false claim that Olivia is a knight or Harper is a knave.
Assume Harper is a knight. No contradiction is found in their claim that Ethan is a knave if and only if Olivia is a knight.
Assume Ethan is a knight. No contradiction is found in their claim that Harper is a knight.
Therefore, (1) Olivia is a knave
(2) Harper is a knight
(3) Ethan is a knight </think>
<answer> (1) Olivia is a knave
(2) Harper is a knight
(3) Ethan is a knight </answer> | math | {
"ground_truth": {
"names": [
"Olivia",
"Harper",
"Ethan"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Olivia is a knave\n(2) Harper is a knight\n(3) Ethan is a knight",
"statements": "(('or', ('telling-truth', 0), ('lying', 1)), ('<=>', ('lying', 2), ('telling-truth', 0)), ('telling-truth', 1))"
},
"style": "rule"
} | {
"index": 26,
"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, Joseph, and Emily. \"Joseph is a knight if and only if Emily is a knave\" - Evelyn. Joseph told you that Emily is a knight. According to Emily, \"Joseph is a knight or Evelyn 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 Evelyn is a knight. ",
"No contradiction is found in their claim that Joseph is a knight if and only if Emily is a knave.\n",
"Assume Joseph is a knight. ",
"No contradiction is found in their claim that Emily is a knight.\n",
"Emily cannot be a knight, because this would contradict the claim of Evelyn that Joseph is a knight if and only if Emily is a knave.\n",
"Emily cannot be a knave, because this would contradict the claim of Joseph that Emily is a knight.\n",
"We have exhausted all possibilities for Emily, so let us go back and reconsider Joseph.\n",
"Assume Joseph is a knave. ",
"No contradiction is found in their false claim that Emily is a knight.\n",
"Emily cannot be a knight, because this would contradict the false claim of Joseph that Emily is a knight.\n",
"Emily cannot be a knave, because this would contradict the claim of Evelyn that Joseph is a knight if and only if Emily is a knave.\n",
"We have exhausted all possibilities for Emily and Joseph, so let us go back and reconsider Evelyn.\n",
"Assume Evelyn is a knave. ",
"No contradiction is found in their false claim that Joseph is a knight if and only if Emily is a knave.\n",
"Assume Joseph is a knight. ",
"No contradiction is found in their claim that Emily is a knight.\n",
"Assume Emily is a knight. ",
"No contradiction is found in their claim that Joseph is a knight or Evelyn is a knave.\n",
"Therefore, (1) Evelyn is a knave\n",
"(2) Joseph 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: Evelyn, Joseph, and Emily. "Joseph is a knight if and only if Emily is a knave" - Evelyn. Joseph told you that Emily is a knight. According to Emily, "Joseph is a knight or Evelyn 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 Evelyn is a knight. No contradiction is found in their claim that Joseph is a knight if and only if Emily is a knave.
Assume Joseph is a knight. No contradiction is found in their claim that Emily is a knight.
Emily cannot be a knight, because this would contradict the claim of Evelyn that Joseph is a knight if and only if Emily is a knave.
Emily cannot be a knave, because this would contradict the claim of Joseph that Emily is a knight.
We have exhausted all possibilities for Emily, so let us go back and reconsider Joseph.
Assume Joseph is a knave. No contradiction is found in their false claim that Emily is a knight.
Emily cannot be a knight, because this would contradict the false claim of Joseph that Emily is a knight.
Emily cannot be a knave, because this would contradict the claim of Evelyn that Joseph is a knight if and only if Emily is a knave.
We have exhausted all possibilities for Emily and Joseph, so let us go back and reconsider Evelyn.
Assume Evelyn is a knave. No contradiction is found in their false claim that Joseph is a knight if and only if Emily is a knave.
Assume Joseph is a knight. No contradiction is found in their claim that Emily is a knight.
Assume Emily is a knight. No contradiction is found in their claim that Joseph is a knight or Evelyn is a knave.
Therefore, (1) Evelyn is a knave
(2) Joseph is a knight
(3) Emily is a knight </think>
<answer> (1) Evelyn is a knave
(2) Joseph is a knight
(3) Emily is a knight </answer> | math | {
"ground_truth": {
"names": [
"Evelyn",
"Joseph",
"Emily"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Evelyn is a knave\n(2) Joseph is a knight\n(3) Emily is a knight",
"statements": "(('<=>', ('telling-truth', 1), ('lying', 2)), ('telling-truth', 2), ('or', ('telling-truth', 1), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 27,
"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, Ava, and Benjamin. Scarlett was heard saying, \"Benjamin is a knight\". Ava expressed that Scarlett is a knave and Scarlett is a knight. In Benjamin's words: \"Benjamin is a knight if and only if Scarlett 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 Benjamin is a knight.\n",
"Benjamin cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight if and only if Scarlett is a knave.\n",
"Benjamin cannot be a knave, because this would contradict the claim of Scarlett that Benjamin is a knight.\n",
"We have exhausted all possibilities for Benjamin, so let us go back and reconsider Scarlett.\n",
"Assume Scarlett is a knave. ",
"No contradiction is found in their false claim that Benjamin is a knight.\n",
"Benjamin cannot be a knight, because this would contradict the false claim of Scarlett that Benjamin is a knight.\n",
"Assume Benjamin is a knave. ",
"No contradiction is found in their false claim that Benjamin is a knight if and only if Scarlett is a knave.\n",
"Ava cannot be a knight, because this would contradict the claim of their own that Scarlett is a knave and Scarlett is a knight.\n",
"Assume Ava is a knave. ",
"No contradiction is found in their false claim that Scarlett is a knave and Scarlett is a knight.\n",
"Therefore, (1) Scarlett is a knave\n",
"(2) Ava is a knave\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: Scarlett, Ava, and Benjamin. Scarlett was heard saying, "Benjamin is a knight". Ava expressed that Scarlett is a knave and Scarlett is a knight. In Benjamin's words: "Benjamin is a knight if and only if Scarlett 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 Benjamin is a knight.
Benjamin cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight if and only if Scarlett is a knave.
Benjamin cannot be a knave, because this would contradict the claim of Scarlett that Benjamin is a knight.
We have exhausted all possibilities for Benjamin, so let us go back and reconsider Scarlett.
Assume Scarlett is a knave. No contradiction is found in their false claim that Benjamin is a knight.
Benjamin cannot be a knight, because this would contradict the false claim of Scarlett that Benjamin is a knight.
Assume Benjamin is a knave. No contradiction is found in their false claim that Benjamin is a knight if and only if Scarlett is a knave.
Ava cannot be a knight, because this would contradict the claim of their own that Scarlett is a knave and Scarlett is a knight.
Assume Ava is a knave. No contradiction is found in their false claim that Scarlett is a knave and Scarlett is a knight.
Therefore, (1) Scarlett is a knave
(2) Ava is a knave
(3) Benjamin is a knave </think>
<answer> (1) Scarlett is a knave
(2) Ava is a knave
(3) Benjamin is a knave </answer> | math | {
"ground_truth": {
"names": [
"Scarlett",
"Ava",
"Benjamin"
],
"solution": [
false,
false,
false
],
"solution_text_format": "(1) Scarlett is a knave\n(2) Ava is a knave\n(3) Benjamin is a knave",
"statements": "(('telling-truth', 2), ('and', ('lying', 0), ('telling-truth', 0)), ('<=>', ('telling-truth', 2), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 28,
"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 Victoria. \"Daniel is a knight if and only if Isabella is a knight,\" Daniel declared. \"Daniel is a knight\" - Isabella. Victoria told you that Isabella is a knave and 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 Daniel is a knight. ",
"No contradiction is found in their claim that Daniel is a knight if and only if Isabella is a knight.\n",
"Assume Isabella is a knight. ",
"No contradiction is found in their claim that Daniel is a knight.\n",
"Victoria cannot be a knight, because this would contradict the claim of their own that Isabella is a knave and Isabella is a knight.\n",
"Assume Victoria is a knave. ",
"No contradiction is found in their false claim that Isabella is a knave and Isabella is a knight.\n",
"Therefore, (1) Daniel is a knight\n",
"(2) Isabella 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: Daniel, Isabella, and Victoria. "Daniel is a knight if and only if Isabella is a knight," Daniel declared. "Daniel is a knight" - Isabella. Victoria told you that Isabella is a knave and 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 Daniel is a knight. No contradiction is found in their claim that Daniel is a knight if and only if Isabella is a knight.
Assume Isabella is a knight. No contradiction is found in their claim that Daniel is a knight.
Victoria cannot be a knight, because this would contradict the claim of their own that Isabella is a knave and Isabella is a knight.
Assume Victoria is a knave. No contradiction is found in their false claim that Isabella is a knave and Isabella is a knight.
Therefore, (1) Daniel is a knight
(2) Isabella is a knight
(3) Victoria is a knave </think>
<answer> (1) Daniel is a knight
(2) Isabella is a knight
(3) Victoria is a knave </answer> | math | {
"ground_truth": {
"names": [
"Daniel",
"Isabella",
"Victoria"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Daniel is a knight\n(2) Isabella is a knight\n(3) Victoria is a knave",
"statements": "(('<=>', ('telling-truth', 0), ('telling-truth', 1)), ('telling-truth', 0), ('and', ('lying', 1), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 29,
"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, Luke, and Matthew. Liam remarked, \"Matthew is a knave if and only if Luke is a knave\". Luke remarked, \"If Matthew is a knight then Matthew is a knave\". \"Luke is a knight or Luke is a knave,\" Matthew 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 Liam is a knight. ",
"No contradiction is found in their claim that Matthew is a knave if and only if Luke is a knave.\n",
"Assume Matthew is a knight. ",
"No contradiction is found in their claim that Luke is a knight or Luke is a knave.\n",
"Luke cannot be a knight, because this would contradict the claim of their own that If Matthew is a knight then Matthew is a knave.\n",
"Luke cannot be a knave, because this would contradict the claim of Liam that Matthew is a knave if and only if Luke is a knave.\n",
"We have exhausted all possibilities for Luke, so let us go back and reconsider Matthew.\n",
"Matthew cannot be a knave, because this would contradict the false claim of their own that Luke is a knight or Luke is a knave.\n",
"We have exhausted all possibilities for Matthew, so let us go back and reconsider Liam.\n",
"Assume Liam is a knave. ",
"No contradiction is found in their false claim that Matthew is a knave if and only if Luke is a knave.\n",
"Assume Matthew is a knight. ",
"No contradiction is found in their claim that Luke is a knight or Luke is a knave.\n",
"Luke cannot be a knight, because this would contradict the false claim of Liam that Matthew is a knave if and only if Luke is a knave.\n",
"Assume Luke is a knave. ",
"No contradiction is found in their false claim that If Matthew is a knight then Matthew is a knave.\n",
"Therefore, (1) Liam is a knave\n",
"(2) Luke is a knave\n",
"(3) Matthew 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, Luke, and Matthew. Liam remarked, "Matthew is a knave if and only if Luke is a knave". Luke remarked, "If Matthew is a knight then Matthew is a knave". "Luke is a knight or Luke is a knave," Matthew 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 Liam is a knight. No contradiction is found in their claim that Matthew is a knave if and only if Luke is a knave.
Assume Matthew is a knight. No contradiction is found in their claim that Luke is a knight or Luke is a knave.
Luke cannot be a knight, because this would contradict the claim of their own that If Matthew is a knight then Matthew is a knave.
Luke cannot be a knave, because this would contradict the claim of Liam that Matthew is a knave if and only if Luke is a knave.
We have exhausted all possibilities for Luke, so let us go back and reconsider Matthew.
Matthew cannot be a knave, because this would contradict the false claim of their own that Luke is a knight or Luke is a knave.
We have exhausted all possibilities for Matthew, so let us go back and reconsider Liam.
Assume Liam is a knave. No contradiction is found in their false claim that Matthew is a knave if and only if Luke is a knave.
Assume Matthew is a knight. No contradiction is found in their claim that Luke is a knight or Luke is a knave.
Luke cannot be a knight, because this would contradict the false claim of Liam that Matthew is a knave if and only if Luke is a knave.
Assume Luke is a knave. No contradiction is found in their false claim that If Matthew is a knight then Matthew is a knave.
Therefore, (1) Liam is a knave
(2) Luke is a knave
(3) Matthew is a knight </think>
<answer> (1) Liam is a knave
(2) Luke is a knave
(3) Matthew is a knight </answer> | math | {
"ground_truth": {
"names": [
"Liam",
"Luke",
"Matthew"
],
"solution": [
false,
false,
true
],
"solution_text_format": "(1) Liam is a knave\n(2) Luke is a knave\n(3) Matthew is a knight",
"statements": "(('<=>', ('lying', 2), ('lying', 1)), ('->', ('telling-truth', 2), ('lying', 2)), ('or', ('telling-truth', 1), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 30,
"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: Noah, Amelia, and Isabella. Noah remarked, \"Isabella is a knight if and only if Isabella is a knave\". Amelia remarked, \"Noah is not a knave\". Isabella stated, \"Amelia is a knave or 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"
}
]
| [
"Noah cannot be a knight, because this would contradict the claim of their own that Isabella is a knight if and only if Isabella is a knave.\n",
"Assume Noah is a knave. ",
"No contradiction is found in their false claim that Isabella is a knight if and only if Isabella is a knave.\n",
"Assume Isabella is a knight. ",
"No contradiction is found in their claim that Amelia is a knave or Isabella is a knight.\n",
"Amelia cannot be a knight, because this would contradict the claim of their own that Noah is not a knave.\n",
"Assume Amelia is a knave. ",
"No contradiction is found in their false claim that Noah is not a knave.\n",
"Therefore, (1) Noah is a knave\n",
"(2) Amelia 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: Noah, Amelia, and Isabella. Noah remarked, "Isabella is a knight if and only if Isabella is a knave". Amelia remarked, "Noah is not a knave". Isabella stated, "Amelia is a knave or 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> | Noah cannot be a knight, because this would contradict the claim of their own that Isabella is a knight if and only if Isabella is a knave.
Assume Noah is a knave. No contradiction is found in their false claim that Isabella is a knight if and only if Isabella is a knave.
Assume Isabella is a knight. No contradiction is found in their claim that Amelia is a knave or Isabella is a knight.
Amelia cannot be a knight, because this would contradict the claim of their own that Noah is not a knave.
Assume Amelia is a knave. No contradiction is found in their false claim that Noah is not a knave.
Therefore, (1) Noah is a knave
(2) Amelia is a knave
(3) Isabella is a knight </think>
<answer> (1) Noah is a knave
(2) Amelia is a knave
(3) Isabella is a knight </answer> | math | {
"ground_truth": {
"names": [
"Noah",
"Amelia",
"Isabella"
],
"solution": [
false,
false,
true
],
"solution_text_format": "(1) Noah is a knave\n(2) Amelia is a knave\n(3) Isabella is a knight",
"statements": "(('<=>', ('telling-truth', 2), ('lying', 2)), ('not', ('lying', 0)), ('or', ('lying', 1), ('telling-truth', 2)))"
},
"style": "rule"
} | {
"index": 31,
"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, Mia, and Matthew. Riley remarked, \"Mia is a knave or Matthew is a knave\". Mia asserted: \"Matthew is a knight\". \"Matthew is a knight and Riley is a knight,\" Matthew 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 Riley is a knight. ",
"No contradiction is found in their claim that Mia is a knave or Matthew is a knave.\n",
"Assume Mia is a knight. ",
"No contradiction is found in their claim that Matthew is a knight.\n",
"Matthew cannot be a knight, because this would contradict the claim of Riley that Mia is a knave or Matthew is a knave.\n",
"Matthew cannot be a knave, because this would contradict the claim of Mia that Matthew is a knight.\n",
"We have exhausted all possibilities for Matthew, so let us go back and reconsider Mia.\n",
"Assume Mia is a knave. ",
"No contradiction is found in their false claim that Matthew is a knight.\n",
"Matthew cannot be a knight, because this would contradict the false claim of Mia that Matthew is a knight.\n",
"Assume Matthew is a knave. ",
"No contradiction is found in their false claim that Matthew is a knight and Riley is a knight.\n",
"Therefore, (1) Riley is a knight\n",
"(2) Mia 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: Riley, Mia, and Matthew. Riley remarked, "Mia is a knave or Matthew is a knave". Mia asserted: "Matthew is a knight". "Matthew is a knight and Riley is a knight," Matthew 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 Riley is a knight. No contradiction is found in their claim that Mia is a knave or Matthew is a knave.
Assume Mia is a knight. No contradiction is found in their claim that Matthew is a knight.
Matthew cannot be a knight, because this would contradict the claim of Riley that Mia is a knave or Matthew is a knave.
Matthew cannot be a knave, because this would contradict the claim of Mia that Matthew is a knight.
We have exhausted all possibilities for Matthew, so let us go back and reconsider Mia.
Assume Mia is a knave. No contradiction is found in their false claim that Matthew is a knight.
Matthew cannot be a knight, because this would contradict the false claim of Mia that Matthew is a knight.
Assume Matthew is a knave. No contradiction is found in their false claim that Matthew is a knight and Riley is a knight.
Therefore, (1) Riley is a knight
(2) Mia is a knave
(3) Matthew is a knave </think>
<answer> (1) Riley is a knight
(2) Mia is a knave
(3) Matthew is a knave </answer> | math | {
"ground_truth": {
"names": [
"Riley",
"Mia",
"Matthew"
],
"solution": [
true,
false,
false
],
"solution_text_format": "(1) Riley is a knight\n(2) Mia is a knave\n(3) Matthew is a knave",
"statements": "(('or', ('lying', 1), ('lying', 2)), ('telling-truth', 2), ('and', ('telling-truth', 2), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 32,
"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, Charlotte, and Jack. Aurora noted, \"Jack is a knight or Charlotte is a knave\". According to Charlotte, \"Aurora is not a knight\". Jack commented, \"Aurora 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 Aurora is a knight. ",
"No contradiction is found in their claim that Jack is a knight or Charlotte is a knave.\n",
"Jack cannot be a knight, because this would contradict the claim of their own that Aurora is not a knight.\n",
"Assume Jack is a knave. ",
"No contradiction is found in their false claim that Aurora is not a knight.\n",
"Charlotte cannot be a knight, because this would contradict the claim of Aurora that Jack is a knight or Charlotte is a knave.\n",
"Assume Charlotte is a knave. ",
"No contradiction is found in their false claim that Aurora is not a knight.\n",
"Therefore, (1) Aurora is a knight\n",
"(2) Charlotte 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: Aurora, Charlotte, and Jack. Aurora noted, "Jack is a knight or Charlotte is a knave". According to Charlotte, "Aurora is not a knight". Jack commented, "Aurora 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 Aurora is a knight. No contradiction is found in their claim that Jack is a knight or Charlotte is a knave.
Jack cannot be a knight, because this would contradict the claim of their own that Aurora is not a knight.
Assume Jack is a knave. No contradiction is found in their false claim that Aurora is not a knight.
Charlotte cannot be a knight, because this would contradict the claim of Aurora that Jack is a knight or Charlotte is a knave.
Assume Charlotte is a knave. No contradiction is found in their false claim that Aurora is not a knight.
Therefore, (1) Aurora is a knight
(2) Charlotte is a knave
(3) Jack is a knave </think>
<answer> (1) Aurora is a knight
(2) Charlotte is a knave
(3) Jack is a knave </answer> | math | {
"ground_truth": {
"names": [
"Aurora",
"Charlotte",
"Jack"
],
"solution": [
true,
false,
false
],
"solution_text_format": "(1) Aurora is a knight\n(2) Charlotte is a knave\n(3) Jack is a knave",
"statements": "(('or', ('telling-truth', 2), ('lying', 1)), ('not', ('telling-truth', 0)), ('not', ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 33,
"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, Jacob, and Aiden. Scarlett remarked, \"Aiden is a knight or Scarlett is a knight\". \"Aiden is a knight or Scarlett is a knight\" - Jacob. \"Scarlett is a knave or Jacob is a knight\" - Aiden. 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 Aiden is a knight or Scarlett is a knight.\n",
"Assume Aiden is a knight. ",
"No contradiction is found in their claim that Scarlett is a knave or Jacob is a knight.\n",
"Assume Jacob is a knight. ",
"No contradiction is found in their claim that Aiden is a knight or Scarlett is a knight.\n",
"Therefore, (1) Scarlett is a knight\n",
"(2) Jacob 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: Scarlett, Jacob, and Aiden. Scarlett remarked, "Aiden is a knight or Scarlett is a knight". "Aiden is a knight or Scarlett is a knight" - Jacob. "Scarlett is a knave or Jacob is a knight" - Aiden. 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 Aiden is a knight or Scarlett is a knight.
Assume Aiden is a knight. No contradiction is found in their claim that Scarlett is a knave or Jacob is a knight.
Assume Jacob is a knight. No contradiction is found in their claim that Aiden is a knight or Scarlett is a knight.
Therefore, (1) Scarlett is a knight
(2) Jacob is a knight
(3) Aiden is a knight </think>
<answer> (1) Scarlett is a knight
(2) Jacob is a knight
(3) Aiden is a knight </answer> | math | {
"ground_truth": {
"names": [
"Scarlett",
"Jacob",
"Aiden"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Scarlett is a knight\n(2) Jacob is a knight\n(3) Aiden is a knight",
"statements": "(('or', ('telling-truth', 2), ('telling-truth', 0)), ('or', ('telling-truth', 2), ('telling-truth', 0)), ('or', ('lying', 0), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 34,
"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, Sofia, and Liam. In a statement by Daniel: \"If Liam is a knight then Sofia is a knight\". \"Liam is a knave or Liam is a knight,\" Sofia mentioned. Liam asserted: \"Sofia 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 Daniel is a knight. ",
"No contradiction is found in their claim that If Liam is a knight then Sofia is a knight.\n",
"Assume Liam 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 Liam that Sofia is a knave.\n",
"Sofia cannot be a knave, because this would contradict the claim of Daniel that If Liam is a knight then Sofia is a knight.\n",
"We have exhausted all possibilities for Sofia, so let us go back and reconsider Liam.\n",
"Assume Liam is a knave. ",
"No contradiction is found in their false claim that Sofia is a knave.\n",
"Assume Sofia is a knight. ",
"No contradiction is found in their claim that Liam is a knave or Liam is a knight.\n",
"Therefore, (1) Daniel is a knight\n",
"(2) Sofia is a knight\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: Daniel, Sofia, and Liam. In a statement by Daniel: "If Liam is a knight then Sofia is a knight". "Liam is a knave or Liam is a knight," Sofia mentioned. Liam asserted: "Sofia 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 Daniel is a knight. No contradiction is found in their claim that If Liam is a knight then Sofia is a knight.
Assume Liam 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 Liam that Sofia is a knave.
Sofia cannot be a knave, because this would contradict the claim of Daniel that If Liam is a knight then Sofia is a knight.
We have exhausted all possibilities for Sofia, so let us go back and reconsider Liam.
Assume Liam is a knave. No contradiction is found in their false claim that Sofia is a knave.
Assume Sofia is a knight. No contradiction is found in their claim that Liam is a knave or Liam is a knight.
Therefore, (1) Daniel is a knight
(2) Sofia is a knight
(3) Liam is a knave </think>
<answer> (1) Daniel is a knight
(2) Sofia is a knight
(3) Liam is a knave </answer> | math | {
"ground_truth": {
"names": [
"Daniel",
"Sofia",
"Liam"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Daniel is a knight\n(2) Sofia is a knight\n(3) Liam is a knave",
"statements": "(('->', ('telling-truth', 2), ('telling-truth', 1)), ('or', ('lying', 2), ('telling-truth', 2)), ('lying', 1))"
},
"style": "rule"
} | {
"index": 35,
"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, Victoria, and Isabella. Avery remarked, \"Isabella is not a knave\". \"Avery is not a knave,\" Victoria declared. Isabella stated, \"Victoria 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 Isabella is not a knave.\n",
"Assume Isabella is a knight. ",
"No contradiction is found in their claim that Victoria is a knight or Avery is a knave.\n",
"Assume Victoria is a knight. ",
"No contradiction is found in their claim that Avery is not a knave.\n",
"Therefore, (1) Avery is a knight\n",
"(2) Victoria 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: Avery, Victoria, and Isabella. Avery remarked, "Isabella is not a knave". "Avery is not a knave," Victoria declared. Isabella stated, "Victoria 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 Isabella is not a knave.
Assume Isabella is a knight. No contradiction is found in their claim that Victoria is a knight or Avery is a knave.
Assume Victoria is a knight. No contradiction is found in their claim that Avery is not a knave.
Therefore, (1) Avery is a knight
(2) Victoria is a knight
(3) Isabella is a knight </think>
<answer> (1) Avery is a knight
(2) Victoria is a knight
(3) Isabella is a knight </answer> | math | {
"ground_truth": {
"names": [
"Avery",
"Victoria",
"Isabella"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Avery is a knight\n(2) Victoria is a knight\n(3) Isabella is a knight",
"statements": "(('not', ('lying', 2)), ('not', ('lying', 0)), ('or', ('telling-truth', 1), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 36,
"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, Olivia, and Joseph. Benjamin told you that If Olivia is a knight then Olivia is a knave. \"Joseph is a knight or Benjamin is a knight,\" Olivia declared. Joseph asserted: \"Joseph is a knight or 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 If Olivia is a knight then Olivia is a knave.\n",
"Olivia cannot be a knight, because this would contradict the claim of Benjamin that If Olivia is a knight then Olivia is a knave.\n",
"Olivia cannot be a knave, because this would contradict the false claim of their own that Joseph is a knight or Benjamin is a knight.\n",
"We have exhausted all possibilities for Olivia, so let us go back and reconsider Benjamin.\n",
"Assume Benjamin is a knave. ",
"No contradiction is found in their false claim that If Olivia is a knight then Olivia is a knave.\n",
"Assume Olivia is a knight. ",
"No contradiction is found in their claim that Joseph is a knight or Benjamin is a knight.\n",
"Assume Joseph is a knight. ",
"No contradiction is found in their claim that Joseph is a knight or Benjamin is a knight.\n",
"Therefore, (1) Benjamin is a knave\n",
"(2) Olivia 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: Benjamin, Olivia, and Joseph. Benjamin told you that If Olivia is a knight then Olivia is a knave. "Joseph is a knight or Benjamin is a knight," Olivia declared. Joseph asserted: "Joseph is a knight or 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 If Olivia is a knight then Olivia is a knave.
Olivia cannot be a knight, because this would contradict the claim of Benjamin that If Olivia is a knight then Olivia is a knave.
Olivia cannot be a knave, because this would contradict the false claim of their own that Joseph is a knight or Benjamin is a knight.
We have exhausted all possibilities for Olivia, so let us go back and reconsider Benjamin.
Assume Benjamin is a knave. No contradiction is found in their false claim that If Olivia is a knight then Olivia is a knave.
Assume Olivia is a knight. No contradiction is found in their claim that Joseph is a knight or Benjamin is a knight.
Assume Joseph is a knight. No contradiction is found in their claim that Joseph is a knight or Benjamin is a knight.
Therefore, (1) Benjamin is a knave
(2) Olivia is a knight
(3) Joseph is a knight </think>
<answer> (1) Benjamin is a knave
(2) Olivia is a knight
(3) Joseph is a knight </answer> | math | {
"ground_truth": {
"names": [
"Benjamin",
"Olivia",
"Joseph"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Benjamin is a knave\n(2) Olivia is a knight\n(3) Joseph is a knight",
"statements": "(('->', ('telling-truth', 1), ('lying', 1)), ('or', ('telling-truth', 2), ('telling-truth', 0)), ('or', ('telling-truth', 2), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 37,
"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, Mason, and Harper. \"If David is a knight then Mason is a knight,\" David mentioned. Mason stated, \"David is a knight\". Harper was heard saying, \"David is a knight or 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 David is a knight. ",
"No contradiction is found in their claim that If David is a knight then Mason is a knight.\n",
"Assume Mason is a knight. ",
"No contradiction is found in their claim that David is a knight.\n",
"Assume Harper is a knight. ",
"No contradiction is found in their claim that David is a knight or Harper is a knight.\n",
"Therefore, (1) David is a knight\n",
"(2) Mason is a knight\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: David, Mason, and Harper. "If David is a knight then Mason is a knight," David mentioned. Mason stated, "David is a knight". Harper was heard saying, "David is a knight or 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 David is a knight. No contradiction is found in their claim that If David is a knight then Mason is a knight.
Assume Mason is a knight. No contradiction is found in their claim that David is a knight.
Assume Harper is a knight. No contradiction is found in their claim that David is a knight or Harper is a knight.
Therefore, (1) David is a knight
(2) Mason is a knight
(3) Harper is a knight </think>
<answer> (1) David is a knight
(2) Mason is a knight
(3) Harper is a knight </answer> | math | {
"ground_truth": {
"names": [
"David",
"Mason",
"Harper"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) David is a knight\n(2) Mason is a knight\n(3) Harper is a knight",
"statements": "(('->', ('telling-truth', 0), ('telling-truth', 1)), ('telling-truth', 0), ('or', ('telling-truth', 0), ('telling-truth', 2)))"
},
"style": "rule"
} | {
"index": 38,
"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, Sophia, and Evelyn. \"Evelyn is a knight or Evelyn is a knave\" - James. Sophia noted, \"Sophia is a knight and James is a knave\". In a statement by Evelyn: \"Sophia is a knight and James 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 James is a knight. ",
"No contradiction is found in their claim that Evelyn is a knight or Evelyn is a knave.\n",
"Evelyn cannot be a knight, because this would contradict the claim of their own that Sophia is a knight and James is a knave.\n",
"Assume Evelyn is a knave. ",
"No contradiction is found in their false claim that Sophia is a knight and James is a knave.\n",
"Sophia cannot be a knight, because this would contradict the claim of their own that Sophia is a knight and James is a knave.\n",
"Assume Sophia is a knave. ",
"No contradiction is found in their false claim that Sophia is a knight and James is a knave.\n",
"Therefore, (1) James is a knight\n",
"(2) Sophia is a knave\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: James, Sophia, and Evelyn. "Evelyn is a knight or Evelyn is a knave" - James. Sophia noted, "Sophia is a knight and James is a knave". In a statement by Evelyn: "Sophia is a knight and James 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 James is a knight. No contradiction is found in their claim that Evelyn is a knight or Evelyn is a knave.
Evelyn cannot be a knight, because this would contradict the claim of their own that Sophia is a knight and James is a knave.
Assume Evelyn is a knave. No contradiction is found in their false claim that Sophia is a knight and James is a knave.
Sophia cannot be a knight, because this would contradict the claim of their own that Sophia is a knight and James is a knave.
Assume Sophia is a knave. No contradiction is found in their false claim that Sophia is a knight and James is a knave.
Therefore, (1) James is a knight
(2) Sophia is a knave
(3) Evelyn is a knave </think>
<answer> (1) James is a knight
(2) Sophia is a knave
(3) Evelyn is a knave </answer> | math | {
"ground_truth": {
"names": [
"James",
"Sophia",
"Evelyn"
],
"solution": [
true,
false,
false
],
"solution_text_format": "(1) James is a knight\n(2) Sophia is a knave\n(3) Evelyn is a knave",
"statements": "(('or', ('telling-truth', 2), ('lying', 2)), ('and', ('telling-truth', 1), ('lying', 0)), ('and', ('telling-truth', 1), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 39,
"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, William, and Aurora. Owen stated, \"Aurora is a knight or William is a knight\". William stated, \"If Owen is a knight then Owen is a knave\". Aurora remarked, \"If William is a knight then 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 Owen is a knight. ",
"No contradiction is found in their claim that Aurora is a knight or William is a knight.\n",
"Assume Aurora is a knight. ",
"No contradiction is found in their claim that If William is a knight then Owen is a knight.\n",
"William cannot be a knight, because this would contradict the claim of their own that If Owen is a knight then Owen is a knave.\n",
"Assume William is a knave. ",
"No contradiction is found in their false claim that If Owen is a knight then Owen is a knave.\n",
"Therefore, (1) Owen is a knight\n",
"(2) William is a knave\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: Owen, William, and Aurora. Owen stated, "Aurora is a knight or William is a knight". William stated, "If Owen is a knight then Owen is a knave". Aurora remarked, "If William is a knight then 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 Owen is a knight. No contradiction is found in their claim that Aurora is a knight or William is a knight.
Assume Aurora is a knight. No contradiction is found in their claim that If William is a knight then Owen is a knight.
William cannot be a knight, because this would contradict the claim of their own that If Owen is a knight then Owen is a knave.
Assume William is a knave. No contradiction is found in their false claim that If Owen is a knight then Owen is a knave.
Therefore, (1) Owen is a knight
(2) William is a knave
(3) Aurora is a knight </think>
<answer> (1) Owen is a knight
(2) William is a knave
(3) Aurora is a knight </answer> | math | {
"ground_truth": {
"names": [
"Owen",
"William",
"Aurora"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Owen is a knight\n(2) William is a knave\n(3) Aurora is a knight",
"statements": "(('or', ('telling-truth', 2), ('telling-truth', 1)), ('->', ('telling-truth', 0), ('lying', 0)), ('->', ('telling-truth', 1), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 40,
"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: Noah, Jacob, and Sophia. In a statement by Noah: \"If Sophia is a knight then Jacob is a knight\". Jacob expressed that If Sophia is a knave then Noah is a knight. Sophia said that Noah is a knight or Sophia 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 Noah is a knight. ",
"No contradiction is found in their claim that If Sophia is a knight then Jacob is a knight.\n",
"Assume Sophia is a knight. ",
"No contradiction is found in their claim that Noah is a knight or Sophia is a knight.\n",
"Assume Jacob is a knight. ",
"No contradiction is found in their claim that If Sophia is a knave then Noah is a knight.\n",
"Therefore, (1) Noah is a knight\n",
"(2) Jacob is a knight\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: Noah, Jacob, and Sophia. In a statement by Noah: "If Sophia is a knight then Jacob is a knight". Jacob expressed that If Sophia is a knave then Noah is a knight. Sophia said that Noah is a knight or Sophia 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 Noah is a knight. No contradiction is found in their claim that If Sophia is a knight then Jacob is a knight.
Assume Sophia is a knight. No contradiction is found in their claim that Noah is a knight or Sophia is a knight.
Assume Jacob is a knight. No contradiction is found in their claim that If Sophia is a knave then Noah is a knight.
Therefore, (1) Noah is a knight
(2) Jacob is a knight
(3) Sophia is a knight </think>
<answer> (1) Noah is a knight
(2) Jacob is a knight
(3) Sophia is a knight </answer> | math | {
"ground_truth": {
"names": [
"Noah",
"Jacob",
"Sophia"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Noah is a knight\n(2) Jacob is a knight\n(3) Sophia is a knight",
"statements": "(('->', ('telling-truth', 2), ('telling-truth', 1)), ('->', ('lying', 2), ('telling-truth', 0)), ('or', ('telling-truth', 0), ('telling-truth', 2)))"
},
"style": "rule"
} | {
"index": 41,
"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, Henry, and Riley. Charlotte remarked, \"Henry is a knight\". Henry asserted: \"Charlotte is a knave if and only if Henry is a knight\". Riley commented, \"If Henry is a knave then Charlotte 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 Charlotte is a knight. ",
"No contradiction is found in their claim that Henry is a knight.\n",
"Henry cannot be a knight, because this would contradict the claim of their own that Charlotte is a knave if and only if Henry is a knight.\n",
"Henry cannot be a knave, because this would contradict the claim of Charlotte that Henry is a knight.\n",
"We have exhausted all possibilities for Henry, so let us go back and reconsider Charlotte.\n",
"Assume Charlotte is a knave. ",
"No contradiction is found in their false claim that Henry is a knight.\n",
"Henry cannot be a knight, because this would contradict the false claim of Charlotte that Henry is a knight.\n",
"Assume Henry is a knave. ",
"No contradiction is found in their false claim that Charlotte is a knave if and only if Henry is a knight.\n",
"Riley cannot be a knight, because this would contradict the claim of their own that If Henry is a knave then Charlotte is a knight.\n",
"Assume Riley is a knave. ",
"No contradiction is found in their false claim that If Henry is a knave then Charlotte is a knight.\n",
"Therefore, (1) Charlotte is a knave\n",
"(2) Henry is a knave\n",
"(3) Riley 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, Henry, and Riley. Charlotte remarked, "Henry is a knight". Henry asserted: "Charlotte is a knave if and only if Henry is a knight". Riley commented, "If Henry is a knave then Charlotte 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 Charlotte is a knight. No contradiction is found in their claim that Henry is a knight.
Henry cannot be a knight, because this would contradict the claim of their own that Charlotte is a knave if and only if Henry is a knight.
Henry cannot be a knave, because this would contradict the claim of Charlotte that Henry is a knight.
We have exhausted all possibilities for Henry, so let us go back and reconsider Charlotte.
Assume Charlotte is a knave. No contradiction is found in their false claim that Henry is a knight.
Henry cannot be a knight, because this would contradict the false claim of Charlotte that Henry is a knight.
Assume Henry is a knave. No contradiction is found in their false claim that Charlotte is a knave if and only if Henry is a knight.
Riley cannot be a knight, because this would contradict the claim of their own that If Henry is a knave then Charlotte is a knight.
Assume Riley is a knave. No contradiction is found in their false claim that If Henry is a knave then Charlotte is a knight.
Therefore, (1) Charlotte is a knave
(2) Henry is a knave
(3) Riley is a knave </think>
<answer> (1) Charlotte is a knave
(2) Henry is a knave
(3) Riley is a knave </answer> | math | {
"ground_truth": {
"names": [
"Charlotte",
"Henry",
"Riley"
],
"solution": [
false,
false,
false
],
"solution_text_format": "(1) Charlotte is a knave\n(2) Henry is a knave\n(3) Riley is a knave",
"statements": "(('telling-truth', 1), ('<=>', ('lying', 0), ('telling-truth', 1)), ('->', ('lying', 1), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 42,
"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, Mason, and Daniel. Jack said that Daniel is a knave if and only if Daniel is a knight. Mason remarked, \"Daniel is a knight if and only if Mason is a knight\". Daniel stated, \"Jack is a knight if and only if 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"
}
]
| [
"Jack cannot be a knight, because this would contradict the claim of their own that Daniel is a knave if and only if Daniel is a knight.\n",
"Assume Jack is a knave. ",
"No contradiction is found in their false claim that Daniel is a knave if and only if Daniel is a knight.\n",
"Assume Daniel is a knight. ",
"No contradiction is found in their claim that Jack is a knight if and only if Mason is a knave.\n",
"Assume Mason is a knight. ",
"No contradiction is found in their claim that Daniel is a knight if and only if Mason is a knight.\n",
"Therefore, (1) Jack is a knave\n",
"(2) Mason is a knight\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: Jack, Mason, and Daniel. Jack said that Daniel is a knave if and only if Daniel is a knight. Mason remarked, "Daniel is a knight if and only if Mason is a knight". Daniel stated, "Jack is a knight if and only if 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> | Jack cannot be a knight, because this would contradict the claim of their own that Daniel is a knave if and only if Daniel is a knight.
Assume Jack is a knave. No contradiction is found in their false claim that Daniel is a knave if and only if Daniel is a knight.
Assume Daniel is a knight. No contradiction is found in their claim that Jack is a knight if and only if Mason is a knave.
Assume Mason is a knight. No contradiction is found in their claim that Daniel is a knight if and only if Mason is a knight.
Therefore, (1) Jack is a knave
(2) Mason is a knight
(3) Daniel is a knight </think>
<answer> (1) Jack is a knave
(2) Mason is a knight
(3) Daniel is a knight </answer> | math | {
"ground_truth": {
"names": [
"Jack",
"Mason",
"Daniel"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Jack is a knave\n(2) Mason is a knight\n(3) Daniel is a knight",
"statements": "(('<=>', ('lying', 2), ('telling-truth', 2)), ('<=>', ('telling-truth', 2), ('telling-truth', 1)), ('<=>', ('telling-truth', 0), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 43,
"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, Evelyn, and Jack. Lucas told you that Evelyn is a knight if and only if Jack is a knight. In Evelyn's words: \"Evelyn is a knight or Jack is a knight\". \"If Evelyn is a knight then Evelyn is a knave,\" Jack 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 Evelyn is a knight if and only if Jack is a knight.\n",
"Assume Evelyn is a knight. ",
"No contradiction is found in their claim that Evelyn is a knight or Jack is a knight.\n",
"Jack cannot be a knight, because this would contradict the claim of their own that If Evelyn is a knight then Evelyn is a knave.\n",
"Jack cannot be a knave, because this would contradict the claim of Lucas that Evelyn is a knight if and only if Jack is a knight.\n",
"We have exhausted all possibilities for Jack, so let us go back and reconsider Evelyn.\n",
"Assume Evelyn is a knave. ",
"No contradiction is found in their false claim that Evelyn is a knight or Jack is a knight.\n",
"Jack cannot be a knight, because this would contradict the claim of Lucas that Evelyn is a knight if and only if Jack is a knight.\n",
"Jack cannot be a knave, because this would contradict the false claim of their own that If Evelyn is a knight then Evelyn is a knave.\n",
"We have exhausted all possibilities for Jack and Evelyn, so let us go back and reconsider Lucas.\n",
"Assume Lucas is a knave. ",
"No contradiction is found in their false claim that Evelyn is a knight if and only if Jack is a knight.\n",
"Assume Evelyn is a knight. ",
"No contradiction is found in their claim that Evelyn is a knight or Jack is a knight.\n",
"Jack cannot be a knight, because this would contradict the false claim of Lucas that Evelyn is a knight if and only if Jack is a knight.\n",
"Assume Jack is a knave. ",
"No contradiction is found in their false claim that If Evelyn is a knight then Evelyn is a knave.\n",
"Therefore, (1) Lucas is a knave\n",
"(2) Evelyn 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: Lucas, Evelyn, and Jack. Lucas told you that Evelyn is a knight if and only if Jack is a knight. In Evelyn's words: "Evelyn is a knight or Jack is a knight". "If Evelyn is a knight then Evelyn is a knave," Jack 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 Evelyn is a knight if and only if Jack is a knight.
Assume Evelyn is a knight. No contradiction is found in their claim that Evelyn is a knight or Jack is a knight.
Jack cannot be a knight, because this would contradict the claim of their own that If Evelyn is a knight then Evelyn is a knave.
Jack cannot be a knave, because this would contradict the claim of Lucas that Evelyn is a knight if and only if Jack is a knight.
We have exhausted all possibilities for Jack, so let us go back and reconsider Evelyn.
Assume Evelyn is a knave. No contradiction is found in their false claim that Evelyn is a knight or Jack is a knight.
Jack cannot be a knight, because this would contradict the claim of Lucas that Evelyn is a knight if and only if Jack is a knight.
Jack cannot be a knave, because this would contradict the false claim of their own that If Evelyn is a knight then Evelyn is a knave.
We have exhausted all possibilities for Jack and Evelyn, so let us go back and reconsider Lucas.
Assume Lucas is a knave. No contradiction is found in their false claim that Evelyn is a knight if and only if Jack is a knight.
Assume Evelyn is a knight. No contradiction is found in their claim that Evelyn is a knight or Jack is a knight.
Jack cannot be a knight, because this would contradict the false claim of Lucas that Evelyn is a knight if and only if Jack is a knight.
Assume Jack is a knave. No contradiction is found in their false claim that If Evelyn is a knight then Evelyn is a knave.
Therefore, (1) Lucas is a knave
(2) Evelyn is a knight
(3) Jack is a knave </think>
<answer> (1) Lucas is a knave
(2) Evelyn is a knight
(3) Jack is a knave </answer> | math | {
"ground_truth": {
"names": [
"Lucas",
"Evelyn",
"Jack"
],
"solution": [
false,
true,
false
],
"solution_text_format": "(1) Lucas is a knave\n(2) Evelyn is a knight\n(3) Jack is a knave",
"statements": "(('<=>', ('telling-truth', 1), ('telling-truth', 2)), ('or', ('telling-truth', 1), ('telling-truth', 2)), ('->', ('telling-truth', 1), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 44,
"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, Michael, and Alexander. Logan noted, \"Alexander is a knave if and only if Logan is a knight\". Michael stated, \"Logan is a knave\". \"Logan is a knave and Michael 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 Logan is a knight. ",
"No contradiction is found in their claim that Alexander is a knave if and only if Logan is a knight.\n",
"Alexander cannot be a knight, because this would contradict the claim of Logan that Alexander is a knave if and only if Logan is a knight.\n",
"Assume Alexander is a knave. ",
"No contradiction is found in their false claim that Logan is a knave and Michael is a knight.\n",
"Michael cannot be a knight, because this would contradict the claim of their own that Logan is a knave.\n",
"Assume Michael is a knave. ",
"No contradiction is found in their false claim that Logan is a knave.\n",
"Therefore, (1) Logan is a knight\n",
"(2) Michael 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: Logan, Michael, and Alexander. Logan noted, "Alexander is a knave if and only if Logan is a knight". Michael stated, "Logan is a knave". "Logan is a knave and Michael 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 Logan is a knight. No contradiction is found in their claim that Alexander is a knave if and only if Logan is a knight.
Alexander cannot be a knight, because this would contradict the claim of Logan that Alexander is a knave if and only if Logan is a knight.
Assume Alexander is a knave. No contradiction is found in their false claim that Logan is a knave and Michael is a knight.
Michael cannot be a knight, because this would contradict the claim of their own that Logan is a knave.
Assume Michael is a knave. No contradiction is found in their false claim that Logan is a knave.
Therefore, (1) Logan is a knight
(2) Michael is a knave
(3) Alexander is a knave </think>
<answer> (1) Logan is a knight
(2) Michael is a knave
(3) Alexander is a knave </answer> | math | {
"ground_truth": {
"names": [
"Logan",
"Michael",
"Alexander"
],
"solution": [
true,
false,
false
],
"solution_text_format": "(1) Logan is a knight\n(2) Michael is a knave\n(3) Alexander is a knave",
"statements": "(('<=>', ('lying', 2), ('telling-truth', 0)), ('lying', 0), ('and', ('lying', 0), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 45,
"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, Zoey, and Elizabeth. Luke remarked, \"Elizabeth is not a knave\". Zoey asserted: \"If Elizabeth is a knight then Luke is a knave\". According to Elizabeth, \"Elizabeth is a knight if and only if 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 Luke is a knight. ",
"No contradiction is found in their claim that Elizabeth is not a knave.\n",
"Assume Elizabeth is a knight. ",
"No contradiction is found in their claim that Elizabeth is a knight if and only if Zoey is a knave.\n",
"Zoey cannot be a knight, because this would contradict the claim of their own that If Elizabeth is a knight then Luke is a knave.\n",
"Assume Zoey is a knave. ",
"No contradiction is found in their false claim that If Elizabeth is a knight then Luke is a knave.\n",
"Therefore, (1) Luke is a knight\n",
"(2) Zoey 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, Zoey, and Elizabeth. Luke remarked, "Elizabeth is not a knave". Zoey asserted: "If Elizabeth is a knight then Luke is a knave". According to Elizabeth, "Elizabeth is a knight if and only if 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 Luke is a knight. No contradiction is found in their claim that Elizabeth is not a knave.
Assume Elizabeth is a knight. No contradiction is found in their claim that Elizabeth is a knight if and only if Zoey is a knave.
Zoey cannot be a knight, because this would contradict the claim of their own that If Elizabeth is a knight then Luke is a knave.
Assume Zoey is a knave. No contradiction is found in their false claim that If Elizabeth is a knight then Luke is a knave.
Therefore, (1) Luke is a knight
(2) Zoey is a knave
(3) Elizabeth is a knight </think>
<answer> (1) Luke is a knight
(2) Zoey is a knave
(3) Elizabeth is a knight </answer> | math | {
"ground_truth": {
"names": [
"Luke",
"Zoey",
"Elizabeth"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Luke is a knight\n(2) Zoey is a knave\n(3) Elizabeth is a knight",
"statements": "(('not', ('lying', 2)), ('->', ('telling-truth', 2), ('lying', 0)), ('<=>', ('telling-truth', 2), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 46,
"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, Sophia, and Samuel. Benjamin commented, \"Samuel is a knight if and only if Samuel is a knave\". Sophia said, \"Samuel is a knave if and only if Benjamin is a knave.\" Samuel remarked, \"Sophia is a knight and 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"
}
]
| [
"Benjamin cannot be a knight, because this would contradict the claim of their own that Samuel is a knight if and only if Samuel is a knave.\n",
"Assume Benjamin is a knave. ",
"No contradiction is found in their false claim that Samuel is a knight if and only if Samuel is a knave.\n",
"Samuel cannot be a knight, because this would contradict the claim of their own that Sophia is a knight and Benjamin is a knight.\n",
"Assume Samuel is a knave. ",
"No contradiction is found in their false claim that Sophia is a knight and Benjamin is a knight.\n",
"Assume Sophia is a knight. ",
"No contradiction is found in their claim that Samuel is a knave if and only if Benjamin is a knave.\n",
"Therefore, (1) Benjamin is a knave\n",
"(2) Sophia 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: Benjamin, Sophia, and Samuel. Benjamin commented, "Samuel is a knight if and only if Samuel is a knave". Sophia said, "Samuel is a knave if and only if Benjamin is a knave." Samuel remarked, "Sophia is a knight and 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> | Benjamin cannot be a knight, because this would contradict the claim of their own that Samuel is a knight if and only if Samuel is a knave.
Assume Benjamin is a knave. No contradiction is found in their false claim that Samuel is a knight if and only if Samuel is a knave.
Samuel cannot be a knight, because this would contradict the claim of their own that Sophia is a knight and Benjamin is a knight.
Assume Samuel is a knave. No contradiction is found in their false claim that Sophia is a knight and Benjamin is a knight.
Assume Sophia is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Benjamin is a knave.
Therefore, (1) Benjamin is a knave
(2) Sophia is a knight
(3) Samuel is a knave </think>
<answer> (1) Benjamin is a knave
(2) Sophia is a knight
(3) Samuel is a knave </answer> | math | {
"ground_truth": {
"names": [
"Benjamin",
"Sophia",
"Samuel"
],
"solution": [
false,
true,
false
],
"solution_text_format": "(1) Benjamin is a knave\n(2) Sophia is a knight\n(3) Samuel is a knave",
"statements": "(('<=>', ('telling-truth', 2), ('lying', 2)), ('<=>', ('lying', 2), ('lying', 0)), ('and', ('telling-truth', 1), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 47,
"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, Oliver, and Zoey. Mia noted, \"Zoey is a knave if and only if Mia is a knight\". \"Mia is a knave,\" Oliver claimed. Zoey said that Oliver 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"
}
]
| [
"Assume Mia is a knight. ",
"No contradiction is found in their claim that Zoey is a knave if and only if Mia is a knight.\n",
"Zoey cannot be a knight, because this would contradict the claim of Mia that Zoey is a knave if and only if Mia is a knight.\n",
"Assume Zoey is a knave. ",
"No contradiction is found in their false claim that Oliver is a knight or Zoey is a knight.\n",
"Oliver cannot be a knight, because this would contradict the claim of their own that Mia is a knave.\n",
"Assume Oliver is a knave. ",
"No contradiction is found in their false claim that Mia is a knave.\n",
"Therefore, (1) Mia is a knight\n",
"(2) Oliver 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: Mia, Oliver, and Zoey. Mia noted, "Zoey is a knave if and only if Mia is a knight". "Mia is a knave," Oliver claimed. Zoey said that Oliver 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> | Assume Mia is a knight. No contradiction is found in their claim that Zoey is a knave if and only if Mia is a knight.
Zoey cannot be a knight, because this would contradict the claim of Mia that Zoey is a knave if and only if Mia is a knight.
Assume Zoey is a knave. No contradiction is found in their false claim that Oliver is a knight or Zoey is a knight.
Oliver cannot be a knight, because this would contradict the claim of their own that Mia is a knave.
Assume Oliver is a knave. No contradiction is found in their false claim that Mia is a knave.
Therefore, (1) Mia is a knight
(2) Oliver is a knave
(3) Zoey is a knave </think>
<answer> (1) Mia is a knight
(2) Oliver is a knave
(3) Zoey is a knave </answer> | math | {
"ground_truth": {
"names": [
"Mia",
"Oliver",
"Zoey"
],
"solution": [
true,
false,
false
],
"solution_text_format": "(1) Mia is a knight\n(2) Oliver is a knave\n(3) Zoey is a knave",
"statements": "(('<=>', ('lying', 2), ('telling-truth', 0)), ('lying', 0), ('or', ('telling-truth', 1), ('telling-truth', 2)))"
},
"style": "rule"
} | {
"index": 48,
"split": "train"
} |
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