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: James, Liam, and Henry. James told you that Liam is a knave or Liam is a knight. Liam asserted: \"Liam is a knight\". Henry commented, \"If Henry is a knight then 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 James is a knight. ",
"No contradiction is found in their claim that Liam is a knave or Liam is a knight.\n",
"Assume Liam is a knight. ",
"No contradiction is found in their claim that Liam is a knight.\n",
"Henry cannot be a knight, because this would contradict the claim of their own that If Henry is a knight then Liam is a knave.\n",
"Henry cannot be a knave, because this would contradict the false claim of their own that If Henry is a knight then Liam is a knave.\n",
"We have exhausted all possibilities for Henry, so let us go back and reconsider Liam.\n",
"Assume Liam is a knave. ",
"No contradiction is found in their false claim that Liam is a knight.\n",
"Assume Henry is a knight. ",
"No contradiction is found in their claim that If Henry is a knight then Liam is a knave.\n",
"Therefore, (1) James is a knight\n",
"(2) Liam is a knave\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: James, Liam, and Henry. James told you that Liam is a knave or Liam is a knight. Liam asserted: "Liam is a knight". Henry commented, "If Henry is a knight then 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 James is a knight. No contradiction is found in their claim that Liam is a knave or Liam is a knight.
Assume Liam is a knight. No contradiction is found in their claim that Liam is a knight.
Henry cannot be a knight, because this would contradict the claim of their own that If Henry is a knight then Liam is a knave.
Henry cannot be a knave, because this would contradict the false claim of their own that If Henry is a knight then Liam is a knave.
We have exhausted all possibilities for Henry, so let us go back and reconsider Liam.
Assume Liam is a knave. No contradiction is found in their false claim that Liam is a knight.
Assume Henry is a knight. No contradiction is found in their claim that If Henry is a knight then Liam is a knave.
Therefore, (1) James is a knight
(2) Liam is a knave
(3) Henry is a knight </think>
<answer> (1) James is a knight
(2) Liam is a knave
(3) Henry is a knight </answer> | math | {
"ground_truth": {
"names": [
"James",
"Liam",
"Henry"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) James is a knight\n(2) Liam is a knave\n(3) Henry is a knight",
"statements": "(('or', ('lying', 1), ('telling-truth', 1)), ('telling-truth', 1), ('->', ('telling-truth', 2), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 300,
"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, Alexander, and Riley. Benjamin said that Riley is a knight. Alexander stated, \"Benjamin is a knave if and only if Riley is a knight\". Riley was heard saying, \"Riley is a knight or Alexander 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 Benjamin is a knight. ",
"No contradiction is found in their claim that Riley is a knight.\n",
"Assume Riley is a knight. ",
"No contradiction is found in their claim that Riley is a knight or Alexander is a knave.\n",
"Alexander cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave if and only if Riley is a knight.\n",
"Assume Alexander is a knave. ",
"No contradiction is found in their false claim that Benjamin is a knave if and only if Riley is a knight.\n",
"Therefore, (1) Benjamin is a knight\n",
"(2) Alexander is a knave\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: Benjamin, Alexander, and Riley. Benjamin said that Riley is a knight. Alexander stated, "Benjamin is a knave if and only if Riley is a knight". Riley was heard saying, "Riley is a knight or Alexander 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 Benjamin is a knight. No contradiction is found in their claim that Riley is a knight.
Assume Riley is a knight. No contradiction is found in their claim that Riley is a knight or Alexander is a knave.
Alexander cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave if and only if Riley is a knight.
Assume Alexander is a knave. No contradiction is found in their false claim that Benjamin is a knave if and only if Riley is a knight.
Therefore, (1) Benjamin is a knight
(2) Alexander is a knave
(3) Riley is a knight </think>
<answer> (1) Benjamin is a knight
(2) Alexander is a knave
(3) Riley is a knight </answer> | math | {
"ground_truth": {
"names": [
"Benjamin",
"Alexander",
"Riley"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Benjamin is a knight\n(2) Alexander is a knave\n(3) Riley is a knight",
"statements": "(('telling-truth', 2), ('<=>', ('lying', 0), ('telling-truth', 2)), ('or', ('telling-truth', 2), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 301,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Mason, Sophia, and Michael. Mason remarked, \"Michael is a knave if and only if Michael is a knight\". \"Mason is a knight and Michael is a knight,\" Sophia claimed. \"Sophia is a knave or Mason is a knave\" - Michael. So who is a knight and who is a knave? 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"
}
]
| [
"Mason cannot be a knight, because this would contradict the claim of their own that Michael is a knave if and only if Michael is a knight.\n",
"Assume Mason is a knave. ",
"No contradiction is found in their false claim that Michael is a knave if and only if Michael is a knight.\n",
"Assume Michael is a knight. ",
"No contradiction is found in their claim that Sophia is a knave or Mason is a knave.\n",
"Sophia cannot be a knight, because this would contradict the claim of their own that Mason is a knight and Michael is a knight.\n",
"Assume Sophia is a knave. ",
"No contradiction is found in their false claim that Mason is a knight and Michael is a knight.\n",
"Therefore, (1) Mason is a knave\n",
"(2) Sophia is a knave\n",
"(3) Michael is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Mason, Sophia, and Michael. Mason remarked, "Michael is a knave if and only if Michael is a knight". "Mason is a knight and Michael is a knight," Sophia claimed. "Sophia is a knave or Mason is a knave" - Michael. So who is a knight and who is a knave? 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> | Mason cannot be a knight, because this would contradict the claim of their own that Michael is a knave if and only if Michael is a knight.
Assume Mason is a knave. No contradiction is found in their false claim that Michael is a knave if and only if Michael is a knight.
Assume Michael is a knight. No contradiction is found in their claim that Sophia is a knave or Mason is a knave.
Sophia cannot be a knight, because this would contradict the claim of their own that Mason is a knight and Michael is a knight.
Assume Sophia is a knave. No contradiction is found in their false claim that Mason is a knight and Michael is a knight.
Therefore, (1) Mason is a knave
(2) Sophia is a knave
(3) Michael is a knight </think>
<answer> (1) Mason is a knave
(2) Sophia is a knave
(3) Michael is a knight </answer> | math | {
"ground_truth": {
"names": [
"Mason",
"Sophia",
"Michael"
],
"solution": [
false,
false,
true
],
"solution_text_format": "(1) Mason is a knave\n(2) Sophia is a knave\n(3) Michael is a knight",
"statements": "(('<=>', ('lying', 2), ('telling-truth', 2)), ('and', ('telling-truth', 0), ('telling-truth', 2)), ('or', ('lying', 1), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 302,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Sophia, Alexander, and Jacob. According to Sophia, \"Alexander is not a knave\". In Alexander's words: \"Jacob is a knave or Jacob is a knight\". Jacob commented, \"If Sophia is a knight then Sophia 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 Sophia is a knight. ",
"No contradiction is found in their claim that Alexander is not a knave.\n",
"Assume Alexander is a knight. ",
"No contradiction is found in their claim that Jacob is a knave or Jacob is a knight.\n",
"Jacob cannot be a knight, because this would contradict the claim of their own that If Sophia is a knight then Sophia is a knave.\n",
"Assume Jacob is a knave. ",
"No contradiction is found in their false claim that If Sophia is a knight then Sophia is a knave.\n",
"Therefore, (1) Sophia is a knight\n",
"(2) Alexander is a knight\n",
"(3) Jacob 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: Sophia, Alexander, and Jacob. According to Sophia, "Alexander is not a knave". In Alexander's words: "Jacob is a knave or Jacob is a knight". Jacob commented, "If Sophia is a knight then Sophia 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 Sophia is a knight. No contradiction is found in their claim that Alexander is not a knave.
Assume Alexander is a knight. No contradiction is found in their claim that Jacob is a knave or Jacob is a knight.
Jacob cannot be a knight, because this would contradict the claim of their own that If Sophia is a knight then Sophia is a knave.
Assume Jacob is a knave. No contradiction is found in their false claim that If Sophia is a knight then Sophia is a knave.
Therefore, (1) Sophia is a knight
(2) Alexander is a knight
(3) Jacob is a knave </think>
<answer> (1) Sophia is a knight
(2) Alexander is a knight
(3) Jacob is a knave </answer> | math | {
"ground_truth": {
"names": [
"Sophia",
"Alexander",
"Jacob"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Sophia is a knight\n(2) Alexander is a knight\n(3) Jacob is a knave",
"statements": "(('not', ('lying', 1)), ('or', ('lying', 2), ('telling-truth', 2)), ('->', ('telling-truth', 0), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 303,
"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, Amelia, and David. \"David is a knave,\" Olivia claimed. \"David is a knave if and only if Olivia is a knight,\" Amelia declared. According to David, \"Amelia is a knave and Olivia 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 Olivia is a knight. ",
"No contradiction is found in their claim that David is a knave.\n",
"David cannot be a knight, because this would contradict the claim of Olivia that David is a knave.\n",
"Assume David is a knave. ",
"No contradiction is found in their false claim that Amelia is a knave and Olivia is a knave.\n",
"Assume Amelia is a knight. ",
"No contradiction is found in their claim that David is a knave if and only if Olivia is a knight.\n",
"Therefore, (1) Olivia is a knight\n",
"(2) Amelia is a knight\n",
"(3) David is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Olivia, Amelia, and David. "David is a knave," Olivia claimed. "David is a knave if and only if Olivia is a knight," Amelia declared. According to David, "Amelia is a knave and Olivia 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 Olivia is a knight. No contradiction is found in their claim that David is a knave.
David cannot be a knight, because this would contradict the claim of Olivia that David is a knave.
Assume David is a knave. No contradiction is found in their false claim that Amelia is a knave and Olivia is a knave.
Assume Amelia is a knight. No contradiction is found in their claim that David is a knave if and only if Olivia is a knight.
Therefore, (1) Olivia is a knight
(2) Amelia is a knight
(3) David is a knave </think>
<answer> (1) Olivia is a knight
(2) Amelia is a knight
(3) David is a knave </answer> | math | {
"ground_truth": {
"names": [
"Olivia",
"Amelia",
"David"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Olivia is a knight\n(2) Amelia is a knight\n(3) David is a knave",
"statements": "(('lying', 2), ('<=>', ('lying', 2), ('telling-truth', 0)), ('and', ('lying', 1), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 304,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Sophia, Oliver, and William. As Sophia put it, \"Oliver is a knave if and only if William is a knave\". Oliver expressed that Sophia is a knight. As William put it, \"Sophia is a knight and 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 Sophia is a knight. ",
"No contradiction is found in their claim that Oliver is a knave if and only if William is a knave.\n",
"Assume Oliver is a knight. ",
"No contradiction is found in their claim that Sophia is a knight.\n",
"Assume William is a knight. ",
"No contradiction is found in their claim that Sophia is a knight and Oliver is a knight.\n",
"Therefore, (1) Sophia is a knight\n",
"(2) Oliver is a knight\n",
"(3) William is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Sophia, Oliver, and William. As Sophia put it, "Oliver is a knave if and only if William is a knave". Oliver expressed that Sophia is a knight. As William put it, "Sophia is a knight and 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 Sophia is a knight. No contradiction is found in their claim that Oliver is a knave if and only if William is a knave.
Assume Oliver is a knight. No contradiction is found in their claim that Sophia is a knight.
Assume William is a knight. No contradiction is found in their claim that Sophia is a knight and Oliver is a knight.
Therefore, (1) Sophia is a knight
(2) Oliver is a knight
(3) William is a knight </think>
<answer> (1) Sophia is a knight
(2) Oliver is a knight
(3) William is a knight </answer> | math | {
"ground_truth": {
"names": [
"Sophia",
"Oliver",
"William"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Sophia is a knight\n(2) Oliver is a knight\n(3) William is a knight",
"statements": "(('<=>', ('lying', 1), ('lying', 2)), ('telling-truth', 0), ('and', ('telling-truth', 0), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 305,
"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: Zoey, Owen, and Daniel. Zoey said, \"If Daniel is a knight then Owen is a knight.\" Owen remarked, \"If Daniel is a knight then Owen is a knight\". Daniel was heard saying, \"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 Zoey is a knight. ",
"No contradiction is found in their claim that If Daniel is a knight then Owen is a knight.\n",
"Assume Daniel is a knight. ",
"No contradiction is found in their claim that Zoey is a knight.\n",
"Assume Owen is a knight. ",
"No contradiction is found in their claim that If Daniel is a knight then Owen is a knight.\n",
"Therefore, (1) Zoey is a knight\n",
"(2) Owen 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: Zoey, Owen, and Daniel. Zoey said, "If Daniel is a knight then Owen is a knight." Owen remarked, "If Daniel is a knight then Owen is a knight". Daniel was heard saying, "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 Zoey is a knight. No contradiction is found in their claim that If Daniel is a knight then Owen is a knight.
Assume Daniel is a knight. No contradiction is found in their claim that Zoey is a knight.
Assume Owen is a knight. No contradiction is found in their claim that If Daniel is a knight then Owen is a knight.
Therefore, (1) Zoey is a knight
(2) Owen is a knight
(3) Daniel is a knight </think>
<answer> (1) Zoey is a knight
(2) Owen is a knight
(3) Daniel is a knight </answer> | math | {
"ground_truth": {
"names": [
"Zoey",
"Owen",
"Daniel"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Zoey is a knight\n(2) Owen is a knight\n(3) Daniel is a knight",
"statements": "(('->', ('telling-truth', 2), ('telling-truth', 1)), ('->', ('telling-truth', 2), ('telling-truth', 1)), ('telling-truth', 0))"
},
"style": "rule"
} | {
"index": 306,
"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, Zoey, and Emma. Logan commented, \"Zoey is not a knight\". Zoey stated, \"Zoey is a knight and Emma is a knight\". Emma stated, \"Logan is a knight and Logan 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 Logan is a knight. ",
"No contradiction is found in their claim that Zoey is not a knight.\n",
"Zoey cannot be a knight, because this would contradict the claim of Logan that Zoey is not a knight.\n",
"Assume Zoey is a knave. ",
"No contradiction is found in their false claim that Zoey is a knight and Emma is a knight.\n",
"Emma cannot be a knight, because this would contradict the claim of their own that Logan is a knight and Logan is a knave.\n",
"Assume Emma is a knave. ",
"No contradiction is found in their false claim that Logan is a knight and Logan is a knave.\n",
"Therefore, (1) Logan is a knight\n",
"(2) Zoey is a knave\n",
"(3) Emma is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Logan, Zoey, and Emma. Logan commented, "Zoey is not a knight". Zoey stated, "Zoey is a knight and Emma is a knight". Emma stated, "Logan is a knight and Logan 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 Logan is a knight. No contradiction is found in their claim that Zoey is not a knight.
Zoey cannot be a knight, because this would contradict the claim of Logan that Zoey is not a knight.
Assume Zoey is a knave. No contradiction is found in their false claim that Zoey is a knight and Emma is a knight.
Emma cannot be a knight, because this would contradict the claim of their own that Logan is a knight and Logan is a knave.
Assume Emma is a knave. No contradiction is found in their false claim that Logan is a knight and Logan is a knave.
Therefore, (1) Logan is a knight
(2) Zoey is a knave
(3) Emma is a knave </think>
<answer> (1) Logan is a knight
(2) Zoey is a knave
(3) Emma is a knave </answer> | math | {
"ground_truth": {
"names": [
"Logan",
"Zoey",
"Emma"
],
"solution": [
true,
false,
false
],
"solution_text_format": "(1) Logan is a knight\n(2) Zoey is a knave\n(3) Emma is a knave",
"statements": "(('not', ('telling-truth', 1)), ('and', ('telling-truth', 1), ('telling-truth', 2)), ('and', ('telling-truth', 0), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 307,
"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, Lucas, and Jacob. As Grace put it, \"Lucas is a knight\". \"Jacob is a knight,\" Lucas mentioned. \"Grace is a knave if and only if Grace is a knight\" - Jacob. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Grace is a knight. ",
"No contradiction is found in their claim that Lucas is a knight.\n",
"Assume Lucas is a knight. ",
"No contradiction is found in their claim that Jacob is a knight.\n",
"Jacob cannot be a knight, because this would contradict the claim of their own that Grace is a knave if and only if Grace is a knight.\n",
"Jacob cannot be a knave, because this would contradict the claim of Lucas that Jacob is a knight.\n",
"We have exhausted all possibilities for Jacob, so let us go back and reconsider Lucas.\n",
"Lucas cannot be a knave, because this would contradict the claim of Grace that Lucas is a knight.\n",
"We have exhausted all possibilities for Lucas, so let us go back and reconsider Grace.\n",
"Assume Grace is a knave. ",
"No contradiction is found in their false claim that Lucas is a knight.\n",
"Lucas cannot be a knight, because this would contradict the false claim of Grace that Lucas is a knight.\n",
"Assume Lucas is a knave. ",
"No contradiction is found in their false claim that Jacob is a knight.\n",
"Jacob cannot be a knight, because this would contradict the false claim of Lucas that Jacob is a knight.\n",
"Assume Jacob is a knave. ",
"No contradiction is found in their false claim that Grace is a knave if and only if Grace is a knight.\n",
"Therefore, (1) Grace is a knave\n",
"(2) Lucas is a knave\n",
"(3) Jacob 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, Lucas, and Jacob. As Grace put it, "Lucas is a knight". "Jacob is a knight," Lucas mentioned. "Grace is a knave if and only if Grace is a knight" - Jacob. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Grace is a knight. No contradiction is found in their claim that Lucas is a knight.
Assume Lucas is a knight. No contradiction is found in their claim that Jacob is a knight.
Jacob cannot be a knight, because this would contradict the claim of their own that Grace is a knave if and only if Grace is a knight.
Jacob cannot be a knave, because this would contradict the claim of Lucas that Jacob is a knight.
We have exhausted all possibilities for Jacob, so let us go back and reconsider Lucas.
Lucas cannot be a knave, because this would contradict the claim of Grace that Lucas is a knight.
We have exhausted all possibilities for Lucas, so let us go back and reconsider Grace.
Assume Grace is a knave. No contradiction is found in their false claim that Lucas is a knight.
Lucas cannot be a knight, because this would contradict the false claim of Grace that Lucas is a knight.
Assume Lucas is a knave. No contradiction is found in their false claim that Jacob is a knight.
Jacob cannot be a knight, because this would contradict the false claim of Lucas that Jacob is a knight.
Assume Jacob is a knave. No contradiction is found in their false claim that Grace is a knave if and only if Grace is a knight.
Therefore, (1) Grace is a knave
(2) Lucas is a knave
(3) Jacob is a knave </think>
<answer> (1) Grace is a knave
(2) Lucas is a knave
(3) Jacob is a knave </answer> | math | {
"ground_truth": {
"names": [
"Grace",
"Lucas",
"Jacob"
],
"solution": [
false,
false,
false
],
"solution_text_format": "(1) Grace is a knave\n(2) Lucas is a knave\n(3) Jacob is a knave",
"statements": "(('telling-truth', 1), ('telling-truth', 2), ('<=>', ('lying', 0), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 308,
"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, Abigail, and Oliver. Luke expressed that Abigail is a knave or Oliver is a knave. According to Abigail, \"Luke is a knave if and only if Abigail is a knight\". As Oliver put it, \"If Abigail is a knave then Luke 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 Luke is a knight. ",
"No contradiction is found in their claim that Abigail is a knave or Oliver is a knave.\n",
"Abigail cannot be a knight, because this would contradict the claim of their own that Luke is a knave if and only if Abigail is a knight.\n",
"Abigail cannot be a knave, because this would contradict the false claim of their own that Luke is a knave if and only if Abigail is a knight.\n",
"We have exhausted all possibilities for Abigail, so let us go back and reconsider Luke.\n",
"Assume Luke is a knave. ",
"No contradiction is found in their false claim that Abigail is a knave or Oliver is a knave.\n",
"Assume Abigail is a knight. ",
"No contradiction is found in their claim that Luke is a knave if and only if Abigail is a knight.\n",
"Assume Oliver is a knight. ",
"No contradiction is found in their claim that If Abigail is a knave then Luke is a knight.\n",
"Therefore, (1) Luke is a knave\n",
"(2) Abigail is a knight\n",
"(3) Oliver is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Luke, Abigail, and Oliver. Luke expressed that Abigail is a knave or Oliver is a knave. According to Abigail, "Luke is a knave if and only if Abigail is a knight". As Oliver put it, "If Abigail is a knave then Luke 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 Luke is a knight. No contradiction is found in their claim that Abigail is a knave or Oliver is a knave.
Abigail cannot be a knight, because this would contradict the claim of their own that Luke is a knave if and only if Abigail is a knight.
Abigail cannot be a knave, because this would contradict the false claim of their own that Luke is a knave if and only if Abigail is a knight.
We have exhausted all possibilities for Abigail, so let us go back and reconsider Luke.
Assume Luke is a knave. No contradiction is found in their false claim that Abigail is a knave or Oliver is a knave.
Assume Abigail is a knight. No contradiction is found in their claim that Luke is a knave if and only if Abigail is a knight.
Assume Oliver is a knight. No contradiction is found in their claim that If Abigail is a knave then Luke is a knight.
Therefore, (1) Luke is a knave
(2) Abigail is a knight
(3) Oliver is a knight </think>
<answer> (1) Luke is a knave
(2) Abigail is a knight
(3) Oliver is a knight </answer> | math | {
"ground_truth": {
"names": [
"Luke",
"Abigail",
"Oliver"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Luke is a knave\n(2) Abigail is a knight\n(3) Oliver is a knight",
"statements": "(('or', ('lying', 1), ('lying', 2)), ('<=>', ('lying', 0), ('telling-truth', 1)), ('->', ('lying', 1), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 309,
"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, Benjamin, and Riley. In a statement by Liam: \"Benjamin is not a knave\". Benjamin asserted: \"Liam is a knave or Riley is a knave\". \"Benjamin is a knight and Liam is a knave,\" Riley mentioned. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Liam is a knight. ",
"No contradiction is found in their claim that Benjamin is not a knave.\n",
"Assume Benjamin is a knight. ",
"No contradiction is found in their claim that Liam is a knave or Riley is a knave.\n",
"Riley cannot be a knight, because this would contradict the claim of Benjamin that Liam is a knave or Riley is a knave.\n",
"Assume Riley is a knave. ",
"No contradiction is found in their false claim that Benjamin is a knight and Liam is a knave.\n",
"Therefore, (1) Liam is a knight\n",
"(2) Benjamin 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: Liam, Benjamin, and Riley. In a statement by Liam: "Benjamin is not a knave". Benjamin asserted: "Liam is a knave or Riley is a knave". "Benjamin is a knight and Liam is a knave," Riley mentioned. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Liam is a knight. No contradiction is found in their claim that Benjamin is not a knave.
Assume Benjamin is a knight. No contradiction is found in their claim that Liam is a knave or Riley is a knave.
Riley cannot be a knight, because this would contradict the claim of Benjamin that Liam is a knave or Riley is a knave.
Assume Riley is a knave. No contradiction is found in their false claim that Benjamin is a knight and Liam is a knave.
Therefore, (1) Liam is a knight
(2) Benjamin is a knight
(3) Riley is a knave </think>
<answer> (1) Liam is a knight
(2) Benjamin is a knight
(3) Riley is a knave </answer> | math | {
"ground_truth": {
"names": [
"Liam",
"Benjamin",
"Riley"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Liam is a knight\n(2) Benjamin is a knight\n(3) Riley is a knave",
"statements": "(('not', ('lying', 1)), ('or', ('lying', 0), ('lying', 2)), ('and', ('telling-truth', 1), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 310,
"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, Mason, and Scarlett. According to Elizabeth, \"Mason is a knight and Scarlett is a knave\". Mason asserted: \"If Elizabeth is a knave then Elizabeth is a knight\". \"Elizabeth is a knight or Elizabeth is a knave,\" Scarlett mentioned. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Elizabeth is a knight. ",
"No contradiction is found in their claim that Mason is a knight and Scarlett is a knave.\n",
"Assume Mason is a knight. ",
"No contradiction is found in their claim that If Elizabeth is a knave then Elizabeth is a knight.\n",
"Scarlett cannot be a knight, because this would contradict the claim of Elizabeth that Mason is a knight and Scarlett is a knave.\n",
"Scarlett cannot be a knave, because this would contradict the false claim of their own that Elizabeth is a knight or Elizabeth is a knave.\n",
"We have exhausted all possibilities for Scarlett, so let us go back and reconsider Mason.\n",
"Mason cannot be a knave, because this would contradict the claim of Elizabeth that Mason is a knight and Scarlett is a knave.\n",
"We have exhausted all possibilities for Mason, so let us go back and reconsider Elizabeth.\n",
"Assume Elizabeth is a knave. ",
"No contradiction is found in their false claim that Mason is a knight and Scarlett is a knave.\n",
"Mason cannot be a knight, because this would contradict the claim of their own that If Elizabeth is a knave then Elizabeth is a knight.\n",
"Assume Mason is a knave. ",
"No contradiction is found in their false claim that If Elizabeth is a knave then Elizabeth is a knight.\n",
"Assume Scarlett is a knight. ",
"No contradiction is found in their claim that Elizabeth is a knight or Elizabeth is a knave.\n",
"Therefore, (1) Elizabeth is a knave\n",
"(2) Mason is a knave\n",
"(3) Scarlett is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Elizabeth, Mason, and Scarlett. According to Elizabeth, "Mason is a knight and Scarlett is a knave". Mason asserted: "If Elizabeth is a knave then Elizabeth is a knight". "Elizabeth is a knight or Elizabeth is a knave," Scarlett mentioned. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Elizabeth is a knight. No contradiction is found in their claim that Mason is a knight and Scarlett is a knave.
Assume Mason is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Elizabeth is a knight.
Scarlett cannot be a knight, because this would contradict the claim of Elizabeth that Mason is a knight and Scarlett is a knave.
Scarlett cannot be a knave, because this would contradict the false claim of their own that Elizabeth is a knight or Elizabeth is a knave.
We have exhausted all possibilities for Scarlett, so let us go back and reconsider Mason.
Mason cannot be a knave, because this would contradict the claim of Elizabeth that Mason is a knight and Scarlett is a knave.
We have exhausted all possibilities for Mason, so let us go back and reconsider Elizabeth.
Assume Elizabeth is a knave. No contradiction is found in their false claim that Mason is a knight and Scarlett is a knave.
Mason cannot be a knight, because this would contradict the claim of their own that If Elizabeth is a knave then Elizabeth is a knight.
Assume Mason is a knave. No contradiction is found in their false claim that If Elizabeth is a knave then Elizabeth is a knight.
Assume Scarlett is a knight. No contradiction is found in their claim that Elizabeth is a knight or Elizabeth is a knave.
Therefore, (1) Elizabeth is a knave
(2) Mason is a knave
(3) Scarlett is a knight </think>
<answer> (1) Elizabeth is a knave
(2) Mason is a knave
(3) Scarlett is a knight </answer> | math | {
"ground_truth": {
"names": [
"Elizabeth",
"Mason",
"Scarlett"
],
"solution": [
false,
false,
true
],
"solution_text_format": "(1) Elizabeth is a knave\n(2) Mason is a knave\n(3) Scarlett is a knight",
"statements": "(('and', ('telling-truth', 1), ('lying', 2)), ('->', ('lying', 0), ('telling-truth', 0)), ('or', ('telling-truth', 0), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 311,
"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, Victoria, and Sebastian. \"Victoria is not a knight,\" Abigail claimed. Victoria noted, \"Abigail is a knave if and only if Sebastian is a knight\". According to Sebastian, \"Victoria 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 Victoria is not a knight.\n",
"Victoria cannot be a knight, because this would contradict the claim of Abigail that Victoria is not a knight.\n",
"Assume Victoria is a knave. ",
"No contradiction is found in their false claim that Abigail is a knave if and only if Sebastian is a knight.\n",
"Assume Sebastian is a knight. ",
"No contradiction is found in their claim that Victoria is not a knight.\n",
"Therefore, (1) Abigail is a knight\n",
"(2) Victoria is a knave\n",
"(3) Sebastian is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Abigail, Victoria, and Sebastian. "Victoria is not a knight," Abigail claimed. Victoria noted, "Abigail is a knave if and only if Sebastian is a knight". According to Sebastian, "Victoria 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 Victoria is not a knight.
Victoria cannot be a knight, because this would contradict the claim of Abigail that Victoria is not a knight.
Assume Victoria is a knave. No contradiction is found in their false claim that Abigail is a knave if and only if Sebastian is a knight.
Assume Sebastian is a knight. No contradiction is found in their claim that Victoria is not a knight.
Therefore, (1) Abigail is a knight
(2) Victoria is a knave
(3) Sebastian is a knight </think>
<answer> (1) Abigail is a knight
(2) Victoria is a knave
(3) Sebastian is a knight </answer> | math | {
"ground_truth": {
"names": [
"Abigail",
"Victoria",
"Sebastian"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Abigail is a knight\n(2) Victoria is a knave\n(3) Sebastian is a knight",
"statements": "(('not', ('telling-truth', 1)), ('<=>', ('lying', 0), ('telling-truth', 2)), ('not', ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 312,
"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, Evelyn, and Riley. According to Oliver, \"If Riley is a knight then Evelyn is a knave\". Evelyn was heard saying, \"Oliver is a knight\". Riley commented, \"Evelyn is a knight if and only if 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 Oliver is a knight. ",
"No contradiction is found in their claim that If Riley is a knight then Evelyn is a knave.\n",
"Riley cannot be a knight, because this would contradict the claim of their own that Evelyn is a knight if and only if Evelyn is a knave.\n",
"Assume Riley is a knave. ",
"No contradiction is found in their false claim that Evelyn is a knight if and only if Evelyn is a knave.\n",
"Assume Evelyn is a knight. ",
"No contradiction is found in their claim that Oliver is a knight.\n",
"Therefore, (1) Oliver is a knight\n",
"(2) Evelyn 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: Oliver, Evelyn, and Riley. According to Oliver, "If Riley is a knight then Evelyn is a knave". Evelyn was heard saying, "Oliver is a knight". Riley commented, "Evelyn is a knight if and only if 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 Oliver is a knight. No contradiction is found in their claim that If Riley is a knight then Evelyn is a knave.
Riley cannot be a knight, because this would contradict the claim of their own that Evelyn is a knight if and only if Evelyn is a knave.
Assume Riley is a knave. No contradiction is found in their false claim that Evelyn is a knight if and only if Evelyn is a knave.
Assume Evelyn is a knight. No contradiction is found in their claim that Oliver is a knight.
Therefore, (1) Oliver is a knight
(2) Evelyn is a knight
(3) Riley is a knave </think>
<answer> (1) Oliver is a knight
(2) Evelyn is a knight
(3) Riley is a knave </answer> | math | {
"ground_truth": {
"names": [
"Oliver",
"Evelyn",
"Riley"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Oliver is a knight\n(2) Evelyn is a knight\n(3) Riley is a knave",
"statements": "(('->', ('telling-truth', 2), ('lying', 1)), ('telling-truth', 0), ('<=>', ('telling-truth', 1), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 313,
"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, Henry, and Avery. In Liam's words: \"If Henry is a knight then Liam is a knight\". Henry told you that Liam is a knight or Avery is a knave. In a statement by Avery: \"If Avery is a knight then Liam is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Liam is a knight. ",
"No contradiction is found in their claim that If Henry is a knight then Liam is a knight.\n",
"Assume Henry is a knight. ",
"No contradiction is found in their claim that Liam is a knight or Avery is a knave.\n",
"Assume Avery is a knight. ",
"No contradiction is found in their claim that If Avery is a knight then Liam is a knight.\n",
"Therefore, (1) Liam is a knight\n",
"(2) Henry is a knight\n",
"(3) Avery 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, Henry, and Avery. In Liam's words: "If Henry is a knight then Liam is a knight". Henry told you that Liam is a knight or Avery is a knave. In a statement by Avery: "If Avery is a knight then Liam is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Liam is a knight. No contradiction is found in their claim that If Henry is a knight then Liam is a knight.
Assume Henry is a knight. No contradiction is found in their claim that Liam is a knight or Avery is a knave.
Assume Avery is a knight. No contradiction is found in their claim that If Avery is a knight then Liam is a knight.
Therefore, (1) Liam is a knight
(2) Henry is a knight
(3) Avery is a knight </think>
<answer> (1) Liam is a knight
(2) Henry is a knight
(3) Avery is a knight </answer> | math | {
"ground_truth": {
"names": [
"Liam",
"Henry",
"Avery"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Liam is a knight\n(2) Henry is a knight\n(3) Avery is a knight",
"statements": "(('->', ('telling-truth', 1), ('telling-truth', 0)), ('or', ('telling-truth', 0), ('lying', 2)), ('->', ('telling-truth', 2), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 314,
"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, Michael, and Ella. As Jack put it, \"If Ella is a knight then Jack is a knight\". Michael was heard saying, \"Jack is not a knight\". Ella said that Jack is a knight or Michael 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 Jack is a knight. ",
"No contradiction is found in their claim that If Ella is a knight then Jack is a knight.\n",
"Assume Ella is a knight. ",
"No contradiction is found in their claim that Jack is a knight or Michael is a knave.\n",
"Michael cannot be a knight, because this would contradict the claim of their own that Jack is not a knight.\n",
"Assume Michael is a knave. ",
"No contradiction is found in their false claim that Jack is not a knight.\n",
"Therefore, (1) Jack is a knight\n",
"(2) Michael is a knave\n",
"(3) Ella is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Jack, Michael, and Ella. As Jack put it, "If Ella is a knight then Jack is a knight". Michael was heard saying, "Jack is not a knight". Ella said that Jack is a knight or Michael 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 Jack is a knight. No contradiction is found in their claim that If Ella is a knight then Jack is a knight.
Assume Ella is a knight. No contradiction is found in their claim that Jack is a knight or Michael is a knave.
Michael cannot be a knight, because this would contradict the claim of their own that Jack is not a knight.
Assume Michael is a knave. No contradiction is found in their false claim that Jack is not a knight.
Therefore, (1) Jack is a knight
(2) Michael is a knave
(3) Ella is a knight </think>
<answer> (1) Jack is a knight
(2) Michael is a knave
(3) Ella is a knight </answer> | math | {
"ground_truth": {
"names": [
"Jack",
"Michael",
"Ella"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Jack is a knight\n(2) Michael is a knave\n(3) Ella is a knight",
"statements": "(('->', ('telling-truth', 2), ('telling-truth', 0)), ('not', ('telling-truth', 0)), ('or', ('telling-truth', 0), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 315,
"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, Jacob, and Lucas. As Benjamin put it, \"Jacob is a knave if and only if Benjamin is a knight\". Jacob noted, \"Benjamin is a knight and Lucas is a knave\". \"Jacob is a knight and Jacob is a knave\" - Lucas. So who is a knight and who is a knave? 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 Jacob is a knave if and only if Benjamin is a knight.\n",
"Jacob cannot be a knight, because this would contradict the claim of Benjamin that Jacob is a knave if and only if Benjamin is a knight.\n",
"Assume Jacob is a knave. ",
"No contradiction is found in their false claim that Benjamin is a knight and Lucas is a knave.\n",
"Lucas cannot be a knight, because this would contradict the claim of their own that Jacob is a knight and Jacob is a knave.\n",
"Lucas cannot be a knave, because this would contradict the false claim of Jacob that Benjamin is a knight and Lucas is a knave.\n",
"We have exhausted all possibilities for Lucas and Jacob, so let us go back and reconsider Benjamin.\n",
"Assume Benjamin is a knave. ",
"No contradiction is found in their false claim that Jacob is a knave if and only if Benjamin is a knight.\n",
"Jacob cannot be a knight, because this would contradict the false claim of Benjamin that Jacob is a knave if and only if Benjamin is a knight.\n",
"Assume Jacob is a knave. ",
"No contradiction is found in their false claim that Benjamin is a knight and Lucas is a knave.\n",
"Lucas cannot be a knight, because this would contradict the claim of their own that Jacob is a knight and Jacob is a knave.\n",
"Assume Lucas is a knave. ",
"No contradiction is found in their false claim that Jacob is a knight and Jacob is a knave.\n",
"Therefore, (1) Benjamin is a knave\n",
"(2) Jacob is a knave\n",
"(3) Lucas 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, Jacob, and Lucas. As Benjamin put it, "Jacob is a knave if and only if Benjamin is a knight". Jacob noted, "Benjamin is a knight and Lucas is a knave". "Jacob is a knight and Jacob is a knave" - Lucas. So who is a knight and who is a knave? 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 Jacob is a knave if and only if Benjamin is a knight.
Jacob cannot be a knight, because this would contradict the claim of Benjamin that Jacob is a knave if and only if Benjamin is a knight.
Assume Jacob is a knave. No contradiction is found in their false claim that Benjamin is a knight and Lucas is a knave.
Lucas cannot be a knight, because this would contradict the claim of their own that Jacob is a knight and Jacob is a knave.
Lucas cannot be a knave, because this would contradict the false claim of Jacob that Benjamin is a knight and Lucas is a knave.
We have exhausted all possibilities for Lucas and Jacob, so let us go back and reconsider Benjamin.
Assume Benjamin is a knave. No contradiction is found in their false claim that Jacob is a knave if and only if Benjamin is a knight.
Jacob cannot be a knight, because this would contradict the false claim of Benjamin that Jacob is a knave if and only if Benjamin is a knight.
Assume Jacob is a knave. No contradiction is found in their false claim that Benjamin is a knight and Lucas is a knave.
Lucas cannot be a knight, because this would contradict the claim of their own that Jacob is a knight and Jacob is a knave.
Assume Lucas is a knave. No contradiction is found in their false claim that Jacob is a knight and Jacob is a knave.
Therefore, (1) Benjamin is a knave
(2) Jacob is a knave
(3) Lucas is a knave </think>
<answer> (1) Benjamin is a knave
(2) Jacob is a knave
(3) Lucas is a knave </answer> | math | {
"ground_truth": {
"names": [
"Benjamin",
"Jacob",
"Lucas"
],
"solution": [
false,
false,
false
],
"solution_text_format": "(1) Benjamin is a knave\n(2) Jacob is a knave\n(3) Lucas is a knave",
"statements": "(('<=>', ('lying', 1), ('telling-truth', 0)), ('and', ('telling-truth', 0), ('lying', 2)), ('and', ('telling-truth', 1), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 316,
"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, Matthew, and James. Liam noted, \"Liam is a knight\". Matthew was heard saying, \"Liam is a knave or James is a knight\". \"If Matthew is a knight then Liam is a knave,\" James 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 Liam is a knight. ",
"No contradiction is found in their claim that Liam is a knight.\n",
"Assume Matthew is a knight. ",
"No contradiction is found in their claim that Liam is a knave or James is a knight.\n",
"James cannot be a knight, because this would contradict the claim of their own that If Matthew is a knight then Liam is a knave.\n",
"James cannot be a knave, because this would contradict the claim of Matthew that Liam is a knave or James is a knight.\n",
"We have exhausted all possibilities for James, so let us go back and reconsider Matthew.\n",
"Assume Matthew is a knave. ",
"No contradiction is found in their false claim that Liam is a knave or James is a knight.\n",
"James cannot be a knight, because this would contradict the false claim of Matthew that Liam is a knave or James is a knight.\n",
"James cannot be a knave, because this would contradict the false claim of their own that If Matthew is a knight then Liam is a knave.\n",
"We have exhausted all possibilities for James and Matthew, so let us go back and reconsider Liam.\n",
"Assume Liam is a knave. ",
"No contradiction is found in their false claim that Liam is a knight.\n",
"Assume Matthew is a knight. ",
"No contradiction is found in their claim that Liam is a knave or James is a knight.\n",
"Assume James is a knight. ",
"No contradiction is found in their claim that If Matthew is a knight then Liam is a knave.\n",
"Therefore, (1) Liam is a knave\n",
"(2) Matthew is a knight\n",
"(3) James 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, Matthew, and James. Liam noted, "Liam is a knight". Matthew was heard saying, "Liam is a knave or James is a knight". "If Matthew is a knight then Liam is a knave," James 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 Liam is a knight. No contradiction is found in their claim that Liam is a knight.
Assume Matthew is a knight. No contradiction is found in their claim that Liam is a knave or James is a knight.
James cannot be a knight, because this would contradict the claim of their own that If Matthew is a knight then Liam is a knave.
James cannot be a knave, because this would contradict the claim of Matthew that Liam is a knave or James is a knight.
We have exhausted all possibilities for James, so let us go back and reconsider Matthew.
Assume Matthew is a knave. No contradiction is found in their false claim that Liam is a knave or James is a knight.
James cannot be a knight, because this would contradict the false claim of Matthew that Liam is a knave or James is a knight.
James cannot be a knave, because this would contradict the false claim of their own that If Matthew is a knight then Liam is a knave.
We have exhausted all possibilities for James and Matthew, so let us go back and reconsider Liam.
Assume Liam is a knave. No contradiction is found in their false claim that Liam is a knight.
Assume Matthew is a knight. No contradiction is found in their claim that Liam is a knave or James is a knight.
Assume James is a knight. No contradiction is found in their claim that If Matthew is a knight then Liam is a knave.
Therefore, (1) Liam is a knave
(2) Matthew is a knight
(3) James is a knight </think>
<answer> (1) Liam is a knave
(2) Matthew is a knight
(3) James is a knight </answer> | math | {
"ground_truth": {
"names": [
"Liam",
"Matthew",
"James"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Liam is a knave\n(2) Matthew is a knight\n(3) James is a knight",
"statements": "(('telling-truth', 0), ('or', ('lying', 0), ('telling-truth', 2)), ('->', ('telling-truth', 1), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 317,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Emma, Chloe, and Ethan. \"If Chloe is a knave then Ethan is a knight,\" Emma declared. \"Emma is a knight or Ethan is a knight,\" Chloe declared. \"Chloe is a knave or Chloe is a knight,\" Ethan 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 Emma is a knight. ",
"No contradiction is found in their claim that If Chloe is a knave then Ethan is a knight.\n",
"Assume Chloe is a knight. ",
"No contradiction is found in their claim that Emma is a knight or Ethan is a knight.\n",
"Assume Ethan is a knight. ",
"No contradiction is found in their claim that Chloe is a knave or Chloe is a knight.\n",
"Therefore, (1) Emma is a knight\n",
"(2) Chloe 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: Emma, Chloe, and Ethan. "If Chloe is a knave then Ethan is a knight," Emma declared. "Emma is a knight or Ethan is a knight," Chloe declared. "Chloe is a knave or Chloe is a knight," Ethan 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 Emma is a knight. No contradiction is found in their claim that If Chloe is a knave then Ethan is a knight.
Assume Chloe is a knight. No contradiction is found in their claim that Emma is a knight or Ethan is a knight.
Assume Ethan is a knight. No contradiction is found in their claim that Chloe is a knave or Chloe is a knight.
Therefore, (1) Emma is a knight
(2) Chloe is a knight
(3) Ethan is a knight </think>
<answer> (1) Emma is a knight
(2) Chloe is a knight
(3) Ethan is a knight </answer> | math | {
"ground_truth": {
"names": [
"Emma",
"Chloe",
"Ethan"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Emma is a knight\n(2) Chloe is a knight\n(3) Ethan is a knight",
"statements": "(('->', ('lying', 1), ('telling-truth', 2)), ('or', ('telling-truth', 0), ('telling-truth', 2)), ('or', ('lying', 1), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 318,
"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, Daniel, and Benjamin. Penelope said that Penelope is a knight. \"Penelope is a knight,\" Daniel claimed. According to Benjamin, \"If Benjamin is a knight then Daniel is a knave\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Penelope is a knight. ",
"No contradiction is found in their claim that Penelope is a knight.\n",
"Assume Daniel is a knight. ",
"No contradiction is found in their claim that Penelope is a knight.\n",
"Benjamin cannot be a knight, because this would contradict the claim of their own that If Benjamin is a knight then Daniel is a knave.\n",
"Benjamin cannot be a knave, because this would contradict the false claim of their own that If Benjamin is a knight then Daniel is a knave.\n",
"We have exhausted all possibilities for Benjamin, so let us go back and reconsider Daniel.\n",
"Daniel cannot be a knave, because this would contradict the false claim of their own that Penelope is a knight.\n",
"We have exhausted all possibilities for Daniel, 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.\n",
"Daniel cannot be a knight, because this would contradict the claim of their own that Penelope is a knight.\n",
"Assume Daniel is a knave. ",
"No contradiction is found in their false claim that Penelope is a knight.\n",
"Assume Benjamin is a knight. ",
"No contradiction is found in their claim that If Benjamin is a knight then Daniel is a knave.\n",
"Therefore, (1) Penelope is a knave\n",
"(2) Daniel is a knave\n",
"(3) Benjamin is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Penelope, Daniel, and Benjamin. Penelope said that Penelope is a knight. "Penelope is a knight," Daniel claimed. According to Benjamin, "If Benjamin is a knight then Daniel is a knave". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Penelope is a knight. No contradiction is found in their claim that Penelope is a knight.
Assume Daniel is a knight. No contradiction is found in their claim that Penelope is a knight.
Benjamin cannot be a knight, because this would contradict the claim of their own that If Benjamin is a knight then Daniel is a knave.
Benjamin cannot be a knave, because this would contradict the false claim of their own that If Benjamin is a knight then Daniel is a knave.
We have exhausted all possibilities for Benjamin, so let us go back and reconsider Daniel.
Daniel cannot be a knave, because this would contradict the false claim of their own that Penelope is a knight.
We have exhausted all possibilities for Daniel, 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.
Daniel cannot be a knight, because this would contradict the claim of their own that Penelope is a knight.
Assume Daniel is a knave. No contradiction is found in their false claim that Penelope is a knight.
Assume Benjamin is a knight. No contradiction is found in their claim that If Benjamin is a knight then Daniel is a knave.
Therefore, (1) Penelope is a knave
(2) Daniel is a knave
(3) Benjamin is a knight </think>
<answer> (1) Penelope is a knave
(2) Daniel is a knave
(3) Benjamin is a knight </answer> | math | {
"ground_truth": {
"names": [
"Penelope",
"Daniel",
"Benjamin"
],
"solution": [
false,
false,
true
],
"solution_text_format": "(1) Penelope is a knave\n(2) Daniel is a knave\n(3) Benjamin is a knight",
"statements": "(('telling-truth', 0), ('telling-truth', 0), ('->', ('telling-truth', 2), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 319,
"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, Samuel, and Ava. \"Ava is a knight,\" Olivia mentioned. In Samuel's words: \"Samuel is a knight and Ava is a knight\". Ava stated, \"Samuel is a knight and Samuel is a knave\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Olivia is a knight. ",
"No contradiction is found in their claim that Ava is a knight.\n",
"Ava cannot be a knight, because this would contradict the claim of their own that Samuel is a knight and Samuel is a knave.\n",
"Ava cannot be a knave, because this would contradict the claim of Olivia that Ava is a knight.\n",
"We have exhausted all possibilities for Ava, so let us go back and reconsider Olivia.\n",
"Assume Olivia is a knave. ",
"No contradiction is found in their false claim that Ava is a knight.\n",
"Ava cannot be a knight, because this would contradict the false claim of Olivia that Ava is a knight.\n",
"Assume Ava is a knave. ",
"No contradiction is found in their false claim that Samuel is a knight and Samuel is a knave.\n",
"Samuel cannot be a knight, because this would contradict the claim of their own that Samuel is a knight and Ava is a knight.\n",
"Assume Samuel is a knave. ",
"No contradiction is found in their false claim that Samuel is a knight and Ava is a knight.\n",
"Therefore, (1) Olivia is a knave\n",
"(2) Samuel is a knave\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: Olivia, Samuel, and Ava. "Ava is a knight," Olivia mentioned. In Samuel's words: "Samuel is a knight and Ava is a knight". Ava stated, "Samuel is a knight and Samuel is a knave". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Olivia is a knight. No contradiction is found in their claim that Ava is a knight.
Ava cannot be a knight, because this would contradict the claim of their own that Samuel is a knight and Samuel is a knave.
Ava cannot be a knave, because this would contradict the claim of Olivia that Ava is a knight.
We have exhausted all possibilities for Ava, so let us go back and reconsider Olivia.
Assume Olivia is a knave. No contradiction is found in their false claim that Ava is a knight.
Ava cannot be a knight, because this would contradict the false claim of Olivia that Ava is a knight.
Assume Ava is a knave. No contradiction is found in their false claim that Samuel is a knight and Samuel is a knave.
Samuel cannot be a knight, because this would contradict the claim of their own that Samuel is a knight and Ava is a knight.
Assume Samuel is a knave. No contradiction is found in their false claim that Samuel is a knight and Ava is a knight.
Therefore, (1) Olivia is a knave
(2) Samuel is a knave
(3) Ava is a knave </think>
<answer> (1) Olivia is a knave
(2) Samuel is a knave
(3) Ava is a knave </answer> | math | {
"ground_truth": {
"names": [
"Olivia",
"Samuel",
"Ava"
],
"solution": [
false,
false,
false
],
"solution_text_format": "(1) Olivia is a knave\n(2) Samuel is a knave\n(3) Ava is a knave",
"statements": "(('telling-truth', 2), ('and', ('telling-truth', 1), ('telling-truth', 2)), ('and', ('telling-truth', 1), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 320,
"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: Zoey, Aria, and Benjamin. \"Benjamin is not a knave,\" Zoey declared. Aria noted, \"Zoey is a knave\". Benjamin noted, \"Aria 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 Zoey is a knight. ",
"No contradiction is found in their claim that Benjamin is not a knave.\n",
"Assume Benjamin is a knight. ",
"No contradiction is found in their claim that Aria is a knight if and only if Zoey is a knave.\n",
"Aria cannot be a knight, because this would contradict the claim of their own that Zoey is a knave.\n",
"Assume Aria is a knave. ",
"No contradiction is found in their false claim that Zoey is a knave.\n",
"Therefore, (1) Zoey is a knight\n",
"(2) Aria is a knave\n",
"(3) Benjamin is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Zoey, Aria, and Benjamin. "Benjamin is not a knave," Zoey declared. Aria noted, "Zoey is a knave". Benjamin noted, "Aria 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 Zoey is a knight. No contradiction is found in their claim that Benjamin is not a knave.
Assume Benjamin is a knight. No contradiction is found in their claim that Aria is a knight if and only if Zoey is a knave.
Aria cannot be a knight, because this would contradict the claim of their own that Zoey is a knave.
Assume Aria is a knave. No contradiction is found in their false claim that Zoey is a knave.
Therefore, (1) Zoey is a knight
(2) Aria is a knave
(3) Benjamin is a knight </think>
<answer> (1) Zoey is a knight
(2) Aria is a knave
(3) Benjamin is a knight </answer> | math | {
"ground_truth": {
"names": [
"Zoey",
"Aria",
"Benjamin"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Zoey is a knight\n(2) Aria is a knave\n(3) Benjamin is a knight",
"statements": "(('not', ('lying', 2)), ('lying', 0), ('<=>', ('telling-truth', 1), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 321,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Matthew, Logan, and Joseph. \"Logan is a knave,\" Matthew mentioned. According to Logan, \"Joseph is a knight\". In a statement by Joseph: \"Logan is a knave and Joseph is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Matthew is a knight. ",
"No contradiction is found in their claim that Logan is a knave.\n",
"Logan cannot be a knight, because this would contradict the claim of Matthew that Logan is a knave.\n",
"Assume Logan is a knave. ",
"No contradiction is found in their false claim that Joseph is a knight.\n",
"Joseph cannot be a knight, because this would contradict the false claim of Logan that Joseph is a knight.\n",
"Assume Joseph is a knave. ",
"No contradiction is found in their false claim that Logan is a knave and Joseph is a knight.\n",
"Therefore, (1) Matthew is a knight\n",
"(2) Logan is a knave\n",
"(3) Joseph is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Matthew, Logan, and Joseph. "Logan is a knave," Matthew mentioned. According to Logan, "Joseph is a knight". In a statement by Joseph: "Logan is a knave and Joseph is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Matthew is a knight. No contradiction is found in their claim that Logan is a knave.
Logan cannot be a knight, because this would contradict the claim of Matthew that Logan is a knave.
Assume Logan is a knave. No contradiction is found in their false claim that Joseph is a knight.
Joseph cannot be a knight, because this would contradict the false claim of Logan that Joseph is a knight.
Assume Joseph is a knave. No contradiction is found in their false claim that Logan is a knave and Joseph is a knight.
Therefore, (1) Matthew is a knight
(2) Logan is a knave
(3) Joseph is a knave </think>
<answer> (1) Matthew is a knight
(2) Logan is a knave
(3) Joseph is a knave </answer> | math | {
"ground_truth": {
"names": [
"Matthew",
"Logan",
"Joseph"
],
"solution": [
true,
false,
false
],
"solution_text_format": "(1) Matthew is a knight\n(2) Logan is a knave\n(3) Joseph is a knave",
"statements": "(('lying', 1), ('telling-truth', 2), ('and', ('lying', 1), ('telling-truth', 2)))"
},
"style": "rule"
} | {
"index": 322,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Ava, Joseph, and Jackson. Ava said, \"Jackson is a knight if and only if Ava is a knight.\" Joseph asserted: \"Jackson is a knave or Ava is a knave\". In a statement by Jackson: \"Joseph is a knave and Ava 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 Ava is a knight. ",
"No contradiction is found in their claim that Jackson is a knight if and only if Ava is a knight.\n",
"Assume Jackson is a knight. ",
"No contradiction is found in their claim that Joseph is a knave and Ava is a knight.\n",
"Joseph cannot be a knight, because this would contradict the claim of their own that Jackson is a knave or Ava is a knave.\n",
"Assume Joseph is a knave. ",
"No contradiction is found in their false claim that Jackson is a knave or Ava is a knave.\n",
"Therefore, (1) Ava is a knight\n",
"(2) Joseph is a knave\n",
"(3) Jackson 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: Ava, Joseph, and Jackson. Ava said, "Jackson is a knight if and only if Ava is a knight." Joseph asserted: "Jackson is a knave or Ava is a knave". In a statement by Jackson: "Joseph is a knave and Ava 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 Ava is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Ava is a knight.
Assume Jackson is a knight. No contradiction is found in their claim that Joseph is a knave and Ava is a knight.
Joseph cannot be a knight, because this would contradict the claim of their own that Jackson is a knave or Ava is a knave.
Assume Joseph is a knave. No contradiction is found in their false claim that Jackson is a knave or Ava is a knave.
Therefore, (1) Ava is a knight
(2) Joseph is a knave
(3) Jackson is a knight </think>
<answer> (1) Ava is a knight
(2) Joseph is a knave
(3) Jackson is a knight </answer> | math | {
"ground_truth": {
"names": [
"Ava",
"Joseph",
"Jackson"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Ava is a knight\n(2) Joseph is a knave\n(3) Jackson is a knight",
"statements": "(('<=>', ('telling-truth', 2), ('telling-truth', 0)), ('or', ('lying', 2), ('lying', 0)), ('and', ('lying', 1), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 323,
"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, Abigail, and Zoey. \"Zoey is a knave if and only if Abigail is a knave,\" Penelope mentioned. Abigail asserted: \"Zoey is a knave if and only if Zoey is a knight\". \"Abigail is a knave if and only if Abigail is a knight,\" Zoey mentioned. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Penelope is a knight. ",
"No contradiction is found in their claim that Zoey is a knave if and only if Abigail is a knave.\n",
"Zoey cannot be a knight, because this would contradict the claim of their own that Abigail is a knave if and only if Abigail is a knight.\n",
"Assume Zoey is a knave. ",
"No contradiction is found in their false claim that Abigail is a knave if and only if Abigail is a knight.\n",
"Abigail cannot be a knight, because this would contradict the claim of Penelope that Zoey is a knave if and only if Abigail is a knave.\n",
"Assume Abigail is a knave. ",
"No contradiction is found in their false claim that Zoey is a knave if and only if Zoey is a knight.\n",
"Therefore, (1) Penelope is a knight\n",
"(2) Abigail 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: Penelope, Abigail, and Zoey. "Zoey is a knave if and only if Abigail is a knave," Penelope mentioned. Abigail asserted: "Zoey is a knave if and only if Zoey is a knight". "Abigail is a knave if and only if Abigail is a knight," Zoey mentioned. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Penelope is a knight. No contradiction is found in their claim that Zoey is a knave if and only if Abigail is a knave.
Zoey cannot be a knight, because this would contradict the claim of their own that Abigail is a knave if and only if Abigail is a knight.
Assume Zoey is a knave. No contradiction is found in their false claim that Abigail is a knave if and only if Abigail is a knight.
Abigail cannot be a knight, because this would contradict the claim of Penelope that Zoey is a knave if and only if Abigail is a knave.
Assume Abigail is a knave. No contradiction is found in their false claim that Zoey is a knave if and only if Zoey is a knight.
Therefore, (1) Penelope is a knight
(2) Abigail is a knave
(3) Zoey is a knave </think>
<answer> (1) Penelope is a knight
(2) Abigail is a knave
(3) Zoey is a knave </answer> | math | {
"ground_truth": {
"names": [
"Penelope",
"Abigail",
"Zoey"
],
"solution": [
true,
false,
false
],
"solution_text_format": "(1) Penelope is a knight\n(2) Abigail is a knave\n(3) Zoey is a knave",
"statements": "(('<=>', ('lying', 2), ('lying', 1)), ('<=>', ('lying', 2), ('telling-truth', 2)), ('<=>', ('lying', 1), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 324,
"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, Avery, and Henry. Owen commented, \"Avery is a knight\". In a statement by Avery: \"Henry is a knave if and only if Avery is a knight\". Henry said that 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 Avery is a knight.\n",
"Assume Avery is a knight. ",
"No contradiction is found in their claim that Henry is a knave if and only if Avery is a knight.\n",
"Henry cannot be a knight, because this would contradict the claim of Avery that Henry is a knave if and only if Avery is a knight.\n",
"Assume Henry 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) Avery is a knight\n",
"(3) Henry 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, Avery, and Henry. Owen commented, "Avery is a knight". In a statement by Avery: "Henry is a knave if and only if Avery is a knight". Henry said that 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 Avery is a knight.
Assume Avery is a knight. No contradiction is found in their claim that Henry is a knave if and only if Avery is a knight.
Henry cannot be a knight, because this would contradict the claim of Avery that Henry is a knave if and only if Avery is a knight.
Assume Henry 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) Avery is a knight
(3) Henry is a knave </think>
<answer> (1) Owen is a knight
(2) Avery is a knight
(3) Henry is a knave </answer> | math | {
"ground_truth": {
"names": [
"Owen",
"Avery",
"Henry"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Owen is a knight\n(2) Avery is a knight\n(3) Henry is a knave",
"statements": "(('telling-truth', 1), ('<=>', ('lying', 2), ('telling-truth', 1)), ('->', ('telling-truth', 0), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 325,
"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, Michael, and Samuel. Scarlett remarked, \"If Michael is a knave then Scarlett is a knight\". \"If Samuel is a knave then Scarlett is a knave,\" Michael mentioned. \"Samuel is a knight if and only if Michael is a knave,\" Samuel mentioned. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Scarlett is a knight. ",
"No contradiction is found in their claim that If Michael is a knave then Scarlett is a knight.\n",
"Assume Michael is a knight. ",
"No contradiction is found in their claim that If Samuel is a knave then Scarlett is a knave.\n",
"Samuel cannot be a knight, because this would contradict the claim of their own that Samuel is a knight if and only if Michael is a knave.\n",
"Samuel cannot be a knave, because this would contradict the claim of Michael that If Samuel is a knave then Scarlett is a knave.\n",
"We have exhausted all possibilities for Samuel, so let us go back and reconsider Michael.\n",
"Assume Michael is a knave. ",
"No contradiction is found in their false claim that If Samuel is a knave then Scarlett is a knave.\n",
"Samuel cannot be a knight, because this would contradict the false claim of Michael that If Samuel is a knave then Scarlett is a knave.\n",
"Assume Samuel is a knave. ",
"No contradiction is found in their false claim that Samuel is a knight if and only if Michael is a knave.\n",
"Therefore, (1) Scarlett is a knight\n",
"(2) Michael is a knave\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: Scarlett, Michael, and Samuel. Scarlett remarked, "If Michael is a knave then Scarlett is a knight". "If Samuel is a knave then Scarlett is a knave," Michael mentioned. "Samuel is a knight if and only if Michael is a knave," Samuel mentioned. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Scarlett is a knight. No contradiction is found in their claim that If Michael is a knave then Scarlett is a knight.
Assume Michael is a knight. No contradiction is found in their claim that If Samuel is a knave then Scarlett is a knave.
Samuel cannot be a knight, because this would contradict the claim of their own that Samuel is a knight if and only if Michael is a knave.
Samuel cannot be a knave, because this would contradict the claim of Michael that If Samuel is a knave then Scarlett is a knave.
We have exhausted all possibilities for Samuel, so let us go back and reconsider Michael.
Assume Michael is a knave. No contradiction is found in their false claim that If Samuel is a knave then Scarlett is a knave.
Samuel cannot be a knight, because this would contradict the false claim of Michael that If Samuel is a knave then Scarlett is a knave.
Assume Samuel is a knave. No contradiction is found in their false claim that Samuel is a knight if and only if Michael is a knave.
Therefore, (1) Scarlett is a knight
(2) Michael is a knave
(3) Samuel is a knave </think>
<answer> (1) Scarlett is a knight
(2) Michael is a knave
(3) Samuel is a knave </answer> | math | {
"ground_truth": {
"names": [
"Scarlett",
"Michael",
"Samuel"
],
"solution": [
true,
false,
false
],
"solution_text_format": "(1) Scarlett is a knight\n(2) Michael is a knave\n(3) Samuel is a knave",
"statements": "(('->', ('lying', 1), ('telling-truth', 0)), ('->', ('lying', 2), ('lying', 0)), ('<=>', ('telling-truth', 2), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 326,
"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, Liam, and Henry. Lucas said, \"Liam is not a knight.\" Liam noted, \"Henry is a knight\". Henry commented, \"Liam 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 Lucas is a knight. ",
"No contradiction is found in their claim that Liam is not a knight.\n",
"Liam cannot be a knight, because this would contradict the claim of Lucas that Liam is not a knight.\n",
"Assume Liam 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 Liam that Henry is a knight.\n",
"Henry cannot be a knave, because this would contradict the false claim of their own that Liam is a knave if and only if Lucas is a knight.\n",
"We have exhausted all possibilities for Henry and Liam, so let us go back and reconsider Lucas.\n",
"Assume Lucas is a knave. ",
"No contradiction is found in their false claim that Liam is not a knight.\n",
"Assume Liam is a knight. ",
"No contradiction is found in their claim that Henry is a knight.\n",
"Assume Henry is a knight. ",
"No contradiction is found in their claim that Liam is a knave if and only if Lucas is a knight.\n",
"Therefore, (1) Lucas is a knave\n",
"(2) Liam 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: Lucas, Liam, and Henry. Lucas said, "Liam is not a knight." Liam noted, "Henry is a knight". Henry commented, "Liam 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 Lucas is a knight. No contradiction is found in their claim that Liam is not a knight.
Liam cannot be a knight, because this would contradict the claim of Lucas that Liam is not a knight.
Assume Liam 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 Liam that Henry is a knight.
Henry cannot be a knave, because this would contradict the false claim of their own that Liam is a knave if and only if Lucas is a knight.
We have exhausted all possibilities for Henry and Liam, so let us go back and reconsider Lucas.
Assume Lucas is a knave. No contradiction is found in their false claim that Liam is not a knight.
Assume Liam is a knight. No contradiction is found in their claim that Henry is a knight.
Assume Henry is a knight. No contradiction is found in their claim that Liam is a knave if and only if Lucas is a knight.
Therefore, (1) Lucas is a knave
(2) Liam is a knight
(3) Henry is a knight </think>
<answer> (1) Lucas is a knave
(2) Liam is a knight
(3) Henry is a knight </answer> | math | {
"ground_truth": {
"names": [
"Lucas",
"Liam",
"Henry"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Lucas is a knave\n(2) Liam is a knight\n(3) Henry is a knight",
"statements": "(('not', ('telling-truth', 1)), ('telling-truth', 2), ('<=>', ('lying', 1), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 327,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Emma, Avery, and Liam. Emma was heard saying, \"Emma is a knight if and only if Avery is a knave\". Avery asserted: \"Emma is a knight if and only if Liam is a knave\". Liam noted, \"If Avery is a knight then Liam is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Emma is a knight. ",
"No contradiction is found in their claim that Emma is a knight if and only if Avery is a knave.\n",
"Avery cannot be a knight, because this would contradict the claim of Emma that Emma is a knight if and only if Avery is a knave.\n",
"Assume Avery is a knave. ",
"No contradiction is found in their false claim that Emma is a knight if and only if Liam is a knave.\n",
"Assume Liam is a knight. ",
"No contradiction is found in their claim that If Avery is a knight then Liam is a knight.\n",
"Therefore, (1) Emma is a knight\n",
"(2) Avery is a knave\n",
"(3) Liam is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Emma, Avery, and Liam. Emma was heard saying, "Emma is a knight if and only if Avery is a knave". Avery asserted: "Emma is a knight if and only if Liam is a knave". Liam noted, "If Avery is a knight then Liam is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Emma is a knight. No contradiction is found in their claim that Emma is a knight if and only if Avery is a knave.
Avery cannot be a knight, because this would contradict the claim of Emma that Emma is a knight if and only if Avery is a knave.
Assume Avery is a knave. No contradiction is found in their false claim that Emma is a knight if and only if Liam is a knave.
Assume Liam is a knight. No contradiction is found in their claim that If Avery is a knight then Liam is a knight.
Therefore, (1) Emma is a knight
(2) Avery is a knave
(3) Liam is a knight </think>
<answer> (1) Emma is a knight
(2) Avery is a knave
(3) Liam is a knight </answer> | math | {
"ground_truth": {
"names": [
"Emma",
"Avery",
"Liam"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Emma is a knight\n(2) Avery is a knave\n(3) Liam is a knight",
"statements": "(('<=>', ('telling-truth', 0), ('lying', 1)), ('<=>', ('telling-truth', 0), ('lying', 2)), ('->', ('telling-truth', 1), ('telling-truth', 2)))"
},
"style": "rule"
} | {
"index": 328,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Matthew, Logan, and Scarlett. \"Scarlett is a knave,\" Matthew declared. Logan said, \"Matthew is a knave if and only if Scarlett is a knight.\" \"Logan is a knight if and only if Logan is a knave\" - Scarlett. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Matthew is a knight. ",
"No contradiction is found in their claim that Scarlett is a knave.\n",
"Scarlett cannot be a knight, because this would contradict the claim of Matthew that Scarlett is a knave.\n",
"Assume Scarlett is a knave. ",
"No contradiction is found in their false claim that Logan is a knight if and only if Logan is a knave.\n",
"Assume Logan is a knight. ",
"No contradiction is found in their claim that Matthew is a knave if and only if Scarlett is a knight.\n",
"Therefore, (1) Matthew is a knight\n",
"(2) Logan is a knight\n",
"(3) Scarlett is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Matthew, Logan, and Scarlett. "Scarlett is a knave," Matthew declared. Logan said, "Matthew is a knave if and only if Scarlett is a knight." "Logan is a knight if and only if Logan is a knave" - Scarlett. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Matthew is a knight. No contradiction is found in their claim that Scarlett is a knave.
Scarlett cannot be a knight, because this would contradict the claim of Matthew that Scarlett is a knave.
Assume Scarlett is a knave. No contradiction is found in their false claim that Logan is a knight if and only if Logan is a knave.
Assume Logan is a knight. No contradiction is found in their claim that Matthew is a knave if and only if Scarlett is a knight.
Therefore, (1) Matthew is a knight
(2) Logan is a knight
(3) Scarlett is a knave </think>
<answer> (1) Matthew is a knight
(2) Logan is a knight
(3) Scarlett is a knave </answer> | math | {
"ground_truth": {
"names": [
"Matthew",
"Logan",
"Scarlett"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Matthew is a knight\n(2) Logan is a knight\n(3) Scarlett is a knave",
"statements": "(('lying', 2), ('<=>', ('lying', 0), ('telling-truth', 2)), ('<=>', ('telling-truth', 1), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 329,
"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, Olivia, and William. As Luke put it, \"Luke is a knight if and only if William is a knight\". Olivia told you that William is a knave. William commented, \"If Luke is a knave then Olivia 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 Luke is a knight. ",
"No contradiction is found in their claim that Luke is a knight if and only if William is a knight.\n",
"Assume William is a knight. ",
"No contradiction is found in their claim that If Luke is a knave then Olivia is a knight.\n",
"Olivia cannot be a knight, because this would contradict the claim of their own that William is a knave.\n",
"Assume Olivia is a knave. ",
"No contradiction is found in their false claim that William is a knave.\n",
"Therefore, (1) Luke is a knight\n",
"(2) Olivia is a knave\n",
"(3) William 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, Olivia, and William. As Luke put it, "Luke is a knight if and only if William is a knight". Olivia told you that William is a knave. William commented, "If Luke is a knave then Olivia 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 Luke is a knight. No contradiction is found in their claim that Luke is a knight if and only if William is a knight.
Assume William is a knight. No contradiction is found in their claim that If Luke is a knave then Olivia is a knight.
Olivia cannot be a knight, because this would contradict the claim of their own that William is a knave.
Assume Olivia is a knave. No contradiction is found in their false claim that William is a knave.
Therefore, (1) Luke is a knight
(2) Olivia is a knave
(3) William is a knight </think>
<answer> (1) Luke is a knight
(2) Olivia is a knave
(3) William is a knight </answer> | math | {
"ground_truth": {
"names": [
"Luke",
"Olivia",
"William"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Luke is a knight\n(2) Olivia is a knave\n(3) William is a knight",
"statements": "(('<=>', ('telling-truth', 0), ('telling-truth', 2)), ('lying', 2), ('->', ('lying', 0), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 330,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Emma, Mia, and Olivia. In Emma's words: \"Olivia is a knight or Emma is a knight\". Mia expressed that Emma is a knight or Olivia is a knight. As Olivia put it, \"Emma is a knave or Mia is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Emma is a knight. ",
"No contradiction is found in their claim that Olivia is a knight or Emma is a knight.\n",
"Assume Olivia is a knight. ",
"No contradiction is found in their claim that Emma is a knave or Mia is a knight.\n",
"Assume Mia is a knight. ",
"No contradiction is found in their claim that Emma is a knight or Olivia is a knight.\n",
"Therefore, (1) Emma is a knight\n",
"(2) Mia is a knight\n",
"(3) Olivia is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Emma, Mia, and Olivia. In Emma's words: "Olivia is a knight or Emma is a knight". Mia expressed that Emma is a knight or Olivia is a knight. As Olivia put it, "Emma is a knave or Mia is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Emma is a knight. No contradiction is found in their claim that Olivia is a knight or Emma is a knight.
Assume Olivia is a knight. No contradiction is found in their claim that Emma is a knave or Mia is a knight.
Assume Mia is a knight. No contradiction is found in their claim that Emma is a knight or Olivia is a knight.
Therefore, (1) Emma is a knight
(2) Mia is a knight
(3) Olivia is a knight </think>
<answer> (1) Emma is a knight
(2) Mia is a knight
(3) Olivia is a knight </answer> | math | {
"ground_truth": {
"names": [
"Emma",
"Mia",
"Olivia"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Emma is a knight\n(2) Mia is a knight\n(3) Olivia is a knight",
"statements": "(('or', ('telling-truth', 2), ('telling-truth', 0)), ('or', ('telling-truth', 0), ('telling-truth', 2)), ('or', ('lying', 0), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 331,
"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, Mia, and William. \"William is a knave if and only if William is a knight,\" Sebastian claimed. Mia asserted: \"Sebastian is a knave and Sebastian is a knight\". William noted, \"If Sebastian is a knight then William 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"
}
]
| [
"Sebastian cannot be a knight, because this would contradict the claim of their own that William is a knave if and only if William is a knight.\n",
"Assume Sebastian is a knave. ",
"No contradiction is found in their false claim that William is a knave if and only if William is a knight.\n",
"Assume William is a knight. ",
"No contradiction is found in their claim that If Sebastian is a knight then William is a knight.\n",
"Mia cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave and Sebastian is a knight.\n",
"Assume Mia is a knave. ",
"No contradiction is found in their false claim that Sebastian is a knave and Sebastian is a knight.\n",
"Therefore, (1) Sebastian is a knave\n",
"(2) Mia is a knave\n",
"(3) William 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, Mia, and William. "William is a knave if and only if William is a knight," Sebastian claimed. Mia asserted: "Sebastian is a knave and Sebastian is a knight". William noted, "If Sebastian is a knight then William 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> | Sebastian cannot be a knight, because this would contradict the claim of their own that William is a knave if and only if William is a knight.
Assume Sebastian is a knave. No contradiction is found in their false claim that William is a knave if and only if William is a knight.
Assume William is a knight. No contradiction is found in their claim that If Sebastian is a knight then William is a knight.
Mia cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave and Sebastian is a knight.
Assume Mia is a knave. No contradiction is found in their false claim that Sebastian is a knave and Sebastian is a knight.
Therefore, (1) Sebastian is a knave
(2) Mia is a knave
(3) William is a knight </think>
<answer> (1) Sebastian is a knave
(2) Mia is a knave
(3) William is a knight </answer> | math | {
"ground_truth": {
"names": [
"Sebastian",
"Mia",
"William"
],
"solution": [
false,
false,
true
],
"solution_text_format": "(1) Sebastian is a knave\n(2) Mia is a knave\n(3) William is a knight",
"statements": "(('<=>', ('lying', 2), ('telling-truth', 2)), ('and', ('lying', 0), ('telling-truth', 0)), ('->', ('telling-truth', 0), ('telling-truth', 2)))"
},
"style": "rule"
} | {
"index": 332,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Samuel, Daniel, and Olivia. Samuel said that Samuel is a knight and Olivia is a knight. \"Samuel is a knight or Samuel is a knave,\" Daniel mentioned. According to Olivia, \"Daniel 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 Samuel is a knight. ",
"No contradiction is found in their claim that Samuel is a knight and Olivia is a knight.\n",
"Assume Olivia is a knight. ",
"No contradiction is found in their claim that Daniel is not a knight.\n",
"Daniel cannot be a knight, because this would contradict the claim of Olivia that Daniel is not a knight.\n",
"Daniel cannot be a knave, because this would contradict the false claim of their own that Samuel is a knight or Samuel is a knave.\n",
"We have exhausted all possibilities for Daniel, so let us go back and reconsider Olivia.\n",
"Olivia cannot be a knave, because this would contradict the claim of Samuel that Samuel is a knight and Olivia is a knight.\n",
"We have exhausted all possibilities for Olivia, so let us go back and reconsider Samuel.\n",
"Assume Samuel is a knave. ",
"No contradiction is found in their false claim that Samuel is a knight and Olivia is a knight.\n",
"Assume Olivia is a knight. ",
"No contradiction is found in their claim that Daniel is not a knight.\n",
"Daniel cannot be a knight, because this would contradict the claim of Olivia that Daniel is not a knight.\n",
"Daniel cannot be a knave, because this would contradict the false claim of their own that Samuel is a knight or Samuel is a knave.\n",
"We have exhausted all possibilities for Daniel, so let us go back and reconsider Olivia.\n",
"Assume Olivia is a knave. ",
"No contradiction is found in their false claim that Daniel is not a knight.\n",
"Assume Daniel is a knight. ",
"No contradiction is found in their claim that Samuel is a knight or Samuel is a knave.\n",
"Therefore, (1) Samuel is a knave\n",
"(2) Daniel is a knight\n",
"(3) Olivia is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Samuel, Daniel, and Olivia. Samuel said that Samuel is a knight and Olivia is a knight. "Samuel is a knight or Samuel is a knave," Daniel mentioned. According to Olivia, "Daniel 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 Samuel is a knight. No contradiction is found in their claim that Samuel is a knight and Olivia is a knight.
Assume Olivia is a knight. No contradiction is found in their claim that Daniel is not a knight.
Daniel cannot be a knight, because this would contradict the claim of Olivia that Daniel is not a knight.
Daniel cannot be a knave, because this would contradict the false claim of their own that Samuel is a knight or Samuel is a knave.
We have exhausted all possibilities for Daniel, so let us go back and reconsider Olivia.
Olivia cannot be a knave, because this would contradict the claim of Samuel that Samuel is a knight and Olivia is a knight.
We have exhausted all possibilities for Olivia, so let us go back and reconsider Samuel.
Assume Samuel is a knave. No contradiction is found in their false claim that Samuel is a knight and Olivia is a knight.
Assume Olivia is a knight. No contradiction is found in their claim that Daniel is not a knight.
Daniel cannot be a knight, because this would contradict the claim of Olivia that Daniel is not a knight.
Daniel cannot be a knave, because this would contradict the false claim of their own that Samuel is a knight or Samuel is a knave.
We have exhausted all possibilities for Daniel, so let us go back and reconsider Olivia.
Assume Olivia is a knave. No contradiction is found in their false claim that Daniel is not a knight.
Assume Daniel is a knight. No contradiction is found in their claim that Samuel is a knight or Samuel is a knave.
Therefore, (1) Samuel is a knave
(2) Daniel is a knight
(3) Olivia is a knave </think>
<answer> (1) Samuel is a knave
(2) Daniel is a knight
(3) Olivia is a knave </answer> | math | {
"ground_truth": {
"names": [
"Samuel",
"Daniel",
"Olivia"
],
"solution": [
false,
true,
false
],
"solution_text_format": "(1) Samuel is a knave\n(2) Daniel is a knight\n(3) Olivia is a knave",
"statements": "(('and', ('telling-truth', 0), ('telling-truth', 2)), ('or', ('telling-truth', 0), ('lying', 0)), ('not', ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 333,
"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, Lucas, and Joseph. Grace asserted: \"Joseph is a knight\". Lucas said, \"Grace is a knight.\" Joseph expressed that Grace is a knight 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 Grace is a knight. ",
"No contradiction is found in their claim that Joseph is a knight.\n",
"Assume Joseph is a knight. ",
"No contradiction is found in their claim that Grace is a knight if and only if Lucas is a knight.\n",
"Assume Lucas is a knight. ",
"No contradiction is found in their claim that Grace is a knight.\n",
"Therefore, (1) Grace is a knight\n",
"(2) Lucas 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: Grace, Lucas, and Joseph. Grace asserted: "Joseph is a knight". Lucas said, "Grace is a knight." Joseph expressed that Grace is a knight 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 Grace is a knight. No contradiction is found in their claim that Joseph is a knight.
Assume Joseph is a knight. No contradiction is found in their claim that Grace is a knight if and only if Lucas is a knight.
Assume Lucas is a knight. No contradiction is found in their claim that Grace is a knight.
Therefore, (1) Grace is a knight
(2) Lucas is a knight
(3) Joseph is a knight </think>
<answer> (1) Grace is a knight
(2) Lucas is a knight
(3) Joseph is a knight </answer> | math | {
"ground_truth": {
"names": [
"Grace",
"Lucas",
"Joseph"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Grace is a knight\n(2) Lucas is a knight\n(3) Joseph is a knight",
"statements": "(('telling-truth', 2), ('telling-truth', 0), ('<=>', ('telling-truth', 0), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 334,
"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, Jacob, and Aria. Alexander said that Aria is not a knave. \"Aria is not a knave,\" Jacob claimed. \"Jacob is a knave if and only if Jacob is a knight\" - Aria. So who is a knight and who is a knave? 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 Aria is not a knave.\n",
"Aria cannot be a knight, because this would contradict the claim of their own that Jacob is a knave if and only if Jacob is a knight.\n",
"Aria cannot be a knave, because this would contradict the claim of Alexander that Aria is not a knave.\n",
"We have exhausted all possibilities for Aria, so let us go back and reconsider Alexander.\n",
"Assume Alexander is a knave. ",
"No contradiction is found in their false claim that Aria is not a knave.\n",
"Aria cannot be a knight, because this would contradict the false claim of Alexander that Aria is not a knave.\n",
"Assume Aria is a knave. ",
"No contradiction is found in their false claim that Jacob is a knave if and only if Jacob is a knight.\n",
"Jacob cannot be a knight, because this would contradict the claim of their own that Aria is not a knave.\n",
"Assume Jacob is a knave. ",
"No contradiction is found in their false claim that Aria is not a knave.\n",
"Therefore, (1) Alexander is a knave\n",
"(2) Jacob is a knave\n",
"(3) Aria is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Alexander, Jacob, and Aria. Alexander said that Aria is not a knave. "Aria is not a knave," Jacob claimed. "Jacob is a knave if and only if Jacob is a knight" - Aria. So who is a knight and who is a knave? 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 Aria is not a knave.
Aria cannot be a knight, because this would contradict the claim of their own that Jacob is a knave if and only if Jacob is a knight.
Aria cannot be a knave, because this would contradict the claim of Alexander that Aria is not a knave.
We have exhausted all possibilities for Aria, so let us go back and reconsider Alexander.
Assume Alexander is a knave. No contradiction is found in their false claim that Aria is not a knave.
Aria cannot be a knight, because this would contradict the false claim of Alexander that Aria is not a knave.
Assume Aria is a knave. No contradiction is found in their false claim that Jacob is a knave if and only if Jacob is a knight.
Jacob cannot be a knight, because this would contradict the claim of their own that Aria is not a knave.
Assume Jacob is a knave. No contradiction is found in their false claim that Aria is not a knave.
Therefore, (1) Alexander is a knave
(2) Jacob is a knave
(3) Aria is a knave </think>
<answer> (1) Alexander is a knave
(2) Jacob is a knave
(3) Aria is a knave </answer> | math | {
"ground_truth": {
"names": [
"Alexander",
"Jacob",
"Aria"
],
"solution": [
false,
false,
false
],
"solution_text_format": "(1) Alexander is a knave\n(2) Jacob is a knave\n(3) Aria is a knave",
"statements": "(('not', ('lying', 2)), ('not', ('lying', 2)), ('<=>', ('lying', 1), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 335,
"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, Grace, and William. \"William is a knave and William is a knight\" - Luke. Grace asserted: \"Luke is a knight\". William noted, \"Luke 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"
}
]
| [
"Luke cannot be a knight, because this would contradict the claim of their own that William is a knave and William is a knight.\n",
"Assume Luke is a knave. ",
"No contradiction is found in their false claim that William is a knave and William is a knight.\n",
"Assume William is a knight. ",
"No contradiction is found in their claim that Luke is not a knight.\n",
"Grace cannot be a knight, because this would contradict the claim of their own that Luke is a knight.\n",
"Assume Grace is a knave. ",
"No contradiction is found in their false claim that Luke is a knight.\n",
"Therefore, (1) Luke is a knave\n",
"(2) Grace is a knave\n",
"(3) William 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, Grace, and William. "William is a knave and William is a knight" - Luke. Grace asserted: "Luke is a knight". William noted, "Luke 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> | Luke cannot be a knight, because this would contradict the claim of their own that William is a knave and William is a knight.
Assume Luke is a knave. No contradiction is found in their false claim that William is a knave and William is a knight.
Assume William is a knight. No contradiction is found in their claim that Luke is not a knight.
Grace cannot be a knight, because this would contradict the claim of their own that Luke is a knight.
Assume Grace is a knave. No contradiction is found in their false claim that Luke is a knight.
Therefore, (1) Luke is a knave
(2) Grace is a knave
(3) William is a knight </think>
<answer> (1) Luke is a knave
(2) Grace is a knave
(3) William is a knight </answer> | math | {
"ground_truth": {
"names": [
"Luke",
"Grace",
"William"
],
"solution": [
false,
false,
true
],
"solution_text_format": "(1) Luke is a knave\n(2) Grace is a knave\n(3) William is a knight",
"statements": "(('and', ('lying', 2), ('telling-truth', 2)), ('telling-truth', 0), ('not', ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 336,
"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, Daniel, and Zoey. Charlotte stated, \"Zoey is a knight or Zoey is a knave\". \"If Charlotte is a knave then Zoey is a knave,\" Daniel declared. Zoey noted, \"Charlotte 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 Charlotte is a knight. ",
"No contradiction is found in their claim that Zoey is a knight or Zoey is a knave.\n",
"Zoey cannot be a knight, because this would contradict the claim of their own that Charlotte is not a knight.\n",
"Assume Zoey is a knave. ",
"No contradiction is found in their false claim that Charlotte is not a knight.\n",
"Assume Daniel is a knight. ",
"No contradiction is found in their claim that If Charlotte is a knave then Zoey is a knave.\n",
"Therefore, (1) Charlotte is a knight\n",
"(2) Daniel is a knight\n",
"(3) Zoey is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Charlotte, Daniel, and Zoey. Charlotte stated, "Zoey is a knight or Zoey is a knave". "If Charlotte is a knave then Zoey is a knave," Daniel declared. Zoey noted, "Charlotte 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 Charlotte is a knight. No contradiction is found in their claim that Zoey is a knight or Zoey is a knave.
Zoey cannot be a knight, because this would contradict the claim of their own that Charlotte is not a knight.
Assume Zoey is a knave. No contradiction is found in their false claim that Charlotte is not a knight.
Assume Daniel is a knight. No contradiction is found in their claim that If Charlotte is a knave then Zoey is a knave.
Therefore, (1) Charlotte is a knight
(2) Daniel is a knight
(3) Zoey is a knave </think>
<answer> (1) Charlotte is a knight
(2) Daniel is a knight
(3) Zoey is a knave </answer> | math | {
"ground_truth": {
"names": [
"Charlotte",
"Daniel",
"Zoey"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Charlotte is a knight\n(2) Daniel is a knight\n(3) Zoey is a knave",
"statements": "(('or', ('telling-truth', 2), ('lying', 2)), ('->', ('lying', 0), ('lying', 2)), ('not', ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 337,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Ella, Aurora, and Harper. According to Ella, \"Harper is a knave if and only if Aurora is a knight\". Aurora commented, \"Harper is not a knave\". Harper remarked, \"Ella is a knave if and only if Ella 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 Ella is a knight. ",
"No contradiction is found in their claim that Harper is a knave if and only if Aurora is a knight.\n",
"Harper cannot be a knight, because this would contradict the claim of their own that Ella is a knave if and only if Ella is a knight.\n",
"Assume Harper is a knave. ",
"No contradiction is found in their false claim that Ella is a knave if and only if Ella is a knight.\n",
"Aurora cannot be a knight, because this would contradict the claim of their own that Harper is not a knave.\n",
"Aurora cannot be a knave, because this would contradict the claim of Ella that Harper is a knave if and only if Aurora is a knight.\n",
"We have exhausted all possibilities for Aurora and Harper, so let us go back and reconsider Ella.\n",
"Assume Ella is a knave. ",
"No contradiction is found in their false claim that Harper is a knave if and only if Aurora is a knight.\n",
"Harper cannot be a knight, because this would contradict the claim of their own that Ella is a knave if and only if Ella is a knight.\n",
"Assume Harper is a knave. ",
"No contradiction is found in their false claim that Ella is a knave if and only if Ella is a knight.\n",
"Aurora cannot be a knight, because this would contradict the false claim of Ella that Harper is a knave if and only if Aurora is a knight.\n",
"Assume Aurora is a knave. ",
"No contradiction is found in their false claim that Harper is not a knave.\n",
"Therefore, (1) Ella is a knave\n",
"(2) Aurora is a knave\n",
"(3) Harper is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Ella, Aurora, and Harper. According to Ella, "Harper is a knave if and only if Aurora is a knight". Aurora commented, "Harper is not a knave". Harper remarked, "Ella is a knave if and only if Ella 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 Ella is a knight. No contradiction is found in their claim that Harper is a knave if and only if Aurora is a knight.
Harper cannot be a knight, because this would contradict the claim of their own that Ella is a knave if and only if Ella is a knight.
Assume Harper is a knave. No contradiction is found in their false claim that Ella is a knave if and only if Ella is a knight.
Aurora cannot be a knight, because this would contradict the claim of their own that Harper is not a knave.
Aurora cannot be a knave, because this would contradict the claim of Ella that Harper is a knave if and only if Aurora is a knight.
We have exhausted all possibilities for Aurora and Harper, so let us go back and reconsider Ella.
Assume Ella is a knave. No contradiction is found in their false claim that Harper is a knave if and only if Aurora is a knight.
Harper cannot be a knight, because this would contradict the claim of their own that Ella is a knave if and only if Ella is a knight.
Assume Harper is a knave. No contradiction is found in their false claim that Ella is a knave if and only if Ella is a knight.
Aurora cannot be a knight, because this would contradict the false claim of Ella that Harper is a knave if and only if Aurora is a knight.
Assume Aurora is a knave. No contradiction is found in their false claim that Harper is not a knave.
Therefore, (1) Ella is a knave
(2) Aurora is a knave
(3) Harper is a knave </think>
<answer> (1) Ella is a knave
(2) Aurora is a knave
(3) Harper is a knave </answer> | math | {
"ground_truth": {
"names": [
"Ella",
"Aurora",
"Harper"
],
"solution": [
false,
false,
false
],
"solution_text_format": "(1) Ella is a knave\n(2) Aurora is a knave\n(3) Harper is a knave",
"statements": "(('<=>', ('lying', 2), ('telling-truth', 1)), ('not', ('lying', 2)), ('<=>', ('lying', 0), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 338,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Chloe, Scarlett, and Charlotte. As Chloe put it, \"If Scarlett is a knight then Scarlett is a knave\". Scarlett commented, \"Scarlett is a knight or Charlotte is a knave\". Charlotte said that Chloe is a knave and Chloe is a knight. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Chloe is a knight. ",
"No contradiction is found in their claim that If Scarlett is a knight then Scarlett is a knave.\n",
"Scarlett cannot be a knight, because this would contradict the claim of Chloe that If Scarlett is a knight then Scarlett is a knave.\n",
"Assume Scarlett is a knave. ",
"No contradiction is found in their false claim that Scarlett is a knight or Charlotte is a knave.\n",
"Charlotte cannot be a knight, because this would contradict the claim of their own that Chloe is a knave and Chloe is a knight.\n",
"Charlotte cannot be a knave, because this would contradict the false claim of Scarlett that Scarlett is a knight or Charlotte is a knave.\n",
"We have exhausted all possibilities for Charlotte and Scarlett, so let us go back and reconsider Chloe.\n",
"Assume Chloe is a knave. ",
"No contradiction is found in their false claim that If Scarlett is a knight then Scarlett is a knave.\n",
"Assume Scarlett is a knight. ",
"No contradiction is found in their claim that Scarlett is a knight or Charlotte is a knave.\n",
"Charlotte cannot be a knight, because this would contradict the claim of their own that Chloe is a knave and Chloe is a knight.\n",
"Assume Charlotte is a knave. ",
"No contradiction is found in their false claim that Chloe is a knave and Chloe is a knight.\n",
"Therefore, (1) Chloe is a knave\n",
"(2) Scarlett 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: Chloe, Scarlett, and Charlotte. As Chloe put it, "If Scarlett is a knight then Scarlett is a knave". Scarlett commented, "Scarlett is a knight or Charlotte is a knave". Charlotte said that Chloe is a knave and Chloe is a knight. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Chloe is a knight. No contradiction is found in their claim that If Scarlett is a knight then Scarlett is a knave.
Scarlett cannot be a knight, because this would contradict the claim of Chloe that If Scarlett is a knight then Scarlett is a knave.
Assume Scarlett is a knave. No contradiction is found in their false claim that Scarlett is a knight or Charlotte is a knave.
Charlotte cannot be a knight, because this would contradict the claim of their own that Chloe is a knave and Chloe is a knight.
Charlotte cannot be a knave, because this would contradict the false claim of Scarlett that Scarlett is a knight or Charlotte is a knave.
We have exhausted all possibilities for Charlotte and Scarlett, so let us go back and reconsider Chloe.
Assume Chloe is a knave. No contradiction is found in their false claim that If Scarlett is a knight then Scarlett is a knave.
Assume Scarlett is a knight. No contradiction is found in their claim that Scarlett is a knight or Charlotte is a knave.
Charlotte cannot be a knight, because this would contradict the claim of their own that Chloe is a knave and Chloe is a knight.
Assume Charlotte is a knave. No contradiction is found in their false claim that Chloe is a knave and Chloe is a knight.
Therefore, (1) Chloe is a knave
(2) Scarlett is a knight
(3) Charlotte is a knave </think>
<answer> (1) Chloe is a knave
(2) Scarlett is a knight
(3) Charlotte is a knave </answer> | math | {
"ground_truth": {
"names": [
"Chloe",
"Scarlett",
"Charlotte"
],
"solution": [
false,
true,
false
],
"solution_text_format": "(1) Chloe is a knave\n(2) Scarlett is a knight\n(3) Charlotte is a knave",
"statements": "(('->', ('telling-truth', 1), ('lying', 1)), ('or', ('telling-truth', 1), ('lying', 2)), ('and', ('lying', 0), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 339,
"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, Grace, and Charlotte. Liam commented, \"If Grace is a knave then Charlotte is a knave\". \"Grace is a knight and Charlotte is a knave,\" Grace declared. Charlotte told you that If Grace is a knight then Liam is a knight. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Liam is a knight. ",
"No contradiction is found in their claim that If Grace is a knave then Charlotte is a knave.\n",
"Assume Grace is a knight. ",
"No contradiction is found in their claim that Grace is a knight and Charlotte is a knave.\n",
"Charlotte cannot be a knight, because this would contradict the claim of Grace that Grace is a knight and Charlotte is a knave.\n",
"Charlotte cannot be a knave, because this would contradict the false claim of their own that If Grace is a knight then Liam is a knight.\n",
"We have exhausted all possibilities for Charlotte, so let us go back and reconsider Grace.\n",
"Assume Grace is a knave. ",
"No contradiction is found in their false claim that Grace is a knight and Charlotte is a knave.\n",
"Charlotte cannot be a knight, because this would contradict the claim of Liam that If Grace is a knave then Charlotte is a knave.\n",
"Charlotte cannot be a knave, because this would contradict the false claim of their own that If Grace is a knight then Liam is a knight.\n",
"We have exhausted all possibilities for Charlotte and Grace, so let us go back and reconsider Liam.\n",
"Assume Liam is a knave. ",
"No contradiction is found in their false claim that If Grace is a knave then Charlotte is a knave.\n",
"Grace cannot be a knight, because this would contradict the false claim of Liam that If Grace is a knave then Charlotte is a knave.\n",
"Assume Grace is a knave. ",
"No contradiction is found in their false claim that Grace is a knight and Charlotte is a knave.\n",
"Assume Charlotte is a knight. ",
"No contradiction is found in their claim that If Grace is a knight then Liam is a knight.\n",
"Therefore, (1) Liam is a knave\n",
"(2) Grace 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: Liam, Grace, and Charlotte. Liam commented, "If Grace is a knave then Charlotte is a knave". "Grace is a knight and Charlotte is a knave," Grace declared. Charlotte told you that If Grace is a knight then Liam is a knight. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Liam is a knight. No contradiction is found in their claim that If Grace is a knave then Charlotte is a knave.
Assume Grace is a knight. No contradiction is found in their claim that Grace is a knight and Charlotte is a knave.
Charlotte cannot be a knight, because this would contradict the claim of Grace that Grace is a knight and Charlotte is a knave.
Charlotte cannot be a knave, because this would contradict the false claim of their own that If Grace is a knight then Liam is a knight.
We have exhausted all possibilities for Charlotte, so let us go back and reconsider Grace.
Assume Grace is a knave. No contradiction is found in their false claim that Grace is a knight and Charlotte is a knave.
Charlotte cannot be a knight, because this would contradict the claim of Liam that If Grace is a knave then Charlotte is a knave.
Charlotte cannot be a knave, because this would contradict the false claim of their own that If Grace is a knight then Liam is a knight.
We have exhausted all possibilities for Charlotte and Grace, so let us go back and reconsider Liam.
Assume Liam is a knave. No contradiction is found in their false claim that If Grace is a knave then Charlotte is a knave.
Grace cannot be a knight, because this would contradict the false claim of Liam that If Grace is a knave then Charlotte is a knave.
Assume Grace is a knave. No contradiction is found in their false claim that Grace is a knight and Charlotte is a knave.
Assume Charlotte is a knight. No contradiction is found in their claim that If Grace is a knight then Liam is a knight.
Therefore, (1) Liam is a knave
(2) Grace is a knave
(3) Charlotte is a knight </think>
<answer> (1) Liam is a knave
(2) Grace is a knave
(3) Charlotte is a knight </answer> | math | {
"ground_truth": {
"names": [
"Liam",
"Grace",
"Charlotte"
],
"solution": [
false,
false,
true
],
"solution_text_format": "(1) Liam is a knave\n(2) Grace is a knave\n(3) Charlotte is a knight",
"statements": "(('->', ('lying', 1), ('lying', 2)), ('and', ('telling-truth', 1), ('lying', 2)), ('->', ('telling-truth', 1), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 340,
"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, Evelyn, and Emma. Olivia said that Emma is a knave or Evelyn is a knave. \"Emma is not a knight\" - Evelyn. According to Emma, \"If Olivia is a knight then Olivia 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 Olivia is a knight. ",
"No contradiction is found in their claim that Emma is a knave or Evelyn is a knave.\n",
"Emma cannot be a knight, because this would contradict the claim of their own that If Olivia is a knight then Olivia is a knave.\n",
"Assume Emma is a knave. ",
"No contradiction is found in their false claim that If Olivia is a knight then Olivia is a knave.\n",
"Assume Evelyn is a knight. ",
"No contradiction is found in their claim that Emma is not a knight.\n",
"Therefore, (1) Olivia is a knight\n",
"(2) Evelyn is a knight\n",
"(3) Emma is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Olivia, Evelyn, and Emma. Olivia said that Emma is a knave or Evelyn is a knave. "Emma is not a knight" - Evelyn. According to Emma, "If Olivia is a knight then Olivia 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 Olivia is a knight. No contradiction is found in their claim that Emma is a knave or Evelyn is a knave.
Emma cannot be a knight, because this would contradict the claim of their own that If Olivia is a knight then Olivia is a knave.
Assume Emma is a knave. No contradiction is found in their false claim that If Olivia is a knight then Olivia is a knave.
Assume Evelyn is a knight. No contradiction is found in their claim that Emma is not a knight.
Therefore, (1) Olivia is a knight
(2) Evelyn is a knight
(3) Emma is a knave </think>
<answer> (1) Olivia is a knight
(2) Evelyn is a knight
(3) Emma is a knave </answer> | math | {
"ground_truth": {
"names": [
"Olivia",
"Evelyn",
"Emma"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Olivia is a knight\n(2) Evelyn is a knight\n(3) Emma is a knave",
"statements": "(('or', ('lying', 2), ('lying', 1)), ('not', ('telling-truth', 2)), ('->', ('telling-truth', 0), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 341,
"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, Daniel, and Sophia. Harper commented, \"If Daniel is a knight then Sophia is a knave\". In Daniel's words: \"Sophia is a knight\". Sophia asserted: \"If Sophia is a knight then Daniel 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 If Daniel is a knight then Sophia is a knave.\n",
"Assume Daniel is a knight. ",
"No contradiction is found in their claim that Sophia is a knight.\n",
"Sophia cannot be a knight, because this would contradict the claim of Harper that If Daniel is a knight then Sophia is a knave.\n",
"Sophia cannot be a knave, because this would contradict the claim of Daniel that Sophia is a knight.\n",
"We have exhausted all possibilities for Sophia, so let us go back and reconsider Daniel.\n",
"Assume Daniel 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 Daniel that Sophia is a knight.\n",
"Sophia cannot be a knave, because this would contradict the false claim of their own that If Sophia is a knight then Daniel is a knight.\n",
"We have exhausted all possibilities for Sophia and Daniel, so let us go back and reconsider Harper.\n",
"Assume Harper is a knave. ",
"No contradiction is found in their false claim that If Daniel is a knight then Sophia is a knave.\n",
"Assume Daniel 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 If Sophia is a knight then Daniel is a knight.\n",
"Therefore, (1) Harper is a knave\n",
"(2) Daniel 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: Harper, Daniel, and Sophia. Harper commented, "If Daniel is a knight then Sophia is a knave". In Daniel's words: "Sophia is a knight". Sophia asserted: "If Sophia is a knight then Daniel 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 If Daniel is a knight then Sophia is a knave.
Assume Daniel is a knight. No contradiction is found in their claim that Sophia is a knight.
Sophia cannot be a knight, because this would contradict the claim of Harper that If Daniel is a knight then Sophia is a knave.
Sophia cannot be a knave, because this would contradict the claim of Daniel that Sophia is a knight.
We have exhausted all possibilities for Sophia, so let us go back and reconsider Daniel.
Assume Daniel 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 Daniel that Sophia is a knight.
Sophia cannot be a knave, because this would contradict the false claim of their own that If Sophia is a knight then Daniel is a knight.
We have exhausted all possibilities for Sophia and Daniel, so let us go back and reconsider Harper.
Assume Harper is a knave. No contradiction is found in their false claim that If Daniel is a knight then Sophia is a knave.
Assume Daniel 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 If Sophia is a knight then Daniel is a knight.
Therefore, (1) Harper is a knave
(2) Daniel is a knight
(3) Sophia is a knight </think>
<answer> (1) Harper is a knave
(2) Daniel is a knight
(3) Sophia is a knight </answer> | math | {
"ground_truth": {
"names": [
"Harper",
"Daniel",
"Sophia"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Harper is a knave\n(2) Daniel is a knight\n(3) Sophia is a knight",
"statements": "(('->', ('telling-truth', 1), ('lying', 2)), ('telling-truth', 2), ('->', ('telling-truth', 2), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 342,
"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, Victoria, and Liam. Charlotte was heard saying, \"Liam is a knight if and only if Charlotte is a knight\". Victoria said that Charlotte is a knight. In a statement by Liam: \"If Charlotte 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 Liam is a knight if and only if Charlotte is a knight.\n",
"Assume Liam is a knight. ",
"No contradiction is found in their claim that If Charlotte is a knave then Charlotte is a knight.\n",
"Assume Victoria is a knight. ",
"No contradiction is found in their claim that Charlotte is a knight.\n",
"Therefore, (1) Charlotte is a knight\n",
"(2) Victoria is a knight\n",
"(3) Liam is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Charlotte, Victoria, and Liam. Charlotte was heard saying, "Liam is a knight if and only if Charlotte is a knight". Victoria said that Charlotte is a knight. In a statement by Liam: "If Charlotte 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 Liam is a knight if and only if Charlotte is a knight.
Assume Liam is a knight. No contradiction is found in their claim that If Charlotte is a knave then Charlotte is a knight.
Assume Victoria is a knight. No contradiction is found in their claim that Charlotte is a knight.
Therefore, (1) Charlotte is a knight
(2) Victoria is a knight
(3) Liam is a knight </think>
<answer> (1) Charlotte is a knight
(2) Victoria is a knight
(3) Liam is a knight </answer> | math | {
"ground_truth": {
"names": [
"Charlotte",
"Victoria",
"Liam"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Charlotte is a knight\n(2) Victoria is a knight\n(3) Liam is a knight",
"statements": "(('<=>', ('telling-truth', 2), ('telling-truth', 0)), ('telling-truth', 0), ('->', ('lying', 0), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 343,
"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, Henry, and Aiden. Olivia said, \"If Olivia is a knight then Aiden is a knave.\" Henry remarked, \"If Aiden is a knight then Olivia is a knave\". Aiden asserted: \"Henry is a knave and Aiden is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Olivia is a knight. ",
"No contradiction is found in their claim that If Olivia is a knight then Aiden is a knave.\n",
"Aiden cannot be a knight, because this would contradict the claim of Olivia that If Olivia is a knight then Aiden is a knave.\n",
"Assume Aiden is a knave. ",
"No contradiction is found in their false claim that Henry is a knave and Aiden is a knight.\n",
"Assume Henry is a knight. ",
"No contradiction is found in their claim that If Aiden is a knight then Olivia is a knave.\n",
"Therefore, (1) Olivia is a knight\n",
"(2) Henry is a knight\n",
"(3) Aiden is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Olivia, Henry, and Aiden. Olivia said, "If Olivia is a knight then Aiden is a knave." Henry remarked, "If Aiden is a knight then Olivia is a knave". Aiden asserted: "Henry is a knave and Aiden is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Olivia is a knight. No contradiction is found in their claim that If Olivia is a knight then Aiden is a knave.
Aiden cannot be a knight, because this would contradict the claim of Olivia that If Olivia is a knight then Aiden is a knave.
Assume Aiden is a knave. No contradiction is found in their false claim that Henry is a knave and Aiden is a knight.
Assume Henry is a knight. No contradiction is found in their claim that If Aiden is a knight then Olivia is a knave.
Therefore, (1) Olivia is a knight
(2) Henry is a knight
(3) Aiden is a knave </think>
<answer> (1) Olivia is a knight
(2) Henry is a knight
(3) Aiden is a knave </answer> | math | {
"ground_truth": {
"names": [
"Olivia",
"Henry",
"Aiden"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Olivia is a knight\n(2) Henry is a knight\n(3) Aiden is a knave",
"statements": "(('->', ('telling-truth', 0), ('lying', 2)), ('->', ('telling-truth', 2), ('lying', 0)), ('and', ('lying', 1), ('telling-truth', 2)))"
},
"style": "rule"
} | {
"index": 344,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Chloe, Aria, and Abigail. Chloe said, \"Aria is a knight if and only if Abigail is a knave.\" According to Aria, \"If Abigail is a knave then Abigail is a knight\". Abigail asserted: \"Aria is a knight if and only if Aria is a knave\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Chloe is a knight. ",
"No contradiction is found in their claim that Aria is a knight if and only if Abigail is a knave.\n",
"Assume Aria is a knight. ",
"No contradiction is found in their claim that If Abigail is a knave then Abigail is a knight.\n",
"Abigail cannot be a knight, because this would contradict the claim of Chloe that Aria is a knight if and only if Abigail is a knave.\n",
"Abigail cannot be a knave, because this would contradict the claim of Aria that If Abigail is a knave then Abigail is a knight.\n",
"We have exhausted all possibilities for Abigail, so let us go back and reconsider Aria.\n",
"Assume Aria is a knave. ",
"No contradiction is found in their false claim that If Abigail is a knave then Abigail is a knight.\n",
"Abigail cannot be a knight, because this would contradict the false claim of Aria that If Abigail is a knave then Abigail is a knight.\n",
"Abigail cannot be a knave, because this would contradict the claim of Chloe that Aria is a knight if and only if Abigail is a knave.\n",
"We have exhausted all possibilities for Abigail and Aria, so let us go back and reconsider Chloe.\n",
"Assume Chloe is a knave. ",
"No contradiction is found in their false claim that Aria is a knight if and only if Abigail is a knave.\n",
"Assume Aria is a knight. ",
"No contradiction is found in their claim that If Abigail is a knave then Abigail is a knight.\n",
"Abigail cannot be a knight, because this would contradict the claim of their own that Aria is a knight if and only if Aria is a knave.\n",
"Abigail cannot be a knave, because this would contradict the false claim of Chloe that Aria is a knight if and only if Abigail is a knave.\n",
"We have exhausted all possibilities for Abigail, so let us go back and reconsider Aria.\n",
"Assume Aria is a knave. ",
"No contradiction is found in their false claim that If Abigail is a knave then Abigail is a knight.\n",
"Abigail cannot be a knight, because this would contradict the false claim of Chloe that Aria is a knight if and only if Abigail is a knave.\n",
"Assume Abigail is a knave. ",
"No contradiction is found in their false claim that Aria is a knight if and only if Aria is a knave.\n",
"Therefore, (1) Chloe is a knave\n",
"(2) Aria is a knave\n",
"(3) Abigail is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Chloe, Aria, and Abigail. Chloe said, "Aria is a knight if and only if Abigail is a knave." According to Aria, "If Abigail is a knave then Abigail is a knight". Abigail asserted: "Aria is a knight if and only if Aria is a knave". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Chloe is a knight. No contradiction is found in their claim that Aria is a knight if and only if Abigail is a knave.
Assume Aria is a knight. No contradiction is found in their claim that If Abigail is a knave then Abigail is a knight.
Abigail cannot be a knight, because this would contradict the claim of Chloe that Aria is a knight if and only if Abigail is a knave.
Abigail cannot be a knave, because this would contradict the claim of Aria that If Abigail is a knave then Abigail is a knight.
We have exhausted all possibilities for Abigail, so let us go back and reconsider Aria.
Assume Aria is a knave. No contradiction is found in their false claim that If Abigail is a knave then Abigail is a knight.
Abigail cannot be a knight, because this would contradict the false claim of Aria that If Abigail is a knave then Abigail is a knight.
Abigail cannot be a knave, because this would contradict the claim of Chloe that Aria is a knight if and only if Abigail is a knave.
We have exhausted all possibilities for Abigail and Aria, so let us go back and reconsider Chloe.
Assume Chloe is a knave. No contradiction is found in their false claim that Aria is a knight if and only if Abigail is a knave.
Assume Aria is a knight. No contradiction is found in their claim that If Abigail is a knave then Abigail is a knight.
Abigail cannot be a knight, because this would contradict the claim of their own that Aria is a knight if and only if Aria is a knave.
Abigail cannot be a knave, because this would contradict the false claim of Chloe that Aria is a knight if and only if Abigail is a knave.
We have exhausted all possibilities for Abigail, so let us go back and reconsider Aria.
Assume Aria is a knave. No contradiction is found in their false claim that If Abigail is a knave then Abigail is a knight.
Abigail cannot be a knight, because this would contradict the false claim of Chloe that Aria is a knight if and only if Abigail is a knave.
Assume Abigail is a knave. No contradiction is found in their false claim that Aria is a knight if and only if Aria is a knave.
Therefore, (1) Chloe is a knave
(2) Aria is a knave
(3) Abigail is a knave </think>
<answer> (1) Chloe is a knave
(2) Aria is a knave
(3) Abigail is a knave </answer> | math | {
"ground_truth": {
"names": [
"Chloe",
"Aria",
"Abigail"
],
"solution": [
false,
false,
false
],
"solution_text_format": "(1) Chloe is a knave\n(2) Aria is a knave\n(3) Abigail is a knave",
"statements": "(('<=>', ('telling-truth', 1), ('lying', 2)), ('->', ('lying', 2), ('telling-truth', 2)), ('<=>', ('telling-truth', 1), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 345,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Sophia, Olivia, and Elizabeth. Sophia noted, \"Olivia is a knave and Elizabeth is a knight\". As Olivia put it, \"If Sophia is a knave then Olivia is a knight\". Elizabeth commented, \"Sophia is a knight or Olivia 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 Sophia is a knight. ",
"No contradiction is found in their claim that Olivia is a knave and Elizabeth is a knight.\n",
"Olivia cannot be a knight, because this would contradict the claim of Sophia that Olivia is a knave and Elizabeth is a knight.\n",
"Olivia cannot be a knave, because this would contradict the false claim of their own that If Sophia is a knave then Olivia is a knight.\n",
"We have exhausted all possibilities for Olivia, so let us go back and reconsider Sophia.\n",
"Assume Sophia is a knave. ",
"No contradiction is found in their false claim that Olivia is a knave and Elizabeth is a knight.\n",
"Assume Olivia is a knight. ",
"No contradiction is found in their claim that If Sophia is a knave then Olivia is a knight.\n",
"Elizabeth cannot be a knight, because this would contradict the claim of their own that Sophia is a knight or Olivia is a knave.\n",
"Assume Elizabeth is a knave. ",
"No contradiction is found in their false claim that Sophia is a knight or Olivia is a knave.\n",
"Therefore, (1) Sophia is a knave\n",
"(2) Olivia 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: Sophia, Olivia, and Elizabeth. Sophia noted, "Olivia is a knave and Elizabeth is a knight". As Olivia put it, "If Sophia is a knave then Olivia is a knight". Elizabeth commented, "Sophia is a knight or Olivia 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 Sophia is a knight. No contradiction is found in their claim that Olivia is a knave and Elizabeth is a knight.
Olivia cannot be a knight, because this would contradict the claim of Sophia that Olivia is a knave and Elizabeth is a knight.
Olivia cannot be a knave, because this would contradict the false claim of their own that If Sophia is a knave then Olivia is a knight.
We have exhausted all possibilities for Olivia, so let us go back and reconsider Sophia.
Assume Sophia is a knave. No contradiction is found in their false claim that Olivia is a knave and Elizabeth is a knight.
Assume Olivia is a knight. No contradiction is found in their claim that If Sophia is a knave then Olivia is a knight.
Elizabeth cannot be a knight, because this would contradict the claim of their own that Sophia is a knight or Olivia is a knave.
Assume Elizabeth is a knave. No contradiction is found in their false claim that Sophia is a knight or Olivia is a knave.
Therefore, (1) Sophia is a knave
(2) Olivia is a knight
(3) Elizabeth is a knave </think>
<answer> (1) Sophia is a knave
(2) Olivia is a knight
(3) Elizabeth is a knave </answer> | math | {
"ground_truth": {
"names": [
"Sophia",
"Olivia",
"Elizabeth"
],
"solution": [
false,
true,
false
],
"solution_text_format": "(1) Sophia is a knave\n(2) Olivia is a knight\n(3) Elizabeth is a knave",
"statements": "(('and', ('lying', 1), ('telling-truth', 2)), ('->', ('lying', 0), ('telling-truth', 1)), ('or', ('telling-truth', 0), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 346,
"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, Lucas, and Grace. In James's words: \"Grace is a knight or Lucas is a knave\". Lucas asserted: \"James is a knight and James is a knave\". Grace remarked, \"James 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 James is a knight. ",
"No contradiction is found in their claim that Grace is a knight or Lucas is a knave.\n",
"Assume Grace is a knight. ",
"No contradiction is found in their claim that James is not a knave.\n",
"Lucas cannot be a knight, because this would contradict the claim of their own that James is a knight and James is a knave.\n",
"Assume Lucas is a knave. ",
"No contradiction is found in their false claim that James is a knight and James is a knave.\n",
"Therefore, (1) James is a knight\n",
"(2) Lucas is a knave\n",
"(3) Grace is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: James, Lucas, and Grace. In James's words: "Grace is a knight or Lucas is a knave". Lucas asserted: "James is a knight and James is a knave". Grace remarked, "James 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 James is a knight. No contradiction is found in their claim that Grace is a knight or Lucas is a knave.
Assume Grace is a knight. No contradiction is found in their claim that James is not a knave.
Lucas cannot be a knight, because this would contradict the claim of their own that James is a knight and James is a knave.
Assume Lucas is a knave. No contradiction is found in their false claim that James is a knight and James is a knave.
Therefore, (1) James is a knight
(2) Lucas is a knave
(3) Grace is a knight </think>
<answer> (1) James is a knight
(2) Lucas is a knave
(3) Grace is a knight </answer> | math | {
"ground_truth": {
"names": [
"James",
"Lucas",
"Grace"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) James is a knight\n(2) Lucas is a knave\n(3) Grace is a knight",
"statements": "(('or', ('telling-truth', 2), ('lying', 1)), ('and', ('telling-truth', 0), ('lying', 0)), ('not', ('lying', 0)))"
},
"style": "rule"
} | {
"index": 347,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Ethan, Matthew, and Sebastian. In Ethan's words: \"Sebastian is not a knave\". \"Ethan is a knave,\" Matthew mentioned. Sebastian was heard saying, \"Ethan is a knave and Matthew is a knave\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Ethan is a knight. ",
"No contradiction is found in their claim that Sebastian is not a knave.\n",
"Sebastian cannot be a knight, because this would contradict the claim of their own that Ethan is a knave and Matthew is a knave.\n",
"Sebastian cannot be a knave, because this would contradict the claim of Ethan that Sebastian is not a knave.\n",
"We have exhausted all possibilities for Sebastian, so let us go back and reconsider Ethan.\n",
"Assume Ethan is a knave. ",
"No contradiction is found in their false claim that Sebastian is not a knave.\n",
"Sebastian cannot be a knight, because this would contradict the false claim of Ethan that Sebastian is not a knave.\n",
"Assume Sebastian is a knave. ",
"No contradiction is found in their false claim that Ethan is a knave and Matthew is a knave.\n",
"Assume Matthew is a knight. ",
"No contradiction is found in their claim that Ethan is a knave.\n",
"Therefore, (1) Ethan is a knave\n",
"(2) Matthew is a knight\n",
"(3) Sebastian is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Ethan, Matthew, and Sebastian. In Ethan's words: "Sebastian is not a knave". "Ethan is a knave," Matthew mentioned. Sebastian was heard saying, "Ethan is a knave and Matthew is a knave". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Ethan is a knight. No contradiction is found in their claim that Sebastian is not a knave.
Sebastian cannot be a knight, because this would contradict the claim of their own that Ethan is a knave and Matthew is a knave.
Sebastian cannot be a knave, because this would contradict the claim of Ethan that Sebastian is not a knave.
We have exhausted all possibilities for Sebastian, so let us go back and reconsider Ethan.
Assume Ethan is a knave. No contradiction is found in their false claim that Sebastian is not a knave.
Sebastian cannot be a knight, because this would contradict the false claim of Ethan that Sebastian is not a knave.
Assume Sebastian is a knave. No contradiction is found in their false claim that Ethan is a knave and Matthew is a knave.
Assume Matthew is a knight. No contradiction is found in their claim that Ethan is a knave.
Therefore, (1) Ethan is a knave
(2) Matthew is a knight
(3) Sebastian is a knave </think>
<answer> (1) Ethan is a knave
(2) Matthew is a knight
(3) Sebastian is a knave </answer> | math | {
"ground_truth": {
"names": [
"Ethan",
"Matthew",
"Sebastian"
],
"solution": [
false,
true,
false
],
"solution_text_format": "(1) Ethan is a knave\n(2) Matthew is a knight\n(3) Sebastian is a knave",
"statements": "(('not', ('lying', 2)), ('lying', 0), ('and', ('lying', 0), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 348,
"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, Sophia, and Aurora. \"Sophia is not a knave\" - Liam. As Sophia put it, \"Aurora is a knave and Aurora is a knight\". Aurora told you that Sophia is a knight if and only if Sophia 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 Liam is a knight. ",
"No contradiction is found in their claim that Sophia is not a knave.\n",
"Sophia cannot be a knight, because this would contradict the claim of their own that Aurora is a knave and Aurora is a knight.\n",
"Sophia cannot be a knave, because this would contradict the claim of Liam that Sophia is not a knave.\n",
"We have exhausted all possibilities for Sophia, so let us go back and reconsider Liam.\n",
"Assume Liam is a knave. ",
"No contradiction is found in their false claim that Sophia is not a knave.\n",
"Sophia cannot be a knight, because this would contradict the false claim of Liam that Sophia is not a knave.\n",
"Assume Sophia is a knave. ",
"No contradiction is found in their false claim that Aurora is a knave and Aurora is a knight.\n",
"Aurora cannot be a knight, because this would contradict the claim of their own that Sophia is a knight if and only if Sophia is a knave.\n",
"Assume Aurora is a knave. ",
"No contradiction is found in their false claim that Sophia is a knight if and only if Sophia is a knave.\n",
"Therefore, (1) Liam is a knave\n",
"(2) Sophia is a knave\n",
"(3) Aurora is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Liam, Sophia, and Aurora. "Sophia is not a knave" - Liam. As Sophia put it, "Aurora is a knave and Aurora is a knight". Aurora told you that Sophia is a knight if and only if Sophia 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 Liam is a knight. No contradiction is found in their claim that Sophia is not a knave.
Sophia cannot be a knight, because this would contradict the claim of their own that Aurora is a knave and Aurora is a knight.
Sophia cannot be a knave, because this would contradict the claim of Liam that Sophia is not a knave.
We have exhausted all possibilities for Sophia, so let us go back and reconsider Liam.
Assume Liam is a knave. No contradiction is found in their false claim that Sophia is not a knave.
Sophia cannot be a knight, because this would contradict the false claim of Liam that Sophia is not a knave.
Assume Sophia is a knave. No contradiction is found in their false claim that Aurora is a knave and Aurora is a knight.
Aurora cannot be a knight, because this would contradict the claim of their own that Sophia is a knight if and only if Sophia is a knave.
Assume Aurora is a knave. No contradiction is found in their false claim that Sophia is a knight if and only if Sophia is a knave.
Therefore, (1) Liam is a knave
(2) Sophia is a knave
(3) Aurora is a knave </think>
<answer> (1) Liam is a knave
(2) Sophia is a knave
(3) Aurora is a knave </answer> | math | {
"ground_truth": {
"names": [
"Liam",
"Sophia",
"Aurora"
],
"solution": [
false,
false,
false
],
"solution_text_format": "(1) Liam is a knave\n(2) Sophia is a knave\n(3) Aurora is a knave",
"statements": "(('not', ('lying', 1)), ('and', ('lying', 2), ('telling-truth', 2)), ('<=>', ('telling-truth', 1), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 349,
"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, Zoey, and Ethan. \"Ethan is a knight and Zoey is a knave,\" Liam declared. Zoey asserted: \"Liam is not a knave\". As Ethan put it, \"Ethan is a knight and 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 Liam is a knight. ",
"No contradiction is found in their claim that Ethan is a knight and Zoey is a knave.\n",
"Assume Ethan is a knight. ",
"No contradiction is found in their claim that Ethan is a knight and Zoey is a knight.\n",
"Zoey cannot be a knight, because this would contradict the claim of Liam that Ethan is a knight and Zoey is a knave.\n",
"Zoey cannot be a knave, because this would contradict the false claim of their own that Liam is not a knave.\n",
"We have exhausted all possibilities for Zoey, so let us go back and reconsider Ethan.\n",
"Ethan cannot be a knave, because this would contradict the claim of Liam that Ethan is a knight and Zoey is a knave.\n",
"We have exhausted all possibilities for Ethan, so let us go back and reconsider Liam.\n",
"Assume Liam is a knave. ",
"No contradiction is found in their false claim that Ethan is a knight and Zoey is a knave.\n",
"Assume Ethan is a knight. ",
"No contradiction is found in their claim that Ethan is a knight and Zoey is a knight.\n",
"Zoey cannot be a knight, because this would contradict the claim of their own that Liam is not a knave.\n",
"Zoey cannot be a knave, because this would contradict the false claim of Liam that Ethan is a knight and Zoey is a knave.\n",
"We have exhausted all possibilities for Zoey, so let us go back and reconsider Ethan.\n",
"Assume Ethan is a knave. ",
"No contradiction is found in their false claim that Ethan is a knight and Zoey is a knight.\n",
"Zoey cannot be a knight, because this would contradict the claim of their own that Liam is not a knave.\n",
"Assume Zoey is a knave. ",
"No contradiction is found in their false claim that Liam is not a knave.\n",
"Therefore, (1) Liam is a knave\n",
"(2) Zoey is a knave\n",
"(3) Ethan 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: Liam, Zoey, and Ethan. "Ethan is a knight and Zoey is a knave," Liam declared. Zoey asserted: "Liam is not a knave". As Ethan put it, "Ethan is a knight and 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 Liam is a knight. No contradiction is found in their claim that Ethan is a knight and Zoey is a knave.
Assume Ethan is a knight. No contradiction is found in their claim that Ethan is a knight and Zoey is a knight.
Zoey cannot be a knight, because this would contradict the claim of Liam that Ethan is a knight and Zoey is a knave.
Zoey cannot be a knave, because this would contradict the false claim of their own that Liam is not a knave.
We have exhausted all possibilities for Zoey, so let us go back and reconsider Ethan.
Ethan cannot be a knave, because this would contradict the claim of Liam that Ethan is a knight and Zoey is a knave.
We have exhausted all possibilities for Ethan, so let us go back and reconsider Liam.
Assume Liam is a knave. No contradiction is found in their false claim that Ethan is a knight and Zoey is a knave.
Assume Ethan is a knight. No contradiction is found in their claim that Ethan is a knight and Zoey is a knight.
Zoey cannot be a knight, because this would contradict the claim of their own that Liam is not a knave.
Zoey cannot be a knave, because this would contradict the false claim of Liam that Ethan is a knight and Zoey is a knave.
We have exhausted all possibilities for Zoey, so let us go back and reconsider Ethan.
Assume Ethan is a knave. No contradiction is found in their false claim that Ethan is a knight and Zoey is a knight.
Zoey cannot be a knight, because this would contradict the claim of their own that Liam is not a knave.
Assume Zoey is a knave. No contradiction is found in their false claim that Liam is not a knave.
Therefore, (1) Liam is a knave
(2) Zoey is a knave
(3) Ethan is a knave </think>
<answer> (1) Liam is a knave
(2) Zoey is a knave
(3) Ethan is a knave </answer> | math | {
"ground_truth": {
"names": [
"Liam",
"Zoey",
"Ethan"
],
"solution": [
false,
false,
false
],
"solution_text_format": "(1) Liam is a knave\n(2) Zoey is a knave\n(3) Ethan is a knave",
"statements": "(('and', ('telling-truth', 2), ('lying', 1)), ('not', ('lying', 0)), ('and', ('telling-truth', 2), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 350,
"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, Ethan, and Emily. In David's words: \"Ethan is a knave if and only if Ethan is a knight\". \"Emily is a knave if and only if Emily is a knight,\" Ethan mentioned. According to Emily, \"Ethan is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"David cannot be a knight, because this would contradict the claim of their own that Ethan is a knave if and only if Ethan is a knight.\n",
"Assume David is a knave. ",
"No contradiction is found in their false claim that Ethan is a knave if and only if Ethan is a knight.\n",
"Ethan cannot be a knight, because this would contradict the claim of their own that Emily is a knave if and only if Emily is a knight.\n",
"Assume Ethan is a knave. ",
"No contradiction is found in their false claim that Emily is a knave if and only if Emily is a knight.\n",
"Emily cannot be a knight, because this would contradict the claim of their own that Ethan is a knight.\n",
"Assume Emily is a knave. ",
"No contradiction is found in their false claim that Ethan is a knight.\n",
"Therefore, (1) David is a knave\n",
"(2) Ethan is a knave\n",
"(3) Emily is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: David, Ethan, and Emily. In David's words: "Ethan is a knave if and only if Ethan is a knight". "Emily is a knave if and only if Emily is a knight," Ethan mentioned. According to Emily, "Ethan is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | David cannot be a knight, because this would contradict the claim of their own that Ethan is a knave if and only if Ethan is a knight.
Assume David is a knave. No contradiction is found in their false claim that Ethan is a knave if and only if Ethan is a knight.
Ethan cannot be a knight, because this would contradict the claim of their own that Emily is a knave if and only if Emily is a knight.
Assume Ethan is a knave. No contradiction is found in their false claim that Emily is a knave if and only if Emily is a knight.
Emily cannot be a knight, because this would contradict the claim of their own that Ethan is a knight.
Assume Emily is a knave. No contradiction is found in their false claim that Ethan is a knight.
Therefore, (1) David is a knave
(2) Ethan is a knave
(3) Emily is a knave </think>
<answer> (1) David is a knave
(2) Ethan is a knave
(3) Emily is a knave </answer> | math | {
"ground_truth": {
"names": [
"David",
"Ethan",
"Emily"
],
"solution": [
false,
false,
false
],
"solution_text_format": "(1) David is a knave\n(2) Ethan is a knave\n(3) Emily is a knave",
"statements": "(('<=>', ('lying', 1), ('telling-truth', 1)), ('<=>', ('lying', 2), ('telling-truth', 2)), ('telling-truth', 1))"
},
"style": "rule"
} | {
"index": 351,
"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, Scarlett, and Benjamin. Luke noted, \"Scarlett is a knight or Scarlett is a knave\". \"Luke is a knight if and only if Luke is a knave,\" Scarlett claimed. Benjamin asserted: \"Scarlett is a knave if and only if 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 Luke is a knight. ",
"No contradiction is found in their claim that Scarlett is a knight or Scarlett is a knave.\n",
"Scarlett cannot be a knight, because this would contradict the claim of their own that Luke is a knight if and only if Luke is a knave.\n",
"Assume Scarlett is a knave. ",
"No contradiction is found in their false claim that Luke is a knight if and only if Luke is a knave.\n",
"Benjamin cannot be a knight, because this would contradict the claim of their own that Scarlett is a knave if and only if Scarlett is a knight.\n",
"Assume Benjamin is a knave. ",
"No contradiction is found in their false claim that Scarlett is a knave if and only if Scarlett is a knight.\n",
"Therefore, (1) Luke is a knight\n",
"(2) Scarlett 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: Luke, Scarlett, and Benjamin. Luke noted, "Scarlett is a knight or Scarlett is a knave". "Luke is a knight if and only if Luke is a knave," Scarlett claimed. Benjamin asserted: "Scarlett is a knave if and only if 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 Luke is a knight. No contradiction is found in their claim that Scarlett is a knight or Scarlett is a knave.
Scarlett cannot be a knight, because this would contradict the claim of their own that Luke is a knight if and only if Luke is a knave.
Assume Scarlett is a knave. No contradiction is found in their false claim that Luke is a knight if and only if Luke is a knave.
Benjamin cannot be a knight, because this would contradict the claim of their own that Scarlett is a knave if and only if Scarlett is a knight.
Assume Benjamin is a knave. No contradiction is found in their false claim that Scarlett is a knave if and only if Scarlett is a knight.
Therefore, (1) Luke is a knight
(2) Scarlett is a knave
(3) Benjamin is a knave </think>
<answer> (1) Luke is a knight
(2) Scarlett is a knave
(3) Benjamin is a knave </answer> | math | {
"ground_truth": {
"names": [
"Luke",
"Scarlett",
"Benjamin"
],
"solution": [
true,
false,
false
],
"solution_text_format": "(1) Luke is a knight\n(2) Scarlett is a knave\n(3) Benjamin is a knave",
"statements": "(('or', ('telling-truth', 1), ('lying', 1)), ('<=>', ('telling-truth', 0), ('lying', 0)), ('<=>', ('lying', 1), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 352,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Joseph, Ava, and Jack. Joseph asserted: \"Ava is a knight or Jack is a knave\". \"Jack is a knight or Jack is a knave,\" Ava claimed. Jack stated, \"Ava is a knight and Joseph is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Joseph is a knight. ",
"No contradiction is found in their claim that Ava is a knight or Jack is a knave.\n",
"Assume Ava is a knight. ",
"No contradiction is found in their claim that Jack is a knight or Jack is a knave.\n",
"Assume Jack is a knight. ",
"No contradiction is found in their claim that Ava is a knight and Joseph is a knight.\n",
"Therefore, (1) Joseph is a knight\n",
"(2) Ava is a knight\n",
"(3) Jack 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: Joseph, Ava, and Jack. Joseph asserted: "Ava is a knight or Jack is a knave". "Jack is a knight or Jack is a knave," Ava claimed. Jack stated, "Ava is a knight and Joseph is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Joseph is a knight. No contradiction is found in their claim that Ava is a knight or Jack is a knave.
Assume Ava is a knight. No contradiction is found in their claim that Jack is a knight or Jack is a knave.
Assume Jack is a knight. No contradiction is found in their claim that Ava is a knight and Joseph is a knight.
Therefore, (1) Joseph is a knight
(2) Ava is a knight
(3) Jack is a knight </think>
<answer> (1) Joseph is a knight
(2) Ava is a knight
(3) Jack is a knight </answer> | math | {
"ground_truth": {
"names": [
"Joseph",
"Ava",
"Jack"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Joseph is a knight\n(2) Ava is a knight\n(3) Jack is a knight",
"statements": "(('or', ('telling-truth', 1), ('lying', 2)), ('or', ('telling-truth', 2), ('lying', 2)), ('and', ('telling-truth', 1), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 353,
"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 Joseph. In Lucas's words: \"If Evelyn is a knight then Evelyn is a knave\". In a statement by Evelyn: \"Lucas is a knight and Lucas is a knave\". \"Lucas is a knight and Evelyn is a knight,\" Joseph 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 If Evelyn is a knight then Evelyn is a knave.\n",
"Evelyn cannot be a knight, because this would contradict the claim of Lucas that If Evelyn is a knight then Evelyn is a knave.\n",
"Assume Evelyn is a knave. ",
"No contradiction is found in their false claim that Lucas is a knight and Lucas is a knave.\n",
"Joseph cannot be a knight, because this would contradict the claim of their own that Lucas is a knight and Evelyn is a knight.\n",
"Assume Joseph is a knave. ",
"No contradiction is found in their false claim that Lucas is a knight and Evelyn is a knight.\n",
"Therefore, (1) Lucas is a knight\n",
"(2) Evelyn is a knave\n",
"(3) Joseph 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 Joseph. In Lucas's words: "If Evelyn is a knight then Evelyn is a knave". In a statement by Evelyn: "Lucas is a knight and Lucas is a knave". "Lucas is a knight and Evelyn is a knight," Joseph 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 If Evelyn is a knight then Evelyn is a knave.
Evelyn cannot be a knight, because this would contradict the claim of Lucas that If Evelyn is a knight then Evelyn is a knave.
Assume Evelyn is a knave. No contradiction is found in their false claim that Lucas is a knight and Lucas is a knave.
Joseph cannot be a knight, because this would contradict the claim of their own that Lucas is a knight and Evelyn is a knight.
Assume Joseph is a knave. No contradiction is found in their false claim that Lucas is a knight and Evelyn is a knight.
Therefore, (1) Lucas is a knight
(2) Evelyn is a knave
(3) Joseph is a knave </think>
<answer> (1) Lucas is a knight
(2) Evelyn is a knave
(3) Joseph is a knave </answer> | math | {
"ground_truth": {
"names": [
"Lucas",
"Evelyn",
"Joseph"
],
"solution": [
true,
false,
false
],
"solution_text_format": "(1) Lucas is a knight\n(2) Evelyn is a knave\n(3) Joseph is a knave",
"statements": "(('->', ('telling-truth', 1), ('lying', 1)), ('and', ('telling-truth', 0), ('lying', 0)), ('and', ('telling-truth', 0), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 354,
"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, Riley, and Jack. \"Riley is a knight and Jack is a knight\" - Avery. As Riley put it, \"Avery is not a knight\". \"Jack is a knight and Riley is a knight\" - Jack. So who is a knight and who is a knave? 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 Riley is a knight and Jack is a knight.\n",
"Riley cannot be a knight, because this would contradict the claim of their own that Avery is not a knight.\n",
"Riley cannot be a knave, because this would contradict the claim of Avery that Riley is a knight and Jack is a knight.\n",
"We have exhausted all possibilities for Riley, so let us go back and reconsider Avery.\n",
"Assume Avery is a knave. ",
"No contradiction is found in their false claim that Riley is a knight and Jack is a knight.\n",
"Assume Riley is a knight. ",
"No contradiction is found in their claim that Avery is not a knight.\n",
"Jack cannot be a knight, because this would contradict the false claim of Avery that Riley is a knight and Jack is a knight.\n",
"Assume Jack is a knave. ",
"No contradiction is found in their false claim that Jack is a knight and Riley is a knight.\n",
"Therefore, (1) Avery is a knave\n",
"(2) Riley 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: Avery, Riley, and Jack. "Riley is a knight and Jack is a knight" - Avery. As Riley put it, "Avery is not a knight". "Jack is a knight and Riley is a knight" - Jack. So who is a knight and who is a knave? 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 Riley is a knight and Jack is a knight.
Riley cannot be a knight, because this would contradict the claim of their own that Avery is not a knight.
Riley cannot be a knave, because this would contradict the claim of Avery that Riley is a knight and Jack is a knight.
We have exhausted all possibilities for Riley, so let us go back and reconsider Avery.
Assume Avery is a knave. No contradiction is found in their false claim that Riley is a knight and Jack is a knight.
Assume Riley is a knight. No contradiction is found in their claim that Avery is not a knight.
Jack cannot be a knight, because this would contradict the false claim of Avery that Riley is a knight and Jack is a knight.
Assume Jack is a knave. No contradiction is found in their false claim that Jack is a knight and Riley is a knight.
Therefore, (1) Avery is a knave
(2) Riley is a knight
(3) Jack is a knave </think>
<answer> (1) Avery is a knave
(2) Riley is a knight
(3) Jack is a knave </answer> | math | {
"ground_truth": {
"names": [
"Avery",
"Riley",
"Jack"
],
"solution": [
false,
true,
false
],
"solution_text_format": "(1) Avery is a knave\n(2) Riley is a knight\n(3) Jack is a knave",
"statements": "(('and', ('telling-truth', 1), ('telling-truth', 2)), ('not', ('telling-truth', 0)), ('and', ('telling-truth', 2), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 355,
"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, Samuel, and Mason. As James put it, \"Mason is not a knight\". In a statement by Samuel: \"If James is a knave then James is a knight\". According to Mason, \"Samuel is a knight if and only if Samuel is a knave\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume James 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 James that Mason is not a knight.\n",
"Assume Mason 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",
"Assume Samuel is a knight. ",
"No contradiction is found in their claim that If James is a knave then James is a knight.\n",
"Therefore, (1) James is a knight\n",
"(2) Samuel is a knight\n",
"(3) Mason 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, Samuel, and Mason. As James put it, "Mason is not a knight". In a statement by Samuel: "If James is a knave then James is a knight". According to Mason, "Samuel is a knight if and only if Samuel is a knave". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume James 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 James that Mason is not a knight.
Assume Mason is a knave. No contradiction is found in their false claim that Samuel is a knight if and only if Samuel is a knave.
Assume Samuel is a knight. No contradiction is found in their claim that If James is a knave then James is a knight.
Therefore, (1) James is a knight
(2) Samuel is a knight
(3) Mason is a knave </think>
<answer> (1) James is a knight
(2) Samuel is a knight
(3) Mason is a knave </answer> | math | {
"ground_truth": {
"names": [
"James",
"Samuel",
"Mason"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) James is a knight\n(2) Samuel is a knight\n(3) Mason is a knave",
"statements": "(('not', ('telling-truth', 2)), ('->', ('lying', 0), ('telling-truth', 0)), ('<=>', ('telling-truth', 1), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 356,
"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, Owen, and Sofia. Avery was heard saying, \"If Sofia is a knight then Sofia is a knave\". Owen was heard saying, \"Sofia is a knave\". Sofia told you that Avery is a knave if and only if 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 Avery is a knight. ",
"No contradiction is found in their claim that If Sofia is a knight then Sofia is a knave.\n",
"Sofia cannot be a knight, because this would contradict the claim of Avery that If Sofia is a knight then Sofia is a knave.\n",
"Assume Sofia is a knave. ",
"No contradiction is found in their false claim that Avery is a knave if and only if Owen is a knave.\n",
"Owen cannot be a knight, because this would contradict the false claim of Sofia that Avery is a knave if and only if Owen is a knave.\n",
"Owen cannot be a knave, because this would contradict the false claim of their own that Sofia is a knave.\n",
"We have exhausted all possibilities for Owen and Sofia, so let us go back and reconsider Avery.\n",
"Assume Avery is a knave. ",
"No contradiction is found in their false claim that If Sofia is a knight then Sofia is a knave.\n",
"Assume Sofia is a knight. ",
"No contradiction is found in their claim that Avery is a knave if and only if Owen is a knave.\n",
"Owen cannot be a knight, because this would contradict the claim of their own that Sofia is a knave.\n",
"Assume Owen is a knave. ",
"No contradiction is found in their false claim that Sofia is a knave.\n",
"Therefore, (1) Avery is a knave\n",
"(2) Owen is a knave\n",
"(3) Sofia 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, Owen, and Sofia. Avery was heard saying, "If Sofia is a knight then Sofia is a knave". Owen was heard saying, "Sofia is a knave". Sofia told you that Avery is a knave if and only if 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 Avery is a knight. No contradiction is found in their claim that If Sofia is a knight then Sofia is a knave.
Sofia cannot be a knight, because this would contradict the claim of Avery that If Sofia is a knight then Sofia is a knave.
Assume Sofia is a knave. No contradiction is found in their false claim that Avery is a knave if and only if Owen is a knave.
Owen cannot be a knight, because this would contradict the false claim of Sofia that Avery is a knave if and only if Owen is a knave.
Owen cannot be a knave, because this would contradict the false claim of their own that Sofia is a knave.
We have exhausted all possibilities for Owen and Sofia, so let us go back and reconsider Avery.
Assume Avery is a knave. No contradiction is found in their false claim that If Sofia is a knight then Sofia is a knave.
Assume Sofia is a knight. No contradiction is found in their claim that Avery is a knave if and only if Owen is a knave.
Owen cannot be a knight, because this would contradict the claim of their own that Sofia is a knave.
Assume Owen is a knave. No contradiction is found in their false claim that Sofia is a knave.
Therefore, (1) Avery is a knave
(2) Owen is a knave
(3) Sofia is a knight </think>
<answer> (1) Avery is a knave
(2) Owen is a knave
(3) Sofia is a knight </answer> | math | {
"ground_truth": {
"names": [
"Avery",
"Owen",
"Sofia"
],
"solution": [
false,
false,
true
],
"solution_text_format": "(1) Avery is a knave\n(2) Owen is a knave\n(3) Sofia is a knight",
"statements": "(('->', ('telling-truth', 2), ('lying', 2)), ('lying', 2), ('<=>', ('lying', 0), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 357,
"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, Samuel, and Olivia. Avery remarked, \"Olivia is a knave\". Samuel expressed that Avery is a knight and Samuel is a knight. Olivia said, \"If Olivia is a knight then Samuel is a knave.\" So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Avery is a knight. ",
"No contradiction is found in their claim that Olivia is a knave.\n",
"Olivia cannot be a knight, because this would contradict the claim of Avery that Olivia is a knave.\n",
"Olivia cannot be a knave, because this would contradict the false claim of their own that If Olivia is a knight then Samuel is a knave.\n",
"We have exhausted all possibilities for Olivia, so let us go back and reconsider Avery.\n",
"Assume Avery is a knave. ",
"No contradiction is found in their false claim that Olivia is a knave.\n",
"Assume Olivia is a knight. ",
"No contradiction is found in their claim that If Olivia is a knight then Samuel is a knave.\n",
"Samuel cannot be a knight, because this would contradict the claim of their own that Avery is a knight and Samuel is a knight.\n",
"Assume Samuel is a knave. ",
"No contradiction is found in their false claim that Avery is a knight and Samuel is a knight.\n",
"Therefore, (1) Avery is a knave\n",
"(2) Samuel is a knave\n",
"(3) Olivia is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Avery, Samuel, and Olivia. Avery remarked, "Olivia is a knave". Samuel expressed that Avery is a knight and Samuel is a knight. Olivia said, "If Olivia is a knight then Samuel is a knave." So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Avery is a knight. No contradiction is found in their claim that Olivia is a knave.
Olivia cannot be a knight, because this would contradict the claim of Avery that Olivia is a knave.
Olivia cannot be a knave, because this would contradict the false claim of their own that If Olivia is a knight then Samuel is a knave.
We have exhausted all possibilities for Olivia, so let us go back and reconsider Avery.
Assume Avery is a knave. No contradiction is found in their false claim that Olivia is a knave.
Assume Olivia is a knight. No contradiction is found in their claim that If Olivia is a knight then Samuel is a knave.
Samuel cannot be a knight, because this would contradict the claim of their own that Avery is a knight and Samuel is a knight.
Assume Samuel is a knave. No contradiction is found in their false claim that Avery is a knight and Samuel is a knight.
Therefore, (1) Avery is a knave
(2) Samuel is a knave
(3) Olivia is a knight </think>
<answer> (1) Avery is a knave
(2) Samuel is a knave
(3) Olivia is a knight </answer> | math | {
"ground_truth": {
"names": [
"Avery",
"Samuel",
"Olivia"
],
"solution": [
false,
false,
true
],
"solution_text_format": "(1) Avery is a knave\n(2) Samuel is a knave\n(3) Olivia is a knight",
"statements": "(('lying', 2), ('and', ('telling-truth', 0), ('telling-truth', 1)), ('->', ('telling-truth', 2), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 358,
"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, Riley, and Elizabeth. In a statement by Noah: \"Elizabeth is a knight and Riley is a knight\". Riley stated, \"Noah is a knight and Elizabeth is a knave\". In a statement by Elizabeth: \"Riley is a knight if and only if Noah 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 Elizabeth is a knight and Riley is a knight.\n",
"Assume Elizabeth is a knight. ",
"No contradiction is found in their claim that Riley is a knight if and only if Noah is a knight.\n",
"Riley cannot be a knight, because this would contradict the claim of their own that Noah is a knight and Elizabeth is a knave.\n",
"Riley cannot be a knave, because this would contradict the claim of Noah that Elizabeth is a knight and Riley is a knight.\n",
"We have exhausted all possibilities for Riley, so let us go back and reconsider Elizabeth.\n",
"Elizabeth cannot be a knave, because this would contradict the claim of Noah that Elizabeth is a knight and Riley is a knight.\n",
"We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Noah.\n",
"Assume Noah is a knave. ",
"No contradiction is found in their false claim that Elizabeth is a knight and Riley is a knight.\n",
"Assume Elizabeth is a knight. ",
"No contradiction is found in their claim that Riley is a knight if and only if Noah is a knight.\n",
"Riley cannot be a knight, because this would contradict the false claim of Noah that Elizabeth is a knight and Riley is a knight.\n",
"Assume Riley is a knave. ",
"No contradiction is found in their false claim that Noah is a knight and Elizabeth is a knave.\n",
"Therefore, (1) Noah is a knave\n",
"(2) Riley 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: Noah, Riley, and Elizabeth. In a statement by Noah: "Elizabeth is a knight and Riley is a knight". Riley stated, "Noah is a knight and Elizabeth is a knave". In a statement by Elizabeth: "Riley is a knight if and only if Noah 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 Elizabeth is a knight and Riley is a knight.
Assume Elizabeth is a knight. No contradiction is found in their claim that Riley is a knight if and only if Noah is a knight.
Riley cannot be a knight, because this would contradict the claim of their own that Noah is a knight and Elizabeth is a knave.
Riley cannot be a knave, because this would contradict the claim of Noah that Elizabeth is a knight and Riley is a knight.
We have exhausted all possibilities for Riley, so let us go back and reconsider Elizabeth.
Elizabeth cannot be a knave, because this would contradict the claim of Noah that Elizabeth is a knight and Riley is a knight.
We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Noah.
Assume Noah is a knave. No contradiction is found in their false claim that Elizabeth is a knight and Riley is a knight.
Assume Elizabeth is a knight. No contradiction is found in their claim that Riley is a knight if and only if Noah is a knight.
Riley cannot be a knight, because this would contradict the false claim of Noah that Elizabeth is a knight and Riley is a knight.
Assume Riley is a knave. No contradiction is found in their false claim that Noah is a knight and Elizabeth is a knave.
Therefore, (1) Noah is a knave
(2) Riley is a knave
(3) Elizabeth is a knight </think>
<answer> (1) Noah is a knave
(2) Riley is a knave
(3) Elizabeth is a knight </answer> | math | {
"ground_truth": {
"names": [
"Noah",
"Riley",
"Elizabeth"
],
"solution": [
false,
false,
true
],
"solution_text_format": "(1) Noah is a knave\n(2) Riley is a knave\n(3) Elizabeth is a knight",
"statements": "(('and', ('telling-truth', 2), ('telling-truth', 1)), ('and', ('telling-truth', 0), ('lying', 2)), ('<=>', ('telling-truth', 1), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 359,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Matthew, Jackson, and Isabella. Matthew commented, \"Jackson is a knave if and only if Isabella is a knave\". In a statement by Jackson: \"If Matthew is a knight then Isabella is a knave\". Isabella told you that Isabella is a knight or Jackson is a knave. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Matthew is a knight. ",
"No contradiction is found in their claim that Jackson is a knave if and only if Isabella is a knave.\n",
"Assume Jackson is a knight. ",
"No contradiction is found in their claim that If Matthew is a knight then Isabella is a knave.\n",
"Isabella cannot be a knight, because this would contradict the claim of Jackson that If Matthew is a knight then Isabella is a knave.\n",
"Isabella cannot be a knave, because this would contradict the claim of Matthew that Jackson is a knave if and only if Isabella is a knave.\n",
"We have exhausted all possibilities for Isabella, so let us go back and reconsider Jackson.\n",
"Assume Jackson is a knave. ",
"No contradiction is found in their false claim that If Matthew is a knight then Isabella is a knave.\n",
"Isabella cannot be a knight, because this would contradict the claim of Matthew that Jackson is a knave if and only if Isabella is a knave.\n",
"Isabella cannot be a knave, because this would contradict the false claim of Jackson that If Matthew is a knight then Isabella is a knave.\n",
"We have exhausted all possibilities for Isabella and Jackson, so let us go back and reconsider Matthew.\n",
"Assume Matthew is a knave. ",
"No contradiction is found in their false claim that Jackson is a knave if and only if Isabella is a knave.\n",
"Assume Jackson is a knight. ",
"No contradiction is found in their claim that If Matthew is a knight then Isabella is a knave.\n",
"Isabella cannot be a knight, because this would contradict the false claim of Matthew that Jackson is a knave if and only if Isabella is a knave.\n",
"Assume Isabella is a knave. ",
"No contradiction is found in their false claim that Isabella is a knight or Jackson is a knave.\n",
"Therefore, (1) Matthew is a knave\n",
"(2) Jackson is a knight\n",
"(3) Isabella is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Matthew, Jackson, and Isabella. Matthew commented, "Jackson is a knave if and only if Isabella is a knave". In a statement by Jackson: "If Matthew is a knight then Isabella is a knave". Isabella told you that Isabella is a knight or Jackson is a knave. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Matthew is a knight. No contradiction is found in their claim that Jackson is a knave if and only if Isabella is a knave.
Assume Jackson is a knight. No contradiction is found in their claim that If Matthew is a knight then Isabella is a knave.
Isabella cannot be a knight, because this would contradict the claim of Jackson that If Matthew is a knight then Isabella is a knave.
Isabella cannot be a knave, because this would contradict the claim of Matthew that Jackson is a knave if and only if Isabella is a knave.
We have exhausted all possibilities for Isabella, so let us go back and reconsider Jackson.
Assume Jackson is a knave. No contradiction is found in their false claim that If Matthew is a knight then Isabella is a knave.
Isabella cannot be a knight, because this would contradict the claim of Matthew that Jackson is a knave if and only if Isabella is a knave.
Isabella cannot be a knave, because this would contradict the false claim of Jackson that If Matthew is a knight then Isabella is a knave.
We have exhausted all possibilities for Isabella and Jackson, so let us go back and reconsider Matthew.
Assume Matthew is a knave. No contradiction is found in their false claim that Jackson is a knave if and only if Isabella is a knave.
Assume Jackson is a knight. No contradiction is found in their claim that If Matthew is a knight then Isabella is a knave.
Isabella cannot be a knight, because this would contradict the false claim of Matthew that Jackson is a knave if and only if Isabella is a knave.
Assume Isabella is a knave. No contradiction is found in their false claim that Isabella is a knight or Jackson is a knave.
Therefore, (1) Matthew is a knave
(2) Jackson is a knight
(3) Isabella is a knave </think>
<answer> (1) Matthew is a knave
(2) Jackson is a knight
(3) Isabella is a knave </answer> | math | {
"ground_truth": {
"names": [
"Matthew",
"Jackson",
"Isabella"
],
"solution": [
false,
true,
false
],
"solution_text_format": "(1) Matthew is a knave\n(2) Jackson is a knight\n(3) Isabella is a knave",
"statements": "(('<=>', ('lying', 1), ('lying', 2)), ('->', ('telling-truth', 0), ('lying', 2)), ('or', ('telling-truth', 2), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 360,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Henry, Sophia, and Avery. Henry asserted: \"Sophia is a knave if and only if Sophia is a knight\". Sophia commented, \"Avery is not a knave\". Avery said, \"Henry is a knight and Henry is a knave.\" So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Henry cannot be a knight, because this would contradict the claim of their own that Sophia is a knave if and only if Sophia is a knight.\n",
"Assume Henry is a knave. ",
"No contradiction is found in their false claim that Sophia is a knave if and only if Sophia is a knight.\n",
"Assume Sophia is a knight. ",
"No contradiction is found in their claim that Avery is not a knave.\n",
"Avery cannot be a knight, because this would contradict the claim of their own that Henry is a knight and Henry is a knave.\n",
"Avery cannot be a knave, because this would contradict the claim of Sophia that Avery is not a knave.\n",
"We have exhausted all possibilities for Avery, so let us go back and reconsider Sophia.\n",
"Assume Sophia is a knave. ",
"No contradiction is found in their false claim that Avery is not a knave.\n",
"Avery cannot be a knight, because this would contradict the false claim of Sophia that Avery is not a knave.\n",
"Assume Avery is a knave. ",
"No contradiction is found in their false claim that Henry is a knight and Henry is a knave.\n",
"Therefore, (1) Henry is a knave\n",
"(2) Sophia is a knave\n",
"(3) Avery is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Henry, Sophia, and Avery. Henry asserted: "Sophia is a knave if and only if Sophia is a knight". Sophia commented, "Avery is not a knave". Avery said, "Henry is a knight and Henry is a knave." So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Henry cannot be a knight, because this would contradict the claim of their own that Sophia is a knave if and only if Sophia is a knight.
Assume Henry is a knave. No contradiction is found in their false claim that Sophia is a knave if and only if Sophia is a knight.
Assume Sophia is a knight. No contradiction is found in their claim that Avery is not a knave.
Avery cannot be a knight, because this would contradict the claim of their own that Henry is a knight and Henry is a knave.
Avery cannot be a knave, because this would contradict the claim of Sophia that Avery is not a knave.
We have exhausted all possibilities for Avery, so let us go back and reconsider Sophia.
Assume Sophia is a knave. No contradiction is found in their false claim that Avery is not a knave.
Avery cannot be a knight, because this would contradict the false claim of Sophia that Avery is not a knave.
Assume Avery is a knave. No contradiction is found in their false claim that Henry is a knight and Henry is a knave.
Therefore, (1) Henry is a knave
(2) Sophia is a knave
(3) Avery is a knave </think>
<answer> (1) Henry is a knave
(2) Sophia is a knave
(3) Avery is a knave </answer> | math | {
"ground_truth": {
"names": [
"Henry",
"Sophia",
"Avery"
],
"solution": [
false,
false,
false
],
"solution_text_format": "(1) Henry is a knave\n(2) Sophia is a knave\n(3) Avery is a knave",
"statements": "(('<=>', ('lying', 1), ('telling-truth', 1)), ('not', ('lying', 2)), ('and', ('telling-truth', 0), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 361,
"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, Charlotte, and Luke. As Owen put it, \"Charlotte is a knave and Luke is a knave\". Charlotte noted, \"Owen is a knight or Owen is a knave\". As Luke put it, \"Owen is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Owen is a knight. ",
"No contradiction is found in their claim that Charlotte is a knave and Luke is a knave.\n",
"Charlotte cannot be a knight, because this would contradict the claim of Owen that Charlotte is a knave and Luke is a knave.\n",
"Charlotte cannot be a knave, because this would contradict the false claim of their own that Owen is a knight or Owen is a knave.\n",
"We have exhausted all possibilities for Charlotte, so let us go back and reconsider Owen.\n",
"Assume Owen is a knave. ",
"No contradiction is found in their false claim that Charlotte is a knave and Luke is a knave.\n",
"Assume Charlotte is a knight. ",
"No contradiction is found in their claim that Owen is a knight or Owen is a knave.\n",
"Luke cannot be a knight, because this would contradict the claim of their own that Owen is a knight.\n",
"Assume Luke is a knave. ",
"No contradiction is found in their false claim that Owen is a knight.\n",
"Therefore, (1) Owen is a knave\n",
"(2) Charlotte 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: Owen, Charlotte, and Luke. As Owen put it, "Charlotte is a knave and Luke is a knave". Charlotte noted, "Owen is a knight or Owen is a knave". As Luke put it, "Owen is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Owen is a knight. No contradiction is found in their claim that Charlotte is a knave and Luke is a knave.
Charlotte cannot be a knight, because this would contradict the claim of Owen that Charlotte is a knave and Luke is a knave.
Charlotte cannot be a knave, because this would contradict the false claim of their own that Owen is a knight or Owen is a knave.
We have exhausted all possibilities for Charlotte, so let us go back and reconsider Owen.
Assume Owen is a knave. No contradiction is found in their false claim that Charlotte is a knave and Luke is a knave.
Assume Charlotte is a knight. No contradiction is found in their claim that Owen is a knight or Owen is a knave.
Luke cannot be a knight, because this would contradict the claim of their own that Owen is a knight.
Assume Luke is a knave. No contradiction is found in their false claim that Owen is a knight.
Therefore, (1) Owen is a knave
(2) Charlotte is a knight
(3) Luke is a knave </think>
<answer> (1) Owen is a knave
(2) Charlotte is a knight
(3) Luke is a knave </answer> | math | {
"ground_truth": {
"names": [
"Owen",
"Charlotte",
"Luke"
],
"solution": [
false,
true,
false
],
"solution_text_format": "(1) Owen is a knave\n(2) Charlotte is a knight\n(3) Luke is a knave",
"statements": "(('and', ('lying', 1), ('lying', 2)), ('or', ('telling-truth', 0), ('lying', 0)), ('telling-truth', 0))"
},
"style": "rule"
} | {
"index": 362,
"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, Owen, and Victoria. \"Owen is a knight if and only if Owen is a knave,\" Evelyn mentioned. Owen told you that Owen is a knight and Evelyn is a knight. \"Owen is a knave and Owen is a knight,\" Victoria 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"
}
]
| [
"Evelyn cannot be a knight, because this would contradict the claim of their own that Owen is a knight if and only if Owen is a knave.\n",
"Assume Evelyn is a knave. ",
"No contradiction is found in their false claim that Owen is a knight if and only if Owen is a knave.\n",
"Owen cannot be a knight, because this would contradict the claim of their own that Owen is a knight and Evelyn is a knight.\n",
"Assume Owen is a knave. ",
"No contradiction is found in their false claim that Owen is a knight and Evelyn is a knight.\n",
"Victoria cannot be a knight, because this would contradict the claim of their own that Owen is a knave and Owen is a knight.\n",
"Assume Victoria is a knave. ",
"No contradiction is found in their false claim that Owen is a knave and Owen is a knight.\n",
"Therefore, (1) Evelyn is a knave\n",
"(2) Owen is a knave\n",
"(3) Victoria is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Evelyn, Owen, and Victoria. "Owen is a knight if and only if Owen is a knave," Evelyn mentioned. Owen told you that Owen is a knight and Evelyn is a knight. "Owen is a knave and Owen is a knight," Victoria 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> | Evelyn cannot be a knight, because this would contradict the claim of their own that Owen is a knight if and only if Owen is a knave.
Assume Evelyn is a knave. No contradiction is found in their false claim that Owen is a knight if and only if Owen is a knave.
Owen cannot be a knight, because this would contradict the claim of their own that Owen is a knight and Evelyn is a knight.
Assume Owen is a knave. No contradiction is found in their false claim that Owen is a knight and Evelyn is a knight.
Victoria cannot be a knight, because this would contradict the claim of their own that Owen is a knave and Owen is a knight.
Assume Victoria is a knave. No contradiction is found in their false claim that Owen is a knave and Owen is a knight.
Therefore, (1) Evelyn is a knave
(2) Owen is a knave
(3) Victoria is a knave </think>
<answer> (1) Evelyn is a knave
(2) Owen is a knave
(3) Victoria is a knave </answer> | math | {
"ground_truth": {
"names": [
"Evelyn",
"Owen",
"Victoria"
],
"solution": [
false,
false,
false
],
"solution_text_format": "(1) Evelyn is a knave\n(2) Owen is a knave\n(3) Victoria is a knave",
"statements": "(('<=>', ('telling-truth', 1), ('lying', 1)), ('and', ('telling-truth', 1), ('telling-truth', 0)), ('and', ('lying', 1), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 363,
"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, Jack, and Charlotte. \"James is a knight if and only if Charlotte is a knave,\" James mentioned. \"James is a knave or Jack is a knight\" - Jack. Charlotte remarked, \"If Jack is a knight then 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 James is a knight if and only if Charlotte is a knave.\n",
"Charlotte cannot be a knight, because this would contradict the claim of James that James is a knight if and only if Charlotte is a knave.\n",
"Assume Charlotte is a knave. ",
"No contradiction is found in their false claim that If Jack is a knight then James is a knave.\n",
"Assume Jack is a knight. ",
"No contradiction is found in their claim that James is a knave or Jack is a knight.\n",
"Therefore, (1) James is a knight\n",
"(2) Jack 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: James, Jack, and Charlotte. "James is a knight if and only if Charlotte is a knave," James mentioned. "James is a knave or Jack is a knight" - Jack. Charlotte remarked, "If Jack is a knight then 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 James is a knight if and only if Charlotte is a knave.
Charlotte cannot be a knight, because this would contradict the claim of James that James is a knight if and only if Charlotte is a knave.
Assume Charlotte is a knave. No contradiction is found in their false claim that If Jack is a knight then James is a knave.
Assume Jack is a knight. No contradiction is found in their claim that James is a knave or Jack is a knight.
Therefore, (1) James is a knight
(2) Jack is a knight
(3) Charlotte is a knave </think>
<answer> (1) James is a knight
(2) Jack is a knight
(3) Charlotte is a knave </answer> | math | {
"ground_truth": {
"names": [
"James",
"Jack",
"Charlotte"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) James is a knight\n(2) Jack is a knight\n(3) Charlotte is a knave",
"statements": "(('<=>', ('telling-truth', 0), ('lying', 2)), ('or', ('lying', 0), ('telling-truth', 1)), ('->', ('telling-truth', 1), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 364,
"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, Jackson, and Isabella. In Mia's words: \"Isabella is a knave if and only if Isabella is a knight\". Jackson expressed that Mia is a knave. \"Jackson is not a knight\" - Isabella. So who is a knight and who is a knave? 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"
}
]
| [
"Mia cannot be a knight, because this would contradict the claim of their own that Isabella is a knave if and only if Isabella is a knight.\n",
"Assume Mia is a knave. ",
"No contradiction is found in their false claim that Isabella is a knave if and only if Isabella is a knight.\n",
"Assume Isabella is a knight. ",
"No contradiction is found in their claim that Jackson is not a knight.\n",
"Jackson cannot be a knight, because this would contradict the claim of Isabella that Jackson is not a knight.\n",
"Jackson cannot be a knave, because this would contradict the false claim of their own that Mia is a knave.\n",
"We have exhausted all possibilities for Jackson, so let us go back and reconsider Isabella.\n",
"Assume Isabella is a knave. ",
"No contradiction is found in their false claim that Jackson is not a knight.\n",
"Assume Jackson is a knight. ",
"No contradiction is found in their claim that Mia is a knave.\n",
"Therefore, (1) Mia is a knave\n",
"(2) Jackson is a knight\n",
"(3) Isabella is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Mia, Jackson, and Isabella. In Mia's words: "Isabella is a knave if and only if Isabella is a knight". Jackson expressed that Mia is a knave. "Jackson is not a knight" - Isabella. So who is a knight and who is a knave? 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> | Mia cannot be a knight, because this would contradict the claim of their own that Isabella is a knave if and only if Isabella is a knight.
Assume Mia is a knave. No contradiction is found in their false claim that Isabella is a knave if and only if Isabella is a knight.
Assume Isabella is a knight. No contradiction is found in their claim that Jackson is not a knight.
Jackson cannot be a knight, because this would contradict the claim of Isabella that Jackson is not a knight.
Jackson cannot be a knave, because this would contradict the false claim of their own that Mia is a knave.
We have exhausted all possibilities for Jackson, so let us go back and reconsider Isabella.
Assume Isabella is a knave. No contradiction is found in their false claim that Jackson is not a knight.
Assume Jackson is a knight. No contradiction is found in their claim that Mia is a knave.
Therefore, (1) Mia is a knave
(2) Jackson is a knight
(3) Isabella is a knave </think>
<answer> (1) Mia is a knave
(2) Jackson is a knight
(3) Isabella is a knave </answer> | math | {
"ground_truth": {
"names": [
"Mia",
"Jackson",
"Isabella"
],
"solution": [
false,
true,
false
],
"solution_text_format": "(1) Mia is a knave\n(2) Jackson is a knight\n(3) Isabella is a knave",
"statements": "(('<=>', ('lying', 2), ('telling-truth', 2)), ('lying', 0), ('not', ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 365,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Ava, Emma, and Joseph. Ava expressed that Emma is a knight if and only if Joseph is a knave. Emma stated, \"If Emma is a knight then Ava is a knave\". In Joseph's words: \"Emma is a knight or Joseph is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Ava is a knight. ",
"No contradiction is found in their claim that Emma is a knight if and only if Joseph is a knave.\n",
"Emma cannot be a knight, because this would contradict the claim of their own that If Emma is a knight then Ava is a knave.\n",
"Emma cannot be a knave, because this would contradict the false claim of their own that If Emma is a knight then Ava is a knave.\n",
"We have exhausted all possibilities for Emma, so let us go back and reconsider Ava.\n",
"Assume Ava is a knave. ",
"No contradiction is found in their false claim that Emma is a knight if and only if Joseph is a knave.\n",
"Assume Emma is a knight. ",
"No contradiction is found in their claim that If Emma is a knight then Ava is a knave.\n",
"Assume Joseph is a knight. ",
"No contradiction is found in their claim that Emma is a knight or Joseph is a knight.\n",
"Therefore, (1) Ava is a knave\n",
"(2) Emma 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: Ava, Emma, and Joseph. Ava expressed that Emma is a knight if and only if Joseph is a knave. Emma stated, "If Emma is a knight then Ava is a knave". In Joseph's words: "Emma is a knight or Joseph is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Ava is a knight. No contradiction is found in their claim that Emma is a knight if and only if Joseph is a knave.
Emma cannot be a knight, because this would contradict the claim of their own that If Emma is a knight then Ava is a knave.
Emma cannot be a knave, because this would contradict the false claim of their own that If Emma is a knight then Ava is a knave.
We have exhausted all possibilities for Emma, so let us go back and reconsider Ava.
Assume Ava is a knave. No contradiction is found in their false claim that Emma is a knight if and only if Joseph is a knave.
Assume Emma is a knight. No contradiction is found in their claim that If Emma is a knight then Ava is a knave.
Assume Joseph is a knight. No contradiction is found in their claim that Emma is a knight or Joseph is a knight.
Therefore, (1) Ava is a knave
(2) Emma is a knight
(3) Joseph is a knight </think>
<answer> (1) Ava is a knave
(2) Emma is a knight
(3) Joseph is a knight </answer> | math | {
"ground_truth": {
"names": [
"Ava",
"Emma",
"Joseph"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Ava is a knave\n(2) Emma is a knight\n(3) Joseph is a knight",
"statements": "(('<=>', ('telling-truth', 1), ('lying', 2)), ('->', ('telling-truth', 1), ('lying', 0)), ('or', ('telling-truth', 1), ('telling-truth', 2)))"
},
"style": "rule"
} | {
"index": 366,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Ava, Abigail, and Lily. Ava asserted: \"Lily is a knight\". \"Ava is a knight,\" Abigail declared. Lily said, \"Abigail is a knave if and only if Lily 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 Ava is a knight. ",
"No contradiction is found in their claim that Lily is a knight.\n",
"Assume Lily is a knight. ",
"No contradiction is found in their claim that Abigail is a knave if and only if Lily is a knight.\n",
"Abigail cannot be a knight, because this would contradict the claim of Lily that Abigail is a knave if and only if Lily is a knight.\n",
"Abigail cannot be a knave, because this would contradict the false claim of their own that Ava is a knight.\n",
"We have exhausted all possibilities for Abigail, so let us go back and reconsider Lily.\n",
"Lily cannot be a knave, because this would contradict the claim of Ava that Lily is a knight.\n",
"We have exhausted all possibilities for Lily, so let us go back and reconsider Ava.\n",
"Assume Ava is a knave. ",
"No contradiction is found in their false claim that Lily is a knight.\n",
"Lily cannot be a knight, because this would contradict the false claim of Ava that Lily is a knight.\n",
"Assume Lily is a knave. ",
"No contradiction is found in their false claim that Abigail is a knave if and only if Lily is a knight.\n",
"Abigail cannot be a knight, because this would contradict the claim of their own that Ava is a knight.\n",
"Assume Abigail is a knave. ",
"No contradiction is found in their false claim that Ava is a knight.\n",
"Therefore, (1) Ava is a knave\n",
"(2) Abigail is a knave\n",
"(3) Lily is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Ava, Abigail, and Lily. Ava asserted: "Lily is a knight". "Ava is a knight," Abigail declared. Lily said, "Abigail is a knave if and only if Lily 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 Ava is a knight. No contradiction is found in their claim that Lily is a knight.
Assume Lily is a knight. No contradiction is found in their claim that Abigail is a knave if and only if Lily is a knight.
Abigail cannot be a knight, because this would contradict the claim of Lily that Abigail is a knave if and only if Lily is a knight.
Abigail cannot be a knave, because this would contradict the false claim of their own that Ava is a knight.
We have exhausted all possibilities for Abigail, so let us go back and reconsider Lily.
Lily cannot be a knave, because this would contradict the claim of Ava that Lily is a knight.
We have exhausted all possibilities for Lily, so let us go back and reconsider Ava.
Assume Ava is a knave. No contradiction is found in their false claim that Lily is a knight.
Lily cannot be a knight, because this would contradict the false claim of Ava that Lily is a knight.
Assume Lily is a knave. No contradiction is found in their false claim that Abigail is a knave if and only if Lily is a knight.
Abigail cannot be a knight, because this would contradict the claim of their own that Ava is a knight.
Assume Abigail is a knave. No contradiction is found in their false claim that Ava is a knight.
Therefore, (1) Ava is a knave
(2) Abigail is a knave
(3) Lily is a knave </think>
<answer> (1) Ava is a knave
(2) Abigail is a knave
(3) Lily is a knave </answer> | math | {
"ground_truth": {
"names": [
"Ava",
"Abigail",
"Lily"
],
"solution": [
false,
false,
false
],
"solution_text_format": "(1) Ava is a knave\n(2) Abigail is a knave\n(3) Lily is a knave",
"statements": "(('telling-truth', 2), ('telling-truth', 0), ('<=>', ('lying', 1), ('telling-truth', 2)))"
},
"style": "rule"
} | {
"index": 367,
"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: William, Jack, and Amelia. William told you that Amelia is a knight or Jack is a knight. Jack stated, \"Jack is a knight if and only if William is a knave\". Amelia stated, \"Jack 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 William is a knight. ",
"No contradiction is found in their claim that Amelia is a knight or Jack is a knight.\n",
"Assume Amelia is a knight. ",
"No contradiction is found in their claim that Jack is a knight.\n",
"Jack cannot be a knight, because this would contradict the claim of their own that Jack is a knight if and only if William is a knave.\n",
"Jack cannot be a knave, because this would contradict the false claim of their own that Jack is a knight if and only if William is a knave.\n",
"We have exhausted all possibilities for Jack, so let us go back and reconsider Amelia.\n",
"Assume Amelia is a knave. ",
"No contradiction is found in their false claim that Jack is a knight.\n",
"Jack cannot be a knight, because this would contradict the claim of their own that Jack is a knight if and only if William is a knave.\n",
"Jack cannot be a knave, because this would contradict the claim of William that Amelia is a knight or Jack is a knight.\n",
"We have exhausted all possibilities for Jack and Amelia, so let us go back and reconsider William.\n",
"Assume William is a knave. ",
"No contradiction is found in their false claim that Amelia is a knight or Jack is a knight.\n",
"Amelia cannot be a knight, because this would contradict the false claim of William that Amelia is a knight or Jack is a knight.\n",
"Assume Amelia is a knave. ",
"No contradiction is found in their false claim that Jack is a knight.\n",
"Jack cannot be a knight, because this would contradict the false claim of William that Amelia is a knight or Jack is a knight.\n",
"Assume Jack is a knave. ",
"No contradiction is found in their false claim that Jack is a knight if and only if William is a knave.\n",
"Therefore, (1) William is a knave\n",
"(2) Jack is a knave\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: William, Jack, and Amelia. William told you that Amelia is a knight or Jack is a knight. Jack stated, "Jack is a knight if and only if William is a knave". Amelia stated, "Jack 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 William is a knight. No contradiction is found in their claim that Amelia is a knight or Jack is a knight.
Assume Amelia is a knight. No contradiction is found in their claim that Jack is a knight.
Jack cannot be a knight, because this would contradict the claim of their own that Jack is a knight if and only if William is a knave.
Jack cannot be a knave, because this would contradict the false claim of their own that Jack is a knight if and only if William is a knave.
We have exhausted all possibilities for Jack, so let us go back and reconsider Amelia.
Assume Amelia is a knave. No contradiction is found in their false claim that Jack is a knight.
Jack cannot be a knight, because this would contradict the claim of their own that Jack is a knight if and only if William is a knave.
Jack cannot be a knave, because this would contradict the claim of William that Amelia is a knight or Jack is a knight.
We have exhausted all possibilities for Jack and Amelia, so let us go back and reconsider William.
Assume William is a knave. No contradiction is found in their false claim that Amelia is a knight or Jack is a knight.
Amelia cannot be a knight, because this would contradict the false claim of William that Amelia is a knight or Jack is a knight.
Assume Amelia is a knave. No contradiction is found in their false claim that Jack is a knight.
Jack cannot be a knight, because this would contradict the false claim of William that Amelia is a knight or Jack is a knight.
Assume Jack is a knave. No contradiction is found in their false claim that Jack is a knight if and only if William is a knave.
Therefore, (1) William is a knave
(2) Jack is a knave
(3) Amelia is a knave </think>
<answer> (1) William is a knave
(2) Jack is a knave
(3) Amelia is a knave </answer> | math | {
"ground_truth": {
"names": [
"William",
"Jack",
"Amelia"
],
"solution": [
false,
false,
false
],
"solution_text_format": "(1) William is a knave\n(2) Jack is a knave\n(3) Amelia is a knave",
"statements": "(('or', ('telling-truth', 2), ('telling-truth', 1)), ('<=>', ('telling-truth', 1), ('lying', 0)), ('telling-truth', 1))"
},
"style": "rule"
} | {
"index": 368,
"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, Alexander, and Luke. In a statement by Victoria: \"Alexander is a knave\". Alexander told you that If Luke is a knave then Alexander is a knight. According to Luke, \"If Alexander is a knight then Victoria is a knave\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Victoria is a knight. ",
"No contradiction is found in their claim that Alexander is a knave.\n",
"Alexander cannot be a knight, because this would contradict the claim of Victoria that Alexander is a knave.\n",
"Assume Alexander is a knave. ",
"No contradiction is found in their false claim that If Luke is a knave then Alexander is a knight.\n",
"Luke cannot be a knight, because this would contradict the false claim of Alexander that If Luke is a knave then Alexander is a knight.\n",
"Luke cannot be a knave, because this would contradict the false claim of their own that If Alexander is a knight then Victoria is a knave.\n",
"We have exhausted all possibilities for Luke and Alexander, so let us go back and reconsider Victoria.\n",
"Assume Victoria is a knave. ",
"No contradiction is found in their false claim that Alexander is a knave.\n",
"Assume Alexander is a knight. ",
"No contradiction is found in their claim that If Luke is a knave then Alexander is a knight.\n",
"Assume Luke is a knight. ",
"No contradiction is found in their claim that If Alexander is a knight then Victoria is a knave.\n",
"Therefore, (1) Victoria is a knave\n",
"(2) Alexander is a knight\n",
"(3) Luke is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Victoria, Alexander, and Luke. In a statement by Victoria: "Alexander is a knave". Alexander told you that If Luke is a knave then Alexander is a knight. According to Luke, "If Alexander is a knight then Victoria is a knave". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Victoria is a knight. No contradiction is found in their claim that Alexander is a knave.
Alexander cannot be a knight, because this would contradict the claim of Victoria that Alexander is a knave.
Assume Alexander is a knave. No contradiction is found in their false claim that If Luke is a knave then Alexander is a knight.
Luke cannot be a knight, because this would contradict the false claim of Alexander that If Luke is a knave then Alexander is a knight.
Luke cannot be a knave, because this would contradict the false claim of their own that If Alexander is a knight then Victoria is a knave.
We have exhausted all possibilities for Luke and Alexander, so let us go back and reconsider Victoria.
Assume Victoria is a knave. No contradiction is found in their false claim that Alexander is a knave.
Assume Alexander is a knight. No contradiction is found in their claim that If Luke is a knave then Alexander is a knight.
Assume Luke is a knight. No contradiction is found in their claim that If Alexander is a knight then Victoria is a knave.
Therefore, (1) Victoria is a knave
(2) Alexander is a knight
(3) Luke is a knight </think>
<answer> (1) Victoria is a knave
(2) Alexander is a knight
(3) Luke is a knight </answer> | math | {
"ground_truth": {
"names": [
"Victoria",
"Alexander",
"Luke"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Victoria is a knave\n(2) Alexander is a knight\n(3) Luke is a knight",
"statements": "(('lying', 1), ('->', ('lying', 2), ('telling-truth', 1)), ('->', ('telling-truth', 1), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 369,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Emma, Sofia, and Daniel. \"If Sofia is a knight then Daniel is a knight,\" Emma claimed. \"Daniel is a knave or Emma is a knave\" - Sofia. Daniel told you that Emma is a knave or 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 Emma is a knight. ",
"No contradiction is found in their claim that If Sofia is a knight then Daniel is a knight.\n",
"Assume Sofia is a knight. ",
"No contradiction is found in their claim that Daniel is a knave or Emma is a knave.\n",
"Daniel cannot be a knight, because this would contradict the claim of Sofia that Daniel is a knave or Emma is a knave.\n",
"Daniel cannot be a knave, because this would contradict the claim of Emma that If Sofia is a knight then Daniel is a knight.\n",
"We have exhausted all possibilities for Daniel, so let us go back and reconsider Sofia.\n",
"Assume Sofia is a knave. ",
"No contradiction is found in their false claim that Daniel is a knave or Emma is a knave.\n",
"Assume Daniel is a knight. ",
"No contradiction is found in their claim that Emma is a knave or Sofia is a knave.\n",
"Therefore, (1) Emma is a knight\n",
"(2) Sofia is a knave\n",
"(3) Daniel is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Emma, Sofia, and Daniel. "If Sofia is a knight then Daniel is a knight," Emma claimed. "Daniel is a knave or Emma is a knave" - Sofia. Daniel told you that Emma is a knave or 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 Emma is a knight. No contradiction is found in their claim that If Sofia is a knight then Daniel is a knight.
Assume Sofia is a knight. No contradiction is found in their claim that Daniel is a knave or Emma is a knave.
Daniel cannot be a knight, because this would contradict the claim of Sofia that Daniel is a knave or Emma is a knave.
Daniel cannot be a knave, because this would contradict the claim of Emma that If Sofia is a knight then Daniel is a knight.
We have exhausted all possibilities for Daniel, so let us go back and reconsider Sofia.
Assume Sofia is a knave. No contradiction is found in their false claim that Daniel is a knave or Emma is a knave.
Assume Daniel is a knight. No contradiction is found in their claim that Emma is a knave or Sofia is a knave.
Therefore, (1) Emma is a knight
(2) Sofia is a knave
(3) Daniel is a knight </think>
<answer> (1) Emma is a knight
(2) Sofia is a knave
(3) Daniel is a knight </answer> | math | {
"ground_truth": {
"names": [
"Emma",
"Sofia",
"Daniel"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Emma is a knight\n(2) Sofia is a knave\n(3) Daniel is a knight",
"statements": "(('->', ('telling-truth', 1), ('telling-truth', 2)), ('or', ('lying', 2), ('lying', 0)), ('or', ('lying', 0), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 370,
"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 Lily. Logan stated, \"Michael is not a knight\". According to Michael, \"Lily is a knave or Logan is a knave\". \"Logan is a knight and Michael is a knight,\" Lily 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 Logan is a knight. ",
"No contradiction is found in their claim that Michael is not a knight.\n",
"Michael cannot be a knight, because this would contradict the claim of Logan that Michael is not a knight.\n",
"Assume Michael is a knave. ",
"No contradiction is found in their false claim that Lily is a knave or Logan is a knave.\n",
"Lily cannot be a knight, because this would contradict the claim of their own that Logan is a knight and Michael is a knight.\n",
"Lily cannot be a knave, because this would contradict the false claim of Michael that Lily is a knave or Logan is a knave.\n",
"We have exhausted all possibilities for Lily and Michael, so let us go back and reconsider Logan.\n",
"Assume Logan is a knave. ",
"No contradiction is found in their false claim that Michael is not a knight.\n",
"Assume Michael is a knight. ",
"No contradiction is found in their claim that Lily is a knave or Logan is a knave.\n",
"Lily cannot be a knight, because this would contradict the claim of their own that Logan is a knight and Michael is a knight.\n",
"Assume Lily is a knave. ",
"No contradiction is found in their false claim that Logan is a knight and Michael is a knight.\n",
"Therefore, (1) Logan is a knave\n",
"(2) Michael is a knight\n",
"(3) Lily is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Logan, Michael, and Lily. Logan stated, "Michael is not a knight". According to Michael, "Lily is a knave or Logan is a knave". "Logan is a knight and Michael is a knight," Lily 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 Logan is a knight. No contradiction is found in their claim that Michael is not a knight.
Michael cannot be a knight, because this would contradict the claim of Logan that Michael is not a knight.
Assume Michael is a knave. No contradiction is found in their false claim that Lily is a knave or Logan is a knave.
Lily cannot be a knight, because this would contradict the claim of their own that Logan is a knight and Michael is a knight.
Lily cannot be a knave, because this would contradict the false claim of Michael that Lily is a knave or Logan is a knave.
We have exhausted all possibilities for Lily and Michael, so let us go back and reconsider Logan.
Assume Logan is a knave. No contradiction is found in their false claim that Michael is not a knight.
Assume Michael is a knight. No contradiction is found in their claim that Lily is a knave or Logan is a knave.
Lily cannot be a knight, because this would contradict the claim of their own that Logan is a knight and Michael is a knight.
Assume Lily is a knave. No contradiction is found in their false claim that Logan is a knight and Michael is a knight.
Therefore, (1) Logan is a knave
(2) Michael is a knight
(3) Lily is a knave </think>
<answer> (1) Logan is a knave
(2) Michael is a knight
(3) Lily is a knave </answer> | math | {
"ground_truth": {
"names": [
"Logan",
"Michael",
"Lily"
],
"solution": [
false,
true,
false
],
"solution_text_format": "(1) Logan is a knave\n(2) Michael is a knight\n(3) Lily is a knave",
"statements": "(('not', ('telling-truth', 1)), ('or', ('lying', 2), ('lying', 0)), ('and', ('telling-truth', 0), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 371,
"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, Emma, and Zoey. Benjamin remarked, \"Emma is a knave or Emma is a knight\". Emma stated, \"Zoey is a knight or Zoey is a knave\". \"Benjamin is not a knight,\" Zoey claimed. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Benjamin is a knight. ",
"No contradiction is found in their claim that Emma is a knave or Emma is a knight.\n",
"Assume Emma is a knight. ",
"No contradiction is found in their claim that Zoey is a knight or Zoey is a knave.\n",
"Zoey cannot be a knight, because this would contradict the claim of their own that Benjamin is not a knight.\n",
"Assume Zoey is a knave. ",
"No contradiction is found in their false claim that Benjamin is not a knight.\n",
"Therefore, (1) Benjamin is a knight\n",
"(2) Emma is a knight\n",
"(3) Zoey is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Benjamin, Emma, and Zoey. Benjamin remarked, "Emma is a knave or Emma is a knight". Emma stated, "Zoey is a knight or Zoey is a knave". "Benjamin is not a knight," Zoey claimed. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Benjamin is a knight. No contradiction is found in their claim that Emma is a knave or Emma is a knight.
Assume Emma is a knight. No contradiction is found in their claim that Zoey is a knight or Zoey is a knave.
Zoey cannot be a knight, because this would contradict the claim of their own that Benjamin is not a knight.
Assume Zoey is a knave. No contradiction is found in their false claim that Benjamin is not a knight.
Therefore, (1) Benjamin is a knight
(2) Emma is a knight
(3) Zoey is a knave </think>
<answer> (1) Benjamin is a knight
(2) Emma is a knight
(3) Zoey is a knave </answer> | math | {
"ground_truth": {
"names": [
"Benjamin",
"Emma",
"Zoey"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Benjamin is a knight\n(2) Emma is a knight\n(3) Zoey is a knave",
"statements": "(('or', ('lying', 1), ('telling-truth', 1)), ('or', ('telling-truth', 2), ('lying', 2)), ('not', ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 372,
"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, Isabella, and Joseph. Scarlett remarked, \"Isabella is a knight\". Isabella stated, \"Isabella is a knight if and only if Scarlett is a knave\". In a statement by Joseph: \"Scarlett is a knight and Joseph is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Scarlett is a knight. ",
"No contradiction is found in their claim that Isabella is a knight.\n",
"Isabella cannot be a knight, because this would contradict the claim of their own that Isabella is a knight if and only if Scarlett is a knave.\n",
"Isabella cannot be a knave, because this would contradict the claim of Scarlett that Isabella is a knight.\n",
"We have exhausted all possibilities for Isabella, so let us go back and reconsider Scarlett.\n",
"Assume Scarlett is a knave. ",
"No contradiction is found in their false claim that Isabella is a knight.\n",
"Isabella cannot be a knight, because this would contradict the false claim of Scarlett that Isabella is a knight.\n",
"Assume Isabella is a knave. ",
"No contradiction is found in their false claim that Isabella is a knight if and only if Scarlett is a knave.\n",
"Joseph cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight and Joseph is a knight.\n",
"Assume Joseph is a knave. ",
"No contradiction is found in their false claim that Scarlett is a knight and Joseph is a knight.\n",
"Therefore, (1) Scarlett is a knave\n",
"(2) Isabella is a knave\n",
"(3) Joseph 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, Isabella, and Joseph. Scarlett remarked, "Isabella is a knight". Isabella stated, "Isabella is a knight if and only if Scarlett is a knave". In a statement by Joseph: "Scarlett is a knight and Joseph is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Scarlett is a knight. No contradiction is found in their claim that Isabella is a knight.
Isabella cannot be a knight, because this would contradict the claim of their own that Isabella is a knight if and only if Scarlett is a knave.
Isabella cannot be a knave, because this would contradict the claim of Scarlett that Isabella is a knight.
We have exhausted all possibilities for Isabella, so let us go back and reconsider Scarlett.
Assume Scarlett is a knave. No contradiction is found in their false claim that Isabella is a knight.
Isabella cannot be a knight, because this would contradict the false claim of Scarlett that Isabella is a knight.
Assume Isabella is a knave. No contradiction is found in their false claim that Isabella is a knight if and only if Scarlett is a knave.
Joseph cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight and Joseph is a knight.
Assume Joseph is a knave. No contradiction is found in their false claim that Scarlett is a knight and Joseph is a knight.
Therefore, (1) Scarlett is a knave
(2) Isabella is a knave
(3) Joseph is a knave </think>
<answer> (1) Scarlett is a knave
(2) Isabella is a knave
(3) Joseph is a knave </answer> | math | {
"ground_truth": {
"names": [
"Scarlett",
"Isabella",
"Joseph"
],
"solution": [
false,
false,
false
],
"solution_text_format": "(1) Scarlett is a knave\n(2) Isabella is a knave\n(3) Joseph is a knave",
"statements": "(('telling-truth', 1), ('<=>', ('telling-truth', 1), ('lying', 0)), ('and', ('telling-truth', 0), ('telling-truth', 2)))"
},
"style": "rule"
} | {
"index": 373,
"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, Ava, and Charlotte. Alexander said, \"Charlotte is a knave.\" Ava remarked, \"If Alexander is a knight then Charlotte is a knight\". According to Charlotte, \"If Ava is a knight then Alexander 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 Alexander is a knight. ",
"No contradiction is found in their claim that Charlotte is a knave.\n",
"Charlotte cannot be a knight, because this would contradict the claim of Alexander that Charlotte is a knave.\n",
"Assume Charlotte is a knave. ",
"No contradiction is found in their false claim that If Ava is a knight then Alexander is a knave.\n",
"Ava cannot be a knight, because this would contradict the claim of their own that If Alexander is a knight then Charlotte is a knight.\n",
"Ava cannot be a knave, because this would contradict the false claim of Charlotte that If Ava is a knight then Alexander is a knave.\n",
"We have exhausted all possibilities for Ava and Charlotte, so let us go back and reconsider Alexander.\n",
"Assume Alexander is a knave. ",
"No contradiction is found in their false claim that Charlotte is a knave.\n",
"Assume Charlotte is a knight. ",
"No contradiction is found in their claim that If Ava is a knight then Alexander is a knave.\n",
"Assume Ava is a knight. ",
"No contradiction is found in their claim that If Alexander is a knight then Charlotte is a knight.\n",
"Therefore, (1) Alexander is a knave\n",
"(2) Ava is a knight\n",
"(3) Charlotte is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Alexander, Ava, and Charlotte. Alexander said, "Charlotte is a knave." Ava remarked, "If Alexander is a knight then Charlotte is a knight". According to Charlotte, "If Ava is a knight then Alexander 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 Alexander is a knight. No contradiction is found in their claim that Charlotte is a knave.
Charlotte cannot be a knight, because this would contradict the claim of Alexander that Charlotte is a knave.
Assume Charlotte is a knave. No contradiction is found in their false claim that If Ava is a knight then Alexander is a knave.
Ava cannot be a knight, because this would contradict the claim of their own that If Alexander is a knight then Charlotte is a knight.
Ava cannot be a knave, because this would contradict the false claim of Charlotte that If Ava is a knight then Alexander is a knave.
We have exhausted all possibilities for Ava and Charlotte, so let us go back and reconsider Alexander.
Assume Alexander is a knave. No contradiction is found in their false claim that Charlotte is a knave.
Assume Charlotte is a knight. No contradiction is found in their claim that If Ava is a knight then Alexander is a knave.
Assume Ava is a knight. No contradiction is found in their claim that If Alexander is a knight then Charlotte is a knight.
Therefore, (1) Alexander is a knave
(2) Ava is a knight
(3) Charlotte is a knight </think>
<answer> (1) Alexander is a knave
(2) Ava is a knight
(3) Charlotte is a knight </answer> | math | {
"ground_truth": {
"names": [
"Alexander",
"Ava",
"Charlotte"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Alexander is a knave\n(2) Ava is a knight\n(3) Charlotte is a knight",
"statements": "(('lying', 2), ('->', ('telling-truth', 0), ('telling-truth', 2)), ('->', ('telling-truth', 1), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 374,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Ethan, Noah, and Scarlett. Ethan noted, \"Scarlett is a knave and Scarlett is a knight\". Noah stated, \"If Noah is a knight then Scarlett is a knight\". \"Noah is a knave or Noah is a knight\" - Scarlett. So who is a knight and who is a knave? 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"
}
]
| [
"Ethan 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 Ethan is a knave. ",
"No contradiction is found in their false claim that Scarlett is a knave and Scarlett is a knight.\n",
"Assume Scarlett is a knight. ",
"No contradiction is found in their claim that Noah is a knave or Noah is a knight.\n",
"Assume Noah is a knight. ",
"No contradiction is found in their claim that If Noah is a knight then Scarlett is a knight.\n",
"Therefore, (1) Ethan is a knave\n",
"(2) Noah is a knight\n",
"(3) Scarlett is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Ethan, Noah, and Scarlett. Ethan noted, "Scarlett is a knave and Scarlett is a knight". Noah stated, "If Noah is a knight then Scarlett is a knight". "Noah is a knave or Noah is a knight" - Scarlett. So who is a knight and who is a knave? 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> | Ethan cannot be a knight, because this would contradict the claim of their own that Scarlett is a knave and Scarlett is a knight.
Assume Ethan is a knave. No contradiction is found in their false claim that Scarlett is a knave and Scarlett is a knight.
Assume Scarlett is a knight. No contradiction is found in their claim that Noah is a knave or Noah is a knight.
Assume Noah is a knight. No contradiction is found in their claim that If Noah is a knight then Scarlett is a knight.
Therefore, (1) Ethan is a knave
(2) Noah is a knight
(3) Scarlett is a knight </think>
<answer> (1) Ethan is a knave
(2) Noah is a knight
(3) Scarlett is a knight </answer> | math | {
"ground_truth": {
"names": [
"Ethan",
"Noah",
"Scarlett"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Ethan is a knave\n(2) Noah is a knight\n(3) Scarlett is a knight",
"statements": "(('and', ('lying', 2), ('telling-truth', 2)), ('->', ('telling-truth', 1), ('telling-truth', 2)), ('or', ('lying', 1), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 375,
"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, Zoey, and Victoria. \"Sebastian is a knight or Zoey is a knave\" - Sebastian. Zoey commented, \"Sebastian is a knight\". Victoria told you that Sebastian is a knight and 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 Sebastian is a knight. ",
"No contradiction is found in their claim that Sebastian is a knight or Zoey is a knave.\n",
"Assume Zoey is a knight. ",
"No contradiction is found in their claim that Sebastian is a knight.\n",
"Assume Victoria is a knight. ",
"No contradiction is found in their claim that Sebastian is a knight and Zoey is a knight.\n",
"Therefore, (1) Sebastian is a knight\n",
"(2) Zoey is a knight\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: Sebastian, Zoey, and Victoria. "Sebastian is a knight or Zoey is a knave" - Sebastian. Zoey commented, "Sebastian is a knight". Victoria told you that Sebastian is a knight and 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 Sebastian is a knight. No contradiction is found in their claim that Sebastian is a knight or Zoey is a knave.
Assume Zoey is a knight. No contradiction is found in their claim that Sebastian is a knight.
Assume Victoria is a knight. No contradiction is found in their claim that Sebastian is a knight and Zoey is a knight.
Therefore, (1) Sebastian is a knight
(2) Zoey is a knight
(3) Victoria is a knight </think>
<answer> (1) Sebastian is a knight
(2) Zoey is a knight
(3) Victoria is a knight </answer> | math | {
"ground_truth": {
"names": [
"Sebastian",
"Zoey",
"Victoria"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Sebastian is a knight\n(2) Zoey is a knight\n(3) Victoria is a knight",
"statements": "(('or', ('telling-truth', 0), ('lying', 1)), ('telling-truth', 0), ('and', ('telling-truth', 0), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 376,
"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, James, and Alexander. \"Lily is a knight if and only if Alexander is a knight,\" Lily mentioned. \"James is a knight and Lily is a knight,\" James declared. In Alexander's words: \"Alexander is a knight and James is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Lily is a knight. ",
"No contradiction is found in their claim that Lily is a knight if and only if Alexander is a knight.\n",
"Assume Alexander is a knight. ",
"No contradiction is found in their claim that Alexander is a knight and James is a knight.\n",
"Assume James is a knight. ",
"No contradiction is found in their claim that James is a knight and Lily is a knight.\n",
"Therefore, (1) Lily is a knight\n",
"(2) James is a knight\n",
"(3) Alexander is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Lily, James, and Alexander. "Lily is a knight if and only if Alexander is a knight," Lily mentioned. "James is a knight and Lily is a knight," James declared. In Alexander's words: "Alexander is a knight and James is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Lily is a knight. No contradiction is found in their claim that Lily is a knight if and only if Alexander is a knight.
Assume Alexander is a knight. No contradiction is found in their claim that Alexander is a knight and James is a knight.
Assume James is a knight. No contradiction is found in their claim that James is a knight and Lily is a knight.
Therefore, (1) Lily is a knight
(2) James is a knight
(3) Alexander is a knight </think>
<answer> (1) Lily is a knight
(2) James is a knight
(3) Alexander is a knight </answer> | math | {
"ground_truth": {
"names": [
"Lily",
"James",
"Alexander"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Lily is a knight\n(2) James is a knight\n(3) Alexander is a knight",
"statements": "(('<=>', ('telling-truth', 0), ('telling-truth', 2)), ('and', ('telling-truth', 1), ('telling-truth', 0)), ('and', ('telling-truth', 2), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 377,
"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, Daniel, and Alexander. \"Alexander is not a knight,\" Michael claimed. Daniel commented, \"Alexander is a knave and Michael is a knight\". Alexander said that Daniel is a knave if and only if Michael 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 Alexander is not a knight.\n",
"Alexander cannot be a knight, because this would contradict the claim of Michael that Alexander is not a knight.\n",
"Assume Alexander is a knave. ",
"No contradiction is found in their false claim that Daniel is a knave if and only if Michael is a knave.\n",
"Daniel cannot be a knight, because this would contradict the false claim of Alexander that Daniel is a knave if and only if Michael is a knave.\n",
"Daniel cannot be a knave, because this would contradict the false claim of their own that Alexander is a knave and Michael is a knight.\n",
"We have exhausted all possibilities for Daniel and Alexander, so let us go back and reconsider Michael.\n",
"Assume Michael is a knave. ",
"No contradiction is found in their false claim that Alexander is not a knight.\n",
"Assume Alexander is a knight. ",
"No contradiction is found in their claim that Daniel is a knave if and only if Michael is a knave.\n",
"Daniel cannot be a knight, because this would contradict the claim of their own that Alexander is a knave and Michael is a knight.\n",
"Assume Daniel is a knave. ",
"No contradiction is found in their false claim that Alexander is a knave and Michael is a knight.\n",
"Therefore, (1) Michael is a knave\n",
"(2) Daniel is a knave\n",
"(3) Alexander is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Michael, Daniel, and Alexander. "Alexander is not a knight," Michael claimed. Daniel commented, "Alexander is a knave and Michael is a knight". Alexander said that Daniel is a knave if and only if Michael 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 Alexander is not a knight.
Alexander cannot be a knight, because this would contradict the claim of Michael that Alexander is not a knight.
Assume Alexander is a knave. No contradiction is found in their false claim that Daniel is a knave if and only if Michael is a knave.
Daniel cannot be a knight, because this would contradict the false claim of Alexander that Daniel is a knave if and only if Michael is a knave.
Daniel cannot be a knave, because this would contradict the false claim of their own that Alexander is a knave and Michael is a knight.
We have exhausted all possibilities for Daniel and Alexander, so let us go back and reconsider Michael.
Assume Michael is a knave. No contradiction is found in their false claim that Alexander is not a knight.
Assume Alexander is a knight. No contradiction is found in their claim that Daniel is a knave if and only if Michael is a knave.
Daniel cannot be a knight, because this would contradict the claim of their own that Alexander is a knave and Michael is a knight.
Assume Daniel is a knave. No contradiction is found in their false claim that Alexander is a knave and Michael is a knight.
Therefore, (1) Michael is a knave
(2) Daniel is a knave
(3) Alexander is a knight </think>
<answer> (1) Michael is a knave
(2) Daniel is a knave
(3) Alexander is a knight </answer> | math | {
"ground_truth": {
"names": [
"Michael",
"Daniel",
"Alexander"
],
"solution": [
false,
false,
true
],
"solution_text_format": "(1) Michael is a knave\n(2) Daniel is a knave\n(3) Alexander is a knight",
"statements": "(('not', ('telling-truth', 2)), ('and', ('lying', 2), ('telling-truth', 0)), ('<=>', ('lying', 1), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 378,
"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, William, and Amelia. \"Michael is a knight or Amelia is a knight,\" Michael mentioned. William expressed that Michael is not a knight. In a statement by Amelia: \"If Michael is a knight then William 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 Michael is a knight or Amelia is a knight.\n",
"Assume Amelia is a knight. ",
"No contradiction is found in their claim that If Michael is a knight then William is a knight.\n",
"William cannot be a knight, because this would contradict the claim of their own that Michael is not a knight.\n",
"William cannot be a knave, because this would contradict the claim of Amelia that If Michael is a knight then William is a knight.\n",
"We have exhausted all possibilities for William, so let us go back and reconsider Amelia.\n",
"Assume Amelia is a knave. ",
"No contradiction is found in their false claim that If Michael is a knight then William is a knight.\n",
"William cannot be a knight, because this would contradict the claim of their own that Michael is not a knight.\n",
"Assume William is a knave. ",
"No contradiction is found in their false claim that Michael is not a knight.\n",
"Therefore, (1) Michael is a knight\n",
"(2) William is a knave\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: Michael, William, and Amelia. "Michael is a knight or Amelia is a knight," Michael mentioned. William expressed that Michael is not a knight. In a statement by Amelia: "If Michael is a knight then William 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 Michael is a knight or Amelia is a knight.
Assume Amelia is a knight. No contradiction is found in their claim that If Michael is a knight then William is a knight.
William cannot be a knight, because this would contradict the claim of their own that Michael is not a knight.
William cannot be a knave, because this would contradict the claim of Amelia that If Michael is a knight then William is a knight.
We have exhausted all possibilities for William, so let us go back and reconsider Amelia.
Assume Amelia is a knave. No contradiction is found in their false claim that If Michael is a knight then William is a knight.
William cannot be a knight, because this would contradict the claim of their own that Michael is not a knight.
Assume William is a knave. No contradiction is found in their false claim that Michael is not a knight.
Therefore, (1) Michael is a knight
(2) William is a knave
(3) Amelia is a knave </think>
<answer> (1) Michael is a knight
(2) William is a knave
(3) Amelia is a knave </answer> | math | {
"ground_truth": {
"names": [
"Michael",
"William",
"Amelia"
],
"solution": [
true,
false,
false
],
"solution_text_format": "(1) Michael is a knight\n(2) William is a knave\n(3) Amelia is a knave",
"statements": "(('or', ('telling-truth', 0), ('telling-truth', 2)), ('not', ('telling-truth', 0)), ('->', ('telling-truth', 0), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 379,
"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, Ava, and David. As Harper put it, \"If Ava is a knight then David is a knave\". Ava commented, \"David is a knave or Harper is a knight\". David stated, \"Harper is a knave and Harper is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Harper is a knight. ",
"No contradiction is found in their claim that If Ava is a knight then David is a knave.\n",
"Assume Ava is a knight. ",
"No contradiction is found in their claim that David is a knave or Harper is a knight.\n",
"David cannot be a knight, because this would contradict the claim of Harper that If Ava is a knight then David is a knave.\n",
"Assume David is a knave. ",
"No contradiction is found in their false claim that Harper is a knave and Harper is a knight.\n",
"Therefore, (1) Harper is a knight\n",
"(2) Ava is a knight\n",
"(3) David 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: Harper, Ava, and David. As Harper put it, "If Ava is a knight then David is a knave". Ava commented, "David is a knave or Harper is a knight". David stated, "Harper is a knave and Harper is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Harper is a knight. No contradiction is found in their claim that If Ava is a knight then David is a knave.
Assume Ava is a knight. No contradiction is found in their claim that David is a knave or Harper is a knight.
David cannot be a knight, because this would contradict the claim of Harper that If Ava is a knight then David is a knave.
Assume David is a knave. No contradiction is found in their false claim that Harper is a knave and Harper is a knight.
Therefore, (1) Harper is a knight
(2) Ava is a knight
(3) David is a knave </think>
<answer> (1) Harper is a knight
(2) Ava is a knight
(3) David is a knave </answer> | math | {
"ground_truth": {
"names": [
"Harper",
"Ava",
"David"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Harper is a knight\n(2) Ava is a knight\n(3) David is a knave",
"statements": "(('->', ('telling-truth', 1), ('lying', 2)), ('or', ('lying', 2), ('telling-truth', 0)), ('and', ('lying', 0), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 380,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Sophia, Emily, and Zoey. As Sophia put it, \"Zoey is not a knight\". Emily said that If Zoey is a knave then Sophia is a knight. \"Emily is not a knight,\" Zoey 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 Sophia is a knight. ",
"No contradiction is found in their claim that Zoey is not a knight.\n",
"Zoey cannot be a knight, because this would contradict the claim of Sophia that Zoey is not a knight.\n",
"Assume Zoey is a knave. ",
"No contradiction is found in their false claim that Emily is not a knight.\n",
"Assume Emily is a knight. ",
"No contradiction is found in their claim that If Zoey is a knave then Sophia is a knight.\n",
"Therefore, (1) Sophia is a knight\n",
"(2) Emily is a knight\n",
"(3) Zoey is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Sophia, Emily, and Zoey. As Sophia put it, "Zoey is not a knight". Emily said that If Zoey is a knave then Sophia is a knight. "Emily is not a knight," Zoey 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 Sophia is a knight. No contradiction is found in their claim that Zoey is not a knight.
Zoey cannot be a knight, because this would contradict the claim of Sophia that Zoey is not a knight.
Assume Zoey is a knave. No contradiction is found in their false claim that Emily is not a knight.
Assume Emily is a knight. No contradiction is found in their claim that If Zoey is a knave then Sophia is a knight.
Therefore, (1) Sophia is a knight
(2) Emily is a knight
(3) Zoey is a knave </think>
<answer> (1) Sophia is a knight
(2) Emily is a knight
(3) Zoey is a knave </answer> | math | {
"ground_truth": {
"names": [
"Sophia",
"Emily",
"Zoey"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Sophia is a knight\n(2) Emily is a knight\n(3) Zoey is a knave",
"statements": "(('not', ('telling-truth', 2)), ('->', ('lying', 2), ('telling-truth', 0)), ('not', ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 381,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Chloe, Noah, and Evelyn. Chloe noted, \"Noah is not a knave\". \"If Chloe is a knave then Evelyn is a knight,\" Noah claimed. Evelyn noted, \"If Chloe is a knight then Noah is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Chloe is a knight. ",
"No contradiction is found in their claim that Noah is not a knave.\n",
"Assume Noah is a knight. ",
"No contradiction is found in their claim that If Chloe is a knave then Evelyn is a knight.\n",
"Assume Evelyn is a knight. ",
"No contradiction is found in their claim that If Chloe is a knight then Noah is a knight.\n",
"Therefore, (1) Chloe is a knight\n",
"(2) Noah 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: Chloe, Noah, and Evelyn. Chloe noted, "Noah is not a knave". "If Chloe is a knave then Evelyn is a knight," Noah claimed. Evelyn noted, "If Chloe is a knight then Noah is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Chloe is a knight. No contradiction is found in their claim that Noah is not a knave.
Assume Noah is a knight. No contradiction is found in their claim that If Chloe is a knave then Evelyn is a knight.
Assume Evelyn is a knight. No contradiction is found in their claim that If Chloe is a knight then Noah is a knight.
Therefore, (1) Chloe is a knight
(2) Noah is a knight
(3) Evelyn is a knight </think>
<answer> (1) Chloe is a knight
(2) Noah is a knight
(3) Evelyn is a knight </answer> | math | {
"ground_truth": {
"names": [
"Chloe",
"Noah",
"Evelyn"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Chloe is a knight\n(2) Noah is a knight\n(3) Evelyn is a knight",
"statements": "(('not', ('lying', 1)), ('->', ('lying', 0), ('telling-truth', 2)), ('->', ('telling-truth', 0), ('telling-truth', 1)))"
},
"style": "rule"
} | {
"index": 382,
"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, Isabella, and Sophia. Owen remarked, \"If Owen is a knight then Sophia is a knight\". Isabella told you that Sophia is not a knight. Sophia asserted: \"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 If Owen is a knight then Sophia is a knight.\n",
"Assume Sophia is a knight. ",
"No contradiction is found in their claim that Owen is a knight.\n",
"Isabella cannot be a knight, because this would contradict the claim of their own that Sophia is not a knight.\n",
"Assume Isabella is a knave. ",
"No contradiction is found in their false claim that Sophia is not a knight.\n",
"Therefore, (1) Owen is a knight\n",
"(2) Isabella is a knave\n",
"(3) Sophia is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Owen, Isabella, and Sophia. Owen remarked, "If Owen is a knight then Sophia is a knight". Isabella told you that Sophia is not a knight. Sophia asserted: "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 If Owen is a knight then Sophia is a knight.
Assume Sophia is a knight. No contradiction is found in their claim that Owen is a knight.
Isabella cannot be a knight, because this would contradict the claim of their own that Sophia is not a knight.
Assume Isabella is a knave. No contradiction is found in their false claim that Sophia is not a knight.
Therefore, (1) Owen is a knight
(2) Isabella is a knave
(3) Sophia is a knight </think>
<answer> (1) Owen is a knight
(2) Isabella is a knave
(3) Sophia is a knight </answer> | math | {
"ground_truth": {
"names": [
"Owen",
"Isabella",
"Sophia"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Owen is a knight\n(2) Isabella is a knave\n(3) Sophia is a knight",
"statements": "(('->', ('telling-truth', 0), ('telling-truth', 2)), ('not', ('telling-truth', 2)), ('telling-truth', 0))"
},
"style": "rule"
} | {
"index": 383,
"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, Sofia, and Penelope. Grace said, \"Penelope is a knight if and only if Sofia is a knave.\" Sofia said, \"Sofia is a knight and Grace is a knight.\" Penelope said, \"Sofia is a knight or 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 Grace is a knight. ",
"No contradiction is found in their claim that Penelope is a knight if and only if Sofia is a knave.\n",
"Assume Penelope is a knight. ",
"No contradiction is found in their claim that Sofia is a knight or Sofia is a knave.\n",
"Sofia cannot be a knight, because this would contradict the claim of Grace that Penelope is a knight if and only if Sofia is a knave.\n",
"Assume Sofia is a knave. ",
"No contradiction is found in their false claim that Sofia is a knight and Grace is a knight.\n",
"Therefore, (1) Grace is a knight\n",
"(2) Sofia is a knave\n",
"(3) Penelope is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Grace, Sofia, and Penelope. Grace said, "Penelope is a knight if and only if Sofia is a knave." Sofia said, "Sofia is a knight and Grace is a knight." Penelope said, "Sofia is a knight or 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 Grace is a knight. No contradiction is found in their claim that Penelope is a knight if and only if Sofia is a knave.
Assume Penelope is a knight. No contradiction is found in their claim that Sofia is a knight or Sofia is a knave.
Sofia cannot be a knight, because this would contradict the claim of Grace that Penelope is a knight if and only if Sofia is a knave.
Assume Sofia is a knave. No contradiction is found in their false claim that Sofia is a knight and Grace is a knight.
Therefore, (1) Grace is a knight
(2) Sofia is a knave
(3) Penelope is a knight </think>
<answer> (1) Grace is a knight
(2) Sofia is a knave
(3) Penelope is a knight </answer> | math | {
"ground_truth": {
"names": [
"Grace",
"Sofia",
"Penelope"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Grace is a knight\n(2) Sofia is a knave\n(3) Penelope is a knight",
"statements": "(('<=>', ('telling-truth', 2), ('lying', 1)), ('and', ('telling-truth', 1), ('telling-truth', 0)), ('or', ('telling-truth', 1), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 384,
"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, Scarlett, and Luke. In Aurora's words: \"If Luke is a knave then Luke is a knight\". In a statement by Scarlett: \"Luke is a knave and Aurora is a knight\". \"Scarlett is a knave\" - Luke. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Aurora is a knight. ",
"No contradiction is found in their claim that If Luke is a knave then Luke is a knight.\n",
"Assume Luke is a knight. ",
"No contradiction is found in their claim that Scarlett is a knave.\n",
"Scarlett cannot be a knight, because this would contradict the claim of their own that Luke is a knave and Aurora is a knight.\n",
"Assume Scarlett is a knave. ",
"No contradiction is found in their false claim that Luke is a knave and Aurora is a knight.\n",
"Therefore, (1) Aurora is a knight\n",
"(2) Scarlett is a knave\n",
"(3) Luke is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Aurora, Scarlett, and Luke. In Aurora's words: "If Luke is a knave then Luke is a knight". In a statement by Scarlett: "Luke is a knave and Aurora is a knight". "Scarlett is a knave" - Luke. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Aurora is a knight. No contradiction is found in their claim that If Luke is a knave then Luke is a knight.
Assume Luke is a knight. No contradiction is found in their claim that Scarlett is a knave.
Scarlett cannot be a knight, because this would contradict the claim of their own that Luke is a knave and Aurora is a knight.
Assume Scarlett is a knave. No contradiction is found in their false claim that Luke is a knave and Aurora is a knight.
Therefore, (1) Aurora is a knight
(2) Scarlett is a knave
(3) Luke is a knight </think>
<answer> (1) Aurora is a knight
(2) Scarlett is a knave
(3) Luke is a knight </answer> | math | {
"ground_truth": {
"names": [
"Aurora",
"Scarlett",
"Luke"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Aurora is a knight\n(2) Scarlett is a knave\n(3) Luke is a knight",
"statements": "(('->', ('lying', 2), ('telling-truth', 2)), ('and', ('lying', 2), ('telling-truth', 0)), ('lying', 1))"
},
"style": "rule"
} | {
"index": 385,
"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, Benjamin, and Elizabeth. Liam said that If Elizabeth is a knave then Elizabeth is a knight. In Benjamin's words: \"Elizabeth is a knight if and only if Liam is a knave\". \"Liam is a knave or Liam is a knight,\" Elizabeth 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 If Elizabeth is a knave then Elizabeth is a knight.\n",
"Assume Elizabeth is a knight. ",
"No contradiction is found in their claim that Liam is a knave or Liam is a knight.\n",
"Benjamin cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight if and only if Liam is a knave.\n",
"Assume Benjamin is a knave. ",
"No contradiction is found in their false claim that Elizabeth is a knight if and only if Liam is a knave.\n",
"Therefore, (1) Liam is a knight\n",
"(2) Benjamin 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: Liam, Benjamin, and Elizabeth. Liam said that If Elizabeth is a knave then Elizabeth is a knight. In Benjamin's words: "Elizabeth is a knight if and only if Liam is a knave". "Liam is a knave or Liam is a knight," Elizabeth 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 If Elizabeth is a knave then Elizabeth is a knight.
Assume Elizabeth is a knight. No contradiction is found in their claim that Liam is a knave or Liam is a knight.
Benjamin cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight if and only if Liam is a knave.
Assume Benjamin is a knave. No contradiction is found in their false claim that Elizabeth is a knight if and only if Liam is a knave.
Therefore, (1) Liam is a knight
(2) Benjamin is a knave
(3) Elizabeth is a knight </think>
<answer> (1) Liam is a knight
(2) Benjamin is a knave
(3) Elizabeth is a knight </answer> | math | {
"ground_truth": {
"names": [
"Liam",
"Benjamin",
"Elizabeth"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Liam is a knight\n(2) Benjamin is a knave\n(3) Elizabeth is a knight",
"statements": "(('->', ('lying', 2), ('telling-truth', 2)), ('<=>', ('telling-truth', 2), ('lying', 0)), ('or', ('lying', 0), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 386,
"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: Zoey, Evelyn, and Jackson. According to Zoey, \"Evelyn is a knave if and only if Jackson is a knight\". As Evelyn put it, \"Zoey is a knave\". According to Jackson, \"Zoey 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 Zoey is a knight. ",
"No contradiction is found in their claim that Evelyn is a knave if and only if Jackson is a knight.\n",
"Evelyn cannot be a knight, because this would contradict the claim of their own that Zoey is a knave.\n",
"Assume Evelyn is a knave. ",
"No contradiction is found in their false claim that Zoey is a knave.\n",
"Assume Jackson is a knight. ",
"No contradiction is found in their claim that Zoey is not a knave.\n",
"Therefore, (1) Zoey is a knight\n",
"(2) Evelyn is a knave\n",
"(3) Jackson 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: Zoey, Evelyn, and Jackson. According to Zoey, "Evelyn is a knave if and only if Jackson is a knight". As Evelyn put it, "Zoey is a knave". According to Jackson, "Zoey 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 Zoey is a knight. No contradiction is found in their claim that Evelyn is a knave if and only if Jackson is a knight.
Evelyn cannot be a knight, because this would contradict the claim of their own that Zoey is a knave.
Assume Evelyn is a knave. No contradiction is found in their false claim that Zoey is a knave.
Assume Jackson is a knight. No contradiction is found in their claim that Zoey is not a knave.
Therefore, (1) Zoey is a knight
(2) Evelyn is a knave
(3) Jackson is a knight </think>
<answer> (1) Zoey is a knight
(2) Evelyn is a knave
(3) Jackson is a knight </answer> | math | {
"ground_truth": {
"names": [
"Zoey",
"Evelyn",
"Jackson"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Zoey is a knight\n(2) Evelyn is a knave\n(3) Jackson is a knight",
"statements": "(('<=>', ('lying', 1), ('telling-truth', 2)), ('lying', 0), ('not', ('lying', 0)))"
},
"style": "rule"
} | {
"index": 387,
"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, Olivia, and Aurora. In a statement by Lucas: \"Olivia is a knight or Aurora is a knight\". Olivia commented, \"Aurora is a knave and Aurora is a knight\". Aurora said that Lucas is a knave and Aurora is a knight. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Lucas is a knight. ",
"No contradiction is found in their claim that Olivia is a knight or Aurora is a knight.\n",
"Olivia cannot be a knight, because this would contradict the claim of their own that Aurora is a knave and Aurora is a knight.\n",
"Assume Olivia is a knave. ",
"No contradiction is found in their false claim that Aurora is a knave and Aurora is a knight.\n",
"Aurora cannot be a knight, because this would contradict the claim of their own that Lucas is a knave and Aurora is a knight.\n",
"Aurora cannot be a knave, because this would contradict the claim of Lucas that Olivia is a knight or Aurora is a knight.\n",
"We have exhausted all possibilities for Aurora and Olivia, so let us go back and reconsider Lucas.\n",
"Assume Lucas is a knave. ",
"No contradiction is found in their false claim that Olivia is a knight or Aurora is a knight.\n",
"Olivia cannot be a knight, because this would contradict the false claim of Lucas that Olivia is a knight or Aurora is a knight.\n",
"Assume Olivia is a knave. ",
"No contradiction is found in their false claim that Aurora is a knave and Aurora is a knight.\n",
"Aurora cannot be a knight, because this would contradict the false claim of Lucas that Olivia is a knight or Aurora is a knight.\n",
"Assume Aurora is a knave. ",
"No contradiction is found in their false claim that Lucas is a knave and Aurora is a knight.\n",
"Therefore, (1) Lucas is a knave\n",
"(2) Olivia is a knave\n",
"(3) Aurora is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Lucas, Olivia, and Aurora. In a statement by Lucas: "Olivia is a knight or Aurora is a knight". Olivia commented, "Aurora is a knave and Aurora is a knight". Aurora said that Lucas is a knave and Aurora is a knight. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Lucas is a knight. No contradiction is found in their claim that Olivia is a knight or Aurora is a knight.
Olivia cannot be a knight, because this would contradict the claim of their own that Aurora is a knave and Aurora is a knight.
Assume Olivia is a knave. No contradiction is found in their false claim that Aurora is a knave and Aurora is a knight.
Aurora cannot be a knight, because this would contradict the claim of their own that Lucas is a knave and Aurora is a knight.
Aurora cannot be a knave, because this would contradict the claim of Lucas that Olivia is a knight or Aurora is a knight.
We have exhausted all possibilities for Aurora and Olivia, so let us go back and reconsider Lucas.
Assume Lucas is a knave. No contradiction is found in their false claim that Olivia is a knight or Aurora is a knight.
Olivia cannot be a knight, because this would contradict the false claim of Lucas that Olivia is a knight or Aurora is a knight.
Assume Olivia is a knave. No contradiction is found in their false claim that Aurora is a knave and Aurora is a knight.
Aurora cannot be a knight, because this would contradict the false claim of Lucas that Olivia is a knight or Aurora is a knight.
Assume Aurora is a knave. No contradiction is found in their false claim that Lucas is a knave and Aurora is a knight.
Therefore, (1) Lucas is a knave
(2) Olivia is a knave
(3) Aurora is a knave </think>
<answer> (1) Lucas is a knave
(2) Olivia is a knave
(3) Aurora is a knave </answer> | math | {
"ground_truth": {
"names": [
"Lucas",
"Olivia",
"Aurora"
],
"solution": [
false,
false,
false
],
"solution_text_format": "(1) Lucas is a knave\n(2) Olivia is a knave\n(3) Aurora is a knave",
"statements": "(('or', ('telling-truth', 1), ('telling-truth', 2)), ('and', ('lying', 2), ('telling-truth', 2)), ('and', ('lying', 0), ('telling-truth', 2)))"
},
"style": "rule"
} | {
"index": 388,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Mason, Avery, and Owen. \"If Owen is a knight then Avery is a knight,\" Mason declared. \"Mason is a knight if and only if Avery is a knight\" - Avery. According to Owen, \"If Owen is a knight then Mason is a knight\". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Mason is a knight. ",
"No contradiction is found in their claim that If Owen is a knight then Avery is a knight.\n",
"Assume Owen is a knight. ",
"No contradiction is found in their claim that If Owen is a knight then Mason is a knight.\n",
"Assume Avery is a knight. ",
"No contradiction is found in their claim that Mason is a knight if and only if Avery is a knight.\n",
"Therefore, (1) Mason is a knight\n",
"(2) Avery is a knight\n",
"(3) Owen is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Mason, Avery, and Owen. "If Owen is a knight then Avery is a knight," Mason declared. "Mason is a knight if and only if Avery is a knight" - Avery. According to Owen, "If Owen is a knight then Mason is a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Mason is a knight. No contradiction is found in their claim that If Owen is a knight then Avery is a knight.
Assume Owen is a knight. No contradiction is found in their claim that If Owen is a knight then Mason is a knight.
Assume Avery is a knight. No contradiction is found in their claim that Mason is a knight if and only if Avery is a knight.
Therefore, (1) Mason is a knight
(2) Avery is a knight
(3) Owen is a knight </think>
<answer> (1) Mason is a knight
(2) Avery is a knight
(3) Owen is a knight </answer> | math | {
"ground_truth": {
"names": [
"Mason",
"Avery",
"Owen"
],
"solution": [
true,
true,
true
],
"solution_text_format": "(1) Mason is a knight\n(2) Avery is a knight\n(3) Owen is a knight",
"statements": "(('->', ('telling-truth', 2), ('telling-truth', 1)), ('<=>', ('telling-truth', 0), ('telling-truth', 1)), ('->', ('telling-truth', 2), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 389,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Victoria, Matthew, and Liam. Victoria expressed that Liam is a knave if and only if Matthew is a knight. Matthew told you that Liam is a knight. \"Matthew is a knave or Victoria is a knave,\" Liam mentioned. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Victoria is a knight. ",
"No contradiction is found in their claim that Liam is a knave if and only if Matthew is a knight.\n",
"Assume Liam is a knight. ",
"No contradiction is found in their claim that Matthew is a knave or Victoria is a knave.\n",
"Matthew cannot be a knight, because this would contradict the claim of Victoria that Liam is a knave if and only if Matthew is a knight.\n",
"Matthew cannot be a knave, because this would contradict the false claim of their own that Liam is a knight.\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 or Victoria is a knave.\n",
"Matthew cannot be a knight, because this would contradict the claim of their own that Liam is a knight.\n",
"Matthew cannot be a knave, because this would contradict the claim of Victoria that Liam is a knave if and only if Matthew is a knight.\n",
"We have exhausted all possibilities for Matthew and Liam, so let us go back and reconsider Victoria.\n",
"Assume Victoria is a knave. ",
"No contradiction is found in their false claim that Liam is a knave if and only if Matthew is a knight.\n",
"Assume Liam is a knight. ",
"No contradiction is found in their claim that Matthew is a knave or Victoria is a knave.\n",
"Assume Matthew is a knight. ",
"No contradiction is found in their claim that Liam is a knight.\n",
"Therefore, (1) Victoria is a knave\n",
"(2) Matthew is a knight\n",
"(3) Liam is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Victoria, Matthew, and Liam. Victoria expressed that Liam is a knave if and only if Matthew is a knight. Matthew told you that Liam is a knight. "Matthew is a knave or Victoria is a knave," Liam mentioned. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Victoria is a knight. No contradiction is found in their claim that Liam is a knave if and only if Matthew is a knight.
Assume Liam is a knight. No contradiction is found in their claim that Matthew is a knave or Victoria is a knave.
Matthew cannot be a knight, because this would contradict the claim of Victoria that Liam is a knave if and only if Matthew is a knight.
Matthew cannot be a knave, because this would contradict the false claim of their own that Liam is a knight.
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 or Victoria is a knave.
Matthew cannot be a knight, because this would contradict the claim of their own that Liam is a knight.
Matthew cannot be a knave, because this would contradict the claim of Victoria that Liam is a knave if and only if Matthew is a knight.
We have exhausted all possibilities for Matthew and Liam, so let us go back and reconsider Victoria.
Assume Victoria is a knave. No contradiction is found in their false claim that Liam is a knave if and only if Matthew is a knight.
Assume Liam is a knight. No contradiction is found in their claim that Matthew is a knave or Victoria is a knave.
Assume Matthew is a knight. No contradiction is found in their claim that Liam is a knight.
Therefore, (1) Victoria is a knave
(2) Matthew is a knight
(3) Liam is a knight </think>
<answer> (1) Victoria is a knave
(2) Matthew is a knight
(3) Liam is a knight </answer> | math | {
"ground_truth": {
"names": [
"Victoria",
"Matthew",
"Liam"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Victoria is a knave\n(2) Matthew is a knight\n(3) Liam is a knight",
"statements": "(('<=>', ('lying', 2), ('telling-truth', 1)), ('telling-truth', 2), ('or', ('lying', 1), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 390,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Isabella, Chloe, and Benjamin. Isabella told you that Chloe is a knight if and only if Isabella is a knight. \"Isabella is not a knave,\" Chloe declared. Benjamin asserted: \"If Isabella is a knight then Isabella 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 Isabella is a knight. ",
"No contradiction is found in their claim that Chloe is a knight if and only if Isabella is a knight.\n",
"Assume Chloe is a knight. ",
"No contradiction is found in their claim that Isabella is not a knave.\n",
"Benjamin cannot be a knight, because this would contradict the claim of their own that If Isabella is a knight then Isabella is a knave.\n",
"Assume Benjamin is a knave. ",
"No contradiction is found in their false claim that If Isabella is a knight then Isabella is a knave.\n",
"Therefore, (1) Isabella is a knight\n",
"(2) Chloe is a knight\n",
"(3) Benjamin is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Isabella, Chloe, and Benjamin. Isabella told you that Chloe is a knight if and only if Isabella is a knight. "Isabella is not a knave," Chloe declared. Benjamin asserted: "If Isabella is a knight then Isabella 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 Isabella is a knight. No contradiction is found in their claim that Chloe is a knight if and only if Isabella is a knight.
Assume Chloe is a knight. No contradiction is found in their claim that Isabella is not a knave.
Benjamin cannot be a knight, because this would contradict the claim of their own that If Isabella is a knight then Isabella is a knave.
Assume Benjamin is a knave. No contradiction is found in their false claim that If Isabella is a knight then Isabella is a knave.
Therefore, (1) Isabella is a knight
(2) Chloe is a knight
(3) Benjamin is a knave </think>
<answer> (1) Isabella is a knight
(2) Chloe is a knight
(3) Benjamin is a knave </answer> | math | {
"ground_truth": {
"names": [
"Isabella",
"Chloe",
"Benjamin"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Isabella is a knight\n(2) Chloe is a knight\n(3) Benjamin is a knave",
"statements": "(('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('not', ('lying', 0)), ('->', ('telling-truth', 0), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 391,
"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, Alexander, and Amelia. \"Amelia is not a knight,\" Michael declared. Alexander expressed that Amelia is a knave. Amelia asserted: \"Amelia is a knight and 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 Amelia is not a knight.\n",
"Amelia cannot be a knight, because this would contradict the claim of Michael that Amelia is not a knight.\n",
"Assume Amelia is a knave. ",
"No contradiction is found in their false claim that Amelia is a knight and Michael is a knight.\n",
"Assume Alexander is a knight. ",
"No contradiction is found in their claim that Amelia is a knave.\n",
"Therefore, (1) Michael is a knight\n",
"(2) Alexander 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: Michael, Alexander, and Amelia. "Amelia is not a knight," Michael declared. Alexander expressed that Amelia is a knave. Amelia asserted: "Amelia is a knight and 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 Amelia is not a knight.
Amelia cannot be a knight, because this would contradict the claim of Michael that Amelia is not a knight.
Assume Amelia is a knave. No contradiction is found in their false claim that Amelia is a knight and Michael is a knight.
Assume Alexander is a knight. No contradiction is found in their claim that Amelia is a knave.
Therefore, (1) Michael is a knight
(2) Alexander is a knight
(3) Amelia is a knave </think>
<answer> (1) Michael is a knight
(2) Alexander is a knight
(3) Amelia is a knave </answer> | math | {
"ground_truth": {
"names": [
"Michael",
"Alexander",
"Amelia"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Michael is a knight\n(2) Alexander is a knight\n(3) Amelia is a knave",
"statements": "(('not', ('telling-truth', 2)), ('lying', 2), ('and', ('telling-truth', 2), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 392,
"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 Jacob. Mia said that Oliver is a knight if and only if Mia is a knight. Oliver remarked, \"Mia is not a knave\". Jacob remarked, \"Mia 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 Mia is a knight. ",
"No contradiction is found in their claim that Oliver is a knight if and only if Mia is a knight.\n",
"Assume Oliver is a knight. ",
"No contradiction is found in their claim that Mia is not a knave.\n",
"Jacob cannot be a knight, because this would contradict the claim of their own that Mia is not a knight.\n",
"Assume Jacob is a knave. ",
"No contradiction is found in their false claim that Mia is not a knight.\n",
"Therefore, (1) Mia is a knight\n",
"(2) Oliver is a knight\n",
"(3) Jacob 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 Jacob. Mia said that Oliver is a knight if and only if Mia is a knight. Oliver remarked, "Mia is not a knave". Jacob remarked, "Mia 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 Mia is a knight. No contradiction is found in their claim that Oliver is a knight if and only if Mia is a knight.
Assume Oliver is a knight. No contradiction is found in their claim that Mia is not a knave.
Jacob cannot be a knight, because this would contradict the claim of their own that Mia is not a knight.
Assume Jacob is a knave. No contradiction is found in their false claim that Mia is not a knight.
Therefore, (1) Mia is a knight
(2) Oliver is a knight
(3) Jacob is a knave </think>
<answer> (1) Mia is a knight
(2) Oliver is a knight
(3) Jacob is a knave </answer> | math | {
"ground_truth": {
"names": [
"Mia",
"Oliver",
"Jacob"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Mia is a knight\n(2) Oliver is a knight\n(3) Jacob is a knave",
"statements": "(('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('not', ('lying', 0)), ('not', ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 393,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Sophia, Victoria, and Lucas. Sophia noted, \"Lucas is a knave or Victoria is a knave\". In a statement by Victoria: \"Sophia is not a knight\". Lucas asserted: \"If Lucas is a knight then Sophia 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 Sophia is a knight. ",
"No contradiction is found in their claim that Lucas is a knave or Victoria is a knave.\n",
"Lucas cannot be a knight, because this would contradict the claim of their own that If Lucas is a knight then Sophia is a knave.\n",
"Lucas cannot be a knave, because this would contradict the false claim of their own that If Lucas is a knight then Sophia is a knave.\n",
"We have exhausted all possibilities for Lucas, so let us go back and reconsider Sophia.\n",
"Assume Sophia is a knave. ",
"No contradiction is found in their false claim that Lucas is a knave or Victoria is a knave.\n",
"Assume Lucas is a knight. ",
"No contradiction is found in their claim that If Lucas is a knight then Sophia is a knave.\n",
"Assume Victoria is a knight. ",
"No contradiction is found in their claim that Sophia is not a knight.\n",
"Therefore, (1) Sophia is a knave\n",
"(2) Victoria is a knight\n",
"(3) Lucas is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Sophia, Victoria, and Lucas. Sophia noted, "Lucas is a knave or Victoria is a knave". In a statement by Victoria: "Sophia is not a knight". Lucas asserted: "If Lucas is a knight then Sophia 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 Sophia is a knight. No contradiction is found in their claim that Lucas is a knave or Victoria is a knave.
Lucas cannot be a knight, because this would contradict the claim of their own that If Lucas is a knight then Sophia is a knave.
Lucas cannot be a knave, because this would contradict the false claim of their own that If Lucas is a knight then Sophia is a knave.
We have exhausted all possibilities for Lucas, so let us go back and reconsider Sophia.
Assume Sophia is a knave. No contradiction is found in their false claim that Lucas is a knave or Victoria is a knave.
Assume Lucas is a knight. No contradiction is found in their claim that If Lucas is a knight then Sophia is a knave.
Assume Victoria is a knight. No contradiction is found in their claim that Sophia is not a knight.
Therefore, (1) Sophia is a knave
(2) Victoria is a knight
(3) Lucas is a knight </think>
<answer> (1) Sophia is a knave
(2) Victoria is a knight
(3) Lucas is a knight </answer> | math | {
"ground_truth": {
"names": [
"Sophia",
"Victoria",
"Lucas"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Sophia is a knave\n(2) Victoria is a knight\n(3) Lucas is a knight",
"statements": "(('or', ('lying', 2), ('lying', 1)), ('not', ('telling-truth', 0)), ('->', ('telling-truth', 2), ('lying', 0)))"
},
"style": "rule"
} | {
"index": 394,
"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, Liam, and Owen. In Evelyn's words: \"Evelyn is a knight if and only if Liam is a knave\". Liam told you that If Evelyn is a knight then Liam is a knight. \"Liam is a knave or Evelyn is a knight\" - Owen. So who is a knight and who is a knave? 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 Evelyn is a knight if and only if Liam is a knave.\n",
"Liam cannot be a knight, because this would contradict the claim of Evelyn that Evelyn is a knight if and only if Liam is a knave.\n",
"Assume Liam is a knave. ",
"No contradiction is found in their false claim that If Evelyn is a knight then Liam is a knight.\n",
"Assume Owen is a knight. ",
"No contradiction is found in their claim that Liam is a knave or Evelyn is a knight.\n",
"Therefore, (1) Evelyn is a knight\n",
"(2) Liam is a knave\n",
"(3) Owen is a knight"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Evelyn, Liam, and Owen. In Evelyn's words: "Evelyn is a knight if and only if Liam is a knave". Liam told you that If Evelyn is a knight then Liam is a knight. "Liam is a knave or Evelyn is a knight" - Owen. So who is a knight and who is a knave? 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 Evelyn is a knight if and only if Liam is a knave.
Liam cannot be a knight, because this would contradict the claim of Evelyn that Evelyn is a knight if and only if Liam is a knave.
Assume Liam is a knave. No contradiction is found in their false claim that If Evelyn is a knight then Liam is a knight.
Assume Owen is a knight. No contradiction is found in their claim that Liam is a knave or Evelyn is a knight.
Therefore, (1) Evelyn is a knight
(2) Liam is a knave
(3) Owen is a knight </think>
<answer> (1) Evelyn is a knight
(2) Liam is a knave
(3) Owen is a knight </answer> | math | {
"ground_truth": {
"names": [
"Evelyn",
"Liam",
"Owen"
],
"solution": [
true,
false,
true
],
"solution_text_format": "(1) Evelyn is a knight\n(2) Liam is a knave\n(3) Owen is a knight",
"statements": "(('<=>', ('telling-truth', 0), ('lying', 1)), ('->', ('telling-truth', 0), ('telling-truth', 1)), ('or', ('lying', 1), ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 395,
"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, Penelope, and Emily. Jack asserted: \"Penelope is a knight or Jack is a knight\". \"If Jack is a knave then Emily is a knight,\" Penelope declared. Emily asserted: \"Jack 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 Jack is a knight. ",
"No contradiction is found in their claim that Penelope is a knight or Jack is a knight.\n",
"Assume Penelope is a knight. ",
"No contradiction is found in their claim that If Jack is a knave then Emily is a knight.\n",
"Emily cannot be a knight, because this would contradict the claim of their own that Jack is not a knight.\n",
"Assume Emily is a knave. ",
"No contradiction is found in their false claim that Jack is not a knight.\n",
"Therefore, (1) Jack is a knight\n",
"(2) Penelope is a knight\n",
"(3) Emily 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: Jack, Penelope, and Emily. Jack asserted: "Penelope is a knight or Jack is a knight". "If Jack is a knave then Emily is a knight," Penelope declared. Emily asserted: "Jack 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 Jack is a knight. No contradiction is found in their claim that Penelope is a knight or Jack is a knight.
Assume Penelope is a knight. No contradiction is found in their claim that If Jack is a knave then Emily is a knight.
Emily cannot be a knight, because this would contradict the claim of their own that Jack is not a knight.
Assume Emily is a knave. No contradiction is found in their false claim that Jack is not a knight.
Therefore, (1) Jack is a knight
(2) Penelope is a knight
(3) Emily is a knave </think>
<answer> (1) Jack is a knight
(2) Penelope is a knight
(3) Emily is a knave </answer> | math | {
"ground_truth": {
"names": [
"Jack",
"Penelope",
"Emily"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Jack is a knight\n(2) Penelope is a knight\n(3) Emily is a knave",
"statements": "(('or', ('telling-truth', 1), ('telling-truth', 0)), ('->', ('lying', 0), ('telling-truth', 2)), ('not', ('telling-truth', 0)))"
},
"style": "rule"
} | {
"index": 396,
"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, Logan, and Henry. Charlotte noted, \"Logan is not a knight\". Logan noted, \"Charlotte is a knight or Henry is a knight\". Henry expressed that If Charlotte is a knave then Henry 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 Logan is not a knight.\n",
"Logan cannot be a knight, because this would contradict the claim of Charlotte that Logan is not a knight.\n",
"Logan cannot be a knave, because this would contradict the false claim of their own that Charlotte is a knight or Henry is a knight.\n",
"We have exhausted all possibilities for Logan, so let us go back and reconsider Charlotte.\n",
"Assume Charlotte is a knave. ",
"No contradiction is found in their false claim that Logan is not a knight.\n",
"Assume Logan is a knight. ",
"No contradiction is found in their claim that Charlotte is a knight or Henry is a knight.\n",
"Assume Henry is a knight. ",
"No contradiction is found in their claim that If Charlotte is a knave then Henry is a knight.\n",
"Therefore, (1) Charlotte is a knave\n",
"(2) Logan 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: Charlotte, Logan, and Henry. Charlotte noted, "Logan is not a knight". Logan noted, "Charlotte is a knight or Henry is a knight". Henry expressed that If Charlotte is a knave then Henry 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 Logan is not a knight.
Logan cannot be a knight, because this would contradict the claim of Charlotte that Logan is not a knight.
Logan cannot be a knave, because this would contradict the false claim of their own that Charlotte is a knight or Henry is a knight.
We have exhausted all possibilities for Logan, so let us go back and reconsider Charlotte.
Assume Charlotte is a knave. No contradiction is found in their false claim that Logan is not a knight.
Assume Logan is a knight. No contradiction is found in their claim that Charlotte is a knight or Henry is a knight.
Assume Henry is a knight. No contradiction is found in their claim that If Charlotte is a knave then Henry is a knight.
Therefore, (1) Charlotte is a knave
(2) Logan is a knight
(3) Henry is a knight </think>
<answer> (1) Charlotte is a knave
(2) Logan is a knight
(3) Henry is a knight </answer> | math | {
"ground_truth": {
"names": [
"Charlotte",
"Logan",
"Henry"
],
"solution": [
false,
true,
true
],
"solution_text_format": "(1) Charlotte is a knave\n(2) Logan is a knight\n(3) Henry is a knight",
"statements": "(('not', ('telling-truth', 1)), ('or', ('telling-truth', 0), ('telling-truth', 2)), ('->', ('lying', 0), ('telling-truth', 2)))"
},
"style": "rule"
} | {
"index": 397,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Grace, Noah, and Lily. Grace said that Noah is a knave or Noah is a knight. \"Grace is a knight,\" Noah claimed. \"If Noah is a knight then Noah is a knave\" - Lily. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Assume Grace is a knight. ",
"No contradiction is found in their claim that Noah is a knave or Noah is a knight.\n",
"Assume Noah is a knight. ",
"No contradiction is found in their claim that Grace is a knight.\n",
"Lily cannot be a knight, because this would contradict the claim of their own that If Noah is a knight then Noah is a knave.\n",
"Assume Lily is a knave. ",
"No contradiction is found in their false claim that If Noah is a knight then Noah is a knave.\n",
"Therefore, (1) Grace is a knight\n",
"(2) Noah is a knight\n",
"(3) Lily is a knave"
] | A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Grace, Noah, and Lily. Grace said that Noah is a knave or Noah is a knight. "Grace is a knight," Noah claimed. "If Noah is a knight then Noah is a knave" - Lily. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Assume Grace is a knight. No contradiction is found in their claim that Noah is a knave or Noah is a knight.
Assume Noah is a knight. No contradiction is found in their claim that Grace is a knight.
Lily cannot be a knight, because this would contradict the claim of their own that If Noah is a knight then Noah is a knave.
Assume Lily is a knave. No contradiction is found in their false claim that If Noah is a knight then Noah is a knave.
Therefore, (1) Grace is a knight
(2) Noah is a knight
(3) Lily is a knave </think>
<answer> (1) Grace is a knight
(2) Noah is a knight
(3) Lily is a knave </answer> | math | {
"ground_truth": {
"names": [
"Grace",
"Noah",
"Lily"
],
"solution": [
true,
true,
false
],
"solution_text_format": "(1) Grace is a knight\n(2) Noah is a knight\n(3) Lily is a knave",
"statements": "(('or', ('lying', 1), ('telling-truth', 1)), ('telling-truth', 0), ('->', ('telling-truth', 1), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 398,
"split": "train"
} |
kk_logic | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.\nUser: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Sophia, Penelope, and Mason. \"Mason is a knave if and only if Mason is a knight,\" Sophia declared. Penelope was heard saying, \"Penelope is a knight or Sophia is a knave\". \"Sophia is a knight and Penelope is a knave,\" Mason mentioned. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight\n(2) Oliver is a knight\n(3)... </answer>.\nAssistant: Let me solve this step by step.\n<think> ",
"role": "user"
}
]
| [
"Sophia 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 Sophia 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",
"Mason cannot be a knight, because this would contradict the claim of their own that Sophia is a knight and Penelope is a knave.\n",
"Assume Mason is a knave. ",
"No contradiction is found in their false claim that Sophia is a knight and Penelope is a knave.\n",
"Assume Penelope is a knight. ",
"No contradiction is found in their claim that Penelope is a knight or Sophia is a knave.\n",
"Therefore, (1) Sophia is a knave\n",
"(2) Penelope is a knight\n",
"(3) Mason 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: Sophia, Penelope, and Mason. "Mason is a knave if and only if Mason is a knight," Sophia declared. Penelope was heard saying, "Penelope is a knight or Sophia is a knave". "Sophia is a knight and Penelope is a knave," Mason mentioned. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> | Sophia 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 Sophia is a knave. No contradiction is found in their false claim that Mason is a knave if and only if Mason is a knight.
Mason cannot be a knight, because this would contradict the claim of their own that Sophia is a knight and Penelope is a knave.
Assume Mason is a knave. No contradiction is found in their false claim that Sophia is a knight and Penelope is a knave.
Assume Penelope is a knight. No contradiction is found in their claim that Penelope is a knight or Sophia is a knave.
Therefore, (1) Sophia is a knave
(2) Penelope is a knight
(3) Mason is a knave </think>
<answer> (1) Sophia is a knave
(2) Penelope is a knight
(3) Mason is a knave </answer> | math | {
"ground_truth": {
"names": [
"Sophia",
"Penelope",
"Mason"
],
"solution": [
false,
true,
false
],
"solution_text_format": "(1) Sophia is a knave\n(2) Penelope is a knight\n(3) Mason is a knave",
"statements": "(('<=>', ('lying', 2), ('telling-truth', 2)), ('or', ('telling-truth', 1), ('lying', 0)), ('and', ('telling-truth', 0), ('lying', 1)))"
},
"style": "rule"
} | {
"index": 399,
"split": "train"
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.