Search is not available for this dataset
names
sequencelengths 2
8
| knight_knave
dict | solution
sequencelengths 2
8
| solution_text
stringlengths 37
171
| solution_text_format
stringlengths 39
191
| cot_head
stringclasses 1
value | cot_repeat_steps
sequencelengths 2
123
| cot_foot
stringclasses 1
value | statements
stringlengths 58
390
| index
int64 100
1.1k
| n_ppl
int64 2
8
| data_source
stringclasses 1
value | prompt
listlengths 2
2
| ability
stringclasses 1
value | difficulty
int64 2
8
| reward_model
dict | extra_info
dict |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
[
"Oliver",
"Ethan"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
true
] |
Oliver is a knight, and Ethan is a knight.
|
(1) Oliver is a knight
(2) Ethan is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Oliver is a knight. No contradiction is found in their claim that Oliver is a knight or Ethan is a knave.",
"Assume Ethan is a knight. No contradiction is found in their claim that Oliver is a knight."
] |
This leads to a feasible solution.
|
(('or', ('telling-truth', 0), ('lying', 1)), ('telling-truth', 0))
| 100
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Oliver, and Ethan. Oliver told you that Oliver is a knight or Ethan is a knave. In a statement by Ethan: \"Oliver is a knight\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Oliver is a knight\n(2) Ethan is a knight",
"statements": "(('or', ('telling-truth', 0), ('lying', 1)), ('telling-truth', 0))"
},
"style": "rule"
}
|
{
"index": 0,
"split": "train"
}
|
[
"Michael",
"Jacob"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
false
] |
Michael is a knight, and Jacob is a knave.
|
(1) Michael is a knight
(2) Jacob is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Michael is a knight. No contradiction is found in their claim that Jacob is a knave.",
"Jacob cannot be a knight, because this would contradict the claim of Michael that Jacob is a knave.",
"Assume Jacob is a knave. No contradiction is found in their false claim that Michael is a knave if and only if Michael is a knight."
] |
This leads to a feasible solution.
|
(('lying', 1), ('<=>', ('lying', 0), ('telling-truth', 0)))
| 101
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Michael, and Jacob. Michael said, \"Jacob is a knave.\" \"Michael is a knave if and only if Michael is a knight,\" Jacob declared. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Michael is a knight\n(2) Jacob is a knave",
"statements": "(('lying', 1), ('<=>', ('lying', 0), ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 1,
"split": "train"
}
|
[
"Amelia",
"Harper"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
false
] |
Amelia is a knight, and Harper is a knave.
|
(1) Amelia is a knight
(2) Harper is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Amelia is a knight. No contradiction is found in their claim that Harper is a knight or Harper is a knave.",
"Harper cannot be a knight, because this would contradict the claim of their own that Amelia is a knight and Amelia is a knave.",
"Assume Harper is a knave. No contradiction is found in their false claim that Amelia is a knight and Amelia is a knave."
] |
This leads to a feasible solution.
|
(('or', ('telling-truth', 1), ('lying', 1)), ('and', ('telling-truth', 0), ('lying', 0)))
| 102
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Amelia, and Harper. Amelia was heard saying, \"Harper is a knight or Harper is a knave\". \"Amelia is a knight and Amelia is a knave,\" Harper claimed. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Amelia is a knight\n(2) Harper is a knave",
"statements": "(('or', ('telling-truth', 1), ('lying', 1)), ('and', ('telling-truth', 0), ('lying', 0)))"
},
"style": "rule"
}
|
{
"index": 2,
"split": "train"
}
|
[
"Logan",
"Lily"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
false
] |
Logan is a knave, and Lily is a knave.
|
(1) Logan is a knave
(2) Lily is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Logan is a knight. No contradiction is found in their claim that Lily is not a knave.",
"Lily cannot be a knight, because this would contradict the claim of their own that Logan is a knave and Lily is a knight.",
"Lily cannot be a knave, because this would contradict the claim of Logan that Lily is not a knave.",
"We have exhausted all possibilities for Lily, so let us go back and reconsider Logan.",
"Assume Logan is a knave. No contradiction is found in their false claim that Lily is not a knave.",
"Lily cannot be a knight, because this would contradict the false claim of Logan that Lily is not a knave.",
"Assume Lily is a knave. No contradiction is found in their false claim that Logan is a knave and Lily is a knight."
] |
This leads to a feasible solution.
|
(('not', ('lying', 1)), ('and', ('lying', 0), ('telling-truth', 1)))
| 103
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Logan, and Lily. Logan stated, \"Lily is not a knave\". Lily expressed that Logan is a knave and Lily is a knight. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Logan is a knave\n(2) Lily is a knave",
"statements": "(('not', ('lying', 1)), ('and', ('lying', 0), ('telling-truth', 1)))"
},
"style": "rule"
}
|
{
"index": 3,
"split": "train"
}
|
[
"Jack",
"Evelyn"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
true
] |
Jack is a knight, and Evelyn is a knight.
|
(1) Jack is a knight
(2) Evelyn is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Jack is a knight. No contradiction is found in their claim that Evelyn is a knight or Evelyn is a knave.",
"Assume Evelyn is a knight. No contradiction is found in their claim that If Jack is a knave then Evelyn is a knight."
] |
This leads to a feasible solution.
|
(('or', ('telling-truth', 1), ('lying', 1)), ('->', ('lying', 0), ('telling-truth', 1)))
| 104
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Jack, and Evelyn. In Jack's words: \"Evelyn is a knight or Evelyn is a knave\". Evelyn asserted: \"If Jack is a knave then Evelyn is a knight\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Jack is a knight\n(2) Evelyn is a knight",
"statements": "(('or', ('telling-truth', 1), ('lying', 1)), ('->', ('lying', 0), ('telling-truth', 1)))"
},
"style": "rule"
}
|
{
"index": 4,
"split": "train"
}
|
[
"Samuel",
"Aria"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
true
] |
Samuel is a knave, and Aria is a knight.
|
(1) Samuel is a knave
(2) Aria is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Samuel 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.",
"Assume Samuel is a knave. No contradiction is found in their false claim that Aria is a knight if and only if Aria is a knave.",
"Assume Aria is a knight. No contradiction is found in their claim that Samuel is a knave or Samuel is a knight."
] |
This leads to a feasible solution.
|
(('<=>', ('telling-truth', 1), ('lying', 1)), ('or', ('lying', 0), ('telling-truth', 0)))
| 105
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Samuel, and Aria. In Samuel's words: \"Aria is a knight if and only if Aria is a knave\". Aria commented, \"Samuel is a knave or Samuel is a knight\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Samuel is a knave\n(2) Aria is a knight",
"statements": "(('<=>', ('telling-truth', 1), ('lying', 1)), ('or', ('lying', 0), ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 5,
"split": "train"
}
|
[
"Daniel",
"Liam"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
false
] |
Daniel is a knave, and Liam is a knave.
|
(1) Daniel is a knave
(2) Liam is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Daniel is a knight. No contradiction is found in their claim that Liam is a knave if and only if Daniel is a knight.",
"Liam cannot be a knight, because this would contradict the claim of Daniel that Liam is a knave if and only if Daniel is a knight.",
"Liam cannot be a knave, because this would contradict the false claim of their own that Daniel is a knight or Liam is a knight.",
"We have exhausted all possibilities for Liam, so let us go back and reconsider Daniel.",
"Assume Daniel is a knave. No contradiction is found in their false claim that Liam is a knave if and only if Daniel is a knight.",
"Liam cannot be a knight, because this would contradict the false claim of Daniel that Liam is a knave if and only if Daniel is a knight.",
"Assume Liam is a knave. No contradiction is found in their false claim that Daniel is a knight or Liam is a knight."
] |
This leads to a feasible solution.
|
(('<=>', ('lying', 1), ('telling-truth', 0)), ('or', ('telling-truth', 0), ('telling-truth', 1)))
| 106
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Daniel, and Liam. In a statement by Daniel: \"Liam is a knave if and only if Daniel is a knight\". Liam said, \"Daniel is a knight or Liam is a knight.\" So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Daniel is a knave\n(2) Liam is a knave",
"statements": "(('<=>', ('lying', 1), ('telling-truth', 0)), ('or', ('telling-truth', 0), ('telling-truth', 1)))"
},
"style": "rule"
}
|
{
"index": 6,
"split": "train"
}
|
[
"Ava",
"Henry"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
false
] |
Ava is a knight, and Henry is a knave.
|
(1) Ava is a knight
(2) Henry is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Ava is a knight. No contradiction is found in their claim that Henry is a knight or Henry is a knave.",
"Henry cannot be a knight, because this would contradict the claim of their own that Ava is a knight if and only if Ava is a knave.",
"Assume Henry is a knave. No contradiction is found in their false claim that Ava is a knight if and only if Ava is a knave."
] |
This leads to a feasible solution.
|
(('or', ('telling-truth', 1), ('lying', 1)), ('<=>', ('telling-truth', 0), ('lying', 0)))
| 107
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Ava, and Henry. Ava told you that Henry is a knight or Henry is a knave. \"Ava is a knight if and only if Ava is a knave,\" Henry claimed. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Ava is a knight\n(2) Henry is a knave",
"statements": "(('or', ('telling-truth', 1), ('lying', 1)), ('<=>', ('telling-truth', 0), ('lying', 0)))"
},
"style": "rule"
}
|
{
"index": 7,
"split": "train"
}
|
[
"Penelope",
"Alexander"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
true
] |
Penelope is a knight, and Alexander is a knight.
|
(1) Penelope is a knight
(2) Alexander is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Penelope is a knight. No contradiction is found in their claim that If Penelope is a knight then Alexander is a knight.",
"Assume Alexander is a knight. No contradiction is found in their claim that Penelope is a knight."
] |
This leads to a feasible solution.
|
(('->', ('telling-truth', 0), ('telling-truth', 1)), ('telling-truth', 0))
| 108
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Penelope, and Alexander. Penelope asserted: \"If Penelope is a knight then Alexander is a knight\". According to Alexander, \"Penelope is a knight\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Penelope is a knight\n(2) Alexander is a knight",
"statements": "(('->', ('telling-truth', 0), ('telling-truth', 1)), ('telling-truth', 0))"
},
"style": "rule"
}
|
{
"index": 8,
"split": "train"
}
|
[
"Riley",
"Sophia"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
true
] |
Riley is a knave, and Sophia is a knight.
|
(1) Riley is a knave
(2) Sophia is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Riley 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 Riley is a knave. No contradiction is found in their false claim that Sophia is a knight if and only if Sophia is a knave.",
"Assume Sophia is a knight. No contradiction is found in their claim that Riley is a knave or Sophia is a knight."
] |
This leads to a feasible solution.
|
(('<=>', ('telling-truth', 1), ('lying', 1)), ('or', ('lying', 0), ('telling-truth', 1)))
| 109
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Riley, and Sophia. \"Sophia is a knight if and only if Sophia is a knave\" - Riley. Sophia remarked, \"Riley is a knave or Sophia is a knight\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Riley is a knave\n(2) Sophia is a knight",
"statements": "(('<=>', ('telling-truth', 1), ('lying', 1)), ('or', ('lying', 0), ('telling-truth', 1)))"
},
"style": "rule"
}
|
{
"index": 9,
"split": "train"
}
|
[
"Liam",
"Benjamin"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
true
] |
Liam is a knight, and Benjamin is a knight.
|
(1) Liam is a knight
(2) Benjamin is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Liam is a knight. No contradiction is found in their claim that If Benjamin is a knave then Liam is a knight.",
"Assume Benjamin is a knight. No contradiction is found in their claim that Liam is a knight or Liam is a knave."
] |
This leads to a feasible solution.
|
(('->', ('lying', 1), ('telling-truth', 0)), ('or', ('telling-truth', 0), ('lying', 0)))
| 110
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Liam, and Benjamin. Liam said that If Benjamin is a knave then Liam is a knight. \"Liam is a knight or Liam is a knave,\" Benjamin declared. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Liam is a knight\n(2) Benjamin is a knight",
"statements": "(('->', ('lying', 1), ('telling-truth', 0)), ('or', ('telling-truth', 0), ('lying', 0)))"
},
"style": "rule"
}
|
{
"index": 10,
"split": "train"
}
|
[
"Scarlett",
"Aria"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
false
] |
Scarlett is a knave, and Aria is a knave.
|
(1) Scarlett is a knave
(2) Aria is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Scarlett cannot be a knight, because this would contradict the claim of their own that Aria is a knave and Aria is a knight.",
"Assume Scarlett is a knave. No contradiction is found in their false claim that Aria is a knave and Aria is a knight.",
"Aria cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight if and only if Scarlett is a knave.",
"Assume Aria is a knave. No contradiction is found in their false claim that Scarlett is a knight if and only if Scarlett is a knave."
] |
This leads to a feasible solution.
|
(('and', ('lying', 1), ('telling-truth', 1)), ('<=>', ('telling-truth', 0), ('lying', 0)))
| 111
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Scarlett, and Aria. \"Aria is a knave and Aria is a knight,\" Scarlett mentioned. \"Scarlett is a knight if and only if Scarlett is a knave\" - Aria. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Scarlett is a knave\n(2) Aria is a knave",
"statements": "(('and', ('lying', 1), ('telling-truth', 1)), ('<=>', ('telling-truth', 0), ('lying', 0)))"
},
"style": "rule"
}
|
{
"index": 11,
"split": "train"
}
|
[
"Harper",
"Luke"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
true
] |
Harper is a knight, and Luke is a knight.
|
(1) Harper is a knight
(2) Luke is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Harper is a knight. No contradiction is found in their claim that Luke is a knight.",
"Assume Luke is a knight. No contradiction is found in their claim that Harper is a knight if and only if Luke is a knight."
] |
This leads to a feasible solution.
|
(('telling-truth', 1), ('<=>', ('telling-truth', 0), ('telling-truth', 1)))
| 112
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Harper, and Luke. Harper was heard saying, \"Luke is a knight\". \"Harper is a knight if and only if Luke is a knight,\" Luke declared. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Harper is a knight\n(2) Luke is a knight",
"statements": "(('telling-truth', 1), ('<=>', ('telling-truth', 0), ('telling-truth', 1)))"
},
"style": "rule"
}
|
{
"index": 12,
"split": "train"
}
|
[
"Ava",
"Charlotte"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
false
] |
Ava is a knight, and Charlotte is a knave.
|
(1) Ava is a knight
(2) Charlotte is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Ava 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 Ava that Charlotte is a knave.",
"Assume Charlotte is a knave. No contradiction is found in their false claim that Ava is a knight if and only if Charlotte is a knight."
] |
This leads to a feasible solution.
|
(('lying', 1), ('<=>', ('telling-truth', 0), ('telling-truth', 1)))
| 113
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Ava, and Charlotte. Ava expressed that Charlotte is a knave. Charlotte asserted: \"Ava is a knight if and only if Charlotte is a knight\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Ava is a knight\n(2) Charlotte is a knave",
"statements": "(('lying', 1), ('<=>', ('telling-truth', 0), ('telling-truth', 1)))"
},
"style": "rule"
}
|
{
"index": 13,
"split": "train"
}
|
[
"Joseph",
"Samuel"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
false
] |
Joseph is a knave, and Samuel is a knave.
|
(1) Joseph is a knave
(2) Samuel is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Joseph cannot be a knight, because this would contradict the claim of their own that Samuel is a knight and Samuel is a knave.",
"Assume Joseph 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 Joseph is a knight if and only if Joseph is a knave.",
"Assume Samuel is a knave. No contradiction is found in their false claim that Joseph is a knight if and only if Joseph is a knave."
] |
This leads to a feasible solution.
|
(('and', ('telling-truth', 1), ('lying', 1)), ('<=>', ('telling-truth', 0), ('lying', 0)))
| 114
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Joseph, and Samuel. Joseph remarked, \"Samuel is a knight and Samuel is a knave\". Samuel expressed that Joseph is a knight if and only if Joseph is a knave. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Joseph is a knave\n(2) Samuel is a knave",
"statements": "(('and', ('telling-truth', 1), ('lying', 1)), ('<=>', ('telling-truth', 0), ('lying', 0)))"
},
"style": "rule"
}
|
{
"index": 14,
"split": "train"
}
|
[
"Sebastian",
"Benjamin"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
false
] |
Sebastian is a knight, and Benjamin is a knave.
|
(1) Sebastian is a knight
(2) Benjamin is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Sebastian is a knight. No contradiction is found in their claim that If Sebastian is a knight then Benjamin is a knave.",
"Benjamin cannot be a knight, because this would contradict the claim of Sebastian that If Sebastian is a knight then Benjamin is a knave.",
"Assume Benjamin is a knave. No contradiction is found in their false claim that Sebastian is a knight and Sebastian is a knave."
] |
This leads to a feasible solution.
|
(('->', ('telling-truth', 0), ('lying', 1)), ('and', ('telling-truth', 0), ('lying', 0)))
| 115
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Sebastian, and Benjamin. \"If Sebastian is a knight then Benjamin is a knave,\" Sebastian claimed. \"Sebastian is a knight and Sebastian is a knave\" - Benjamin. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Sebastian is a knight\n(2) Benjamin is a knave",
"statements": "(('->', ('telling-truth', 0), ('lying', 1)), ('and', ('telling-truth', 0), ('lying', 0)))"
},
"style": "rule"
}
|
{
"index": 15,
"split": "train"
}
|
[
"Amelia",
"Jacob"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
false
] |
Amelia is a knave, and Jacob is a knave.
|
(1) Amelia is a knave
(2) Jacob is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Amelia cannot be a knight, because this would contradict the claim of their own that Jacob is a knight and Jacob is a knave.",
"Assume Amelia is a knave. No contradiction is found in their false claim that Jacob is a knight and Jacob is a knave.",
"Jacob cannot be a knight, because this would contradict the claim of their own that If Amelia is a knave then Amelia is a knight.",
"Assume Jacob is a knave. No contradiction is found in their false claim that If Amelia is a knave then Amelia is a knight."
] |
This leads to a feasible solution.
|
(('and', ('telling-truth', 1), ('lying', 1)), ('->', ('lying', 0), ('telling-truth', 0)))
| 116
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Amelia, and Jacob. Amelia said that Jacob is a knight and Jacob is a knave. Jacob commented, \"If Amelia is a knave then Amelia is a knight\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Amelia is a knave\n(2) Jacob is a knave",
"statements": "(('and', ('telling-truth', 1), ('lying', 1)), ('->', ('lying', 0), ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 16,
"split": "train"
}
|
[
"Abigail",
"Harper"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
true
] |
Abigail is a knight, and Harper is a knight.
|
(1) Abigail is a knight
(2) Harper is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Abigail is a knight. No contradiction is found in their claim that If Abigail is a knight then Harper is a knight.",
"Assume Harper is a knight. No contradiction is found in their claim that Abigail is a knight or Harper is a knight."
] |
This leads to a feasible solution.
|
(('->', ('telling-truth', 0), ('telling-truth', 1)), ('or', ('telling-truth', 0), ('telling-truth', 1)))
| 117
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Abigail, and Harper. Abigail asserted: \"If Abigail is a knight then Harper is a knight\". According to Harper, \"Abigail is a knight or Harper is a knight\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Abigail is a knight\n(2) Harper is a knight",
"statements": "(('->', ('telling-truth', 0), ('telling-truth', 1)), ('or', ('telling-truth', 0), ('telling-truth', 1)))"
},
"style": "rule"
}
|
{
"index": 17,
"split": "train"
}
|
[
"Scarlett",
"Joseph"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
false
] |
Scarlett is a knave, and Joseph is a knave.
|
(1) Scarlett is a knave
(2) Joseph is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Scarlett is a knight. No contradiction is found in their claim that Scarlett is a knight if and only if Joseph is a knave.",
"Joseph cannot be a knight, because this would contradict the claim of Scarlett that Scarlett is a knight if and only if Joseph is a knave.",
"Joseph cannot be a knave, because this would contradict the false claim of their own that If Scarlett is a knave then Joseph is a knight.",
"We have exhausted all possibilities for Joseph, so let us go back and reconsider Scarlett.",
"Assume Scarlett is a knave. No contradiction is found in their false claim that Scarlett is a knight if and only if Joseph is a knave.",
"Joseph cannot be a knight, because this would contradict the false claim of Scarlett that Scarlett is a knight if and only if Joseph is a knave.",
"Assume Joseph is a knave. No contradiction is found in their false claim that If Scarlett is a knave then Joseph is a knight."
] |
This leads to a feasible solution.
|
(('<=>', ('telling-truth', 0), ('lying', 1)), ('->', ('lying', 0), ('telling-truth', 1)))
| 118
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Scarlett, and Joseph. \"Scarlett is a knight if and only if Joseph is a knave,\" Scarlett claimed. Joseph was heard saying, \"If Scarlett is a knave then Joseph is a knight\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Scarlett is a knave\n(2) Joseph is a knave",
"statements": "(('<=>', ('telling-truth', 0), ('lying', 1)), ('->', ('lying', 0), ('telling-truth', 1)))"
},
"style": "rule"
}
|
{
"index": 18,
"split": "train"
}
|
[
"Daniel",
"Riley"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
false
] |
Daniel is a knight, and Riley is a knave.
|
(1) Daniel is a knight
(2) Riley is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Daniel is a knight. No contradiction is found in their claim that Riley is not a knight.",
"Riley cannot be a knight, because this would contradict the claim of Daniel that Riley is not a knight.",
"Assume Riley is a knave. No contradiction is found in their false claim that Daniel is a knight if and only if Riley is a knight."
] |
This leads to a feasible solution.
|
(('not', ('telling-truth', 1)), ('<=>', ('telling-truth', 0), ('telling-truth', 1)))
| 119
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Daniel, and Riley. According to Daniel, \"Riley is not a knight\". \"Daniel is a knight if and only if Riley is a knight,\" Riley declared. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Daniel is a knight\n(2) Riley is a knave",
"statements": "(('not', ('telling-truth', 1)), ('<=>', ('telling-truth', 0), ('telling-truth', 1)))"
},
"style": "rule"
}
|
{
"index": 19,
"split": "train"
}
|
[
"Elizabeth",
"Oliver"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
true
] |
Elizabeth is a knight, and Oliver is a knight.
|
(1) Elizabeth is a knight
(2) Oliver is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Elizabeth is a knight. No contradiction is found in their claim that Oliver is not a knave.",
"Assume Oliver is a knight. No contradiction is found in their claim that Oliver is a knight or Elizabeth is a knave."
] |
This leads to a feasible solution.
|
(('not', ('lying', 1)), ('or', ('telling-truth', 1), ('lying', 0)))
| 120
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Elizabeth, and Oliver. \"Oliver is not a knave,\" Elizabeth mentioned. Oliver remarked, \"Oliver is a knight or Elizabeth is a knave\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Elizabeth is a knight\n(2) Oliver is a knight",
"statements": "(('not', ('lying', 1)), ('or', ('telling-truth', 1), ('lying', 0)))"
},
"style": "rule"
}
|
{
"index": 20,
"split": "train"
}
|
[
"Daniel",
"Abigail"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
true
] |
Daniel is a knave, and Abigail is a knight.
|
(1) Daniel is a knave
(2) Abigail is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Daniel cannot be a knight, because this would contradict the claim of their own that Abigail is a knave and Abigail is a knight.",
"Assume Daniel is a knave. No contradiction is found in their false claim that Abigail is a knave and Abigail is a knight.",
"Assume Abigail is a knight. No contradiction is found in their claim that Daniel is a knight or Daniel is a knave."
] |
This leads to a feasible solution.
|
(('and', ('lying', 1), ('telling-truth', 1)), ('or', ('telling-truth', 0), ('lying', 0)))
| 121
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Daniel, and Abigail. According to Daniel, \"Abigail is a knave and Abigail is a knight\". Abigail noted, \"Daniel is a knight or Daniel is a knave\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Daniel is a knave\n(2) Abigail is a knight",
"statements": "(('and', ('lying', 1), ('telling-truth', 1)), ('or', ('telling-truth', 0), ('lying', 0)))"
},
"style": "rule"
}
|
{
"index": 21,
"split": "train"
}
|
[
"Sophia",
"Logan"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
true
] |
Sophia is a knight, and Logan is a knight.
|
(1) Sophia is a knight
(2) Logan is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Sophia is a knight. No contradiction is found in their claim that Logan is a knight or Logan is a knave.",
"Assume Logan is a knight. No contradiction is found in their claim that Sophia is a knight or Sophia is a knave."
] |
This leads to a feasible solution.
|
(('or', ('telling-truth', 1), ('lying', 1)), ('or', ('telling-truth', 0), ('lying', 0)))
| 122
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Sophia, and Logan. \"Logan is a knight or Logan is a knave,\" Sophia declared. \"Sophia is a knight or Sophia is a knave,\" Logan claimed. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Sophia is a knight\n(2) Logan is a knight",
"statements": "(('or', ('telling-truth', 1), ('lying', 1)), ('or', ('telling-truth', 0), ('lying', 0)))"
},
"style": "rule"
}
|
{
"index": 22,
"split": "train"
}
|
[
"Charlotte",
"Alexander"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
true
] |
Charlotte is a knave, and Alexander is a knight.
|
(1) Charlotte is a knave
(2) Alexander is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Charlotte is a knight. No contradiction is found in their claim that If Alexander is a knight then Alexander is a knave.",
"Alexander cannot be a knight, because this would contradict the claim of Charlotte that If Alexander is a knight then Alexander is a knave.",
"Alexander cannot be a knave, because this would contradict the false claim of their own that Charlotte is a knight or Alexander is a knight.",
"We have exhausted all possibilities for Alexander, so let us go back and reconsider Charlotte.",
"Assume Charlotte is a knave. No contradiction is found in their false claim that If Alexander is a knight then Alexander is a knave.",
"Assume Alexander is a knight. No contradiction is found in their claim that Charlotte is a knight or Alexander is a knight."
] |
This leads to a feasible solution.
|
(('->', ('telling-truth', 1), ('lying', 1)), ('or', ('telling-truth', 0), ('telling-truth', 1)))
| 123
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Charlotte, and Alexander. Charlotte said, \"If Alexander is a knight then Alexander is a knave.\" \"Charlotte is a knight or Alexander is a knight,\" Alexander declared. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Charlotte is a knave\n(2) Alexander is a knight",
"statements": "(('->', ('telling-truth', 1), ('lying', 1)), ('or', ('telling-truth', 0), ('telling-truth', 1)))"
},
"style": "rule"
}
|
{
"index": 23,
"split": "train"
}
|
[
"Charlotte",
"Aiden"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
true
] |
Charlotte is a knave, and Aiden is a knight.
|
(1) Charlotte is a knave
(2) Aiden is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Charlotte is a knight. No contradiction is found in their claim that Aiden is a knave.",
"Aiden cannot be a knight, because this would contradict the claim of Charlotte that Aiden is a knave.",
"Aiden cannot be a knave, because this would contradict the false claim of their own that Charlotte is a knave or Charlotte is a knight.",
"We have exhausted all possibilities for Aiden, so let us go back and reconsider Charlotte.",
"Assume Charlotte is a knave. No contradiction is found in their false claim that Aiden is a knave.",
"Assume Aiden is a knight. No contradiction is found in their claim that Charlotte is a knave or Charlotte is a knight."
] |
This leads to a feasible solution.
|
(('lying', 1), ('or', ('lying', 0), ('telling-truth', 0)))
| 124
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Charlotte, and Aiden. Charlotte told you that Aiden is a knave. Aiden stated, \"Charlotte is a knave or Charlotte is a knight\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Charlotte is a knave\n(2) Aiden is a knight",
"statements": "(('lying', 1), ('or', ('lying', 0), ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 24,
"split": "train"
}
|
[
"Charlotte",
"Scarlett"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
false
] |
Charlotte is a knave, and Scarlett is a knave.
|
(1) Charlotte is a knave
(2) Scarlett is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Charlotte cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight and Scarlett is a knave.",
"Assume Charlotte is a knave. No contradiction is found in their false claim that Scarlett is a knight and Scarlett is a knave.",
"Scarlett cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight and Charlotte is a knight.",
"Assume Scarlett is a knave. No contradiction is found in their false claim that Scarlett is a knight and Charlotte is a knight."
] |
This leads to a feasible solution.
|
(('and', ('telling-truth', 1), ('lying', 1)), ('and', ('telling-truth', 1), ('telling-truth', 0)))
| 125
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Charlotte, and Scarlett. \"Scarlett is a knight and Scarlett is a knave\" - Charlotte. Scarlett stated, \"Scarlett is a knight and Charlotte is a knight\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Charlotte is a knave\n(2) Scarlett is a knave",
"statements": "(('and', ('telling-truth', 1), ('lying', 1)), ('and', ('telling-truth', 1), ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 25,
"split": "train"
}
|
[
"Olivia",
"Henry"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
false
] |
Olivia is a knight, and Henry is a knave.
|
(1) Olivia is a knight
(2) Henry is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Olivia is a knight. No contradiction is found in their claim that Henry is a knight or Henry is a knave.",
"Henry cannot be a knight, because this would contradict the claim of their own that Olivia is a knave and Olivia is a knight.",
"Assume Henry is a knave. No contradiction is found in their false claim that Olivia is a knave and Olivia is a knight."
] |
This leads to a feasible solution.
|
(('or', ('telling-truth', 1), ('lying', 1)), ('and', ('lying', 0), ('telling-truth', 0)))
| 126
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Olivia, and Henry. Olivia asserted: \"Henry is a knight or Henry is a knave\". In Henry's words: \"Olivia is a knave and Olivia is a knight\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Olivia is a knight\n(2) Henry is a knave",
"statements": "(('or', ('telling-truth', 1), ('lying', 1)), ('and', ('lying', 0), ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 26,
"split": "train"
}
|
[
"Daniel",
"Lily"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
true
] |
Daniel is a knave, and Lily is a knight.
|
(1) Daniel is a knave
(2) Lily is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Daniel is a knight. No contradiction is found in their claim that If Lily is a knight then Lily is a knave.",
"Lily cannot be a knight, because this would contradict the claim of Daniel that If Lily is a knight then Lily is a knave.",
"Lily cannot be a knave, because this would contradict the false claim of their own that Lily is a knight or Daniel is a knight.",
"We have exhausted all possibilities for Lily, so let us go back and reconsider Daniel.",
"Assume Daniel is a knave. No contradiction is found in their false claim that If Lily is a knight then Lily is a knave.",
"Assume Lily is a knight. No contradiction is found in their claim that Lily is a knight or Daniel is a knight."
] |
This leads to a feasible solution.
|
(('->', ('telling-truth', 1), ('lying', 1)), ('or', ('telling-truth', 1), ('telling-truth', 0)))
| 127
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Daniel, and Lily. Daniel was heard saying, \"If Lily is a knight then Lily is a knave\". Lily was heard saying, \"Lily is a knight or Daniel is a knight\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Daniel is a knave\n(2) Lily is a knight",
"statements": "(('->', ('telling-truth', 1), ('lying', 1)), ('or', ('telling-truth', 1), ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 27,
"split": "train"
}
|
[
"Jack",
"Benjamin"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
false
] |
Jack is a knight, and Benjamin is a knave.
|
(1) Jack is a knight
(2) Benjamin is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Jack is a knight. No contradiction is found in their claim that Benjamin is a knight or Jack is a knight.",
"Benjamin cannot be a knight, because this would contradict the claim of their own that If Jack is a knight then Jack is a knave.",
"Assume Benjamin is a knave. No contradiction is found in their false claim that If Jack is a knight then Jack is a knave."
] |
This leads to a feasible solution.
|
(('or', ('telling-truth', 1), ('telling-truth', 0)), ('->', ('telling-truth', 0), ('lying', 0)))
| 128
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Jack, and Benjamin. Jack told you that Benjamin is a knight or Jack is a knight. Benjamin remarked, \"If Jack is a knight then Jack is a knave\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Jack is a knight\n(2) Benjamin is a knave",
"statements": "(('or', ('telling-truth', 1), ('telling-truth', 0)), ('->', ('telling-truth', 0), ('lying', 0)))"
},
"style": "rule"
}
|
{
"index": 28,
"split": "train"
}
|
[
"Daniel",
"Samuel"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
true
] |
Daniel is a knight, and Samuel is a knight.
|
(1) Daniel is a knight
(2) Samuel is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Daniel is a knight. No contradiction is found in their claim that Samuel is a knave or Samuel is a knight.",
"Assume Samuel is a knight. No contradiction is found in their claim that Samuel is a knight or Daniel is a knight."
] |
This leads to a feasible solution.
|
(('or', ('lying', 1), ('telling-truth', 1)), ('or', ('telling-truth', 1), ('telling-truth', 0)))
| 129
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Daniel, and Samuel. Daniel said, \"Samuel is a knave or Samuel is a knight.\" Samuel said that Samuel is a knight or Daniel is a knight. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Daniel is a knight\n(2) Samuel is a knight",
"statements": "(('or', ('lying', 1), ('telling-truth', 1)), ('or', ('telling-truth', 1), ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 29,
"split": "train"
}
|
[
"Liam",
"Aria"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
true
] |
Liam is a knight, and Aria is a knight.
|
(1) Liam is a knight
(2) Aria is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Liam is a knight. No contradiction is found in their claim that Aria is not a knave.",
"Assume Aria is a knight. No contradiction is found in their claim that Aria is a knight if and only if Liam is a knight."
] |
This leads to a feasible solution.
|
(('not', ('lying', 1)), ('<=>', ('telling-truth', 1), ('telling-truth', 0)))
| 130
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Liam, and Aria. \"Aria is not a knave\" - Liam. Aria asserted: \"Aria is a knight if and only if Liam is a knight\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Liam is a knight\n(2) Aria is a knight",
"statements": "(('not', ('lying', 1)), ('<=>', ('telling-truth', 1), ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 30,
"split": "train"
}
|
[
"William",
"Noah"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
false
] |
William is a knight, and Noah is a knave.
|
(1) William is a knight
(2) Noah is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume William is a knight. No contradiction is found in their claim that Noah is a knave or Noah is a knight.",
"Noah cannot be a knight, because this would contradict the claim of their own that William is a knight if and only if William is a knave.",
"Assume Noah is a knave. No contradiction is found in their false claim that William is a knight if and only if William is a knave."
] |
This leads to a feasible solution.
|
(('or', ('lying', 1), ('telling-truth', 1)), ('<=>', ('telling-truth', 0), ('lying', 0)))
| 131
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: William, and Noah. William expressed that Noah is a knave or Noah is a knight. In a statement by Noah: \"William is a knight if and only if William is a knave\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) William is a knight\n(2) Noah is a knave",
"statements": "(('or', ('lying', 1), ('telling-truth', 1)), ('<=>', ('telling-truth', 0), ('lying', 0)))"
},
"style": "rule"
}
|
{
"index": 31,
"split": "train"
}
|
[
"Mia",
"Aria"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
false
] |
Mia is a knight, and Aria is a knave.
|
(1) Mia is a knight
(2) Aria is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Mia is a knight. No contradiction is found in their claim that Mia is a knight or Aria is a knight.",
"Aria cannot be a knight, because this would contradict the claim of their own that If Mia is a knight then Mia is a knave.",
"Assume Aria is a knave. No contradiction is found in their false claim that If Mia is a knight then Mia is a knave."
] |
This leads to a feasible solution.
|
(('or', ('telling-truth', 0), ('telling-truth', 1)), ('->', ('telling-truth', 0), ('lying', 0)))
| 132
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Mia, and Aria. \"Mia is a knight or Aria is a knight,\" Mia declared. Aria said, \"If Mia is a knight then Mia is a knave.\" So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Mia is a knight\n(2) Aria is a knave",
"statements": "(('or', ('telling-truth', 0), ('telling-truth', 1)), ('->', ('telling-truth', 0), ('lying', 0)))"
},
"style": "rule"
}
|
{
"index": 32,
"split": "train"
}
|
[
"Aurora",
"Charlotte"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
true
] |
Aurora is a knight, and Charlotte is a knight.
|
(1) Aurora is a knight
(2) Charlotte is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Aurora is a knight. No contradiction is found in their claim that Charlotte is a knight if and only if Aurora is a knight.",
"Assume Charlotte is a knight. No contradiction is found in their claim that If Charlotte is a knight then Aurora is a knight."
] |
This leads to a feasible solution.
|
(('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('->', ('telling-truth', 1), ('telling-truth', 0)))
| 133
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Aurora, and Charlotte. Aurora noted, \"Charlotte is a knight if and only if Aurora is a knight\". As Charlotte put it, \"If Charlotte is a knight then Aurora is a knight\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Aurora is a knight\n(2) Charlotte is a knight",
"statements": "(('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('->', ('telling-truth', 1), ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 33,
"split": "train"
}
|
[
"Chloe",
"Jacob"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
true
] |
Chloe is a knave, and Jacob is a knight.
|
(1) Chloe is a knave
(2) Jacob is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Chloe cannot be a knight, because this would contradict the claim of their own that Jacob is a knight and Jacob is a knave.",
"Assume Chloe is a knave. No contradiction is found in their false claim that Jacob is a knight and Jacob is a knave.",
"Assume Jacob is a knight. No contradiction is found in their claim that Chloe is a knave."
] |
This leads to a feasible solution.
|
(('and', ('telling-truth', 1), ('lying', 1)), ('lying', 0))
| 134
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Chloe, and Jacob. Chloe stated, \"Jacob is a knight and Jacob is a knave\". Jacob asserted: \"Chloe is a knave\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Chloe is a knave\n(2) Jacob is a knight",
"statements": "(('and', ('telling-truth', 1), ('lying', 1)), ('lying', 0))"
},
"style": "rule"
}
|
{
"index": 34,
"split": "train"
}
|
[
"Liam",
"Logan"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
false
] |
Liam is a knave, and Logan is a knave.
|
(1) Liam is a knave
(2) Logan is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Liam is a knight. No contradiction is found in their claim that Liam is a knight if and only if Logan is a knave.",
"Logan cannot be a knight, because this would contradict the claim of Liam that Liam is a knight if and only if Logan is a knave.",
"Logan 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 Logan, 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 if and only if Logan is a knave.",
"Logan cannot be a knight, because this would contradict the false claim of Liam that Liam is a knight if and only if Logan is a knave.",
"Assume Logan is a knave. No contradiction is found in their false claim that Liam is not a knave."
] |
This leads to a feasible solution.
|
(('<=>', ('telling-truth', 0), ('lying', 1)), ('not', ('lying', 0)))
| 135
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Liam, and Logan. Liam was heard saying, \"Liam is a knight if and only if Logan is a knave\". Logan said, \"Liam is not a knave.\" So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Liam is a knave\n(2) Logan is a knave",
"statements": "(('<=>', ('telling-truth', 0), ('lying', 1)), ('not', ('lying', 0)))"
},
"style": "rule"
}
|
{
"index": 35,
"split": "train"
}
|
[
"Samuel",
"Isabella"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
false
] |
Samuel is a knave, and Isabella is a knave.
|
(1) Samuel is a knave
(2) Isabella is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Samuel 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 Samuel is a knave and Isabella is a knight.",
"Isabella cannot be a knave, because this would contradict the claim of Samuel that Isabella is a knight.",
"We have exhausted all possibilities for Isabella, so let us go back and reconsider Samuel.",
"Assume Samuel 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 Samuel that Isabella is a knight.",
"Assume Isabella is a knave. No contradiction is found in their false claim that Samuel is a knave and Isabella is a knight."
] |
This leads to a feasible solution.
|
(('telling-truth', 1), ('and', ('lying', 0), ('telling-truth', 1)))
| 136
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Samuel, and Isabella. \"Isabella is a knight\" - Samuel. Isabella said that Samuel is a knave and Isabella is a knight. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Samuel is a knave\n(2) Isabella is a knave",
"statements": "(('telling-truth', 1), ('and', ('lying', 0), ('telling-truth', 1)))"
},
"style": "rule"
}
|
{
"index": 36,
"split": "train"
}
|
[
"Benjamin",
"Lily"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
false
] |
Benjamin is a knave, and Lily is a knave.
|
(1) Benjamin is a knave
(2) Lily is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Benjamin is a knight. No contradiction is found in their claim that If Lily is a knave then Lily is a knight.",
"Lily cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave and Benjamin is a knight.",
"Lily cannot be a knave, because this would contradict the claim of Benjamin that If Lily is a knave then Lily is a knight.",
"We have exhausted all possibilities for Lily, so let us go back and reconsider Benjamin.",
"Assume Benjamin is a knave. No contradiction is found in their false claim that If Lily is a knave then Lily is a knight.",
"Lily cannot be a knight, because this would contradict the false claim of Benjamin that If Lily is a knave then Lily is a knight.",
"Assume Lily is a knave. No contradiction is found in their false claim that Benjamin is a knave and Benjamin is a knight."
] |
This leads to a feasible solution.
|
(('->', ('lying', 1), ('telling-truth', 1)), ('and', ('lying', 0), ('telling-truth', 0)))
| 137
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Benjamin, and Lily. In Benjamin's words: \"If Lily is a knave then Lily is a knight\". \"Benjamin is a knave and Benjamin is a knight,\" Lily declared. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Benjamin is a knave\n(2) Lily is a knave",
"statements": "(('->', ('lying', 1), ('telling-truth', 1)), ('and', ('lying', 0), ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 37,
"split": "train"
}
|
[
"Mason",
"Zoey"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
false
] |
Mason is a knave, and Zoey is a knave.
|
(1) Mason is a knave
(2) Zoey is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Mason cannot be a knight, because this would contradict the claim of their own that Zoey is a knight and Zoey is a knave.",
"Assume Mason is a knave. No contradiction is found in their false claim that Zoey is a knight and Zoey is a knave.",
"Zoey cannot be a knight, because this would contradict the claim of their own that Mason is a knight.",
"Assume Zoey is a knave. No contradiction is found in their false claim that Mason is a knight."
] |
This leads to a feasible solution.
|
(('and', ('telling-truth', 1), ('lying', 1)), ('telling-truth', 0))
| 138
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Mason, and Zoey. Mason noted, \"Zoey is a knight and Zoey is a knave\". Zoey asserted: \"Mason is a knight\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Mason is a knave\n(2) Zoey is a knave",
"statements": "(('and', ('telling-truth', 1), ('lying', 1)), ('telling-truth', 0))"
},
"style": "rule"
}
|
{
"index": 38,
"split": "train"
}
|
[
"Sophia",
"Charlotte"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
false
] |
Sophia is a knight, and Charlotte is a knave.
|
(1) Sophia is a knight
(2) Charlotte is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Sophia is a knight. No contradiction is found in their claim that If Sophia is a knight then Charlotte is a knave.",
"Charlotte cannot be a knight, because this would contradict the claim of Sophia that If Sophia is a knight then Charlotte is a knave.",
"Assume Charlotte is a knave. No contradiction is found in their false claim that Sophia is a knave and Sophia is a knight."
] |
This leads to a feasible solution.
|
(('->', ('telling-truth', 0), ('lying', 1)), ('and', ('lying', 0), ('telling-truth', 0)))
| 139
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Sophia, and Charlotte. Sophia commented, \"If Sophia is a knight then Charlotte is a knave\". \"Sophia is a knave and Sophia is a knight\" - Charlotte. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Sophia is a knight\n(2) Charlotte is a knave",
"statements": "(('->', ('telling-truth', 0), ('lying', 1)), ('and', ('lying', 0), ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 39,
"split": "train"
}
|
[
"William",
"David"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
true
] |
William is a knave, and David is a knight.
|
(1) William is a knave
(2) David is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"William cannot be a knight, because this would contradict the claim of their own that David is a knave and David is a knight.",
"Assume William is a knave. No contradiction is found in their false claim that David is a knave and David is a knight.",
"Assume David is a knight. No contradiction is found in their claim that If William is a knight then David is a knight."
] |
This leads to a feasible solution.
|
(('and', ('lying', 1), ('telling-truth', 1)), ('->', ('telling-truth', 0), ('telling-truth', 1)))
| 140
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: William, and David. As William put it, \"David is a knave and David is a knight\". David remarked, \"If William is a knight then David is a knight\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) William is a knave\n(2) David is a knight",
"statements": "(('and', ('lying', 1), ('telling-truth', 1)), ('->', ('telling-truth', 0), ('telling-truth', 1)))"
},
"style": "rule"
}
|
{
"index": 40,
"split": "train"
}
|
[
"Sophia",
"Noah"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
false
] |
Sophia is a knight, and Noah is a knave.
|
(1) Sophia is a knight
(2) Noah is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Sophia is a knight. No contradiction is found in their claim that If Sophia is a knight then Noah is a knave.",
"Noah cannot be a knight, because this would contradict the claim of Sophia that If Sophia is a knight then Noah is a knave.",
"Assume Noah is a knave. No contradiction is found in their false claim that If Sophia is a knight then Noah is a knight."
] |
This leads to a feasible solution.
|
(('->', ('telling-truth', 0), ('lying', 1)), ('->', ('telling-truth', 0), ('telling-truth', 1)))
| 141
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Sophia, and Noah. \"If Sophia is a knight then Noah is a knave\" - Sophia. Noah noted, \"If Sophia is a knight then Noah is a knight\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Sophia is a knight\n(2) Noah is a knave",
"statements": "(('->', ('telling-truth', 0), ('lying', 1)), ('->', ('telling-truth', 0), ('telling-truth', 1)))"
},
"style": "rule"
}
|
{
"index": 41,
"split": "train"
}
|
[
"Charlotte",
"Evelyn"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
true
] |
Charlotte is a knight, and Evelyn is a knight.
|
(1) Charlotte is a knight
(2) Evelyn is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Charlotte is a knight. No contradiction is found in their claim that If Charlotte is a knight then Evelyn is a knight.",
"Assume Evelyn is a knight. No contradiction is found in their claim that Evelyn is a knight if and only if Charlotte is a knight."
] |
This leads to a feasible solution.
|
(('->', ('telling-truth', 0), ('telling-truth', 1)), ('<=>', ('telling-truth', 1), ('telling-truth', 0)))
| 142
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Charlotte, and Evelyn. Charlotte noted, \"If Charlotte is a knight then Evelyn is a knight\". Evelyn noted, \"Evelyn is a knight if and only if Charlotte is a knight\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Charlotte is a knight\n(2) Evelyn is a knight",
"statements": "(('->', ('telling-truth', 0), ('telling-truth', 1)), ('<=>', ('telling-truth', 1), ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 42,
"split": "train"
}
|
[
"Daniel",
"Jack"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
true
] |
Daniel is a knight, and Jack is a knight.
|
(1) Daniel is a knight
(2) Jack is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Daniel is a knight. No contradiction is found in their claim that If Daniel is a knight then Jack is a knight.",
"Assume Jack is a knight. No contradiction is found in their claim that Jack is a knight."
] |
This leads to a feasible solution.
|
(('->', ('telling-truth', 0), ('telling-truth', 1)), ('telling-truth', 1))
| 143
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Daniel, and Jack. Daniel expressed that If Daniel is a knight then Jack is a knight. \"Jack is a knight,\" Jack mentioned. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Daniel is a knight\n(2) Jack is a knight",
"statements": "(('->', ('telling-truth', 0), ('telling-truth', 1)), ('telling-truth', 1))"
},
"style": "rule"
}
|
{
"index": 43,
"split": "train"
}
|
[
"Evelyn",
"Harper"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
false
] |
Evelyn is a knight, and Harper is a knave.
|
(1) Evelyn is a knight
(2) Harper is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Evelyn is a knight. No contradiction is found in their claim that Harper is not a knight.",
"Harper cannot be a knight, because this would contradict the claim of Evelyn that Harper is not a knight.",
"Assume Harper is a knave. No contradiction is found in their false claim that Evelyn is a knave if and only if Evelyn is a knight."
] |
This leads to a feasible solution.
|
(('not', ('telling-truth', 1)), ('<=>', ('lying', 0), ('telling-truth', 0)))
| 144
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Evelyn, and Harper. \"Harper is not a knight,\" Evelyn mentioned. In Harper's words: \"Evelyn is a knave if and only if Evelyn is a knight\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Evelyn is a knight\n(2) Harper is a knave",
"statements": "(('not', ('telling-truth', 1)), ('<=>', ('lying', 0), ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 44,
"split": "train"
}
|
[
"Avery",
"Michael"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
false
] |
Avery is a knight, and Michael is a knave.
|
(1) Avery is a knight
(2) Michael is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Avery is a knight. No contradiction is found in their claim that Avery is a knight if and only if Michael is a knave.",
"Michael cannot be a knight, because this would contradict the claim of Avery that Avery is a knight if and only if Michael is a knave.",
"Assume Michael is a knave. No contradiction is found in their false claim that Avery is not a knight."
] |
This leads to a feasible solution.
|
(('<=>', ('telling-truth', 0), ('lying', 1)), ('not', ('telling-truth', 0)))
| 145
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Avery, and Michael. \"Avery is a knight if and only if Michael is a knave,\" Avery mentioned. \"Avery is not a knight,\" Michael declared. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Avery is a knight\n(2) Michael is a knave",
"statements": "(('<=>', ('telling-truth', 0), ('lying', 1)), ('not', ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 45,
"split": "train"
}
|
[
"Elizabeth",
"Aurora"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
true
] |
Elizabeth is a knight, and Aurora is a knight.
|
(1) Elizabeth is a knight
(2) Aurora is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Elizabeth is a knight. No contradiction is found in their claim that Elizabeth is a knight if and only if Aurora is a knight.",
"Assume Aurora is a knight. No contradiction is found in their claim that Elizabeth is a knight."
] |
This leads to a feasible solution.
|
(('<=>', ('telling-truth', 0), ('telling-truth', 1)), ('telling-truth', 0))
| 146
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Elizabeth, and Aurora. According to Elizabeth, \"Elizabeth is a knight if and only if Aurora is a knight\". Aurora remarked, \"Elizabeth is a knight\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Elizabeth is a knight\n(2) Aurora is a knight",
"statements": "(('<=>', ('telling-truth', 0), ('telling-truth', 1)), ('telling-truth', 0))"
},
"style": "rule"
}
|
{
"index": 46,
"split": "train"
}
|
[
"Riley",
"Benjamin"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
true
] |
Riley is a knave, and Benjamin is a knight.
|
(1) Riley is a knave
(2) Benjamin is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Riley is a knight. No contradiction is found in their claim that Riley is a knight or Benjamin is a knave.",
"Benjamin cannot be a knight, because this would contradict the claim of their own that Riley is a knave if and only if Benjamin is a knight.",
"Benjamin cannot be a knave, because this would contradict the false claim of their own that Riley is a knave if and only if Benjamin is a knight.",
"We have exhausted all possibilities for Benjamin, so let us go back and reconsider Riley.",
"Assume Riley is a knave. No contradiction is found in their false claim that Riley is a knight or Benjamin is a knave.",
"Assume Benjamin is a knight. No contradiction is found in their claim that Riley is a knave if and only if Benjamin is a knight."
] |
This leads to a feasible solution.
|
(('or', ('telling-truth', 0), ('lying', 1)), ('<=>', ('lying', 0), ('telling-truth', 1)))
| 147
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Riley, and Benjamin. As Riley put it, \"Riley is a knight or Benjamin is a knave\". Benjamin asserted: \"Riley is a knave if and only if Benjamin is a knight\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Riley is a knave\n(2) Benjamin is a knight",
"statements": "(('or', ('telling-truth', 0), ('lying', 1)), ('<=>', ('lying', 0), ('telling-truth', 1)))"
},
"style": "rule"
}
|
{
"index": 47,
"split": "train"
}
|
[
"Penelope",
"Oliver"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
false
] |
Penelope is a knave, and Oliver is a knave.
|
(1) Penelope is a knave
(2) Oliver is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Penelope is a knight. No contradiction is found in their claim that Oliver is a knave if and only if Penelope is a knight.",
"Oliver cannot be a knight, because this would contradict the claim of Penelope that Oliver is a knave if and only if Penelope is a knight.",
"Oliver cannot be a knave, because this would contradict the false claim of their own that If Penelope is a knave then Penelope is a knight.",
"We have exhausted all possibilities for Oliver, so let us go back and reconsider Penelope.",
"Assume Penelope is a knave. No contradiction is found in their false claim that Oliver is a knave if and only if Penelope is a knight.",
"Oliver cannot be a knight, because this would contradict the false claim of Penelope that Oliver is a knave if and only if Penelope is a knight.",
"Assume Oliver is a knave. No contradiction is found in their false claim that If Penelope is a knave then Penelope is a knight."
] |
This leads to a feasible solution.
|
(('<=>', ('lying', 1), ('telling-truth', 0)), ('->', ('lying', 0), ('telling-truth', 0)))
| 148
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Penelope, and Oliver. Penelope said that Oliver is a knave if and only if Penelope is a knight. Oliver expressed that If Penelope is a knave then Penelope is a knight. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Penelope is a knave\n(2) Oliver is a knave",
"statements": "(('<=>', ('lying', 1), ('telling-truth', 0)), ('->', ('lying', 0), ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 48,
"split": "train"
}
|
[
"Chloe",
"James"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
true
] |
Chloe is a knave, and James is a knight.
|
(1) Chloe is a knave
(2) James is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Chloe is a knight. No contradiction is found in their claim that James is a knave.",
"James cannot be a knight, because this would contradict the claim of Chloe that James is a knave.",
"James cannot be a knave, because this would contradict the false claim of their own that Chloe is a knave if and only if James is a knight.",
"We have exhausted all possibilities for James, so let us go back and reconsider Chloe.",
"Assume Chloe is a knave. No contradiction is found in their false claim that James is a knave.",
"Assume James is a knight. No contradiction is found in their claim that Chloe is a knave if and only if James is a knight."
] |
This leads to a feasible solution.
|
(('lying', 1), ('<=>', ('lying', 0), ('telling-truth', 1)))
| 149
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Chloe, and James. As Chloe put it, \"James is a knave\". According to James, \"Chloe is a knave if and only if James is a knight\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Chloe is a knave\n(2) James is a knight",
"statements": "(('lying', 1), ('<=>', ('lying', 0), ('telling-truth', 1)))"
},
"style": "rule"
}
|
{
"index": 49,
"split": "train"
}
|
[
"Henry",
"David"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
true
] |
Henry is a knave, and David is a knight.
|
(1) Henry is a knave
(2) David is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Henry cannot be a knight, because this would contradict the claim of their own that David is a knave and David is a knight.",
"Assume Henry is a knave. No contradiction is found in their false claim that David is a knave and David is a knight.",
"Assume David is a knight. No contradiction is found in their claim that Henry is a knave."
] |
This leads to a feasible solution.
|
(('and', ('lying', 1), ('telling-truth', 1)), ('lying', 0))
| 150
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Henry, and David. \"David is a knave and David is a knight,\" Henry mentioned. In a statement by David: \"Henry is a knave\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Henry is a knave\n(2) David is a knight",
"statements": "(('and', ('lying', 1), ('telling-truth', 1)), ('lying', 0))"
},
"style": "rule"
}
|
{
"index": 50,
"split": "train"
}
|
[
"Evelyn",
"Elizabeth"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
false
] |
Evelyn is a knave, and Elizabeth is a knave.
|
(1) Evelyn is a knave
(2) Elizabeth is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Evelyn is a knight. No contradiction is found in their claim that Evelyn is a knight if and only if Elizabeth is a knave.",
"Elizabeth cannot be a knight, because this would contradict the claim of Evelyn that Evelyn is a knight if and only if Elizabeth is a knave.",
"Elizabeth cannot be a knave, because this would contradict the false claim of their own that Evelyn is a knight.",
"We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Evelyn.",
"Assume Evelyn is a knave. No contradiction is found in their false claim that Evelyn is a knight if and only if Elizabeth is a knave.",
"Elizabeth cannot be a knight, because this would contradict the false claim of Evelyn that Evelyn is a knight if and only if Elizabeth is a knave.",
"Assume Elizabeth is a knave. No contradiction is found in their false claim that Evelyn is a knight."
] |
This leads to a feasible solution.
|
(('<=>', ('telling-truth', 0), ('lying', 1)), ('telling-truth', 0))
| 151
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Evelyn, and Elizabeth. Evelyn told you that Evelyn is a knight if and only if Elizabeth is a knave. \"Evelyn is a knight\" - Elizabeth. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Evelyn is a knave\n(2) Elizabeth is a knave",
"statements": "(('<=>', ('telling-truth', 0), ('lying', 1)), ('telling-truth', 0))"
},
"style": "rule"
}
|
{
"index": 51,
"split": "train"
}
|
[
"Jackson",
"Elizabeth"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
false
] |
Jackson is a knave, and Elizabeth is a knave.
|
(1) Jackson is a knave
(2) Elizabeth is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Jackson is a knight. No contradiction is found in their claim that Elizabeth is a knave and Jackson is a knight.",
"Elizabeth cannot be a knight, because this would contradict the claim of Jackson that Elizabeth is a knave and Jackson is a knight.",
"Elizabeth cannot be a knave, because this would contradict the false claim of their own that If Jackson is a knave then Jackson is a knight.",
"We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Jackson.",
"Assume Jackson is a knave. No contradiction is found in their false claim that Elizabeth is a knave and Jackson is a knight.",
"Elizabeth cannot be a knight, because this would contradict the claim of their own that If Jackson is a knave then Jackson is a knight.",
"Assume Elizabeth is a knave. No contradiction is found in their false claim that If Jackson is a knave then Jackson is a knight."
] |
This leads to a feasible solution.
|
(('and', ('lying', 1), ('telling-truth', 0)), ('->', ('lying', 0), ('telling-truth', 0)))
| 152
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Jackson, and Elizabeth. As Jackson put it, \"Elizabeth is a knave and Jackson is a knight\". \"If Jackson is a knave then Jackson is a knight,\" Elizabeth declared. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Jackson is a knave\n(2) Elizabeth is a knave",
"statements": "(('and', ('lying', 1), ('telling-truth', 0)), ('->', ('lying', 0), ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 52,
"split": "train"
}
|
[
"Aiden",
"Emma"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
true
] |
Aiden is a knight, and Emma is a knight.
|
(1) Aiden is a knight
(2) Emma is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Aiden is a knight. No contradiction is found in their claim that Aiden is a knight and Emma is a knight.",
"Assume Emma is a knight. No contradiction is found in their claim that If Emma is a knight then Aiden is a knight."
] |
This leads to a feasible solution.
|
(('and', ('telling-truth', 0), ('telling-truth', 1)), ('->', ('telling-truth', 1), ('telling-truth', 0)))
| 153
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Aiden, and Emma. Aiden stated, \"Aiden is a knight and Emma is a knight\". \"If Emma is a knight then Aiden is a knight\" - Emma. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Aiden is a knight\n(2) Emma is a knight",
"statements": "(('and', ('telling-truth', 0), ('telling-truth', 1)), ('->', ('telling-truth', 1), ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 53,
"split": "train"
}
|
[
"Sebastian",
"Ava"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
true
] |
Sebastian is a knight, and Ava is a knight.
|
(1) Sebastian is a knight
(2) Ava is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Sebastian is a knight. No contradiction is found in their claim that Ava is a knight.",
"Assume Ava is a knight. No contradiction is found in their claim that If Sebastian is a knight then Ava is a knight."
] |
This leads to a feasible solution.
|
(('telling-truth', 1), ('->', ('telling-truth', 0), ('telling-truth', 1)))
| 154
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Sebastian, and Ava. In a statement by Sebastian: \"Ava is a knight\". \"If Sebastian is a knight then Ava is a knight,\" Ava declared. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Sebastian is a knight\n(2) Ava is a knight",
"statements": "(('telling-truth', 1), ('->', ('telling-truth', 0), ('telling-truth', 1)))"
},
"style": "rule"
}
|
{
"index": 54,
"split": "train"
}
|
[
"James",
"Oliver"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
true
] |
James is a knight, and Oliver is a knight.
|
(1) James is a knight
(2) Oliver is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume James is a knight. No contradiction is found in their claim that If Oliver is a knave then Oliver is a knight.",
"Assume Oliver is a knight. No contradiction is found in their claim that James is a knight or James is a knave."
] |
This leads to a feasible solution.
|
(('->', ('lying', 1), ('telling-truth', 1)), ('or', ('telling-truth', 0), ('lying', 0)))
| 155
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: James, and Oliver. James asserted: \"If Oliver is a knave then Oliver is a knight\". Oliver told you that James is a knight or James is a knave. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) James is a knight\n(2) Oliver is a knight",
"statements": "(('->', ('lying', 1), ('telling-truth', 1)), ('or', ('telling-truth', 0), ('lying', 0)))"
},
"style": "rule"
}
|
{
"index": 55,
"split": "train"
}
|
[
"Riley",
"Matthew"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
true
] |
Riley is a knight, and Matthew is a knight.
|
(1) Riley is a knight
(2) Matthew is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Riley is a knight. No contradiction is found in their claim that Matthew is a knave or Matthew is a knight.",
"Assume Matthew is a knight. No contradiction is found in their claim that If Riley is a knave then Matthew is a knight."
] |
This leads to a feasible solution.
|
(('or', ('lying', 1), ('telling-truth', 1)), ('->', ('lying', 0), ('telling-truth', 1)))
| 156
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Riley, and Matthew. \"Matthew is a knave or Matthew is a knight,\" Riley claimed. Matthew remarked, \"If Riley is a knave then Matthew is a knight\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Riley is a knight\n(2) Matthew is a knight",
"statements": "(('or', ('lying', 1), ('telling-truth', 1)), ('->', ('lying', 0), ('telling-truth', 1)))"
},
"style": "rule"
}
|
{
"index": 56,
"split": "train"
}
|
[
"Jackson",
"Michael"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
false
] |
Jackson is a knight, and Michael is a knave.
|
(1) Jackson is a knight
(2) Michael is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Jackson is a knight. No contradiction is found in their claim that If Jackson is a knight then Michael is a knave.",
"Michael cannot be a knight, because this would contradict the claim of Jackson that If Jackson is a knight then Michael is a knave.",
"Assume Michael is a knave. No contradiction is found in their false claim that Jackson is not a knight."
] |
This leads to a feasible solution.
|
(('->', ('telling-truth', 0), ('lying', 1)), ('not', ('telling-truth', 0)))
| 157
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Jackson, and Michael. Jackson said, \"If Jackson is a knight then Michael is a knave.\" Michael noted, \"Jackson is not a knight\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Jackson is a knight\n(2) Michael is a knave",
"statements": "(('->', ('telling-truth', 0), ('lying', 1)), ('not', ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 57,
"split": "train"
}
|
[
"Penelope",
"Alexander"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
false
] |
Penelope is a knave, and Alexander is a knave.
|
(1) Penelope is a knave
(2) Alexander is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Penelope is a knight. No contradiction is found in their claim that Alexander is a knight.",
"Alexander cannot be a knight, because this would contradict the claim of their own that Penelope is a knave if and only if Penelope is a knight.",
"Alexander cannot be a knave, because this would contradict the claim of Penelope that Alexander is a knight.",
"We have exhausted all possibilities for Alexander, so let us go back and reconsider Penelope.",
"Assume Penelope is a knave. No contradiction is found in their false claim that Alexander is a knight.",
"Alexander cannot be a knight, because this would contradict the false claim of Penelope that Alexander is a knight.",
"Assume Alexander is a knave. No contradiction is found in their false claim that Penelope is a knave if and only if Penelope is a knight."
] |
This leads to a feasible solution.
|
(('telling-truth', 1), ('<=>', ('lying', 0), ('telling-truth', 0)))
| 158
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Penelope, and Alexander. Penelope said, \"Alexander is a knight.\" \"Penelope is a knave if and only if Penelope is a knight,\" Alexander declared. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Penelope is a knave\n(2) Alexander is a knave",
"statements": "(('telling-truth', 1), ('<=>', ('lying', 0), ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 58,
"split": "train"
}
|
[
"Aria",
"Noah"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
true
] |
Aria is a knave, and Noah is a knight.
|
(1) Aria is a knave
(2) Noah is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Aria is a knight. No contradiction is found in their claim that Noah is not a knight.",
"Noah cannot be a knight, because this would contradict the claim of Aria that Noah is not a knight.",
"Noah cannot be a knave, because this would contradict the false claim of their own that Aria is a knave if and only if Noah is a knight.",
"We have exhausted all possibilities for Noah, so let us go back and reconsider Aria.",
"Assume Aria is a knave. No contradiction is found in their false claim that Noah is not a knight.",
"Assume Noah is a knight. No contradiction is found in their claim that Aria is a knave if and only if Noah is a knight."
] |
This leads to a feasible solution.
|
(('not', ('telling-truth', 1)), ('<=>', ('lying', 0), ('telling-truth', 1)))
| 159
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Aria, and Noah. \"Noah is not a knight,\" Aria mentioned. \"Aria is a knave if and only if Noah is a knight,\" Noah declared. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Aria is a knave\n(2) Noah is a knight",
"statements": "(('not', ('telling-truth', 1)), ('<=>', ('lying', 0), ('telling-truth', 1)))"
},
"style": "rule"
}
|
{
"index": 59,
"split": "train"
}
|
[
"Noah",
"Jackson"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
false
] |
Noah is a knight, and Jackson is a knave.
|
(1) Noah is a knight
(2) Jackson is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Noah is a knight. No contradiction is found in their claim that Jackson is a knave if and only if Noah is a knight.",
"Jackson cannot be a knight, because this would contradict the claim of Noah that Jackson is a knave if and only if Noah is a knight.",
"Assume Jackson is a knave. No contradiction is found in their false claim that If Noah is a knight then Noah is a knave."
] |
This leads to a feasible solution.
|
(('<=>', ('lying', 1), ('telling-truth', 0)), ('->', ('telling-truth', 0), ('lying', 0)))
| 160
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Noah, and Jackson. Noah stated, \"Jackson is a knave if and only if Noah is a knight\". Jackson told you that If Noah is a knight then Noah is a knave. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Noah is a knight\n(2) Jackson is a knave",
"statements": "(('<=>', ('lying', 1), ('telling-truth', 0)), ('->', ('telling-truth', 0), ('lying', 0)))"
},
"style": "rule"
}
|
{
"index": 60,
"split": "train"
}
|
[
"Ava",
"Ethan"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
false
] |
Ava is a knight, and Ethan is a knave.
|
(1) Ava is a knight
(2) Ethan is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Ava is a knight. No contradiction is found in their claim that Ava is a knight if and only if Ethan is a knave.",
"Ethan cannot be a knight, because this would contradict the claim of Ava that Ava is a knight if and only if Ethan is a knave.",
"Assume Ethan is a knave. No contradiction is found in their false claim that Ethan is a knight or Ava is a knave."
] |
This leads to a feasible solution.
|
(('<=>', ('telling-truth', 0), ('lying', 1)), ('or', ('telling-truth', 1), ('lying', 0)))
| 161
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Ava, and Ethan. Ava asserted: \"Ava is a knight if and only if Ethan is a knave\". Ethan said, \"Ethan is a knight or Ava is a knave.\" So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Ava is a knight\n(2) Ethan is a knave",
"statements": "(('<=>', ('telling-truth', 0), ('lying', 1)), ('or', ('telling-truth', 1), ('lying', 0)))"
},
"style": "rule"
}
|
{
"index": 61,
"split": "train"
}
|
[
"Abigail",
"Victoria"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
false
] |
Abigail is a knave, and Victoria is a knave.
|
(1) Abigail is a knave
(2) Victoria is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Abigail is a knight. No contradiction is found in their claim that If Victoria is a knave then Victoria is a knight.",
"Victoria cannot be a knight, because this would contradict the claim of their own that Victoria is a knight and Abigail is a knave.",
"Victoria cannot be a knave, because this would contradict the claim of Abigail that If Victoria is a knave then Victoria is a knight.",
"We have exhausted all possibilities for Victoria, so let us go back and reconsider Abigail.",
"Assume Abigail is a knave. No contradiction is found in their false claim that If Victoria is a knave then Victoria is a knight.",
"Victoria cannot be a knight, because this would contradict the false claim of Abigail that If Victoria is a knave then Victoria is a knight.",
"Assume Victoria is a knave. No contradiction is found in their false claim that Victoria is a knight and Abigail is a knave."
] |
This leads to a feasible solution.
|
(('->', ('lying', 1), ('telling-truth', 1)), ('and', ('telling-truth', 1), ('lying', 0)))
| 162
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Abigail, and Victoria. Abigail noted, \"If Victoria is a knave then Victoria is a knight\". In a statement by Victoria: \"Victoria is a knight and Abigail is a knave\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Abigail is a knave\n(2) Victoria is a knave",
"statements": "(('->', ('lying', 1), ('telling-truth', 1)), ('and', ('telling-truth', 1), ('lying', 0)))"
},
"style": "rule"
}
|
{
"index": 62,
"split": "train"
}
|
[
"Joseph",
"Jackson"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
true
] |
Joseph is a knight, and Jackson is a knight.
|
(1) Joseph is a knight
(2) Jackson is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Joseph is a knight. No contradiction is found in their claim that If Jackson is a knight then Joseph is a knight.",
"Assume Jackson is a knight. No contradiction is found in their claim that If Jackson is a knight then Joseph is a knight."
] |
This leads to a feasible solution.
|
(('->', ('telling-truth', 1), ('telling-truth', 0)), ('->', ('telling-truth', 1), ('telling-truth', 0)))
| 163
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Joseph, and Jackson. \"If Jackson is a knight then Joseph is a knight\" - Joseph. \"If Jackson is a knight then Joseph is a knight,\" Jackson claimed. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Joseph is a knight\n(2) Jackson is a knight",
"statements": "(('->', ('telling-truth', 1), ('telling-truth', 0)), ('->', ('telling-truth', 1), ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 63,
"split": "train"
}
|
[
"Noah",
"Charlotte"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
true
] |
Noah is a knight, and Charlotte is a knight.
|
(1) Noah is a knight
(2) Charlotte is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Noah is a knight. No contradiction is found in their claim that Charlotte is a knight and Noah is a knight.",
"Assume Charlotte is a knight. No contradiction is found in their claim that Charlotte is a knight if and only if Noah is a knight."
] |
This leads to a feasible solution.
|
(('and', ('telling-truth', 1), ('telling-truth', 0)), ('<=>', ('telling-truth', 1), ('telling-truth', 0)))
| 164
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Noah, and Charlotte. Noah told you that Charlotte is a knight and Noah is a knight. Charlotte was heard saying, \"Charlotte is a knight if and only if Noah is a knight\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Noah is a knight\n(2) Charlotte is a knight",
"statements": "(('and', ('telling-truth', 1), ('telling-truth', 0)), ('<=>', ('telling-truth', 1), ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 64,
"split": "train"
}
|
[
"Avery",
"Chloe"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
true
] |
Avery is a knave, and Chloe is a knight.
|
(1) Avery is a knave
(2) Chloe is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Avery cannot be a knight, because this would contradict the claim of their own that Chloe is a knight and Chloe is a knave.",
"Assume Avery is a knave. No contradiction is found in their false claim that Chloe is a knight and Chloe is a knave.",
"Assume Chloe is a knight. No contradiction is found in their claim that Avery is not a knight."
] |
This leads to a feasible solution.
|
(('and', ('telling-truth', 1), ('lying', 1)), ('not', ('telling-truth', 0)))
| 165
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Avery, and Chloe. Avery said that Chloe is a knight and Chloe is a knave. \"Avery is not a knight,\" Chloe mentioned. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Avery is a knave\n(2) Chloe is a knight",
"statements": "(('and', ('telling-truth', 1), ('lying', 1)), ('not', ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 65,
"split": "train"
}
|
[
"Evelyn",
"Ava"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
true
] |
Evelyn is a knight, and Ava is a knight.
|
(1) Evelyn is a knight
(2) Ava is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Evelyn is a knight. No contradiction is found in their claim that If Evelyn is a knight then Ava is a knight.",
"Assume Ava is a knight. No contradiction is found in their claim that Ava is a knight or Evelyn is a knight."
] |
This leads to a feasible solution.
|
(('->', ('telling-truth', 0), ('telling-truth', 1)), ('or', ('telling-truth', 1), ('telling-truth', 0)))
| 166
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Evelyn, and Ava. \"If Evelyn is a knight then Ava is a knight,\" Evelyn claimed. Ava told you that Ava is a knight or Evelyn is a knight. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Evelyn is a knight\n(2) Ava is a knight",
"statements": "(('->', ('telling-truth', 0), ('telling-truth', 1)), ('or', ('telling-truth', 1), ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 66,
"split": "train"
}
|
[
"Matthew",
"Victoria"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
false
] |
Matthew is a knight, and Victoria is a knave.
|
(1) Matthew is a knight
(2) Victoria is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Matthew 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 Matthew that Victoria is not a knight.",
"Assume Victoria is a knave. No contradiction is found in their false claim that Victoria is a knight and Matthew is a knight."
] |
This leads to a feasible solution.
|
(('not', ('telling-truth', 1)), ('and', ('telling-truth', 1), ('telling-truth', 0)))
| 167
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Matthew, and Victoria. In Matthew's words: \"Victoria is not a knight\". In Victoria's words: \"Victoria is a knight and Matthew is a knight\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Matthew is a knight\n(2) Victoria is a knave",
"statements": "(('not', ('telling-truth', 1)), ('and', ('telling-truth', 1), ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 67,
"split": "train"
}
|
[
"Daniel",
"William"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
true
] |
Daniel is a knight, and William is a knight.
|
(1) Daniel is a knight
(2) William is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Daniel is a knight. No contradiction is found in their claim that William is a knight or Daniel is a knight.",
"Assume William is a knight. No contradiction is found in their claim that Daniel is a knight or Daniel is a knave."
] |
This leads to a feasible solution.
|
(('or', ('telling-truth', 1), ('telling-truth', 0)), ('or', ('telling-truth', 0), ('lying', 0)))
| 168
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Daniel, and William. \"William is a knight or Daniel is a knight,\" Daniel declared. William expressed that Daniel is a knight or Daniel is a knave. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Daniel is a knight\n(2) William is a knight",
"statements": "(('or', ('telling-truth', 1), ('telling-truth', 0)), ('or', ('telling-truth', 0), ('lying', 0)))"
},
"style": "rule"
}
|
{
"index": 68,
"split": "train"
}
|
[
"Luke",
"Alexander"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
false
] |
Luke is a knight, and Alexander is a knave.
|
(1) Luke is a knight
(2) Alexander is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Luke is a knight. No contradiction is found in their claim that If Luke is a knight then Alexander is a knave.",
"Alexander cannot be a knight, because this would contradict the claim of Luke that If Luke is a knight then Alexander is a knave.",
"Assume Alexander is a knave. No contradiction is found in their false claim that Alexander is a knight and Luke is a knight."
] |
This leads to a feasible solution.
|
(('->', ('telling-truth', 0), ('lying', 1)), ('and', ('telling-truth', 1), ('telling-truth', 0)))
| 169
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Luke, and Alexander. Luke said, \"If Luke is a knight then Alexander is a knave.\" Alexander said, \"Alexander is a knight and Luke is a knight.\" So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Luke is a knight\n(2) Alexander is a knave",
"statements": "(('->', ('telling-truth', 0), ('lying', 1)), ('and', ('telling-truth', 1), ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 69,
"split": "train"
}
|
[
"Mia",
"Samuel"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
false
] |
Mia is a knave, and Samuel is a knave.
|
(1) Mia is a knave
(2) Samuel is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Mia is a knight. No contradiction is found in their claim that Mia is a knight and Samuel is a knight.",
"Samuel cannot be a knight, because this would contradict the claim of their own that Mia is a knight and Mia is a knave.",
"Samuel cannot be a knave, because this would contradict the claim of Mia that Mia is a knight and Samuel is a knight.",
"We have exhausted all possibilities for Samuel, so let us go back and reconsider Mia.",
"Assume Mia is a knave. No contradiction is found in their false claim that Mia is a knight and Samuel is a knight.",
"Samuel cannot be a knight, because this would contradict the claim of their own that Mia is a knight and Mia is a knave.",
"Assume Samuel is a knave. No contradiction is found in their false claim that Mia is a knight and Mia is a knave."
] |
This leads to a feasible solution.
|
(('and', ('telling-truth', 0), ('telling-truth', 1)), ('and', ('telling-truth', 0), ('lying', 0)))
| 170
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Mia, and Samuel. Mia expressed that Mia is a knight and Samuel is a knight. Samuel expressed that Mia is a knight and Mia is a knave. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Mia is a knave\n(2) Samuel is a knave",
"statements": "(('and', ('telling-truth', 0), ('telling-truth', 1)), ('and', ('telling-truth', 0), ('lying', 0)))"
},
"style": "rule"
}
|
{
"index": 70,
"split": "train"
}
|
[
"Liam",
"Henry"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
true
] |
Liam is a knight, and Henry is a knight.
|
(1) Liam is a knight
(2) Henry is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Liam is a knight. No contradiction is found in their claim that Liam is a knight if and only if Henry is a knight.",
"Assume Henry is a knight. No contradiction is found in their claim that Liam is not a knave."
] |
This leads to a feasible solution.
|
(('<=>', ('telling-truth', 0), ('telling-truth', 1)), ('not', ('lying', 0)))
| 171
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Liam, and Henry. According to Liam, \"Liam is a knight if and only if Henry is a knight\". Henry said, \"Liam is not a knave.\" So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Liam is a knight\n(2) Henry is a knight",
"statements": "(('<=>', ('telling-truth', 0), ('telling-truth', 1)), ('not', ('lying', 0)))"
},
"style": "rule"
}
|
{
"index": 71,
"split": "train"
}
|
[
"Olivia",
"Joseph"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
false
] |
Olivia is a knight, and Joseph is a knave.
|
(1) Olivia is a knight
(2) Joseph is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Olivia is a knight. No contradiction is found in their claim that If Joseph is a knight then Olivia is a knight.",
"Joseph cannot be a knight, because this would contradict the claim of their own that Olivia is a knave if and only if Olivia is a knight.",
"Assume Joseph is a knave. No contradiction is found in their false claim that Olivia is a knave if and only if Olivia is a knight."
] |
This leads to a feasible solution.
|
(('->', ('telling-truth', 1), ('telling-truth', 0)), ('<=>', ('lying', 0), ('telling-truth', 0)))
| 172
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Olivia, and Joseph. \"If Joseph is a knight then Olivia is a knight\" - Olivia. Joseph commented, \"Olivia is a knave if and only if Olivia is a knight\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Olivia is a knight\n(2) Joseph is a knave",
"statements": "(('->', ('telling-truth', 1), ('telling-truth', 0)), ('<=>', ('lying', 0), ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 72,
"split": "train"
}
|
[
"Jack",
"Jackson"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
false
] |
Jack is a knave, and Jackson is a knave.
|
(1) Jack is a knave
(2) Jackson is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Jack is a knight. No contradiction is found in their claim that Jack is a knight and Jackson is a knave.",
"Jackson cannot be a knight, because this would contradict the claim of Jack that Jack is a knight and Jackson is a knave.",
"Jackson cannot be a knave, because this would contradict the false claim of their own that Jack is not a knave.",
"We have exhausted all possibilities for Jackson, so let us go back and reconsider Jack.",
"Assume Jack is a knave. No contradiction is found in their false claim that Jack is a knight and Jackson is a knave.",
"Jackson cannot be a knight, because this would contradict the claim of their own that Jack is not a knave.",
"Assume Jackson is a knave. No contradiction is found in their false claim that Jack is not a knave."
] |
This leads to a feasible solution.
|
(('and', ('telling-truth', 0), ('lying', 1)), ('not', ('lying', 0)))
| 173
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Jack, and Jackson. \"Jack is a knight and Jackson is a knave,\" Jack claimed. Jackson told you that Jack is not a knave. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Jack is a knave\n(2) Jackson is a knave",
"statements": "(('and', ('telling-truth', 0), ('lying', 1)), ('not', ('lying', 0)))"
},
"style": "rule"
}
|
{
"index": 73,
"split": "train"
}
|
[
"Evelyn",
"Ethan"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
false
] |
Evelyn is a knave, and Ethan is a knave.
|
(1) Evelyn is a knave
(2) Ethan is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Evelyn is a knight. No contradiction is found in their claim that Evelyn is a knight if and only if Ethan is a knave.",
"Ethan cannot be a knight, because this would contradict the claim of Evelyn that Evelyn is a knight if and only if Ethan is a knave.",
"Ethan cannot be a knave, because this would contradict the false claim of their own that Ethan is a knight if and only if Evelyn is a knave.",
"We have exhausted all possibilities for Ethan, so let us go back and reconsider Evelyn.",
"Assume Evelyn is a knave. No contradiction is found in their false claim that Evelyn is a knight if and only if Ethan is a knave.",
"Ethan cannot be a knight, because this would contradict the false claim of Evelyn that Evelyn is a knight if and only if Ethan is a knave.",
"Assume Ethan is a knave. No contradiction is found in their false claim that Ethan is a knight if and only if Evelyn is a knave."
] |
This leads to a feasible solution.
|
(('<=>', ('telling-truth', 0), ('lying', 1)), ('<=>', ('telling-truth', 1), ('lying', 0)))
| 174
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Evelyn, and Ethan. In a statement by Evelyn: \"Evelyn is a knight if and only if Ethan is a knave\". As Ethan put it, \"Ethan is a knight if and only if Evelyn is a knave\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Evelyn is a knave\n(2) Ethan is a knave",
"statements": "(('<=>', ('telling-truth', 0), ('lying', 1)), ('<=>', ('telling-truth', 1), ('lying', 0)))"
},
"style": "rule"
}
|
{
"index": 74,
"split": "train"
}
|
[
"Avery",
"Aurora"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
false
] |
Avery is a knight, and Aurora is a knave.
|
(1) Avery is a knight
(2) Aurora is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Avery is a knight. No contradiction is found in their claim that If Aurora is a knight then Avery is a knight.",
"Aurora cannot be a knight, because this would contradict the claim of their own that Avery is a knight and Avery is a knave.",
"Assume Aurora is a knave. No contradiction is found in their false claim that Avery is a knight and Avery is a knave."
] |
This leads to a feasible solution.
|
(('->', ('telling-truth', 1), ('telling-truth', 0)), ('and', ('telling-truth', 0), ('lying', 0)))
| 175
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Avery, and Aurora. Avery commented, \"If Aurora is a knight then Avery is a knight\". According to Aurora, \"Avery is a knight and Avery is a knave\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Avery is a knight\n(2) Aurora is a knave",
"statements": "(('->', ('telling-truth', 1), ('telling-truth', 0)), ('and', ('telling-truth', 0), ('lying', 0)))"
},
"style": "rule"
}
|
{
"index": 75,
"split": "train"
}
|
[
"Isabella",
"Evelyn"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
true
] |
Isabella is a knave, and Evelyn is a knight.
|
(1) Isabella is a knave
(2) Evelyn is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Isabella is a knight. No contradiction is found in their claim that Evelyn is not a knight.",
"Evelyn cannot be a knight, because this would contradict the claim of Isabella that Evelyn is not a knight.",
"Evelyn cannot be a knave, because this would contradict the false claim of their own that Isabella is a knave or Isabella is a knight.",
"We have exhausted all possibilities for Evelyn, so let us go back and reconsider Isabella.",
"Assume Isabella is a knave. No contradiction is found in their false claim that Evelyn is not a knight.",
"Assume Evelyn is a knight. No contradiction is found in their claim that Isabella is a knave or Isabella is a knight."
] |
This leads to a feasible solution.
|
(('not', ('telling-truth', 1)), ('or', ('lying', 0), ('telling-truth', 0)))
| 176
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Isabella, and Evelyn. In a statement by Isabella: \"Evelyn is not a knight\". Evelyn stated, \"Isabella is a knave or Isabella is a knight\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Isabella is a knave\n(2) Evelyn is a knight",
"statements": "(('not', ('telling-truth', 1)), ('or', ('lying', 0), ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 76,
"split": "train"
}
|
[
"Samuel",
"Scarlett"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
false
] |
Samuel is a knight, and Scarlett is a knave.
|
(1) Samuel is a knight
(2) Scarlett is a knave
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Samuel is a knight. No contradiction is found in their claim that If Scarlett is a knave then Samuel is a knight.",
"Scarlett cannot be a knight, because this would contradict the claim of their own that Samuel is not a knight.",
"Assume Scarlett is a knave. No contradiction is found in their false claim that Samuel is not a knight."
] |
This leads to a feasible solution.
|
(('->', ('lying', 1), ('telling-truth', 0)), ('not', ('telling-truth', 0)))
| 177
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Samuel, and Scarlett. \"If Scarlett is a knave then Samuel is a knight,\" Samuel declared. \"Samuel is not a knight,\" Scarlett declared. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Samuel is a knight\n(2) Scarlett is a knave",
"statements": "(('->', ('lying', 1), ('telling-truth', 0)), ('not', ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 77,
"split": "train"
}
|
[
"James",
"Samuel"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
true
] |
James is a knight, and Samuel is a knight.
|
(1) James is a knight
(2) Samuel is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume James is a knight. No contradiction is found in their claim that Samuel is a knight or James is a knight.",
"Assume Samuel is a knight. No contradiction is found in their claim that James is a knave or James is a knight."
] |
This leads to a feasible solution.
|
(('or', ('telling-truth', 1), ('telling-truth', 0)), ('or', ('lying', 0), ('telling-truth', 0)))
| 178
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: James, and Samuel. James expressed that Samuel is a knight or James is a knight. \"James is a knave or James is a knight,\" Samuel claimed. So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) James is a knight\n(2) Samuel is a knight",
"statements": "(('or', ('telling-truth', 1), ('telling-truth', 0)), ('or', ('lying', 0), ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 78,
"split": "train"
}
|
[
"Harper",
"Zoey"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
false,
true
] |
Harper is a knave, and Zoey is a knight.
|
(1) Harper is a knave
(2) Zoey is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Harper cannot be a knight, because this would contradict the claim of their own that Zoey is a knave if and only if Zoey is a knight.",
"Assume Harper is a knave. No contradiction is found in their false claim that Zoey is a knave if and only if Zoey is a knight.",
"Assume Zoey is a knight. No contradiction is found in their claim that Harper is a knave or Harper is a knight."
] |
This leads to a feasible solution.
|
(('<=>', ('lying', 1), ('telling-truth', 1)), ('or', ('lying', 0), ('telling-truth', 0)))
| 179
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Harper, and Zoey. Harper commented, \"Zoey is a knave if and only if Zoey is a knight\". Zoey was heard saying, \"Harper is a knave or Harper is a knight\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Harper is a knave\n(2) Zoey is a knight",
"statements": "(('<=>', ('lying', 1), ('telling-truth', 1)), ('or', ('lying', 0), ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 79,
"split": "train"
}
|
[
"Riley",
"Elizabeth"
] |
{
"knight": "knight",
"knave": "knave",
"a_knight": "a knight",
"a_knave": "a knave",
"Knight": "Knight",
"Knave": "Knave"
}
|
[
true,
true
] |
Riley is a knight, and Elizabeth is a knight.
|
(1) Riley is a knight
(2) Elizabeth is a knight
|
Let's think step by step, by considering whether each person is lying and if that leads to contradiction.
|
[
"Assume Riley 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 Riley is a knave or Riley is a knight."
] |
This leads to a feasible solution.
|
(('->', ('lying', 1), ('telling-truth', 1)), ('or', ('lying', 0), ('telling-truth', 0)))
| 180
| 2
|
K-and-K/knights-and-knaves
|
[
{
"content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and<answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer>. Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> </answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... </answer>.",
"role": "system"
},
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 2 inhabitants: Riley, and Elizabeth. Riley stated, \"If Elizabeth is a knave then Elizabeth is a knight\". Elizabeth stated, \"Riley is a knave or Riley is a knight\". So who is a knight and who is a knave?",
"role": "user"
}
] |
logic
| 2
|
{
"ground_truth": {
"solution_text_format": "(1) Riley is a knight\n(2) Elizabeth is a knight",
"statements": "(('->', ('lying', 1), ('telling-truth', 1)), ('or', ('lying', 0), ('telling-truth', 0)))"
},
"style": "rule"
}
|
{
"index": 80,
"split": "train"
}
|
End of preview. Expand
in Data Studio
knights-and-knaves dataset for curriculum learning.
data from knights-and-knaves
formation from Logic-RL
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