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><... | 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 Mi... | 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><... | 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 fal... | 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><... | 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 ... | 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><... | 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><... | 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... | 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><... | 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 contrad... | 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><... | 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... | 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><... | 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><... | 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 contradi... | 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><... | 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><... | 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 cla... | 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><... | 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><... | 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 ... | 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><... | 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 t... | 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><... | 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 contradic... | 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><... | 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 cl... | 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><... | 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><... | 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 th... | 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><... | 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 on... | 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><... | 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><... | 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 ... | 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><... | 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><... | 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 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><... | 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... | 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><... | 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 wo... | 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><... | 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 c... | 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><... | 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 clai... | 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><... | 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 ... | 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><... | 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><... | 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><... | 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 the... | 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><... | 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... | 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><... | 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><... | 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 cla... | 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><... | 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 ... | 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><... | 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 t... | 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><... | 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 c... | 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><... | 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 ... | 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><... | 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 ... | 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><... | 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... | 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><... | 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... | 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><... | 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><... | 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><... | 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... | 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><... | 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 i... | 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><... | 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><... | 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 con... | 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><... | 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 th... | 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><... | 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... | 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><... | 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 cla... | 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><... | 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, becaus... | 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><... | 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 contr... | 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><... | 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><... | 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><... | 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><... | 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><... | 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 foun... | 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><... | 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... | 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><... | 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 o... | 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><... | 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 fo... | 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><... | 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... | 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><... | 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 co... | 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><... | 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><... | 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><... | 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 cla... | 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><... | 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><... | 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 ... | 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><... | 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><... | 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... | 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><... | 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 t... | 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><... | 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><... | 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 f... | 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><... | 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 clai... | 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><... | 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 con... | 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><... | 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 f... | 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><... | 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... | 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><... | 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 clai... | 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><... | 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><... | 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... | 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><... | 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><... | 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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