conversation listlengths 2 2 | seed int64 48.3k 200M | task_id int64 5.39M 900M | task_metadata dict | task_type stringclasses 8
values | usage dict |
|---|---|---|---|---|---|
[
{
"content": "A sequence of brackets was cut, and only the end remains:\n\n\">)){}}()]<><>)>>>)]]}>)>]})}>]\"\n\nRestore the missing beginning so that:\n- Every closing bracket has its opening partner\n- No extra brackets are added\n- The sequence is properly nested\n\nPlease provide your final answer (the rest... | 161,616,133 | 561,616,133 | {
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"depth": null,
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"digit_map": null,
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"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 22,
"full_sequence": "[<{({[<(<{[[(<<<([{((<>)){}}()]<><>)>>>)]]}>)>]})}>]",
"generation_error": null,
"generati... | dyck_language2 | {
"completion_tokens": 1579,
"completion_tokens_details": null,
"prompt_tokens": 88,
"prompt_tokens_details": null,
"total_tokens": 1667
} |
[
{
"content": "As a Dyck language expert, you need to verify the correctness of bracket matching reasoning steps.\n\nA Dyck sequence must have all brackets properly matched and nested. The reasoning process tracks a stack: opening brackets are pushed, and closing brackets pop the matching opening bracket.\n\nSeq... | 27,716,238 | 827,716,238 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "()(([])[][{[]{[[]][()]}}][][])",
"error_indices": [
14,
16,
23,
29
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,... | dyck_language_reasoning_errors | {
"completion_tokens": 474,
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"prompt_tokens": 493,
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"total_tokens": 967
} |
[
{
"content": "As a Dyck language expert, you need to verify the correctness of bracket matching reasoning steps.\n\nA Dyck sequence must have all brackets properly matched and nested. The reasoning process tracks a stack: opening brackets are pushed, and closing brackets pop the matching opening bracket.\n\nSeq... | 43,379,825 | 843,379,825 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "[]()({()})[]",
"error_indices": [
5,
9
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"gen... | dyck_language_reasoning_errors | {
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"prompt_tokens": 274,
"prompt_tokens_details": null,
"total_tokens": 482
} |
[
{
"content": "考虑以下布尔表达式：\n\nA. ((not not ((尼日利亚的首都是曼谷。) or (not ((4 * -19) < (-14 * -5))))) and (not ((2 ** 2) > (3 - 10)))) and (((not (波兰的货币是兹罗提。)) and (((火烈鸟是鸟类。) or (1924年奥运会在巴黎举办。)) and ((鸡有2条腿。) or (越南的首都是哈瓦那。)))) or ((2024年奥运会在巴黎举办。) or (((-10 * -10 + 1 * -2) > (-17 + 18)) or (443是斐波那契数。)) or (((企鹅能飞翔。) ... | 80,125,444 | 680,125,444 | {
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"depth": 5,
"difficulty": null,
"digit_map": null,
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"expressions": [
[
"((not not ((尼日利亚的首都是曼谷。) or (not ((4 * -19) < (-14 * -5))))) and (not ((2 ** 2) > (3 - 10)))) and (((not (波兰的货币是兹罗提。)) and (((火烈鸟... | boolean_expressions | {
"completion_tokens": 1464,
"completion_tokens_details": null,
"prompt_tokens": 638,
"prompt_tokens_details": null,
"total_tokens": 2102
} |
[
{
"content": "You are given the ending portion of a bracket sequence. Find the beginning.\n\nEnding: ()}<>()\n\nYour task:\n- Determine what opening brackets must come before this ending\n- The result must be a valid, balanced bracket sequence\n- Use the minimum number of opening brackets necessary\n\nPlease pr... | 47,295,526 | 447,295,526 | {
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"depth": null,
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"fill_length": 1,
"full_sequence": "{()}<>()",
"generation_error": null,
"generation_failed": null,
"generation_traceback": n... | dyck_language2 | {
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} |
[
{
"content": "You are an expert in Dyck language, where you must complete bracket sequences (e.g., [], {}, <>). You need to analyze whether the bracket matching steps are correct according to Dyck language rules.\n\nGiven an initial Dyck language sequence and steps for deriving the closing bracket sequence (giv... | 11,765,978 | 811,765,978 | {
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"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "{}((){}{})[{()}][()[]][][][]",
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17,
23
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_fai... | dyck_language_reasoning_errors | {
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} |
[
{
"content": "As a Dyck language expert, you need to verify the correctness of bracket matching reasoning steps.\n\nA Dyck sequence must have all brackets properly matched and nested. The reasoning process tracks a stack: opening brackets are pushed, and closing brackets pop the matching opening bracket.\n\nSeq... | 45,190,154 | 845,190,154 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "({{}({}[]{})}[])",
"error_indices": [
6,
8,
9,
13
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_fa... | dyck_language_reasoning_errors | {
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} |
[
{
"content": "As a Dyck language expert, you need to verify the correctness of bracket matching reasoning steps.\n\nA Dyck sequence must have all brackets properly matched and nested. The reasoning process tracks a stack: opening brackets are pushed, and closing brackets pop the matching opening bracket.\n\nSeq... | 65,697,496 | 865,697,496 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "{()}{}()([][])[]{{}}",
"error_indices": [
5,
19
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": nul... | dyck_language_reasoning_errors | {
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"prompt_tokens": 363,
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"total_tokens": 665
} |
[
{
"content": "A sequence of brackets was cut, and only the end remains:\n\n\"()>}()})[]}]<>()[]()\"\n\nRestore the missing beginning so that:\n- Every closing bracket has its opening partner\n- No extra brackets are added\n- The sequence is properly nested\n\nPlease provide your final answer (the restored compl... | 62,644,014 | 462,644,014 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 6,
"full_sequence": "[{({{<()>}()})[]}]<>()[]()",
"generation_error": null,
"generation_failed": null,
"genera... | dyck_language2 | {
"completion_tokens": 609,
"completion_tokens_details": null,
"prompt_tokens": 83,
"prompt_tokens_details": null,
"total_tokens": 692
} |
[
{
"content": "Given the following boolean expressions:\n\nA. not (((not not (not (There are 30 days in September.))) or ((not not (not not ((-9 * 9) <= (15 + -6)))) or (The chemical symbol for Sodium is Mn.))) and (not (not not ((The currency of Nigeria is the Forint.) and (((20 * -7) < (18 - -12)) and (Saturn ... | 11,563,831 | 611,563,831 | {
"closing_sequence": null,
"depth": 6,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"not (((not not (not (There are 30 days in September.))) or ((not not (not not ((-9 * 9) <= (15 + -6)))) or (The chemical symbol f... | boolean_expressions | {
"completion_tokens": 1728,
"completion_tokens_details": null,
"prompt_tokens": 765,
"prompt_tokens_details": null,
"total_tokens": 2493
} |
[
{
"content": "Given the following boolean expressions:\n\nA. (not not (((Morocco is in Africa.) and (Water is a gas at room temperature.)) and ((A human is a mammal.) or ((0 * 5) < (-13 * 6))))) and (not not (not not ((5 * -10 + -10 * 3) < (2 * 10 * -9 * 9))))\nB. (not not ((not not (The 2008 Olympics were held... | 64,997,826 | 664,997,826 | {
"closing_sequence": null,
"depth": 4,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"(not not (((Morocco is in Africa.) and (Water is a gas at room temperature.)) and ((A human is a mammal.) or ((0 * 5) < (-13 * 6)... | boolean_expressions | {
"completion_tokens": 454,
"completion_tokens_details": null,
"prompt_tokens": 217,
"prompt_tokens_details": null,
"total_tokens": 671
} |
[
{
"content": "Let S = \"())⟦⟧⟨⟩<>]>()\" be a suffix of a Dyck word.\n\nFind the minimal prefix P such that P + S forms a valid Dyck word.\n\nPlease provide your final answer (P + S, the complete Dyck word) in backticks like `answer`.",
"reasoning_content": null,
"role": "user"
},
{
"content": "`... | 38,282,667 | 438,282,667 | {
"closing_sequence": null,
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"fill_length": 3,
"full_sequence": "<[(())⟦⟧⟨⟩<>]>()",
"generation_error": null,
"generation_failed": null,
"generation_trace... | dyck_language2 | {
"completion_tokens": 430,
"completion_tokens_details": null,
"prompt_tokens": 72,
"prompt_tokens_details": null,
"total_tokens": 502
} |
[
{
"content": "定义 ◇，规则如下：\n当x大于y时，x ◇ y = x + y + x；\n其他情况下，x ◇ y = x - y - y。\n运算优先级：◇ > ** > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 7 * 9 + 9 ◇ 8\n请将最终答案填入\\boxed{}中。",
"reasoning_content": null,
"role": "user"
},
{
"content": "根据给定的运算规则，◇ 的优先级高于乘法和加法。首先计算 9 ◇ 8：由于 9 > 8，所以 9 ... | 9,293,513 | 209,293,513 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "7 * 9 + 9 ◇ 8",
"expressions": null,
"fill_length": null,
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"generation_error": null,
"generation_failed": null,
"generation_trace... | operation | {
"completion_tokens": 777,
"completion_tokens_details": null,
"prompt_tokens": 113,
"prompt_tokens_details": null,
"total_tokens": 890
} |
[
{
"content": "数字：[6, 7, 8, 10, 12, 12]，运算符：['+', '-', '*']，目标：100。\n\n在回答的最后，请输出一个 ```python 代码块。代码块中仅包含一个代表答案的表达式，并且该表达式可以直接被 Python 中的 eval() 函数求值。如果无解，请输出 ```python\\nNone\\n```。",
"reasoning_content": null,
"role": "user"
},
{
"content": "```python\n6*(7+8)+10+12-12\n```",
"reasoning_con... | 21,878,507 | 121,878,507 | {
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"generation_error": null,
"generation_failed": null,
"generation_traceback": null... | game_of_24 | {
"completion_tokens": 3033,
"completion_tokens_details": null,
"prompt_tokens": 102,
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"total_tokens": 3135
} |
[
{
"content": "You are an expert in Dyck language, where you must complete bracket sequences (e.g., [], {}, <>). You need to analyze whether the bracket matching steps are correct according to Dyck language rules.\n\nGiven an initial Dyck language sequence and steps for deriving the closing bracket sequence (giv... | 36,956,323 | 836,956,323 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "[](())((())([]())([]))[]()",
"error_indices": [
5,
14,
19
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generatio... | dyck_language_reasoning_errors | {
"completion_tokens": 391,
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} |
[
{
"content": "Fill in the blank:\n\n_____ + ⟩)> = valid Dyck sequence\n\nRules:\n- The blank contains only opening brackets\n- Use the minimum required\n\nPlease provide your final answer (the complete filled sequence) in backticks like `answer`.",
"reasoning_content": null,
"role": "user"
},
{
... | 124,609,269 | 524,609,269 | {
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"digit_map": null,
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"error_indices": null,
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"expressions": null,
"fill_length": 3,
"full_sequence": "<(⟨⟩)>",
"generation_error": null,
"generation_failed": null,
"generation_traceback": nul... | dyck_language2 | {
"completion_tokens": 291,
"completion_tokens_details": null,
"prompt_tokens": 60,
"prompt_tokens_details": null,
"total_tokens": 351
} |
[
{
"content": "Analyze these boolean expressions:\n\nA. not (not not (Humans have three lungs.))\nB. ((((Australia is in Oceania.) and (A lizard is a reptile.)) or (not (Mars is the 4th planet from the Sun.))) or ((18 + -10) <= (-15 + -6)) or (not ((Vietnam is in South America.) and (The 2016 Olympics were held ... | 70,080,892 | 670,080,892 | {
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"expressions": [
[
"not (not not (Humans have three lungs.))",
"True"
],
[
"((((Australia is in Oceania.) and (A lizard is a rept... | boolean_expressions | {
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"completion_tokens_details": null,
"prompt_tokens": 348,
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} |
[
{
"content": "Let S = \")⟧⟧)>⦄])⟧>}}⟩>⟩\" be a suffix of a Dyck word.\n\nFind the minimal prefix P such that P + S forms a valid Dyck word.\n\nPlease provide your final answer (P + S, the complete Dyck word) in backticks like `answer`.",
"reasoning_content": null,
"role": "user"
},
{
"content": ... | 101,706,456 | 501,706,456 | {
"closing_sequence": null,
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"error_indices": null,
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"fill_length": 15,
"full_sequence": "⟨<⟨{{<⟦([⦃<(⟦⟦()⟧⟧)>⦄])⟧>}}⟩>⟩",
"generation_error": null,
"generation_failed": null,
"g... | dyck_language2 | {
"completion_tokens": 1048,
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} |
[
{
"content": "Fill in the blank:\n\n_____ + {}]⟩]<>]]()>)[]⟩}<>[][]⟨⟩{}<><>[][] = valid Dyck sequence\n\nRules:\n- The blank contains only opening brackets\n- Use the minimum required\n\nPlease provide your final answer (the complete filled sequence) in backticks like `answer`.",
"reasoning_content": null,
... | 75,985,816 | 475,985,816 | {
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"fill_length": 9,
"full_sequence": "{⟨(<[[[⟨[{}]⟩]<>]]()>)[]⟩}<>[][]⟨⟩{}<><>[][]",
"generation_error": null,
"generation_failed... | dyck_language2 | {
"completion_tokens": 970,
"completion_tokens_details": null,
"prompt_tokens": 77,
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} |
[
{
"content": "A sequence of brackets was cut, and only the end remains:\n\n\"()<>⦃⦄()}⟧⦄>⟩]⟧⟧>>}⟧⦄}⟧}⟧⟧⟩⦄\"\n\nRestore the missing beginning so that:\n- Every closing bracket has its opening partner\n- No extra brackets are added\n- The sequence is properly nested\n\nPlease provide your final answer (the restor... | 82,811,652 | 482,811,652 | {
"closing_sequence": null,
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"error_indices": null,
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"expressions": null,
"fill_length": 20,
"full_sequence": "⦃⟨⟦⟦{⟦{⦃⟦{<<⟦⟦[⟨<⦃⟦{()<>⦃⦄()}⟧⦄>⟩]⟧⟧>>}⟧⦄}⟧}⟧⟧⟩⦄",
"generation_error": null,
"generation_f... | dyck_language2 | {
"completion_tokens": 1709,
"completion_tokens_details": null,
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} |
[
{
"content": "Use the numbers [9, 10, 19, 20] with ['+', '-'] to reach 72.\n\nAt the end of your response, please output a ```python code block. The code block should contain only a single expression representing the answer, which can be directly evaluated using Python's eval() function. If there is no solution... | 68,065,045 | 168,065,045 | {
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"generation_error": null,
"generation_failed": null,
"generation_traceback": null... | game_of_24 | {
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"completion_tokens_details": null,
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} |
[
{
"content": "定义 ⊙，规则如下：\n实数域上，x ⊙ y = x + y + x。\n和 △，规则如下：\n当x是偶数时，x △ y = y ⊙ 4 + (x) - y * x；\n其他情况下，x △ y = (x - y ⊙ y) + x + 5。\n和 ▽，规则如下：\n实数域上，x ▽ y = y * x / 5 - x + 1。\n运算优先级：⊙ = △ = ▽ > ** > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 2 ▽ 7 ⊙ 10 △ 9\n请将最终答案填入\\boxed{}中。",
"reason... | 24,369,862 | 224,369,862 | {
"closing_sequence": null,
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"digit_map": null,
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"error_indices": null,
"expression": "2 ▽ 7 ⊙ 10 △ 9",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_trac... | operation | {
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} |
[
{
"content": "Given the numbers [3, 5, 6, 7], apply ['+', '-'] to get 100.\n\nAt the end of your response, please output a ```python code block. The code block should contain only a single expression representing the answer, which can be directly evaluated using Python's eval() function. If there is no solution... | 62,537,380 | 162,537,380 | {
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"generation_error": null,
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"generation_traceback": null... | game_of_24 | {
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} |
[
{
"content": "用这些数字 [3, 5, 7, 7, 9] 通过 ['+', '-', '*'] 算出 72。\n\n在回答的最后，请输出一个 ```python 代码块。代码块中仅包含一个代表答案的表达式，并且该表达式可以直接被 Python 中的 eval() 函数求值。如果无解，请输出 ```python\\nNone\\n```。",
"reasoning_content": null,
"role": "user"
},
{
"content": "通过使用数字 [3, 5, 7, 7, 9] 和运算符 ['+', '-', '*']，可以构造表达式 `(3 + ... | 24,586,459 | 124,586,459 | {
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"generation_error": null,
"generation_failed": null,
"generation_traceback": null... | game_of_24 | {
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"completion_tokens_details": null,
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} |
[
{
"content": "Given: RTIRP + PRIRN = DDDIPR, where each letter represents a unique digit (RTIRP is a 5-digit number, PRIRN is a 5-digit number, and DDDIPR is a 6-digit number). Find the numeric equation that makes the equality valid. Please end your response in the last line with the following format: The answe... | 53,122,457 | 353,122,457 | {
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"A": null,
"B": null,
"C": null,
"D": 1,
"E": null,
"F": null,
"G": null,
"H": null,
"I": 0,
"J": null,
"K": null,
"L": null,
"M": null,
"N": 6,
"O": null,
"P": 7,
"Q... | cryptarithm | {
"completion_tokens": 4002,
"completion_tokens_details": null,
"prompt_tokens": 110,
"prompt_tokens_details": null,
"total_tokens": 4112
} |
[
{
"content": "Bracket Puzzle: What's missing at the start?\n\nGiven suffix: ⟩>[]}<>)]⟩)}]]⟩⟩>}\n\nSolve:\n1. Each closing bracket needs a matching opening bracket\n2. Add the minimal opening brackets to the left\n3. The final sequence must be properly nested\n\nPlease provide your final answer (the full balance... | 54,031,710 | 454,031,710 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 14,
"full_sequence": "{<⟨⟨[[{(⟨[({<⟨⟩>[]}<>)]⟩)}]]⟩⟩>}",
"generation_error": null,
"generation_failed": null,
... | dyck_language2 | {
"completion_tokens": 983,
"completion_tokens_details": null,
"prompt_tokens": 89,
"prompt_tokens_details": null,
"total_tokens": 1072
} |
[
{
"content": "评估以下每个表达式：\n\nA. (((1948年奥运会在伦敦举办。) and ((not (智利位于欧洲。)) or (not not (人类只使用了大脑的10%。)))) and ((((2 * 7 + -7 * -4) < (-17 - 6)) and ((1 + -20) == (-17 - -3))) and (泰坦尼克号沉没发生在1910年。))) or ((((1 ** 2) >= (-1 - -15)) and ((1916年是闰年。) and ((声音在真空中传播更快。) or (猪是哺乳动物。)))) or (((澳大利亚位于南美洲。) or ((22 % 9) < (... | 69,391,229 | 669,391,229 | {
"closing_sequence": null,
"depth": 5,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"(((1948年奥运会在伦敦举办。) and ((not (智利位于欧洲。)) or (not not (人类只使用了大脑的10%。)))) and ((((2 * 7 + -7 * -4) < (-17 - 6)) and ((1 + -20) == (-... | boolean_expressions | {
"completion_tokens": 3837,
"completion_tokens_details": null,
"prompt_tokens": 1592,
"prompt_tokens_details": null,
"total_tokens": 5429
} |
[
{
"content": "Here are some boolean expressions to evaluate:\n\nA. (not (((((-5 - 0) != (9 + 14)) and ((13 * -6) != (18 * 17))) or (((8 + 8) < (-10 - -9) < (10 + 7)) or ((7 + 14) != (0 - 18)))) and ((((3 - -11) < (-17 + 18)) and (Carbon dioxide is a solid at room temperature.)) and ((Uranus is the 1st planet fr... | 1,753,426 | 601,753,426 | {
"closing_sequence": null,
"depth": 5,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"(not (((((-5 - 0) != (9 + 14)) and ((13 * -6) != (18 * 17))) or (((8 + 8) < (-10 - -9) < (10 + 7)) or ((7 + 14) != (0 - 18)))) an... | boolean_expressions | {
"completion_tokens": 1933,
"completion_tokens_details": null,
"prompt_tokens": 835,
"prompt_tokens_details": null,
"total_tokens": 2768
} |
[
{
"content": "Fill in the blank:\n\n_____ + ]})) = valid Dyck sequence\n\nRules:\n- The blank contains only opening brackets\n- Use the minimum required\n\nPlease provide your final answer (the complete filled sequence) in backticks like `answer`.",
"reasoning_content": null,
"role": "user"
},
{
... | 127,626,741 | 527,626,741 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 4,
"full_sequence": "(({[]}))",
"generation_error": null,
"generation_failed": null,
"generation_traceback": n... | dyck_language2 | {
"completion_tokens": 326,
"completion_tokens_details": null,
"prompt_tokens": 59,
"prompt_tokens_details": null,
"total_tokens": 385
} |
[
{
"content": "Complete the following Dyck language sequence by adding the minimal necessary closing brackets.\n\nSequence: ((⦃⟦⟧⦄⟨⟩))(({\n\nRules:\n- Add only the closing brackets needed to match all unmatched opening brackets\n- Do not add any extra bracket pairs beyond what is required\n\nProvide only the com... | 7,130,446 | 7,130,446 | {
"closing_sequence": "}))",
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 3,
"full_sequence": "((⦃⟦⟧⦄⟨⟩))(({}))",
"generation_error": null,
"generation_failed": null,
"generation_trac... | dyck_language | {
"completion_tokens": 396,
"completion_tokens_details": null,
"prompt_tokens": 75,
"prompt_tokens_details": null,
"total_tokens": 471
} |
[
{
"content": "用 [10, 15, 16, 19, 19] 这几个数，通过 ['+', '-'] 运算得到 48。\n\n在回答的最后，请输出一个 ```python 代码块。代码块中仅包含一个代表答案的表达式，并且该表达式可以直接被 Python 中的 eval() 函数求值。如果无解，请输出 ```python\\nNone\\n```。",
"reasoning_content": null,
"role": "user"
},
{
"content": "根据给定的数字 [10, 15, 16, 19, 19] 和运算符 ['+', '-']，需要通过组合这些数字... | 66,030,955 | 166,030,955 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback": null... | game_of_24 | {
"completion_tokens": 4503,
"completion_tokens_details": null,
"prompt_tokens": 102,
"prompt_tokens_details": null,
"total_tokens": 4605
} |
[
{
"content": "As a Dyck language expert, you need to verify the correctness of bracket matching reasoning steps.\n\nA Dyck sequence must have all brackets properly matched and nested. The reasoning process tracks a stack: opening brackets are pushed, and closing brackets pop the matching opening bracket.\n\nSeq... | 18,696,652 | 818,696,652 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "[<[[]]<>>]()",
"error_indices": [
9,
14
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"ge... | dyck_language_reasoning_errors | {
"completion_tokens": 214,
"completion_tokens_details": null,
"prompt_tokens": 279,
"prompt_tokens_details": null,
"total_tokens": 493
} |
[
{
"content": "Apply ['+', '-', '*', '/'] to [5, 6, 8, 8, 11] to obtain 48.\n\nAt the end of your response, please output a ```python code block. The code block should contain only a single expression representing the answer, which can be directly evaluated using Python's eval() function. If there is no solution... | 48,602,691 | 148,602,691 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback": null... | game_of_24 | {
"completion_tokens": 5479,
"completion_tokens_details": null,
"prompt_tokens": 95,
"prompt_tokens_details": null,
"total_tokens": 5574
} |
[
{
"content": "A sequence of brackets was cut, and only the end remains:\n\n\")⦄)>⦆⟧>⦆]⟩}⦄}}}⟧]⟧)]⟧⟩\"\n\nRestore the missing beginning so that:\n- Every closing bracket has its opening partner\n- No extra brackets are added\n- The sequence is properly nested\n\nPlease provide your final answer (the restored com... | 162,393,193 | 562,393,193 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 22,
"full_sequence": "⟨⟦[(⟦[⟦{{{⦃{⟨[⦅<⟦⦅<(⦃()⦄)>⦆⟧>⦆]⟩}⦄}}}⟧]⟧)]⟧⟩",
"generation_error": null,
"generation_faile... | dyck_language2 | {
"completion_tokens": 1745,
"completion_tokens_details": null,
"prompt_tokens": 94,
"prompt_tokens_details": null,
"total_tokens": 1839
} |
[
{
"content": "As a Dyck language expert, you need to verify the correctness of bracket matching reasoning steps.\n\nA Dyck sequence must have all brackets properly matched and nested. The reasoning process tracks a stack: opening brackets are pushed, and closing brackets pop the matching opening bracket.\n\nSeq... | 78,346,046 | 878,346,046 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "<>[]<><(){}{}>",
"error_indices": [
3,
10,
16
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": n... | dyck_language_reasoning_errors | {
"completion_tokens": 256,
"completion_tokens_details": null,
"prompt_tokens": 298,
"prompt_tokens_details": null,
"total_tokens": 554
} |
[
{
"content": "In this alphametic puzzle: UGGUG - GIG - UIIZ = GUIGZ, each letter represents a distinct digit from 0-9. Determine the digits that make the equation valid. Please end your response in the last line with the following format: The answer is $YOUR_ANSWER. $YOUR_ANSWER should be the equation with lett... | 16,189,379 | 316,189,379 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": {
"A": null,
"B": null,
"C": null,
"D": null,
"E": null,
"F": null,
"G": 8,
"H": null,
"I": 0,
"J": null,
"K": null,
"L": null,
"M": null,
"N": null,
"O": null,
"P": null,
... | cryptarithm | {
"completion_tokens": 3488,
"completion_tokens_details": null,
"prompt_tokens": 87,
"prompt_tokens_details": null,
"total_tokens": 3575
} |
[
{
"content": "Apply ['+', '-'] to [8, 14, 20, 20, 20] to obtain 36.\n\nAt the end of your response, please output a ```python code block. The code block should contain only a single expression representing the answer, which can be directly evaluated using Python's eval() function. If there is no solution, pleas... | 2,962,741 | 102,962,741 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback": null... | game_of_24 | {
"completion_tokens": 4464,
"completion_tokens_details": null,
"prompt_tokens": 96,
"prompt_tokens_details": null,
"total_tokens": 4560
} |
[
{
"content": "Define ▽, the rules are as follows:\non the real number field, x ▽ y = x * y + x - 2.\nThe precedence of operations: ** > * = / = % = ▽ > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 5... | 5,810,802 | 205,810,802 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "5",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback": null,... | operation | {
"completion_tokens": 33,
"completion_tokens_details": null,
"prompt_tokens": 98,
"prompt_tokens_details": null,
"total_tokens": 131
} |
[
{
"content": "定义 ♢，规则如下：\n当x是偶数时，x ♢ y = y + x；\n其他情况下，x ♢ y = y * y - x。\n和 □，规则如下：\n当x是3的倍数时，x □ y = x ♢ x ** y；\n其他情况下，x □ y = y + x * y。\n和 ▽，规则如下：\n实数域上，x ▽ y = x + y - y。\n运算优先级：** = □ > * = / = % = ♢ = ▽ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 1 * 5 □ 3 ♢ 6 ▽ 10\n请将最终答案填入\\boxed{}中。",
"r... | 19,235,632 | 219,235,632 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "1 * 5 □ 3 ♢ 6 ▽ 10",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_... | operation | {
"completion_tokens": 855,
"completion_tokens_details": null,
"prompt_tokens": 193,
"prompt_tokens_details": null,
"total_tokens": 1048
} |
[
{
"content": "数字组合 [2, 3, 4, 7]，运算 ['+', '-', '*', '/']，目标值 24。\n\n在回答的最后，请输出一个 ```python 代码块。代码块中仅包含一个代表答案的表达式，并且该表达式可以直接被 Python 中的 eval() 函数求值。如果无解，请输出 ```python\\nNone\\n```。",
"reasoning_content": null,
"role": "user"
},
{
"content": "```python\n(2 + 4) * (7 - 3)\n```",
"reasoning_conte... | 41,175,215 | 141,175,215 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback": null... | game_of_24 | {
"completion_tokens": 3869,
"completion_tokens_details": null,
"prompt_tokens": 92,
"prompt_tokens_details": null,
"total_tokens": 3961
} |
[
{
"content": "Bracket Puzzle: What's missing at the start?\n\nGiven suffix: ()}}[])())}][]{})[][]{}\n\nSolve:\n1. Each closing bracket needs a matching opening bracket\n2. Add the minimal opening brackets to the left\n3. The final sequence must be properly nested\n\nPlease provide your final answer (the full ba... | 23,866,137 | 423,866,137 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 7,
"full_sequence": "([{(({{()}}[])())}][]{})[][]{}",
"generation_error": null,
"generation_failed": null,
"ge... | dyck_language2 | {
"completion_tokens": 680,
"completion_tokens_details": null,
"prompt_tokens": 85,
"prompt_tokens_details": null,
"total_tokens": 765
} |
[
{
"content": "Q: What opening brackets should precede \"][]]()[]}{}]())}{}}]))]]]}})\" to form a valid bracket sequence?\n\nRequirements:\n- Use exactly the brackets needed (no more, no less)\n- Maintain proper nesting order\n\nPlease provide your final answer (the entire resulting sequence) in backticks like `... | 21,653,479 | 421,653,479 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 16,
"full_sequence": "({{[[[(([{{([{[[][]]()[]}{}]())}{}}]))]]]}})",
"generation_error": null,
"generation_faile... | dyck_language2 | {
"completion_tokens": 1171,
"completion_tokens_details": null,
"prompt_tokens": 77,
"prompt_tokens_details": null,
"total_tokens": 1248
} |
[
{
"content": "As a Dyck language expert, you need to verify the correctness of bracket matching reasoning steps.\n\nA Dyck sequence must have all brackets properly matched and nested. The reasoning process tracks a stack: opening brackets are pushed, and closing brackets pop the matching opening bracket.\n\nSeq... | 60,773,056 | 860,773,056 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "[([])(([]())[[]]([]))[]]",
"error_indices": [
10,
11,
18,
23
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"ge... | dyck_language_reasoning_errors | {
"completion_tokens": 398,
"completion_tokens_details": null,
"prompt_tokens": 418,
"prompt_tokens_details": null,
"total_tokens": 816
} |
[
{
"content": "You are an expert in Dyck language, where you must complete bracket sequences (e.g., [], {}, <>). You need to analyze whether the bracket matching steps are correct according to Dyck language rules.\n\nGiven an initial Dyck language sequence and steps for deriving the closing bracket sequence (giv... | 78,849,265 | 878,849,265 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "<>(){{{<{{}}[]<<>><>><>}}}<>",
"error_indices": [
5,
8,
14
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generati... | dyck_language_reasoning_errors | {
"completion_tokens": 421,
"completion_tokens_details": null,
"prompt_tokens": 544,
"prompt_tokens_details": null,
"total_tokens": 965
} |
[
{
"content": "You are an expert in Dyck language, where you must complete bracket sequences (e.g., [], {}, <>). You need to analyze whether the bracket matching steps are correct according to Dyck language rules.\n\nGiven an initial Dyck language sequence and steps for deriving the closing bracket sequence (giv... | 32,118,056 | 832,118,056 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "{[]()}{}<>()(<>[])",
"error_indices": [
3,
15,
18
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed... | dyck_language_reasoning_errors | {
"completion_tokens": 300,
"completion_tokens_details": null,
"prompt_tokens": 418,
"prompt_tokens_details": null,
"total_tokens": 718
} |
[
{
"content": "You are given the ending portion of a bracket sequence. Find the beginning.\n\nEnding: ⟩}})⟧⦄]⟩\n\nYour task:\n- Determine what opening brackets must come before this ending\n- The result must be a valid, balanced bracket sequence\n- Use the minimum number of opening brackets necessary\n\nPlease p... | 33,183,051 | 433,183,051 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 8,
"full_sequence": "⟨[⦃⟦({{⟨⟩}})⟧⦄]⟩",
"generation_error": null,
"generation_failed": null,
"generation_trace... | dyck_language2 | {
"completion_tokens": 581,
"completion_tokens_details": null,
"prompt_tokens": 90,
"prompt_tokens_details": null,
"total_tokens": 671
} |
[
{
"content": "Q: What opening brackets should precede \"())()>()⟦⟧⟨⟩{}⟧<>)⟧>⟩]⟩)⦄⟩>>}}>}⦄⟩⦄\" to form a valid bracket sequence?\n\nRequirements:\n- Use exactly the brackets needed (no more, no less)\n- Maintain proper nesting order\n\nPlease provide your final answer (the entire resulting sequence) in backticks... | 189,099,280 | 589,099,280 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 21,
"full_sequence": "⦃⟨⦃{<{{<<⟨⦃(⟨[⟨<⟦(⟦<(())()>()⟦⟧⟨⟩{}⟧<>)⟧>⟩]⟩)⦄⟩>>}}>}⦄⟩⦄",
"generation_error": null,
"gene... | dyck_language2 | {
"completion_tokens": 1785,
"completion_tokens_details": null,
"prompt_tokens": 94,
"prompt_tokens_details": null,
"total_tokens": 1879
} |
[
{
"content": "As a Dyck language expert, you need to verify the correctness of bracket matching reasoning steps.\n\nA Dyck sequence must have all brackets properly matched and nested. The reasoning process tracks a stack: opening brackets are pushed, and closing brackets pop the matching opening bracket.\n\nSeq... | 65,409,648 | 865,409,648 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "([])()<{}>{<>}<{}()({}())>[]",
"error_indices": [
21,
30
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_fai... | dyck_language_reasoning_errors | {
"completion_tokens": 385,
"completion_tokens_details": null,
"prompt_tokens": 454,
"prompt_tokens_details": null,
"total_tokens": 839
} |
[
{
"content": "As a Dyck language expert, you need to verify the correctness of bracket matching reasoning steps.\n\nA Dyck sequence must have all brackets properly matched and nested. The reasoning process tracks a stack: opening brackets are pushed, and closing brackets pop the matching opening bracket.\n\nSeq... | 82,228,223 | 882,228,223 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "(){}(){}[()][]{[]{}}",
"error_indices": [
6,
8,
11,
16
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generati... | dyck_language_reasoning_errors | {
"completion_tokens": 336,
"completion_tokens_details": null,
"prompt_tokens": 360,
"prompt_tokens_details": null,
"total_tokens": 696
} |
[
{
"content": "Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.\n\nSuffix: ⟩)}\n\nRules:\n- Add only the opening brackets needed to match all unmatched closing brackets\n- The opening brackets should be prepended to form a valid sequence\n- Do not a... | 65,579,197 | 465,579,197 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 3,
"full_sequence": "{(⟨⟩)}",
"generation_error": null,
"generation_failed": null,
"generation_traceback": nul... | dyck_language2 | {
"completion_tokens": 291,
"completion_tokens_details": null,
"prompt_tokens": 94,
"prompt_tokens_details": null,
"total_tokens": 385
} |
[
{
"content": "评估以下每个表达式：\n\nA. 南非位于非洲。\nB. 人类首次登月发生在1970年。\nC. 蚱蜢是爬行动物。\nD. ((苏联解体发生在1991年。) or (镍的化学符号是Ni。)) or (新加坡的首都是布加勒斯特。)\nE. 匈牙利的货币是加元。\nF. not not (not not ((-5 * -7 - -2 * -7) == (13 + -11)))\n\n列出所有值为 True 的选项，在 \\boxed{} 中用逗号分隔。",
"reasoning_content": null,
"role": "user"
},
{
"conte... | 70,994,708 | 670,994,708 | {
"closing_sequence": null,
"depth": 2,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"南非位于非洲。",
"True"
],
[
"人类首次登月发生在1970年。",
"False"
],
[
"蚱蜢是爬行动物。",
"False"
],
... | boolean_expressions | {
"completion_tokens": 350,
"completion_tokens_details": null,
"prompt_tokens": 144,
"prompt_tokens_details": null,
"total_tokens": 494
} |
[
{
"content": "Bracket Puzzle: What's missing at the start?\n\nGiven suffix: )}⟨⟩⟩()]\n\nSolve:\n1. Each closing bracket needs a matching opening bracket\n2. Add the minimal opening brackets to the left\n3. The final sequence must be properly nested\n\nPlease provide your final answer (the full balanced sequence... | 181,678,539 | 581,678,539 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 4,
"full_sequence": "[⟨{()}⟨⟩⟩()]",
"generation_error": null,
"generation_failed": null,
"generation_traceback... | dyck_language2 | {
"completion_tokens": 395,
"completion_tokens_details": null,
"prompt_tokens": 82,
"prompt_tokens_details": null,
"total_tokens": 477
} |
[
{
"content": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not ((The currency of China is the Yuan.) or ((-2 * 1 * -5 * 3) >= (-15 + 10)))\nB. (((((3 - 7) < (3 % 7) < (0 - -12)) or (The first moon landing occurred in 1969.)) or (not (The Berlin Wall fell occurred in 1989.)... | 59,473,101 | 659,473,101 | {
"closing_sequence": null,
"depth": 4,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"not ((The currency of China is the Yuan.) or ((-2 * 1 * -5 * 3) >= (-15 + 10)))",
"False"
],
[
"(((((3 - 7) <... | boolean_expressions | {
"completion_tokens": 799,
"completion_tokens_details": null,
"prompt_tokens": 371,
"prompt_tokens_details": null,
"total_tokens": 1170
} |
[
{
"content": "分析以下逻辑表达式：\n\nA. not not ((not not ((14 + -8) >= (-3 * -5))) or (锡的化学符号是Ti。))\nB. (法国大革命开始发生在1787年。) and ((((4 - 17) < (-12 * 7)) and ((-7 - 15) < (10 * 6))) or ((5 ** 2) > (-7 * 6 * -1 * 6)))\nC. ((((1 % 2) != (-13 + 1)) and ((10 * -2 - -3 * -5) != (0 * 4 - -5 * 6))) or (((10 + -6) < (16 + -15) <... | 98,625,017 | 698,625,017 | {
"closing_sequence": null,
"depth": 3,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"not not ((not not ((14 + -8) >= (-3 * -5))) or (锡的化学符号是Ti。))",
"False"
],
[
"(法国大革命开始发生在1787年。) and ((((4 - 1... | boolean_expressions | {
"completion_tokens": 1378,
"completion_tokens_details": null,
"prompt_tokens": 548,
"prompt_tokens_details": null,
"total_tokens": 1926
} |
[
{
"content": "You are an expert in Dyck language, where you must complete bracket sequences (e.g., [], {}, <>). You need to analyze whether the bracket matching steps are correct according to Dyck language rules.\n\nGiven an initial Dyck language sequence and steps for deriving the closing bracket sequence (giv... | 27,301,673 | 827,301,673 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "[(()[([[]]()[][])()])[]]",
"error_indices": [
4,
12,
17,
24
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"gen... | dyck_language_reasoning_errors | {
"completion_tokens": 404,
"completion_tokens_details": null,
"prompt_tokens": 502,
"prompt_tokens_details": null,
"total_tokens": 906
} |
[
{
"content": "A sequence of brackets was cut, and only the end remains:\n\n\"<>)]]}<><>]]>}}>[]})]()()(){}{}[]<>{}()[]()<>()\"\n\nRestore the missing beginning so that:\n- Every closing bracket has its opening partner\n- No extra brackets are added\n- The sequence is properly nested\n\nPlease provide your final... | 118,124,664 | 518,124,664 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 13,
"full_sequence": "[({<{{<[[{[[(<>)]]}<><>]]>}}>[]})]()()(){}{}[]<>{}()[]()<>()",
"generation_error": null,
"... | dyck_language2 | {
"completion_tokens": 1270,
"completion_tokens_details": null,
"prompt_tokens": 95,
"prompt_tokens_details": null,
"total_tokens": 1365
} |
[
{
"content": "Fill in the blank:\n\n_____ + >}⟩]<>]⟨⟩)]]]⟨⟩<>⟩>]⟩(){}}⟩}>)>}} = valid Dyck sequence\n\nRules:\n- The blank contains only opening brackets\n- Use the minimum required\n\nPlease provide your final answer (the complete filled sequence) in backticks like `answer`.",
"reasoning_content": null,
... | 98,824,067 | 498,824,067 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 21,
"full_sequence": "{{<(<{⟨{⟨[<⟨[[[([[⟨{<>}⟩]<>]⟨⟩)]]]⟨⟩<>⟩>]⟩(){}}⟩}>)>}}",
"generation_error": null,
"genera... | dyck_language2 | {
"completion_tokens": 1662,
"completion_tokens_details": null,
"prompt_tokens": 81,
"prompt_tokens_details": null,
"total_tokens": 1743
} |
[
{
"content": "Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.\n\nSuffix: ()}[]⟩)})]⟨⟩()[]⟩]⟩))}(){}()[]()(){}⟨⟩\n\nRules:\n- Add only the opening brackets needed to match all unmatched closing brackets\n- The opening brackets should be prepended t... | 158,636,139 | 558,636,139 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 12,
"full_sequence": "{((⟨[⟨[({(⟨{()}[]⟩)})]⟨⟩()[]⟩]⟩))}(){}()[]()(){}⟨⟩",
"generation_error": null,
"generation... | dyck_language2 | {
"completion_tokens": 1169,
"completion_tokens_details": null,
"prompt_tokens": 116,
"prompt_tokens_details": null,
"total_tokens": 1285
} |
[
{
"content": "给定以下布尔表达式：\n\nA. ((not (((-1 - -3) < (2 ** 3)) and ((11 + -2) >= (5 + 14)))) and ((-5 * -6 * -2 * 8) > (-17 + 15))) and ((((氧气对人类生存是必需的。) and ((5 * 20) <= (1 % 6))) or ((1972年奥运会在慕尼黑举办。) and ((8 * 7 + -1 * -4) >= (5 * 10)))) or (((三文鱼是鱼类。) or (酒精在常温下是固体。)) or ((-7 * -10 + -8 * 2) != (9 - -20))))\n... | 15,087,840 | 615,087,840 | {
"closing_sequence": null,
"depth": 4,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"((not (((-1 - -3) < (2 ** 3)) and ((11 + -2) >= (5 + 14)))) and ((-5 * -6 * -2 * 8) > (-17 + 15))) and ((((氧气对人类生存是必需的。) and ((5 ... | boolean_expressions | {
"completion_tokens": 1173,
"completion_tokens_details": null,
"prompt_tokens": 497,
"prompt_tokens_details": null,
"total_tokens": 1670
} |
[
{
"content": "已知：QBN + PQQ = QENP，每个字母代表一个数字（QBN 是 3 位数、PQQ 是 3 位数、QENP 是 4 位数），字母与字母之间代表的数字不重复。若要让等式成立，求得题中的数字等式。 请在回答的最后一行使用以下格式：答案是 $YOUR_ANSWER。$YOUR_ANSWER 应该是替换为数字后的等式。",
"reasoning_content": null,
"role": "user"
},
{
"content": "已知等式 QBN + PQQ = QENP，其中每个字母代表不同的数字，且 QBN 和 PQQ 为三位数，QENP 为四... | 99,682,468 | 399,682,468 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": {
"A": null,
"B": 7,
"C": null,
"D": null,
"E": 0,
"F": null,
"G": null,
"H": null,
"I": null,
"J": null,
"K": null,
"L": null,
"M": null,
"N": 8,
"O": null,
"P": 9,
"Q... | cryptarithm | {
"completion_tokens": 4541,
"completion_tokens_details": null,
"prompt_tokens": 114,
"prompt_tokens_details": null,
"total_tokens": 4655
} |
[
{
"content": "Q: What opening brackets should precede \"}[]{}⟩[]>⟩⟩}}}⟨⟩\" to form a valid bracket sequence?\n\nRequirements:\n- Use exactly the brackets needed (no more, no less)\n- Maintain proper nesting order\n\nPlease provide your final answer (the entire resulting sequence) in backticks like `answer`.",
... | 65,322,263 | 465,322,263 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 8,
"full_sequence": "{{{⟨⟨<⟨{}[]{}⟩[]>⟩⟩}}}⟨⟩",
"generation_error": null,
"generation_failed": null,
"generati... | dyck_language2 | {
"completion_tokens": 679,
"completion_tokens_details": null,
"prompt_tokens": 75,
"prompt_tokens_details": null,
"total_tokens": 754
} |
[
{
"content": "定义 ○，规则如下：\n实数域上，x ○ y = y + x + y - 1。\n和 ⊗，规则如下：\n实数域上，x ⊗ y = x + y * x - x ○ x。\n和 ♡，规则如下：\n当x是3的倍数时，x ♡ y = x ⊗ x - y - x；\n其他情况下，x ♡ y = y + x ⊗ x * y。\n运算优先级：○ > ** = ⊗ = ♡ > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 4 ⊗ 3 ♡ 10 ○ 5\n请将最终答案填入\\boxed{}中。",
"reasoning_co... | 64,902,032 | 264,902,032 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "4 ⊗ 3 ♡ 10 ○ 5",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_trac... | operation | {
"completion_tokens": 797,
"completion_tokens_details": null,
"prompt_tokens": 183,
"prompt_tokens_details": null,
"total_tokens": 980
} |
[
{
"content": "Define ⊗, the rules are as follows:\non the real number field, x ⊗ y = (x * 5 + y) - x.\nand ○, the rules are as follows:\non the real number field, x ○ y = abs(x + y - x / x).\nand △, the rules are as follows:\non the real number field, x △ y = x ○ x + x + y.\nThe precedence of operations: ... | 22,487,753 | 222,487,753 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "8 ○ 1 △ 2 ⊗ 4",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_trace... | operation | {
"completion_tokens": 575,
"completion_tokens_details": null,
"prompt_tokens": 175,
"prompt_tokens_details": null,
"total_tokens": 750
} |
[
{
"content": "As a Dyck language expert, you need to verify the correctness of bracket matching reasoning steps.\n\nA Dyck sequence must have all brackets properly matched and nested. The reasoning process tracks a stack: opening brackets are pushed, and closing brackets pop the matching opening bracket.\n\nSeq... | 90,455,670 | 890,455,670 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "()()[[]]()[[([[]()]()())]]()",
"error_indices": [
7,
28,
29,
30
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
... | dyck_language_reasoning_errors | {
"completion_tokens": 428,
"completion_tokens_details": null,
"prompt_tokens": 457,
"prompt_tokens_details": null,
"total_tokens": 885
} |
[
{
"content": "请评估以下布尔表达式，选择其中为真的选项：\n\nA. 地球绕太阳运转。\nB. not not (not (not not (((4 * 4 - -7 * -2) >= (4 ** 1)) or ((-5 * 0 * -2 * -2) != (-7 - 11)))))\nC. not not ((((not not (((-8 * 5) <= (0 - 0)) or ((1 - -3) < (3 ** 3) < (6 * -6 - 9 * 0)))) or ((-17 * -1) != (35 % 9))) or ((not (not not (澳大利亚位于大洋洲。))) or ((-1... | 15,139,457 | 615,139,457 | {
"closing_sequence": null,
"depth": 6,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"地球绕太阳运转。",
"True"
],
[
"not not (not (not not (((4 * 4 - -7 * -2) >= (4 ** 1)) or ((-5 * 0 * -2 * -2) != (-7 ... | boolean_expressions | {
"completion_tokens": 1162,
"completion_tokens_details": null,
"prompt_tokens": 529,
"prompt_tokens_details": null,
"total_tokens": 1691
} |
[
{
"content": "使用数字 [4, 5, 6, 8]，运算符 ['+', '-', '*']，计算结果 24。\n\n在回答的最后，请输出一个 ```python 代码块。代码块中仅包含一个代表答案的表达式，并且该表达式可以直接被 Python 中的 eval() 函数求值。如果无解，请输出 ```python\\nNone\\n```。",
"reasoning_content": null,
"role": "user"
},
{
"content": "使用数字 [4, 5, 6, 8] 和运算符 ['+', '-', '*']，可以构造表达式 `8 * (4 + 5 ... | 7,219,962 | 107,219,962 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback": null... | game_of_24 | {
"completion_tokens": 5924,
"completion_tokens_details": null,
"prompt_tokens": 92,
"prompt_tokens_details": null,
"total_tokens": 6016
} |
[
{
"content": "定义 ▽，规则如下：\n实数域上，x ▽ y = abs(x * y)。\n运算优先级：▽ > ** > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 10 ▽ 5\n请将最终答案填入\\boxed{}中。",
"reasoning_content": null,
"role": "user"
},
{
"content": "\\[\n10 \\,\\▽\\, 5 \\;=\\; \\big|10 \\times 5\\big| \\;=\\; \\big|50\\big| \\;=\\; 5... | 13,358,981 | 213,358,981 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "10 ▽ 5",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback": ... | operation | {
"completion_tokens": 91,
"completion_tokens_details": null,
"prompt_tokens": 92,
"prompt_tokens_details": null,
"total_tokens": 183
} |
[
{
"content": "Bracket Puzzle: What's missing at the start?\n\nGiven suffix: {}>>]})>}))}>]>]\n\nSolve:\n1. Each closing bracket needs a matching opening bracket\n2. Add the minimal opening brackets to the left\n3. The final sequence must be properly nested\n\nPlease provide your final answer (the full balanced ... | 135,693,853 | 535,693,853 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 14,
"full_sequence": "[<[<{(({<({[<<{}>>]})>}))}>]>]",
"generation_error": null,
"generation_failed": null,
"g... | dyck_language2 | {
"completion_tokens": 909,
"completion_tokens_details": null,
"prompt_tokens": 85,
"prompt_tokens_details": null,
"total_tokens": 994
} |
[
{
"content": "You are an expert in Dyck language, where you must complete bracket sequences (e.g., [], {}, <>). You need to analyze whether the bracket matching steps are correct according to Dyck language rules.\n\nGiven an initial Dyck language sequence and steps for deriving the closing bracket sequence (giv... | 49,222,251 | 849,222,251 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "<{{}[]}><>({}){}",
"error_indices": [
10,
16
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
... | dyck_language_reasoning_errors | {
"completion_tokens": 259,
"completion_tokens_details": null,
"prompt_tokens": 396,
"prompt_tokens_details": null,
"total_tokens": 655
} |
[
{
"content": "已知字母等式：GTF + TG + LTFTL + FGL = LLTGF（其中GTF是3位数、TG是2位数、LTFTL是5位数、FGL是3位数、LLTGF是5位数），每个字母代表一个数字，不同字母代表不同数字。请找出让等式成立的数字替换方案。 请在回答的最后一行使用以下格式：答案是 $YOUR_ANSWER。$YOUR_ANSWER 应该是替换为数字后的等式。",
"reasoning_content": null,
"role": "user"
},
{
"content": "通过分析字母等式 GTF + TG + LTFTL + FGL = LLTG... | 58,886,441 | 358,886,441 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": {
"A": null,
"B": null,
"C": null,
"D": null,
"E": null,
"F": 5,
"G": 2,
"H": null,
"I": null,
"J": null,
"K": null,
"L": 4,
"M": null,
"N": null,
"O": null,
"P": null,
... | cryptarithm | {
"completion_tokens": 6397,
"completion_tokens_details": null,
"prompt_tokens": 124,
"prompt_tokens_details": null,
"total_tokens": 6521
} |
[
{
"content": "Given [8, 11, 12, 13, 13, 14], compute 100 using ['+', '-'].\n\nAt the end of your response, please output a ```python code block. The code block should contain only a single expression representing the answer, which can be directly evaluated using Python's eval() function. If there is no solution... | 6,242,043 | 106,242,043 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback": null... | game_of_24 | {
"completion_tokens": 3011,
"completion_tokens_details": null,
"prompt_tokens": 100,
"prompt_tokens_details": null,
"total_tokens": 3111
} |
[
{
"content": "研究以下逻辑语句：\n\nA. (17 - 10) != (4 ** 3)\nB. ((355是斐波那契数。) and (银在常温下是气体。)) and ((古巴的首都是哈瓦那。) and ((29 % 5) == (-18 * 5)))\nC. ((人类有三个肺。) and ((9 * 3) != (-10 * 8 * 0 * -7))) or (((-20 - -4) < (-8 + 10)) or (氧气在常温下是固体。))\nD. 二氧化碳在常温下是气体。\nE. (not not ((10 + 9) < (8 * 10 * -2 * 6) < (-4 * -6))) and ((... | 75,178,934 | 675,178,934 | {
"closing_sequence": null,
"depth": 2,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"(17 - 10) != (4 ** 3)",
"True"
],
[
"((355是斐波那契数。) and (银在常温下是气体。)) and ((古巴的首都是哈瓦那。) and ((29 % 5) == (-18 *... | boolean_expressions | {
"completion_tokens": 662,
"completion_tokens_details": null,
"prompt_tokens": 269,
"prompt_tokens_details": null,
"total_tokens": 931
} |
[
{
"content": "As a Dyck language expert, you need to verify the correctness of bracket matching reasoning steps.\n\nA Dyck sequence must have all brackets properly matched and nested. The reasoning process tracks a stack: opening brackets are pushed, and closing brackets pop the matching opening bracket.\n\nSeq... | 77,970,979 | 877,970,979 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "<{}>(()[({})]){}",
"error_indices": [
7,
14,
18
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed":... | dyck_language_reasoning_errors | {
"completion_tokens": 280,
"completion_tokens_details": null,
"prompt_tokens": 320,
"prompt_tokens_details": null,
"total_tokens": 600
} |
[
{
"content": "Define ◇, the rules are as follows:\non the real number field, x ◇ y = y + y * y - abs(x + x).\nThe precedence of operations: ◇ > ** > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expr... | 14,758,810 | 214,758,810 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "1 * 9 ◇ 5",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback... | operation | {
"completion_tokens": 325,
"completion_tokens_details": null,
"prompt_tokens": 107,
"prompt_tokens_details": null,
"total_tokens": 432
} |
[
{
"content": "Numbers [1, 4, 6, 6, 8], target value 36, operators ['+', '-', '*', '/'].\n\nAt the end of your response, please output a ```python code block. The code block should contain only a single expression representing the answer, which can be directly evaluated using Python's eval() function. If there i... | 28,627,894 | 128,627,894 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback": null... | game_of_24 | {
"completion_tokens": 5189,
"completion_tokens_details": null,
"prompt_tokens": 95,
"prompt_tokens_details": null,
"total_tokens": 5284
} |
[
{
"content": "Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.\n\nSuffix: ⦄}⟧⦄{}()>))⦄>}⟩⦄\n\nRules:\n- Add only the opening brackets needed to match all unmatched closing brackets\n- The opening brackets should be prepended to form a valid sequenc... | 108,096,570 | 508,096,570 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 12,
"full_sequence": "⦃⟨{<⦃((<⦃⟦{⦃⦄}⟧⦄{}()>))⦄>}⟩⦄",
"generation_error": null,
"generation_failed": null,
"gen... | dyck_language2 | {
"completion_tokens": 951,
"completion_tokens_details": null,
"prompt_tokens": 108,
"prompt_tokens_details": null,
"total_tokens": 1059
} |
[
{
"content": "Q: What opening brackets should precede \"]))><>)>{}()}<>[]⟨⟩⟨⟩{}\" to form a valid bracket sequence?\n\nRequirements:\n- Use exactly the brackets needed (no more, no less)\n- Maintain proper nesting order\n\nPlease provide your final answer (the entire resulting sequence) in backticks like `answe... | 113,789,078 | 513,789,078 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 7,
"full_sequence": "{<(<(([]))><>)>{}()}<>[]⟨⟩⟨⟩{}",
"generation_error": null,
"generation_failed": null,
"ge... | dyck_language2 | {
"completion_tokens": 708,
"completion_tokens_details": null,
"prompt_tokens": 79,
"prompt_tokens_details": null,
"total_tokens": 787
} |
[
{
"content": "数字：[3, 5, 5, 7, 8]，运算符：['+', '-', '*', '/']，目标：48。\n\n在回答的最后，请输出一个 ```python 代码块。代码块中仅包含一个代表答案的表达式，并且该表达式可以直接被 Python 中的 eval() 函数求值。如果无解，请输出 ```python\\nNone\\n```。",
"reasoning_content": null,
"role": "user"
},
{
"content": "```python\n8*(5+5+3-7)\n```",
"reasoning_content": ... | 12,279,807 | 112,279,807 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback": null... | game_of_24 | {
"completion_tokens": 1130,
"completion_tokens_details": null,
"prompt_tokens": 96,
"prompt_tokens_details": null,
"total_tokens": 1226
} |
[
{
"content": "Fill in the blank:\n\n_____ + ⟨⟩⦄>]⟩⟦⟧⦄}⟩[][] = valid Dyck sequence\n\nRules:\n- The blank contains only opening brackets\n- Use the minimum required\n\nPlease provide your final answer (the complete filled sequence) in backticks like `answer`.",
"reasoning_content": null,
"role": "user"
... | 178,792,603 | 578,792,603 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 7,
"full_sequence": "⟨{⦃⟨[<⦃⟨⟩⦄>]⟩⟦⟧⦄}⟩[][]",
"generation_error": null,
"generation_failed": null,
"generation... | dyck_language2 | {
"completion_tokens": 666,
"completion_tokens_details": null,
"prompt_tokens": 70,
"prompt_tokens_details": null,
"total_tokens": 736
} |
[
{
"content": "定义 ▽，规则如下：\n当x大于y时，x ▽ y = y * x / x * x；\n其他情况下，x ▽ y = y / abs(x)。\n运算优先级：▽ > ** > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 8 ▽ 7 % 5 % 2\n请将最终答案填入\\boxed{}中。",
"reasoning_content": null,
"role": "user"
},
{
"content": "先计算 **▽** 运算：\n\n- 判断 \\(8 > 7\\) 为真，故 \n ... | 89,314,029 | 289,314,029 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "8 ▽ 7 % 5 % 2",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_trace... | operation | {
"completion_tokens": 263,
"completion_tokens_details": null,
"prompt_tokens": 115,
"prompt_tokens_details": null,
"total_tokens": 378
} |
[
{
"content": "给定数字 [4, 4, 9, 10, 11]，用 ['+', '-', '*', '/'] 得到 36。\n\n在回答的最后，请输出一个 ```python 代码块。代码块中仅包含一个代表答案的表达式，并且该表达式可以直接被 Python 中的 eval() 函数求值。如果无解，请输出 ```python\\nNone\\n```。",
"reasoning_content": null,
"role": "user"
},
{
"content": "通过使用数字 [4, 4, 9, 10, 11] 和运算符 ['+', '-', '*', '/']，可以... | 65,256,251 | 165,256,251 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback": null... | game_of_24 | {
"completion_tokens": 4686,
"completion_tokens_details": null,
"prompt_tokens": 98,
"prompt_tokens_details": null,
"total_tokens": 4784
} |
[
{
"content": "As a Dyck language expert, you need to verify the correctness of bracket matching reasoning steps.\n\nA Dyck sequence must have all brackets properly matched and nested. The reasoning process tracks a stack: opening brackets are pushed, and closing brackets pop the matching opening bracket.\n\nSeq... | 91,760,442 | 891,760,442 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "()()[()[[]]()[]()[]]",
"error_indices": [
16,
18,
19,
20,
22
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
... | dyck_language_reasoning_errors | {
"completion_tokens": 367,
"completion_tokens_details": null,
"prompt_tokens": 363,
"prompt_tokens_details": null,
"total_tokens": 730
} |
[
{
"content": "Complete the following Dyck language sequence by adding the minimal necessary closing brackets.\n\nSequence: ⟨[[]]⟩[⟨⟨⟩⟩()⟦⟧⟦⟨⦅\n\nRules:\n- Add only the closing brackets needed to match all unmatched opening brackets\n- Do not add any extra bracket pairs beyond what is required\n\nProvide only th... | 27,070,696 | 27,070,696 | {
"closing_sequence": "⦆⟩⟧]",
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 4,
"full_sequence": "⟨[[]]⟩[⟨⟨⟩⟩()⟦⟧⟦⟨⦅⦆⟩⟧]",
"generation_error": null,
"generation_failed": null,
"generati... | dyck_language | {
"completion_tokens": 530,
"completion_tokens_details": null,
"prompt_tokens": 81,
"prompt_tokens_details": null,
"total_tokens": 611
} |
[
{
"content": "分析以下逻辑表达式：\n\nA. (not not ((((委内瑞拉的首都是华沙。) and ((-9 * -7) != (-9 * 5))) or ((0 + 7) < (6 * 11) < (2 * 1))) or (1917年是闰年。))) and (((((18 + -17) >= (9 % 2)) and (海王星是距离太阳第8近的行星。)) and (not not (墨西哥位于北美洲。))) or (not (((1 * -3 + 9 * -6) > (35 % 3)) and (二氧化碳在常温下是气体。)))) and (not not (not not ((12 * 4)... | 61,495,483 | 661,495,483 | {
"closing_sequence": null,
"depth": 5,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"(not not ((((委内瑞拉的首都是华沙。) and ((-9 * -7) != (-9 * 5))) or ((0 + 7) < (6 * 11) < (2 * 1))) or (1917年是闰年。))) and (((((18 + -17) >= ... | boolean_expressions | {
"completion_tokens": 1973,
"completion_tokens_details": null,
"prompt_tokens": 850,
"prompt_tokens_details": null,
"total_tokens": 2823
} |
[
{
"content": "Bracket Puzzle: What's missing at the start?\n\nGiven suffix: )]}{}[]>>]]]\n\nSolve:\n1. Each closing bracket needs a matching opening bracket\n2. Add the minimal opening brackets to the left\n3. The final sequence must be properly nested\n\nPlease provide your final answer (the full balanced sequ... | 116,356,217 | 516,356,217 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 8,
"full_sequence": "[[[<<{[()]}{}[]>>]]]",
"generation_error": null,
"generation_failed": null,
"generation_t... | dyck_language2 | {
"completion_tokens": 576,
"completion_tokens_details": null,
"prompt_tokens": 83,
"prompt_tokens_details": null,
"total_tokens": 659
} |
[
{
"content": "Numbers [4, 5, 5, 9, 9], target value 36, operators ['+', '-', '*', '/'].\n\nAt the end of your response, please output a ```python code block. The code block should contain only a single expression representing the answer, which can be directly evaluated using Python's eval() function. If there i... | 57,764,094 | 157,764,094 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback": null... | game_of_24 | {
"completion_tokens": 6700,
"completion_tokens_details": null,
"prompt_tokens": 95,
"prompt_tokens_details": null,
"total_tokens": 6795
} |
[
{
"content": "You are given the ending portion of a bracket sequence. Find the beginning.\n\nEnding: ⟩⟧<>⦄[]⟦⟧()}}}>))])⦃⦄<>⟦⟧⦃⦄⟨⟩⦃⦄<>[]<><>\n\nYour task:\n- Determine what opening brackets must come before this ending\n- The result must be a valid, balanced bracket sequence\n- Use the minimum number of opening... | 165,224,202 | 565,224,202 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 11,
"full_sequence": "([((<{{{⦃⟦⟨⟩⟧<>⦄[]⟦⟧()}}}>))])⦃⦄<>⟦⟧⦃⦄⟨⟩⦃⦄<>[]<><>",
"generation_error": null,
"generation... | dyck_language2 | {
"completion_tokens": 1211,
"completion_tokens_details": null,
"prompt_tokens": 116,
"prompt_tokens_details": null,
"total_tokens": 1327
} |
[
{
"content": "定义 ♡，规则如下：\n实数域上，x ♡ y = y - abs(x * y - 5) / 4。\n和 △，规则如下：\n实数域上，x △ y = y / x * x * y ♡ 4。\n运算优先级：♡ > ** > * = / = % = △ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 2 △ 5 % 5 ♡ 10\n请将最终答案填入\\boxed{}中。",
"reasoning_content": null,
"role": "user"
},
{
"content": "\\[\n\\boxed{0}... | 80,237,117 | 280,237,117 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "2 △ 5 % 5 ♡ 10",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_trac... | operation | {
"completion_tokens": 745,
"completion_tokens_details": null,
"prompt_tokens": 140,
"prompt_tokens_details": null,
"total_tokens": 885
} |
[
{
"content": "评估以下每个表达式：\n\nA. ((not not ((铁的化学符号是Au。) and (((-9 * 3 - 5 * -8) > (20 - -8)) and ((35 % 1) > (-2 * 4))))) and ((2 ** 1) <= (12 * -6)) and (((-18 - 3) < (-9 - -19) < (17 % 1)) or (not (not not ((1 ** 2) <= (20 * -14)))))) and (((南非位于非洲。) and ((not (南极洲是最冷的大陆。)) or (蚂蚁有8条腿。))) or (((15 - -18) >= (2... | 3,887,012 | 603,887,012 | {
"closing_sequence": null,
"depth": 5,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"((not not ((铁的化学符号是Au。) and (((-9 * 3 - 5 * -8) > (20 - -8)) and ((35 % 1) > (-2 * 4))))) and ((2 ** 1) <= (12 * -6)) and (((-18 ... | boolean_expressions | {
"completion_tokens": 2013,
"completion_tokens_details": null,
"prompt_tokens": 848,
"prompt_tokens_details": null,
"total_tokens": 2861
} |
[
{
"content": "计算：[6, 9, 12, 13] → 48，运算符：['+', '-', '*', '/']。\n\n在回答的最后，请输出一个 ```python 代码块。代码块中仅包含一个代表答案的表达式，并且该表达式可以直接被 Python 中的 eval() 函数求值。如果无解，请输出 ```python\\nNone\\n```。",
"reasoning_content": null,
"role": "user"
},
{
"content": "要使用数字 [6, 9, 12, 13] 和运算符 ['+', '-', '*', '/'] 计算得到 48，一个... | 6,249,752 | 106,249,752 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback": null... | game_of_24 | {
"completion_tokens": 5097,
"completion_tokens_details": null,
"prompt_tokens": 94,
"prompt_tokens_details": null,
"total_tokens": 5191
} |
[
{
"content": "As a Dyck language expert, you need to verify the correctness of bracket matching reasoning steps.\n\nA Dyck sequence must have all brackets properly matched and nested. The reasoning process tracks a stack: opening brackets are pushed, and closing brackets pop the matching opening bracket.\n\nSeq... | 19,367,551 | 819,367,551 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "[](<[][[][]({{<>}[]})]()>)<>",
"error_indices": [
3,
12,
24
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generat... | dyck_language_reasoning_errors | {
"completion_tokens": 433,
"completion_tokens_details": null,
"prompt_tokens": 478,
"prompt_tokens_details": null,
"total_tokens": 911
} |
[
{
"content": "Bracket Puzzle: What's missing at the start?\n\nGiven suffix: >>]⦆}}{}>⦅⦆⟧()[]⦃⦄\n\nSolve:\n1. Each closing bracket needs a matching opening bracket\n2. Add the minimal opening brackets to the left\n3. The final sequence must be properly nested\n\nPlease provide your final answer (the full balance... | 12,603,082 | 412,603,082 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 8,
"full_sequence": "⟦<{{⦅[<<>>]⦆}}{}>⦅⦆⟧()[]⦃⦄",
"generation_error": null,
"generation_failed": null,
"genera... | dyck_language2 | {
"completion_tokens": 738,
"completion_tokens_details": null,
"prompt_tokens": 95,
"prompt_tokens_details": null,
"total_tokens": 833
} |
[
{
"content": "有一个等式：KG + WG = SS，其中每个字母代表一个不同的数字（KG 是 2 位数、WG 是 2 位数、SS 是 2 位数）。请找出每个字母代表的数字，使等式成立。 请在回答的最后一行使用以下格式：答案是 $YOUR_ANSWER。$YOUR_ANSWER 应该是替换为数字后的等式。",
"reasoning_content": null,
"role": "user"
},
{
"content": "根据等式 KG + WG = SS，其中每个字母代表不同的数字，且 KG、WG、SS 均为两位数。通过分析，得到多个可能的解。其中一个简单的解是：K=... | 12,833,900 | 312,833,900 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": {
"A": null,
"B": null,
"C": null,
"D": null,
"E": null,
"F": null,
"G": 3,
"H": null,
"I": null,
"J": null,
"K": 1,
"L": null,
"M": null,
"N": null,
"O": null,
"P": null,
... | cryptarithm | {
"completion_tokens": 6715,
"completion_tokens_details": null,
"prompt_tokens": 97,
"prompt_tokens_details": null,
"total_tokens": 6812
} |
[
{
"content": "Below are several boolean expressions:\n\nA. (not not ((((The human body has 206 bones.) and ((5 - -10) < (9 * 1 * 5 * 6))) and (((7 * 8 - 4 * 3) != (3 * 6 + 1 * 5)) and ((The 1988 Olympics were held in Seoul.) or (New Zealand is in North America.)))) or (not ((10 - -9) <= (10 + 8))) or (not not (... | 20,175,045 | 620,175,045 | {
"closing_sequence": null,
"depth": 6,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"(not not ((((The human body has 206 bones.) and ((5 - -10) < (9 * 1 * 5 * 6))) and (((7 * 8 - 4 * 3) != (3 * 6 + 1 * 5)) and ((Th... | boolean_expressions | {
"completion_tokens": 2021,
"completion_tokens_details": null,
"prompt_tokens": 882,
"prompt_tokens_details": null,
"total_tokens": 2903
} |
[
{
"content": "Q: What opening brackets should precede \"}{}]())])())]]}}]])\" to form a valid bracket sequence?\n\nRequirements:\n- Use exactly the brackets needed (no more, no less)\n- Maintain proper nesting order\n\nPlease provide your final answer (the entire resulting sequence) in backticks like `answer`."... | 23,277,370 | 423,277,370 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 13,
"full_sequence": "([[{{[[(([([{}{}]())])())]]}}]])",
"generation_error": null,
"generation_failed": null,
... | dyck_language2 | {
"completion_tokens": 886,
"completion_tokens_details": null,
"prompt_tokens": 73,
"prompt_tokens_details": null,
"total_tokens": 959
} |
[
{
"content": "Numbers [7, 8, 10, 13], target value 72, operators ['+', '-'].\n\nAt the end of your response, please output a ```python code block. The code block should contain only a single expression representing the answer, which can be directly evaluated using Python's eval() function. If there is no soluti... | 15,606,344 | 115,606,344 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_traceback": null... | game_of_24 | {
"completion_tokens": 3140,
"completion_tokens_details": null,
"prompt_tokens": 92,
"prompt_tokens_details": null,
"total_tokens": 3232
} |
[
{
"content": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not not (((((The capital of Kenya is Copenhagen.) and ((9 * -7) < (6 * 6 * 10 * -8))) and ((The 1952 Olympics were held in Helsinki.) or ((A day on Earth is 24 hours.) or ((1 ** 1) <= (-2 + -19))))) or ((not (((2 *... | 59,394,889 | 659,394,889 | {
"closing_sequence": null,
"depth": 6,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"not not (((((The capital of Kenya is Copenhagen.) and ((9 * -7) < (6 * 6 * 10 * -8))) and ((The 1952 Olympics were held in Helsin... | boolean_expressions | {
"completion_tokens": 2025,
"completion_tokens_details": null,
"prompt_tokens": 899,
"prompt_tokens_details": null,
"total_tokens": 2924
} |
[
{
"content": "定义 ⊕，规则如下：\n实数域上，x ⊕ y = 1 + y * 1 - x + x。\n和 □，规则如下：\n实数域上，x □ y = x * x ⊕ x / y - x。\n和 ⊙，规则如下：\n实数域上，x ⊙ y = x + 1 ** y + y - y。\n运算优先级：** > * = / = % = □ = ⊙ > + = - = ⊕。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 3 ⊙ 4 □ 1 ⊕ 10\n请将最终答案填入\\boxed{}中。",
"reasoning_content": null,
"role": "... | 79,101,303 | 279,101,303 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "3 ⊙ 4 □ 1 ⊕ 10",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"generation_error": null,
"generation_failed": null,
"generation_trac... | operation | {
"completion_tokens": 1210,
"completion_tokens_details": null,
"prompt_tokens": 171,
"prompt_tokens_details": null,
"total_tokens": 1381
} |
[
{
"content": "Q: What opening brackets should precede \"⟩>{}<>⟩][]>⟩⟩}}}\" to form a valid bracket sequence?\n\nRequirements:\n- Use exactly the brackets needed (no more, no less)\n- Maintain proper nesting order\n\nPlease provide your final answer (the entire resulting sequence) in backticks like `answer`.",
... | 37,227,284 | 437,227,284 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 10,
"full_sequence": "{{{⟨⟨<[⟨<⟨⟩>{}<>⟩][]>⟩⟩}}}",
"generation_error": null,
"generation_failed": null,
"gener... | dyck_language2 | {
"completion_tokens": 764,
"completion_tokens_details": null,
"prompt_tokens": 76,
"prompt_tokens_details": null,
"total_tokens": 840
} |
[
{
"content": "给定以下布尔表达式：\n\nA. ((not not ((28 % 7) <= (-15 + 10))) and (2大于15。)) and ((36 % 2) >= (-2 + 11)) and (((((-8 * 8 - -8 * -3) < (2 * 17)) and ((9 * 4 + 2 * -2) != (-14 + -17))) or (印度尼西亚的货币是印尼盾。)) and ((not not ((46 % 1) <= (1 ** 2) <= (18 * 1))) and (not (空气在常温下是液体。))))\nB. ((not not (1920年奥运会在安特卫普举办... | 32,549,940 | 632,549,940 | {
"closing_sequence": null,
"depth": 4,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"((not not ((28 % 7) <= (-15 + 10))) and (2大于15。)) and ((36 % 2) >= (-2 + 11)) and (((((-8 * 8 - -8 * -3) < (2 * 17)) and ((9 * 4 ... | boolean_expressions | {
"completion_tokens": 1018,
"completion_tokens_details": null,
"prompt_tokens": 435,
"prompt_tokens_details": null,
"total_tokens": 1453
} |
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