data_source stringclasses 1 value | prompt listlengths 1 1 | ability stringclasses 1 value | reward_model dict | member bool 1 class | extra_info dict |
|---|---|---|---|---|---|
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!CD & !A!D!E & !ABD & !B!C!D & !B!CE & !BDE & !C!D!E & A!BE & A!C!E & ABE & AC!D & BDE & CD!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!CD & !A!D!E & !ABD & !B!C!D & !B!CE & !BDE & !C!D!E & A!BE & A!C!E & ABE & AC!D & BDE & CD!E",
"ground_truth": 10010,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 473
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!C & !A!B!D & !ABC & !ACD & !BCE & !BDE & !C!DE & ACE & B!DE & BCE & BDE & C!DE & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!C & !A!B!D & !ABC & !ACD & !BCE & !BDE & !C!DE & ACE & B!DE & BCE & BDE & C!DE & CDE",
"ground_truth": 1111,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 132
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!E & !A!BC & !A!DE & !ABE & !ACD & !B!CE & !BC!D & A!C!D & AB!D & AC!E & BC!D & BCD & C!DE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!E & !A!BC & !A!DE & !ABE & !ACD & !B!CE & !BC!D & A!C!D & AB!D & AC!E & BC!D & BCD & C!DE",
"ground_truth": 1000,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 472
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!CD & !AD!E & !ADE & !BC!E & !BCE & !BDE & A!BC & A!BD & AC!D & B!C!D & B!D!E & BDE & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!CD & !AD!E & !ADE & !BC!E & !BCE & !BDE & A!BC & A!BD & AC!D & B!C!D & B!D!E & BDE & CDE",
"ground_truth": 10010,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 46
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!C & !A!BD & !A!DE & !AB!C & !ABE & !AC!D & !ACE & !B!D!E & !BC!E & !CD!E & A!B!C & A!B!D & BC!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!C & !A!BD & !A!DE & !AB!C & !ABE & !AC!D & !ACE & !B!D!E & !BC!E & !CD!E & A!B!C & A!B!D & BC!E",
"ground_truth": 0,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 40
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!E & !A!C!E & !ABD & !AD!E & !CDE & A!D!E & ABE & AC!E & ACE & ADE & B!C!E & B!CD & BDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!E & !A!C!E & !ABD & !AD!E & !CDE & A!D!E & ABE & AC!E & ACE & ADE & B!C!E & B!CD & BDE",
"ground_truth": 11010,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 232
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!E & !A!C!D & !AB!D & !ABE & !AC!D & !ACD & !BCE & !BDE & A!BE & A!CD & A!DE & B!CD & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!E & !A!C!D & !AB!D & !ABE & !AC!D & !ACD & !BCE & !BDE & A!BE & A!CD & A!DE & B!CD & CDE",
"ground_truth": 1111,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 45
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!D & !A!C!D & !A!D!E & !BD!E & !BDE & !C!DE & A!BC & AB!D & AB!E & ABD & ABE & B!C!D & B!DE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!D & !A!C!D & !A!D!E & !BD!E & !BDE & !C!DE & A!BC & AB!D & AB!E & ABD & ABE & B!C!D & B!DE",
"ground_truth": 10000,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 428
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!C & !A!B!D & !A!BC & !A!BD & !A!CE & !AC!E & !BCD & A!B!D & AB!E & AC!E & ADE & B!DE & C!DE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!C & !A!B!D & !A!BC & !A!BD & !A!CE & !AC!E & !BCD & A!B!D & AB!E & AC!E & ADE & B!DE & C!DE",
"ground_truth": 1101,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 326
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!D & !A!C!E & !A!CE & !AC!D & !B!C!D & !B!CD & !BDE & !CDE & ABC & B!C!D & BC!E & BCD & CD!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!D & !A!C!E & !A!CE & !AC!D & !B!C!D & !B!CD & !BDE & !CDE & ABC & B!C!D & BC!E & BCD & CD!E",
"ground_truth": 1010,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 159
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!D & !A!BC & !B!C!D & !BC!E & !CD!E & !CDE & A!B!E & A!C!D & ABD & ACE & AD!E & B!CE & B!DE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!D & !A!BC & !B!C!D & !BC!E & !CD!E & !CDE & A!B!E & A!C!D & ABD & ACE & AD!E & B!CE & B!DE",
"ground_truth": 11,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 291
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!C & !A!B!E & !A!BC & !A!BD & !A!C!E & !AB!C & !BC!D & !C!D!E & !C!DE & A!B!D & A!CE & B!C!E & BC!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!C & !A!B!E & !A!BC & !A!BD & !A!C!E & !AB!C & !BC!D & !C!D!E & !C!DE & A!B!D & A!CE & B!C!E & BC!E",
"ground_truth": 1101,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 235
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!BE & !A!C!D & !A!CD & !A!CE & !AB!E & !B!CD & !BD!E & A!C!D & ABC & AC!E & B!C!E & B!CE & BC!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!BE & !A!C!D & !A!CD & !A!CE & !AB!E & !B!CD & !BD!E & A!C!D & ABC & AC!E & B!C!E & B!CE & BC!E",
"ground_truth": 10010,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 453
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!E & !ACD & !ACE & !B!C!D & !B!C!E & !B!CE & !B!DE & !BCD & !CDE & AC!E & BCE & BDE & CD!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!E & !ACD & !ACE & !B!C!D & !B!C!E & !B!CE & !B!DE & !BCD & !CDE & AC!E & BCE & BDE & CD!E",
"ground_truth": 10011,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 107
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!BC & !A!CD & !AB!D & !ABC & !ABE & !ACD & !B!C!E & !B!DE & !C!D!E & A!BD & ABC & B!C!D & B!CE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!BC & !A!CD & !AB!D & !ABC & !ABE & !ACD & !B!C!E & !B!DE & !C!D!E & A!BD & ABC & B!C!D & B!CE",
"ground_truth": 1011,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 367
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!D!E & !AB!E & !ABC & !ACE & !B!D!E & !BCD & !BD!E & !C!D!E & !CD!E & A!BC & A!D!E & AB!E & B!CE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!D!E & !AB!E & !ABC & !ACE & !B!D!E & !BCD & !BD!E & !C!D!E & !CD!E & A!BC & A!D!E & AB!E & B!CE",
"ground_truth": 1110,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 115
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!C!E & !A!CE & !ABC & !ABD & !B!CD & !B!CE & !B!D!E & !C!DE & AB!E & B!C!D & B!CD & B!D!E & BC!D\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!C!E & !A!CE & !ABC & !ABD & !B!CD & !B!CE & !B!D!E & !C!DE & AB!E & B!C!D & B!CD & B!D!E & BC!D",
"ground_truth": 0,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 280
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!BC & !AD!E & !ADE & !B!CD & A!B!D & A!BE & AB!D & ABE & AC!D & ACD & AD!E & C!D!E & C!DE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!BC & !AD!E & !ADE & !B!CD & A!B!D & A!BE & AB!D & ABE & AC!D & ACD & AD!E & C!D!E & C!DE",
"ground_truth": 11111,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 357
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!BE & !A!C!D & !A!CD & !AB!D & !ACD & !ACE & !CDE & A!BE & A!C!D & A!C!E & BDE & CD!E & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!BE & !A!C!D & !A!CD & !AB!D & !ACD & !ACE & !CDE & A!BE & A!C!D & A!C!E & BDE & CD!E & CDE",
"ground_truth": 11,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 185
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!D & !A!DE & !AB!C & !ABD & !ABE & !ADE & !BCE & A!D!E & AB!D & AB!E & BC!E & C!D!E & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!D & !A!DE & !AB!C & !ABD & !ABE & !ADE & !BCE & A!D!E & AB!D & AB!E & BC!E & C!D!E & CDE",
"ground_truth": 1100,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 327
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!C & !A!B!E & !A!D!E & !A!DE & !B!C!D & !B!CE & !BCE & !BD!E & A!BE & A!C!D & A!DE & AB!E & C!D!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!C & !A!B!E & !A!D!E & !A!DE & !B!C!D & !B!CE & !BCE & !BD!E & A!BE & A!C!D & A!DE & AB!E & C!D!E",
"ground_truth": 100,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 53
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!CD & !AB!C & !AB!D & !ABC & !AC!E & !ADE & !B!CE & !B!DE & !BCE & !BDE & !CDE & ADE & BCE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!CD & !AB!C & !AB!D & !ABC & !AC!E & !ADE & !B!CE & !B!DE & !BCE & !BDE & !CDE & ADE & BCE",
"ground_truth": 110,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 217
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!D!E & !BC!E & !C!D!E & !CDE & A!B!D & A!BC & A!C!E & ABE & ACE & ADE & B!CE & B!DE & BC!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!D!E & !BC!E & !C!D!E & !CDE & A!B!D & A!BC & A!C!E & ABE & ACE & ADE & B!CE & B!DE & BC!E",
"ground_truth": 10101,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 486
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!C & !A!C!E & !A!CE & !AB!C & !B!CE & !C!D!E & !CDE & ACD & ACE & B!C!E & B!CE & B!DE & BDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!C & !A!C!E & !A!CE & !AB!C & !B!CE & !C!D!E & !CDE & ACD & ACE & B!C!E & B!CE & B!DE & BDE",
"ground_truth": 1101,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 51
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!D & !A!BD & !A!CD & !B!D!E & !BCD & !C!D!E & A!B!E & A!C!E & AD!E & BC!E & BD!E & C!D!E & CD!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!D & !A!BD & !A!CD & !B!D!E & !BCD & !C!D!E & A!B!E & A!C!E & AD!E & BC!E & BD!E & C!D!E & CD!E",
"ground_truth": 1100,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 340
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!BC & !A!BD & !A!C!D & !A!C!E & !AB!D & !AB!E & !B!D!E & !B!DE & !BC!E & !BDE & !C!DE & A!B!D & A!BC\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!BC & !A!BD & !A!C!D & !A!C!E & !AB!D & !AB!E & !B!D!E & !B!DE & !BC!E & !BDE & !C!DE & A!B!D & A!BC",
"ground_truth": 11,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 96
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!D & !A!BC & !A!C!D & !A!D!E & !AB!C & !ACE & !BCE & !BDE & A!B!E & A!D!E & AB!D & B!C!D & CD!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!D & !A!BC & !A!C!D & !A!D!E & !AB!C & !ACE & !BCE & !BDE & A!B!E & A!D!E & AB!D & B!C!D & CD!E",
"ground_truth": 0,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 376
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!CE & !AB!C & !ABC & !ACD & !BD!E & !CDE & A!BE & A!C!E & ADE & B!CD & B!D!E & BCE & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!CE & !AB!C & !ABC & !ACD & !BD!E & !CDE & A!BE & A!C!E & ADE & B!CD & B!D!E & BCE & CDE",
"ground_truth": 11010,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 446
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!C!D & !AB!C & !ABC & !AD!E & !B!C!D & !BC!D & A!B!C & A!BD & A!CE & AB!C & ABD & ACE & BC!D\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!C!D & !AB!C & !ABC & !AD!E & !B!C!D & !BC!D & A!B!C & A!BD & A!CE & AB!C & ABD & ACE & BC!D",
"ground_truth": 11100,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 197
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!C!E & !A!DE & !AB!C & !AB!E & !AC!E & !ACE & A!BC & A!BD & ABD & ABE & ACE & BC!E & BD!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!C!E & !A!DE & !AB!C & !AB!E & !AC!E & !ACE & A!BC & A!BD & ABD & ABE & ACE & BC!E & BD!E",
"ground_truth": 111,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 245
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!C!D & !A!CD & !ADE & !BC!E & !BCD & !BDE & !CDE & AD!E & B!C!E & B!CE & B!DE & BD!E & C!D!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!C!D & !A!CD & !ADE & !BC!E & !BCD & !BDE & !CDE & AD!E & B!C!E & B!CE & B!DE & BD!E & C!D!E",
"ground_truth": 1010,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 225
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!BE & !AB!E & !ABE & !B!C!D & !B!D!E & !BDE & A!CD & ABE & ACD & BCD & BD!E & BDE & CD!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!BE & !AB!E & !ABE & !B!C!D & !B!D!E & !BDE & A!CD & ABE & ACD & BCD & BD!E & BDE & CD!E",
"ground_truth": 11101,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 0
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!C!D & !AB!D & !BCD & !BCE & !C!D!E & A!CE & AB!C & ABC & ABD & B!D!E & BCE & C!D!E & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!C!D & !AB!D & !BCD & !BCE & !C!D!E & A!CE & AB!C & ABC & ABD & B!D!E & BCE & C!D!E & CDE",
"ground_truth": 11101,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 249
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!E & !A!CE & !AB!E & !AC!D & !AC!E & !ACE & !BC!D & A!B!D & ACD & AD!E & B!C!D & B!C!E & BDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!E & !A!CE & !AB!E & !AC!D & !AC!E & !ACE & !BC!D & A!B!D & ACD & AD!E & B!C!D & B!C!E & BDE",
"ground_truth": 1100,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 390
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!AB!C & !AD!E & !BC!D & !BCE & A!B!E & A!CD & ABD & ABE & AC!D & B!C!D & B!CD & BCE & C!DE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!AB!C & !AD!E & !BC!D & !BCE & A!B!E & A!CD & ABD & ABE & AC!D & B!C!D & B!CD & BCE & C!DE",
"ground_truth": 10011,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 191
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!E & !ABE & !ACE & !C!D!E & A!B!E & A!CD & A!CE & AB!C & AB!E & ABD & B!CE & B!D!E & BD!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!E & !ABE & !ACE & !C!D!E & A!B!E & A!CD & A!CE & AB!C & AB!E & ABD & B!CE & B!D!E & BD!E",
"ground_truth": 1000,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 464
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!C & !A!BC & !A!BE & !A!C!D & !A!C!E & !A!CE & !BCD & !CDE & A!C!E & A!CD & ABD & ACE & B!CE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!C & !A!BC & !A!BE & !A!C!D & !A!C!E & !A!CE & !BCD & !CDE & A!C!E & A!CD & ABD & ACE & B!CE",
"ground_truth": 10010,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 80
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!BC & !A!C!D & !A!CE & !ABD & !AD!E & !B!CE & !BC!D & !CD!E & A!BE & A!DE & BC!D & BCD & C!DE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!BC & !A!C!D & !A!CE & !ABD & !AD!E & !B!CE & !BC!D & !CD!E & A!BE & A!DE & BC!D & BCD & C!DE",
"ground_truth": 1001,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 239
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!C & !A!B!D & !A!D!E & !ACD & !BC!E & !BDE & A!C!E & ABC & ACE & B!C!E & BC!E & BCD & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!C & !A!B!D & !A!D!E & !ACD & !BC!E & !BDE & A!C!E & ABC & ACE & B!C!E & BC!E & BCD & CDE",
"ground_truth": 100,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 55
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!DE & !ABC & !ADE & !BC!D & !C!D!E & !CD!E & A!C!E & AB!D & ABC & ABD & B!D!E & C!DE & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!DE & !ABC & !ADE & !BC!D & !C!D!E & !CD!E & A!C!E & AB!D & ABC & ABD & B!D!E & C!DE & CDE",
"ground_truth": 1110,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 434
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!BC & !A!CD & !AC!E & !AD!E & !B!C!E & !BCD & !BD!E & A!B!D & A!CE & B!C!D & B!C!E & B!D!E & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!BC & !A!CD & !AC!E & !AD!E & !B!C!E & !BCD & !BD!E & A!B!D & A!CE & B!C!D & B!C!E & B!D!E & CDE",
"ground_truth": 10010,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 469
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!CE & !ACD & !AD!E & !BCD & !C!DE & A!C!E & A!DE & ABE & ACD & B!CE & C!D!E & C!DE & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!CE & !ACD & !AD!E & !BCD & !C!DE & A!C!E & A!DE & ABE & ACD & B!CE & C!D!E & C!DE & CDE",
"ground_truth": 10111,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 378
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!BD & !A!BE & !ABD & !ACD & !ACE & !BD!E & A!B!C & A!B!D & A!BC & A!D!E & ACE & B!DE & BCE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!BD & !A!BE & !ABD & !ACD & !ACE & !BD!E & A!B!C & A!B!D & A!BC & A!D!E & ACE & B!DE & BCE",
"ground_truth": 100,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 295
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!C & !A!B!D & !B!CD & !BCE & A!B!D & A!BE & A!D!E & A!DE & AB!E & ACE & ADE & B!CD & B!D!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!C & !A!B!D & !B!CD & !BCE & A!B!D & A!BE & A!D!E & A!DE & AB!E & ACE & ADE & B!CD & B!D!E",
"ground_truth": 10001,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 171
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!BD & !A!C!D & !A!D!E & !A!DE & !AB!E & !ABC & !AC!D & !AD!E & !BD!E & A!BC & BC!D & BCD & CD!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!BD & !A!C!D & !A!D!E & !A!DE & !AB!E & !ABC & !AC!D & !AD!E & !BD!E & A!BC & BC!D & BCD & CD!E",
"ground_truth": 101,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 20
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!BD & !A!C!E & !ABE & !BC!E & !BD!E & A!BD & A!BE & A!C!D & A!CE & A!D!E & A!DE & ABD & ACE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!BD & !A!C!E & !ABE & !BC!E & !BD!E & A!BD & A!BE & A!C!D & A!CE & A!D!E & A!DE & ABD & ACE",
"ground_truth": 10001,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 466
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!BC & !AB!D & !ABD & !AC!E & !B!CD & !B!D!E & !BDE & !C!D!E & !C!DE & A!BC & A!C!D & A!D!E & C!D!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!BC & !AB!D & !ABD & !AC!E & !B!CD & !B!D!E & !BDE & !C!D!E & !C!DE & A!BC & A!C!D & A!D!E & C!D!E",
"ground_truth": 100,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 397
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!DE & !AC!D & !B!CD & !B!CE & !CD!E & A!B!D & A!BC & A!C!E & A!DE & ACE & ADE & B!C!D & B!DE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!DE & !AC!D & !B!CD & !B!CE & !CD!E & A!B!D & A!BC & A!C!E & A!DE & ACE & ADE & B!C!D & B!DE",
"ground_truth": 10000,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 496
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!BE & !B!C!D & !B!D!E & !BD!E & A!B!D & A!BC & A!DE & AB!D & ABE & B!DE & BC!E & BCD & C!D!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!BE & !B!C!D & !B!D!E & !BD!E & A!B!D & A!BC & A!DE & AB!D & ABE & B!DE & BC!E & BCD & C!D!E",
"ground_truth": 1100,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 364
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!AC!D & !B!D!E & !BC!E & !C!DE & A!B!D & A!B!E & A!BD & A!CE & AB!C & ABE & ACE & B!CD & CD!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!AC!D & !B!D!E & !BC!E & !C!DE & A!B!D & A!B!E & A!BD & A!CE & AB!C & ABE & ACE & B!CD & CD!E",
"ground_truth": 11100,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 166
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!E & !A!CD & !ABC & !B!C!E & A!C!E & A!CE & A!D!E & AB!C & AB!E & B!CE & B!DE & BCD & BDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!E & !A!CD & !ABC & !B!C!E & A!C!E & A!CE & A!D!E & AB!C & AB!E & B!CE & B!DE & BCD & BDE",
"ground_truth": 11000,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 489
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!C & !A!B!E & !A!CE & !ABE & !C!DE & A!B!E & A!BE & A!D!E & AB!D & ABC & BC!D & BC!E & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!C & !A!B!E & !A!CE & !ABE & !C!DE & A!B!E & A!BE & A!D!E & AB!D & ABC & BC!D & BC!E & CDE",
"ground_truth": 10111,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 454
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!E & !A!D!E & !AB!C & !AB!D & !ACD & !BDE & A!BD & A!BE & A!CD & A!CE & B!C!D & BDE & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!E & !A!D!E & !AB!C & !AB!D & !ACD & !BDE & A!BD & A!BE & A!CD & A!CE & B!C!D & BDE & CDE",
"ground_truth": 1,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 164
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!E & !A!BD & !A!BE & !ABE & !B!CD & !B!CE & A!BE & A!C!D & A!C!E & A!D!E & AC!E & ACD & B!C!D\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!E & !A!BD & !A!BE & !ABE & !B!CD & !B!CE & A!BE & A!C!D & A!C!E & A!D!E & AC!E & ACD & B!C!D",
"ground_truth": 10001,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 174
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!CD & !A!DE & !AB!D & !ABD & !ABE & !AC!D & !ACD & A!C!E & ABE & AC!D & B!CD & BC!E & C!DE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!CD & !A!DE & !AB!D & !ABD & !ABE & !AC!D & !ACD & A!C!E & ABE & AC!D & B!CD & BC!E & C!DE",
"ground_truth": 1110,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 494
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!C!E & !A!CE & !AB!D & !ABD & !B!D!E & !B!DE & !C!D!E & A!B!C & A!CD & A!DE & AB!C & AC!E & BC!D\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!C!E & !A!CE & !AB!D & !ABD & !B!D!E & !B!DE & !C!D!E & A!B!C & A!CD & A!DE & AB!C & AC!E & BC!D",
"ground_truth": 1000,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 289
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!BE & !A!CD & !A!DE & !AB!E & !ACD & !B!C!E & !CDE & A!CD & A!CE & ACE & B!CD & B!CE & BC!D\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!BE & !A!CD & !A!DE & !AB!E & !ACD & !B!C!E & !CDE & A!CD & A!CE & ACE & B!CD & B!CE & BC!D",
"ground_truth": 1001,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 144
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!BC & !A!CE & !A!D!E & !ABE & !ACE & !B!C!D & !B!CE & !BCD & A!D!E & AB!D & ACD & B!C!D & CD!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!BC & !A!CE & !A!D!E & !ABE & !ACE & !B!C!D & !B!CE & !BCD & A!D!E & AB!D & ACD & B!C!D & CD!E",
"ground_truth": 11101,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 33
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!C & !AB!E & !B!CE & !BC!E & A!B!E & A!BC & A!C!D & ABE & B!C!D & B!CD & B!D!E & B!DE & BC!D\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!C & !AB!E & !B!CE & !BC!E & A!B!E & A!BC & A!C!D & ABE & B!C!D & B!CD & B!D!E & B!DE & BC!D",
"ground_truth": 10000,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 176
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!BC & !AB!E & !ABD & !AC!D & !AD!E & A!BC & A!C!D & A!DE & B!C!E & BC!E & BDE & C!DE & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!BC & !AB!E & !ABD & !AC!D & !AD!E & A!BC & A!C!D & A!DE & B!C!E & BC!E & BDE & C!DE & CDE",
"ground_truth": 10110,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 145
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!ABD & !B!CD & !B!DE & !BCD & !BDE & A!B!C & A!B!E & A!CE & ACD & ACE & B!DE & CD!E & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!ABD & !B!CD & !B!DE & !BCD & !BDE & A!B!C & A!B!E & A!CE & ACD & ACE & B!DE & CD!E & CDE",
"ground_truth": 10011,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 168
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!BC & !A!C!D & !A!C!E & !A!D!E & !ABE & !AC!D & !ACE & !B!C!E & !B!D!E & !BCE & A!CE & A!DE & AC!D\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!BC & !A!C!D & !A!C!E & !A!D!E & !ABE & !AC!D & !ACE & !B!C!E & !B!D!E & !BCE & A!CE & A!DE & AC!D",
"ground_truth": 101,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 100
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!BC & !AB!C & !ABC & !AC!E & !ACD & !AD!E & !B!DE & !CDE & A!CE & AB!C & AD!E & B!C!E & B!CE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!BC & !AB!C & !ABC & !AC!E & !ACD & !AD!E & !B!DE & !CDE & A!CE & AB!C & AD!E & B!C!E & B!CE",
"ground_truth": 10,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 253
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!D & !A!B!E & !AC!D & !B!CE & !BDE & !CDE & A!B!D & A!BE & AC!E & AD!E & B!C!E & BC!D & CD!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!D & !A!B!E & !AC!D & !B!CE & !BDE & !CDE & A!B!D & A!BE & AC!E & AD!E & B!C!E & BC!D & CD!E",
"ground_truth": 10110,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 61
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!C!E & !A!CD & !A!CE & !A!D!E & !ABE & !AC!E & !ACE & A!C!E & AB!C & ABE & AD!E & B!CE & B!DE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!C!E & !A!CD & !A!CE & !A!D!E & !ABE & !AC!E & !ACE & A!C!E & AB!C & ABE & AD!E & B!CE & B!DE",
"ground_truth": 1100,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 302
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!C!D & !AB!C & !AB!D & !AC!D & !B!CE & !BCE & !CD!E & A!BC & A!BE & A!CD & B!C!D & B!CE & C!D!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!C!D & !AB!C & !AB!D & !AC!D & !B!CE & !BCE & !CD!E & A!BC & A!BE & A!CD & B!C!D & B!CE & C!D!E",
"ground_truth": 1111,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 138
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!E & !A!DE & !AB!E & !ABC & !ABD & !AD!E & !B!CE & A!B!C & A!BC & ABD & AC!E & BC!D & BCD\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!E & !A!DE & !AB!E & !ABC & !ABD & !AD!E & !B!CE & A!B!C & A!BC & ABD & AC!E & BC!D & BCD",
"ground_truth": 11000,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 131
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!BD & !A!C!D & !AC!D & !ACD & !ACE & !ADE & !B!CE & !B!D!E & !BC!E & !BCD & !C!DE & ACD & B!CD\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!BD & !A!C!D & !AC!D & !ACD & !ACE & !ADE & !B!CE & !B!D!E & !BC!E & !BCD & !C!DE & ACD & B!CD",
"ground_truth": 1010,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 273
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!D & !AC!E & !B!C!E & A!C!E & A!CD & AB!E & ABD & AC!E & ADE & B!DE & BC!D & BCD & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!D & !AC!E & !B!C!E & A!C!E & A!CD & AB!E & ABD & AC!E & ADE & B!DE & BC!D & BCD & CDE",
"ground_truth": 10100,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 468
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!CE & !A!DE & !AB!D & !AB!E & !ACD & !B!CE & !C!DE & A!BE & A!D!E & A!DE & BCD & BD!E & C!D!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!CE & !A!DE & !AB!D & !AB!E & !ACD & !B!CE & !C!DE & A!BE & A!D!E & A!DE & BCD & BD!E & C!D!E",
"ground_truth": 11111,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 455
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!E & !A!BC & !A!BD & !A!C!D & !A!CD & !AB!E & !AC!E & !ACD & !B!C!D & !B!DE & !CDE & ACD & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!E & !A!BC & !A!BD & !A!C!D & !A!CD & !AB!E & !AC!E & !ACD & !B!C!D & !B!DE & !CDE & ACD & CDE",
"ground_truth": 11,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 150
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!E & !A!CD & !A!D!E & !A!DE & !ABE & !ACD & AB!E & AC!E & ACE & B!D!E & B!DE & BCE & BDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!E & !A!CD & !A!D!E & !A!DE & !ABE & !ACD & AB!E & AC!E & ACE & B!D!E & B!DE & BCE & BDE",
"ground_truth": 1111,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 135
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!DE & !ABE & !AD!E & !B!C!D & !B!CE & A!BC & ACE & B!CD & B!CE & B!DE & BC!D & CD!E & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!DE & !ABE & !AD!E & !B!C!D & !B!CE & A!BC & ACE & B!CD & B!CE & B!DE & BC!D & CD!E & CDE",
"ground_truth": 11011,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 305
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!BE & !A!C!E & !A!CE & !AC!E & !B!C!D & !B!C!E & !BCE & !BD!E & A!BC & AB!C & B!C!D & B!CE & BCD\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!BE & !A!C!E & !A!CE & !AC!E & !B!C!D & !B!C!E & !BCE & !BD!E & A!BC & AB!C & B!C!D & B!CE & BCD",
"ground_truth": 10010,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 405
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!E & !A!BE & !AB!E & !ABD & !ADE & !C!DE & !CDE & A!BE & A!CE & AB!D & AB!E & AC!D & C!DE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!E & !A!BE & !AB!E & !ABD & !ADE & !C!DE & !CDE & A!BE & A!CE & AB!D & AB!E & AC!D & C!DE",
"ground_truth": 1111,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 307
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!E & !A!C!E & !ACD & !BCD & !BD!E & !BDE & A!B!C & A!CD & AB!E & ABE & B!D!E & BC!D & BDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!E & !A!C!E & !ACD & !BCD & !BD!E & !BDE & A!B!C & A!CD & AB!E & ABE & B!D!E & BC!D & BDE",
"ground_truth": 1010,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 140
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!C & !A!BD & !A!BE & !A!D!E & !AB!D & !AC!E & !ADE & !C!D!E & A!B!D & A!BD & ACE & B!C!D & C!DE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!C & !A!BD & !A!BE & !A!D!E & !AB!D & !AC!E & !ADE & !C!D!E & A!B!D & A!BD & ACE & B!C!D & C!DE",
"ground_truth": 11,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 445
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!C!E & !A!D!E & !AB!C & !AB!E & !ABD & !ABE & !ADE & !B!C!D & !B!CE & A!B!E & AB!C & B!CE & C!DE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!C!E & !A!D!E & !AB!C & !AB!E & !ABD & !ABE & !ADE & !B!C!D & !B!CE & A!B!E & AB!C & B!CE & C!DE",
"ground_truth": 11,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 83
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!D & !A!BD & !A!C!D & !A!CD & !A!DE & !ABD & !AC!E & !B!C!D & !B!D!E & !B!DE & A!BE & B!C!D & BD!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!D & !A!BD & !A!C!D & !A!CD & !A!DE & !ABD & !AC!E & !B!C!D & !B!D!E & !B!DE & A!BE & B!C!D & BD!E",
"ground_truth": 0,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 415
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!ABC & !ACE & !B!C!D & !B!C!E & !BCE & !C!D!E & A!B!E & A!BC & A!BD & ABC & BC!E & BCD & BDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!ABC & !ACE & !B!C!D & !B!C!E & !BCE & !C!D!E & A!B!E & A!BC & A!BD & ABC & BC!E & BCD & BDE",
"ground_truth": 11011,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 180
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!D & !A!CD & !A!CE & !AB!E & !ACD & !CDE & A!D!E & B!CD & B!CE & B!D!E & BC!E & BD!E & C!DE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!D & !A!CD & !A!CE & !AB!E & !ACD & !CDE & A!D!E & B!CD & B!CE & B!D!E & BC!E & BD!E & C!DE",
"ground_truth": 0,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 265
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!C & !A!B!E & !A!C!E & !A!CD & !AB!D & !AB!E & !B!D!E & !BCD & !CD!E & A!B!C & AB!C & AB!E & B!CE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!C & !A!B!E & !A!C!E & !A!CD & !AB!D & !AB!E & !B!D!E & !BCD & !CD!E & A!B!C & AB!C & AB!E & B!CE",
"ground_truth": 10,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 425
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!BC & !A!BD & !AB!C & !ABE & !ACD & !AD!E & !ADE & !CD!E & A!BC & A!CE & A!DE & AC!E & BDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!BC & !A!BD & !AB!C & !ABE & !ACD & !AD!E & !ADE & !CD!E & A!BC & A!CE & A!DE & AC!E & BDE",
"ground_truth": 10011,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 252
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!BD & !AB!D & !C!D!E & !C!DE & A!B!D & A!BC & A!C!D & A!C!E & A!D!E & ABC & ACD & ACE & C!D!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!BD & !AB!D & !C!D!E & !C!DE & A!B!D & A!BC & A!C!D & A!C!E & A!D!E & ABC & ACD & ACE & C!D!E",
"ground_truth": 11010,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 321
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!C!D & !ABC & !ABD & !ABE & !AC!D & !ADE & !B!C!E & !BC!E & !BCD & AB!E & B!DE & BCD & C!DE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!C!D & !ABC & !ABD & !ABE & !AC!D & !ADE & !B!C!E & !BC!E & !BCD & AB!E & B!DE & BCD & C!DE",
"ground_truth": 100,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 476
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!BD & !A!C!E & !AC!D & !AD!E & !BD!E & !C!D!E & !C!DE & A!C!D & A!D!E & B!C!D & B!DE & BC!D & BCE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!BD & !A!C!E & !AC!D & !AD!E & !BD!E & !C!D!E & !C!DE & A!C!D & A!D!E & B!C!D & B!DE & BC!D & BCE",
"ground_truth": 10100,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 124
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!C!E & !AB!C & !AB!D & !AB!E & !ADE & !B!C!D & !B!CD & !B!D!E & !BCE & !BD!E & !CD!E & ABE & B!C!D\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!C!E & !AB!C & !AB!D & !AB!E & !ADE & !B!C!D & !B!CD & !B!D!E & !BCE & !BD!E & !CD!E & ABE & B!C!D",
"ground_truth": 1,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 330
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!E & !A!CE & !ACD & !B!C!E & !BD!E & !C!DE & A!DE & AB!C & ABE & ACE & ADE & BCD & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!E & !A!CE & !ACD & !B!C!E & !BD!E & !C!DE & A!DE & AB!C & ABE & ACE & ADE & BCD & CDE",
"ground_truth": 10111,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 222
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!BD & !A!BE & !A!C!D & !A!CE & !AB!C & !ACE & !B!DE & !BD!E & AB!C & AC!E & ACD & AD!E & B!CE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!BD & !A!BE & !A!C!D & !A!CE & !AB!C & !ACE & !B!DE & !BD!E & AB!C & AC!E & ACD & AD!E & B!CE",
"ground_truth": 1111,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 91
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!E & !A!BD & !A!C!E & !AB!D & !BCD & !C!D!E & A!C!D & ABD & ACD & AD!E & B!C!E & BC!D & CD!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!E & !A!BD & !A!C!E & !AB!D & !BCD & !C!D!E & A!C!D & ABD & ACD & AD!E & B!C!E & BC!D & CD!E",
"ground_truth": 1100,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 151
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!BD & !A!D!E & !AB!C & !AC!D & !AC!E & !ACD & !B!D!E & !BCD & !BD!E & AB!E & ABC & ACD & B!D!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!BD & !A!D!E & !AB!C & !AC!D & !AC!E & !ACD & !B!D!E & !BCD & !BD!E & AB!E & ABC & ACD & B!D!E",
"ground_truth": 1010,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 373
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!C & !A!BE & !A!CE & !ACE & !CD!E & !CDE & A!B!E & A!BC & A!CE & A!DE & AC!D & B!DE & C!D!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!C & !A!BE & !A!CE & !ACE & !CD!E & !CDE & A!B!E & A!BC & A!CE & A!DE & AC!D & B!DE & C!D!E",
"ground_truth": 10111,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 351
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!C & !A!B!D & !A!BD & !AB!D & !ABE & !B!DE & A!CE & A!D!E & AB!C & AB!E & ABC & BC!E & BCD\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!C & !A!B!D & !A!BD & !AB!D & !ABE & !B!DE & A!CE & A!D!E & AB!C & AB!E & ABC & BC!E & BCD",
"ground_truth": 1001,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 44
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!AB!D & !B!CD & !BC!E & !C!D!E & !C!DE & !CD!E & A!B!C & A!CD & AC!E & AD!E & B!C!E & BCD & BCE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!AB!D & !B!CD & !BC!E & !C!D!E & !C!DE & !CD!E & A!B!C & A!CD & AC!E & AD!E & B!C!E & BCD & BCE",
"ground_truth": 1010,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 84
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!CE & !A!D!E & !ABE & !AC!E & !ACD & !B!D!E & !BD!E & A!BC & A!C!E & A!CE & AB!E & ACD & B!CD\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!CE & !A!D!E & !ABE & !AC!E & !ACD & !B!D!E & !BD!E & A!BC & A!C!E & A!CE & AB!E & ACD & B!CD",
"ground_truth": 11010,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 108
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!E & !A!CD & !A!D!E & !A!DE & !AB!D & !ABC & !BCD & !BD!E & !C!DE & A!D!E & ABE & B!D!E & C!D!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!E & !A!CD & !A!D!E & !A!DE & !AB!D & !ABC & !BCD & !BD!E & !C!DE & A!D!E & ABE & B!D!E & C!D!E",
"ground_truth": 101,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 184
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!D & !A!C!E & !A!CD & !AB!C & !AB!D & !C!D!E & !CDE & A!B!E & A!D!E & AB!D & ACE & AD!E & B!C!D\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!D & !A!C!E & !A!CD & !AB!C & !AB!D & !C!D!E & !CDE & A!B!E & A!D!E & AB!D & ACE & AD!E & B!C!D",
"ground_truth": 11000,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 77
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!BD & !AC!E & !ACD & !ADE & !B!D!E & !BD!E & A!B!C & A!B!D & AB!C & AB!E & B!C!D & B!D!E & BCE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!BD & !AC!E & !ACD & !ADE & !B!D!E & !BD!E & A!B!C & A!B!D & AB!C & AB!E & B!C!D & B!D!E & BCE",
"ground_truth": 11010,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 79
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!AC!D & !AC!E & !B!D!E & !BC!E & !BD!E & !C!D!E & !C!DE & A!BC & A!DE & AB!E & ABC & B!D!E & C!D!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!AC!D & !AC!E & !B!D!E & !BC!E & !BD!E & !C!D!E & !C!DE & A!BC & A!DE & AB!E & ABC & B!D!E & C!D!E",
"ground_truth": 11100,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 193
} |
sat | [
{
"content": "You are now required to solve a SAT (Boolean Satisfiability) problem. The problem is provided in JSON format, containing the following fields:\n\n- \"n_sat\": The number of variables in each clause (n-SAT problem).\n- \"k\": The total number of distinct variables in the problem.\n- \"clause\": A string representation of the SAT formula, where clauses are separated by \" & \" (representing logical AND). Within each clause, variables are combined using concatenation (representing logical OR). A negation is indicated by \"!\" before a variable.\n\nYour task is to provide a valid solution. The answer is a string of length k representing the truth values of the variables in order (1 for true, 0 for false). If there are multiple solutions, provide any one of them.\nPlease reason step by step, and put your final answer within \\boxed{}.\n\n**Example**\n{\"n_sat\": 3, \"k\": 4, \"clause\": \"!B!C!D & A!B!D & AB!D\"}\n**Final Answer**\n\\boxed{1101}\n\nBelow is the SAT problem you need to solve:\n{\"n_sat\": 3, \"k\": 5, \"clause\": \"!A!B!C & !A!C!D & !A!DE & !AC!D & !AC!E & !ACD & !ACE & !ADE & !B!DE & A!DE & ABE & ACD & B!D!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"clause": "!A!B!C & !A!C!D & !A!DE & !AC!D & !AC!E & !ACD & !ACE & !ADE & !B!DE & A!DE & ABE & ACD & B!D!E",
"ground_truth": 10101,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 213
} |
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