data_source stringclasses 1 value | prompt listlengths 1 1 | ability stringclasses 1 value | reward_model dict | member bool 2 classes | 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!BD & !A!CE & !A!D!E & !ABC & !ABD & !ACE & !B!DE & !C!DE & !CD!E & !CDE & A!BE & AB!D & ABD & ABE & ACD & ADE & B!C!E & B!CD & BCE & C!D!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 1111,
"ground_truth": 1111,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 9
} |
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!E & !B!C!E & !B!CD & !CDE & A!B!D & A!C!D & AB!D & ABC & ABD & AC!D & AD!E & BC!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 1000,
"ground_truth": 1000,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 21
} |
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 & !AB!C & !ABC & !AD!E & !ADE & !B!CE & A!BC & A!BE & A!CE & A!DE & AC!D & AD!E & ADE & B!C!D & B!C!E & B!CD & BC!D & BD!E & C!D!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 1111,
"ground_truth": 1111,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 6
} |
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!BE & !A!C!D & !A!CE & !ABD & !ACE & A!C!E & AB!D & AB!E & ABC & ABE & ACE & C!D!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 1110,
"ground_truth": 1110,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 18
} |
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 | {
"full_solution": 11101,
"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!D & !A!D!E & !AC!D & !BC!D & !BC!E & !BCE & A!B!E & A!BD & ABC & AC!E & ACE & C!DE & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 1110,
"ground_truth": 1110,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 42
} |
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!CD & !A!CE & !A!D!E & !A!DE & !AD!E & !B!CE & !BD!E & !CDE & A!CD & A!D!E & ABD & AD!E & ADE & B!CD & BC!D & BCD & BDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 1010,
"ground_truth": 1010,
"style": "rule"
} | false | {
"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!B!D & !A!C!D & !AB!E & !ABD & !B!CE & !CD!E & A!C!E & A!CD & B!DE & BCE & BD!E & C!DE & CD!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 1000,
"ground_truth": 1000,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 27
} |
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 & !AB!D & !AC!D & !BC!D & !BCD & !BD!E & !BDE & !CD!E & !CDE & A!B!D & A!BD & A!C!D & A!CD & AB!C & ABD & AC!D & B!C!E & B!CE & BCE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 11110,
"ground_truth": 11110,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 42
} |
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!BE & !AD!E & !B!CE & !BC!E & !BDE & !C!D!E & !C!DE & !CDE & A!B!D & A!BC & AC!D & ACD & ACE & ADE & B!C!E & BCD & C!DE & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 10011,
"ground_truth": 10011,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 21
} |
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!BE & !A!CD & !B!CE & !BCD & !C!D!E & A!B!C & A!B!E & A!BD & A!CE & A!DE & ACE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 11,
"ground_truth": 11,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 2
} |
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!CD & !A!DE & !ABE & !ACE & !ADE & !B!C!D & !BC!D & !C!D!E & ACD & B!C!D & B!C!E & BCD\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 10011,
"ground_truth": 10011,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 25
} |
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\": \"!ADE & !B!C!D & !BCD & !C!DE & !CDE & A!B!C & A!D!E & AB!D & ABE & B!C!D & B!C!E & BCD & BCE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 11101,
"ground_truth": 11101,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 24
} |
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!BD & !A!BE & !A!CD & !ABC & !ABD & !ACE & !BC!D & A!C!E & A!CE & A!DE & ABC & ABE & ADE & B!C!E & B!D!E & BCE & CD!E & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 10110,
"ground_truth": 10110,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 2
} |
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 & !A!CD & !AC!E & !AD!E & !B!C!E & !BD!E & !CD!E & A!B!D & A!C!E & A!D!E & ACE & AD!E & B!C!E & B!D!E & BC!D & BC!E & BCE & BD!E & C!DE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 10110,
"ground_truth": 10110,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 31
} |
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 & !ABC & !AC!E & !ADE & !B!CD & !CDE & A!B!C & A!B!D & A!BC & A!CE & AB!C & AB!E & ABE & AD!E & B!C!D & B!C!E & B!CE & B!D!E & BD!E & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 11010,
"ground_truth": 11010,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 49
} |
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!E & !ABD & !AC!D & !AC!E & !B!CE & !BC!D & !C!D!E & !C!DE & !CDE & A!BD & A!CD & AB!E & ABE & AC!D & AC!E & AD!E & ADE & B!C!D & B!C!E & C!DE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 11000,
"ground_truth": 11000,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 1
} |
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!BE & !A!C!D & !ABD & !AC!D & !B!C!D & !B!C!E & !B!CE & !BC!E & !BCE & !CDE & A!D!E & A!DE & B!D!E & B!DE & BC!D & BCE & BDE & C!D!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 1,
"ground_truth": 1,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 11
} |
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 & !AB!C & !AB!D & !AB!E & !ABC & !BCE & !CDE & A!BC & A!DE & ACE & B!CD & C!DE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 11101,
"ground_truth": 11101,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 4
} |
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 & !A!CE & !A!D!E & !AB!C & !ABE & !ACD & !BC!D & !BC!E & !BCD & !BCE & !BDE & !CDE & A!C!E & A!CD & AC!E & ACD & ACE & B!DE & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 1110,
"ground_truth": 1110,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 47
} |
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!DE & !ABC & !ABD & !ABE & !AC!D & !AD!E & !ADE & !B!C!E & !B!CD & !B!D!E & !BCD & !C!DE & A!BD & A!C!D & B!C!E & BC!E & BD!E & C!D!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 100,
"ground_truth": 100,
"style": "rule"
} | false | {
"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\": \"!A!B!D & !A!C!E & !AB!E & !ABD & !ACD & !B!C!E & !B!DE & !BC!D & !BC!E & !BCE & ACD & BC!E & CD!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 1100,
"ground_truth": 1100,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 37
} |
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 & !AB!C & !B!D!E & !BD!E & !C!DE & A!B!D & A!BD & A!BE & ABC & AC!E & AD!E & ADE & BC!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 11100,
"ground_truth": 11100,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 28
} |
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!CD & !A!CE & !A!D!E & !A!DE & !B!C!D & !B!CE & !BCE & !BDE & A!B!E & A!BC & A!C!D & A!C!E & AB!D & ABE & B!CE & B!DE & BC!D & BC!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 10000,
"ground_truth": 10000,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 30
} |
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!D!E & !ABD & !ACD & !ADE & !BCD & A!B!E & A!C!D & A!C!E & ABE & ACE & B!CE & B!DE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 11,
"ground_truth": 11,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 7
} |
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 & !A!CE & !AB!E & !ABC & !ABE & !AC!E & !ACD & !AD!E & !BC!E & !BCD & !BCE & A!C!D & A!CE & A!D!E & AB!D & B!CE & BD!E & C!D!E & CD!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 0,
"ground_truth": 0,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 7
} |
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 & !A!BE & !A!C!D & !A!C!E & !AB!E & !ABD & !B!CE & !BDE & !C!DE & !CD!E & A!B!C & A!BD & A!CD & A!CE & A!DE & ABD & ACE & BC!D & BCD\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 111,
"ground_truth": 111,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 29
} |
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!DE & !AB!D & !AB!E & !AC!E & !ACD & !AD!E & !BCD & !C!D!E & A!BC & AC!E & B!C!E & C!DE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 1101,
"ground_truth": 1101,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 26
} |
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 & !AB!D & !ABE & !ACD & !ADE & !B!D!E & !BD!E & !BDE & !CD!E & A!B!C & A!C!D & A!CD & AB!C & AB!D & AB!E & AC!E & ACD & C!D!E & CD!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 11110,
"ground_truth": 11110,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 26
} |
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!B!E & !A!BC & !AC!E & !B!C!D & !B!C!E & !CDE & A!B!E & A!BC & A!BD & A!BE & A!CE & A!DE & AB!E & AC!E & AD!E & B!C!E & BD!E & C!DE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 0,
"ground_truth": 0,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 28
} |
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 & !AC!E & !B!C!D & !B!CD & !B!CE & A!B!C & AC!D & ACE & BD!E & BDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 1001,
"ground_truth": 1001,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 38
} |
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 | {
"full_solution": 11101,
"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!B!C & !A!DE & !ABC & !AD!E & !ADE & !B!C!E & A!BD & A!BE & A!C!D & A!DE & ABC & ABE & AC!D & B!CE & B!DE & BCD & BCE & BDE & C!DE & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 101,
"ground_truth": 101,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 36
} |
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 | {
"full_solution": 10010,
"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!D & !A!BE & !ACD & !ADE & !B!C!E & !B!CD & !BCE & A!B!C & A!C!E & B!CE & B!D!E & C!D!E & C!DE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 1,
"ground_truth": 1,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 10
} |
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 & !AB!E & !ADE & !CD!E & AB!C & ABE & AC!D & ACD & ACE & B!C!D & B!CD & BCD\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 11010,
"ground_truth": 11010,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 29
} |
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!CD & !A!CE & !AB!C & !AB!E & !ACE & !ADE & !B!CE & !BC!D & !BCD & !CDE & A!B!C & A!D!E & AB!C & AB!D & B!C!E & B!CD & B!CE & B!D!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 1,
"ground_truth": 1,
"style": "rule"
} | false | {
"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!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 | {
"full_solution": 1111,
"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!BE & !A!C!D & !ACD & !ACE & !BC!D & !BC!E & !C!D!E & A!BD & AB!C & ABD & ADE & B!C!E & BCD\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 11101,
"ground_truth": 11101,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 17
} |
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 & !ACD & !ACE & !BC!E & !BCE & !C!DE & !CD!E & A!BD & ABE & AC!E & ACD & BDE & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 11100,
"ground_truth": 11100,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 39
} |
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!D!E & !A!DE & !B!C!E & !B!CE & !BC!E & !BDE & !C!D!E & !CD!E & A!B!E & A!BC & A!C!D & A!CD & A!CE & AB!D & ABE & AC!E & ACE & BC!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 10000,
"ground_truth": 10000,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 41
} |
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 | {
"full_solution": 0,
"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!D & !A!C!D & !A!C!E & !AB!E & !ABE & !AC!D & !ACE & !ADE & !B!DE & !BC!E & !BCD & !C!D!E & A!B!C & ABD & AC!E & ACD & AD!E & ADE & BDE & C!DE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 110,
"ground_truth": 110,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 39
} |
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!D!E & !BC!D & !BC!E & !BCD & !BCE & !C!D!E & A!B!D & AB!C & ABD & ACD & B!C!D & C!D!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 11100,
"ground_truth": 11100,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 5
} |
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 & !A!CD & !A!DE & !AB!D & !ACD & !B!C!D & !B!D!E & !B!DE & !BC!E & !CD!E & A!B!E & A!BC & AB!E & AC!D & AC!E & B!C!D & B!D!E & BD!E & C!DE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 0,
"ground_truth": 0,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 18
} |
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 & !ABD & !ACD & !ACE & !B!CD & !B!CE & !BCE & A!CE & AB!C & ABC & ABD & BCE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 10011,
"ground_truth": 10011,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 1
} |
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 & !A!BE & !ABE & !ACD & !ACE & !B!C!D & !B!CD & !B!CE & !B!DE & !BC!E & !BD!E & A!BD & AB!D & ACD & BC!D & BC!E & C!D!E & CD!E & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 10111,
"ground_truth": 10111,
"style": "rule"
} | false | {
"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!D!E & !AB!D & !ABD & !ABE & !AC!D & !ACD & !AD!E & !B!D!E & !BCD & !BD!E & !C!D!E & !CD!E & A!B!D & A!BC & A!C!E & AC!D & AD!E & B!CE & BC!E & C!DE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 11100,
"ground_truth": 11100,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 34
} |
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!D!E & !A!DE & !AB!D & !ABC & !ABE & !AC!E & !ADE & !BCE & !CD!E & !CDE & A!D!E & ACE & ADE & B!C!D & B!C!E & B!CE & BD!E & CD!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 1110,
"ground_truth": 1110,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 13
} |
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 & !ABC & !ABE & !B!C!E & !BCE & !BD!E & ABC & AC!D & BC!D & BC!E & BCD & BD!E & C!D!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 11100,
"ground_truth": 11100,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 3
} |
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 & !ABC & !AC!E & !ACE & !ADE & !B!CE & !BC!D & !BCE & A!BC & A!BD & A!BE & A!D!E & AB!C & B!C!D & B!D!E & BC!D & BCD & BD!E & C!DE & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 11101,
"ground_truth": 11101,
"style": "rule"
} | false | {
"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!C!D & !A!D!E & !A!DE & !AB!D & !ABD & !ABE & !BC!D & !BDE & !C!D!E & !CD!E & A!B!D & A!BC & A!C!E & ACE & ADE & B!C!D & B!DE & BCE & BD!E & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 11001,
"ground_truth": 11001,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 43
} |
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 | {
"full_solution": 101,
"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!C!E & !A!DE & !ABE & !B!CD & !B!D!E & !B!DE & !CD!E & A!B!D & A!BC & A!C!D & A!C!E & ABC & AC!E & ADE & B!CD & B!CE & B!DE & BDE & C!DE & CD!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 11000,
"ground_truth": 11000,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 37
} |
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 & !AB!E & !ADE & !BC!D & !BC!E & !CDE & A!B!E & A!CE & A!DE & AB!C & BC!E & BCE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 10110,
"ground_truth": 10110,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 43
} |
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 & !AC!E & !B!C!E & !BCD & !C!DE & !CD!E & A!BD & A!BE & A!C!E & A!CE & AB!C & ABD & ACD & B!C!D & B!D!E & BC!D & BCD & CD!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 1011,
"ground_truth": 1011,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 23
} |
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!C!E & !A!DE & !B!C!E & !B!CD & A!B!C & A!BD & A!D!E & AC!E & ACE & B!C!D & BC!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 100,
"ground_truth": 100,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 32
} |
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 & !AB!D & !AB!E & !ABE & !AC!E & !ACE & !BC!E & !BCD & !BDE & !C!D!E & !C!DE & A!BD & A!C!E & AB!D & AB!E & ABE & ACE & ADE & B!D!E & BC!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 11101,
"ground_truth": 11101,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 25
} |
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!DE & !ABE & !AC!E & !ACD & !B!C!E & !BC!E & !BD!E & A!B!E & A!BC & AD!E & B!CD & BC!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 1110,
"ground_truth": 1110,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 23
} |
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!CE & !A!D!E & !ABC & !AC!E & !B!C!D & !B!CE & !B!DE & !BC!D & !BDE & !C!D!E & A!BE & A!C!D & A!CE & A!D!E & A!DE & AB!E & B!D!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 0,
"ground_truth": 0,
"style": "rule"
} | false | {
"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!E & !A!BD & !A!BE & !A!CE & !A!D!E & !A!DE & !ABC & !AC!D & !AD!E & !ADE & !B!CE & !BCD & !BDE & AC!D & ACD & ADE & B!CD & B!DE & BD!E & BDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 111,
"ground_truth": 111,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 19
} |
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 & !A!DE & !AB!C & !B!D!E & !B!DE & !BC!E & !BDE & A!BE & A!C!D & A!DE & ACD & B!D!E & BCE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 100,
"ground_truth": 100,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 15
} |
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!D!E & !ABD & !ACD & !B!D!E & !BD!E & !BDE & A!C!D & A!CD & AC!E & AD!E & BCE & C!DE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 10110,
"ground_truth": 10110,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 48
} |
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!E & !ABD & !B!C!E & !B!CE & !B!D!E & !BC!D & !C!DE & !CD!E & A!B!E & A!CD & A!DE & AB!E & ADE & B!C!E & B!CD & B!DE & BCD & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 11001,
"ground_truth": 11001,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 5
} |
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!E & !ABE & !ACD & !ADE & !BC!D & !BCD & !BDE & !CDE & A!B!C & A!BC & A!D!E & AB!C & ABC & ADE & B!CD & BC!D & BC!E & BD!E & CD!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 11111,
"ground_truth": 11111,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 10
} |
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 & !BCE & !CD!E & A!C!E & ABC & ADE & B!D!E & BC!E & C!D!E & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 11110,
"ground_truth": 11110,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 9
} |
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!CE & !AB!C & !AB!D & !AB!E & !AC!D & !ACD & !B!C!D & !BC!D & !BD!E & A!B!D & A!CD & ABE & AC!E & ACE & AD!E & ADE & BC!E & CD!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 111,
"ground_truth": 111,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 12
} |
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 & !ABC & !ADE & !B!C!D & !B!CD & !BC!E & !C!DE & A!B!E & A!BD & A!CD & A!CE & ADE & BC!D\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 1010,
"ground_truth": 1010,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 31
} |
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 & !ABC & !ABD & !AC!D & !B!CD & !B!CE & !BCD & !C!DE & A!B!C & A!B!D & A!B!E & AB!E & AD!E & B!CD & B!CE & B!D!E & C!D!E & C!DE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 0,
"ground_truth": 0,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 22
} |
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!BE & !ABE & !AC!E & !AD!E & !B!C!E & !B!DE & !BC!D & !C!DE & !CDE & A!BC & BC!E & C!D!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 111,
"ground_truth": 111,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 16
} |
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 | {
"full_solution": 1001,
"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\": \"!A!B!D & !A!BC & !A!C!D & !A!CE & !A!DE & !AC!D & !ADE & !BC!D & !BC!E & !BCD & A!D!E & A!DE & ABC & ABE & AC!D & ACE & ADE & B!C!D & B!DE & BCE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 11101,
"ground_truth": 11101,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 32
} |
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 & !A!D!E & !AD!E & !ADE & !BC!E & !BCE & !C!D!E & A!BC & A!C!D & A!C!E & A!CE & AC!E & ACD & ACE & AD!E & B!C!D & B!C!E & C!D!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 10010,
"ground_truth": 10010,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 17
} |
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 & !AB!C & !AB!E & !ABC & !ACD & !C!D!E & A!CD & AB!E & AC!D & BCE & BDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 1000,
"ground_truth": 1000,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 34
} |
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 & !ABC & !B!C!D & !B!CD & !BC!D & A!B!C & A!D!E & AB!D & AB!E & B!C!D & BC!E & BCE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 1000,
"ground_truth": 1000,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 30
} |
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!C!E & !A!D!E & !AB!C & !AB!D & !B!C!E & !B!CD & !B!DE & !BD!E & !C!D!E & !CDE & A!B!E & A!CE & AB!E & AD!E & BC!D & BCD & C!D!E & C!DE & CD!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 1000,
"ground_truth": 1000,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 8
} |
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!D & !AB!C & !AB!D & !ABE & !AC!D & !B!C!E & A!B!C & A!B!D & A!BC & A!BE & A!CD & A!DE & AB!E & ABC & AC!D & BC!D & BD!E & BDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 11000,
"ground_truth": 11000,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 24
} |
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 & !ABD & !B!C!D & !B!C!E & !B!DE & !BC!E & !BD!E & !CD!E & A!B!D & A!B!E & A!CE & A!D!E & AB!D & AB!E & AC!E & B!C!E & B!DE & BD!E & BDE & CD!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 11100,
"ground_truth": 11100,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 38
} |
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 & !ABC & !ABE & !B!C!E & !B!DE & !BCD & !BCE & !C!D!E & !CD!E & A!BC & A!CD & A!D!E & AB!D & AB!E & AC!E & B!CD & B!DE & BC!E & C!DE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 11011,
"ground_truth": 11011,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 48
} |
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!DE & !B!C!E & !B!D!E & !BDE & A!CD & A!CE & A!DE & AB!D & ABC & ACE & B!CD & B!CE & BC!D & BC!E & BCD & BDE & CD!E & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 10111,
"ground_truth": 10111,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 4
} |
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 & !ABE & A!BD & A!CD & AB!D & AB!E & ABD & AC!E & B!CE & BC!E & BCE & BDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 1010,
"ground_truth": 1010,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 49
} |
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!E & !ABD & !ACE & !B!CE & !CD!E & A!B!D & A!BC & A!C!D & ABC & AC!E & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 100,
"ground_truth": 100,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 6
} |
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 & !AD!E & !B!C!D & !B!C!E & !CD!E & A!B!E & A!BC & A!C!D & A!C!E & A!CE & AB!D & AC!D & AC!E & ADE & B!C!D & B!D!E & BCD & C!D!E & C!DE & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 10100,
"ground_truth": 10100,
"style": "rule"
} | false | {
"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!C & !A!CE & !AC!E & !BCE & A!C!D & A!CE & A!D!E & AB!D & ABC & ACD & ADE & BDE & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 10101,
"ground_truth": 10101,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 11
} |
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 & !AB!C & !ABC & !AC!D & !B!C!E & !B!CD & !B!D!E & !BC!D & !BD!E & !C!D!E & !C!DE & A!BE & A!C!D & A!CD & A!CE & ACE & AD!E & B!DE & BCE & C!DE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 11000,
"ground_truth": 11000,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 35
} |
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 & !A!D!E & !AB!C & !BC!D & !BCD & !C!D!E & A!BC & A!C!D & ABD & B!CD & BD!E & BDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 10,
"ground_truth": 10,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 41
} |
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 & !B!CE & !BC!D & !C!DE & A!B!E & A!C!E & A!CE & A!D!E & A!DE & ABD & ABE & B!C!E & BC!D\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 1000,
"ground_truth": 1000,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 22
} |
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!D & !ABC & !ACD & !ADE & !B!D!E & A!C!E & A!DE & AB!C & B!DE & C!D!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 0,
"ground_truth": 0,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 19
} |
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!D!E & !B!C!E & A!BC & ABD & ABE & AC!E & ACE & ADE & B!C!D & B!DE & BC!E & CD!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 10101,
"ground_truth": 10101,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 35
} |
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!B!E & !A!BC & !B!C!D & !B!CD & !BC!E & !C!DE & A!B!C & A!B!D & A!BC & A!CD & A!CE & AC!D & AC!E & ACE & B!DE & BDE & C!DE & CD!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 10111,
"ground_truth": 10111,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 14
} |
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 & !ACD & !BCE & !C!DE & !CDE & A!B!C & A!BD & A!CE & ADE & B!CE & B!DE & BCE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 10011,
"ground_truth": 10011,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 47
} |
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 & !AB!C & !AB!D & !AB!E & !ABD & !AD!E & !B!C!E & !BD!E & A!B!E & AB!D & AB!E & CD!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 1110,
"ground_truth": 1110,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 12
} |
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 & !ABC & !AD!E & !B!C!E & !B!CD & !B!D!E & !C!D!E & !CD!E & !CDE & A!B!C & AB!D & ABE & AC!E & B!C!E & BC!E & BCD & BCE & C!D!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 1010,
"ground_truth": 1010,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 3
} |
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 & !ACE & !ADE & !B!C!D & !B!CE & !BDE & A!BE & A!C!D & A!CD & A!D!E & AC!E & BCD\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 10,
"ground_truth": 10,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 14
} |
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 & !AB!E & !ABE & !AC!D & !AD!E & !B!C!D & A!B!C & A!B!E & A!BC & A!BD & A!BE & A!C!E & AB!D\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 0,
"ground_truth": 0,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 13
} |
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 & !ABC & !ABE & !ACE & !AD!E & !BD!E & !C!DE & !CD!E & A!B!E & A!C!D & ABC & ABD & AC!E & B!C!E & B!CD & BC!D & BC!E & BCE & BDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 11100,
"ground_truth": 11100,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 16
} |
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 & !AB!E & !ABC & !ACE & !BC!D & !BDE & !CDE & A!D!E & AB!E & ACE & B!D!E & BC!D & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 1001,
"ground_truth": 1001,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 36
} |
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!CE & !A!DE & !AB!E & !AC!D & !ACD & !ACE & !AD!E & !B!C!E & !B!CD & !BCE & !BD!E & A!CD & ACE & ADE & B!CD & B!CE & B!DE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 11,
"ground_truth": 11,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 15
} |
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!D & !AC!D & !ACD & !B!C!E & !B!DE & !BCD & !C!DE & !CD!E & ABD & ACD & B!C!D & B!D!E & BC!D & BCE & C!D!E & CDE\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 10100,
"ground_truth": 10100,
"style": "rule"
} | false | {
"k_vars": 5,
"n_sat": 3,
"original_id": 27
} |
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 & !ABE & !ACE & !B!CD & !B!D!E & !BC!E & !BCD & A!B!D & A!BC & A!BD & A!BE & AB!E & BD!E\"}\n",
"role": "user"
}
] | logical_reasoning | {
"full_solution": 100,
"ground_truth": 100,
"style": "rule"
} | true | {
"k_vars": 5,
"n_sat": 3,
"original_id": 8
} |
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