TSTP Solution File: SET979+1 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SET979+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Mar 25 14:32:55 EDT 2024
% Result : Theorem 0.19s 0.35s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET979+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Mar 20 21:17:48 EDT 2024
% 0.19/0.34 % CPUTime :
% 0.19/0.35 % SZS status Theorem for theBenchmark
% 0.19/0.35 % SZS output start Proof for theBenchmark
% 0.19/0.35
% 0.19/0.35 % Formula: commutativity_k2_tarski ( axiom ) converted to clauses:
% 0.19/0.35 cnf(commutativity_k2_tarski-1, axiom, ( ( unordered_pair(_u1, _u0) = unordered_pair(_u0, _u1)) )).
% 0.19/0.35
% 0.19/0.35 % Formula: commutativity_k2_xboole_0 ( axiom ) converted to clauses:
% 0.19/0.35 cnf(commutativity_k2_xboole_0-1, axiom, ( ( set_union2(_u3, _u2) = set_union2(_u2, _u3)) )).
% 0.19/0.35
% 0.19/0.35 % Formula: fc2_xboole_0 ( axiom ) converted to clauses:
% 0.19/0.35 cnf(fc2_xboole_0-1, axiom, ( empty(_u5) | ~empty(set_union2(_u5, _u4)) )).
% 0.19/0.35
% 0.19/0.35 % Formula: fc3_xboole_0 ( axiom ) converted to clauses:
% 0.19/0.35 cnf(fc3_xboole_0-1, axiom, ( empty(_u7) | ~empty(set_union2(_u6, _u7)) )).
% 0.19/0.35
% 0.19/0.35 % Formula: idempotence_k2_xboole_0 ( axiom ) converted to clauses:
% 0.19/0.35 cnf(idempotence_k2_xboole_0-1, axiom, ( ( set_union2(_u9, _u9) = _u9) )).
% 0.19/0.35
% 0.19/0.35 % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 0.19/0.35 cnf(rc1_xboole_0-1, axiom, ( empty(skolem1) )).
% 0.19/0.35
% 0.19/0.35 % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 0.19/0.35 cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem2) )).
% 0.19/0.35
% 0.19/0.35 % Formula: t120_zfmisc_1 ( axiom ) converted to clauses:
% 0.19/0.35 cnf(t120_zfmisc_1-1, axiom, ( ( cartesian_product2(set_union2(_u19, _u17), _u15) = set_union2(cartesian_product2(_u19, _u15), cartesian_product2(_u17, _u15))) )).
% 0.19/0.35 cnf(t120_zfmisc_1-2, axiom, ( ( cartesian_product2(_u16, set_union2(_u20, _u18)) = set_union2(cartesian_product2(_u16, _u20), cartesian_product2(_u16, _u18))) )).
% 0.19/0.35
% 0.19/0.35 % Formula: t132_zfmisc_1 ( conjecture ) (definitionally) converted to clauses:
% 0.19/0.35 cnf(t132_zfmisc_1-1, negated_conjecture, ( ( cartesian_product2(unordered_pair(skolem3, skolem4), skolem5) != set_union2(cartesian_product2(singleton(skolem3), skolem5), cartesian_product2(singleton(skolem4), skolem5))) | ( cartesian_product2(skolem5, unordered_pair(skolem3, skolem4)) != set_union2(cartesian_product2(skolem5, singleton(skolem3)), cartesian_product2(skolem5, singleton(skolem4)))) )).
% 0.19/0.35
% 0.19/0.35 % Formula: t41_enumset1 ( axiom ) converted to clauses:
% 0.19/0.35 cnf(t41_enumset1-1, axiom, ( ( unordered_pair(_u25, _u24) = set_union2(singleton(_u25), singleton(_u24))) )).
% 0.19/0.35
% 0.19/0.35 % Problem matrix:
% 0.19/0.35 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 0.19/0.35 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 0.19/0.35 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 0.19/0.35 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( unordered_pair(__eqx_0, __eqx_1) = unordered_pair(__eqy_0, __eqy_1)) )).
% 0.19/0.35 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_union2(__eqx_0, __eqx_1) = set_union2(__eqy_0, __eqy_1)) )).
% 0.19/0.35 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( cartesian_product2(__eqx_0, __eqx_1) = cartesian_product2(__eqy_0, __eqy_1)) )).
% 0.19/0.35 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( singleton(__eqx_0) = singleton(__eqy_0)) )).
% 0.19/0.35 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 0.19/0.35 cnf(matrix-8, plain, ( ( unordered_pair(_u1, _u0) = unordered_pair(_u0, _u1)) )).
% 0.19/0.35 cnf(matrix-9, plain, ( ( set_union2(_u3, _u2) = set_union2(_u2, _u3)) )).
% 0.19/0.35 cnf(matrix-10, plain, ( empty(_u5) | ~empty(set_union2(_u5, _u4)) )).
% 0.19/0.35 cnf(matrix-11, plain, ( empty(_u7) | ~empty(set_union2(_u6, _u7)) )).
% 0.19/0.35 cnf(matrix-12, plain, ( ( set_union2(_u9, _u9) = _u9) )).
% 0.19/0.35 cnf(matrix-13, plain, ( empty(skolem1) )).
% 0.19/0.35 cnf(matrix-14, plain, ( ~empty(skolem2) )).
% 0.19/0.35 cnf(matrix-15, plain, ( ( cartesian_product2(set_union2(_u19, _u17), _u15) = set_union2(cartesian_product2(_u19, _u15), cartesian_product2(_u17, _u15))) )).
% 0.19/0.35 cnf(matrix-16, plain, ( ( cartesian_product2(_u16, set_union2(_u20, _u18)) = set_union2(cartesian_product2(_u16, _u20), cartesian_product2(_u16, _u18))) )).
% 0.19/0.35 cnf(matrix-17, plain, ( ( cartesian_product2(unordered_pair(skolem3, skolem4), skolem5) != set_union2(cartesian_product2(singleton(skolem3), skolem5), cartesian_product2(singleton(skolem4), skolem5))) | ( cartesian_product2(skolem5, unordered_pair(skolem3, skolem4)) != set_union2(cartesian_product2(skolem5, singleton(skolem3)), cartesian_product2(skolem5, singleton(skolem4)))) )).
% 0.19/0.35 cnf(matrix-18, plain, ( ( unordered_pair(_u25, _u24) = set_union2(singleton(_u25), singleton(_u24))) )).
% 0.19/0.35
% 0.19/0.35 % Proof stack:
% 0.19/0.35 cnf(proof-stack, plain,
% 0.19/0.35 proof_stack(
% 0.19/0.35 start(17),
% 0.19/0.35 left_branch(0, 2, 2, 2),
% 0.19/0.35 left_branch(0, 5, 2, 3),
% 0.19/0.35 left_branch(0, 18, 0, 4),
% 0.19/0.35 right_branch(4),
% 0.19/0.35 left_branch(0, 0, 0, 5),
% 0.19/0.35 right_branch(5),
% 0.19/0.35 right_branch(3),
% 0.19/0.35 left_branch(0, 15, 0, 4),
% 0.19/0.35 right_branch(4),
% 0.19/0.35 right_branch(2),
% 0.19/0.35 left_branch(0, 2, 2, 3),
% 0.19/0.35 left_branch(0, 5, 2, 4),
% 0.19/0.35 left_branch(0, 0, 0, 5),
% 0.19/0.35 right_branch(5),
% 0.19/0.35 left_branch(0, 18, 0, 6),
% 0.19/0.35 right_branch(6),
% 0.19/0.35 right_branch(4),
% 0.19/0.35 left_branch(0, 16, 0, 5),
% 0.19/0.35 right_branch(5),
% 0.19/0.35 right_branch(3)
% 0.19/0.35 )).
% 0.19/0.35 % SZS output end Proof for theBenchmark
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