TSTP Solution File: SET975+1 by ConnectPP---0.3.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SET975+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 : n031.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 14:32:54 EDT 2024
% Result : Theorem 1.76s 1.92s
% Output : Proof 1.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET975+1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.14/0.34 % Computer : n031.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Mar 20 22:25:03 EDT 2024
% 0.14/0.35 % CPUTime :
% 1.76/1.92 % SZS status Theorem for theBenchmark
% 1.76/1.92 % SZS output start Proof for theBenchmark
% 1.76/1.92
% 1.76/1.92 % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 1.76/1.92 cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 1.76/1.92
% 1.76/1.92 % Formula: commutativity_k2_tarski ( axiom ) converted to clauses:
% 1.76/1.92 cnf(commutativity_k2_tarski-1, axiom, ( ( unordered_pair(_u3, _u2) = unordered_pair(_u2, _u3)) )).
% 1.76/1.92
% 1.76/1.92 % Formula: d1_tarski ( axiom ) converted to clauses:
% 1.76/1.92 cnf(d1_tarski-1, axiom, ( ( _u12 != singleton(_u14)) | ~in(_u8, _u12) | ( _u8 = _u14) )).
% 1.76/1.92 cnf(d1_tarski-2, axiom, ( ( _u12 != singleton(_u14)) | ( _u9 != _u14) | in(_u9, _u12) )).
% 1.76/1.92 cnf(d1_tarski-3, axiom, ( ( _u13 = singleton(_u15)) | in(skolem1(_u15, _u13), _u13) | ( skolem2(_u15, _u13) = _u15) )).
% 1.76/1.92 cnf(d1_tarski-4, axiom, ( ( _u13 = singleton(_u15)) | in(skolem1(_u15, _u13), _u13) | ~in(skolem2(_u15, _u13), _u13) )).
% 1.76/1.92 cnf(d1_tarski-5, axiom, ( ( _u13 = singleton(_u15)) | ( skolem1(_u15, _u13) != _u15) | ( skolem2(_u15, _u13) = _u15) )).
% 1.76/1.92 cnf(d1_tarski-6, axiom, ( ( _u13 = singleton(_u15)) | ( skolem1(_u15, _u13) != _u15) | ~in(skolem2(_u15, _u13), _u13) )).
% 1.76/1.92
% 1.76/1.92 % Formula: d5_tarski ( axiom ) converted to clauses:
% 1.76/1.92 cnf(d5_tarski-1, axiom, ( ( ordered_pair(_u17, _u16) = unordered_pair(unordered_pair(_u17, _u16), singleton(_u17))) )).
% 1.76/1.92
% 1.76/1.92 % Formula: fc1_zfmisc_1 ( axiom ) converted to clauses:
% 1.76/1.92 cnf(fc1_zfmisc_1-1, axiom, ( ~empty(ordered_pair(_u19, _u18)) )).
% 1.76/1.92
% 1.76/1.92 % Formula: l55_zfmisc_1 ( axiom ) converted to clauses:
% 1.76/1.92 cnf(l55_zfmisc_1-1, axiom, ( ~in(ordered_pair(_u30, _u28), cartesian_product2(_u26, _u24)) | in(_u30, _u26) )).
% 1.76/1.92 cnf(l55_zfmisc_1-2, axiom, ( ~in(ordered_pair(_u30, _u28), cartesian_product2(_u26, _u24)) | in(_u28, _u24) )).
% 1.76/1.92 cnf(l55_zfmisc_1-3, axiom, ( ~in(_u31, _u27) | ~in(_u29, _u25) | in(ordered_pair(_u31, _u29), cartesian_product2(_u27, _u25)) )).
% 1.76/1.92
% 1.76/1.92 % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 1.76/1.92 cnf(rc1_xboole_0-1, axiom, ( empty(skolem3) )).
% 1.76/1.92
% 1.76/1.92 % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 1.76/1.92 cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem4) )).
% 1.76/1.92
% 1.76/1.92 % Formula: t128_zfmisc_1 ( conjecture ) (definitionally) converted to clauses:
% 1.76/1.92 cnf(t128_zfmisc_1-1, negated_conjecture, ( ~_def0 | ~_def1 )).
% 1.76/1.92 cnf(t128_zfmisc_1-2, negated_conjecture, ( _def0 | in(ordered_pair(skolem5, skolem6), cartesian_product2(singleton(skolem7), skolem8)) )).
% 1.76/1.92 cnf(t128_zfmisc_1-3, negated_conjecture, ( _def0 | ( skolem5 != skolem7) | ~in(skolem6, skolem8) )).
% 1.76/1.92 cnf(t128_zfmisc_1-4, negated_conjecture, ( _def1 | ( skolem5 = skolem7) )).
% 1.76/1.92 cnf(t128_zfmisc_1-5, negated_conjecture, ( _def1 | in(skolem6, skolem8) )).
% 1.76/1.92 cnf(t128_zfmisc_1-6, negated_conjecture, ( _def1 | ~in(ordered_pair(skolem5, skolem6), cartesian_product2(singleton(skolem7), skolem8)) )).
% 1.76/1.92
% 1.76/1.92 % Problem matrix:
% 1.76/1.92 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 1.76/1.92 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 1.76/1.92 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 1.76/1.92 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( unordered_pair(__eqx_0, __eqx_1) = unordered_pair(__eqy_0, __eqy_1)) )).
% 1.76/1.92 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( singleton(__eqx_0) = singleton(__eqy_0)) )).
% 1.76/1.92 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( ordered_pair(__eqx_0, __eqx_1) = ordered_pair(__eqy_0, __eqy_1)) )).
% 1.76/1.92 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( cartesian_product2(__eqx_0, __eqx_1) = cartesian_product2(__eqy_0, __eqy_1)) )).
% 1.76/1.92 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem1(__eqx_0, __eqx_1) = skolem1(__eqy_0, __eqy_1)) )).
% 1.76/1.92 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem2(__eqx_0, __eqx_1) = skolem2(__eqy_0, __eqy_1)) )).
% 1.76/1.92 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 1.76/1.92 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 1.76/1.92 cnf(matrix-11, plain, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 1.76/1.92 cnf(matrix-12, plain, ( ( unordered_pair(_u3, _u2) = unordered_pair(_u2, _u3)) )).
% 1.76/1.92 cnf(matrix-13, plain, ( ( _u12 != singleton(_u14)) | ~in(_u8, _u12) | ( _u8 = _u14) )).
% 1.76/1.92 cnf(matrix-14, plain, ( ( _u12 != singleton(_u14)) | ( _u9 != _u14) | in(_u9, _u12) )).
% 1.76/1.92 cnf(matrix-15, plain, ( ( _u13 = singleton(_u15)) | in(skolem1(_u15, _u13), _u13) | ( skolem2(_u15, _u13) = _u15) )).
% 1.76/1.92 cnf(matrix-16, plain, ( ( _u13 = singleton(_u15)) | in(skolem1(_u15, _u13), _u13) | ~in(skolem2(_u15, _u13), _u13) )).
% 1.76/1.92 cnf(matrix-17, plain, ( ( _u13 = singleton(_u15)) | ( skolem1(_u15, _u13) != _u15) | ( skolem2(_u15, _u13) = _u15) )).
% 1.76/1.92 cnf(matrix-18, plain, ( ( _u13 = singleton(_u15)) | ( skolem1(_u15, _u13) != _u15) | ~in(skolem2(_u15, _u13), _u13) )).
% 1.76/1.92 cnf(matrix-19, plain, ( ( ordered_pair(_u17, _u16) = unordered_pair(unordered_pair(_u17, _u16), singleton(_u17))) )).
% 1.76/1.92 cnf(matrix-20, plain, ( ~empty(ordered_pair(_u19, _u18)) )).
% 1.76/1.92 cnf(matrix-21, plain, ( ~in(ordered_pair(_u30, _u28), cartesian_product2(_u26, _u24)) | in(_u30, _u26) )).
% 1.76/1.92 cnf(matrix-22, plain, ( ~in(ordered_pair(_u30, _u28), cartesian_product2(_u26, _u24)) | in(_u28, _u24) )).
% 1.76/1.92 cnf(matrix-23, plain, ( ~in(_u31, _u27) | ~in(_u29, _u25) | in(ordered_pair(_u31, _u29), cartesian_product2(_u27, _u25)) )).
% 1.76/1.92 cnf(matrix-24, plain, ( empty(skolem3) )).
% 1.76/1.92 cnf(matrix-25, plain, ( ~empty(skolem4) )).
% 1.76/1.92 cnf(matrix-26, plain, ( ~_def0 | ~_def1 )).
% 1.76/1.92 cnf(matrix-27, plain, ( _def0 | in(ordered_pair(skolem5, skolem6), cartesian_product2(singleton(skolem7), skolem8)) )).
% 1.76/1.92 cnf(matrix-28, plain, ( _def0 | ( skolem5 != skolem7) | ~in(skolem6, skolem8) )).
% 1.76/1.92 cnf(matrix-29, plain, ( _def1 | ( skolem5 = skolem7) )).
% 1.76/1.92 cnf(matrix-30, plain, ( _def1 | in(skolem6, skolem8) )).
% 1.76/1.92 cnf(matrix-31, plain, ( _def1 | ~in(ordered_pair(skolem5, skolem6), cartesian_product2(singleton(skolem7), skolem8)) )).
% 1.76/1.92
% 1.76/1.92 % Proof stack:
% 1.76/1.92 cnf(proof-stack, plain,
% 1.76/1.92 proof_stack(
% 1.76/1.92 start(26),
% 1.76/1.92 left_branch(0, 28, 0, 2),
% 1.76/1.92 left_branch(0, 22, 1, 3),
% 1.76/1.92 left_branch(0, 27, 1, 4),
% 1.76/1.92 reduction(0, 0),
% 1.76/1.92 right_branch(4),
% 1.76/1.92 right_branch(3),
% 1.76/1.92 left_branch(0, 13, 2, 4),
% 1.76/1.92 left_branch(0, 4, 1, 5),
% 1.76/1.92 left_branch(0, 1, 1, 6),
% 1.76/1.92 left_branch(0, 0, 0, 7),
% 1.76/1.92 right_branch(7),
% 1.76/1.92 right_branch(6),
% 1.76/1.92 right_branch(5),
% 1.76/1.92 left_branch(0, 21, 1, 6),
% 1.76/1.92 left_branch(0, 27, 1, 7),
% 1.76/1.92 reduction(0, 0),
% 1.76/1.92 right_branch(7),
% 1.76/1.92 right_branch(6),
% 1.76/1.92 right_branch(4),
% 1.76/1.92 right_branch(2),
% 1.76/1.92 left_branch(0, 31, 0, 3),
% 1.76/1.92 left_branch(0, 23, 2, 4),
% 1.76/1.92 left_branch(0, 14, 2, 5),
% 1.76/1.92 left_branch(0, 4, 1, 6),
% 1.76/1.92 left_branch(0, 0, 0, 7),
% 1.76/1.92 right_branch(7),
% 1.76/1.92 right_branch(6),
% 1.76/1.92 left_branch(0, 29, 1, 7),
% 1.76/1.92 reduction(0, 0),
% 1.76/1.92 right_branch(7),
% 1.76/1.92 right_branch(5),
% 1.76/1.92 left_branch(0, 30, 1, 6),
% 1.76/1.92 reduction(0, 0),
% 1.76/1.92 right_branch(6),
% 1.76/1.92 right_branch(4),
% 1.76/1.92 right_branch(3)
% 1.76/1.92 )).
% 1.76/1.92 % SZS output end Proof for theBenchmark
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