TSTP Solution File: SET964+1 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SET964+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 : n012.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 36.13s 36.38s
% Output : Proof 36.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET964+1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.12 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Mar 20 21:36:00 EDT 2024
% 0.12/0.33 % CPUTime :
% 36.13/36.38 % SZS status Theorem for theBenchmark
% 36.13/36.38 % SZS output start Proof for theBenchmark
% 36.13/36.38
% 36.13/36.38 % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 36.13/36.38 cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 36.13/36.38
% 36.13/36.38 % Formula: commutativity_k2_tarski ( axiom ) converted to clauses:
% 36.13/36.38 cnf(commutativity_k2_tarski-1, axiom, ( ( unordered_pair(_u3, _u2) = unordered_pair(_u2, _u3)) )).
% 36.13/36.38
% 36.13/36.38 % Formula: d1_xboole_0 ( axiom ) converted to clauses:
% 36.13/36.38 cnf(d1_xboole_0-1, axiom, ( ( _u7 != empty_set) | ~in(_u4, _u7) )).
% 36.13/36.38 cnf(d1_xboole_0-2, axiom, ( in(skolem1(_u8), _u8) | ( _u8 = empty_set) )).
% 36.13/36.38
% 36.13/36.38 % Formula: d2_zfmisc_1 ( axiom ) converted to clauses:
% 36.13/36.38 cnf(d2_zfmisc_1-1, axiom, ( ( _u26 != cartesian_product2(_u30, _u28)) | ~in(_u22, _u26) | in(skolem2(_u30, _u28, _u26, _u22), _u30) )).
% 36.13/36.38 cnf(d2_zfmisc_1-2, axiom, ( ( _u26 != cartesian_product2(_u30, _u28)) | ~in(_u22, _u26) | in(skolem3(_u30, _u28, _u26, _u22), _u28) )).
% 36.13/36.38 cnf(d2_zfmisc_1-3, axiom, ( ( _u26 != cartesian_product2(_u30, _u28)) | ~in(_u22, _u26) | ( _u22 = ordered_pair(skolem2(_u30, _u28, _u26, _u22), skolem3(_u30, _u28, _u26, _u22))) )).
% 36.13/36.38 cnf(d2_zfmisc_1-4, axiom, ( ( _u26 != cartesian_product2(_u30, _u28)) | ~in(_u12, _u30) | ~in(_u11, _u28) | ( _u23 != ordered_pair(_u12, _u11)) | in(_u23, _u26) )).
% 36.13/36.38 cnf(d2_zfmisc_1-5, axiom, ( ( _u27 = cartesian_product2(_u31, _u29)) | in(skolem4(_u31, _u29, _u27), _u27) | in(skolem6(_u31, _u29, _u27), _u31) )).
% 36.13/36.38 cnf(d2_zfmisc_1-6, axiom, ( ( _u27 = cartesian_product2(_u31, _u29)) | in(skolem4(_u31, _u29, _u27), _u27) | in(skolem7(_u31, _u29, _u27), _u29) )).
% 36.13/36.38 cnf(d2_zfmisc_1-7, axiom, ( ( _u27 = cartesian_product2(_u31, _u29)) | in(skolem4(_u31, _u29, _u27), _u27) | ( skolem5(_u31, _u29, _u27) = ordered_pair(skolem6(_u31, _u29, _u27), skolem7(_u31, _u29, _u27))) )).
% 36.13/36.38 cnf(d2_zfmisc_1-8, axiom, ( ( _u27 = cartesian_product2(_u31, _u29)) | in(skolem4(_u31, _u29, _u27), _u27) | ~in(skolem5(_u31, _u29, _u27), _u27) )).
% 36.13/36.38 cnf(d2_zfmisc_1-9, axiom, ( ( _u27 = cartesian_product2(_u31, _u29)) | ~in(_u15, _u31) | ~in(_u14, _u29) | ( skolem4(_u31, _u29, _u27) != ordered_pair(_u15, _u14)) | in(skolem6(_u31, _u29, _u27), _u31) )).
% 36.13/36.38 cnf(d2_zfmisc_1-10, axiom, ( ( _u27 = cartesian_product2(_u31, _u29)) | ~in(_u15, _u31) | ~in(_u14, _u29) | ( skolem4(_u31, _u29, _u27) != ordered_pair(_u15, _u14)) | in(skolem7(_u31, _u29, _u27), _u29) )).
% 36.13/36.38 cnf(d2_zfmisc_1-11, axiom, ( ( _u27 = cartesian_product2(_u31, _u29)) | ~in(_u15, _u31) | ~in(_u14, _u29) | ( skolem4(_u31, _u29, _u27) != ordered_pair(_u15, _u14)) | ( skolem5(_u31, _u29, _u27) = ordered_pair(skolem6(_u31, _u29, _u27), skolem7(_u31, _u29, _u27))) )).
% 36.13/36.38 cnf(d2_zfmisc_1-12, axiom, ( ( _u27 = cartesian_product2(_u31, _u29)) | ~in(_u15, _u31) | ~in(_u14, _u29) | ( skolem4(_u31, _u29, _u27) != ordered_pair(_u15, _u14)) | ~in(skolem5(_u31, _u29, _u27), _u27) )).
% 36.13/36.38
% 36.13/36.38 % Formula: d3_tarski ( axiom ) converted to clauses:
% 36.13/36.38 cnf(d3_tarski-1, axiom, ( ~subset(_u38, _u36) | ~in(_u32, _u38) | in(_u32, _u36) )).
% 36.13/36.38 cnf(d3_tarski-2, axiom, ( subset(_u39, _u37) | in(skolem8(_u39, _u37), _u39) )).
% 36.13/36.38 cnf(d3_tarski-3, axiom, ( subset(_u39, _u37) | ~in(skolem8(_u39, _u37), _u37) )).
% 36.13/36.38
% 36.13/36.38 % Formula: d5_tarski ( axiom ) converted to clauses:
% 36.13/36.38 cnf(d5_tarski-1, axiom, ( ( ordered_pair(_u41, _u40) = unordered_pair(unordered_pair(_u41, _u40), singleton(_u41))) )).
% 36.13/36.38
% 36.13/36.38 % Formula: fc1_xboole_0 ( axiom ) converted to clauses:
% 36.13/36.38 cnf(fc1_xboole_0-1, axiom, ( empty(empty_set) )).
% 36.13/36.38
% 36.13/36.38 % Formula: fc1_zfmisc_1 ( axiom ) converted to clauses:
% 36.13/36.38 cnf(fc1_zfmisc_1-1, axiom, ( ~empty(ordered_pair(_u43, _u42)) )).
% 36.13/36.38
% 36.13/36.38 % Formula: l55_zfmisc_1 ( axiom ) converted to clauses:
% 36.13/36.38 cnf(l55_zfmisc_1-1, axiom, ( ~in(ordered_pair(_u54, _u52), cartesian_product2(_u50, _u48)) | in(_u54, _u50) )).
% 36.13/36.38 cnf(l55_zfmisc_1-2, axiom, ( ~in(ordered_pair(_u54, _u52), cartesian_product2(_u50, _u48)) | in(_u52, _u48) )).
% 36.13/36.38 cnf(l55_zfmisc_1-3, axiom, ( ~in(_u55, _u51) | ~in(_u53, _u49) | in(ordered_pair(_u55, _u53), cartesian_product2(_u51, _u49)) )).
% 36.13/36.38
% 36.13/36.38 % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 36.13/36.38 cnf(rc1_xboole_0-1, axiom, ( empty(skolem9) )).
% 36.13/36.38
% 36.13/36.38 % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 36.13/36.38 cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem10) )).
% 36.13/36.38
% 36.13/36.38 % Formula: reflexivity_r1_tarski ( axiom ) converted to clauses:
% 36.13/36.38 cnf(reflexivity_r1_tarski-1, axiom, ( subset(_u59, _u59) )).
% 36.13/36.38
% 36.13/36.38 % Formula: t117_zfmisc_1 ( conjecture ) (definitionally) converted to clauses:
% 36.13/36.38 cnf(t117_zfmisc_1-1, negated_conjecture, ( ( skolem11 != empty_set) )).
% 36.13/36.38 cnf(t117_zfmisc_1-2, negated_conjecture, ( subset(cartesian_product2(skolem12, skolem11), cartesian_product2(skolem13, skolem11)) | subset(cartesian_product2(skolem11, skolem12), cartesian_product2(skolem11, skolem13)) )).
% 36.13/36.38 cnf(t117_zfmisc_1-3, negated_conjecture, ( ~subset(skolem12, skolem13) )).
% 36.13/36.38
% 36.13/36.38 % Problem matrix:
% 36.13/36.38 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 36.13/36.38 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 36.13/36.38 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 36.13/36.38 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( unordered_pair(__eqx_0, __eqx_1) = unordered_pair(__eqy_0, __eqy_1)) )).
% 36.13/36.38 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( cartesian_product2(__eqx_0, __eqx_1) = cartesian_product2(__eqy_0, __eqy_1)) )).
% 36.13/36.38 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( ordered_pair(__eqx_0, __eqx_1) = ordered_pair(__eqy_0, __eqy_1)) )).
% 36.13/36.38 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( singleton(__eqx_0) = singleton(__eqy_0)) )).
% 36.13/36.38 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( skolem1(__eqx_0) = skolem1(__eqy_0)) )).
% 36.13/36.38 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( skolem2(__eqx_0, __eqx_1, __eqx_2, __eqx_3) = skolem2(__eqy_0, __eqy_1, __eqy_2, __eqy_3)) )).
% 36.13/36.38 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( skolem3(__eqx_0, __eqx_1, __eqx_2, __eqx_3) = skolem3(__eqy_0, __eqy_1, __eqy_2, __eqy_3)) )).
% 36.13/36.38 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem4(__eqx_0, __eqx_1, __eqx_2) = skolem4(__eqy_0, __eqy_1, __eqy_2)) )).
% 36.13/36.38 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem5(__eqx_0, __eqx_1, __eqx_2) = skolem5(__eqy_0, __eqy_1, __eqy_2)) )).
% 36.13/36.38 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem6(__eqx_0, __eqx_1, __eqx_2) = skolem6(__eqy_0, __eqy_1, __eqy_2)) )).
% 36.13/36.38 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem7(__eqx_0, __eqx_1, __eqx_2) = skolem7(__eqy_0, __eqy_1, __eqy_2)) )).
% 36.13/36.38 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem8(__eqx_0, __eqx_1) = skolem8(__eqy_0, __eqy_1)) )).
% 36.13/36.38 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 36.13/36.38 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 36.13/36.38 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 36.13/36.38 cnf(matrix-18, plain, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 36.13/36.38 cnf(matrix-19, plain, ( ( unordered_pair(_u3, _u2) = unordered_pair(_u2, _u3)) )).
% 36.13/36.38 cnf(matrix-20, plain, ( ( _u7 != empty_set) | ~in(_u4, _u7) )).
% 36.13/36.38 cnf(matrix-21, plain, ( in(skolem1(_u8), _u8) | ( _u8 = empty_set) )).
% 36.13/36.38 cnf(matrix-22, plain, ( ( _u26 != cartesian_product2(_u30, _u28)) | ~in(_u22, _u26) | in(skolem2(_u30, _u28, _u26, _u22), _u30) )).
% 36.13/36.38 cnf(matrix-23, plain, ( ( _u26 != cartesian_product2(_u30, _u28)) | ~in(_u22, _u26) | in(skolem3(_u30, _u28, _u26, _u22), _u28) )).
% 36.13/36.38 cnf(matrix-24, plain, ( ( _u26 != cartesian_product2(_u30, _u28)) | ~in(_u22, _u26) | ( _u22 = ordered_pair(skolem2(_u30, _u28, _u26, _u22), skolem3(_u30, _u28, _u26, _u22))) )).
% 36.13/36.38 cnf(matrix-25, plain, ( ( _u26 != cartesian_product2(_u30, _u28)) | ~in(_u12, _u30) | ~in(_u11, _u28) | ( _u23 != ordered_pair(_u12, _u11)) | in(_u23, _u26) )).
% 36.13/36.38 cnf(matrix-26, plain, ( ( _u27 = cartesian_product2(_u31, _u29)) | in(skolem4(_u31, _u29, _u27), _u27) | in(skolem6(_u31, _u29, _u27), _u31) )).
% 36.13/36.38 cnf(matrix-27, plain, ( ( _u27 = cartesian_product2(_u31, _u29)) | in(skolem4(_u31, _u29, _u27), _u27) | in(skolem7(_u31, _u29, _u27), _u29) )).
% 36.13/36.38 cnf(matrix-28, plain, ( ( _u27 = cartesian_product2(_u31, _u29)) | in(skolem4(_u31, _u29, _u27), _u27) | ( skolem5(_u31, _u29, _u27) = ordered_pair(skolem6(_u31, _u29, _u27), skolem7(_u31, _u29, _u27))) )).
% 36.13/36.38 cnf(matrix-29, plain, ( ( _u27 = cartesian_product2(_u31, _u29)) | in(skolem4(_u31, _u29, _u27), _u27) | ~in(skolem5(_u31, _u29, _u27), _u27) )).
% 36.13/36.38 cnf(matrix-30, plain, ( ( _u27 = cartesian_product2(_u31, _u29)) | ~in(_u15, _u31) | ~in(_u14, _u29) | ( skolem4(_u31, _u29, _u27) != ordered_pair(_u15, _u14)) | in(skolem6(_u31, _u29, _u27), _u31) )).
% 36.13/36.38 cnf(matrix-31, plain, ( ( _u27 = cartesian_product2(_u31, _u29)) | ~in(_u15, _u31) | ~in(_u14, _u29) | ( skolem4(_u31, _u29, _u27) != ordered_pair(_u15, _u14)) | in(skolem7(_u31, _u29, _u27), _u29) )).
% 36.13/36.38 cnf(matrix-32, plain, ( ( _u27 = cartesian_product2(_u31, _u29)) | ~in(_u15, _u31) | ~in(_u14, _u29) | ( skolem4(_u31, _u29, _u27) != ordered_pair(_u15, _u14)) | ( skolem5(_u31, _u29, _u27) = ordered_pair(skolem6(_u31, _u29, _u27), skolem7(_u31, _u29, _u27))) )).
% 36.13/36.38 cnf(matrix-33, plain, ( ( _u27 = cartesian_product2(_u31, _u29)) | ~in(_u15, _u31) | ~in(_u14, _u29) | ( skolem4(_u31, _u29, _u27) != ordered_pair(_u15, _u14)) | ~in(skolem5(_u31, _u29, _u27), _u27) )).
% 36.13/36.38 cnf(matrix-34, plain, ( ~subset(_u38, _u36) | ~in(_u32, _u38) | in(_u32, _u36) )).
% 36.13/36.38 cnf(matrix-35, plain, ( subset(_u39, _u37) | in(skolem8(_u39, _u37), _u39) )).
% 36.13/36.38 cnf(matrix-36, plain, ( subset(_u39, _u37) | ~in(skolem8(_u39, _u37), _u37) )).
% 36.13/36.38 cnf(matrix-37, plain, ( ( ordered_pair(_u41, _u40) = unordered_pair(unordered_pair(_u41, _u40), singleton(_u41))) )).
% 36.13/36.38 cnf(matrix-38, plain, ( empty(empty_set) )).
% 36.13/36.38 cnf(matrix-39, plain, ( ~empty(ordered_pair(_u43, _u42)) )).
% 36.13/36.38 cnf(matrix-40, plain, ( ~in(ordered_pair(_u54, _u52), cartesian_product2(_u50, _u48)) | in(_u54, _u50) )).
% 36.13/36.38 cnf(matrix-41, plain, ( ~in(ordered_pair(_u54, _u52), cartesian_product2(_u50, _u48)) | in(_u52, _u48) )).
% 36.13/36.38 cnf(matrix-42, plain, ( ~in(_u55, _u51) | ~in(_u53, _u49) | in(ordered_pair(_u55, _u53), cartesian_product2(_u51, _u49)) )).
% 36.13/36.38 cnf(matrix-43, plain, ( empty(skolem9) )).
% 36.13/36.38 cnf(matrix-44, plain, ( ~empty(skolem10) )).
% 36.13/36.38 cnf(matrix-45, plain, ( subset(_u59, _u59) )).
% 36.13/36.38 cnf(matrix-46, plain, ( ( skolem11 != empty_set) )).
% 36.13/36.38 cnf(matrix-47, plain, ( subset(cartesian_product2(skolem12, skolem11), cartesian_product2(skolem13, skolem11)) | subset(cartesian_product2(skolem11, skolem12), cartesian_product2(skolem11, skolem13)) )).
% 36.13/36.38 cnf(matrix-48, plain, ( ~subset(skolem12, skolem13) )).
% 36.13/36.38
% 36.13/36.38 % Proof stack:
% 36.13/36.38 cnf(proof-stack, plain,
% 36.13/36.38 proof_stack(
% 36.13/36.38 start(47),
% 36.13/36.38 left_branch(0, 34, 0, 2),
% 36.13/36.38 left_branch(0, 42, 0, 3),
% 36.13/36.38 left_branch(0, 41, 0, 4),
% 36.13/36.38 left_branch(0, 36, 1, 5),
% 36.13/36.38 left_branch(0, 48, 0, 6),
% 36.13/36.38 right_branch(6),
% 36.13/36.38 right_branch(5),
% 36.13/36.38 right_branch(4),
% 36.13/36.38 left_branch(0, 40, 1, 5),
% 36.13/36.38 reduction(0, 1),
% 36.13/36.38 right_branch(5),
% 36.13/36.38 right_branch(3),
% 36.13/36.38 left_branch(0, 42, 2, 4),
% 36.13/36.38 left_branch(0, 35, 1, 5),
% 36.13/36.38 left_branch(0, 48, 0, 6),
% 36.13/36.38 right_branch(6),
% 36.13/36.38 right_branch(5),
% 36.13/36.38 left_branch(0, 21, 0, 6),
% 36.13/36.38 left_branch(0, 46, 0, 7),
% 36.13/36.38 right_branch(7),
% 36.13/36.38 right_branch(6),
% 36.13/36.38 right_branch(4),
% 36.13/36.38 right_branch(2),
% 36.13/36.38 left_branch(0, 34, 0, 3),
% 36.13/36.38 left_branch(0, 42, 0, 4),
% 36.13/36.38 left_branch(0, 41, 0, 5),
% 36.13/36.38 left_branch(0, 36, 1, 6),
% 36.13/36.38 left_branch(0, 48, 0, 7),
% 36.13/36.38 right_branch(7),
% 36.13/36.38 right_branch(6),
% 36.13/36.38 right_branch(5),
% 36.13/36.38 left_branch(0, 41, 1, 6),
% 36.13/36.38 reduction(0, 1),
% 36.13/36.38 right_branch(6),
% 36.13/36.38 right_branch(4),
% 36.13/36.38 left_branch(0, 42, 2, 5),
% 36.13/36.38 left_branch(0, 21, 0, 6),
% 36.13/36.38 left_branch(0, 46, 0, 7),
% 36.13/36.38 right_branch(7),
% 36.13/36.38 right_branch(6),
% 36.13/36.38 left_branch(0, 35, 1, 7),
% 36.13/36.38 left_branch(0, 48, 0, 8),
% 36.13/36.38 right_branch(8),
% 36.13/36.38 right_branch(7),
% 36.13/36.38 right_branch(5),
% 36.13/36.38 right_branch(3)
% 36.13/36.38 )).
% 36.13/36.38 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------