TSTP Solution File: LAT381+3 by ConnectPP---0.2.2
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%------------------------------------------------------------------------------
% File : ConnectPP---0.2.2
% Problem : LAT381+3 : TPTP v8.1.2. Released v4.0.0.
% 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 : Wed Mar 6 09:08:51 EST 2024
% Result : Theorem 2.95s 3.12s
% Output : Proof 2.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : LAT381+3 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Mar 3 11:24:48 EST 2024
% 0.14/0.35 % CPUTime :
% 2.95/3.12 % SZS status Theorem for theBenchmark
% 2.95/3.12 % SZS output start Proof for theBenchmark
% 2.95/3.12
% 2.95/3.12 % Formula: mSetSort ( axiom ) converted to clauses:
% 2.95/3.12
% 2.95/3.12 % Formula: mElmSort ( axiom ) converted to clauses:
% 2.95/3.12
% 2.95/3.12 % Formula: mEOfElem ( axiom ) converted to clauses:
% 2.95/3.12 cnf(mEOfElem-1, axiom, ( ~aSet0(_u3) | ~aElementOf0(_u2, _u3) | aElement0(_u2) )).
% 2.95/3.12
% 2.95/3.12 % Formula: mDefEmpty ( definition ) converted to clauses:
% 2.95/3.12 cnf(mDefEmpty-1, definition, ( ~aSet0(_u6) | ~isEmpty0(_u6) | ~aElementOf0(_u4, _u6) )).
% 2.95/3.12 cnf(mDefEmpty-2, definition, ( ~aSet0(_u6) | aElementOf0(skolem1(_u6), _u6) | isEmpty0(_u6) )).
% 2.95/3.12
% 2.95/3.12 % Formula: mDefSub ( definition ) converted to clauses:
% 2.95/3.12 cnf(mDefSub-1, definition, ( ~aSet0(_u10) | ~aSubsetOf0(_u11, _u10) | aSet0(_u11) )).
% 2.95/3.12 cnf(mDefSub-2, definition, ( ~aSet0(_u10) | ~aSubsetOf0(_u11, _u10) | ~aElementOf0(_u7, _u11) | aElementOf0(_u7, _u10) )).
% 2.95/3.12 cnf(mDefSub-3, definition, ( ~aSet0(_u10) | aSubsetOf0(_u12, _u10) | ~aSet0(_u12) | aElementOf0(skolem2(_u10, _u12), _u12) )).
% 2.95/3.12 cnf(mDefSub-4, definition, ( ~aSet0(_u10) | aSubsetOf0(_u12, _u10) | ~aSet0(_u12) | ~aElementOf0(skolem2(_u10, _u12), _u10) )).
% 2.95/3.12
% 2.95/3.12 % Formula: mLessRel ( axiom ) converted to clauses:
% 2.95/3.12
% 2.95/3.12 % Formula: mARefl ( axiom ) converted to clauses:
% 2.95/3.12 cnf(mARefl-1, axiom, ( ~aElement0(_u15) | sdtlseqdt0(_u15, _u15) )).
% 2.95/3.12
% 2.95/3.12 % Formula: mASymm ( axiom ) converted to clauses:
% 2.95/3.12 cnf(mASymm-1, axiom, ( ~aElement0(_u17) | ~aElement0(_u16) | ~sdtlseqdt0(_u17, _u16) | ~sdtlseqdt0(_u16, _u17) | ( _u17 = _u16) )).
% 2.95/3.12
% 2.95/3.12 % Formula: mTrans ( axiom ) converted to clauses:
% 2.95/3.12 cnf(mTrans-1, axiom, ( ~aElement0(_u20) | ~aElement0(_u19) | ~aElement0(_u18) | ~sdtlseqdt0(_u20, _u19) | ~sdtlseqdt0(_u19, _u18) | sdtlseqdt0(_u20, _u18) )).
% 2.95/3.12
% 2.95/3.12 % Formula: mDefLB ( definition ) converted to clauses:
% 2.95/3.12 cnf(mDefLB-1, definition, ( ~aSet0(_u25) | ~aSubsetOf0(_u24, _u25) | ~aLowerBoundOfIn0(_u26, _u24, _u25) | aElementOf0(_u26, _u25) )).
% 2.95/3.12 cnf(mDefLB-2, definition, ( ~aSet0(_u25) | ~aSubsetOf0(_u24, _u25) | ~aLowerBoundOfIn0(_u26, _u24, _u25) | ~aElementOf0(_u21, _u24) | sdtlseqdt0(_u26, _u21) )).
% 2.95/3.12 cnf(mDefLB-3, definition, ( ~aSet0(_u25) | ~aSubsetOf0(_u24, _u25) | aLowerBoundOfIn0(_u27, _u24, _u25) | ~aElementOf0(_u27, _u25) | aElementOf0(skolem3(_u25, _u24, _u27), _u24) )).
% 2.95/3.12 cnf(mDefLB-4, definition, ( ~aSet0(_u25) | ~aSubsetOf0(_u24, _u25) | aLowerBoundOfIn0(_u27, _u24, _u25) | ~aElementOf0(_u27, _u25) | ~sdtlseqdt0(_u27, skolem3(_u25, _u24, _u27)) )).
% 2.95/3.12
% 2.95/3.12 % Formula: mDefUB ( definition ) converted to clauses:
% 2.95/3.12 cnf(mDefUB-1, definition, ( ~aSet0(_u32) | ~aSubsetOf0(_u31, _u32) | ~aUpperBoundOfIn0(_u33, _u31, _u32) | aElementOf0(_u33, _u32) )).
% 2.95/3.12 cnf(mDefUB-2, definition, ( ~aSet0(_u32) | ~aSubsetOf0(_u31, _u32) | ~aUpperBoundOfIn0(_u33, _u31, _u32) | ~aElementOf0(_u28, _u31) | sdtlseqdt0(_u28, _u33) )).
% 2.95/3.12 cnf(mDefUB-3, definition, ( ~aSet0(_u32) | ~aSubsetOf0(_u31, _u32) | aUpperBoundOfIn0(_u34, _u31, _u32) | ~aElementOf0(_u34, _u32) | aElementOf0(skolem4(_u32, _u31, _u34), _u31) )).
% 2.95/3.12 cnf(mDefUB-4, definition, ( ~aSet0(_u32) | ~aSubsetOf0(_u31, _u32) | aUpperBoundOfIn0(_u34, _u31, _u32) | ~aElementOf0(_u34, _u32) | ~sdtlseqdt0(skolem4(_u32, _u31, _u34), _u34) )).
% 2.95/3.12
% 2.95/3.12 % Formula: mDefInf ( definition ) converted to clauses:
% 2.95/3.12 cnf(mDefInf-1, definition, ( ~aSet0(_u39) | ~aSubsetOf0(_u38, _u39) | ~aInfimumOfIn0(_u40, _u38, _u39) | aElementOf0(_u40, _u39) )).
% 2.95/3.12 cnf(mDefInf-2, definition, ( ~aSet0(_u39) | ~aSubsetOf0(_u38, _u39) | ~aInfimumOfIn0(_u40, _u38, _u39) | aLowerBoundOfIn0(_u40, _u38, _u39) )).
% 2.95/3.12 cnf(mDefInf-3, definition, ( ~aSet0(_u39) | ~aSubsetOf0(_u38, _u39) | ~aInfimumOfIn0(_u40, _u38, _u39) | ~aLowerBoundOfIn0(_u35, _u38, _u39) | sdtlseqdt0(_u35, _u40) )).
% 2.95/3.12 cnf(mDefInf-4, definition, ( ~aSet0(_u39) | ~aSubsetOf0(_u38, _u39) | aInfimumOfIn0(_u41, _u38, _u39) | ~aElementOf0(_u41, _u39) | ~aLowerBoundOfIn0(_u41, _u38, _u39) | aLowerBoundOfIn0(skolem5(_u39, _u38, _u41), _u38, _u39) )).
% 2.95/3.12 cnf(mDefInf-5, definition, ( ~aSet0(_u39) | ~aSubsetOf0(_u38, _u39) | aInfimumOfIn0(_u41, _u38, _u39) | ~aElementOf0(_u41, _u39) | ~aLowerBoundOfIn0(_u41, _u38, _u39) | ~sdtlseqdt0(skolem5(_u39, _u38, _u41), _u41) )).
% 2.95/3.12
% 2.95/3.12 % Formula: mDefSup ( definition ) converted to clauses:
% 2.95/3.12 cnf(mDefSup-1, definition, ( ~aSet0(_u46) | ~aSubsetOf0(_u45, _u46) | ~aSupremumOfIn0(_u47, _u45, _u46) | aElementOf0(_u47, _u46) )).
% 2.95/3.12 cnf(mDefSup-2, definition, ( ~aSet0(_u46) | ~aSubsetOf0(_u45, _u46) | ~aSupremumOfIn0(_u47, _u45, _u46) | aUpperBoundOfIn0(_u47, _u45, _u46) )).
% 2.95/3.12 cnf(mDefSup-3, definition, ( ~aSet0(_u46) | ~aSubsetOf0(_u45, _u46) | ~aSupremumOfIn0(_u47, _u45, _u46) | ~aUpperBoundOfIn0(_u42, _u45, _u46) | sdtlseqdt0(_u47, _u42) )).
% 2.95/3.12 cnf(mDefSup-4, definition, ( ~aSet0(_u46) | ~aSubsetOf0(_u45, _u46) | aSupremumOfIn0(_u48, _u45, _u46) | ~aElementOf0(_u48, _u46) | ~aUpperBoundOfIn0(_u48, _u45, _u46) | aUpperBoundOfIn0(skolem6(_u46, _u45, _u48), _u45, _u46) )).
% 2.95/3.12 cnf(mDefSup-5, definition, ( ~aSet0(_u46) | ~aSubsetOf0(_u45, _u46) | aSupremumOfIn0(_u48, _u45, _u46) | ~aElementOf0(_u48, _u46) | ~aUpperBoundOfIn0(_u48, _u45, _u46) | ~sdtlseqdt0(_u48, skolem6(_u46, _u45, _u48)) )).
% 2.95/3.12
% 2.95/3.12 % Formula: m__725 ( hypothesis ) converted to clauses:
% 2.95/3.12 cnf(m__725-1, hypothesis, ( aSet0(xT) )).
% 2.95/3.12
% 2.95/3.12 % Formula: m__725_01 ( hypothesis ) converted to clauses:
% 2.95/3.12 cnf(m__725_01-1, hypothesis, ( aSet0(xS) )).
% 2.95/3.12 cnf(m__725_01-2, hypothesis, ( ~aElementOf0(_u49, xS) | aElementOf0(_u49, xT) )).
% 2.95/3.12 cnf(m__725_01-3, hypothesis, ( aSubsetOf0(xS, xT) )).
% 2.95/3.12
% 2.95/3.12 % Formula: m__744 ( hypothesis ) converted to clauses:
% 2.95/3.12 cnf(m__744-1, hypothesis, ( aElementOf0(xu, xT) )).
% 2.95/3.12 cnf(m__744-2, hypothesis, ( aElementOf0(xu, xT) )).
% 2.95/3.12 cnf(m__744-3, hypothesis, ( ~aElementOf0(_u50, xS) | sdtlseqdt0(_u50, xu) )).
% 2.95/3.12 cnf(m__744-4, hypothesis, ( aUpperBoundOfIn0(xu, xS, xT) )).
% 2.95/3.12 cnf(m__744-5, hypothesis, ( sdtlseqdt0(xu, _u52) | ~aElementOf0(_u52, xT) | aElementOf0(skolem7(_u52), xS) )).
% 2.95/3.12 cnf(m__744-6, hypothesis, ( sdtlseqdt0(xu, _u52) | ~aElementOf0(_u52, xT) | ~sdtlseqdt0(skolem7(_u52), _u52) )).
% 2.95/3.12 cnf(m__744-7, hypothesis, ( sdtlseqdt0(xu, _u52) | ~aUpperBoundOfIn0(_u52, xS, xT) )).
% 2.95/3.12 cnf(m__744-8, hypothesis, ( aSupremumOfIn0(xu, xS, xT) )).
% 2.95/3.12 cnf(m__744-9, hypothesis, ( aElementOf0(xv, xT) )).
% 2.95/3.12 cnf(m__744-10, hypothesis, ( aElementOf0(xv, xT) )).
% 2.95/3.12 cnf(m__744-11, hypothesis, ( ~aElementOf0(_u53, xS) | sdtlseqdt0(_u53, xv) )).
% 2.95/3.12 cnf(m__744-12, hypothesis, ( aUpperBoundOfIn0(xv, xS, xT) )).
% 2.95/3.12 cnf(m__744-13, hypothesis, ( sdtlseqdt0(xv, _u55) | ~aElementOf0(_u55, xT) | aElementOf0(skolem8(_u55), xS) )).
% 2.95/3.12 cnf(m__744-14, hypothesis, ( sdtlseqdt0(xv, _u55) | ~aElementOf0(_u55, xT) | ~sdtlseqdt0(skolem8(_u55), _u55) )).
% 2.95/3.12 cnf(m__744-15, hypothesis, ( sdtlseqdt0(xv, _u55) | ~aUpperBoundOfIn0(_u55, xS, xT) )).
% 2.95/3.12 cnf(m__744-16, hypothesis, ( aSupremumOfIn0(xv, xS, xT) )).
% 2.95/3.12
% 2.95/3.12 % Formula: m__ ( conjecture ) converted to clauses:
% 2.95/3.12 cnf(m__-1, negated_conjecture, ( ( xu != xv) )).
% 2.95/3.12
% 2.95/3.12 % Problem matrix:
% 2.95/3.12 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 2.95/3.12 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 2.95/3.12 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 2.95/3.12 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( skolem1(__eqx_0) = skolem1(__eqy_0)) )).
% 2.95/3.12 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem2(__eqx_0, __eqx_1) = skolem2(__eqy_0, __eqy_1)) )).
% 2.95/3.13 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem3(__eqx_0, __eqx_1, __eqx_2) = skolem3(__eqy_0, __eqy_1, __eqy_2)) )).
% 2.95/3.13 cnf(matrix-6, 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)) )).
% 2.95/3.13 cnf(matrix-7, 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)) )).
% 2.95/3.13 cnf(matrix-8, 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)) )).
% 2.95/3.13 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( skolem7(__eqx_0) = skolem7(__eqy_0)) )).
% 2.95/3.13 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( skolem8(__eqx_0) = skolem8(__eqy_0)) )).
% 2.95/3.13 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ~aSet0(__eqx_0) | aSet0(__eqy_0) )).
% 2.95/3.13 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ~aElement0(__eqx_0) | aElement0(__eqy_0) )).
% 2.95/3.13 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~aElementOf0(__eqx_0, __eqx_1) | aElementOf0(__eqy_0, __eqy_1) )).
% 2.95/3.13 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ~isEmpty0(__eqx_0) | isEmpty0(__eqy_0) )).
% 2.95/3.13 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~aSubsetOf0(__eqx_0, __eqx_1) | aSubsetOf0(__eqy_0, __eqy_1) )).
% 2.95/3.13 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~sdtlseqdt0(__eqx_0, __eqx_1) | sdtlseqdt0(__eqy_0, __eqy_1) )).
% 2.95/3.13 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~aLowerBoundOfIn0(__eqx_0, __eqx_1, __eqx_2) | aLowerBoundOfIn0(__eqy_0, __eqy_1, __eqy_2) )).
% 2.95/3.13 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~aUpperBoundOfIn0(__eqx_0, __eqx_1, __eqx_2) | aUpperBoundOfIn0(__eqy_0, __eqy_1, __eqy_2) )).
% 2.95/3.13 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~aInfimumOfIn0(__eqx_0, __eqx_1, __eqx_2) | aInfimumOfIn0(__eqy_0, __eqy_1, __eqy_2) )).
% 2.95/3.13 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~aSupremumOfIn0(__eqx_0, __eqx_1, __eqx_2) | aSupremumOfIn0(__eqy_0, __eqy_1, __eqy_2) )).
% 2.95/3.13 cnf(matrix-21, plain, ( ~aSet0(_u3) | ~aElementOf0(_u2, _u3) | aElement0(_u2) )).
% 2.95/3.13 cnf(matrix-22, plain, ( ~aSet0(_u6) | ~isEmpty0(_u6) | ~aElementOf0(_u4, _u6) )).
% 2.95/3.13 cnf(matrix-23, plain, ( ~aSet0(_u6) | aElementOf0(skolem1(_u6), _u6) | isEmpty0(_u6) )).
% 2.95/3.13 cnf(matrix-24, plain, ( ~aSet0(_u10) | ~aSubsetOf0(_u11, _u10) | aSet0(_u11) )).
% 2.95/3.13 cnf(matrix-25, plain, ( ~aSet0(_u10) | ~aSubsetOf0(_u11, _u10) | ~aElementOf0(_u7, _u11) | aElementOf0(_u7, _u10) )).
% 2.95/3.13 cnf(matrix-26, plain, ( ~aSet0(_u10) | aSubsetOf0(_u12, _u10) | ~aSet0(_u12) | aElementOf0(skolem2(_u10, _u12), _u12) )).
% 2.95/3.13 cnf(matrix-27, plain, ( ~aSet0(_u10) | aSubsetOf0(_u12, _u10) | ~aSet0(_u12) | ~aElementOf0(skolem2(_u10, _u12), _u10) )).
% 2.95/3.13 cnf(matrix-28, plain, ( ~aElement0(_u15) | sdtlseqdt0(_u15, _u15) )).
% 2.95/3.13 cnf(matrix-29, plain, ( ~aElement0(_u17) | ~aElement0(_u16) | ~sdtlseqdt0(_u17, _u16) | ~sdtlseqdt0(_u16, _u17) | ( _u17 = _u16) )).
% 2.95/3.13 cnf(matrix-30, plain, ( ~aElement0(_u20) | ~aElement0(_u19) | ~aElement0(_u18) | ~sdtlseqdt0(_u20, _u19) | ~sdtlseqdt0(_u19, _u18) | sdtlseqdt0(_u20, _u18) )).
% 2.95/3.13 cnf(matrix-31, plain, ( ~aSet0(_u25) | ~aSubsetOf0(_u24, _u25) | ~aLowerBoundOfIn0(_u26, _u24, _u25) | aElementOf0(_u26, _u25) )).
% 2.95/3.13 cnf(matrix-32, plain, ( ~aSet0(_u25) | ~aSubsetOf0(_u24, _u25) | ~aLowerBoundOfIn0(_u26, _u24, _u25) | ~aElementOf0(_u21, _u24) | sdtlseqdt0(_u26, _u21) )).
% 2.95/3.13 cnf(matrix-33, plain, ( ~aSet0(_u25) | ~aSubsetOf0(_u24, _u25) | aLowerBoundOfIn0(_u27, _u24, _u25) | ~aElementOf0(_u27, _u25) | aElementOf0(skolem3(_u25, _u24, _u27), _u24) )).
% 2.95/3.13 cnf(matrix-34, plain, ( ~aSet0(_u25) | ~aSubsetOf0(_u24, _u25) | aLowerBoundOfIn0(_u27, _u24, _u25) | ~aElementOf0(_u27, _u25) | ~sdtlseqdt0(_u27, skolem3(_u25, _u24, _u27)) )).
% 2.95/3.13 cnf(matrix-35, plain, ( ~aSet0(_u32) | ~aSubsetOf0(_u31, _u32) | ~aUpperBoundOfIn0(_u33, _u31, _u32) | aElementOf0(_u33, _u32) )).
% 2.95/3.13 cnf(matrix-36, plain, ( ~aSet0(_u32) | ~aSubsetOf0(_u31, _u32) | ~aUpperBoundOfIn0(_u33, _u31, _u32) | ~aElementOf0(_u28, _u31) | sdtlseqdt0(_u28, _u33) )).
% 2.95/3.13 cnf(matrix-37, plain, ( ~aSet0(_u32) | ~aSubsetOf0(_u31, _u32) | aUpperBoundOfIn0(_u34, _u31, _u32) | ~aElementOf0(_u34, _u32) | aElementOf0(skolem4(_u32, _u31, _u34), _u31) )).
% 2.95/3.13 cnf(matrix-38, plain, ( ~aSet0(_u32) | ~aSubsetOf0(_u31, _u32) | aUpperBoundOfIn0(_u34, _u31, _u32) | ~aElementOf0(_u34, _u32) | ~sdtlseqdt0(skolem4(_u32, _u31, _u34), _u34) )).
% 2.95/3.13 cnf(matrix-39, plain, ( ~aSet0(_u39) | ~aSubsetOf0(_u38, _u39) | ~aInfimumOfIn0(_u40, _u38, _u39) | aElementOf0(_u40, _u39) )).
% 2.95/3.13 cnf(matrix-40, plain, ( ~aSet0(_u39) | ~aSubsetOf0(_u38, _u39) | ~aInfimumOfIn0(_u40, _u38, _u39) | aLowerBoundOfIn0(_u40, _u38, _u39) )).
% 2.95/3.13 cnf(matrix-41, plain, ( ~aSet0(_u39) | ~aSubsetOf0(_u38, _u39) | ~aInfimumOfIn0(_u40, _u38, _u39) | ~aLowerBoundOfIn0(_u35, _u38, _u39) | sdtlseqdt0(_u35, _u40) )).
% 2.95/3.13 cnf(matrix-42, plain, ( ~aSet0(_u39) | ~aSubsetOf0(_u38, _u39) | aInfimumOfIn0(_u41, _u38, _u39) | ~aElementOf0(_u41, _u39) | ~aLowerBoundOfIn0(_u41, _u38, _u39) | aLowerBoundOfIn0(skolem5(_u39, _u38, _u41), _u38, _u39) )).
% 2.95/3.13 cnf(matrix-43, plain, ( ~aSet0(_u39) | ~aSubsetOf0(_u38, _u39) | aInfimumOfIn0(_u41, _u38, _u39) | ~aElementOf0(_u41, _u39) | ~aLowerBoundOfIn0(_u41, _u38, _u39) | ~sdtlseqdt0(skolem5(_u39, _u38, _u41), _u41) )).
% 2.95/3.13 cnf(matrix-44, plain, ( ~aSet0(_u46) | ~aSubsetOf0(_u45, _u46) | ~aSupremumOfIn0(_u47, _u45, _u46) | aElementOf0(_u47, _u46) )).
% 2.95/3.13 cnf(matrix-45, plain, ( ~aSet0(_u46) | ~aSubsetOf0(_u45, _u46) | ~aSupremumOfIn0(_u47, _u45, _u46) | aUpperBoundOfIn0(_u47, _u45, _u46) )).
% 2.95/3.13 cnf(matrix-46, plain, ( ~aSet0(_u46) | ~aSubsetOf0(_u45, _u46) | ~aSupremumOfIn0(_u47, _u45, _u46) | ~aUpperBoundOfIn0(_u42, _u45, _u46) | sdtlseqdt0(_u47, _u42) )).
% 2.95/3.13 cnf(matrix-47, plain, ( ~aSet0(_u46) | ~aSubsetOf0(_u45, _u46) | aSupremumOfIn0(_u48, _u45, _u46) | ~aElementOf0(_u48, _u46) | ~aUpperBoundOfIn0(_u48, _u45, _u46) | aUpperBoundOfIn0(skolem6(_u46, _u45, _u48), _u45, _u46) )).
% 2.95/3.13 cnf(matrix-48, plain, ( ~aSet0(_u46) | ~aSubsetOf0(_u45, _u46) | aSupremumOfIn0(_u48, _u45, _u46) | ~aElementOf0(_u48, _u46) | ~aUpperBoundOfIn0(_u48, _u45, _u46) | ~sdtlseqdt0(_u48, skolem6(_u46, _u45, _u48)) )).
% 2.95/3.13 cnf(matrix-49, plain, ( aSet0(xT) )).
% 2.95/3.13 cnf(matrix-50, plain, ( aSet0(xS) )).
% 2.95/3.13 cnf(matrix-51, plain, ( ~aElementOf0(_u49, xS) | aElementOf0(_u49, xT) )).
% 2.95/3.13 cnf(matrix-52, plain, ( aSubsetOf0(xS, xT) )).
% 2.95/3.13 cnf(matrix-53, plain, ( aElementOf0(xu, xT) )).
% 2.95/3.13 cnf(matrix-54, plain, ( aElementOf0(xu, xT) )).
% 2.95/3.13 cnf(matrix-55, plain, ( ~aElementOf0(_u50, xS) | sdtlseqdt0(_u50, xu) )).
% 2.95/3.13 cnf(matrix-56, plain, ( aUpperBoundOfIn0(xu, xS, xT) )).
% 2.95/3.13 cnf(matrix-57, plain, ( sdtlseqdt0(xu, _u52) | ~aElementOf0(_u52, xT) | aElementOf0(skolem7(_u52), xS) )).
% 2.95/3.13 cnf(matrix-58, plain, ( sdtlseqdt0(xu, _u52) | ~aElementOf0(_u52, xT) | ~sdtlseqdt0(skolem7(_u52), _u52) )).
% 2.95/3.13 cnf(matrix-59, plain, ( sdtlseqdt0(xu, _u52) | ~aUpperBoundOfIn0(_u52, xS, xT) )).
% 2.95/3.13 cnf(matrix-60, plain, ( aSupremumOfIn0(xu, xS, xT) )).
% 2.95/3.13 cnf(matrix-61, plain, ( aElementOf0(xv, xT) )).
% 2.95/3.13 cnf(matrix-62, plain, ( aElementOf0(xv, xT) )).
% 2.95/3.13 cnf(matrix-63, plain, ( ~aElementOf0(_u53, xS) | sdtlseqdt0(_u53, xv) )).
% 2.95/3.13 cnf(matrix-64, plain, ( aUpperBoundOfIn0(xv, xS, xT) )).
% 2.95/3.13 cnf(matrix-65, plain, ( sdtlseqdt0(xv, _u55) | ~aElementOf0(_u55, xT) | aElementOf0(skolem8(_u55), xS) )).
% 2.95/3.13 cnf(matrix-66, plain, ( sdtlseqdt0(xv, _u55) | ~aElementOf0(_u55, xT) | ~sdtlseqdt0(skolem8(_u55), _u55) )).
% 2.95/3.13 cnf(matrix-67, plain, ( sdtlseqdt0(xv, _u55) | ~aUpperBoundOfIn0(_u55, xS, xT) )).
% 2.95/3.13 cnf(matrix-68, plain, ( aSupremumOfIn0(xv, xS, xT) )).
% 2.95/3.13 cnf(matrix-69, plain, ( ( xu != xv) )).
% 2.95/3.13
% 2.95/3.13 % Proof stack:
% 2.95/3.13 cnf(proof-stack, plain,
% 2.95/3.13 proof_stack(
% 2.95/3.13 start(69),
% 2.95/3.13 left_branch(0, 29, 4, 2),
% 2.95/3.13 left_branch(0, 21, 2, 3),
% 2.95/3.13 left_branch(0, 49, 0, 4),
% 2.95/3.13 right_branch(4),
% 2.95/3.13 left_branch(0, 54, 0, 5),
% 2.95/3.13 right_branch(5),
% 2.95/3.13 right_branch(3),
% 2.95/3.13 left_branch(0, 67, 0, 4),
% 2.95/3.13 left_branch(0, 56, 0, 5),
% 2.95/3.13 right_branch(5),
% 2.95/3.13 right_branch(4),
% 2.95/3.13 left_branch(0, 59, 0, 5),
% 2.95/3.13 left_branch(0, 64, 0, 6),
% 2.95/3.13 right_branch(6),
% 2.95/3.13 right_branch(5),
% 2.95/3.13 left_branch(0, 21, 2, 6),
% 2.95/3.13 left_branch(0, 49, 0, 7),
% 2.95/3.13 right_branch(7),
% 2.95/3.13 left_branch(0, 62, 0, 8),
% 2.95/3.13 right_branch(8),
% 2.95/3.13 right_branch(6),
% 2.95/3.13 right_branch(2)
% 2.95/3.13 )).
% 2.95/3.13 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------