TSTP Solution File: LAT388+1 by ConnectPP---0.2.2
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%------------------------------------------------------------------------------
% File : ConnectPP---0.2.2
% Problem : LAT388+1 : 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 : n003.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 09:08:52 EST 2024
% Result : Theorem 0.20s 0.36s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT388+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.14/0.34 % Computer : n003.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
% 0.20/0.34 % CPULimit : 300
% 0.20/0.34 % WCLimit : 300
% 0.20/0.34 % DateTime : Sun Mar 3 11:40:07 EST 2024
% 0.20/0.34 % CPUTime :
% 0.20/0.36 % SZS status Theorem for theBenchmark
% 0.20/0.36 % SZS output start Proof for theBenchmark
% 0.20/0.36
% 0.20/0.36 % Formula: mSetSort ( axiom ) converted to clauses:
% 0.20/0.36
% 0.20/0.36 % Formula: mElmSort ( axiom ) converted to clauses:
% 0.20/0.36
% 0.20/0.36 % Formula: mEOfElem ( axiom ) converted to clauses:
% 0.20/0.36 cnf(mEOfElem-1, axiom, ( ~aSet0(_u3) | ~aElementOf0(_u2, _u3) | aElement0(_u2) )).
% 0.20/0.36
% 0.20/0.36 % Formula: mDefEmpty ( definition ) converted to clauses:
% 0.20/0.36 cnf(mDefEmpty-1, definition, ( ~aSet0(_u6) | ~isEmpty0(_u6) | ~aElementOf0(_u4, _u6) )).
% 0.20/0.36 cnf(mDefEmpty-2, definition, ( ~aSet0(_u6) | aElementOf0(skolem1(_u6), _u6) | isEmpty0(_u6) )).
% 0.20/0.36
% 0.20/0.36 % Formula: mDefSub ( definition ) converted to clauses:
% 0.20/0.36 cnf(mDefSub-1, definition, ( ~aSet0(_u10) | ~aSubsetOf0(_u11, _u10) | aSet0(_u11) )).
% 0.20/0.36 cnf(mDefSub-2, definition, ( ~aSet0(_u10) | ~aSubsetOf0(_u11, _u10) | ~aElementOf0(_u7, _u11) | aElementOf0(_u7, _u10) )).
% 0.20/0.36 cnf(mDefSub-3, definition, ( ~aSet0(_u10) | aSubsetOf0(_u12, _u10) | ~aSet0(_u12) | aElementOf0(skolem2(_u10, _u12), _u12) )).
% 0.20/0.36 cnf(mDefSub-4, definition, ( ~aSet0(_u10) | aSubsetOf0(_u12, _u10) | ~aSet0(_u12) | ~aElementOf0(skolem2(_u10, _u12), _u10) )).
% 0.20/0.36
% 0.20/0.36 % Formula: mLessRel ( axiom ) converted to clauses:
% 0.20/0.36
% 0.20/0.36 % Formula: mARefl ( axiom ) converted to clauses:
% 0.20/0.36 cnf(mARefl-1, axiom, ( ~aElement0(_u15) | sdtlseqdt0(_u15, _u15) )).
% 0.20/0.36
% 0.20/0.36 % Formula: mASymm ( axiom ) converted to clauses:
% 0.20/0.36 cnf(mASymm-1, axiom, ( ~aElement0(_u17) | ~aElement0(_u16) | ~sdtlseqdt0(_u17, _u16) | ~sdtlseqdt0(_u16, _u17) | ( _u17 = _u16) )).
% 0.20/0.36
% 0.20/0.36 % Formula: mTrans ( axiom ) converted to clauses:
% 0.20/0.36 cnf(mTrans-1, axiom, ( ~aElement0(_u20) | ~aElement0(_u19) | ~aElement0(_u18) | ~sdtlseqdt0(_u20, _u19) | ~sdtlseqdt0(_u19, _u18) | sdtlseqdt0(_u20, _u18) )).
% 0.20/0.36
% 0.20/0.36 % Formula: mDefLB ( definition ) converted to clauses:
% 0.20/0.36 cnf(mDefLB-1, definition, ( ~aSet0(_u25) | ~aSubsetOf0(_u24, _u25) | ~aLowerBoundOfIn0(_u26, _u24, _u25) | aElementOf0(_u26, _u25) )).
% 0.20/0.36 cnf(mDefLB-2, definition, ( ~aSet0(_u25) | ~aSubsetOf0(_u24, _u25) | ~aLowerBoundOfIn0(_u26, _u24, _u25) | ~aElementOf0(_u21, _u24) | sdtlseqdt0(_u26, _u21) )).
% 0.20/0.36 cnf(mDefLB-3, definition, ( ~aSet0(_u25) | ~aSubsetOf0(_u24, _u25) | aLowerBoundOfIn0(_u27, _u24, _u25) | ~aElementOf0(_u27, _u25) | aElementOf0(skolem3(_u25, _u24, _u27), _u24) )).
% 0.20/0.36 cnf(mDefLB-4, definition, ( ~aSet0(_u25) | ~aSubsetOf0(_u24, _u25) | aLowerBoundOfIn0(_u27, _u24, _u25) | ~aElementOf0(_u27, _u25) | ~sdtlseqdt0(_u27, skolem3(_u25, _u24, _u27)) )).
% 0.20/0.36
% 0.20/0.36 % Formula: mDefUB ( definition ) converted to clauses:
% 0.20/0.36 cnf(mDefUB-1, definition, ( ~aSet0(_u32) | ~aSubsetOf0(_u31, _u32) | ~aUpperBoundOfIn0(_u33, _u31, _u32) | aElementOf0(_u33, _u32) )).
% 0.20/0.36 cnf(mDefUB-2, definition, ( ~aSet0(_u32) | ~aSubsetOf0(_u31, _u32) | ~aUpperBoundOfIn0(_u33, _u31, _u32) | ~aElementOf0(_u28, _u31) | sdtlseqdt0(_u28, _u33) )).
% 0.20/0.36 cnf(mDefUB-3, definition, ( ~aSet0(_u32) | ~aSubsetOf0(_u31, _u32) | aUpperBoundOfIn0(_u34, _u31, _u32) | ~aElementOf0(_u34, _u32) | aElementOf0(skolem4(_u32, _u31, _u34), _u31) )).
% 0.20/0.36 cnf(mDefUB-4, definition, ( ~aSet0(_u32) | ~aSubsetOf0(_u31, _u32) | aUpperBoundOfIn0(_u34, _u31, _u32) | ~aElementOf0(_u34, _u32) | ~sdtlseqdt0(skolem4(_u32, _u31, _u34), _u34) )).
% 0.20/0.36
% 0.20/0.36 % Formula: mDefInf ( definition ) converted to clauses:
% 0.20/0.36 cnf(mDefInf-1, definition, ( ~aSet0(_u39) | ~aSubsetOf0(_u38, _u39) | ~aInfimumOfIn0(_u40, _u38, _u39) | aElementOf0(_u40, _u39) )).
% 0.20/0.36 cnf(mDefInf-2, definition, ( ~aSet0(_u39) | ~aSubsetOf0(_u38, _u39) | ~aInfimumOfIn0(_u40, _u38, _u39) | aLowerBoundOfIn0(_u40, _u38, _u39) )).
% 0.20/0.36 cnf(mDefInf-3, definition, ( ~aSet0(_u39) | ~aSubsetOf0(_u38, _u39) | ~aInfimumOfIn0(_u40, _u38, _u39) | ~aLowerBoundOfIn0(_u35, _u38, _u39) | sdtlseqdt0(_u35, _u40) )).
% 0.20/0.36 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) )).
% 0.20/0.36 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) )).
% 0.20/0.36
% 0.20/0.36 % Formula: mDefSup ( definition ) converted to clauses:
% 0.20/0.36 cnf(mDefSup-1, definition, ( ~aSet0(_u46) | ~aSubsetOf0(_u45, _u46) | ~aSupremumOfIn0(_u47, _u45, _u46) | aElementOf0(_u47, _u46) )).
% 0.20/0.36 cnf(mDefSup-2, definition, ( ~aSet0(_u46) | ~aSubsetOf0(_u45, _u46) | ~aSupremumOfIn0(_u47, _u45, _u46) | aUpperBoundOfIn0(_u47, _u45, _u46) )).
% 0.20/0.36 cnf(mDefSup-3, definition, ( ~aSet0(_u46) | ~aSubsetOf0(_u45, _u46) | ~aSupremumOfIn0(_u47, _u45, _u46) | ~aUpperBoundOfIn0(_u42, _u45, _u46) | sdtlseqdt0(_u47, _u42) )).
% 0.20/0.36 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) )).
% 0.20/0.36 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)) )).
% 0.20/0.36
% 0.20/0.36 % Formula: mSupUn ( axiom ) converted to clauses:
% 0.20/0.36 cnf(mSupUn-1, axiom, ( ~aSet0(_u52) | ~aSubsetOf0(_u51, _u52) | ~aSupremumOfIn0(_u50, _u51, _u52) | ~aSupremumOfIn0(_u49, _u51, _u52) | ( _u50 = _u49) )).
% 0.20/0.36
% 0.20/0.36 % Formula: mInfUn ( axiom ) converted to clauses:
% 0.20/0.36 cnf(mInfUn-1, axiom, ( ~aSet0(_u56) | ~aSubsetOf0(_u55, _u56) | ~aInfimumOfIn0(_u54, _u55, _u56) | ~aInfimumOfIn0(_u53, _u55, _u56) | ( _u54 = _u53) )).
% 0.20/0.36
% 0.20/0.36 % Formula: mDefCLat ( definition ) converted to clauses:
% 0.20/0.36 cnf(mDefCLat-1, definition, ( ~aCompleteLattice0(_u64) | aSet0(_u64) )).
% 0.20/0.36 cnf(mDefCLat-2, definition, ( ~aCompleteLattice0(_u64) | ~aSubsetOf0(_u59, _u64) | aSupremumOfIn0(skolem7(_u64, _u59), _u59, _u64) )).
% 0.20/0.36 cnf(mDefCLat-3, definition, ( ~aCompleteLattice0(_u64) | ~aSubsetOf0(_u59, _u64) | aInfimumOfIn0(skolem8(_u64, _u59), _u59, _u64) )).
% 0.20/0.36 cnf(mDefCLat-4, definition, ( aCompleteLattice0(_u65) | ~aSet0(_u65) | aSubsetOf0(skolem9(_u65), _u65) )).
% 0.20/0.36 cnf(mDefCLat-5, definition, ( aCompleteLattice0(_u65) | ~aSet0(_u65) | ~aSupremumOfIn0(_u60, skolem9(_u65), _u65) | ~aInfimumOfIn0(_u61, skolem9(_u65), _u65) )).
% 0.20/0.36
% 0.20/0.36 % Formula: mConMap ( axiom ) converted to clauses:
% 0.20/0.36
% 0.20/0.36 % Formula: mDomSort ( axiom ) converted to clauses:
% 0.20/0.36 cnf(mDomSort-1, axiom, ( ~aFunction0(_u67) | aSet0(szDzozmdt0(_u67)) )).
% 0.20/0.36
% 0.20/0.36 % Formula: mRanSort ( axiom ) converted to clauses:
% 0.20/0.36 cnf(mRanSort-1, axiom, ( ~aFunction0(_u68) | aSet0(szRzazndt0(_u68)) )).
% 0.20/0.36
% 0.20/0.36 % Formula: mDefDom ( definition ) converted to clauses:
% 0.20/0.36 cnf(mDefDom-1, definition, ( ~aFunction0(_u70) | ~aSet0(_u69) | ~isOn0(_u70, _u69) | ( szDzozmdt0(_u70) = szRzazndt0(_u70)) )).
% 0.20/0.36 cnf(mDefDom-2, definition, ( ~aFunction0(_u70) | ~aSet0(_u69) | ~isOn0(_u70, _u69) | ( szRzazndt0(_u70) = _u69) )).
% 0.20/0.36 cnf(mDefDom-3, definition, ( ~aFunction0(_u70) | ~aSet0(_u69) | ( szDzozmdt0(_u70) != szRzazndt0(_u70)) | ( szRzazndt0(_u70) != _u69) | isOn0(_u70, _u69) )).
% 0.20/0.36
% 0.20/0.36 % Formula: mImgSort ( axiom ) converted to clauses:
% 0.20/0.36 cnf(mImgSort-1, axiom, ( ~aFunction0(_u72) | ~aElementOf0(_u71, szDzozmdt0(_u72)) | aElementOf0(sdtlpdtrp0(_u72, _u71), szRzazndt0(_u72)) )).
% 0.20/0.36
% 0.20/0.36 % Formula: mDefFix ( definition ) converted to clauses:
% 0.20/0.36 cnf(mDefFix-1, definition, ( ~aFunction0(_u74) | ~aFixedPointOf0(_u75, _u74) | aElementOf0(_u75, szDzozmdt0(_u74)) )).
% 0.20/0.36 cnf(mDefFix-2, definition, ( ~aFunction0(_u74) | ~aFixedPointOf0(_u75, _u74) | ( sdtlpdtrp0(_u74, _u75) = _u75) )).
% 0.20/0.36 cnf(mDefFix-3, definition, ( ~aFunction0(_u74) | ~aElementOf0(_u76, szDzozmdt0(_u74)) | ( sdtlpdtrp0(_u74, _u76) != _u76) | aFixedPointOf0(_u76, _u74) )).
% 0.20/0.36
% 0.20/0.36 % Formula: mDefMonot ( definition ) converted to clauses:
% 0.20/0.36 cnf(mDefMonot-1, definition, ( ~aFunction0(_u81) | ~isMonotone0(_u81) | ~aElementOf0(_u78, szDzozmdt0(_u81)) | ~aElementOf0(_u77, szDzozmdt0(_u81)) | ~sdtlseqdt0(_u78, _u77) | sdtlseqdt0(sdtlpdtrp0(_u81, _u78), sdtlpdtrp0(_u81, _u77)) )).
% 0.20/0.36 cnf(mDefMonot-2, definition, ( ~aFunction0(_u81) | isMonotone0(_u81) | aElementOf0(skolem10(_u81), szDzozmdt0(_u81)) )).
% 0.20/0.36 cnf(mDefMonot-3, definition, ( ~aFunction0(_u81) | isMonotone0(_u81) | aElementOf0(skolem11(_u81), szDzozmdt0(_u81)) )).
% 0.20/0.36 cnf(mDefMonot-4, definition, ( ~aFunction0(_u81) | isMonotone0(_u81) | sdtlseqdt0(skolem10(_u81), skolem11(_u81)) )).
% 0.20/0.36 cnf(mDefMonot-5, definition, ( ~aFunction0(_u81) | isMonotone0(_u81) | ~sdtlseqdt0(sdtlpdtrp0(_u81, skolem10(_u81)), sdtlpdtrp0(_u81, skolem11(_u81))) )).
% 0.20/0.36
% 0.20/0.36 % Formula: m__1123 ( hypothesis ) converted to clauses:
% 0.20/0.36 cnf(m__1123-1, hypothesis, ( aCompleteLattice0(xU) )).
% 0.20/0.36 cnf(m__1123-2, hypothesis, ( aFunction0(xf) )).
% 0.20/0.36 cnf(m__1123-3, hypothesis, ( isMonotone0(xf) )).
% 0.20/0.36 cnf(m__1123-4, hypothesis, ( isOn0(xf, xU) )).
% 0.20/0.36
% 0.20/0.36 % Formula: m__1144 ( hypothesis ) converted to clauses:
% 0.20/0.36 cnf(m__1144-1, hypothesis, ( ( xS = cS1142(xf)) )).
% 0.20/0.36
% 0.20/0.36 % Formula: m__1173 ( hypothesis ) converted to clauses:
% 0.20/0.36 cnf(m__1173-1, hypothesis, ( aSubsetOf0(xT, xS) )).
% 0.20/0.36
% 0.20/0.36 % Formula: m__1244 ( hypothesis ) converted to clauses:
% 0.20/0.36 cnf(m__1244-1, hypothesis, ( ( xP = cS1241(xU, xf, xT)) )).
% 0.20/0.36
% 0.20/0.36 % Formula: m__1261 ( hypothesis ) converted to clauses:
% 0.20/0.36 cnf(m__1261-1, hypothesis, ( aInfimumOfIn0(xp, xP, xU) )).
% 0.20/0.36
% 0.20/0.36 % Formula: m__1299 ( hypothesis ) converted to clauses:
% 0.20/0.36 cnf(m__1299-1, hypothesis, ( aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU) )).
% 0.20/0.36 cnf(m__1299-2, hypothesis, ( aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) )).
% 0.20/0.36
% 0.20/0.36 % Formula: m__1330 ( hypothesis ) converted to clauses:
% 0.20/0.36 cnf(m__1330-1, hypothesis, ( aFixedPointOf0(xp, xf) )).
% 0.20/0.36 cnf(m__1330-2, hypothesis, ( aSupremumOfIn0(xp, xT, xS) )).
% 0.20/0.36
% 0.20/0.36 % Formula: m__ ( conjecture ) converted to clauses:
% 0.20/0.36 cnf(m__-1, negated_conjecture, ( ~aSupremumOfIn0(_u82, xT, xS) )).
% 0.20/0.36
% 0.20/0.36 % Problem matrix:
% 0.20/0.36 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 0.20/0.36 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 0.20/0.36 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 0.20/0.36 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( szDzozmdt0(__eqx_0) = szDzozmdt0(__eqy_0)) )).
% 0.20/0.36 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( szRzazndt0(__eqx_0) = szRzazndt0(__eqy_0)) )).
% 0.20/0.36 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( sdtlpdtrp0(__eqx_0, __eqx_1) = sdtlpdtrp0(__eqy_0, __eqy_1)) )).
% 0.20/0.36 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( cS1142(__eqx_0) = cS1142(__eqy_0)) )).
% 0.20/0.36 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( cS1241(__eqx_0, __eqx_1, __eqx_2) = cS1241(__eqy_0, __eqy_1, __eqy_2)) )).
% 0.20/0.36 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( skolem1(__eqx_0) = skolem1(__eqy_0)) )).
% 0.20/0.36 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem2(__eqx_0, __eqx_1) = skolem2(__eqy_0, __eqy_1)) )).
% 0.20/0.36 cnf(matrix-10, 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)) )).
% 0.20/0.36 cnf(matrix-11, 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)) )).
% 0.20/0.36 cnf(matrix-12, 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)) )).
% 0.20/0.36 cnf(matrix-13, 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)) )).
% 0.20/0.36 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem7(__eqx_0, __eqx_1) = skolem7(__eqy_0, __eqy_1)) )).
% 0.20/0.36 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem8(__eqx_0, __eqx_1) = skolem8(__eqy_0, __eqy_1)) )).
% 0.20/0.36 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ( skolem9(__eqx_0) = skolem9(__eqy_0)) )).
% 0.20/0.36 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ( skolem10(__eqx_0) = skolem10(__eqy_0)) )).
% 0.20/0.36 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ( skolem11(__eqx_0) = skolem11(__eqy_0)) )).
% 0.20/0.36 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ~aSet0(__eqx_0) | aSet0(__eqy_0) )).
% 0.20/0.36 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ~aElement0(__eqx_0) | aElement0(__eqy_0) )).
% 0.20/0.36 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~aElementOf0(__eqx_0, __eqx_1) | aElementOf0(__eqy_0, __eqy_1) )).
% 0.20/0.36 cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ~isEmpty0(__eqx_0) | isEmpty0(__eqy_0) )).
% 0.20/0.36 cnf(matrix-23, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~aSubsetOf0(__eqx_0, __eqx_1) | aSubsetOf0(__eqy_0, __eqy_1) )).
% 0.20/0.36 cnf(matrix-24, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~sdtlseqdt0(__eqx_0, __eqx_1) | sdtlseqdt0(__eqy_0, __eqy_1) )).
% 0.20/0.36 cnf(matrix-25, 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) )).
% 0.20/0.36 cnf(matrix-26, 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) )).
% 0.20/0.36 cnf(matrix-27, 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) )).
% 0.20/0.36 cnf(matrix-28, 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) )).
% 0.20/0.36 cnf(matrix-29, plain, ( ( __eqx_0 != __eqy_0) | ~aCompleteLattice0(__eqx_0) | aCompleteLattice0(__eqy_0) )).
% 0.20/0.36 cnf(matrix-30, plain, ( ( __eqx_0 != __eqy_0) | ~aFunction0(__eqx_0) | aFunction0(__eqy_0) )).
% 0.20/0.36 cnf(matrix-31, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~isOn0(__eqx_0, __eqx_1) | isOn0(__eqy_0, __eqy_1) )).
% 0.20/0.36 cnf(matrix-32, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~aFixedPointOf0(__eqx_0, __eqx_1) | aFixedPointOf0(__eqy_0, __eqy_1) )).
% 0.20/0.36 cnf(matrix-33, plain, ( ( __eqx_0 != __eqy_0) | ~isMonotone0(__eqx_0) | isMonotone0(__eqy_0) )).
% 0.20/0.36 cnf(matrix-34, plain, ( ~aSet0(_u3) | ~aElementOf0(_u2, _u3) | aElement0(_u2) )).
% 0.20/0.36 cnf(matrix-35, plain, ( ~aSet0(_u6) | ~isEmpty0(_u6) | ~aElementOf0(_u4, _u6) )).
% 0.20/0.36 cnf(matrix-36, plain, ( ~aSet0(_u6) | aElementOf0(skolem1(_u6), _u6) | isEmpty0(_u6) )).
% 0.20/0.36 cnf(matrix-37, plain, ( ~aSet0(_u10) | ~aSubsetOf0(_u11, _u10) | aSet0(_u11) )).
% 0.20/0.36 cnf(matrix-38, plain, ( ~aSet0(_u10) | ~aSubsetOf0(_u11, _u10) | ~aElementOf0(_u7, _u11) | aElementOf0(_u7, _u10) )).
% 0.20/0.36 cnf(matrix-39, plain, ( ~aSet0(_u10) | aSubsetOf0(_u12, _u10) | ~aSet0(_u12) | aElementOf0(skolem2(_u10, _u12), _u12) )).
% 0.20/0.36 cnf(matrix-40, plain, ( ~aSet0(_u10) | aSubsetOf0(_u12, _u10) | ~aSet0(_u12) | ~aElementOf0(skolem2(_u10, _u12), _u10) )).
% 0.20/0.36 cnf(matrix-41, plain, ( ~aElement0(_u15) | sdtlseqdt0(_u15, _u15) )).
% 0.20/0.36 cnf(matrix-42, plain, ( ~aElement0(_u17) | ~aElement0(_u16) | ~sdtlseqdt0(_u17, _u16) | ~sdtlseqdt0(_u16, _u17) | ( _u17 = _u16) )).
% 0.20/0.36 cnf(matrix-43, plain, ( ~aElement0(_u20) | ~aElement0(_u19) | ~aElement0(_u18) | ~sdtlseqdt0(_u20, _u19) | ~sdtlseqdt0(_u19, _u18) | sdtlseqdt0(_u20, _u18) )).
% 0.20/0.36 cnf(matrix-44, plain, ( ~aSet0(_u25) | ~aSubsetOf0(_u24, _u25) | ~aLowerBoundOfIn0(_u26, _u24, _u25) | aElementOf0(_u26, _u25) )).
% 0.20/0.36 cnf(matrix-45, plain, ( ~aSet0(_u25) | ~aSubsetOf0(_u24, _u25) | ~aLowerBoundOfIn0(_u26, _u24, _u25) | ~aElementOf0(_u21, _u24) | sdtlseqdt0(_u26, _u21) )).
% 0.20/0.36 cnf(matrix-46, plain, ( ~aSet0(_u25) | ~aSubsetOf0(_u24, _u25) | aLowerBoundOfIn0(_u27, _u24, _u25) | ~aElementOf0(_u27, _u25) | aElementOf0(skolem3(_u25, _u24, _u27), _u24) )).
% 0.20/0.36 cnf(matrix-47, plain, ( ~aSet0(_u25) | ~aSubsetOf0(_u24, _u25) | aLowerBoundOfIn0(_u27, _u24, _u25) | ~aElementOf0(_u27, _u25) | ~sdtlseqdt0(_u27, skolem3(_u25, _u24, _u27)) )).
% 0.20/0.36 cnf(matrix-48, plain, ( ~aSet0(_u32) | ~aSubsetOf0(_u31, _u32) | ~aUpperBoundOfIn0(_u33, _u31, _u32) | aElementOf0(_u33, _u32) )).
% 0.20/0.36 cnf(matrix-49, plain, ( ~aSet0(_u32) | ~aSubsetOf0(_u31, _u32) | ~aUpperBoundOfIn0(_u33, _u31, _u32) | ~aElementOf0(_u28, _u31) | sdtlseqdt0(_u28, _u33) )).
% 0.20/0.36 cnf(matrix-50, plain, ( ~aSet0(_u32) | ~aSubsetOf0(_u31, _u32) | aUpperBoundOfIn0(_u34, _u31, _u32) | ~aElementOf0(_u34, _u32) | aElementOf0(skolem4(_u32, _u31, _u34), _u31) )).
% 0.20/0.36 cnf(matrix-51, plain, ( ~aSet0(_u32) | ~aSubsetOf0(_u31, _u32) | aUpperBoundOfIn0(_u34, _u31, _u32) | ~aElementOf0(_u34, _u32) | ~sdtlseqdt0(skolem4(_u32, _u31, _u34), _u34) )).
% 0.20/0.36 cnf(matrix-52, plain, ( ~aSet0(_u39) | ~aSubsetOf0(_u38, _u39) | ~aInfimumOfIn0(_u40, _u38, _u39) | aElementOf0(_u40, _u39) )).
% 0.20/0.36 cnf(matrix-53, plain, ( ~aSet0(_u39) | ~aSubsetOf0(_u38, _u39) | ~aInfimumOfIn0(_u40, _u38, _u39) | aLowerBoundOfIn0(_u40, _u38, _u39) )).
% 0.20/0.36 cnf(matrix-54, plain, ( ~aSet0(_u39) | ~aSubsetOf0(_u38, _u39) | ~aInfimumOfIn0(_u40, _u38, _u39) | ~aLowerBoundOfIn0(_u35, _u38, _u39) | sdtlseqdt0(_u35, _u40) )).
% 0.20/0.36 cnf(matrix-55, plain, ( ~aSet0(_u39) | ~aSubsetOf0(_u38, _u39) | aInfimumOfIn0(_u41, _u38, _u39) | ~aElementOf0(_u41, _u39) | ~aLowerBoundOfIn0(_u41, _u38, _u39) | aLowerBoundOfIn0(skolem5(_u39, _u38, _u41), _u38, _u39) )).
% 0.20/0.36 cnf(matrix-56, plain, ( ~aSet0(_u39) | ~aSubsetOf0(_u38, _u39) | aInfimumOfIn0(_u41, _u38, _u39) | ~aElementOf0(_u41, _u39) | ~aLowerBoundOfIn0(_u41, _u38, _u39) | ~sdtlseqdt0(skolem5(_u39, _u38, _u41), _u41) )).
% 0.20/0.36 cnf(matrix-57, plain, ( ~aSet0(_u46) | ~aSubsetOf0(_u45, _u46) | ~aSupremumOfIn0(_u47, _u45, _u46) | aElementOf0(_u47, _u46) )).
% 0.20/0.36 cnf(matrix-58, plain, ( ~aSet0(_u46) | ~aSubsetOf0(_u45, _u46) | ~aSupremumOfIn0(_u47, _u45, _u46) | aUpperBoundOfIn0(_u47, _u45, _u46) )).
% 0.20/0.36 cnf(matrix-59, plain, ( ~aSet0(_u46) | ~aSubsetOf0(_u45, _u46) | ~aSupremumOfIn0(_u47, _u45, _u46) | ~aUpperBoundOfIn0(_u42, _u45, _u46) | sdtlseqdt0(_u47, _u42) )).
% 0.20/0.36 cnf(matrix-60, plain, ( ~aSet0(_u46) | ~aSubsetOf0(_u45, _u46) | aSupremumOfIn0(_u48, _u45, _u46) | ~aElementOf0(_u48, _u46) | ~aUpperBoundOfIn0(_u48, _u45, _u46) | aUpperBoundOfIn0(skolem6(_u46, _u45, _u48), _u45, _u46) )).
% 0.20/0.36 cnf(matrix-61, plain, ( ~aSet0(_u46) | ~aSubsetOf0(_u45, _u46) | aSupremumOfIn0(_u48, _u45, _u46) | ~aElementOf0(_u48, _u46) | ~aUpperBoundOfIn0(_u48, _u45, _u46) | ~sdtlseqdt0(_u48, skolem6(_u46, _u45, _u48)) )).
% 0.20/0.36 cnf(matrix-62, plain, ( ~aSet0(_u52) | ~aSubsetOf0(_u51, _u52) | ~aSupremumOfIn0(_u50, _u51, _u52) | ~aSupremumOfIn0(_u49, _u51, _u52) | ( _u50 = _u49) )).
% 0.20/0.36 cnf(matrix-63, plain, ( ~aSet0(_u56) | ~aSubsetOf0(_u55, _u56) | ~aInfimumOfIn0(_u54, _u55, _u56) | ~aInfimumOfIn0(_u53, _u55, _u56) | ( _u54 = _u53) )).
% 0.20/0.36 cnf(matrix-64, plain, ( ~aCompleteLattice0(_u64) | aSet0(_u64) )).
% 0.20/0.36 cnf(matrix-65, plain, ( ~aCompleteLattice0(_u64) | ~aSubsetOf0(_u59, _u64) | aSupremumOfIn0(skolem7(_u64, _u59), _u59, _u64) )).
% 0.20/0.36 cnf(matrix-66, plain, ( ~aCompleteLattice0(_u64) | ~aSubsetOf0(_u59, _u64) | aInfimumOfIn0(skolem8(_u64, _u59), _u59, _u64) )).
% 0.20/0.36 cnf(matrix-67, plain, ( aCompleteLattice0(_u65) | ~aSet0(_u65) | aSubsetOf0(skolem9(_u65), _u65) )).
% 0.20/0.36 cnf(matrix-68, plain, ( aCompleteLattice0(_u65) | ~aSet0(_u65) | ~aSupremumOfIn0(_u60, skolem9(_u65), _u65) | ~aInfimumOfIn0(_u61, skolem9(_u65), _u65) )).
% 0.20/0.36 cnf(matrix-69, plain, ( ~aFunction0(_u67) | aSet0(szDzozmdt0(_u67)) )).
% 0.20/0.36 cnf(matrix-70, plain, ( ~aFunction0(_u68) | aSet0(szRzazndt0(_u68)) )).
% 0.20/0.36 cnf(matrix-71, plain, ( ~aFunction0(_u70) | ~aSet0(_u69) | ~isOn0(_u70, _u69) | ( szDzozmdt0(_u70) = szRzazndt0(_u70)) )).
% 0.20/0.36 cnf(matrix-72, plain, ( ~aFunction0(_u70) | ~aSet0(_u69) | ~isOn0(_u70, _u69) | ( szRzazndt0(_u70) = _u69) )).
% 0.20/0.36 cnf(matrix-73, plain, ( ~aFunction0(_u70) | ~aSet0(_u69) | ( szDzozmdt0(_u70) != szRzazndt0(_u70)) | ( szRzazndt0(_u70) != _u69) | isOn0(_u70, _u69) )).
% 0.20/0.36 cnf(matrix-74, plain, ( ~aFunction0(_u72) | ~aElementOf0(_u71, szDzozmdt0(_u72)) | aElementOf0(sdtlpdtrp0(_u72, _u71), szRzazndt0(_u72)) )).
% 0.20/0.36 cnf(matrix-75, plain, ( ~aFunction0(_u74) | ~aFixedPointOf0(_u75, _u74) | aElementOf0(_u75, szDzozmdt0(_u74)) )).
% 0.20/0.36 cnf(matrix-76, plain, ( ~aFunction0(_u74) | ~aFixedPointOf0(_u75, _u74) | ( sdtlpdtrp0(_u74, _u75) = _u75) )).
% 0.20/0.36 cnf(matrix-77, plain, ( ~aFunction0(_u74) | ~aElementOf0(_u76, szDzozmdt0(_u74)) | ( sdtlpdtrp0(_u74, _u76) != _u76) | aFixedPointOf0(_u76, _u74) )).
% 0.20/0.36 cnf(matrix-78, plain, ( ~aFunction0(_u81) | ~isMonotone0(_u81) | ~aElementOf0(_u78, szDzozmdt0(_u81)) | ~aElementOf0(_u77, szDzozmdt0(_u81)) | ~sdtlseqdt0(_u78, _u77) | sdtlseqdt0(sdtlpdtrp0(_u81, _u78), sdtlpdtrp0(_u81, _u77)) )).
% 0.20/0.36 cnf(matrix-79, plain, ( ~aFunction0(_u81) | isMonotone0(_u81) | aElementOf0(skolem10(_u81), szDzozmdt0(_u81)) )).
% 0.20/0.36 cnf(matrix-80, plain, ( ~aFunction0(_u81) | isMonotone0(_u81) | aElementOf0(skolem11(_u81), szDzozmdt0(_u81)) )).
% 0.20/0.36 cnf(matrix-81, plain, ( ~aFunction0(_u81) | isMonotone0(_u81) | sdtlseqdt0(skolem10(_u81), skolem11(_u81)) )).
% 0.20/0.36 cnf(matrix-82, plain, ( ~aFunction0(_u81) | isMonotone0(_u81) | ~sdtlseqdt0(sdtlpdtrp0(_u81, skolem10(_u81)), sdtlpdtrp0(_u81, skolem11(_u81))) )).
% 0.20/0.36 cnf(matrix-83, plain, ( aCompleteLattice0(xU) )).
% 0.20/0.36 cnf(matrix-84, plain, ( aFunction0(xf) )).
% 0.20/0.36 cnf(matrix-85, plain, ( isMonotone0(xf) )).
% 0.20/0.36 cnf(matrix-86, plain, ( isOn0(xf, xU) )).
% 0.20/0.36 cnf(matrix-87, plain, ( ( xS = cS1142(xf)) )).
% 0.20/0.36 cnf(matrix-88, plain, ( aSubsetOf0(xT, xS) )).
% 0.20/0.36 cnf(matrix-89, plain, ( ( xP = cS1241(xU, xf, xT)) )).
% 0.20/0.36 cnf(matrix-90, plain, ( aInfimumOfIn0(xp, xP, xU) )).
% 0.20/0.36 cnf(matrix-91, plain, ( aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU) )).
% 0.20/0.36 cnf(matrix-92, plain, ( aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) )).
% 0.20/0.36 cnf(matrix-93, plain, ( aFixedPointOf0(xp, xf) )).
% 0.20/0.36 cnf(matrix-94, plain, ( aSupremumOfIn0(xp, xT, xS) )).
% 0.20/0.36 cnf(matrix-95, plain, ( ~aSupremumOfIn0(_u82, xT, xS) )).
% 0.20/0.36
% 0.20/0.36 % Proof stack:
% 0.20/0.36 cnf(proof-stack, plain,
% 0.20/0.36 proof_stack(
% 0.20/0.36 start(95),
% 0.20/0.36 left_branch(0, 94, 0, 2),
% 0.20/0.36 right_branch(2)
% 0.20/0.36 )).
% 0.20/0.36 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------