%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LAT386+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:59:46 PM UTC 2026
% Result : Theorem 18.56s 13.31s
% Output : CNFRefutation 18.56s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f76ERROR: Could not build tree for root c_47497ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f4,axiom,
! [X0] :
( aSet0(X0)
=> ( isEmpty0(X0)
<=> ~ ? [X1] : aElementOf0(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmpty) ).
fof(f5,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(f8,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mASymm) ).
fof(f9,axiom,
! [X0,X1,X2] :
( ( aElement0(X2)
& aElement0(X1)
& aElement0(X0) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X0,X1) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTrans) ).
fof(f12,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
=> ! [X2] :
( aInfimumOfIn0(X2,X1,X0)
<=> ( ! [X3] :
( aLowerBoundOfIn0(X3,X1,X0)
=> sdtlseqdt0(X3,X2) )
& aLowerBoundOfIn0(X2,X1,X0)
& aElementOf0(X2,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefInf) ).
fof(f16,axiom,
! [X0] :
( aCompleteLattice0(X0)
<=> ( ! [X1] :
( aSubsetOf0(X1,X0)
=> ? [X2] :
( ? [X3] : aSupremumOfIn0(X3,X1,X0)
& aInfimumOfIn0(X2,X1,X0) ) )
& aSet0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefCLat) ).
fof(f18,axiom,
! [X0] :
( aFunction0(X0)
=> aSet0(szDzozmdt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDomSort) ).
fof(f21,axiom,
! [X0] :
( aFunction0(X0)
=> ! [X1] :
( aElementOf0(X1,szDzozmdt0(X0))
=> aElementOf0(sdtlpdtrp0(X0,X1),szRzazndt0(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mImgSort) ).
fof(f25,axiom,
( xS = cS1142(xf)
& ! [X0] :
( ( ( aFixedPointOf0(X0,xf)
| ( sdtlpdtrp0(xf,X0) = X0
& aElementOf0(X0,szDzozmdt0(xf)) ) )
=> aElementOf0(X0,xS) )
& ( aElementOf0(X0,xS)
=> ( aFixedPointOf0(X0,xf)
& sdtlpdtrp0(xf,X0) = X0
& aElementOf0(X0,szDzozmdt0(xf)) ) ) )
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1144) ).
fof(f26,axiom,
( aSubsetOf0(xT,xS)
& ! [X0] :
( aElementOf0(X0,xT)
=> aElementOf0(X0,xS) )
& aSet0(xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1173) ).
fof(f27,axiom,
( xP = cS1241(xU,xf,xT)
& ! [X0] :
( ( ( ( aUpperBoundOfIn0(X0,xT,xU)
| ! [X1] :
( aElementOf0(X1,xT)
=> sdtlseqdt0(X1,X0) ) )
& sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
& aElementOf0(X0,xU) )
=> aElementOf0(X0,xP) )
& ( aElementOf0(X0,xP)
=> ( aUpperBoundOfIn0(X0,xT,xU)
& ! [X1] :
( aElementOf0(X1,xT)
=> sdtlseqdt0(X1,X0) )
& sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
& aElementOf0(X0,xU) ) ) )
& aSet0(xP) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1244) ).
fof(f28,axiom,
( aInfimumOfIn0(xp,xP,xU)
& ! [X0] :
( ( aLowerBoundOfIn0(X0,xP,xU)
| ( ! [X1] :
( aElementOf0(X1,xP)
=> sdtlseqdt0(X0,X1) )
& aElementOf0(X0,xU) ) )
=> sdtlseqdt0(X0,xp) )
& aLowerBoundOfIn0(xp,xP,xU)
& ! [X0] :
( aElementOf0(X0,xP)
=> sdtlseqdt0(xp,X0) )
& aElementOf0(xp,xU)
& aElementOf0(xp,xU) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1261) ).
fof(f29,conjecture,
( ( aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
| ! [X0] :
( aElementOf0(X0,xT)
=> sdtlseqdt0(X0,sdtlpdtrp0(xf,xp)) ) )
& ( aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU)
| ! [X0] :
( aElementOf0(X0,xP)
=> sdtlseqdt0(sdtlpdtrp0(xf,xp),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f30,negated_conjecture,
~ ( ( aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
| ! [X0] :
( aElementOf0(X0,xT)
=> sdtlseqdt0(X0,sdtlpdtrp0(xf,xp)) ) )
& ( aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU)
| ! [X0] :
( aElementOf0(X0,xP)
=> sdtlseqdt0(sdtlpdtrp0(xf,xp),X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f36,plain,
( xP = cS1241(xU,xf,xT)
& ! [X0] :
( ( ( ( aUpperBoundOfIn0(X0,xT,xU)
| ! [X2] :
( aElementOf0(X2,xT)
=> sdtlseqdt0(X2,X0) ) )
& sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
& aElementOf0(X0,xU) )
=> aElementOf0(X0,xP) )
& ( aElementOf0(X0,xP)
=> ( aUpperBoundOfIn0(X0,xT,xU)
& ! [X1] :
( aElementOf0(X1,xT)
=> sdtlseqdt0(X1,X0) )
& sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
& aElementOf0(X0,xU) ) ) )
& aSet0(xP) ),
inference(rectify,[],[f27]) ).
fof(f37,plain,
( aInfimumOfIn0(xp,xP,xU)
& ! [X1] :
( ( aLowerBoundOfIn0(X1,xP,xU)
| ( ! [X2] :
( aElementOf0(X2,xP)
=> sdtlseqdt0(X1,X2) )
& aElementOf0(X1,xU) ) )
=> sdtlseqdt0(X1,xp) )
& aLowerBoundOfIn0(xp,xP,xU)
& ! [X0] :
( aElementOf0(X0,xP)
=> sdtlseqdt0(xp,X0) )
& aElementOf0(xp,xU)
& aElementOf0(xp,xU) ),
inference(rectify,[],[f28]) ).
fof(f38,plain,
~ ( ( aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
| ! [X1] :
( aElementOf0(X1,xT)
=> sdtlseqdt0(X1,sdtlpdtrp0(xf,xp)) ) )
& ( aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU)
| ! [X0] :
( aElementOf0(X0,xP)
=> sdtlseqdt0(sdtlpdtrp0(xf,xp),X0) ) ) ),
inference(rectify,[],[f30]) ).
fof(f39,plain,
! [X0] :
( aCompleteLattice0(X0)
=> ( ! [X1] :
( aSubsetOf0(X1,X0)
=> ? [X2] :
( ? [X3] : aSupremumOfIn0(X3,X1,X0)
& aInfimumOfIn0(X2,X1,X0) ) )
& aSet0(X0) ) ),
inference(unused_predicate_definition_removal,[],[f16]) ).
fof(f40,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f41,plain,
! [X0] :
( ~ aSet0(X0)
| ( isEmpty0(X0)
<=> ! [X1] : ~ aElementOf0(X1,X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f42,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f44,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f8]) ).
fof(f45,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(ennf_transformation,[],[f9]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(flattening,[],[f46]) ).
fof(f50,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,X0)
| ! [X2] :
( aInfimumOfIn0(X2,X1,X0)
<=> ( ! [X3] :
( ~ aLowerBoundOfIn0(X3,X1,X0)
| sdtlseqdt0(X3,X2) )
& aLowerBoundOfIn0(X2,X1,X0)
& aElementOf0(X2,X0) ) ) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f56,plain,
! [X0] :
( ~ aCompleteLattice0(X0)
| ( ! [X1] :
( ~ aSubsetOf0(X1,X0)
| ? [X2] :
( ? [X3] : aSupremumOfIn0(X3,X1,X0)
& aInfimumOfIn0(X2,X1,X0) ) )
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f39]) ).
fof(f57,plain,
! [X0] :
( ~ aFunction0(X0)
| aSet0(szDzozmdt0(X0)) ),
inference(ennf_transformation,[],[f18]) ).
fof(f61,plain,
! [X0] :
( ~ aFunction0(X0)
| ! [X1] :
( ~ aElementOf0(X1,szDzozmdt0(X0))
| aElementOf0(sdtlpdtrp0(X0,X1),szRzazndt0(X0)) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f67,plain,
( xS = cS1142(xf)
& ! [X0] :
( ( ( ~ aFixedPointOf0(X0,xf)
& ( sdtlpdtrp0(xf,X0) != X0
| ~ aElementOf0(X0,szDzozmdt0(xf)) ) )
| aElementOf0(X0,xS) )
& ( ~ aElementOf0(X0,xS)
| ( aFixedPointOf0(X0,xf)
& sdtlpdtrp0(xf,X0) = X0
& aElementOf0(X0,szDzozmdt0(xf)) ) ) )
& aSet0(xS) ),
inference(ennf_transformation,[],[f25]) ).
fof(f68,plain,
( aSubsetOf0(xT,xS)
& ! [X0] :
( ~ aElementOf0(X0,xT)
| aElementOf0(X0,xS) )
& aSet0(xT) ),
inference(ennf_transformation,[],[f26]) ).
fof(f69,plain,
( xP = cS1241(xU,xf,xT)
& ! [X0] :
( ( ( ~ aUpperBoundOfIn0(X0,xT,xU)
& ? [X2] :
( aElementOf0(X2,xT)
& ~ sdtlseqdt0(X2,X0) ) )
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
| ~ aElementOf0(X0,xU)
| aElementOf0(X0,xP) )
& ( ~ aElementOf0(X0,xP)
| ( aUpperBoundOfIn0(X0,xT,xU)
& ! [X1] :
( ~ aElementOf0(X1,xT)
| sdtlseqdt0(X1,X0) )
& sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
& aElementOf0(X0,xU) ) ) )
& aSet0(xP) ),
inference(ennf_transformation,[],[f36]) ).
fof(f70,plain,
( xP = cS1241(xU,xf,xT)
& ! [X0] :
( ( ( ~ aUpperBoundOfIn0(X0,xT,xU)
& ? [X2] :
( aElementOf0(X2,xT)
& ~ sdtlseqdt0(X2,X0) ) )
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
| ~ aElementOf0(X0,xU)
| aElementOf0(X0,xP) )
& ( ~ aElementOf0(X0,xP)
| ( aUpperBoundOfIn0(X0,xT,xU)
& ! [X1] :
( ~ aElementOf0(X1,xT)
| sdtlseqdt0(X1,X0) )
& sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
& aElementOf0(X0,xU) ) ) )
& aSet0(xP) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
( aInfimumOfIn0(xp,xP,xU)
& ! [X1] :
( ( ~ aLowerBoundOfIn0(X1,xP,xU)
& ( ? [X2] :
( aElementOf0(X2,xP)
& ~ sdtlseqdt0(X1,X2) )
| ~ aElementOf0(X1,xU) ) )
| sdtlseqdt0(X1,xp) )
& aLowerBoundOfIn0(xp,xP,xU)
& ! [X0] :
( ~ aElementOf0(X0,xP)
| sdtlseqdt0(xp,X0) )
& aElementOf0(xp,xU)
& aElementOf0(xp,xU) ),
inference(ennf_transformation,[],[f37]) ).
fof(f72,plain,
( ( ~ aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
& ? [X1] :
( aElementOf0(X1,xT)
& ~ sdtlseqdt0(X1,sdtlpdtrp0(xf,xp)) ) )
| ( ~ aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU)
& ? [X0] :
( aElementOf0(X0,xP)
& ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),X0) ) ) ),
inference(ennf_transformation,[],[f38]) ).
fof(f79,plain,
! [X0] :
( ~ aSet0(X0)
| ( ( ~ isEmpty0(X0)
| ! [X1] : ~ aElementOf0(X1,X0) )
& ( ? [X1] : aElementOf0(X1,X0)
| isEmpty0(X0) ) ) ),
inference(nnf_transformation,[],[f41]) ).
fof(f80,plain,
! [X0] :
( ~ aSet0(X0)
| ( ( ~ isEmpty0(X0)
| ! [X2] : ~ aElementOf0(X2,X0) )
& ( ? [X1] : aElementOf0(X1,X0)
| isEmpty0(X0) ) ) ),
inference(rectify,[],[f79]) ).
fof(f81,plain,
! [X0] :
( ~ aSet0(X0)
| ( ( ~ isEmpty0(X0)
| ! [X2] : ~ aElementOf0(X2,X0) )
& ( aElementOf0(sK4(X0),X0)
| isEmpty0(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f80]) ).
fof(f82,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(nnf_transformation,[],[f42]) ).
fof(f83,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X3] :
( ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(rectify,[],[f83]) ).
fof(f85,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X3] :
( ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aSet0(X1) ) )
& ( ( aElementOf0(sK5(X0,X1),X1)
& ~ aElementOf0(sK5(X0,X1),X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f84]) ).
fof(f94,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,X0)
| ! [X2] :
( ( ~ aInfimumOfIn0(X2,X1,X0)
| ( ! [X3] :
( ~ aLowerBoundOfIn0(X3,X1,X0)
| sdtlseqdt0(X3,X2) )
& aLowerBoundOfIn0(X2,X1,X0)
& aElementOf0(X2,X0) ) )
& ( ? [X3] :
( aLowerBoundOfIn0(X3,X1,X0)
& ~ sdtlseqdt0(X3,X2) )
| ~ aLowerBoundOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| aInfimumOfIn0(X2,X1,X0) ) ) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f95,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,X0)
| ! [X2] :
( ( ~ aInfimumOfIn0(X2,X1,X0)
| ( ! [X3] :
( ~ aLowerBoundOfIn0(X3,X1,X0)
| sdtlseqdt0(X3,X2) )
& aLowerBoundOfIn0(X2,X1,X0)
& aElementOf0(X2,X0) ) )
& ( ? [X3] :
( aLowerBoundOfIn0(X3,X1,X0)
& ~ sdtlseqdt0(X3,X2) )
| ~ aLowerBoundOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| aInfimumOfIn0(X2,X1,X0) ) ) ) ),
inference(flattening,[],[f94]) ).
fof(f96,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,X0)
| ! [X2] :
( ( ~ aInfimumOfIn0(X2,X1,X0)
| ( ! [X4] :
( ~ aLowerBoundOfIn0(X4,X1,X0)
| sdtlseqdt0(X4,X2) )
& aLowerBoundOfIn0(X2,X1,X0)
& aElementOf0(X2,X0) ) )
& ( ? [X3] :
( aLowerBoundOfIn0(X3,X1,X0)
& ~ sdtlseqdt0(X3,X2) )
| ~ aLowerBoundOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| aInfimumOfIn0(X2,X1,X0) ) ) ) ),
inference(rectify,[],[f95]) ).
fof(f97,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,X0)
| ! [X2] :
( ( ~ aInfimumOfIn0(X2,X1,X0)
| ( ! [X4] :
( ~ aLowerBoundOfIn0(X4,X1,X0)
| sdtlseqdt0(X4,X2) )
& aLowerBoundOfIn0(X2,X1,X0)
& aElementOf0(X2,X0) ) )
& ( ( aLowerBoundOfIn0(sK8(X0,X1,X2),X1,X0)
& ~ sdtlseqdt0(sK8(X0,X1,X2),X2) )
| ~ aLowerBoundOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| aInfimumOfIn0(X2,X1,X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X3,sK8(X0,X1,X2))],[f96]) ).
fof(f102,plain,
! [X0] :
( ~ aCompleteLattice0(X0)
| ( ! [X1] :
( ~ aSubsetOf0(X1,X0)
| ( aSupremumOfIn0(sK11(X0,X1),X1,X0)
& aInfimumOfIn0(sK10(X0,X1),X1,X0) ) )
& aSet0(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X2,sK10(X0,X1)),skolemize(X3,sK11(X0,X1))],[f56]) ).
fof(f119,plain,
( isOn0(xf,xU)
& szRzazndt0(xf) = xU
& szDzozmdt0(xf) = szRzazndt0(xf)
& isMonotone0(xf)
& ! [X2,X3] :
( ~ aElementOf0(X3,szDzozmdt0(xf))
| ~ aElementOf0(X2,szDzozmdt0(xf))
| ~ sdtlseqdt0(X2,X3)
| sdtlseqdt0(sdtlpdtrp0(xf,X2),sdtlpdtrp0(xf,X3)) )
& aFunction0(xf)
& aCompleteLattice0(xU)
& ! [X0] :
( ( ~ aSubsetOf0(X0,xU)
& ( ? [X1] :
( aElementOf0(X1,X0)
& ~ aElementOf0(X1,xU) )
| ~ aSet0(X0) ) )
| sP2(X0) )
& aSet0(xU) ),
inference(rectify,[],[f76]) ).
fof(f120,plain,
( isOn0(xf,xU)
& szRzazndt0(xf) = xU
& szDzozmdt0(xf) = szRzazndt0(xf)
& isMonotone0(xf)
& ! [X2,X3] :
( ~ aElementOf0(X3,szDzozmdt0(xf))
| ~ aElementOf0(X2,szDzozmdt0(xf))
| ~ sdtlseqdt0(X2,X3)
| sdtlseqdt0(sdtlpdtrp0(xf,X2),sdtlpdtrp0(xf,X3)) )
& aFunction0(xf)
& aCompleteLattice0(xU)
& ! [X0] :
( ( ~ aSubsetOf0(X0,xU)
& ( ( aElementOf0(sK18(X0),X0)
& ~ aElementOf0(sK18(X0),xU) )
| ~ aSet0(X0) ) )
| sP2(X0) )
& aSet0(xU) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(X1,sK18(X0))],[f119]) ).
fof(f121,plain,
( xP = cS1241(xU,xf,xT)
& ! [X0] :
( ( ( ~ aUpperBoundOfIn0(X0,xT,xU)
& aElementOf0(sK19(X0),xT)
& ~ sdtlseqdt0(sK19(X0),X0) )
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
| ~ aElementOf0(X0,xU)
| aElementOf0(X0,xP) )
& ( ~ aElementOf0(X0,xP)
| ( aUpperBoundOfIn0(X0,xT,xU)
& ! [X1] :
( ~ aElementOf0(X1,xT)
| sdtlseqdt0(X1,X0) )
& sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
& aElementOf0(X0,xU) ) ) )
& aSet0(xP) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X2,sK19(X0))],[f70]) ).
fof(f122,plain,
( aInfimumOfIn0(xp,xP,xU)
& ! [X1] :
( ( ~ aLowerBoundOfIn0(X1,xP,xU)
& ( ( aElementOf0(sK20(X1),xP)
& ~ sdtlseqdt0(X1,sK20(X1)) )
| ~ aElementOf0(X1,xU) ) )
| sdtlseqdt0(X1,xp) )
& aLowerBoundOfIn0(xp,xP,xU)
& ! [X0] :
( ~ aElementOf0(X0,xP)
| sdtlseqdt0(xp,X0) )
& aElementOf0(xp,xU)
& aElementOf0(xp,xU) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X2,sK20(X1))],[f71]) ).
fof(f126,plain,
( sP3
| ( ~ aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU)
& aElementOf0(sK22,xP)
& ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),sK22) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(X0,sK22)],[f78]) ).
fof(f127,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f128,plain,
! [X2,X0] :
( ~ aSet0(X0)
| ~ isEmpty0(X0)
| ~ aElementOf0(X2,X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f129,plain,
! [X0] :
( ~ aSet0(X0)
| aElementOf0(sK4(X0),X0)
| isEmpty0(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f130,plain,
! [X3,X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f132,plain,
! [X0,X1] :
( ~ aSet0(X0)
| aElementOf0(sK5(X0,X1),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f133,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(sK5(X0,X1),X0)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f135,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f45]) ).
fof(f136,plain,
! [X2,X0,X1] :
( ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(cnf_transformation,[],[f47]) ).
fof(f146,plain,
! [X2,X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aInfimumOfIn0(X2,X1,X0)
| aLowerBoundOfIn0(X2,X1,X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f158,plain,
! [X0,X1] :
( ~ aCompleteLattice0(X0)
| ~ aSubsetOf0(X1,X0)
| aInfimumOfIn0(sK10(X0,X1),X1,X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f160,plain,
! [X0] :
( ~ aFunction0(X0)
| aSet0(szDzozmdt0(X0)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f165,plain,
! [X0,X1] :
( ~ aFunction0(X0)
| ~ aElementOf0(X1,szDzozmdt0(X0))
| aElementOf0(sdtlpdtrp0(X0,X1),szRzazndt0(X0)) ),
inference(cnf_transformation,[],[f61]) ).
fof(f193,plain,
xU = szRzazndt0(xf),
inference(cnf_transformation,[],[f120]) ).
fof(f194,plain,
szDzozmdt0(xf) = szRzazndt0(xf),
inference(cnf_transformation,[],[f120]) ).
fof(f196,plain,
! [X2,X3] :
( ~ aElementOf0(X3,szDzozmdt0(xf))
| ~ aElementOf0(X2,szDzozmdt0(xf))
| ~ sdtlseqdt0(X2,X3)
| sdtlseqdt0(sdtlpdtrp0(xf,X2),sdtlpdtrp0(xf,X3)) ),
inference(cnf_transformation,[],[f120]) ).
fof(f197,plain,
aFunction0(xf),
inference(cnf_transformation,[],[f120]) ).
fof(f198,plain,
aCompleteLattice0(xU),
inference(cnf_transformation,[],[f120]) ).
fof(f202,plain,
aSet0(xU),
inference(cnf_transformation,[],[f120]) ).
fof(f204,plain,
! [X0] :
( ~ aFixedPointOf0(X0,xf)
| aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f67]) ).
fof(f206,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| aFixedPointOf0(X0,xf) ),
inference(cnf_transformation,[],[f67]) ).
fof(f207,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(cnf_transformation,[],[f67]) ).
fof(f208,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| aElementOf0(X0,szDzozmdt0(xf)) ),
inference(cnf_transformation,[],[f67]) ).
fof(f211,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f68]) ).
fof(f212,plain,
aSet0(xT),
inference(cnf_transformation,[],[f68]) ).
fof(f218,plain,
! [X0,X1] :
( ~ aElementOf0(X0,xP)
| ~ aElementOf0(X1,xT)
| sdtlseqdt0(X1,X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f219,plain,
! [X0] :
( ~ aElementOf0(X0,xP)
| sdtlseqdt0(sdtlpdtrp0(xf,X0),X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f220,plain,
! [X0] :
( ~ aElementOf0(X0,xP)
| aElementOf0(X0,xU) ),
inference(cnf_transformation,[],[f121]) ).
fof(f221,plain,
aSet0(xP),
inference(cnf_transformation,[],[f121]) ).
fof(f223,plain,
! [X1] :
( ~ aLowerBoundOfIn0(X1,xP,xU)
| sdtlseqdt0(X1,xp) ),
inference(cnf_transformation,[],[f122]) ).
fof(f224,plain,
! [X1] :
( aElementOf0(sK20(X1),xP)
| ~ aElementOf0(X1,xU)
| sdtlseqdt0(X1,xp) ),
inference(cnf_transformation,[],[f122]) ).
fof(f225,plain,
! [X1] :
( ~ sdtlseqdt0(X1,sK20(X1))
| ~ aElementOf0(X1,xU)
| sdtlseqdt0(X1,xp) ),
inference(cnf_transformation,[],[f122]) ).
fof(f227,plain,
! [X0] :
( ~ aElementOf0(X0,xP)
| sdtlseqdt0(xp,X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f228,plain,
aElementOf0(xp,xU),
inference(cnf_transformation,[],[f122]) ).
fof(f234,plain,
( sP3
| aElementOf0(sK22,xP) ),
inference(cnf_transformation,[],[f126]) ).
fof(f235,plain,
( sP3
| ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),sK22) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_50,plain,
! [X0: $i] :
( isEmpty0(X0)
| aElementOf0(sK4(X0),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( ~ isEmpty0(X1)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aElementOf0(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(X0,X1)
| aElementOf0(sK5(X1,X0),X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,X2)
| ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(X2,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtlseqdt0(X2,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( aLowerBoundOfIn0(X0,X1,X2)
| ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| ~ aInfimumOfIn0(X0,X1,X2) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( aInfimumOfIn0(sK10(X1,X0),X0,X1)
| ~ aCompleteLattice0(X1)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_82,plain,
! [X0: $i] :
( aSet0(szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f160]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sdtlpdtrp0(X1,X0),szRzazndt0(X1))
| ~ aFunction0(X1)
| ~ aElementOf0(X0,szDzozmdt0(X1)) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_114,plain,
aSet0(xU),
inference(cnf_transformation,[],[f202]) ).
tcf(c_118,plain,
aCompleteLattice0(xU),
inference(cnf_transformation,[],[f198]) ).
tcf(c_119,plain,
aFunction0(xf),
inference(cnf_transformation,[],[f197]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sdtlpdtrp0(xf,X0),sdtlpdtrp0(xf,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf)) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_122,plain,
szDzozmdt0(xf) = szRzazndt0(xf),
inference(cnf_transformation,[],[f194]) ).
tcf(c_123,plain,
szRzazndt0(xf) = xU,
inference(cnf_transformation,[],[f193]) ).
tcf(c_126,plain,
! [X0: $i] :
( aElementOf0(X0,szDzozmdt0(xf))
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f208]) ).
tcf(c_127,plain,
! [X0: $i] :
( ( sdtlpdtrp0(xf,X0) = X0 )
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f207]) ).
tcf(c_128,plain,
! [X0: $i] :
( aFixedPointOf0(X0,xf)
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f206]) ).
tcf(c_130,plain,
! [X0: $i] :
( aElementOf0(X0,xS)
| ~ aFixedPointOf0(X0,xf) ),
inference(cnf_transformation,[],[f204]) ).
tcf(c_132,plain,
aSet0(xT),
inference(cnf_transformation,[],[f212]) ).
tcf(c_133,plain,
! [X0: $i] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[],[f211]) ).
tcf(c_135,plain,
aSet0(xP),
inference(cnf_transformation,[],[f221]) ).
tcf(c_136,plain,
! [X0: $i] :
( aElementOf0(X0,xU)
| ~ aElementOf0(X0,xP) ),
inference(cnf_transformation,[],[f220]) ).
tcf(c_137,plain,
! [X0: $i] :
( sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
| ~ aElementOf0(X0,xP) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,xP)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_145,plain,
aElementOf0(xp,xU),
inference(cnf_transformation,[],[f228]) ).
tcf(c_146,plain,
! [X0: $i] :
( sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,xP) ),
inference(cnf_transformation,[],[f227]) ).
tcf(c_148,plain,
! [X0: $i] :
( sdtlseqdt0(X0,xp)
| ~ aElementOf0(X0,xU)
| ~ sdtlseqdt0(X0,sK20(X0)) ),
inference(cnf_transformation,[],[f225]) ).
tcf(c_149,plain,
! [X0: $i] :
( sdtlseqdt0(X0,xp)
| aElementOf0(sK20(X0),xP)
| ~ aElementOf0(X0,xU) ),
inference(cnf_transformation,[],[f224]) ).
tcf(c_150,plain,
! [X0: $i] :
( sdtlseqdt0(X0,xp)
| ~ aLowerBoundOfIn0(X0,xP,xU) ),
inference(cnf_transformation,[],[f223]) ).
tcf(c_155,negated_conjecture,
( sP3
| ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),sK22) ),
inference(cnf_transformation,[],[f235]) ).
tcf(c_156,negated_conjecture,
( sP3
| aElementOf0(sK22,xP) ),
inference(cnf_transformation,[],[f234]) ).
tcf(c_257,plain,
! [X0: $i] :
( aSet0(szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(prop_impl_just,[status(thm)],[c_82]) ).
tcf(c_287,plain,
! [X0: $i] :
( ~ aFixedPointOf0(X0,xf)
| aElementOf0(X0,szDzozmdt0(xf)) ),
inference(prop_impl_just,[status(thm)],[c_130,c_126]) ).
tcf(c_288,plain,
! [X0: $i] :
( aElementOf0(X0,szDzozmdt0(xf))
| ~ aFixedPointOf0(X0,xf) ),
inference(renaming,[status(thm)],[c_287]) ).
tcf(c_291,plain,
! [X0: $i] :
( ( sdtlpdtrp0(xf,X0) = X0 )
| ~ aFixedPointOf0(X0,xf) ),
inference(prop_impl_just,[status(thm)],[c_130,c_127]) ).
tcf(c_295,plain,
! [X0: $i] :
( ~ aElementOf0(X0,xT)
| aFixedPointOf0(X0,xf) ),
inference(prop_impl_just,[status(thm)],[c_133,c_128]) ).
tcf(c_296,plain,
! [X0: $i] :
( aFixedPointOf0(X0,xf)
| ~ aElementOf0(X0,xT) ),
inference(renaming,[status(thm)],[c_295]) ).
tcf(c_1170,plain,
szDzozmdt0(xf) = xU,
inference(light_normalisation,[status(thm)],[c_122,c_123]) ).
tcf(c_1171,plain,
! [X0: $i] :
( aElementOf0(X0,xU)
| ~ aFixedPointOf0(X0,xf) ),
inference(light_normalisation,[status(thm)],[c_288,c_1170]) ).
tcf(c_1173,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sdtlpdtrp0(xf,X0),sdtlpdtrp0(xf,X1))
| ~ aElementOf0(X1,xU)
| ~ aElementOf0(X0,xU)
| ~ sdtlseqdt0(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_120,c_1170]) ).
tcf(c_1199,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(sK4(X1),X1)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aElementOf0(X2,X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_50]) ).
tcf(c_1200,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sK4(X1),X1)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(unflattening,[status(thm)],[c_1199]) ).
tcf(c_1223,plain,
! [X0: $i,X1: $i] :
( aInfimumOfIn0(sK10(X0,X1),X1,X0)
| ~ aSubsetOf0(X1,X0)
| ( X0 != xU ) ),
inference(resolution_lifted,[status(thm)],[c_80,c_118]) ).
tcf(c_1224,plain,
! [X0: $i] :
( aInfimumOfIn0(sK10(xU,X0),X0,xU)
| ~ aSubsetOf0(X0,xU) ),
inference(unflattening,[status(thm)],[c_1223]) ).
tcf(c_1513,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sdtlpdtrp0(X0,X1),szRzazndt0(X0))
| ~ aElementOf0(X1,szDzozmdt0(X0))
| ( X0 != xf ) ),
inference(resolution_lifted,[status(thm)],[c_87,c_119]) ).
tcf(c_1514,plain,
! [X0: $i] :
( aElementOf0(sdtlpdtrp0(xf,X0),szRzazndt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf)) ),
inference(unflattening,[status(thm)],[c_1513]) ).
tcf(c_1546,plain,
! [X0: $i] :
( aSet0(szDzozmdt0(X0))
| ( X0 != xf ) ),
inference(resolution_lifted,[status(thm)],[c_257,c_119]) ).
tcf(c_1547,plain,
aSet0(szDzozmdt0(xf)),
inference(unflattening,[status(thm)],[c_1546]) ).
tcf(c_4017,plain,
! [X0: $i] :
( aElementOf0(sdtlpdtrp0(xf,X0),szRzazndt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf)) ),
inference(prop_impl_just,[status(thm)],[c_1514]) ).
tcf(c_4766,plain,
! [X0: $i] :
( aElementOf0(sdtlpdtrp0(xf,X0),xU)
| ~ aElementOf0(X0,xU) ),
inference(light_normalisation,[status(thm)],[c_4017,c_123,c_1170]) ).
tcf(c_7112,plain,
! [X0: $i] :
( aElementOf0(sdtlpdtrp0(xf,X0),xU)
| ~ aElementOf0(X0,xU) ),
inference(prop_impl_just,[status(thm)],[c_4766]) ).
tcf(c_7114,plain,
! [X0: $i] :
( ~ aFixedPointOf0(X0,xf)
| aElementOf0(X0,xU) ),
inference(prop_impl_just,[status(thm)],[c_1171]) ).
tcf(c_7115,plain,
! [X0: $i] :
( aElementOf0(X0,xU)
| ~ aFixedPointOf0(X0,xf) ),
inference(renaming,[status(thm)],[c_7114]) ).
tcf(c_7122,plain,
! [X0: $i] :
( aInfimumOfIn0(sK10(xU,X0),X0,xU)
| ~ aSubsetOf0(X0,xU) ),
inference(prop_impl_just,[status(thm)],[c_1224]) ).
tcf(c_7126,plain,
! [X0: $i] :
( ( sdtlpdtrp0(xf,X0) = X0 )
| ~ aFixedPointOf0(X0,xf) ),
inference(prop_impl_just,[status(thm)],[c_291]) ).
tcf(c_7130,plain,
! [X0: $i] :
( ~ aElementOf0(X0,xT)
| aFixedPointOf0(X0,xf) ),
inference(prop_impl_just,[status(thm)],[c_296]) ).
tcf(c_7131,plain,
! [X0: $i] :
( aFixedPointOf0(X0,xf)
| ~ aElementOf0(X0,xT) ),
inference(renaming,[status(thm)],[c_7130]) ).
tcf(c_10163,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( aElementOf0(sdtlpdtrp0(xf,X0_iProver_sdtlseqdt0_2),xU)
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xU) ),
inference(subtyping,[status(esa)],[c_7112]) ).
tcf(c_10176,plain,
! [X0_iProver_aElementOf0_2: iProver_aElementOf0_2] :
( aInfimumOfIn0(sK10(xU,X0_iProver_aElementOf0_2),X0_iProver_aElementOf0_2,xU)
| ~ aSubsetOf0(X0_iProver_aElementOf0_2,xU) ),
inference(subtyping,[status(esa)],[c_7122]) ).
tcf(c_10178,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X0_iProver_aElementOf0_2: iProver_aElementOf0_2] :
( aElementOf0(sK4(X0_iProver_aElementOf0_2),X0_iProver_aElementOf0_2)
| ~ aSet0(X0_iProver_aElementOf0_2)
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,X0_iProver_aElementOf0_2) ),
inference(subtyping,[status(esa)],[c_1200]) ).
tcf(c_10179,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sdtlseqdt0(sdtlpdtrp0(xf,X0_iProver_sdtlseqdt0_2),sdtlpdtrp0(xf,X1_iProver_sdtlseqdt0_2))
| ~ aElementOf0(X1_iProver_sdtlseqdt0_2,xU)
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xU)
| ~ sdtlseqdt0(X0_iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2) ),
inference(subtyping,[status(esa)],[c_1173]) ).
tcf(c_10181,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( aElementOf0(X0_iProver_sdtlseqdt0_2,xU)
| ~ aFixedPointOf0(X0_iProver_sdtlseqdt0_2,xf) ),
inference(subtyping,[status(esa)],[c_7115]) ).
tcf(c_10182,plain,
szDzozmdt0(xf) = xU,
inference(subtyping,[status(esa)],[c_1170]) ).
tcf(c_10185,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( aFixedPointOf0(X0_iProver_sdtlseqdt0_2,xf)
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xT) ),
inference(subtyping,[status(esa)],[c_7131]) ).
tcf(c_10186,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( ( sdtlpdtrp0(xf,X0_iProver_sdtlseqdt0_2) = X0_iProver_sdtlseqdt0_2 )
| ~ aFixedPointOf0(X0_iProver_sdtlseqdt0_2,xf) ),
inference(subtyping,[status(esa)],[c_7126]) ).
tcf(c_10190,negated_conjecture,
( sP3
| aElementOf0(sK22,xP) ),
inference(subtyping,[status(esa)],[c_156]) ).
tcf(c_10196,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sdtlseqdt0(X0_iProver_sdtlseqdt0_2,xp)
| ~ aLowerBoundOfIn0(X0_iProver_sdtlseqdt0_2,xP,xU) ),
inference(subtyping,[status(esa)],[c_150]) ).
tcf(c_10197,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sdtlseqdt0(X0_iProver_sdtlseqdt0_2,xp)
| aElementOf0(sK20(X0_iProver_sdtlseqdt0_2),xP)
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xU) ),
inference(subtyping,[status(esa)],[c_149]) ).
tcf(c_10198,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sdtlseqdt0(X0_iProver_sdtlseqdt0_2,xp)
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xU)
| ~ sdtlseqdt0(X0_iProver_sdtlseqdt0_2,sK20(X0_iProver_sdtlseqdt0_2)) ),
inference(subtyping,[status(esa)],[c_148]) ).
tcf(c_10200,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sdtlseqdt0(xp,X0_iProver_sdtlseqdt0_2)
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xP) ),
inference(subtyping,[status(esa)],[c_146]) ).
tcf(c_10207,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sdtlseqdt0(X0_iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2)
| ~ aElementOf0(X1_iProver_sdtlseqdt0_2,xP)
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xT) ),
inference(subtyping,[status(esa)],[c_138]) ).
tcf(c_10208,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sdtlseqdt0(sdtlpdtrp0(xf,X0_iProver_sdtlseqdt0_2),X0_iProver_sdtlseqdt0_2)
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xP) ),
inference(subtyping,[status(esa)],[c_137]) ).
tcf(c_10209,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( aElementOf0(X0_iProver_sdtlseqdt0_2,xU)
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xP) ),
inference(subtyping,[status(esa)],[c_136]) ).
tcf(c_10232,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X0_iProver_aElementOf0_2: iProver_aElementOf0_2,X1_iProver_aElementOf0_2: iProver_aElementOf0_2] :
( aLowerBoundOfIn0(X0_iProver_sdtlseqdt0_2,X0_iProver_aElementOf0_2,X1_iProver_aElementOf0_2)
| ~ aSet0(X1_iProver_aElementOf0_2)
| ~ aSubsetOf0(X0_iProver_aElementOf0_2,X1_iProver_aElementOf0_2)
| ~ aInfimumOfIn0(X0_iProver_sdtlseqdt0_2,X0_iProver_aElementOf0_2,X1_iProver_aElementOf0_2) ),
inference(subtyping,[status(esa)],[c_70]) ).
tcf(c_10242,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X2_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sdtlseqdt0(X2_iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2)
| ~ aElement0(X2_iProver_sdtlseqdt0_2)
| ~ aElement0(X1_iProver_sdtlseqdt0_2)
| ~ aElement0(X0_iProver_sdtlseqdt0_2)
| ~ sdtlseqdt0(X2_iProver_sdtlseqdt0_2,X0_iProver_sdtlseqdt0_2)
| ~ sdtlseqdt0(X0_iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2) ),
inference(subtyping,[status(esa)],[c_58]) ).
tcf(c_10243,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( ( X0_iProver_sdtlseqdt0_2 = X1_iProver_sdtlseqdt0_2 )
| ~ aElement0(X1_iProver_sdtlseqdt0_2)
| ~ aElement0(X0_iProver_sdtlseqdt0_2)
| ~ sdtlseqdt0(X1_iProver_sdtlseqdt0_2,X0_iProver_sdtlseqdt0_2)
| ~ sdtlseqdt0(X0_iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2) ),
inference(subtyping,[status(esa)],[c_57]) ).
tcf(c_10245,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X0_iProver_aElementOf0_2: iProver_aElementOf0_2,X1_iProver_aElementOf0_2: iProver_aElementOf0_2] :
( aElementOf0(X0_iProver_sdtlseqdt0_2,X1_iProver_aElementOf0_2)
| ~ aSet0(X1_iProver_aElementOf0_2)
| ~ aSubsetOf0(X0_iProver_aElementOf0_2,X1_iProver_aElementOf0_2)
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,X0_iProver_aElementOf0_2) ),
inference(subtyping,[status(esa)],[c_55]) ).
tcf(c_10247,plain,
! [X0_iProver_aElementOf0_2: iProver_aElementOf0_2,X1_iProver_aElementOf0_2: iProver_aElementOf0_2] :
( aSubsetOf0(X0_iProver_aElementOf0_2,X1_iProver_aElementOf0_2)
| aElementOf0(sK5(X1_iProver_aElementOf0_2,X0_iProver_aElementOf0_2),X0_iProver_aElementOf0_2)
| ~ aSet0(X1_iProver_aElementOf0_2)
| ~ aSet0(X0_iProver_aElementOf0_2) ),
inference(subtyping,[status(esa)],[c_53]) ).
tcf(c_10248,plain,
! [X0_iProver_aElementOf0_2: iProver_aElementOf0_2,X1_iProver_aElementOf0_2: iProver_aElementOf0_2] :
( aSubsetOf0(X1_iProver_aElementOf0_2,X0_iProver_aElementOf0_2)
| ~ aSet0(X1_iProver_aElementOf0_2)
| ~ aSet0(X0_iProver_aElementOf0_2)
| ~ aElementOf0(sK5(X0_iProver_aElementOf0_2,X1_iProver_aElementOf0_2),X0_iProver_aElementOf0_2) ),
inference(subtyping,[status(esa)],[c_52]) ).
tcf(c_10249,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X0_iProver_aElementOf0_2: iProver_aElementOf0_2] :
( aElement0(X0_iProver_sdtlseqdt0_2)
| ~ aSet0(X0_iProver_aElementOf0_2)
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,X0_iProver_aElementOf0_2) ),
inference(subtyping,[status(esa)],[c_49]) ).
tcf(c_10251,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] : X0_iProver_sdtlseqdt0_2 = X0_iProver_sdtlseqdt0_2,
theory(equality) ).
tcf(c_10255,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X0_iProver_aElementOf0_2: iProver_aElementOf0_2,X1_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X1_iProver_aElementOf0_2: iProver_aElementOf0_2] :
( aElementOf0(X0_iProver_sdtlseqdt0_2,X0_iProver_aElementOf0_2)
| ~ aElementOf0(X1_iProver_sdtlseqdt0_2,X1_iProver_aElementOf0_2)
| ( X0_iProver_aElementOf0_2 != X1_iProver_aElementOf0_2 )
| ( X0_iProver_sdtlseqdt0_2 != X1_iProver_sdtlseqdt0_2 ) ),
theory(equality) ).
tcf(c_10315,plain,
( aElement0(xp)
| ~ aSet0(xU)
| ~ aElementOf0(xp,xU) ),
inference(instantiation,[status(thm)],[c_10249]) ).
tcf(c_12095,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sdtlseqdt0(sdtlpdtrp0(xf,xp),sK22)
| ~ aElement0(sK22)
| ~ aElement0(X0_iProver_sdtlseqdt0_2)
| ~ sdtlseqdt0(X0_iProver_sdtlseqdt0_2,sK22)
| ~ aElement0(sdtlpdtrp0(xf,xp))
| ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),X0_iProver_sdtlseqdt0_2) ),
inference(instantiation,[status(thm)],[c_10242]) ).
tcf(c_12100,plain,
( aSubsetOf0(xP,xU)
| ~ aSet0(xP)
| ~ aSet0(xU)
| ~ aElementOf0(sK5(xU,xP),xU) ),
inference(instantiation,[status(thm)],[c_10248]) ).
tcf(c_12459,plain,
( sdtlseqdt0(sdtlpdtrp0(xf,sK22),sK22)
| ~ aElementOf0(sK22,xP) ),
inference(instantiation,[status(thm)],[c_10208]) ).
tcf(c_13129,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sdtlseqdt0(sK21,X0_iProver_sdtlseqdt0_2)
| ~ aElementOf0(sK21,xT)
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xP) ),
inference(instantiation,[status(thm)],[c_10207]) ).
tcf(c_13495,plain,
( sP3
| sdtlseqdt0(xp,sK22) ),
inference(superposition,[status(thm)],[c_10190,c_10200]) ).
tcf(c_13496,plain,
( sP3
| aElementOf0(sK22,xU) ),
inference(superposition,[status(thm)],[c_10190,c_10209]) ).
tcf(c_13668,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( aElement0(sdtlpdtrp0(xf,X0_iProver_sdtlseqdt0_2))
| ~ aSet0(xU)
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xU) ),
inference(superposition,[status(thm)],[c_10163,c_10249]) ).
tcf(c_13672,plain,
( sP3
| aElement0(sK22)
| ~ aSet0(xU) ),
inference(superposition,[status(thm)],[c_13496,c_10249]) ).
tcf(c_13678,plain,
( aElement0(sdtlpdtrp0(xf,xp))
| ~ aSet0(xU)
| ~ aElementOf0(xp,xU) ),
inference(instantiation,[status(thm)],[c_13668]) ).
tcf(c_13909,plain,
( sdtlseqdt0(sK21,xp)
| ~ aElementOf0(sK21,xU)
| ~ sdtlseqdt0(sK21,sK20(sK21)) ),
inference(instantiation,[status(thm)],[c_10198]) ).
tcf(c_13910,plain,
( sdtlseqdt0(sK21,xp)
| aElementOf0(sK20(sK21),xP)
| ~ aElementOf0(sK21,xU) ),
inference(instantiation,[status(thm)],[c_10197]) ).
tcf(c_14246,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sdtlseqdt0(X0_iProver_sdtlseqdt0_2,xp)
| aElement0(sK20(X0_iProver_sdtlseqdt0_2))
| ~ aSet0(xP)
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xU) ),
inference(superposition,[status(thm)],[c_10197,c_10249]) ).
tcf(c_14392,plain,
( sP3
| aElementOf0(sK4(xP),xP)
| ~ aSet0(xP) ),
inference(superposition,[status(thm)],[c_10190,c_10178]) ).
tcf(c_14463,plain,
( sP3
| aElementOf0(sK4(xP),xP) ),
inference(global_subsumption_just,[status(thm)],[c_14392,c_135,c_14392]) ).
tcf(c_14466,plain,
( sP3
| aElement0(sK4(xP))
| ~ aSet0(xP) ),
inference(superposition,[status(thm)],[c_14463,c_10249]) ).
tcf(c_14679,plain,
! [X0_iProver_aElementOf0_2: iProver_aElementOf0_2] :
( aSubsetOf0(xP,X0_iProver_aElementOf0_2)
| aElementOf0(sK5(X0_iProver_aElementOf0_2,xP),xU)
| ~ aSet0(xP)
| ~ aSet0(X0_iProver_aElementOf0_2) ),
inference(superposition,[status(thm)],[c_10247,c_10209]) ).
tcf(c_14686,plain,
( aSubsetOf0(xP,xU)
| aElementOf0(sK5(xU,xP),xU)
| ~ aSet0(xP)
| ~ aSet0(xU) ),
inference(instantiation,[status(thm)],[c_14679]) ).
tcf(c_14883,plain,
( sP3
| aElementOf0(sK4(xP),xP)
| ~ aSet0(xP) ),
inference(superposition,[status(thm)],[c_10190,c_10178]) ).
tcf(c_14899,plain,
( sP3
| aElementOf0(sK4(xP),xP) ),
inference(global_subsumption_just,[status(thm)],[c_14883,c_135,c_14392]) ).
tcf(c_14951,plain,
! [X0_iProver_aElementOf0_2: iProver_aElementOf0_2] :
( sP3
| aElementOf0(sK4(xP),X0_iProver_aElementOf0_2)
| ~ aSet0(X0_iProver_aElementOf0_2)
| ~ aSubsetOf0(xP,X0_iProver_aElementOf0_2) ),
inference(superposition,[status(thm)],[c_14899,c_10245]) ).
tcf(c_15172,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sP3
| sdtlseqdt0(sK4(xP),X0_iProver_sdtlseqdt0_2)
| ~ aSet0(xT)
| ~ aSubsetOf0(xP,xT)
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xP) ),
inference(superposition,[status(thm)],[c_14951,c_10207]) ).
tcf(c_15453,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sP3
| sdtlseqdt0(sK4(xP),X0_iProver_sdtlseqdt0_2)
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xP)
| ~ aSubsetOf0(xP,xT) ),
inference(global_subsumption_just,[status(thm)],[c_15172,c_132,c_15172]) ).
tcf(c_15454,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sP3
| sdtlseqdt0(sK4(xP),X0_iProver_sdtlseqdt0_2)
| ~ aSubsetOf0(xP,xT)
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xP) ),
inference(renaming,[status(thm)],[c_15453]) ).
tcf(c_15838,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( aElementOf0(X0_iProver_sdtlseqdt0_2,szDzozmdt0(xf))
| ~ aElementOf0(X1_iProver_sdtlseqdt0_2,xU)
| ( X0_iProver_sdtlseqdt0_2 != X1_iProver_sdtlseqdt0_2 ) ),
inference(resolution,[status(thm)],[c_10255,c_10182]) ).
tcf(c_15923,plain,
! [X0_iProver_aElementOf0_2: iProver_aElementOf0_2] :
( aLowerBoundOfIn0(sK10(xU,X0_iProver_aElementOf0_2),X0_iProver_aElementOf0_2,xU)
| ~ aSet0(xU)
| ~ aSubsetOf0(X0_iProver_aElementOf0_2,xU) ),
inference(superposition,[status(thm)],[c_10176,c_10232]) ).
tcf(c_16800,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sP3
| ( sK4(xP) = X0_iProver_sdtlseqdt0_2 )
| ~ aElement0(X0_iProver_sdtlseqdt0_2)
| ~ aSubsetOf0(xP,xT)
| ~ aElement0(sK4(xP))
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xP)
| ~ sdtlseqdt0(X0_iProver_sdtlseqdt0_2,sK4(xP)) ),
inference(superposition,[status(thm)],[c_15454,c_10243]) ).
tcf(c_18279,plain,
( sP3
| aElementOf0(sK4(xP),xP)
| ~ aSet0(xP) ),
inference(superposition,[status(thm)],[c_10190,c_10178]) ).
tcf(c_18329,plain,
( sP3
| aElementOf0(sK4(xP),xP) ),
inference(global_subsumption_just,[status(thm)],[c_18279,c_135,c_14392]) ).
tcf(c_18332,plain,
! [X0_iProver_aElementOf0_2: iProver_aElementOf0_2] :
( sP3
| aElementOf0(sK4(xP),X0_iProver_aElementOf0_2)
| ~ aSet0(X0_iProver_aElementOf0_2)
| ~ aSubsetOf0(xP,X0_iProver_aElementOf0_2) ),
inference(superposition,[status(thm)],[c_18329,c_10245]) ).
tcf(c_18336,plain,
( sP3
| sdtlseqdt0(xp,sK4(xP)) ),
inference(superposition,[status(thm)],[c_18329,c_10200]) ).
tcf(c_18347,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sP3
| sdtlseqdt0(sK4(xP),X0_iProver_sdtlseqdt0_2)
| ~ aSet0(xT)
| ~ aSubsetOf0(xP,xT)
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xP) ),
inference(superposition,[status(thm)],[c_18332,c_10207]) ).
tcf(c_18370,plain,
! [X0_iProver_aElementOf0_2: iProver_aElementOf0_2] :
( aLowerBoundOfIn0(sK10(xU,X0_iProver_aElementOf0_2),X0_iProver_aElementOf0_2,xU)
| ~ aSet0(xU)
| ~ aSubsetOf0(X0_iProver_aElementOf0_2,xU) ),
inference(superposition,[status(thm)],[c_10176,c_10232]) ).
tcf(c_18399,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sP3
| sdtlseqdt0(sK4(xP),X0_iProver_sdtlseqdt0_2)
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xP)
| ~ aSubsetOf0(xP,xT) ),
inference(global_subsumption_just,[status(thm)],[c_18347,c_132,c_15172]) ).
tcf(c_18400,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sP3
| sdtlseqdt0(sK4(xP),X0_iProver_sdtlseqdt0_2)
| ~ aSubsetOf0(xP,xT)
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xP) ),
inference(renaming,[status(thm)],[c_18399]) ).
tcf(c_18428,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sP3
| ( sK4(xP) = X0_iProver_sdtlseqdt0_2 )
| ~ aElement0(X0_iProver_sdtlseqdt0_2)
| ~ aSubsetOf0(xP,xT)
| ~ aElement0(sK4(xP))
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xP)
| ~ sdtlseqdt0(X0_iProver_sdtlseqdt0_2,sK4(xP)) ),
inference(superposition,[status(thm)],[c_18400,c_10243]) ).
tcf(c_18525,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sP3
| ( sK4(xP) = X0_iProver_sdtlseqdt0_2 )
| ~ aElement0(X0_iProver_sdtlseqdt0_2)
| ~ aSubsetOf0(xP,xT)
| ~ sdtlseqdt0(X0_iProver_sdtlseqdt0_2,sK4(xP))
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xP) ),
inference(global_subsumption_just,[status(thm)],[c_18428,c_135,c_14466,c_16800]) ).
tcf(c_18526,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sP3
| ( sK4(xP) = X0_iProver_sdtlseqdt0_2 )
| ~ aElement0(X0_iProver_sdtlseqdt0_2)
| ~ aSubsetOf0(xP,xT)
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xP)
| ~ sdtlseqdt0(X0_iProver_sdtlseqdt0_2,sK4(xP)) ),
inference(renaming,[status(thm)],[c_18525]) ).
tcf(c_18578,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sP3
| sdtlseqdt0(X0_iProver_sdtlseqdt0_2,sK4(xP))
| ~ aElement0(xp)
| ~ aElement0(X0_iProver_sdtlseqdt0_2)
| ~ aElement0(sK4(xP))
| ~ sdtlseqdt0(X0_iProver_sdtlseqdt0_2,xp) ),
inference(superposition,[status(thm)],[c_18336,c_10242]) ).
tcf(c_19002,plain,
( sdtlseqdt0(sK21,sK20(sK21))
| ~ aElementOf0(sK21,xT)
| ~ aElementOf0(sK20(sK21),xP) ),
inference(instantiation,[status(thm)],[c_13129]) ).
tcf(c_19849,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sdtlseqdt0(sdtlpdtrp0(xf,xp),sK22)
| ~ aElement0(sK22)
| ~ aElement0(sdtlpdtrp0(xf,xp))
| ~ aElement0(sdtlpdtrp0(xf,X0_iProver_sdtlseqdt0_2))
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X0_iProver_sdtlseqdt0_2),sK22)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),sdtlpdtrp0(xf,X0_iProver_sdtlseqdt0_2)) ),
inference(instantiation,[status(thm)],[c_12095]) ).
tcf(c_20007,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sP3
| sdtlseqdt0(X0_iProver_sdtlseqdt0_2,sK4(xP))
| ~ sdtlseqdt0(X0_iProver_sdtlseqdt0_2,xp)
| ~ aElement0(X0_iProver_sdtlseqdt0_2) ),
inference(global_subsumption_just,[status(thm)],[c_18578,c_135,c_114,c_145,c_10315,c_14466,c_18578]) ).
tcf(c_20008,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sP3
| sdtlseqdt0(X0_iProver_sdtlseqdt0_2,sK4(xP))
| ~ aElement0(X0_iProver_sdtlseqdt0_2)
| ~ sdtlseqdt0(X0_iProver_sdtlseqdt0_2,xp) ),
inference(renaming,[status(thm)],[c_20007]) ).
tcf(c_20017,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sP3
| ( sK4(xP) = X0_iProver_sdtlseqdt0_2 )
| ~ aElement0(X0_iProver_sdtlseqdt0_2)
| ~ aSubsetOf0(xP,xT)
| ~ sdtlseqdt0(X0_iProver_sdtlseqdt0_2,xp)
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xP) ),
inference(superposition,[status(thm)],[c_20008,c_18526]) ).
tcf(c_20499,plain,
! [X0_iProver_aElementOf0_2: iProver_aElementOf0_2] :
( aLowerBoundOfIn0(sK10(xU,X0_iProver_aElementOf0_2),X0_iProver_aElementOf0_2,xU)
| ~ aSubsetOf0(X0_iProver_aElementOf0_2,xU) ),
inference(global_subsumption_just,[status(thm)],[c_18370,c_114,c_15923]) ).
tcf(c_20505,plain,
( sdtlseqdt0(sK10(xU,xP),xp)
| ~ aSubsetOf0(xP,xU) ),
inference(superposition,[status(thm)],[c_20499,c_10196]) ).
tcf(c_20976,plain,
sdtlseqdt0(sK10(xU,xP),xp),
inference(global_subsumption_just,[status(thm)],[c_20505,c_135,c_114,c_12100,c_14686,c_20505]) ).
tcf(c_22750,plain,
! [X0_iProver_aElementOf0_2: iProver_aElementOf0_2] :
( aElement0(sdtlpdtrp0(xf,sK22))
| ~ aSet0(X0_iProver_aElementOf0_2)
| ~ aElementOf0(sdtlpdtrp0(xf,sK22),X0_iProver_aElementOf0_2) ),
inference(instantiation,[status(thm)],[c_10249]) ).
tcf(c_22751,plain,
( aElement0(sdtlpdtrp0(xf,sK22))
| ~ aSet0(xU)
| ~ aElementOf0(sdtlpdtrp0(xf,sK22),xU) ),
inference(instantiation,[status(thm)],[c_22750]) ).
tcf(c_24123,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( aElementOf0(X0_iProver_sdtlseqdt0_2,szDzozmdt0(xf))
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xU) ),
inference(resolution,[status(thm)],[c_15838,c_10251]) ).
tcf(c_24321,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( aElement0(X0_iProver_sdtlseqdt0_2)
| ~ aSet0(szDzozmdt0(xf))
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xU) ),
inference(resolution,[status(thm)],[c_24123,c_10249]) ).
tcf(c_24479,plain,
( sdtlseqdt0(sdtlpdtrp0(xf,xp),sK22)
| ~ aElement0(sK22)
| ~ aElement0(sdtlpdtrp0(xf,sK22))
| ~ aElement0(sdtlpdtrp0(xf,xp))
| ~ sdtlseqdt0(sdtlpdtrp0(xf,sK22),sK22)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),sdtlpdtrp0(xf,sK22)) ),
inference(instantiation,[status(thm)],[c_19849]) ).
tcf(c_25848,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sdtlseqdt0(X0_iProver_sdtlseqdt0_2,xp)
| aElement0(sK20(X0_iProver_sdtlseqdt0_2))
| ~ aSet0(xP)
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xU) ),
inference(superposition,[status(thm)],[c_10197,c_10249]) ).
tcf(c_25901,plain,
( sP3
| aElementOf0(sK4(xP),xP)
| ~ aSet0(xP) ),
inference(superposition,[status(thm)],[c_10190,c_10178]) ).
tcf(c_25912,plain,
( sP3
| aElementOf0(sK4(xP),xP) ),
inference(global_subsumption_just,[status(thm)],[c_25901,c_14463]) ).
tcf(c_25915,plain,
! [X0_iProver_aElementOf0_2: iProver_aElementOf0_2] :
( sP3
| aElementOf0(sK4(xP),X0_iProver_aElementOf0_2)
| ~ aSet0(X0_iProver_aElementOf0_2)
| ~ aSubsetOf0(xP,X0_iProver_aElementOf0_2) ),
inference(superposition,[status(thm)],[c_25912,c_10245]) ).
tcf(c_25919,plain,
( sP3
| sdtlseqdt0(xp,sK4(xP)) ),
inference(superposition,[status(thm)],[c_25912,c_10200]) ).
tcf(c_25954,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sP3
| sdtlseqdt0(sK4(xP),X0_iProver_sdtlseqdt0_2)
| ~ aSet0(xT)
| ~ aSubsetOf0(xP,xT)
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xP) ),
inference(superposition,[status(thm)],[c_25915,c_10207]) ).
tcf(c_25988,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sP3
| sdtlseqdt0(sK4(xP),X0_iProver_sdtlseqdt0_2)
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xP)
| ~ aSubsetOf0(xP,xT) ),
inference(global_subsumption_just,[status(thm)],[c_25954,c_15454]) ).
tcf(c_25989,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sP3
| sdtlseqdt0(sK4(xP),X0_iProver_sdtlseqdt0_2)
| ~ aSubsetOf0(xP,xT)
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xP) ),
inference(renaming,[status(thm)],[c_25988]) ).
tcf(c_26002,plain,
! [X0_iProver_aElementOf0_2: iProver_aElementOf0_2] :
( aLowerBoundOfIn0(sK10(xU,X0_iProver_aElementOf0_2),X0_iProver_aElementOf0_2,xU)
| ~ aSet0(xU)
| ~ aSubsetOf0(X0_iProver_aElementOf0_2,xU) ),
inference(superposition,[status(thm)],[c_10176,c_10232]) ).
tcf(c_26060,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sP3
| ( sK4(xP) = X0_iProver_sdtlseqdt0_2 )
| ~ aElement0(X0_iProver_sdtlseqdt0_2)
| ~ aSubsetOf0(xP,xT)
| ~ aElement0(sK4(xP))
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xP)
| ~ sdtlseqdt0(X0_iProver_sdtlseqdt0_2,sK4(xP)) ),
inference(superposition,[status(thm)],[c_25989,c_10243]) ).
tcf(c_26122,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sP3
| ( sK4(xP) = X0_iProver_sdtlseqdt0_2 )
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xP)
| ~ sdtlseqdt0(X0_iProver_sdtlseqdt0_2,sK4(xP))
| ~ aSubsetOf0(xP,xT) ),
inference(global_subsumption_just,[status(thm)],[c_26060,c_1547,c_10209,c_18526,c_24321]) ).
tcf(c_26123,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sP3
| ( sK4(xP) = X0_iProver_sdtlseqdt0_2 )
| ~ aSubsetOf0(xP,xT)
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xP)
| ~ sdtlseqdt0(X0_iProver_sdtlseqdt0_2,sK4(xP)) ),
inference(renaming,[status(thm)],[c_26122]) ).
tcf(c_26184,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sP3
| sdtlseqdt0(X0_iProver_sdtlseqdt0_2,sK4(xP))
| ~ aElement0(xp)
| ~ aElement0(X0_iProver_sdtlseqdt0_2)
| ~ aElement0(sK4(xP))
| ~ sdtlseqdt0(X0_iProver_sdtlseqdt0_2,xp) ),
inference(superposition,[status(thm)],[c_25919,c_10242]) ).
tcf(c_26295,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sP3
| sdtlseqdt0(X0_iProver_sdtlseqdt0_2,sK4(xP))
| ~ sdtlseqdt0(X0_iProver_sdtlseqdt0_2,xp)
| ~ aElement0(X0_iProver_sdtlseqdt0_2) ),
inference(global_subsumption_just,[status(thm)],[c_26184,c_20008]) ).
tcf(c_26296,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sP3
| sdtlseqdt0(X0_iProver_sdtlseqdt0_2,sK4(xP))
| ~ aElement0(X0_iProver_sdtlseqdt0_2)
| ~ sdtlseqdt0(X0_iProver_sdtlseqdt0_2,xp) ),
inference(renaming,[status(thm)],[c_26295]) ).
tcf(c_26303,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sP3
| ( sK4(xP) = X0_iProver_sdtlseqdt0_2 )
| ~ aElement0(X0_iProver_sdtlseqdt0_2)
| ~ aSubsetOf0(xP,xT)
| ~ sdtlseqdt0(X0_iProver_sdtlseqdt0_2,xp)
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xP) ),
inference(superposition,[status(thm)],[c_26296,c_26123]) ).
tcf(c_26317,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sdtlseqdt0(X0_iProver_sdtlseqdt0_2,xp)
| aElement0(sK20(X0_iProver_sdtlseqdt0_2))
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xU) ),
inference(global_subsumption_just,[status(thm)],[c_25848,c_135,c_14246]) ).
tcf(c_26432,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sP3
| ( sK4(xP) = X0_iProver_sdtlseqdt0_2 )
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xP)
| ~ sdtlseqdt0(X0_iProver_sdtlseqdt0_2,xp)
| ~ aSubsetOf0(xP,xT) ),
inference(global_subsumption_just,[status(thm)],[c_26303,c_1547,c_10209,c_20017,c_24321]) ).
tcf(c_26433,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sP3
| ( sK4(xP) = X0_iProver_sdtlseqdt0_2 )
| ~ aSubsetOf0(xP,xT)
| ~ sdtlseqdt0(X0_iProver_sdtlseqdt0_2,xp)
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xP) ),
inference(renaming,[status(thm)],[c_26432]) ).
tcf(c_26630,plain,
! [X0_iProver_aElementOf0_2: iProver_aElementOf0_2] :
( aLowerBoundOfIn0(sK10(xU,X0_iProver_aElementOf0_2),X0_iProver_aElementOf0_2,xU)
| ~ aSubsetOf0(X0_iProver_aElementOf0_2,xU) ),
inference(global_subsumption_just,[status(thm)],[c_26002,c_114,c_15923]) ).
tcf(c_26635,plain,
( sdtlseqdt0(sK10(xU,xP),xp)
| ~ aSubsetOf0(xP,xU) ),
inference(superposition,[status(thm)],[c_26630,c_10196]) ).
tcf(c_26680,plain,
sdtlseqdt0(sK10(xU,xP),xp),
inference(global_subsumption_just,[status(thm)],[c_26635,c_20976]) ).
tcf(c_26685,plain,
( sP3
| ( sK10(xU,xP) = sK4(xP) )
| ~ aSubsetOf0(xP,xT)
| ~ aElementOf0(sK10(xU,xP),xP) ),
inference(superposition,[status(thm)],[c_26680,c_26433]) ).
tcf(c_34739,plain,
( aElementOf0(sdtlpdtrp0(xf,sK22),xU)
| ~ aElementOf0(sK22,xU) ),
inference(instantiation,[status(thm)],[c_10163]) ).
tcf(c_35942,plain,
( sdtlseqdt0(sdtlpdtrp0(xf,xp),sdtlpdtrp0(xf,sK22))
| ~ sdtlseqdt0(xp,sK22)
| ~ aElementOf0(sK22,xU)
| ~ aElementOf0(xp,xU) ),
inference(instantiation,[status(thm)],[c_10179]) ).
tcf(c_36400,plain,
sP3,
inference(global_subsumption_just,[status(thm)],[c_26685,c_114,c_145,c_156,c_155,c_12459,c_13495,c_13496,c_13672,c_13678,c_22751,c_24479,c_34739,c_35942]) ).
fof(f77,definition,
( ~ sP3
| ( ~ aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
& ? [X1] :
( aElementOf0(X1,xT)
& ~ sdtlseqdt0(X1,sdtlpdtrp0(xf,xp)) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f78,plain,
( sP3
| ( ~ aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU)
& ? [X0] :
( aElementOf0(X0,xP)
& ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),X0) ) ) ),
inference(definition_folding,[],[f72,f77]) ).
fof(f123,plain,
( ~ sP3
| ( ~ aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
& ? [X1] :
( aElementOf0(X1,xT)
& ~ sdtlseqdt0(X1,sdtlpdtrp0(xf,xp)) ) ) ),
inference(nnf_transformation,[],[f77]) ).
fof(f124,plain,
( ~ sP3
| ( ~ aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
& ? [X0] :
( aElementOf0(X0,xT)
& ~ sdtlseqdt0(X0,sdtlpdtrp0(xf,xp)) ) ) ),
inference(rectify,[],[f123]) ).
fof(f125,plain,
( ~ sP3
| ( ~ aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
& aElementOf0(sK21,xT)
& ~ sdtlseqdt0(sK21,sdtlpdtrp0(xf,xp)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(X0,sK21)],[f124]) ).
fof(f231,plain,
( ~ sP3
| aElementOf0(sK21,xT) ),
inference(cnf_transformation,[],[f125]) ).
fof(f232,plain,
( ~ sP3
| ~ sdtlseqdt0(sK21,sdtlpdtrp0(xf,xp)) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_152,plain,
( ~ sP3
| ~ sdtlseqdt0(sK21,sdtlpdtrp0(xf,xp)) ),
inference(cnf_transformation,[],[f232]) ).
tcf(c_153,plain,
( aElementOf0(sK21,xT)
| ~ sP3 ),
inference(cnf_transformation,[],[f231]) ).
tcf(c_10193,plain,
( aElementOf0(sK21,xT)
| ~ sP3 ),
inference(subtyping,[status(esa)],[c_153]) ).
tcf(c_13473,plain,
( aFixedPointOf0(sK21,xf)
| ~ sP3 ),
inference(superposition,[status(thm)],[c_10193,c_10185]) ).
tcf(c_13474,plain,
( aElementOf0(sK21,xU)
| ~ sP3 ),
inference(superposition,[status(thm)],[c_13473,c_10181]) ).
tcf(c_25813,plain,
( aFixedPointOf0(sK21,xf)
| ~ sP3 ),
inference(superposition,[status(thm)],[c_10193,c_10185]) ).
tcf(c_25814,plain,
( aElementOf0(sK21,xU)
| ~ sP3 ),
inference(superposition,[status(thm)],[c_25813,c_10181]) ).
tcf(c_26331,plain,
( sdtlseqdt0(sK21,xp)
| aElement0(sK20(sK21))
| ~ sP3 ),
inference(superposition,[status(thm)],[c_25814,c_26317]) ).
tcf(c_26408,plain,
( sdtlseqdt0(sK21,xp)
| ~ sP3 ),
inference(global_subsumption_just,[status(thm)],[c_26331,c_153,c_13474,c_13910,c_13909,c_19002]) ).
tcf(c_47245,plain,
aElementOf0(sK21,xT),
inference(global_subsumption_just,[status(thm)],[c_10193,c_153,c_36400]) ).
tcf(c_47248,plain,
aFixedPointOf0(sK21,xf),
inference(superposition,[status(thm)],[c_47245,c_10185]) ).
tcf(c_47288,plain,
sdtlpdtrp0(xf,sK21) = sK21,
inference(superposition,[status(thm)],[c_47248,c_10186]) ).
tcf(c_47485,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sdtlseqdt0(sK21,sdtlpdtrp0(xf,X0_iProver_sdtlseqdt0_2))
| ~ aElementOf0(sK21,xU)
| ~ sdtlseqdt0(sK21,X0_iProver_sdtlseqdt0_2)
| ~ aElementOf0(X0_iProver_sdtlseqdt0_2,xU) ),
inference(superposition,[status(thm)],[c_47288,c_10179]) ).
tcf(c_47496,plain,
( sdtlseqdt0(sK21,sdtlpdtrp0(xf,xp))
| ~ sdtlseqdt0(sK21,xp)
| ~ aElementOf0(sK21,xU)
| ~ aElementOf0(xp,xU) ),
inference(instantiation,[status(thm)],[c_47485]) ).
tcf(c_47497,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_47496,c_36400,c_26408,c_13474,c_152,c_145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT386+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/10.38 % Computer : n009.cluster.edu
% 0.09/10.38 % Model : x86_64 x86_64
% 0.09/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.38 % Memory : 8046.5625MB
% 0.09/10.38 % OS : Linux 6.8.0-71-generic
% 0.09/10.38 % CPULimit : 300
% 0.09/10.38 % WCLimit : 300
% 0.09/10.38 % DateTime : Wed Sep 23 21:31:38 UTC 2026
% 0.09/10.39 % CPUTime :
% 0.09/10.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/10.42 Running first-order theorem proving
% 0.15/10.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/10.43
% 0.15/10.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/10.43
% 0.15/10.44 % Detected problem language: tptp
% 0.15/10.45 % Proving...
% 18.56/13.31 % SZS status Started for theBenchmark.p
% 18.56/13.31 % SZS status Theorem for theBenchmark.p
% 18.56/13.31
% 18.56/13.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 18.56/13.31
% 18.56/13.31 % ------ iProver source info
% 18.56/13.31
% 18.56/13.31 % git: date: 2026-07-19 20:42:38 +0200
% 18.56/13.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 18.56/13.31 % git: non_committed_changes: false
% 18.56/13.31
% 18.56/13.31 % ------ Parsing...
% 18.56/13.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 18.56/13.31
% 18.56/13.31 % ------ Preprocessing... sup_sim: 4 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 5 sf_s rm: 6 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 6 0s sf_e pe_s pe_e %
% 18.56/13.31
% 18.56/13.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 18.56/13.31
% 18.56/13.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 18.56/13.31 % ------ Proving...
% 18.56/13.31 % ------ Problem Properties
% 18.56/13.31
% 18.56/13.31 %
% 18.56/13.31 % clauses 87
% 18.56/13.31 % conjectures 3
% 18.56/13.31 % EPR 38
% 18.56/13.31 % Horn 76
% 18.56/13.31 % unary 14
% 18.56/13.31 % binary 27
% 18.56/13.31 % lits 256
% 18.56/13.31 % lits eq 9
% 18.56/13.31 % fd_pure 0
% 18.56/13.31 % fd_pseudo 0
% 18.56/13.31 % fd_cond 0
% 18.56/13.31 % fd_pseudo_cond 3
% 18.56/13.31 % AC symbols 0
% 18.56/13.31
% 18.56/13.31 % ------ Input Options Time Limit: Unbounded
% 18.56/13.31
% 18.56/13.31
% 18.56/13.31 % ------
% 18.56/13.31 % Current options:
% 18.56/13.31 % ------
% 18.56/13.31
% 18.56/13.31
% 18.56/13.31 %
% 18.56/13.31
% 18.56/13.31 % ------ Proving...
% 18.56/13.31 %
% 18.56/13.31
% 18.56/13.31 % SZS status Theorem for theBenchmark.p
% 18.56/13.31
% 18.56/13.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 18.56/13.31
% 18.56/13.31
%------------------------------------------------------------------------------