TSTP Solution File: LAT386+4 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : LAT386+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n026.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 : Fri May 3 02:35:39 EDT 2024
% Result : Theorem 14.37s 2.63s
% Output : CNFRefutation 14.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 26
% Syntax : Number of formulae : 201 ( 18 unt; 0 def)
% Number of atoms : 886 ( 63 equ)
% Maximal formula atoms : 37 ( 4 avg)
% Number of connectives : 1046 ( 361 ~; 358 |; 264 &)
% ( 4 <=>; 59 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 2 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-3 aty)
% Number of variables : 299 ( 4 sgn 157 !; 41 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(f4,axiom,
! [X0] :
( aSet0(X0)
=> ( isEmpty0(X0)
<=> ~ ? [X1] : aElementOf0(X1,X0) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(f9,axiom,
! [X0,X1,X2] :
( ( aElement0(X2)
& aElement0(X1)
& aElement0(X0) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X0,X1) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTrans) ).
fof(f21,axiom,
! [X0] :
( aFunction0(X0)
=> ! [X1] :
( aElementOf0(X1,szDzozmdt0(X0))
=> aElementOf0(sdtlpdtrp0(X0,X1),szRzazndt0(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mImgSort) ).
fof(f24,axiom,
( isOn0(xf,xU)
& xU = szRzazndt0(xf)
& szDzozmdt0(xf) = szRzazndt0(xf)
& isMonotone0(xf)
& ! [X0,X1] :
( ( aElementOf0(X1,szDzozmdt0(xf))
& aElementOf0(X0,szDzozmdt0(xf)) )
=> ( sdtlseqdt0(X0,X1)
=> sdtlseqdt0(sdtlpdtrp0(xf,X0),sdtlpdtrp0(xf,X1)) ) )
& aFunction0(xf)
& aCompleteLattice0(xU)
& ! [X0] :
( ( aSubsetOf0(X0,xU)
| ( ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xU) )
& aSet0(X0) ) )
=> ? [X1] :
( ? [X2] :
( aSupremumOfIn0(X2,X0,xU)
& ! [X3] :
( ( aUpperBoundOfIn0(X3,X0,xU)
| ( ! [X4] :
( aElementOf0(X4,X0)
=> sdtlseqdt0(X4,X3) )
& aElementOf0(X3,xU) ) )
=> sdtlseqdt0(X2,X3) )
& aUpperBoundOfIn0(X2,X0,xU)
& ! [X3] :
( aElementOf0(X3,X0)
=> sdtlseqdt0(X3,X2) )
& aElementOf0(X2,xU)
& aElementOf0(X2,xU) )
& aInfimumOfIn0(X1,X0,xU)
& ! [X2] :
( ( aLowerBoundOfIn0(X2,X0,xU)
| ( ! [X3] :
( aElementOf0(X3,X0)
=> sdtlseqdt0(X2,X3) )
& aElementOf0(X2,xU) ) )
=> sdtlseqdt0(X2,X1) )
& aLowerBoundOfIn0(X1,X0,xU)
& ! [X2] :
( aElementOf0(X2,X0)
=> sdtlseqdt0(X1,X2) )
& aElementOf0(X1,xU)
& aElementOf0(X1,xU) ) )
& aSet0(xU) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1123) ).
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/sandbox/benchmark/theBenchmark.p',m__1144) ).
fof(f26,axiom,
( aSubsetOf0(xT,xS)
& ! [X0] :
( aElementOf0(X0,xT)
=> aElementOf0(X0,xS) )
& aSet0(xT) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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,[],[f29]) ).
fof(f35,plain,
( isOn0(xf,xU)
& xU = szRzazndt0(xf)
& szDzozmdt0(xf) = szRzazndt0(xf)
& isMonotone0(xf)
& ! [X0,X1] :
( ( aElementOf0(X1,szDzozmdt0(xf))
& aElementOf0(X0,szDzozmdt0(xf)) )
=> ( sdtlseqdt0(X0,X1)
=> sdtlseqdt0(sdtlpdtrp0(xf,X0),sdtlpdtrp0(xf,X1)) ) )
& aFunction0(xf)
& aCompleteLattice0(xU)
& ! [X2] :
( ( aSubsetOf0(X2,xU)
| ( ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,xU) )
& aSet0(X2) ) )
=> ? [X4] :
( ? [X5] :
( aSupremumOfIn0(X5,X2,xU)
& ! [X6] :
( ( aUpperBoundOfIn0(X6,X2,xU)
| ( ! [X7] :
( aElementOf0(X7,X2)
=> sdtlseqdt0(X7,X6) )
& aElementOf0(X6,xU) ) )
=> sdtlseqdt0(X5,X6) )
& aUpperBoundOfIn0(X5,X2,xU)
& ! [X8] :
( aElementOf0(X8,X2)
=> sdtlseqdt0(X8,X5) )
& aElementOf0(X5,xU)
& aElementOf0(X5,xU) )
& aInfimumOfIn0(X4,X2,xU)
& ! [X9] :
( ( aLowerBoundOfIn0(X9,X2,xU)
| ( ! [X10] :
( aElementOf0(X10,X2)
=> sdtlseqdt0(X9,X10) )
& aElementOf0(X9,xU) ) )
=> sdtlseqdt0(X9,X4) )
& aLowerBoundOfIn0(X4,X2,xU)
& ! [X11] :
( aElementOf0(X11,X2)
=> sdtlseqdt0(X4,X11) )
& aElementOf0(X4,xU)
& aElementOf0(X4,xU) ) )
& aSet0(xU) ),
inference(rectify,[],[f24]) ).
fof(f36,plain,
( 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)
& ! [X2] :
( aElementOf0(X2,xT)
=> sdtlseqdt0(X2,X0) )
& sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
& aElementOf0(X0,xU) ) ) )
& aSet0(xP) ),
inference(rectify,[],[f27]) ).
fof(f37,plain,
( 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)
& ! [X2] :
( aElementOf0(X2,xP)
=> sdtlseqdt0(xp,X2) )
& aElementOf0(xp,xU)
& aElementOf0(xp,xU) ),
inference(rectify,[],[f28]) ).
fof(f38,plain,
~ ( ( aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
| ! [X0] :
( aElementOf0(X0,xT)
=> sdtlseqdt0(X0,sdtlpdtrp0(xf,xp)) ) )
& ( aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU)
| ! [X1] :
( aElementOf0(X1,xP)
=> sdtlseqdt0(sdtlpdtrp0(xf,xp),X1) ) ) ),
inference(rectify,[],[f30]) ).
fof(f40,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f41,plain,
! [X0] :
( ( isEmpty0(X0)
<=> ! [X1] : ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f42,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f46,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f47,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f46]) ).
fof(f61,plain,
! [X0] :
( ! [X1] :
( aElementOf0(sdtlpdtrp0(X0,X1),szRzazndt0(X0))
| ~ aElementOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f65,plain,
( isOn0(xf,xU)
& xU = szRzazndt0(xf)
& szDzozmdt0(xf) = szRzazndt0(xf)
& isMonotone0(xf)
& ! [X0,X1] :
( sdtlseqdt0(sdtlpdtrp0(xf,X0),sdtlpdtrp0(xf,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf)) )
& aFunction0(xf)
& aCompleteLattice0(xU)
& ! [X2] :
( ? [X4] :
( ? [X5] :
( aSupremumOfIn0(X5,X2,xU)
& ! [X6] :
( sdtlseqdt0(X5,X6)
| ( ~ aUpperBoundOfIn0(X6,X2,xU)
& ( ? [X7] :
( ~ sdtlseqdt0(X7,X6)
& aElementOf0(X7,X2) )
| ~ aElementOf0(X6,xU) ) ) )
& aUpperBoundOfIn0(X5,X2,xU)
& ! [X8] :
( sdtlseqdt0(X8,X5)
| ~ aElementOf0(X8,X2) )
& aElementOf0(X5,xU)
& aElementOf0(X5,xU) )
& aInfimumOfIn0(X4,X2,xU)
& ! [X9] :
( sdtlseqdt0(X9,X4)
| ( ~ aLowerBoundOfIn0(X9,X2,xU)
& ( ? [X10] :
( ~ sdtlseqdt0(X9,X10)
& aElementOf0(X10,X2) )
| ~ aElementOf0(X9,xU) ) ) )
& aLowerBoundOfIn0(X4,X2,xU)
& ! [X11] :
( sdtlseqdt0(X4,X11)
| ~ aElementOf0(X11,X2) )
& aElementOf0(X4,xU)
& aElementOf0(X4,xU) )
| ( ~ aSubsetOf0(X2,xU)
& ( ? [X3] :
( ~ aElementOf0(X3,xU)
& aElementOf0(X3,X2) )
| ~ aSet0(X2) ) ) )
& aSet0(xU) ),
inference(ennf_transformation,[],[f35]) ).
fof(f66,plain,
( isOn0(xf,xU)
& xU = szRzazndt0(xf)
& szDzozmdt0(xf) = szRzazndt0(xf)
& isMonotone0(xf)
& ! [X0,X1] :
( sdtlseqdt0(sdtlpdtrp0(xf,X0),sdtlpdtrp0(xf,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf)) )
& aFunction0(xf)
& aCompleteLattice0(xU)
& ! [X2] :
( ? [X4] :
( ? [X5] :
( aSupremumOfIn0(X5,X2,xU)
& ! [X6] :
( sdtlseqdt0(X5,X6)
| ( ~ aUpperBoundOfIn0(X6,X2,xU)
& ( ? [X7] :
( ~ sdtlseqdt0(X7,X6)
& aElementOf0(X7,X2) )
| ~ aElementOf0(X6,xU) ) ) )
& aUpperBoundOfIn0(X5,X2,xU)
& ! [X8] :
( sdtlseqdt0(X8,X5)
| ~ aElementOf0(X8,X2) )
& aElementOf0(X5,xU)
& aElementOf0(X5,xU) )
& aInfimumOfIn0(X4,X2,xU)
& ! [X9] :
( sdtlseqdt0(X9,X4)
| ( ~ aLowerBoundOfIn0(X9,X2,xU)
& ( ? [X10] :
( ~ sdtlseqdt0(X9,X10)
& aElementOf0(X10,X2) )
| ~ aElementOf0(X9,xU) ) ) )
& aLowerBoundOfIn0(X4,X2,xU)
& ! [X11] :
( sdtlseqdt0(X4,X11)
| ~ aElementOf0(X11,X2) )
& aElementOf0(X4,xU)
& aElementOf0(X4,xU) )
| ( ~ aSubsetOf0(X2,xU)
& ( ? [X3] :
( ~ aElementOf0(X3,xU)
& aElementOf0(X3,X2) )
| ~ aSet0(X2) ) ) )
& aSet0(xU) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
( xS = cS1142(xf)
& ! [X0] :
( ( aElementOf0(X0,xS)
| ( ~ aFixedPointOf0(X0,xf)
& ( sdtlpdtrp0(xf,X0) != X0
| ~ aElementOf0(X0,szDzozmdt0(xf)) ) ) )
& ( ( aFixedPointOf0(X0,xf)
& sdtlpdtrp0(xf,X0) = X0
& aElementOf0(X0,szDzozmdt0(xf)) )
| ~ aElementOf0(X0,xS) ) )
& aSet0(xS) ),
inference(ennf_transformation,[],[f25]) ).
fof(f68,plain,
( aSubsetOf0(xT,xS)
& ! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xT) )
& aSet0(xT) ),
inference(ennf_transformation,[],[f26]) ).
fof(f69,plain,
( xP = cS1241(xU,xf,xT)
& ! [X0] :
( ( aElementOf0(X0,xP)
| ( ~ aUpperBoundOfIn0(X0,xT,xU)
& ? [X1] :
( ~ sdtlseqdt0(X1,X0)
& aElementOf0(X1,xT) ) )
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
| ~ aElementOf0(X0,xU) )
& ( ( aUpperBoundOfIn0(X0,xT,xU)
& ! [X2] :
( sdtlseqdt0(X2,X0)
| ~ aElementOf0(X2,xT) )
& sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
& aElementOf0(X0,xU) )
| ~ aElementOf0(X0,xP) ) )
& aSet0(xP) ),
inference(ennf_transformation,[],[f36]) ).
fof(f70,plain,
( xP = cS1241(xU,xf,xT)
& ! [X0] :
( ( aElementOf0(X0,xP)
| ( ~ aUpperBoundOfIn0(X0,xT,xU)
& ? [X1] :
( ~ sdtlseqdt0(X1,X0)
& aElementOf0(X1,xT) ) )
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
| ~ aElementOf0(X0,xU) )
& ( ( aUpperBoundOfIn0(X0,xT,xU)
& ! [X2] :
( sdtlseqdt0(X2,X0)
| ~ aElementOf0(X2,xT) )
& sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
& aElementOf0(X0,xU) )
| ~ aElementOf0(X0,xP) ) )
& aSet0(xP) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
( aInfimumOfIn0(xp,xP,xU)
& ! [X0] :
( sdtlseqdt0(X0,xp)
| ( ~ aLowerBoundOfIn0(X0,xP,xU)
& ( ? [X1] :
( ~ sdtlseqdt0(X0,X1)
& aElementOf0(X1,xP) )
| ~ aElementOf0(X0,xU) ) ) )
& aLowerBoundOfIn0(xp,xP,xU)
& ! [X2] :
( sdtlseqdt0(xp,X2)
| ~ aElementOf0(X2,xP) )
& aElementOf0(xp,xU)
& aElementOf0(xp,xU) ),
inference(ennf_transformation,[],[f37]) ).
fof(f72,plain,
( ( ~ aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
& ? [X0] :
( ~ sdtlseqdt0(X0,sdtlpdtrp0(xf,xp))
& aElementOf0(X0,xT) ) )
| ( ~ aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU)
& ? [X1] :
( ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),X1)
& aElementOf0(X1,xP) ) ) ),
inference(ennf_transformation,[],[f38]) ).
fof(f73,plain,
! [X2] :
( ? [X5] :
( aSupremumOfIn0(X5,X2,xU)
& ! [X6] :
( sdtlseqdt0(X5,X6)
| ( ~ aUpperBoundOfIn0(X6,X2,xU)
& ( ? [X7] :
( ~ sdtlseqdt0(X7,X6)
& aElementOf0(X7,X2) )
| ~ aElementOf0(X6,xU) ) ) )
& aUpperBoundOfIn0(X5,X2,xU)
& ! [X8] :
( sdtlseqdt0(X8,X5)
| ~ aElementOf0(X8,X2) )
& aElementOf0(X5,xU)
& aElementOf0(X5,xU) )
| ~ sP0(X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f74,plain,
! [X4,X2] :
( ! [X9] :
( sdtlseqdt0(X9,X4)
| ( ~ aLowerBoundOfIn0(X9,X2,xU)
& ( ? [X10] :
( ~ sdtlseqdt0(X9,X10)
& aElementOf0(X10,X2) )
| ~ aElementOf0(X9,xU) ) ) )
| ~ sP1(X4,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f75,plain,
! [X2] :
( ? [X4] :
( sP0(X2)
& aInfimumOfIn0(X4,X2,xU)
& sP1(X4,X2)
& aLowerBoundOfIn0(X4,X2,xU)
& ! [X11] :
( sdtlseqdt0(X4,X11)
| ~ aElementOf0(X11,X2) )
& aElementOf0(X4,xU)
& aElementOf0(X4,xU) )
| ~ sP2(X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f76,plain,
( isOn0(xf,xU)
& xU = szRzazndt0(xf)
& szDzozmdt0(xf) = szRzazndt0(xf)
& isMonotone0(xf)
& ! [X0,X1] :
( sdtlseqdt0(sdtlpdtrp0(xf,X0),sdtlpdtrp0(xf,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf)) )
& aFunction0(xf)
& aCompleteLattice0(xU)
& ! [X2] :
( sP2(X2)
| ( ~ aSubsetOf0(X2,xU)
& ( ? [X3] :
( ~ aElementOf0(X3,xU)
& aElementOf0(X3,X2) )
| ~ aSet0(X2) ) ) )
& aSet0(xU) ),
inference(definition_folding,[],[f66,f75,f74,f73]) ).
fof(f77,plain,
( ( ~ aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU)
& ? [X1] :
( ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),X1)
& aElementOf0(X1,xP) ) )
| ~ sP3 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f78,plain,
( ( ~ aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
& ? [X0] :
( ~ sdtlseqdt0(X0,sdtlpdtrp0(xf,xp))
& aElementOf0(X0,xT) ) )
| sP3 ),
inference(definition_folding,[],[f72,f77]) ).
fof(f79,plain,
! [X0] :
( ( ( isEmpty0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ! [X1] : ~ aElementOf0(X1,X0)
| ~ isEmpty0(X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f41]) ).
fof(f80,plain,
! [X0] :
( ( ( isEmpty0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ! [X2] : ~ aElementOf0(X2,X0)
| ~ isEmpty0(X0) ) )
| ~ aSet0(X0) ),
inference(rectify,[],[f79]) ).
fof(f81,plain,
! [X0] :
( ? [X1] : aElementOf0(X1,X0)
=> aElementOf0(sK4(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
! [X0] :
( ( ( isEmpty0(X0)
| aElementOf0(sK4(X0),X0) )
& ( ! [X2] : ~ aElementOf0(X2,X0)
| ~ isEmpty0(X0) ) )
| ~ aSet0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f80,f81]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ~ aSet0(X1) )
& ( ( ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f42]) ).
fof(f84,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ~ aSet0(X1) )
& ( ( ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(flattening,[],[f83]) ).
fof(f85,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ~ aSet0(X1) )
& ( ( ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(rectify,[],[f84]) ).
fof(f86,plain,
! [X0,X1] :
( ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
=> ( ~ aElementOf0(sK5(X0,X1),X0)
& aElementOf0(sK5(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f87,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ( ~ aElementOf0(sK5(X0,X1),X0)
& aElementOf0(sK5(X0,X1),X1) )
| ~ aSet0(X1) )
& ( ( ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f85,f86]) ).
fof(f132,plain,
! [X2] :
( ? [X3] :
( ~ aElementOf0(X3,xU)
& aElementOf0(X3,X2) )
=> ( ~ aElementOf0(sK18(X2),xU)
& aElementOf0(sK18(X2),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f133,plain,
( isOn0(xf,xU)
& xU = szRzazndt0(xf)
& szDzozmdt0(xf) = szRzazndt0(xf)
& isMonotone0(xf)
& ! [X0,X1] :
( sdtlseqdt0(sdtlpdtrp0(xf,X0),sdtlpdtrp0(xf,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf)) )
& aFunction0(xf)
& aCompleteLattice0(xU)
& ! [X2] :
( sP2(X2)
| ( ~ aSubsetOf0(X2,xU)
& ( ( ~ aElementOf0(sK18(X2),xU)
& aElementOf0(sK18(X2),X2) )
| ~ aSet0(X2) ) ) )
& aSet0(xU) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f76,f132]) ).
fof(f134,plain,
! [X0] :
( ? [X1] :
( ~ sdtlseqdt0(X1,X0)
& aElementOf0(X1,xT) )
=> ( ~ sdtlseqdt0(sK19(X0),X0)
& aElementOf0(sK19(X0),xT) ) ),
introduced(choice_axiom,[]) ).
fof(f135,plain,
( xP = cS1241(xU,xf,xT)
& ! [X0] :
( ( aElementOf0(X0,xP)
| ( ~ aUpperBoundOfIn0(X0,xT,xU)
& ~ sdtlseqdt0(sK19(X0),X0)
& aElementOf0(sK19(X0),xT) )
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
| ~ aElementOf0(X0,xU) )
& ( ( aUpperBoundOfIn0(X0,xT,xU)
& ! [X2] :
( sdtlseqdt0(X2,X0)
| ~ aElementOf0(X2,xT) )
& sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
& aElementOf0(X0,xU) )
| ~ aElementOf0(X0,xP) ) )
& aSet0(xP) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f70,f134]) ).
fof(f136,plain,
! [X0] :
( ? [X1] :
( ~ sdtlseqdt0(X0,X1)
& aElementOf0(X1,xP) )
=> ( ~ sdtlseqdt0(X0,sK20(X0))
& aElementOf0(sK20(X0),xP) ) ),
introduced(choice_axiom,[]) ).
fof(f137,plain,
( aInfimumOfIn0(xp,xP,xU)
& ! [X0] :
( sdtlseqdt0(X0,xp)
| ( ~ aLowerBoundOfIn0(X0,xP,xU)
& ( ( ~ sdtlseqdt0(X0,sK20(X0))
& aElementOf0(sK20(X0),xP) )
| ~ aElementOf0(X0,xU) ) ) )
& aLowerBoundOfIn0(xp,xP,xU)
& ! [X2] :
( sdtlseqdt0(xp,X2)
| ~ aElementOf0(X2,xP) )
& aElementOf0(xp,xU)
& aElementOf0(xp,xU) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f71,f136]) ).
fof(f138,plain,
( ( ~ aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU)
& ? [X1] :
( ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),X1)
& aElementOf0(X1,xP) ) )
| ~ sP3 ),
inference(nnf_transformation,[],[f77]) ).
fof(f139,plain,
( ( ~ aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU)
& ? [X0] :
( ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),X0)
& aElementOf0(X0,xP) ) )
| ~ sP3 ),
inference(rectify,[],[f138]) ).
fof(f140,plain,
( ? [X0] :
( ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),X0)
& aElementOf0(X0,xP) )
=> ( ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),sK21)
& aElementOf0(sK21,xP) ) ),
introduced(choice_axiom,[]) ).
fof(f141,plain,
( ( ~ aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU)
& ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),sK21)
& aElementOf0(sK21,xP) )
| ~ sP3 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f139,f140]) ).
fof(f142,plain,
( ? [X0] :
( ~ sdtlseqdt0(X0,sdtlpdtrp0(xf,xp))
& aElementOf0(X0,xT) )
=> ( ~ sdtlseqdt0(sK22,sdtlpdtrp0(xf,xp))
& aElementOf0(sK22,xT) ) ),
introduced(choice_axiom,[]) ).
fof(f143,plain,
( ( ~ aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
& ~ sdtlseqdt0(sK22,sdtlpdtrp0(xf,xp))
& aElementOf0(sK22,xT) )
| sP3 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f78,f142]) ).
fof(f144,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f145,plain,
! [X2,X0] :
( ~ aElementOf0(X2,X0)
| ~ isEmpty0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f146,plain,
! [X0] :
( isEmpty0(X0)
| aElementOf0(sK4(X0),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f148,plain,
! [X3,X0,X1] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f153,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f182,plain,
! [X0,X1] :
( aElementOf0(sdtlpdtrp0(X0,X1),szRzazndt0(X0))
| ~ aElementOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f209,plain,
aSet0(xU),
inference(cnf_transformation,[],[f133]) ).
fof(f214,plain,
aFunction0(xf),
inference(cnf_transformation,[],[f133]) ).
fof(f215,plain,
! [X0,X1] :
( sdtlseqdt0(sdtlpdtrp0(xf,X0),sdtlpdtrp0(xf,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf)) ),
inference(cnf_transformation,[],[f133]) ).
fof(f217,plain,
szDzozmdt0(xf) = szRzazndt0(xf),
inference(cnf_transformation,[],[f133]) ).
fof(f218,plain,
xU = szRzazndt0(xf),
inference(cnf_transformation,[],[f133]) ).
fof(f220,plain,
aSet0(xS),
inference(cnf_transformation,[],[f67]) ).
fof(f221,plain,
! [X0] :
( aElementOf0(X0,szDzozmdt0(xf))
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f67]) ).
fof(f222,plain,
! [X0] :
( sdtlpdtrp0(xf,X0) = X0
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f67]) ).
fof(f223,plain,
! [X0] :
( aFixedPointOf0(X0,xf)
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f67]) ).
fof(f225,plain,
! [X0] :
( aElementOf0(X0,xS)
| ~ aFixedPointOf0(X0,xf) ),
inference(cnf_transformation,[],[f67]) ).
fof(f228,plain,
! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[],[f68]) ).
fof(f231,plain,
! [X0] :
( aElementOf0(X0,xU)
| ~ aElementOf0(X0,xP) ),
inference(cnf_transformation,[],[f135]) ).
fof(f232,plain,
! [X0] :
( sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
| ~ aElementOf0(X0,xP) ),
inference(cnf_transformation,[],[f135]) ).
fof(f233,plain,
! [X2,X0] :
( sdtlseqdt0(X2,X0)
| ~ aElementOf0(X2,xT)
| ~ aElementOf0(X0,xP) ),
inference(cnf_transformation,[],[f135]) ).
fof(f239,plain,
aElementOf0(xp,xU),
inference(cnf_transformation,[],[f137]) ).
fof(f241,plain,
! [X2] :
( sdtlseqdt0(xp,X2)
| ~ aElementOf0(X2,xP) ),
inference(cnf_transformation,[],[f137]) ).
fof(f243,plain,
! [X0] :
( sdtlseqdt0(X0,xp)
| aElementOf0(sK20(X0),xP)
| ~ aElementOf0(X0,xU) ),
inference(cnf_transformation,[],[f137]) ).
fof(f244,plain,
! [X0] :
( sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,sK20(X0))
| ~ aElementOf0(X0,xU) ),
inference(cnf_transformation,[],[f137]) ).
fof(f247,plain,
( aElementOf0(sK21,xP)
| ~ sP3 ),
inference(cnf_transformation,[],[f141]) ).
fof(f248,plain,
( ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),sK21)
| ~ sP3 ),
inference(cnf_transformation,[],[f141]) ).
fof(f250,plain,
( aElementOf0(sK22,xT)
| sP3 ),
inference(cnf_transformation,[],[f143]) ).
fof(f251,plain,
( ~ sdtlseqdt0(sK22,sdtlpdtrp0(xf,xp))
| sP3 ),
inference(cnf_transformation,[],[f143]) ).
cnf(c_49,plain,
( ~ aElementOf0(X0,X1)
| ~ aSet0(X1)
| aElement0(X0) ),
inference(cnf_transformation,[],[f144]) ).
cnf(c_50,plain,
( ~ aSet0(X0)
| aElementOf0(sK4(X0),X0)
| isEmpty0(X0) ),
inference(cnf_transformation,[],[f146]) ).
cnf(c_51,plain,
( ~ aElementOf0(X0,X1)
| ~ aSet0(X1)
| ~ isEmpty0(X1) ),
inference(cnf_transformation,[],[f145]) ).
cnf(c_54,plain,
( ~ aElementOf0(X0,X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2)
| aElementOf0(X0,X2) ),
inference(cnf_transformation,[],[f148]) ).
cnf(c_58,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X2,X0)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| sdtlseqdt0(X2,X1) ),
inference(cnf_transformation,[],[f153]) ).
cnf(c_87,plain,
( ~ aElementOf0(X0,szDzozmdt0(X1))
| ~ aFunction0(X1)
| aElementOf0(sdtlpdtrp0(X1,X0),szRzazndt0(X1)) ),
inference(cnf_transformation,[],[f182]) ).
cnf(c_115,plain,
szRzazndt0(xf) = xU,
inference(cnf_transformation,[],[f218]) ).
cnf(c_116,plain,
szDzozmdt0(xf) = szRzazndt0(xf),
inference(cnf_transformation,[],[f217]) ).
cnf(c_118,plain,
( ~ aElementOf0(X0,szDzozmdt0(xf))
| ~ aElementOf0(X1,szDzozmdt0(xf))
| ~ sdtlseqdt0(X1,X0)
| sdtlseqdt0(sdtlpdtrp0(xf,X1),sdtlpdtrp0(xf,X0)) ),
inference(cnf_transformation,[],[f215]) ).
cnf(c_119,plain,
aFunction0(xf),
inference(cnf_transformation,[],[f214]) ).
cnf(c_124,plain,
aSet0(xU),
inference(cnf_transformation,[],[f209]) ).
cnf(c_126,plain,
( ~ aFixedPointOf0(X0,xf)
| aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f225]) ).
cnf(c_128,plain,
( ~ aElementOf0(X0,xS)
| aFixedPointOf0(X0,xf) ),
inference(cnf_transformation,[],[f223]) ).
cnf(c_129,plain,
( ~ aElementOf0(X0,xS)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(cnf_transformation,[],[f222]) ).
cnf(c_130,plain,
( ~ aElementOf0(X0,xS)
| aElementOf0(X0,szDzozmdt0(xf)) ),
inference(cnf_transformation,[],[f221]) ).
cnf(c_131,plain,
aSet0(xS),
inference(cnf_transformation,[],[f220]) ).
cnf(c_133,plain,
( ~ aElementOf0(X0,xT)
| aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f228]) ).
cnf(c_140,plain,
( ~ aElementOf0(X0,xP)
| ~ aElementOf0(X1,xT)
| sdtlseqdt0(X1,X0) ),
inference(cnf_transformation,[],[f233]) ).
cnf(c_141,plain,
( ~ aElementOf0(X0,xP)
| sdtlseqdt0(sdtlpdtrp0(xf,X0),X0) ),
inference(cnf_transformation,[],[f232]) ).
cnf(c_142,plain,
( ~ aElementOf0(X0,xP)
| aElementOf0(X0,xU) ),
inference(cnf_transformation,[],[f231]) ).
cnf(c_146,plain,
( ~ sdtlseqdt0(X0,sK20(X0))
| ~ aElementOf0(X0,xU)
| sdtlseqdt0(X0,xp) ),
inference(cnf_transformation,[],[f244]) ).
cnf(c_147,plain,
( ~ aElementOf0(X0,xU)
| aElementOf0(sK20(X0),xP)
| sdtlseqdt0(X0,xp) ),
inference(cnf_transformation,[],[f243]) ).
cnf(c_149,plain,
( ~ aElementOf0(X0,xP)
| sdtlseqdt0(xp,X0) ),
inference(cnf_transformation,[],[f241]) ).
cnf(c_151,plain,
aElementOf0(xp,xU),
inference(cnf_transformation,[],[f239]) ).
cnf(c_153,plain,
( ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),sK21)
| ~ sP3 ),
inference(cnf_transformation,[],[f248]) ).
cnf(c_154,plain,
( ~ sP3
| aElementOf0(sK21,xP) ),
inference(cnf_transformation,[],[f247]) ).
cnf(c_156,negated_conjecture,
( ~ sdtlseqdt0(sK22,sdtlpdtrp0(xf,xp))
| sP3 ),
inference(cnf_transformation,[],[f251]) ).
cnf(c_157,negated_conjecture,
( aElementOf0(sK22,xT)
| sP3 ),
inference(cnf_transformation,[],[f250]) ).
cnf(c_285,plain,
( aElementOf0(X0,szDzozmdt0(xf))
| ~ aFixedPointOf0(X0,xf) ),
inference(prop_impl_just,[status(thm)],[c_126,c_130]) ).
cnf(c_286,plain,
( ~ aFixedPointOf0(X0,xf)
| aElementOf0(X0,szDzozmdt0(xf)) ),
inference(renaming,[status(thm)],[c_285]) ).
cnf(c_291,plain,
( ~ aFixedPointOf0(X0,xf)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(prop_impl_just,[status(thm)],[c_126,c_129]) ).
cnf(c_293,plain,
( aFixedPointOf0(X0,xf)
| ~ aElementOf0(X0,xT) ),
inference(prop_impl_just,[status(thm)],[c_133,c_128]) ).
cnf(c_294,plain,
( ~ aElementOf0(X0,xT)
| aFixedPointOf0(X0,xf) ),
inference(renaming,[status(thm)],[c_293]) ).
cnf(c_1170,plain,
szDzozmdt0(xf) = xU,
inference(light_normalisation,[status(thm)],[c_116,c_115]) ).
cnf(c_1171,plain,
( ~ aFixedPointOf0(X0,xf)
| aElementOf0(X0,xU) ),
inference(light_normalisation,[status(thm)],[c_286,c_1170]) ).
cnf(c_1173,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X0,xU)
| ~ aElementOf0(X1,xU)
| sdtlseqdt0(sdtlpdtrp0(xf,X0),sdtlpdtrp0(xf,X1)) ),
inference(light_normalisation,[status(thm)],[c_118,c_1170]) ).
cnf(c_1199,plain,
( X0 != X1
| ~ aElementOf0(X2,X0)
| ~ aSet0(X0)
| ~ aSet0(X1)
| aElementOf0(sK4(X1),X1) ),
inference(resolution_lifted,[status(thm)],[c_51,c_50]) ).
cnf(c_1200,plain,
( ~ aElementOf0(X0,X1)
| ~ aSet0(X1)
| aElementOf0(sK4(X1),X1) ),
inference(unflattening,[status(thm)],[c_1199]) ).
cnf(c_1513,plain,
( X0 != xf
| ~ aElementOf0(X1,szDzozmdt0(X0))
| aElementOf0(sdtlpdtrp0(X0,X1),szRzazndt0(X0)) ),
inference(resolution_lifted,[status(thm)],[c_87,c_119]) ).
cnf(c_1514,plain,
( ~ aElementOf0(X0,szDzozmdt0(xf))
| aElementOf0(sdtlpdtrp0(xf,X0),szRzazndt0(xf)) ),
inference(unflattening,[status(thm)],[c_1513]) ).
cnf(c_4011,plain,
( ~ aElementOf0(X0,szDzozmdt0(xf))
| aElementOf0(sdtlpdtrp0(xf,X0),szRzazndt0(xf)) ),
inference(prop_impl_just,[status(thm)],[c_1514]) ).
cnf(c_4766,plain,
( ~ aElementOf0(X0,xU)
| aElementOf0(sdtlpdtrp0(xf,X0),xU) ),
inference(light_normalisation,[status(thm)],[c_4011,c_115,c_1170]) ).
cnf(c_7112,plain,
( ~ aElementOf0(X0,xU)
| aElementOf0(sdtlpdtrp0(xf,X0),xU) ),
inference(prop_impl_just,[status(thm)],[c_4766]) ).
cnf(c_7114,plain,
( aElementOf0(X0,xU)
| ~ aFixedPointOf0(X0,xf) ),
inference(prop_impl_just,[status(thm)],[c_1171]) ).
cnf(c_7115,plain,
( ~ aFixedPointOf0(X0,xf)
| aElementOf0(X0,xU) ),
inference(renaming,[status(thm)],[c_7114]) ).
cnf(c_7126,plain,
( ~ aFixedPointOf0(X0,xf)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(prop_impl_just,[status(thm)],[c_291]) ).
cnf(c_7128,plain,
( aFixedPointOf0(X0,xf)
| ~ aElementOf0(X0,xT) ),
inference(prop_impl_just,[status(thm)],[c_294]) ).
cnf(c_7129,plain,
( ~ aElementOf0(X0,xT)
| aFixedPointOf0(X0,xf) ),
inference(renaming,[status(thm)],[c_7128]) ).
cnf(c_10163,plain,
( ~ aElementOf0(X0_13,xU)
| aElementOf0(sdtlpdtrp0(xf,X0_13),xU) ),
inference(subtyping,[status(esa)],[c_7112]) ).
cnf(c_10178,plain,
( ~ aElementOf0(X0_13,X0_14)
| ~ aSet0(X0_14)
| aElementOf0(sK4(X0_14),X0_14) ),
inference(subtyping,[status(esa)],[c_1200]) ).
cnf(c_10179,plain,
( ~ sdtlseqdt0(X0_13,X1_13)
| ~ aElementOf0(X0_13,xU)
| ~ aElementOf0(X1_13,xU)
| sdtlseqdt0(sdtlpdtrp0(xf,X0_13),sdtlpdtrp0(xf,X1_13)) ),
inference(subtyping,[status(esa)],[c_1173]) ).
cnf(c_10181,plain,
( ~ aFixedPointOf0(X0_13,xf)
| aElementOf0(X0_13,xU) ),
inference(subtyping,[status(esa)],[c_7115]) ).
cnf(c_10185,plain,
( ~ aElementOf0(X0_13,xT)
| aFixedPointOf0(X0_13,xf) ),
inference(subtyping,[status(esa)],[c_7129]) ).
cnf(c_10186,plain,
( ~ aFixedPointOf0(X0_13,xf)
| sdtlpdtrp0(xf,X0_13) = X0_13 ),
inference(subtyping,[status(esa)],[c_7126]) ).
cnf(c_10189,negated_conjecture,
( aElementOf0(sK22,xT)
| sP3 ),
inference(subtyping,[status(esa)],[c_157]) ).
cnf(c_10192,plain,
( ~ sP3
| aElementOf0(sK21,xP) ),
inference(subtyping,[status(esa)],[c_154]) ).
cnf(c_10196,plain,
( ~ aElementOf0(X0_13,xP)
| sdtlseqdt0(xp,X0_13) ),
inference(subtyping,[status(esa)],[c_149]) ).
cnf(c_10198,plain,
( ~ aElementOf0(X0_13,xU)
| aElementOf0(sK20(X0_13),xP)
| sdtlseqdt0(X0_13,xp) ),
inference(subtyping,[status(esa)],[c_147]) ).
cnf(c_10199,plain,
( ~ sdtlseqdt0(X0_13,sK20(X0_13))
| ~ aElementOf0(X0_13,xU)
| sdtlseqdt0(X0_13,xp) ),
inference(subtyping,[status(esa)],[c_146]) ).
cnf(c_10203,plain,
( ~ aElementOf0(X0_13,xP)
| aElementOf0(X0_13,xU) ),
inference(subtyping,[status(esa)],[c_142]) ).
cnf(c_10204,plain,
( ~ aElementOf0(X0_13,xP)
| sdtlseqdt0(sdtlpdtrp0(xf,X0_13),X0_13) ),
inference(subtyping,[status(esa)],[c_141]) ).
cnf(c_10205,plain,
( ~ aElementOf0(X0_13,xT)
| ~ aElementOf0(X1_13,xP)
| sdtlseqdt0(X0_13,X1_13) ),
inference(subtyping,[status(esa)],[c_140]) ).
cnf(c_10215,plain,
( ~ aFixedPointOf0(X0_13,xf)
| aElementOf0(X0_13,xS) ),
inference(subtyping,[status(esa)],[c_126]) ).
cnf(c_10242,plain,
( ~ sdtlseqdt0(X0_13,X1_13)
| ~ sdtlseqdt0(X2_13,X0_13)
| ~ aElement0(X0_13)
| ~ aElement0(X1_13)
| ~ aElement0(X2_13)
| sdtlseqdt0(X2_13,X1_13) ),
inference(subtyping,[status(esa)],[c_58]) ).
cnf(c_10246,plain,
( ~ aElementOf0(X0_13,X0_14)
| ~ aSubsetOf0(X0_14,X1_14)
| ~ aSet0(X1_14)
| aElementOf0(X0_13,X1_14) ),
inference(subtyping,[status(esa)],[c_54]) ).
cnf(c_10249,plain,
( ~ aElementOf0(X0_13,X0_14)
| ~ aSet0(X0_14)
| aElement0(X0_13) ),
inference(subtyping,[status(esa)],[c_49]) ).
cnf(c_10251,plain,
X0_13 = X0_13,
theory(equality) ).
cnf(c_10253,plain,
( X0_13 != X1_13
| X2_13 != X1_13
| X2_13 = X0_13 ),
theory(equality) ).
cnf(c_10258,plain,
( X0_13 != X1_13
| X2_13 != X3_13
| ~ sdtlseqdt0(X1_13,X3_13)
| sdtlseqdt0(X0_13,X2_13) ),
theory(equality) ).
cnf(c_10265,plain,
( X0_13 != X1_13
| sdtlpdtrp0(X0_15,X0_13) = sdtlpdtrp0(X0_15,X1_13) ),
theory(equality) ).
cnf(c_10269,plain,
( xp != xp
| sdtlpdtrp0(xf,xp) = sdtlpdtrp0(xf,xp) ),
inference(instantiation,[status(thm)],[c_10265]) ).
cnf(c_10272,plain,
xp = xp,
inference(instantiation,[status(thm)],[c_10251]) ).
cnf(c_10274,plain,
( ~ aElementOf0(xp,xU)
| aElementOf0(sdtlpdtrp0(xf,xp),xU) ),
inference(instantiation,[status(thm)],[c_10163]) ).
cnf(c_12092,plain,
( sdtlpdtrp0(xf,xp) != X0_13
| sK22 != X1_13
| ~ sdtlseqdt0(X1_13,X0_13)
| sdtlseqdt0(sK22,sdtlpdtrp0(xf,xp)) ),
inference(instantiation,[status(thm)],[c_10258]) ).
cnf(c_12147,plain,
( X0_13 != X1_13
| sK22 != X1_13
| sK22 = X0_13 ),
inference(instantiation,[status(thm)],[c_10253]) ).
cnf(c_12180,plain,
( ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),X0_13)
| ~ aElement0(sdtlpdtrp0(xf,xp))
| ~ sdtlseqdt0(X0_13,sK21)
| ~ aElement0(X0_13)
| ~ aElement0(sK21)
| sdtlseqdt0(sdtlpdtrp0(xf,xp),sK21) ),
inference(instantiation,[status(thm)],[c_10242]) ).
cnf(c_12270,plain,
( X0_13 != sK22
| sK22 != sK22
| sK22 = X0_13 ),
inference(instantiation,[status(thm)],[c_12147]) ).
cnf(c_12471,plain,
sK22 = sK22,
inference(instantiation,[status(thm)],[c_10251]) ).
cnf(c_12646,plain,
( ~ aElementOf0(sdtlpdtrp0(xf,xp),X0_14)
| ~ aSet0(X0_14)
| aElement0(sdtlpdtrp0(xf,xp)) ),
inference(instantiation,[status(thm)],[c_10249]) ).
cnf(c_12647,plain,
( ~ aElementOf0(sdtlpdtrp0(xf,xp),xU)
| ~ aSet0(xU)
| aElement0(sdtlpdtrp0(xf,xp)) ),
inference(instantiation,[status(thm)],[c_12646]) ).
cnf(c_13146,plain,
( sdtlpdtrp0(xf,sK22) != sK22
| sK22 != sK22
| sK22 = sdtlpdtrp0(xf,sK22) ),
inference(instantiation,[status(thm)],[c_12270]) ).
cnf(c_13312,plain,
( aFixedPointOf0(sK22,xf)
| sP3 ),
inference(superposition,[status(thm)],[c_10189,c_10185]) ).
cnf(c_13313,plain,
( aElementOf0(sK22,xU)
| sP3 ),
inference(superposition,[status(thm)],[c_13312,c_10181]) ).
cnf(c_13314,plain,
( ~ sP3
| sdtlseqdt0(xp,sK21) ),
inference(superposition,[status(thm)],[c_10192,c_10196]) ).
cnf(c_13315,plain,
( ~ sP3
| aElementOf0(sK21,xU) ),
inference(superposition,[status(thm)],[c_10192,c_10203]) ).
cnf(c_13330,plain,
( aElementOf0(sK22,xS)
| sP3 ),
inference(superposition,[status(thm)],[c_13312,c_10215]) ).
cnf(c_13460,plain,
( ~ aSet0(xU)
| ~ sP3
| aElement0(sK21) ),
inference(superposition,[status(thm)],[c_13315,c_10249]) ).
cnf(c_13694,plain,
( sdtlpdtrp0(xf,sK22) = sK22
| sP3 ),
inference(superposition,[status(thm)],[c_13312,c_10186]) ).
cnf(c_13881,plain,
( ~ aElementOf0(X0_13,xP)
| sdtlseqdt0(sK22,X0_13)
| sP3 ),
inference(superposition,[status(thm)],[c_10189,c_10205]) ).
cnf(c_13920,plain,
( ~ aElementOf0(X0_13,xU)
| sdtlseqdt0(sK22,sK20(X0_13))
| sdtlseqdt0(X0_13,xp)
| sP3 ),
inference(superposition,[status(thm)],[c_10198,c_13881]) ).
cnf(c_13990,plain,
( ~ aElementOf0(sK22,xU)
| sdtlseqdt0(sK22,xp)
| sP3 ),
inference(superposition,[status(thm)],[c_13920,c_10199]) ).
cnf(c_14001,plain,
( sdtlseqdt0(sK22,xp)
| sP3 ),
inference(global_subsumption_just,[status(thm)],[c_13990,c_13313,c_13990]) ).
cnf(c_14400,plain,
( ~ aSet0(xS)
| aElementOf0(sK4(xS),xS)
| sP3 ),
inference(superposition,[status(thm)],[c_13330,c_10178]) ).
cnf(c_14505,plain,
( aFixedPointOf0(sK22,xf)
| sP3 ),
inference(superposition,[status(thm)],[c_10189,c_10185]) ).
cnf(c_14509,plain,
( aElementOf0(sK22,xS)
| sP3 ),
inference(superposition,[status(thm)],[c_14505,c_10215]) ).
cnf(c_14572,plain,
( ~ aSet0(xS)
| aElementOf0(sK4(xS),xS)
| sP3 ),
inference(superposition,[status(thm)],[c_14509,c_10178]) ).
cnf(c_14587,plain,
( aElementOf0(sK4(xS),xS)
| sP3 ),
inference(global_subsumption_just,[status(thm)],[c_14572,c_131,c_14400]) ).
cnf(c_14838,plain,
( sdtlpdtrp0(xf,xp) != X0_13
| sK22 != sdtlpdtrp0(xf,sK22)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,sK22),X0_13)
| sdtlseqdt0(sK22,sdtlpdtrp0(xf,xp)) ),
inference(instantiation,[status(thm)],[c_12092]) ).
cnf(c_14914,plain,
( ~ aElementOf0(sK21,xP)
| sdtlseqdt0(sdtlpdtrp0(xf,sK21),sK21) ),
inference(instantiation,[status(thm)],[c_10204]) ).
cnf(c_20477,plain,
( sdtlpdtrp0(xf,xp) != sdtlpdtrp0(xf,xp)
| sK22 != sdtlpdtrp0(xf,sK22)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,sK22),sdtlpdtrp0(xf,xp))
| sdtlseqdt0(sK22,sdtlpdtrp0(xf,xp)) ),
inference(instantiation,[status(thm)],[c_14838]) ).
cnf(c_24774,plain,
( aFixedPointOf0(sK22,xf)
| sP3 ),
inference(superposition,[status(thm)],[c_10189,c_10185]) ).
cnf(c_24775,plain,
( aElementOf0(sK22,xS)
| sP3 ),
inference(superposition,[status(thm)],[c_24774,c_10215]) ).
cnf(c_24899,plain,
( ~ aSet0(xS)
| aElementOf0(sK4(xS),xS)
| sP3 ),
inference(superposition,[status(thm)],[c_24775,c_10178]) ).
cnf(c_24936,plain,
( aElementOf0(sK4(xS),xS)
| sP3 ),
inference(global_subsumption_just,[status(thm)],[c_24899,c_14587]) ).
cnf(c_24939,plain,
( ~ aSubsetOf0(xS,X0_14)
| ~ aSet0(X0_14)
| aElementOf0(sK4(xS),X0_14)
| sP3 ),
inference(superposition,[status(thm)],[c_24936,c_10246]) ).
cnf(c_25749,plain,
( ~ aSubsetOf0(xS,X0_14)
| ~ aSet0(X0_14)
| aElementOf0(sK4(X0_14),X0_14)
| sP3 ),
inference(superposition,[status(thm)],[c_24939,c_10178]) ).
cnf(c_25764,plain,
( ~ aSubsetOf0(xS,X0_14)
| ~ aSet0(X0_14)
| aElement0(sK4(X0_14))
| sP3 ),
inference(superposition,[status(thm)],[c_25749,c_10249]) ).
cnf(c_26440,plain,
( ~ aElementOf0(sdtlpdtrp0(xf,sK21),X0_14)
| ~ aSet0(X0_14)
| aElement0(sdtlpdtrp0(xf,sK21)) ),
inference(instantiation,[status(thm)],[c_10249]) ).
cnf(c_26441,plain,
( ~ aElementOf0(sdtlpdtrp0(xf,sK21),xU)
| ~ aSet0(xU)
| aElement0(sdtlpdtrp0(xf,sK21)) ),
inference(instantiation,[status(thm)],[c_26440]) ).
cnf(c_26505,plain,
( ~ aElementOf0(xp,xU)
| ~ aElementOf0(sK22,xU)
| ~ sdtlseqdt0(sK22,xp)
| sdtlseqdt0(sdtlpdtrp0(xf,sK22),sdtlpdtrp0(xf,xp)) ),
inference(instantiation,[status(thm)],[c_10179]) ).
cnf(c_26601,plain,
sP3,
inference(global_subsumption_just,[status(thm)],[c_25764,c_151,c_156,c_10269,c_10272,c_12471,c_13146,c_13313,c_13694,c_14001,c_20477,c_26505]) ).
cnf(c_28897,plain,
( ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),sdtlpdtrp0(xf,X0_13))
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X0_13),sK21)
| ~ aElement0(sdtlpdtrp0(xf,X0_13))
| ~ aElement0(sdtlpdtrp0(xf,xp))
| ~ aElement0(sK21)
| sdtlseqdt0(sdtlpdtrp0(xf,xp),sK21) ),
inference(instantiation,[status(thm)],[c_12180]) ).
cnf(c_37894,plain,
( ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),sdtlpdtrp0(xf,sK21))
| ~ sdtlseqdt0(sdtlpdtrp0(xf,sK21),sK21)
| ~ aElement0(sdtlpdtrp0(xf,xp))
| ~ aElement0(sdtlpdtrp0(xf,sK21))
| ~ aElement0(sK21)
| sdtlseqdt0(sdtlpdtrp0(xf,xp),sK21) ),
inference(instantiation,[status(thm)],[c_28897]) ).
cnf(c_40939,plain,
( ~ aElementOf0(sK21,xU)
| aElementOf0(sdtlpdtrp0(xf,sK21),xU) ),
inference(instantiation,[status(thm)],[c_10163]) ).
cnf(c_41804,plain,
( ~ aElementOf0(xp,xU)
| ~ aElementOf0(sK21,xU)
| ~ sdtlseqdt0(xp,sK21)
| sdtlseqdt0(sdtlpdtrp0(xf,xp),sdtlpdtrp0(xf,sK21)) ),
inference(instantiation,[status(thm)],[c_10179]) ).
cnf(c_41805,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_41804,c_40939,c_37894,c_26601,c_26441,c_14914,c_13460,c_13315,c_13314,c_12647,c_10274,c_153,c_154,c_151,c_124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10 % Problem : LAT386+4 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.11 % Command : run_iprover %s %d THM
% 0.11/0.31 % Computer : n026.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Thu May 2 18:31:06 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.16/0.42 Running first-order theorem proving
% 0.16/0.42 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 14.37/2.63 % SZS status Started for theBenchmark.p
% 14.37/2.63 % SZS status Theorem for theBenchmark.p
% 14.37/2.63
% 14.37/2.63 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 14.37/2.63
% 14.37/2.63 ------ iProver source info
% 14.37/2.63
% 14.37/2.63 git: date: 2024-05-02 19:28:25 +0000
% 14.37/2.63 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 14.37/2.63 git: non_committed_changes: false
% 14.37/2.63
% 14.37/2.63 ------ Parsing...
% 14.37/2.63 ------ Clausification by vclausify_rel & Parsing by iProver...
% 14.37/2.63
% 14.37/2.63 ------ 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
% 14.37/2.63
% 14.37/2.63 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 14.37/2.63
% 14.37/2.63 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 14.37/2.63 ------ Proving...
% 14.37/2.63 ------ Problem Properties
% 14.37/2.63
% 14.37/2.63
% 14.37/2.63 clauses 87
% 14.37/2.63 conjectures 3
% 14.37/2.63 EPR 38
% 14.37/2.63 Horn 76
% 14.37/2.63 unary 14
% 14.37/2.63 binary 27
% 14.37/2.63 lits 256
% 14.37/2.63 lits eq 9
% 14.37/2.63 fd_pure 0
% 14.37/2.63 fd_pseudo 0
% 14.37/2.63 fd_cond 0
% 14.37/2.63 fd_pseudo_cond 3
% 14.37/2.63 AC symbols 0
% 14.37/2.63
% 14.37/2.63 ------ Input Options Time Limit: Unbounded
% 14.37/2.63
% 14.37/2.63
% 14.37/2.63 ------
% 14.37/2.63 Current options:
% 14.37/2.63 ------
% 14.37/2.63
% 14.37/2.63
% 14.37/2.63
% 14.37/2.63
% 14.37/2.63 ------ Proving...
% 14.37/2.63
% 14.37/2.63
% 14.37/2.63 % SZS status Theorem for theBenchmark.p
% 14.37/2.63
% 14.37/2.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 14.37/2.63
% 14.37/2.64
%------------------------------------------------------------------------------