TSTP Solution File: LAT387+4 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : LAT387+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n024.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 : Thu Aug 31 06:18:26 EDT 2023
% Result : Theorem 0.83s 1.07s
% Output : CNFRefutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 29
% Syntax : Number of formulae : 265 ( 41 unt; 0 def)
% Number of atoms : 1214 ( 63 equ)
% Maximal formula atoms : 37 ( 4 avg)
% Number of connectives : 1481 ( 532 ~; 522 |; 342 &)
% ( 8 <=>; 77 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 2 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 8 con; 0-3 aty)
% Number of variables : 395 ( 3 sgn; 254 !; 51 ?)
% 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(f7,axiom,
! [X0] :
( aElement0(X0)
=> sdtlseqdt0(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mARefl) ).
fof(f8,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mTrans) ).
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
=> ! [X2] :
( aLowerBoundOfIn0(X2,X1,X0)
<=> ( ! [X3] :
( aElementOf0(X3,X1)
=> sdtlseqdt0(X2,X3) )
& aElementOf0(X2,X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLB) ).
fof(f11,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
=> ! [X2] :
( aUpperBoundOfIn0(X2,X1,X0)
<=> ( ! [X3] :
( aElementOf0(X3,X1)
=> sdtlseqdt0(X3,X2) )
& aElementOf0(X2,X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefUB) ).
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,axiom,
( 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__1299) ).
fof(f30,conjecture,
( ( aSupremumOfIn0(xp,xT,xS)
| ( ! [X0] :
( ( aUpperBoundOfIn0(X0,xT,xS)
& ! [X1] :
( aElementOf0(X1,xT)
=> sdtlseqdt0(X1,X0) )
& aElementOf0(X0,xS) )
=> sdtlseqdt0(xp,X0) )
& ( aUpperBoundOfIn0(xp,xT,xS)
| ! [X0] :
( aElementOf0(X0,xT)
=> sdtlseqdt0(X0,xp) ) ) ) )
& ( aFixedPointOf0(xp,xf)
| ( xp = sdtlpdtrp0(xf,xp)
& aElementOf0(xp,szDzozmdt0(xf)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f31,negated_conjecture,
~ ( ( aSupremumOfIn0(xp,xT,xS)
| ( ! [X0] :
( ( aUpperBoundOfIn0(X0,xT,xS)
& ! [X1] :
( aElementOf0(X1,xT)
=> sdtlseqdt0(X1,X0) )
& aElementOf0(X0,xS) )
=> sdtlseqdt0(xp,X0) )
& ( aUpperBoundOfIn0(xp,xT,xS)
| ! [X0] :
( aElementOf0(X0,xT)
=> sdtlseqdt0(X0,xp) ) ) ) )
& ( aFixedPointOf0(xp,xf)
| ( xp = sdtlpdtrp0(xf,xp)
& aElementOf0(xp,szDzozmdt0(xf)) ) ) ),
inference(negated_conjecture,[],[f30]) ).
fof(f36,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(f37,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(f38,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(f39,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,[],[f29]) ).
fof(f40,plain,
~ ( ( aSupremumOfIn0(xp,xT,xS)
| ( ! [X0] :
( ( aUpperBoundOfIn0(X0,xT,xS)
& ! [X1] :
( aElementOf0(X1,xT)
=> sdtlseqdt0(X1,X0) )
& aElementOf0(X0,xS) )
=> sdtlseqdt0(xp,X0) )
& ( aUpperBoundOfIn0(xp,xT,xS)
| ! [X2] :
( aElementOf0(X2,xT)
=> sdtlseqdt0(X2,xp) ) ) ) )
& ( aFixedPointOf0(xp,xf)
| ( xp = sdtlpdtrp0(xf,xp)
& aElementOf0(xp,szDzozmdt0(xf)) ) ) ),
inference(rectify,[],[f31]) ).
fof(f42,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f43,plain,
! [X0] :
( ( isEmpty0(X0)
<=> ! [X1] : ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f45,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f46,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f47,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f46]) ).
fof(f48,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f49,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( aLowerBoundOfIn0(X2,X1,X0)
<=> ( ! [X3] :
( sdtlseqdt0(X2,X3)
| ~ aElementOf0(X3,X1) )
& aElementOf0(X2,X0) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f51,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( aUpperBoundOfIn0(X2,X1,X0)
<=> ( ! [X3] :
( sdtlseqdt0(X3,X2)
| ~ aElementOf0(X3,X1) )
& aElementOf0(X2,X0) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( aElementOf0(sdtlpdtrp0(X0,X1),szRzazndt0(X0))
| ~ aElementOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f67,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,[],[f36]) ).
fof(f68,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,[],[f67]) ).
fof(f69,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(f70,plain,
( aSubsetOf0(xT,xS)
& ! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xT) )
& aSet0(xT) ),
inference(ennf_transformation,[],[f26]) ).
fof(f71,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,[],[f37]) ).
fof(f72,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,[],[f71]) ).
fof(f73,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,[],[f38]) ).
fof(f74,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,[],[f39]) ).
fof(f75,plain,
( ( ~ aSupremumOfIn0(xp,xT,xS)
& ( ? [X0] :
( ~ sdtlseqdt0(xp,X0)
& aUpperBoundOfIn0(X0,xT,xS)
& ! [X1] :
( sdtlseqdt0(X1,X0)
| ~ aElementOf0(X1,xT) )
& aElementOf0(X0,xS) )
| ( ~ aUpperBoundOfIn0(xp,xT,xS)
& ? [X2] :
( ~ sdtlseqdt0(X2,xp)
& aElementOf0(X2,xT) ) ) ) )
| ( ~ aFixedPointOf0(xp,xf)
& ( xp != sdtlpdtrp0(xf,xp)
| ~ aElementOf0(xp,szDzozmdt0(xf)) ) ) ),
inference(ennf_transformation,[],[f40]) ).
fof(f76,plain,
( ( ~ aSupremumOfIn0(xp,xT,xS)
& ( ? [X0] :
( ~ sdtlseqdt0(xp,X0)
& aUpperBoundOfIn0(X0,xT,xS)
& ! [X1] :
( sdtlseqdt0(X1,X0)
| ~ aElementOf0(X1,xT) )
& aElementOf0(X0,xS) )
| ( ~ aUpperBoundOfIn0(xp,xT,xS)
& ? [X2] :
( ~ sdtlseqdt0(X2,xp)
& aElementOf0(X2,xT) ) ) ) )
| ( ~ aFixedPointOf0(xp,xf)
& ( xp != sdtlpdtrp0(xf,xp)
| ~ aElementOf0(xp,szDzozmdt0(xf)) ) ) ),
inference(flattening,[],[f75]) ).
fof(f77,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(f78,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(f79,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(f80,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,[],[f68,f79,f78,f77]) ).
fof(f81,plain,
( ? [X0] :
( ~ sdtlseqdt0(xp,X0)
& aUpperBoundOfIn0(X0,xT,xS)
& ! [X1] :
( sdtlseqdt0(X1,X0)
| ~ aElementOf0(X1,xT) )
& aElementOf0(X0,xS) )
| ~ sP3 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f82,plain,
( ( ~ aSupremumOfIn0(xp,xT,xS)
& ( sP3
| ( ~ aUpperBoundOfIn0(xp,xT,xS)
& ? [X2] :
( ~ sdtlseqdt0(X2,xp)
& aElementOf0(X2,xT) ) ) ) )
| ( ~ aFixedPointOf0(xp,xf)
& ( xp != sdtlpdtrp0(xf,xp)
| ~ aElementOf0(xp,szDzozmdt0(xf)) ) ) ),
inference(definition_folding,[],[f76,f81]) ).
fof(f83,plain,
! [X0] :
( ( ( isEmpty0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ! [X1] : ~ aElementOf0(X1,X0)
| ~ isEmpty0(X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f43]) ).
fof(f84,plain,
! [X0] :
( ( ( isEmpty0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ! [X2] : ~ aElementOf0(X2,X0)
| ~ isEmpty0(X0) ) )
| ~ aSet0(X0) ),
inference(rectify,[],[f83]) ).
fof(f85,plain,
! [X0] :
( ? [X1] : aElementOf0(X1,X0)
=> aElementOf0(sK4(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f86,plain,
! [X0] :
( ( ( isEmpty0(X0)
| aElementOf0(sK4(X0),X0) )
& ( ! [X2] : ~ aElementOf0(X2,X0)
| ~ isEmpty0(X0) ) )
| ~ aSet0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f84,f85]) ).
fof(f87,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,[],[f44]) ).
fof(f88,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,[],[f87]) ).
fof(f89,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,[],[f88]) ).
fof(f90,plain,
! [X0,X1] :
( ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
=> ( ~ aElementOf0(sK5(X0,X1),X0)
& aElementOf0(sK5(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f91,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])],[f89,f90]) ).
fof(f92,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( aLowerBoundOfIn0(X2,X1,X0)
| ? [X3] :
( ~ sdtlseqdt0(X2,X3)
& aElementOf0(X3,X1) )
| ~ aElementOf0(X2,X0) )
& ( ( ! [X3] :
( sdtlseqdt0(X2,X3)
| ~ aElementOf0(X3,X1) )
& aElementOf0(X2,X0) )
| ~ aLowerBoundOfIn0(X2,X1,X0) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f50]) ).
fof(f93,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( aLowerBoundOfIn0(X2,X1,X0)
| ? [X3] :
( ~ sdtlseqdt0(X2,X3)
& aElementOf0(X3,X1) )
| ~ aElementOf0(X2,X0) )
& ( ( ! [X3] :
( sdtlseqdt0(X2,X3)
| ~ aElementOf0(X3,X1) )
& aElementOf0(X2,X0) )
| ~ aLowerBoundOfIn0(X2,X1,X0) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(flattening,[],[f92]) ).
fof(f94,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( aLowerBoundOfIn0(X2,X1,X0)
| ? [X3] :
( ~ sdtlseqdt0(X2,X3)
& aElementOf0(X3,X1) )
| ~ aElementOf0(X2,X0) )
& ( ( ! [X4] :
( sdtlseqdt0(X2,X4)
| ~ aElementOf0(X4,X1) )
& aElementOf0(X2,X0) )
| ~ aLowerBoundOfIn0(X2,X1,X0) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(rectify,[],[f93]) ).
fof(f95,plain,
! [X1,X2] :
( ? [X3] :
( ~ sdtlseqdt0(X2,X3)
& aElementOf0(X3,X1) )
=> ( ~ sdtlseqdt0(X2,sK6(X1,X2))
& aElementOf0(sK6(X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f96,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( aLowerBoundOfIn0(X2,X1,X0)
| ( ~ sdtlseqdt0(X2,sK6(X1,X2))
& aElementOf0(sK6(X1,X2),X1) )
| ~ aElementOf0(X2,X0) )
& ( ( ! [X4] :
( sdtlseqdt0(X2,X4)
| ~ aElementOf0(X4,X1) )
& aElementOf0(X2,X0) )
| ~ aLowerBoundOfIn0(X2,X1,X0) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f94,f95]) ).
fof(f97,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( aUpperBoundOfIn0(X2,X1,X0)
| ? [X3] :
( ~ sdtlseqdt0(X3,X2)
& aElementOf0(X3,X1) )
| ~ aElementOf0(X2,X0) )
& ( ( ! [X3] :
( sdtlseqdt0(X3,X2)
| ~ aElementOf0(X3,X1) )
& aElementOf0(X2,X0) )
| ~ aUpperBoundOfIn0(X2,X1,X0) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f51]) ).
fof(f98,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( aUpperBoundOfIn0(X2,X1,X0)
| ? [X3] :
( ~ sdtlseqdt0(X3,X2)
& aElementOf0(X3,X1) )
| ~ aElementOf0(X2,X0) )
& ( ( ! [X3] :
( sdtlseqdt0(X3,X2)
| ~ aElementOf0(X3,X1) )
& aElementOf0(X2,X0) )
| ~ aUpperBoundOfIn0(X2,X1,X0) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(flattening,[],[f97]) ).
fof(f99,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( aUpperBoundOfIn0(X2,X1,X0)
| ? [X3] :
( ~ sdtlseqdt0(X3,X2)
& aElementOf0(X3,X1) )
| ~ aElementOf0(X2,X0) )
& ( ( ! [X4] :
( sdtlseqdt0(X4,X2)
| ~ aElementOf0(X4,X1) )
& aElementOf0(X2,X0) )
| ~ aUpperBoundOfIn0(X2,X1,X0) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(rectify,[],[f98]) ).
fof(f100,plain,
! [X1,X2] :
( ? [X3] :
( ~ sdtlseqdt0(X3,X2)
& aElementOf0(X3,X1) )
=> ( ~ sdtlseqdt0(sK7(X1,X2),X2)
& aElementOf0(sK7(X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( aUpperBoundOfIn0(X2,X1,X0)
| ( ~ sdtlseqdt0(sK7(X1,X2),X2)
& aElementOf0(sK7(X1,X2),X1) )
| ~ aElementOf0(X2,X0) )
& ( ( ! [X4] :
( sdtlseqdt0(X4,X2)
| ~ aElementOf0(X4,X1) )
& aElementOf0(X2,X0) )
| ~ aUpperBoundOfIn0(X2,X1,X0) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f99,f100]) ).
fof(f136,plain,
! [X2] :
( ? [X3] :
( ~ aElementOf0(X3,xU)
& aElementOf0(X3,X2) )
=> ( ~ aElementOf0(sK18(X2),xU)
& aElementOf0(sK18(X2),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f137,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])],[f80,f136]) ).
fof(f138,plain,
! [X0] :
( ? [X1] :
( ~ sdtlseqdt0(X1,X0)
& aElementOf0(X1,xT) )
=> ( ~ sdtlseqdt0(sK19(X0),X0)
& aElementOf0(sK19(X0),xT) ) ),
introduced(choice_axiom,[]) ).
fof(f139,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])],[f72,f138]) ).
fof(f140,plain,
! [X0] :
( ? [X1] :
( ~ sdtlseqdt0(X0,X1)
& aElementOf0(X1,xP) )
=> ( ~ sdtlseqdt0(X0,sK20(X0))
& aElementOf0(sK20(X0),xP) ) ),
introduced(choice_axiom,[]) ).
fof(f141,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])],[f73,f140]) ).
fof(f142,plain,
( ? [X0] :
( ~ sdtlseqdt0(xp,X0)
& aUpperBoundOfIn0(X0,xT,xS)
& ! [X1] :
( sdtlseqdt0(X1,X0)
| ~ aElementOf0(X1,xT) )
& aElementOf0(X0,xS) )
| ~ sP3 ),
inference(nnf_transformation,[],[f81]) ).
fof(f143,plain,
( ? [X0] :
( ~ sdtlseqdt0(xp,X0)
& aUpperBoundOfIn0(X0,xT,xS)
& ! [X1] :
( sdtlseqdt0(X1,X0)
| ~ aElementOf0(X1,xT) )
& aElementOf0(X0,xS) )
=> ( ~ sdtlseqdt0(xp,sK21)
& aUpperBoundOfIn0(sK21,xT,xS)
& ! [X1] :
( sdtlseqdt0(X1,sK21)
| ~ aElementOf0(X1,xT) )
& aElementOf0(sK21,xS) ) ),
introduced(choice_axiom,[]) ).
fof(f144,plain,
( ( ~ sdtlseqdt0(xp,sK21)
& aUpperBoundOfIn0(sK21,xT,xS)
& ! [X1] :
( sdtlseqdt0(X1,sK21)
| ~ aElementOf0(X1,xT) )
& aElementOf0(sK21,xS) )
| ~ sP3 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f142,f143]) ).
fof(f145,plain,
( ( ~ aSupremumOfIn0(xp,xT,xS)
& ( sP3
| ( ~ aUpperBoundOfIn0(xp,xT,xS)
& ? [X0] :
( ~ sdtlseqdt0(X0,xp)
& aElementOf0(X0,xT) ) ) ) )
| ( ~ aFixedPointOf0(xp,xf)
& ( xp != sdtlpdtrp0(xf,xp)
| ~ aElementOf0(xp,szDzozmdt0(xf)) ) ) ),
inference(rectify,[],[f82]) ).
fof(f146,plain,
( ? [X0] :
( ~ sdtlseqdt0(X0,xp)
& aElementOf0(X0,xT) )
=> ( ~ sdtlseqdt0(sK22,xp)
& aElementOf0(sK22,xT) ) ),
introduced(choice_axiom,[]) ).
fof(f147,plain,
( ( ~ aSupremumOfIn0(xp,xT,xS)
& ( sP3
| ( ~ aUpperBoundOfIn0(xp,xT,xS)
& ~ sdtlseqdt0(sK22,xp)
& aElementOf0(sK22,xT) ) ) )
| ( ~ aFixedPointOf0(xp,xf)
& ( xp != sdtlpdtrp0(xf,xp)
| ~ aElementOf0(xp,szDzozmdt0(xf)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f145,f146]) ).
fof(f148,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f149,plain,
! [X2,X0] :
( ~ aElementOf0(X2,X0)
| ~ isEmpty0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f150,plain,
! [X0] :
( isEmpty0(X0)
| aElementOf0(sK4(X0),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f153,plain,
! [X0,X1] :
( aSubsetOf0(X1,X0)
| aElementOf0(sK5(X0,X1),X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f154,plain,
! [X0,X1] :
( aSubsetOf0(X1,X0)
| ~ aElementOf0(sK5(X0,X1),X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f155,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f156,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f157,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f158,plain,
! [X2,X0,X1] :
( aElementOf0(X2,X0)
| ~ aLowerBoundOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f163,plain,
! [X2,X0,X1,X4] :
( sdtlseqdt0(X4,X2)
| ~ aElementOf0(X4,X1)
| ~ aUpperBoundOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f164,plain,
! [X2,X0,X1] :
( aUpperBoundOfIn0(X2,X1,X0)
| aElementOf0(sK7(X1,X2),X1)
| ~ aElementOf0(X2,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f165,plain,
! [X2,X0,X1] :
( aUpperBoundOfIn0(X2,X1,X0)
| ~ sdtlseqdt0(sK7(X1,X2),X2)
| ~ aElementOf0(X2,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f186,plain,
! [X0,X1] :
( aElementOf0(sdtlpdtrp0(X0,X1),szRzazndt0(X0))
| ~ aElementOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f213,plain,
aSet0(xU),
inference(cnf_transformation,[],[f137]) ).
fof(f218,plain,
aFunction0(xf),
inference(cnf_transformation,[],[f137]) ).
fof(f219,plain,
! [X0,X1] :
( sdtlseqdt0(sdtlpdtrp0(xf,X0),sdtlpdtrp0(xf,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf)) ),
inference(cnf_transformation,[],[f137]) ).
fof(f221,plain,
szDzozmdt0(xf) = szRzazndt0(xf),
inference(cnf_transformation,[],[f137]) ).
fof(f222,plain,
xU = szRzazndt0(xf),
inference(cnf_transformation,[],[f137]) ).
fof(f224,plain,
aSet0(xS),
inference(cnf_transformation,[],[f69]) ).
fof(f225,plain,
! [X0] :
( aElementOf0(X0,szDzozmdt0(xf))
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f69]) ).
fof(f226,plain,
! [X0] :
( sdtlpdtrp0(xf,X0) = X0
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f69]) ).
fof(f227,plain,
! [X0] :
( aFixedPointOf0(X0,xf)
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f69]) ).
fof(f228,plain,
! [X0] :
( aElementOf0(X0,xS)
| sdtlpdtrp0(xf,X0) != X0
| ~ aElementOf0(X0,szDzozmdt0(xf)) ),
inference(cnf_transformation,[],[f69]) ).
fof(f229,plain,
! [X0] :
( aElementOf0(X0,xS)
| ~ aFixedPointOf0(X0,xf) ),
inference(cnf_transformation,[],[f69]) ).
fof(f231,plain,
aSet0(xT),
inference(cnf_transformation,[],[f70]) ).
fof(f232,plain,
! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[],[f70]) ).
fof(f233,plain,
aSubsetOf0(xT,xS),
inference(cnf_transformation,[],[f70]) ).
fof(f234,plain,
aSet0(xP),
inference(cnf_transformation,[],[f139]) ).
fof(f235,plain,
! [X0] :
( aElementOf0(X0,xU)
| ~ aElementOf0(X0,xP) ),
inference(cnf_transformation,[],[f139]) ).
fof(f237,plain,
! [X2,X0] :
( sdtlseqdt0(X2,X0)
| ~ aElementOf0(X2,xT)
| ~ aElementOf0(X0,xP) ),
inference(cnf_transformation,[],[f139]) ).
fof(f239,plain,
! [X0] :
( aElementOf0(X0,xP)
| aElementOf0(sK19(X0),xT)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
| ~ aElementOf0(X0,xU) ),
inference(cnf_transformation,[],[f139]) ).
fof(f240,plain,
! [X0] :
( aElementOf0(X0,xP)
| ~ sdtlseqdt0(sK19(X0),X0)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
| ~ aElementOf0(X0,xU) ),
inference(cnf_transformation,[],[f139]) ).
fof(f241,plain,
! [X0] :
( aElementOf0(X0,xP)
| ~ aUpperBoundOfIn0(X0,xT,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
| ~ aElementOf0(X0,xU) ),
inference(cnf_transformation,[],[f139]) ).
fof(f243,plain,
aElementOf0(xp,xU),
inference(cnf_transformation,[],[f141]) ).
fof(f244,plain,
aElementOf0(xp,xU),
inference(cnf_transformation,[],[f141]) ).
fof(f245,plain,
! [X2] :
( sdtlseqdt0(xp,X2)
| ~ aElementOf0(X2,xP) ),
inference(cnf_transformation,[],[f141]) ).
fof(f249,plain,
! [X0] :
( sdtlseqdt0(X0,xp)
| ~ aLowerBoundOfIn0(X0,xP,xU) ),
inference(cnf_transformation,[],[f141]) ).
fof(f252,plain,
aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU),
inference(cnf_transformation,[],[f74]) ).
fof(f253,plain,
! [X0] :
( sdtlseqdt0(X0,sdtlpdtrp0(xf,xp))
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[],[f74]) ).
fof(f254,plain,
aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU),
inference(cnf_transformation,[],[f74]) ).
fof(f255,plain,
( aElementOf0(sK21,xS)
| ~ sP3 ),
inference(cnf_transformation,[],[f144]) ).
fof(f256,plain,
! [X1] :
( sdtlseqdt0(X1,sK21)
| ~ aElementOf0(X1,xT)
| ~ sP3 ),
inference(cnf_transformation,[],[f144]) ).
fof(f258,plain,
( ~ sdtlseqdt0(xp,sK21)
| ~ sP3 ),
inference(cnf_transformation,[],[f144]) ).
fof(f259,plain,
( sP3
| aElementOf0(sK22,xT)
| xp != sdtlpdtrp0(xf,xp)
| ~ aElementOf0(xp,szDzozmdt0(xf)) ),
inference(cnf_transformation,[],[f147]) ).
fof(f264,plain,
( sP3
| ~ aUpperBoundOfIn0(xp,xT,xS)
| ~ aFixedPointOf0(xp,xf) ),
inference(cnf_transformation,[],[f147]) ).
cnf(c_49,plain,
( ~ aElementOf0(X0,X1)
| ~ aSet0(X1)
| aElement0(X0) ),
inference(cnf_transformation,[],[f148]) ).
cnf(c_50,plain,
( ~ aSet0(X0)
| aElementOf0(sK4(X0),X0)
| isEmpty0(X0) ),
inference(cnf_transformation,[],[f150]) ).
cnf(c_51,plain,
( ~ aElementOf0(X0,X1)
| ~ aSet0(X1)
| ~ isEmpty0(X1) ),
inference(cnf_transformation,[],[f149]) ).
cnf(c_52,plain,
( ~ aElementOf0(sK5(X0,X1),X0)
| ~ aSet0(X0)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ),
inference(cnf_transformation,[],[f154]) ).
cnf(c_53,plain,
( ~ aSet0(X0)
| ~ aSet0(X1)
| aElementOf0(sK5(X1,X0),X0)
| aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f153]) ).
cnf(c_56,plain,
( ~ aElement0(X0)
| sdtlseqdt0(X0,X0) ),
inference(cnf_transformation,[],[f155]) ).
cnf(c_57,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f156]) ).
cnf(c_58,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X2,X0)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| sdtlseqdt0(X2,X1) ),
inference(cnf_transformation,[],[f157]) ).
cnf(c_62,plain,
( ~ aLowerBoundOfIn0(X0,X1,X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2)
| aElementOf0(X0,X2) ),
inference(cnf_transformation,[],[f158]) ).
cnf(c_63,plain,
( ~ sdtlseqdt0(sK7(X0,X1),X1)
| ~ aElementOf0(X1,X2)
| ~ aSubsetOf0(X0,X2)
| ~ aSet0(X2)
| aUpperBoundOfIn0(X1,X0,X2) ),
inference(cnf_transformation,[],[f165]) ).
cnf(c_64,plain,
( ~ aElementOf0(X0,X1)
| ~ aSubsetOf0(X2,X1)
| ~ aSet0(X1)
| aElementOf0(sK7(X2,X0),X2)
| aUpperBoundOfIn0(X0,X2,X1) ),
inference(cnf_transformation,[],[f164]) ).
cnf(c_65,plain,
( ~ aUpperBoundOfIn0(X0,X1,X2)
| ~ aElementOf0(X3,X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2)
| sdtlseqdt0(X3,X0) ),
inference(cnf_transformation,[],[f163]) ).
cnf(c_87,plain,
( ~ aElementOf0(X0,szDzozmdt0(X1))
| ~ aFunction0(X1)
| aElementOf0(sdtlpdtrp0(X1,X0),szRzazndt0(X1)) ),
inference(cnf_transformation,[],[f186]) ).
cnf(c_115,plain,
szRzazndt0(xf) = xU,
inference(cnf_transformation,[],[f222]) ).
cnf(c_116,plain,
szDzozmdt0(xf) = szRzazndt0(xf),
inference(cnf_transformation,[],[f221]) ).
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,[],[f219]) ).
cnf(c_119,plain,
aFunction0(xf),
inference(cnf_transformation,[],[f218]) ).
cnf(c_124,plain,
aSet0(xU),
inference(cnf_transformation,[],[f213]) ).
cnf(c_126,plain,
( ~ aFixedPointOf0(X0,xf)
| aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f229]) ).
cnf(c_127,plain,
( sdtlpdtrp0(xf,X0) != X0
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f228]) ).
cnf(c_128,plain,
( ~ aElementOf0(X0,xS)
| aFixedPointOf0(X0,xf) ),
inference(cnf_transformation,[],[f227]) ).
cnf(c_129,plain,
( ~ aElementOf0(X0,xS)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(cnf_transformation,[],[f226]) ).
cnf(c_130,plain,
( ~ aElementOf0(X0,xS)
| aElementOf0(X0,szDzozmdt0(xf)) ),
inference(cnf_transformation,[],[f225]) ).
cnf(c_131,plain,
aSet0(xS),
inference(cnf_transformation,[],[f224]) ).
cnf(c_132,plain,
aSubsetOf0(xT,xS),
inference(cnf_transformation,[],[f233]) ).
cnf(c_133,plain,
( ~ aElementOf0(X0,xT)
| aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f232]) ).
cnf(c_134,plain,
aSet0(xT),
inference(cnf_transformation,[],[f231]) ).
cnf(c_136,plain,
( ~ sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
| ~ aUpperBoundOfIn0(X0,xT,xU)
| ~ aElementOf0(X0,xU)
| aElementOf0(X0,xP) ),
inference(cnf_transformation,[],[f241]) ).
cnf(c_137,plain,
( ~ sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
| ~ sdtlseqdt0(sK19(X0),X0)
| ~ aElementOf0(X0,xU)
| aElementOf0(X0,xP) ),
inference(cnf_transformation,[],[f240]) ).
cnf(c_138,plain,
( ~ sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
| ~ aElementOf0(X0,xU)
| aElementOf0(sK19(X0),xT)
| aElementOf0(X0,xP) ),
inference(cnf_transformation,[],[f239]) ).
cnf(c_140,plain,
( ~ aElementOf0(X0,xP)
| ~ aElementOf0(X1,xT)
| sdtlseqdt0(X1,X0) ),
inference(cnf_transformation,[],[f237]) ).
cnf(c_142,plain,
( ~ aElementOf0(X0,xP)
| aElementOf0(X0,xU) ),
inference(cnf_transformation,[],[f235]) ).
cnf(c_143,plain,
aSet0(xP),
inference(cnf_transformation,[],[f234]) ).
cnf(c_145,plain,
( ~ aLowerBoundOfIn0(X0,xP,xU)
| sdtlseqdt0(X0,xp) ),
inference(cnf_transformation,[],[f249]) ).
cnf(c_149,plain,
( ~ aElementOf0(X0,xP)
| sdtlseqdt0(xp,X0) ),
inference(cnf_transformation,[],[f245]) ).
cnf(c_150,plain,
aElementOf0(xp,xU),
inference(cnf_transformation,[],[f244]) ).
cnf(c_151,plain,
aElementOf0(xp,xU),
inference(cnf_transformation,[],[f243]) ).
cnf(c_152,plain,
aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU),
inference(cnf_transformation,[],[f254]) ).
cnf(c_153,plain,
( ~ aElementOf0(X0,xT)
| sdtlseqdt0(X0,sdtlpdtrp0(xf,xp)) ),
inference(cnf_transformation,[],[f253]) ).
cnf(c_154,plain,
aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU),
inference(cnf_transformation,[],[f252]) ).
cnf(c_156,plain,
( ~ sdtlseqdt0(xp,sK21)
| ~ sP3 ),
inference(cnf_transformation,[],[f258]) ).
cnf(c_158,plain,
( ~ aElementOf0(X0,xT)
| ~ sP3
| sdtlseqdt0(X0,sK21) ),
inference(cnf_transformation,[],[f256]) ).
cnf(c_159,plain,
( ~ sP3
| aElementOf0(sK21,xS) ),
inference(cnf_transformation,[],[f255]) ).
cnf(c_162,negated_conjecture,
( ~ aUpperBoundOfIn0(xp,xT,xS)
| ~ aFixedPointOf0(xp,xf)
| sP3 ),
inference(cnf_transformation,[],[f264]) ).
cnf(c_167,negated_conjecture,
( sdtlpdtrp0(xf,xp) != xp
| ~ aElementOf0(xp,szDzozmdt0(xf))
| aElementOf0(sK22,xT)
| sP3 ),
inference(cnf_transformation,[],[f259]) ).
cnf(c_255,plain,
( aFixedPointOf0(X0,xf)
| ~ aElementOf0(X0,xS) ),
inference(prop_impl_just,[status(thm)],[c_128]) ).
cnf(c_256,plain,
( ~ aElementOf0(X0,xS)
| aFixedPointOf0(X0,xf) ),
inference(renaming,[status(thm)],[c_255]) ).
cnf(c_293,plain,
( aElementOf0(X0,szDzozmdt0(xf))
| ~ aFixedPointOf0(X0,xf) ),
inference(prop_impl_just,[status(thm)],[c_126,c_130]) ).
cnf(c_294,plain,
( ~ aFixedPointOf0(X0,xf)
| aElementOf0(X0,szDzozmdt0(xf)) ),
inference(renaming,[status(thm)],[c_293]) ).
cnf(c_299,plain,
( ~ aFixedPointOf0(X0,xf)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(prop_impl_just,[status(thm)],[c_126,c_129]) ).
cnf(c_301,plain,
( aFixedPointOf0(X0,xf)
| ~ aElementOf0(X0,xT) ),
inference(prop_impl_just,[status(thm)],[c_133,c_128]) ).
cnf(c_302,plain,
( ~ aElementOf0(X0,xT)
| aFixedPointOf0(X0,xf) ),
inference(renaming,[status(thm)],[c_301]) ).
cnf(c_552,plain,
( sdtlpdtrp0(xf,X0) != X0
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aFixedPointOf0(X0,xf) ),
inference(bin_hyper_res,[status(thm)],[c_127,c_256]) ).
cnf(c_1267,plain,
szDzozmdt0(xf) = xU,
inference(light_normalisation,[status(thm)],[c_116,c_115]) ).
cnf(c_1312,plain,
( ~ aFixedPointOf0(X0,xf)
| aElementOf0(X0,xU) ),
inference(light_normalisation,[status(thm)],[c_294,c_1267]) ).
cnf(c_1533,plain,
( sdtlpdtrp0(xf,X0) != X0
| ~ aElementOf0(X0,xU)
| aFixedPointOf0(X0,xf) ),
inference(light_normalisation,[status(thm)],[c_552,c_1267]) ).
cnf(c_1594,plain,
( sdtlpdtrp0(xf,xp) != xp
| ~ aElementOf0(xp,xU)
| aElementOf0(sK22,xT)
| sP3 ),
inference(light_normalisation,[status(thm)],[c_167,c_1267]) ).
cnf(c_1595,plain,
( sdtlpdtrp0(xf,xp) != xp
| aElementOf0(sK22,xT)
| sP3 ),
inference(forward_subsumption_resolution,[status(thm)],[c_1594,c_150]) ).
cnf(c_1794,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_1267]) ).
cnf(c_1920,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_1921,plain,
( ~ aElementOf0(X0,X1)
| ~ aSet0(X1)
| aElementOf0(sK4(X1),X1) ),
inference(unflattening,[status(thm)],[c_1920]) ).
cnf(c_2153,plain,
( X0 != xf
| ~ aElementOf0(X1,szDzozmdt0(X0))
| aElementOf0(sdtlpdtrp0(X0,X1),szRzazndt0(X0)) ),
inference(resolution_lifted,[status(thm)],[c_87,c_119]) ).
cnf(c_2154,plain,
( ~ aElementOf0(X0,szDzozmdt0(xf))
| aElementOf0(sdtlpdtrp0(xf,X0),szRzazndt0(xf)) ),
inference(unflattening,[status(thm)],[c_2153]) ).
cnf(c_5133,plain,
( ~ aElementOf0(X0,szDzozmdt0(xf))
| aElementOf0(sdtlpdtrp0(xf,X0),szRzazndt0(xf)) ),
inference(prop_impl_just,[status(thm)],[c_2154]) ).
cnf(c_6102,plain,
( ~ aElementOf0(X0,xU)
| aElementOf0(sdtlpdtrp0(xf,X0),xU) ),
inference(light_normalisation,[status(thm)],[c_5133,c_115,c_1267]) ).
cnf(c_9201,plain,
( aElementOf0(X0,xU)
| ~ aFixedPointOf0(X0,xf) ),
inference(prop_impl_just,[status(thm)],[c_1312]) ).
cnf(c_9202,plain,
( ~ aFixedPointOf0(X0,xf)
| aElementOf0(X0,xU) ),
inference(renaming,[status(thm)],[c_9201]) ).
cnf(c_9213,plain,
( ~ aFixedPointOf0(X0,xf)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(prop_impl_just,[status(thm)],[c_299]) ).
cnf(c_9215,plain,
( aFixedPointOf0(X0,xf)
| ~ aElementOf0(X0,xT) ),
inference(prop_impl_just,[status(thm)],[c_302]) ).
cnf(c_9216,plain,
( ~ aElementOf0(X0,xT)
| aFixedPointOf0(X0,xf) ),
inference(renaming,[status(thm)],[c_9215]) ).
cnf(c_15259,plain,
( ~ sP3
| aFixedPointOf0(sK21,xf) ),
inference(superposition,[status(thm)],[c_159,c_128]) ).
cnf(c_15283,plain,
( ~ sP3
| aElementOf0(sK21,xU) ),
inference(superposition,[status(thm)],[c_15259,c_9202]) ).
cnf(c_15312,plain,
sdtlseqdt0(sdtlpdtrp0(xf,xp),xp),
inference(superposition,[status(thm)],[c_154,c_145]) ).
cnf(c_15339,plain,
( ~ aSet0(xU)
| aElement0(xp) ),
inference(superposition,[status(thm)],[c_150,c_49]) ).
cnf(c_15341,plain,
( ~ aSet0(xU)
| ~ sP3
| aElement0(sK21) ),
inference(superposition,[status(thm)],[c_15283,c_49]) ).
cnf(c_15342,plain,
aElement0(xp),
inference(forward_subsumption_resolution,[status(thm)],[c_15339,c_124]) ).
cnf(c_15343,plain,
( ~ sP3
| aElement0(sK21) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15341,c_124]) ).
cnf(c_15551,plain,
( ~ sP3
| sdtlpdtrp0(xf,sK21) = sK21 ),
inference(superposition,[status(thm)],[c_15259,c_9213]) ).
cnf(c_15711,plain,
( ~ aSet0(X0)
| ~ aSet0(xP)
| aElementOf0(sK5(X0,xP),xU)
| aSubsetOf0(xP,X0) ),
inference(superposition,[status(thm)],[c_53,c_142]) ).
cnf(c_15720,plain,
( ~ aSet0(X0)
| aElementOf0(sK5(X0,xP),xU)
| aSubsetOf0(xP,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15711,c_143]) ).
cnf(c_16007,plain,
( ~ aSubsetOf0(xP,xU)
| ~ aSet0(xU)
| aElementOf0(sdtlpdtrp0(xf,xp),xU) ),
inference(superposition,[status(thm)],[c_154,c_62]) ).
cnf(c_16008,plain,
( ~ aSubsetOf0(xP,xU)
| aElementOf0(sdtlpdtrp0(xf,xp),xU) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16007,c_124]) ).
cnf(c_16069,plain,
( ~ aSubsetOf0(xP,xU)
| ~ aSet0(xU)
| aElement0(sdtlpdtrp0(xf,xp)) ),
inference(superposition,[status(thm)],[c_16008,c_49]) ).
cnf(c_16071,plain,
( ~ aSubsetOf0(xP,xU)
| aElement0(sdtlpdtrp0(xf,xp)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16069,c_124]) ).
cnf(c_16281,plain,
( ~ aElementOf0(xp,xU)
| aElementOf0(sK19(xp),xT)
| aElementOf0(xp,xP) ),
inference(superposition,[status(thm)],[c_15312,c_138]) ).
cnf(c_16282,plain,
( aElementOf0(sK19(xp),xT)
| aElementOf0(xp,xP) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16281,c_150]) ).
cnf(c_16327,plain,
( ~ sdtlseqdt0(xp,sdtlpdtrp0(xf,xp))
| ~ aElement0(sdtlpdtrp0(xf,xp))
| ~ aElement0(xp)
| sdtlpdtrp0(xf,xp) = xp ),
inference(superposition,[status(thm)],[c_15312,c_57]) ).
cnf(c_16340,plain,
( ~ sdtlseqdt0(xp,sdtlpdtrp0(xf,xp))
| ~ aElement0(sdtlpdtrp0(xf,xp))
| sdtlpdtrp0(xf,xp) = xp ),
inference(forward_subsumption_resolution,[status(thm)],[c_16327,c_15342]) ).
cnf(c_16431,plain,
( ~ aSet0(xT)
| aElementOf0(sK4(xT),xT)
| aElementOf0(xp,xP) ),
inference(superposition,[status(thm)],[c_16282,c_1921]) ).
cnf(c_16444,plain,
( aElementOf0(sK4(xT),xT)
| aElementOf0(xp,xP) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16431,c_134]) ).
cnf(c_16460,plain,
( ~ aElementOf0(X0,xT)
| ~ aSet0(xT)
| aElement0(X0) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_16494,plain,
( aFixedPointOf0(sK4(xT),xf)
| aElementOf0(xp,xP) ),
inference(superposition,[status(thm)],[c_16444,c_9216]) ).
cnf(c_16513,plain,
( sdtlpdtrp0(xf,xp) != xp
| ~ aElementOf0(xp,xU)
| aFixedPointOf0(xp,xf) ),
inference(instantiation,[status(thm)],[c_1533]) ).
cnf(c_16566,plain,
( sdtlpdtrp0(xf,sK4(xT)) = sK4(xT)
| aElementOf0(xp,xP) ),
inference(superposition,[status(thm)],[c_16494,c_9213]) ).
cnf(c_16695,plain,
( ~ aUpperBoundOfIn0(sdtlpdtrp0(xf,X0),xT,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
| ~ aElementOf0(sdtlpdtrp0(xf,X0),xU)
| ~ aElementOf0(X0,xU)
| aElementOf0(sdtlpdtrp0(xf,X0),xP) ),
inference(superposition,[status(thm)],[c_1794,c_136]) ).
cnf(c_16763,plain,
( ~ sdtlseqdt0(sK19(xp),xp)
| ~ aElementOf0(xp,xU)
| aElementOf0(xp,xP) ),
inference(superposition,[status(thm)],[c_15312,c_137]) ).
cnf(c_16764,plain,
( ~ sdtlseqdt0(sK19(xp),xp)
| aElementOf0(xp,xP) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16763,c_150]) ).
cnf(c_17061,plain,
( ~ sdtlseqdt0(X0,sdtlpdtrp0(xf,xp))
| ~ aElement0(sdtlpdtrp0(xf,xp))
| ~ aElement0(X0)
| ~ aElement0(xp)
| sdtlseqdt0(X0,xp) ),
inference(superposition,[status(thm)],[c_15312,c_58]) ).
cnf(c_17076,plain,
( ~ sdtlseqdt0(X0,sdtlpdtrp0(xf,xp))
| ~ aElement0(sdtlpdtrp0(xf,xp))
| ~ aElement0(X0)
| sdtlseqdt0(X0,xp) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17061,c_15342]) ).
cnf(c_17378,plain,
( ~ aElementOf0(xp,xS)
| ~ aSubsetOf0(xT,xS)
| ~ aFixedPointOf0(xp,xf)
| ~ aSet0(xS)
| aElementOf0(sK7(xT,xp),xT)
| sP3 ),
inference(superposition,[status(thm)],[c_64,c_162]) ).
cnf(c_17415,plain,
( ~ aElementOf0(xp,xS)
| ~ aFixedPointOf0(xp,xf)
| aElementOf0(sK7(xT,xp),xT)
| sP3 ),
inference(forward_subsumption_resolution,[status(thm)],[c_17378,c_131,c_132]) ).
cnf(c_17574,plain,
( ~ aSet0(xU)
| ~ aSet0(xP)
| aSubsetOf0(xP,xU) ),
inference(superposition,[status(thm)],[c_15720,c_52]) ).
cnf(c_17577,plain,
aSubsetOf0(xP,xU),
inference(forward_subsumption_resolution,[status(thm)],[c_17574,c_143,c_124]) ).
cnf(c_17596,plain,
aElement0(sdtlpdtrp0(xf,xp)),
inference(backward_subsumption_resolution,[status(thm)],[c_16071,c_17577]) ).
cnf(c_17606,plain,
( ~ aFixedPointOf0(xp,xf)
| aElementOf0(sK7(xT,xp),xT)
| sP3 ),
inference(forward_subsumption_resolution,[status(thm)],[c_17415,c_126]) ).
cnf(c_17613,plain,
( ~ aElementOf0(X0,xP)
| ~ aFixedPointOf0(xp,xf)
| sdtlseqdt0(sK7(xT,xp),X0)
| sP3 ),
inference(superposition,[status(thm)],[c_17606,c_140]) ).
cnf(c_18042,plain,
( ~ aElementOf0(xp,X0)
| ~ aSubsetOf0(xT,X0)
| ~ aElementOf0(xp,xP)
| ~ aFixedPointOf0(xp,xf)
| ~ aSet0(X0)
| aUpperBoundOfIn0(xp,xT,X0)
| sP3 ),
inference(superposition,[status(thm)],[c_17613,c_63]) ).
cnf(c_18399,plain,
( ~ aElementOf0(X0,xT)
| ~ aElementOf0(xp,X1)
| ~ aSubsetOf0(xT,X1)
| ~ aElementOf0(xp,xP)
| ~ aFixedPointOf0(xp,xf)
| ~ aSet0(X1)
| sdtlseqdt0(X0,xp)
| sP3 ),
inference(superposition,[status(thm)],[c_18042,c_65]) ).
cnf(c_18401,plain,
( ~ aElementOf0(xp,xS)
| ~ aElementOf0(xp,xP)
| ~ aSubsetOf0(xT,xS)
| ~ aFixedPointOf0(xp,xf)
| ~ aSet0(xS)
| sP3 ),
inference(superposition,[status(thm)],[c_18042,c_162]) ).
cnf(c_18403,plain,
( ~ aElementOf0(xp,xS)
| ~ aElementOf0(xp,xP)
| ~ aFixedPointOf0(xp,xf)
| sP3 ),
inference(forward_subsumption_resolution,[status(thm)],[c_18401,c_131,c_132]) ).
cnf(c_18430,plain,
( ~ aElementOf0(xp,xP)
| ~ aFixedPointOf0(xp,xf)
| sP3 ),
inference(forward_subsumption_resolution,[status(thm)],[c_18403,c_126]) ).
cnf(c_20539,plain,
( sdtlseqdt0(X0,xp)
| ~ aElementOf0(X0,xT) ),
inference(global_subsumption_just,[status(thm)],[c_18399,c_134,c_153,c_16071,c_16460,c_17076,c_17577]) ).
cnf(c_20540,plain,
( ~ aElementOf0(X0,xT)
| sdtlseqdt0(X0,xp) ),
inference(renaming,[status(thm)],[c_20539]) ).
cnf(c_20554,plain,
( sdtlseqdt0(sK19(xp),xp)
| aElementOf0(xp,xP) ),
inference(superposition,[status(thm)],[c_16282,c_20540]) ).
cnf(c_20611,plain,
aElementOf0(xp,xP),
inference(global_subsumption_just,[status(thm)],[c_16566,c_16764,c_20554]) ).
cnf(c_20613,plain,
( ~ aFixedPointOf0(xp,xf)
| sP3 ),
inference(backward_subsumption_resolution,[status(thm)],[c_18430,c_20611]) ).
cnf(c_20697,plain,
( ~ sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
| ~ aUpperBoundOfIn0(sdtlpdtrp0(xf,X0),xT,xU)
| ~ aElementOf0(X0,xU)
| aElementOf0(sdtlpdtrp0(xf,X0),xP) ),
inference(global_subsumption_just,[status(thm)],[c_16695,c_6102,c_16695]) ).
cnf(c_20698,plain,
( ~ aUpperBoundOfIn0(sdtlpdtrp0(xf,X0),xT,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
| ~ aElementOf0(X0,xU)
| aElementOf0(sdtlpdtrp0(xf,X0),xP) ),
inference(renaming,[status(thm)],[c_20697]) ).
cnf(c_20710,plain,
( ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),xp)
| ~ aElementOf0(xp,xU)
| aElementOf0(sdtlpdtrp0(xf,xp),xP) ),
inference(superposition,[status(thm)],[c_152,c_20698]) ).
cnf(c_20711,plain,
aElementOf0(sdtlpdtrp0(xf,xp),xP),
inference(forward_subsumption_resolution,[status(thm)],[c_20710,c_150,c_15312]) ).
cnf(c_20723,plain,
sdtlseqdt0(xp,sdtlpdtrp0(xf,xp)),
inference(superposition,[status(thm)],[c_20711,c_149]) ).
cnf(c_20730,plain,
( ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),xp)
| ~ aElement0(sdtlpdtrp0(xf,xp))
| ~ aElement0(xp)
| sdtlpdtrp0(xf,xp) = xp ),
inference(superposition,[status(thm)],[c_20723,c_57]) ).
cnf(c_20731,plain,
sdtlpdtrp0(xf,xp) = xp,
inference(forward_subsumption_resolution,[status(thm)],[c_20730,c_15342,c_17596,c_15312]) ).
cnf(c_20738,plain,
( aElementOf0(sK22,xT)
| sP3 ),
inference(backward_subsumption_resolution,[status(thm)],[c_1595,c_20731]) ).
cnf(c_20755,plain,
sP3,
inference(global_subsumption_just,[status(thm)],[c_20738,c_151,c_16071,c_16340,c_16513,c_17577,c_20613,c_20723]) ).
cnf(c_20766,plain,
sdtlpdtrp0(xf,sK21) = sK21,
inference(backward_subsumption_resolution,[status(thm)],[c_15551,c_20755]) ).
cnf(c_20767,plain,
aElement0(sK21),
inference(backward_subsumption_resolution,[status(thm)],[c_15343,c_20755]) ).
cnf(c_20768,plain,
aElementOf0(sK21,xU),
inference(backward_subsumption_resolution,[status(thm)],[c_15283,c_20755]) ).
cnf(c_20771,plain,
( ~ aElementOf0(X0,xT)
| sdtlseqdt0(X0,sK21) ),
inference(backward_subsumption_resolution,[status(thm)],[c_158,c_20755]) ).
cnf(c_20773,plain,
~ sdtlseqdt0(xp,sK21),
inference(backward_subsumption_resolution,[status(thm)],[c_156,c_20755]) ).
cnf(c_20876,plain,
( ~ sdtlseqdt0(sK19(sK21),sK21)
| ~ aElementOf0(sK21,xU)
| ~ sdtlseqdt0(sK21,sK21)
| aElementOf0(sK21,xP) ),
inference(superposition,[status(thm)],[c_20766,c_137]) ).
cnf(c_20878,plain,
( ~ aElementOf0(sK21,xU)
| ~ sdtlseqdt0(sK21,sK21)
| aElementOf0(sK19(sK21),xT)
| aElementOf0(sK21,xP) ),
inference(superposition,[status(thm)],[c_20766,c_138]) ).
cnf(c_20886,plain,
( ~ sdtlseqdt0(sK21,sK21)
| aElementOf0(sK19(sK21),xT)
| aElementOf0(sK21,xP) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20878,c_20768]) ).
cnf(c_20894,plain,
( ~ sdtlseqdt0(sK19(sK21),sK21)
| ~ sdtlseqdt0(sK21,sK21)
| aElementOf0(sK21,xP) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20876,c_20768]) ).
cnf(c_21181,plain,
( ~ sdtlseqdt0(sK21,sK21)
| sdtlseqdt0(sK19(sK21),sK21)
| aElementOf0(sK21,xP) ),
inference(superposition,[status(thm)],[c_20886,c_20771]) ).
cnf(c_21212,plain,
( ~ sdtlseqdt0(sK21,sK21)
| aElementOf0(sK21,xP) ),
inference(global_subsumption_just,[status(thm)],[c_21181,c_20894,c_21181]) ).
cnf(c_21218,plain,
( ~ aElement0(sK21)
| aElementOf0(sK21,xP) ),
inference(superposition,[status(thm)],[c_56,c_21212]) ).
cnf(c_21219,plain,
aElementOf0(sK21,xP),
inference(forward_subsumption_resolution,[status(thm)],[c_21218,c_20767]) ).
cnf(c_21224,plain,
sdtlseqdt0(xp,sK21),
inference(superposition,[status(thm)],[c_21219,c_149]) ).
cnf(c_21226,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_21224,c_20773]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.09 % Problem : LAT387+4 : TPTP v8.1.2. Released v4.0.0.
% 0.09/0.10 % Command : run_iprover %s %d THM
% 0.09/0.30 % Computer : n024.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Thu Aug 24 06:29:24 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.83/1.07 % SZS status Started for theBenchmark.p
% 0.83/1.07 % SZS status Theorem for theBenchmark.p
% 0.83/1.07
% 0.83/1.07 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.83/1.07
% 0.83/1.07 ------ iProver source info
% 0.83/1.07
% 0.83/1.07 git: date: 2023-05-31 18:12:56 +0000
% 0.83/1.07 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.83/1.07 git: non_committed_changes: false
% 0.83/1.07 git: last_make_outside_of_git: false
% 0.83/1.07
% 0.83/1.07 ------ Parsing...
% 0.83/1.07 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.83/1.07
% 0.83/1.07 ------ Preprocessing... sup_sim: 8 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 9 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
% 0.83/1.07
% 0.83/1.07 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.83/1.07
% 0.83/1.07 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.83/1.07 ------ Proving...
% 0.83/1.07 ------ Problem Properties
% 0.83/1.07
% 0.83/1.07
% 0.83/1.07 clauses 95
% 0.83/1.07 conjectures 4
% 0.83/1.07 EPR 44
% 0.83/1.07 Horn 83
% 0.83/1.07 unary 14
% 0.83/1.07 binary 28
% 0.83/1.07 lits 279
% 0.83/1.07 lits eq 13
% 0.83/1.07 fd_pure 0
% 0.83/1.07 fd_pseudo 0
% 0.83/1.07 fd_cond 0
% 0.83/1.07 fd_pseudo_cond 3
% 0.83/1.07 AC symbols 0
% 0.83/1.07
% 0.83/1.07 ------ Schedule dynamic 5 is on
% 0.83/1.07
% 0.83/1.07 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.83/1.07
% 0.83/1.07
% 0.83/1.07 ------
% 0.83/1.07 Current options:
% 0.83/1.07 ------
% 0.83/1.07
% 0.83/1.07
% 0.83/1.07
% 0.83/1.07
% 0.83/1.07 ------ Proving...
% 0.83/1.07
% 0.83/1.07
% 0.83/1.07 % SZS status Theorem for theBenchmark.p
% 0.83/1.07
% 0.83/1.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.83/1.07
% 0.87/1.08
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