TSTP Solution File: NUM569+3 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM569+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n008.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 11:31:32 EDT 2023
% Result : Theorem 202.80s 26.86s
% Output : CNFRefutation 202.80s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f598)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(f12,axiom,
! [X0] :
( aSet0(X0)
=> aSubsetOf0(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
fof(f16,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aSet0(X0) )
=> ! [X2] :
( sdtmndt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(f24,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
fof(f25,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( sz00 != szszuzczcdt0(X0)
& aElementOf0(szszuzczcdt0(X0),szNzAzT0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNum) ).
fof(f27,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ? [X1] :
( szszuzczcdt0(X1) = X0
& aElementOf0(X1,szNzAzT0) )
| sz00 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatExtra) ).
fof(f30,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sdtlseqdt0(sz00,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroLess) ).
fof(f35,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessASymm) ).
fof(f39,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> iLess0(X0,szszuzczcdt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).
fof(f50,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( slbdtrb0(X0) = X1
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSeg) ).
fof(f75,axiom,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,szNzAzT0) )
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
fof(f81,axiom,
( ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ( isCountable0(sdtlpdtrp0(xN,X0))
& ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X0)) ) ) )
=> ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
=> aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X1
& aElementOf0(X1,sdtlpdtrp0(xN,X0))
& aElement0(X1) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ) ) )
& xS = sdtlpdtrp0(xN,sz00)
& szNzAzT0 = szDzozmdt0(xN)
& aFunction0(xN) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3623) ).
fof(f82,conjecture,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( iLess0(X1,X0)
=> ( isCountable0(sdtlpdtrp0(xN,X1))
& aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> aElementOf0(X2,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X1)) ) ) )
=> ( isCountable0(sdtlpdtrp0(xN,X0))
& ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X0)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f83,negated_conjecture,
~ ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( iLess0(X1,X0)
=> ( isCountable0(sdtlpdtrp0(xN,X1))
& aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> aElementOf0(X2,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X1)) ) ) )
=> ( isCountable0(sdtlpdtrp0(xN,X0))
& ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X0)) ) ) ) ) ),
inference(negated_conjecture,[],[f82]) ).
fof(f93,plain,
( ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ( isCountable0(sdtlpdtrp0(xN,X0))
& ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X0)) ) ) )
=> ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( aElementOf0(X4,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ) ) )
& xS = sdtlpdtrp0(xN,sz00)
& szNzAzT0 = szDzozmdt0(xN)
& aFunction0(xN) ),
inference(rectify,[],[f81]) ).
fof(f94,plain,
~ ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( iLess0(X1,X0)
=> ( isCountable0(sdtlpdtrp0(xN,X1))
& aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> aElementOf0(X2,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X1)) ) ) )
=> ( isCountable0(sdtlpdtrp0(xN,X0))
& ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ( ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,X0))
=> aElementOf0(X3,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X0)) ) ) ) ) ),
inference(rectify,[],[f83]) ).
fof(f95,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f101,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f104,plain,
! [X0] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f111,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f112,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f111]) ).
fof(f124,plain,
! [X0] :
( ( sz00 != szszuzczcdt0(X0)
& aElementOf0(szszuzczcdt0(X0),szNzAzT0) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f127,plain,
! [X0] :
( ? [X1] :
( szszuzczcdt0(X1) = X0
& aElementOf0(X1,szNzAzT0) )
| sz00 = X0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f128,plain,
! [X0] :
( ? [X1] :
( szszuzczcdt0(X1) = X0
& aElementOf0(X1,szNzAzT0) )
| sz00 = X0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f127]) ).
fof(f130,plain,
! [X0] :
( sdtlseqdt0(sz00,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f136,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f137,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f136]) ).
fof(f142,plain,
! [X0] :
( iLess0(X0,szszuzczcdt0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f160,plain,
! [X0] :
( ! [X1] :
( slbdtrb0(X0) = X1
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& aSet0(X1) ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f194,plain,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS) )
& aSet0(xS) ),
inference(ennf_transformation,[],[f75]) ).
fof(f199,plain,
( ! [X0] :
( ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ( ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
| ~ aSet0(sdtlpdtrp0(xN,X0)) ) )
| ~ aElementOf0(X0,szNzAzT0) )
& xS = sdtlpdtrp0(xN,sz00)
& szNzAzT0 = szDzozmdt0(xN)
& aFunction0(xN) ),
inference(ennf_transformation,[],[f93]) ).
fof(f200,plain,
( ! [X0] :
( ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ( ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
| ~ aSet0(sdtlpdtrp0(xN,X0)) ) )
| ~ aElementOf0(X0,szNzAzT0) )
& xS = sdtlpdtrp0(xN,sz00)
& szNzAzT0 = szDzozmdt0(xN)
& aFunction0(xN) ),
inference(flattening,[],[f199]) ).
fof(f201,plain,
? [X0] :
( ( ~ isCountable0(sdtlpdtrp0(xN,X0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ( ? [X3] :
( ~ aElementOf0(X3,szNzAzT0)
& aElementOf0(X3,sdtlpdtrp0(xN,X0)) )
| ~ aSet0(sdtlpdtrp0(xN,X0)) ) ) )
& ! [X1] :
( ( isCountable0(sdtlpdtrp0(xN,X1))
& aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
& ! [X2] :
( aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X1)) )
& aSet0(sdtlpdtrp0(xN,X1)) )
| ~ iLess0(X1,X0)
| ~ aElementOf0(X1,szNzAzT0) )
& aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f94]) ).
fof(f202,plain,
? [X0] :
( ( ~ isCountable0(sdtlpdtrp0(xN,X0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ( ? [X3] :
( ~ aElementOf0(X3,szNzAzT0)
& aElementOf0(X3,sdtlpdtrp0(xN,X0)) )
| ~ aSet0(sdtlpdtrp0(xN,X0)) ) ) )
& ! [X1] :
( ( isCountable0(sdtlpdtrp0(xN,X1))
& aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
& ! [X2] :
( aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X1)) )
& aSet0(sdtlpdtrp0(xN,X1)) )
| ~ iLess0(X1,X0)
| ~ aElementOf0(X1,szNzAzT0) )
& aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f201]) ).
fof(f206,plain,
! [X1,X0,X2] :
( sP2(X1,X0,X2)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f207,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X0,X1) = X2
<=> sP2(X1,X0,X2) )
| ~ sP3(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f208,plain,
! [X0,X1] :
( sP3(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(definition_folding,[],[f112,f207,f206]) ).
fof(f214,plain,
! [X0] :
( ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
| ~ sP8(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f215,plain,
! [X0] :
( ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& sP8(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ sP9(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f216,plain,
( ! [X0] :
( sP9(X0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ( ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
| ~ aSet0(sdtlpdtrp0(xN,X0)) ) )
| ~ aElementOf0(X0,szNzAzT0) )
& xS = sdtlpdtrp0(xN,sz00)
& szNzAzT0 = szDzozmdt0(xN)
& aFunction0(xN) ),
inference(definition_folding,[],[f200,f215,f214]) ).
fof(f222,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,[],[f101]) ).
fof(f223,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,[],[f222]) ).
fof(f224,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,[],[f223]) ).
fof(f225,plain,
! [X0,X1] :
( ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
=> ( ~ aElementOf0(sK11(X0,X1),X0)
& aElementOf0(sK11(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f226,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ( ~ aElementOf0(sK11(X0,X1),X0)
& aElementOf0(sK11(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,[sK11])],[f224,f225]) ).
fof(f233,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X0,X1) = X2
| ~ sP2(X1,X0,X2) )
& ( sP2(X1,X0,X2)
| sdtmndt0(X0,X1) != X2 ) )
| ~ sP3(X0,X1) ),
inference(nnf_transformation,[],[f207]) ).
fof(f234,plain,
! [X1,X0,X2] :
( ( sP2(X1,X0,X2)
| ? [X3] :
( ( X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3)
| ~ aElementOf0(X3,X2) )
& ( ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3) )
& ( ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| ~ sP2(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f206]) ).
fof(f235,plain,
! [X1,X0,X2] :
( ( sP2(X1,X0,X2)
| ? [X3] :
( ( X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3)
| ~ aElementOf0(X3,X2) )
& ( ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3) )
& ( ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| ~ sP2(X1,X0,X2) ) ),
inference(flattening,[],[f234]) ).
fof(f236,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ? [X3] :
( ( X0 = X3
| ~ aElementOf0(X3,X1)
| ~ aElement0(X3)
| ~ aElementOf0(X3,X2) )
& ( ( X0 != X3
& aElementOf0(X3,X1)
& aElement0(X3) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X4] :
( ( aElementOf0(X4,X2)
| X0 = X4
| ~ aElementOf0(X4,X1)
| ~ aElement0(X4) )
& ( ( X0 != X4
& aElementOf0(X4,X1)
& aElement0(X4) )
| ~ aElementOf0(X4,X2) ) )
& aSet0(X2) )
| ~ sP2(X0,X1,X2) ) ),
inference(rectify,[],[f235]) ).
fof(f237,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( X0 = X3
| ~ aElementOf0(X3,X1)
| ~ aElement0(X3)
| ~ aElementOf0(X3,X2) )
& ( ( X0 != X3
& aElementOf0(X3,X1)
& aElement0(X3) )
| aElementOf0(X3,X2) ) )
=> ( ( sK13(X0,X1,X2) = X0
| ~ aElementOf0(sK13(X0,X1,X2),X1)
| ~ aElement0(sK13(X0,X1,X2))
| ~ aElementOf0(sK13(X0,X1,X2),X2) )
& ( ( sK13(X0,X1,X2) != X0
& aElementOf0(sK13(X0,X1,X2),X1)
& aElement0(sK13(X0,X1,X2)) )
| aElementOf0(sK13(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f238,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ( ( sK13(X0,X1,X2) = X0
| ~ aElementOf0(sK13(X0,X1,X2),X1)
| ~ aElement0(sK13(X0,X1,X2))
| ~ aElementOf0(sK13(X0,X1,X2),X2) )
& ( ( sK13(X0,X1,X2) != X0
& aElementOf0(sK13(X0,X1,X2),X1)
& aElement0(sK13(X0,X1,X2)) )
| aElementOf0(sK13(X0,X1,X2),X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X4] :
( ( aElementOf0(X4,X2)
| X0 = X4
| ~ aElementOf0(X4,X1)
| ~ aElement0(X4) )
& ( ( X0 != X4
& aElementOf0(X4,X1)
& aElement0(X4) )
| ~ aElementOf0(X4,X2) ) )
& aSet0(X2) )
| ~ sP2(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f236,f237]) ).
fof(f239,plain,
! [X0] :
( ? [X1] :
( szszuzczcdt0(X1) = X0
& aElementOf0(X1,szNzAzT0) )
=> ( szszuzczcdt0(sK14(X0)) = X0
& aElementOf0(sK14(X0),szNzAzT0) ) ),
introduced(choice_axiom,[]) ).
fof(f240,plain,
! [X0] :
( ( szszuzczcdt0(sK14(X0)) = X0
& aElementOf0(sK14(X0),szNzAzT0) )
| sz00 = X0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f128,f239]) ).
fof(f256,plain,
! [X0] :
( ! [X1] :
( ( slbdtrb0(X0) = X1
| ? [X2] :
( ( ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X2,X1) )
& ( ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) )
| aElementOf0(X2,X1) ) )
| ~ aSet0(X1) )
& ( ( ! [X2] :
( ( aElementOf0(X2,X1)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,szNzAzT0) )
& ( ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) )
| ~ aElementOf0(X2,X1) ) )
& aSet0(X1) )
| slbdtrb0(X0) != X1 ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(nnf_transformation,[],[f160]) ).
fof(f257,plain,
! [X0] :
( ! [X1] :
( ( slbdtrb0(X0) = X1
| ? [X2] :
( ( ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X2,X1) )
& ( ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) )
| aElementOf0(X2,X1) ) )
| ~ aSet0(X1) )
& ( ( ! [X2] :
( ( aElementOf0(X2,X1)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,szNzAzT0) )
& ( ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) )
| ~ aElementOf0(X2,X1) ) )
& aSet0(X1) )
| slbdtrb0(X0) != X1 ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f256]) ).
fof(f258,plain,
! [X0] :
( ! [X1] :
( ( slbdtrb0(X0) = X1
| ? [X2] :
( ( ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X2,X1) )
& ( ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) )
| aElementOf0(X2,X1) ) )
| ~ aSet0(X1) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X1)
| ~ sdtlseqdt0(szszuzczcdt0(X3),X0)
| ~ aElementOf0(X3,szNzAzT0) )
& ( ( sdtlseqdt0(szszuzczcdt0(X3),X0)
& aElementOf0(X3,szNzAzT0) )
| ~ aElementOf0(X3,X1) ) )
& aSet0(X1) )
| slbdtrb0(X0) != X1 ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(rectify,[],[f257]) ).
fof(f259,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X2,X1) )
& ( ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) )
| aElementOf0(X2,X1) ) )
=> ( ( ~ sdtlseqdt0(szszuzczcdt0(sK18(X0,X1)),X0)
| ~ aElementOf0(sK18(X0,X1),szNzAzT0)
| ~ aElementOf0(sK18(X0,X1),X1) )
& ( ( sdtlseqdt0(szszuzczcdt0(sK18(X0,X1)),X0)
& aElementOf0(sK18(X0,X1),szNzAzT0) )
| aElementOf0(sK18(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f260,plain,
! [X0] :
( ! [X1] :
( ( slbdtrb0(X0) = X1
| ( ( ~ sdtlseqdt0(szszuzczcdt0(sK18(X0,X1)),X0)
| ~ aElementOf0(sK18(X0,X1),szNzAzT0)
| ~ aElementOf0(sK18(X0,X1),X1) )
& ( ( sdtlseqdt0(szszuzczcdt0(sK18(X0,X1)),X0)
& aElementOf0(sK18(X0,X1),szNzAzT0) )
| aElementOf0(sK18(X0,X1),X1) ) )
| ~ aSet0(X1) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X1)
| ~ sdtlseqdt0(szszuzczcdt0(X3),X0)
| ~ aElementOf0(X3,szNzAzT0) )
& ( ( sdtlseqdt0(szszuzczcdt0(X3),X0)
& aElementOf0(X3,szNzAzT0) )
| ~ aElementOf0(X3,X1) ) )
& aSet0(X1) )
| slbdtrb0(X0) != X1 ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f258,f259]) ).
fof(f318,plain,
! [X0] :
( ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& sP8(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ sP9(X0) ),
inference(nnf_transformation,[],[f215]) ).
fof(f319,plain,
! [X0] :
( ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& sP8(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ sP9(X0) ),
inference(rectify,[],[f318]) ).
fof(f323,plain,
! [X0] :
( ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
=> ( ~ aElementOf0(sK39(X0),szNzAzT0)
& aElementOf0(sK39(X0),sdtlpdtrp0(xN,X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f324,plain,
( ! [X0] :
( sP9(X0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ( ( ~ aElementOf0(sK39(X0),szNzAzT0)
& aElementOf0(sK39(X0),sdtlpdtrp0(xN,X0)) )
| ~ aSet0(sdtlpdtrp0(xN,X0)) ) )
| ~ aElementOf0(X0,szNzAzT0) )
& xS = sdtlpdtrp0(xN,sz00)
& szNzAzT0 = szDzozmdt0(xN)
& aFunction0(xN) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK39])],[f216,f323]) ).
fof(f325,plain,
? [X0] :
( ( ~ isCountable0(sdtlpdtrp0(xN,X0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ( ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
| ~ aSet0(sdtlpdtrp0(xN,X0)) ) ) )
& ! [X2] :
( ( isCountable0(sdtlpdtrp0(xN,X2))
& aSubsetOf0(sdtlpdtrp0(xN,X2),szNzAzT0)
& ! [X3] :
( aElementOf0(X3,szNzAzT0)
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X2)) )
& aSet0(sdtlpdtrp0(xN,X2)) )
| ~ iLess0(X2,X0)
| ~ aElementOf0(X2,szNzAzT0) )
& aElementOf0(X0,szNzAzT0) ),
inference(rectify,[],[f202]) ).
fof(f326,plain,
( ? [X0] :
( ( ~ isCountable0(sdtlpdtrp0(xN,X0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ( ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
| ~ aSet0(sdtlpdtrp0(xN,X0)) ) ) )
& ! [X2] :
( ( isCountable0(sdtlpdtrp0(xN,X2))
& aSubsetOf0(sdtlpdtrp0(xN,X2),szNzAzT0)
& ! [X3] :
( aElementOf0(X3,szNzAzT0)
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X2)) )
& aSet0(sdtlpdtrp0(xN,X2)) )
| ~ iLess0(X2,X0)
| ~ aElementOf0(X2,szNzAzT0) )
& aElementOf0(X0,szNzAzT0) )
=> ( ( ~ isCountable0(sdtlpdtrp0(xN,sK40))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,sK40),szNzAzT0)
& ( ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,sK40)) )
| ~ aSet0(sdtlpdtrp0(xN,sK40)) ) ) )
& ! [X2] :
( ( isCountable0(sdtlpdtrp0(xN,X2))
& aSubsetOf0(sdtlpdtrp0(xN,X2),szNzAzT0)
& ! [X3] :
( aElementOf0(X3,szNzAzT0)
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X2)) )
& aSet0(sdtlpdtrp0(xN,X2)) )
| ~ iLess0(X2,sK40)
| ~ aElementOf0(X2,szNzAzT0) )
& aElementOf0(sK40,szNzAzT0) ) ),
introduced(choice_axiom,[]) ).
fof(f327,plain,
( ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,sK40)) )
=> ( ~ aElementOf0(sK41,szNzAzT0)
& aElementOf0(sK41,sdtlpdtrp0(xN,sK40)) ) ),
introduced(choice_axiom,[]) ).
fof(f328,plain,
( ( ~ isCountable0(sdtlpdtrp0(xN,sK40))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,sK40),szNzAzT0)
& ( ( ~ aElementOf0(sK41,szNzAzT0)
& aElementOf0(sK41,sdtlpdtrp0(xN,sK40)) )
| ~ aSet0(sdtlpdtrp0(xN,sK40)) ) ) )
& ! [X2] :
( ( isCountable0(sdtlpdtrp0(xN,X2))
& aSubsetOf0(sdtlpdtrp0(xN,X2),szNzAzT0)
& ! [X3] :
( aElementOf0(X3,szNzAzT0)
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X2)) )
& aSet0(sdtlpdtrp0(xN,X2)) )
| ~ iLess0(X2,sK40)
| ~ aElementOf0(X2,szNzAzT0) )
& aElementOf0(sK40,szNzAzT0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK40,sK41])],[f325,f327,f326]) ).
fof(f329,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f337,plain,
! [X3,X0,X1] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f226]) ).
fof(f341,plain,
! [X0] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f356,plain,
! [X2,X0,X1] :
( sP2(X1,X0,X2)
| sdtmndt0(X0,X1) != X2
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f233]) ).
fof(f360,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X1)
| ~ aElementOf0(X4,X2)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f238]) ).
fof(f367,plain,
! [X0,X1] :
( sP3(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f208]) ).
fof(f376,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[],[f24]) ).
fof(f377,plain,
! [X0] :
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f380,plain,
! [X0] :
( aElementOf0(sK14(X0),szNzAzT0)
| sz00 = X0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f240]) ).
fof(f381,plain,
! [X0] :
( szszuzczcdt0(sK14(X0)) = X0
| sz00 = X0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f240]) ).
fof(f383,plain,
! [X0] :
( sdtlseqdt0(sz00,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f389,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f392,plain,
! [X0] :
( iLess0(X0,szszuzczcdt0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f412,plain,
! [X0,X1] :
( aSet0(X1)
| slbdtrb0(X0) != X1
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f260]) ).
fof(f413,plain,
! [X3,X0,X1] :
( aElementOf0(X3,szNzAzT0)
| ~ aElementOf0(X3,X1)
| slbdtrb0(X0) != X1
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f260]) ).
fof(f477,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[],[f194]) ).
fof(f478,plain,
isCountable0(xS),
inference(cnf_transformation,[],[f194]) ).
fof(f529,plain,
! [X0] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f319]) ).
fof(f531,plain,
! [X0] :
( aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f319]) ).
fof(f533,plain,
! [X0] :
( aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f319]) ).
fof(f535,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f319]) ).
fof(f536,plain,
! [X0] :
( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f319]) ).
fof(f543,plain,
xS = sdtlpdtrp0(xN,sz00),
inference(cnf_transformation,[],[f324]) ).
fof(f546,plain,
! [X0] :
( sP9(X0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f324]) ).
fof(f547,plain,
aElementOf0(sK40,szNzAzT0),
inference(cnf_transformation,[],[f328]) ).
fof(f548,plain,
! [X2] :
( aSet0(sdtlpdtrp0(xN,X2))
| ~ iLess0(X2,sK40)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(cnf_transformation,[],[f328]) ).
fof(f549,plain,
! [X2,X3] :
( aElementOf0(X3,szNzAzT0)
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X2))
| ~ iLess0(X2,sK40)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(cnf_transformation,[],[f328]) ).
fof(f550,plain,
! [X2] :
( aSubsetOf0(sdtlpdtrp0(xN,X2),szNzAzT0)
| ~ iLess0(X2,sK40)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(cnf_transformation,[],[f328]) ).
fof(f551,plain,
! [X2] :
( isCountable0(sdtlpdtrp0(xN,X2))
| ~ iLess0(X2,sK40)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(cnf_transformation,[],[f328]) ).
fof(f552,plain,
( ~ isCountable0(sdtlpdtrp0(xN,sK40))
| aElementOf0(sK41,sdtlpdtrp0(xN,sK40))
| ~ aSet0(sdtlpdtrp0(xN,sK40)) ),
inference(cnf_transformation,[],[f328]) ).
fof(f553,plain,
( ~ isCountable0(sdtlpdtrp0(xN,sK40))
| ~ aElementOf0(sK41,szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,sK40)) ),
inference(cnf_transformation,[],[f328]) ).
fof(f554,plain,
( ~ isCountable0(sdtlpdtrp0(xN,sK40))
| ~ aSubsetOf0(sdtlpdtrp0(xN,sK40),szNzAzT0) ),
inference(cnf_transformation,[],[f328]) ).
fof(f560,plain,
! [X0,X1] :
( sP2(X1,X0,sdtmndt0(X0,X1))
| ~ sP3(X0,X1) ),
inference(equality_resolution,[],[f356]) ).
fof(f569,plain,
! [X3,X0] :
( aElementOf0(X3,szNzAzT0)
| ~ aElementOf0(X3,slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(equality_resolution,[],[f413]) ).
fof(f570,plain,
! [X0] :
( aSet0(slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(equality_resolution,[],[f412]) ).
cnf(c_49,plain,
( ~ aElementOf0(X0,X1)
| ~ aSet0(X1)
| aElement0(X0) ),
inference(cnf_transformation,[],[f329]) ).
cnf(c_58,plain,
( ~ aElementOf0(X0,X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2)
| aElementOf0(X0,X2) ),
inference(cnf_transformation,[],[f337]) ).
cnf(c_61,plain,
( ~ aSet0(X0)
| aSubsetOf0(X0,X0) ),
inference(cnf_transformation,[],[f341]) ).
cnf(c_77,plain,
( ~ sP3(X0,X1)
| sP2(X1,X0,sdtmndt0(X0,X1)) ),
inference(cnf_transformation,[],[f560]) ).
cnf(c_84,plain,
( ~ sP2(X0,X1,X2)
| ~ aElementOf0(X3,X2)
| aElementOf0(X3,X1) ),
inference(cnf_transformation,[],[f360]) ).
cnf(c_87,plain,
( ~ aElement0(X0)
| ~ aSet0(X1)
| sP3(X1,X0) ),
inference(cnf_transformation,[],[f367]) ).
cnf(c_96,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[],[f376]) ).
cnf(c_98,plain,
( ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(szszuzczcdt0(X0),szNzAzT0) ),
inference(cnf_transformation,[],[f377]) ).
cnf(c_100,plain,
( ~ aElementOf0(X0,szNzAzT0)
| szszuzczcdt0(sK14(X0)) = X0
| X0 = sz00 ),
inference(cnf_transformation,[],[f381]) ).
cnf(c_101,plain,
( ~ aElementOf0(X0,szNzAzT0)
| X0 = sz00
| aElementOf0(sK14(X0),szNzAzT0) ),
inference(cnf_transformation,[],[f380]) ).
cnf(c_103,plain,
( ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(sz00,X0) ),
inference(cnf_transformation,[],[f383]) ).
cnf(c_109,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| X0 = X1 ),
inference(cnf_transformation,[],[f389]) ).
cnf(c_112,plain,
( ~ aElementOf0(X0,szNzAzT0)
| iLess0(X0,szszuzczcdt0(X0)) ),
inference(cnf_transformation,[],[f392]) ).
cnf(c_137,plain,
( ~ aElementOf0(X0,slbdtrb0(X1))
| ~ aElementOf0(X1,szNzAzT0)
| aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f569]) ).
cnf(c_138,plain,
( ~ aElementOf0(X0,szNzAzT0)
| aSet0(slbdtrb0(X0)) ),
inference(cnf_transformation,[],[f570]) ).
cnf(c_141,plain,
( ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(X0,slbdtrb0(szszuzczcdt0(X0))) ),
inference(cnf_transformation,[],[f598]) ).
cnf(c_195,plain,
isCountable0(xS),
inference(cnf_transformation,[],[f478]) ).
cnf(c_196,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[],[f477]) ).
cnf(c_249,plain,
( ~ sP9(X0)
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) ),
inference(cnf_transformation,[],[f536]) ).
cnf(c_250,plain,
( ~ sP9(X0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ),
inference(cnf_transformation,[],[f535]) ).
cnf(c_252,plain,
( ~ sP9(X0)
| aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) ),
inference(cnf_transformation,[],[f533]) ).
cnf(c_254,plain,
( ~ sP9(X0)
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ),
inference(cnf_transformation,[],[f531]) ).
cnf(c_256,plain,
( ~ sP9(X0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ),
inference(cnf_transformation,[],[f529]) ).
cnf(c_261,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0)
| sP9(X0) ),
inference(cnf_transformation,[],[f546]) ).
cnf(c_264,plain,
sdtlpdtrp0(xN,sz00) = xS,
inference(cnf_transformation,[],[f543]) ).
cnf(c_267,negated_conjecture,
( ~ aSubsetOf0(sdtlpdtrp0(xN,sK40),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,sK40)) ),
inference(cnf_transformation,[],[f554]) ).
cnf(c_268,negated_conjecture,
( ~ aSet0(sdtlpdtrp0(xN,sK40))
| ~ isCountable0(sdtlpdtrp0(xN,sK40))
| ~ aElementOf0(sK41,szNzAzT0) ),
inference(cnf_transformation,[],[f553]) ).
cnf(c_269,negated_conjecture,
( ~ aSet0(sdtlpdtrp0(xN,sK40))
| ~ isCountable0(sdtlpdtrp0(xN,sK40))
| aElementOf0(sK41,sdtlpdtrp0(xN,sK40)) ),
inference(cnf_transformation,[],[f552]) ).
cnf(c_270,negated_conjecture,
( ~ aElementOf0(X0,szNzAzT0)
| ~ iLess0(X0,sK40)
| isCountable0(sdtlpdtrp0(xN,X0)) ),
inference(cnf_transformation,[],[f551]) ).
cnf(c_271,negated_conjecture,
( ~ aElementOf0(X0,szNzAzT0)
| ~ iLess0(X0,sK40)
| aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) ),
inference(cnf_transformation,[],[f550]) ).
cnf(c_272,negated_conjecture,
( ~ aElementOf0(X0,sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ iLess0(X1,sK40)
| aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f549]) ).
cnf(c_273,negated_conjecture,
( ~ aElementOf0(X0,szNzAzT0)
| ~ iLess0(X0,sK40)
| aSet0(sdtlpdtrp0(xN,X0)) ),
inference(cnf_transformation,[],[f548]) ).
cnf(c_274,negated_conjecture,
aElementOf0(sK40,szNzAzT0),
inference(cnf_transformation,[],[f547]) ).
cnf(c_2074,plain,
( X0 != X1
| X2 != X3
| ~ aElement0(X0)
| ~ aSet0(X2)
| sP2(X1,X3,sdtmndt0(X3,X1)) ),
inference(resolution_lifted,[status(thm)],[c_87,c_77]) ).
cnf(c_2075,plain,
( ~ aElement0(X0)
| ~ aSet0(X1)
| sP2(X0,X1,sdtmndt0(X1,X0)) ),
inference(unflattening,[status(thm)],[c_2074]) ).
cnf(c_2331,plain,
( szszuzczcdt0(X0) != sK40
| X0 != X1
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| aSet0(sdtlpdtrp0(xN,X1)) ),
inference(resolution_lifted,[status(thm)],[c_112,c_273]) ).
cnf(c_2332,plain,
( szszuzczcdt0(X0) != sK40
| ~ aElementOf0(X0,szNzAzT0)
| aSet0(sdtlpdtrp0(xN,X0)) ),
inference(unflattening,[status(thm)],[c_2331]) ).
cnf(c_2343,plain,
( szszuzczcdt0(X0) != sK40
| X0 != X1
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0) ),
inference(resolution_lifted,[status(thm)],[c_112,c_271]) ).
cnf(c_2344,plain,
( szszuzczcdt0(X0) != sK40
| ~ aElementOf0(X0,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) ),
inference(unflattening,[status(thm)],[c_2343]) ).
cnf(c_2355,plain,
( szszuzczcdt0(X0) != sK40
| X0 != X1
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,X1)) ),
inference(resolution_lifted,[status(thm)],[c_112,c_270]) ).
cnf(c_2356,plain,
( szszuzczcdt0(X0) != sK40
| ~ aElementOf0(X0,szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,X0)) ),
inference(unflattening,[status(thm)],[c_2355]) ).
cnf(c_2367,plain,
( szszuzczcdt0(X0) != sK40
| X0 != X1
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| aElementOf0(X2,szNzAzT0) ),
inference(resolution_lifted,[status(thm)],[c_112,c_272]) ).
cnf(c_2368,plain,
( szszuzczcdt0(X0) != sK40
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(X1,szNzAzT0) ),
inference(unflattening,[status(thm)],[c_2367]) ).
cnf(c_23915,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_23920,plain,
( X0 != X1
| ~ isCountable0(X1)
| isCountable0(X0) ),
theory(equality) ).
cnf(c_27324,plain,
sdtlseqdt0(sz00,sz00),
inference(superposition,[status(thm)],[c_96,c_103]) ).
cnf(c_27335,plain,
aSet0(slbdtrb0(sK40)),
inference(superposition,[status(thm)],[c_274,c_138]) ).
cnf(c_27344,plain,
( ~ aElementOf0(X0,szNzAzT0)
| aSet0(slbdtrb0(szszuzczcdt0(X0))) ),
inference(superposition,[status(thm)],[c_98,c_138]) ).
cnf(c_27437,plain,
( ~ aSet0(slbdtrb0(szszuzczcdt0(X0)))
| ~ aElementOf0(X0,szNzAzT0)
| aElement0(X0) ),
inference(superposition,[status(thm)],[c_141,c_49]) ).
cnf(c_28715,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,sK40),X0)
| ~ aSet0(sdtlpdtrp0(xN,sK40))
| ~ isCountable0(sdtlpdtrp0(xN,sK40))
| ~ aSet0(X0)
| aElementOf0(sK41,X0) ),
inference(superposition,[status(thm)],[c_269,c_58]) ).
cnf(c_28947,plain,
( szszuzczcdt0(sK14(sK40)) = sK40
| sz00 = sK40 ),
inference(superposition,[status(thm)],[c_274,c_100]) ).
cnf(c_29057,plain,
( ~ sP9(sK14(sK40))
| sz00 = sK40
| aSet0(sdtlpdtrp0(xN,sK40)) ),
inference(superposition,[status(thm)],[c_28947,c_252]) ).
cnf(c_29058,plain,
( ~ sP9(sK14(sK40))
| sz00 = sK40
| isCountable0(sdtlpdtrp0(xN,sK40)) ),
inference(superposition,[status(thm)],[c_28947,c_249]) ).
cnf(c_29061,plain,
( ~ aElementOf0(X0,sdtlpdtrp0(xN,sK14(sK40)))
| ~ aElementOf0(sK14(sK40),szNzAzT0)
| sz00 = sK40
| aElementOf0(X0,szNzAzT0) ),
inference(superposition,[status(thm)],[c_28947,c_2368]) ).
cnf(c_29063,plain,
( ~ aElementOf0(sK14(sK40),szNzAzT0)
| sz00 = sK40
| isCountable0(sdtlpdtrp0(xN,sK14(sK40))) ),
inference(superposition,[status(thm)],[c_28947,c_2356]) ).
cnf(c_29069,plain,
( ~ aSet0(sdtlpdtrp0(xN,sK40))
| ~ aElementOf0(sK41,szNzAzT0)
| ~ sP9(sK14(sK40))
| sz00 = sK40 ),
inference(superposition,[status(thm)],[c_29058,c_268]) ).
cnf(c_29286,plain,
( X0 != X1
| sK40 != X1
| X0 = sK40 ),
inference(instantiation,[status(thm)],[c_23915]) ).
cnf(c_29951,plain,
( ~ aElementOf0(sz00,szNzAzT0)
| ~ sdtlseqdt0(sz00,sz00)
| sz00 = sz00 ),
inference(instantiation,[status(thm)],[c_109]) ).
cnf(c_30197,plain,
( ~ sP9(sK14(sK40))
| sz00 = sK40
| aSubsetOf0(sdtlpdtrp0(xN,sK40),sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))))) ),
inference(superposition,[status(thm)],[c_28947,c_250]) ).
cnf(c_30253,plain,
( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))))
| ~ aSet0(sdtlpdtrp0(xN,sK40))
| ~ isCountable0(sdtlpdtrp0(xN,sK40))
| ~ sP9(sK14(sK40))
| sz00 = sK40
| aElementOf0(sK41,sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))))) ),
inference(superposition,[status(thm)],[c_30197,c_28715]) ).
cnf(c_30285,plain,
( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))))
| ~ sP9(sK14(sK40))
| sz00 = sK40
| aElementOf0(sK41,sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))))) ),
inference(global_subsumption_just,[status(thm)],[c_30253,c_29058,c_29057,c_30253]) ).
cnf(c_30414,plain,
( ~ isCountable0(xS)
| isCountable0(sdtlpdtrp0(xN,sz00)) ),
inference(resolution,[status(thm)],[c_23920,c_264]) ).
cnf(c_31058,plain,
( szszuzczcdt0(sK14(sK40)) = sK40
| sz00 = sK40 ),
inference(superposition,[status(thm)],[c_274,c_100]) ).
cnf(c_31127,plain,
( ~ aElementOf0(sK14(sK40),szNzAzT0)
| sz00 = sK40
| aElementOf0(sK14(sK40),slbdtrb0(sK40)) ),
inference(superposition,[status(thm)],[c_31058,c_141]) ).
cnf(c_31137,plain,
( ~ aElementOf0(sK14(sK40),szNzAzT0)
| sz00 = sK40
| aSubsetOf0(sdtlpdtrp0(xN,sK14(sK40)),szNzAzT0) ),
inference(superposition,[status(thm)],[c_31058,c_2344]) ).
cnf(c_31149,plain,
( ~ aSubsetOf0(slbdtrb0(sK40),X0)
| ~ aElementOf0(sK14(sK40),szNzAzT0)
| ~ aSet0(X0)
| sz00 = sK40
| aElementOf0(sK14(sK40),X0) ),
inference(superposition,[status(thm)],[c_31127,c_58]) ).
cnf(c_32194,plain,
( ~ isCountable0(sdtlpdtrp0(xN,sK14(sK40)))
| ~ aElementOf0(sK14(sK40),szNzAzT0)
| sz00 = sK40
| sP9(sK14(sK40)) ),
inference(superposition,[status(thm)],[c_31137,c_261]) ).
cnf(c_32536,plain,
( ~ aElementOf0(sK14(sK40),szNzAzT0)
| sz00 = sK40
| sP9(sK14(sK40)) ),
inference(global_subsumption_just,[status(thm)],[c_32194,c_29063,c_32194]) ).
cnf(c_32539,plain,
( ~ aElementOf0(sK40,szNzAzT0)
| sz00 = sK40
| sP9(sK14(sK40)) ),
inference(superposition,[status(thm)],[c_101,c_32536]) ).
cnf(c_32676,plain,
( ~ aSubsetOf0(slbdtrb0(sK40),X0)
| ~ aElementOf0(sK40,szNzAzT0)
| ~ aSet0(X0)
| sz00 = sK40
| aElementOf0(sK14(sK40),X0) ),
inference(superposition,[status(thm)],[c_101,c_31149]) ).
cnf(c_35905,plain,
( ~ aElementOf0(sK14(sK40),szNzAzT0)
| ~ aElementOf0(sK40,szNzAzT0)
| sK40 = sz00
| aSet0(sdtlpdtrp0(xN,sK14(sK40))) ),
inference(resolution,[status(thm)],[c_100,c_2332]) ).
cnf(c_37457,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,sK40),X0)
| ~ aSet0(sdtlpdtrp0(xN,sK40))
| ~ isCountable0(sdtlpdtrp0(xN,sK40))
| ~ aSet0(X0)
| aElementOf0(sK41,X0) ),
inference(superposition,[status(thm)],[c_269,c_58]) ).
cnf(c_37476,plain,
( szszuzczcdt0(sK14(sK40)) = sK40
| sz00 = sK40 ),
inference(superposition,[status(thm)],[c_274,c_100]) ).
cnf(c_37517,plain,
( ~ aElementOf0(sK14(sK40),szNzAzT0)
| sz00 = sK40
| aElementOf0(sK14(sK40),slbdtrb0(sK40)) ),
inference(superposition,[status(thm)],[c_37476,c_141]) ).
cnf(c_37522,plain,
( ~ sP9(sK14(sK40))
| sz00 = sK40
| aSet0(sdtlpdtrp0(xN,sK40)) ),
inference(superposition,[status(thm)],[c_37476,c_252]) ).
cnf(c_37523,plain,
( ~ sP9(sK14(sK40))
| sz00 = sK40
| isCountable0(sdtlpdtrp0(xN,sK40)) ),
inference(superposition,[status(thm)],[c_37476,c_249]) ).
cnf(c_37533,plain,
( sz00 = sK40
| aSet0(sdtlpdtrp0(xN,sK40)) ),
inference(global_subsumption_just,[status(thm)],[c_37522,c_274,c_29057,c_32539]) ).
cnf(c_37536,plain,
( sz00 = sK40
| isCountable0(sdtlpdtrp0(xN,sK40)) ),
inference(global_subsumption_just,[status(thm)],[c_37523,c_274,c_29058,c_32539]) ).
cnf(c_37539,plain,
( ~ aSet0(sdtlpdtrp0(xN,sK40))
| ~ aElementOf0(sK41,szNzAzT0)
| sz00 = sK40 ),
inference(superposition,[status(thm)],[c_37536,c_268]) ).
cnf(c_37540,plain,
( ~ aElementOf0(sK41,szNzAzT0)
| sz00 = sK40 ),
inference(global_subsumption_just,[status(thm)],[c_37539,c_274,c_29069,c_32539,c_37533]) ).
cnf(c_37576,plain,
( ~ aSubsetOf0(slbdtrb0(sK40),X0)
| ~ aElementOf0(sK14(sK40),szNzAzT0)
| ~ aSet0(X0)
| sz00 = sK40
| aElementOf0(sK14(sK40),X0) ),
inference(superposition,[status(thm)],[c_37517,c_58]) ).
cnf(c_37909,plain,
( ~ sP9(sK14(sK40))
| sz00 = sK40
| aSubsetOf0(sdtlpdtrp0(xN,sK40),sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))))) ),
inference(superposition,[status(thm)],[c_37476,c_250]) ).
cnf(c_37966,plain,
( sz00 = sK40
| aSubsetOf0(sdtlpdtrp0(xN,sK40),sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))))) ),
inference(global_subsumption_just,[status(thm)],[c_37909,c_274,c_30197,c_32539]) ).
cnf(c_37970,plain,
( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))))
| ~ aSet0(sdtlpdtrp0(xN,sK40))
| ~ isCountable0(sdtlpdtrp0(xN,sK40))
| sz00 = sK40
| aElementOf0(sK41,sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))))) ),
inference(superposition,[status(thm)],[c_37966,c_37457]) ).
cnf(c_37971,plain,
( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))))
| sz00 = sK40
| aElementOf0(sK41,sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))))) ),
inference(global_subsumption_just,[status(thm)],[c_37970,c_274,c_30285,c_32539]) ).
cnf(c_38444,plain,
( ~ aSubsetOf0(slbdtrb0(sK40),X0)
| ~ aSet0(X0)
| sz00 = sK40
| aElementOf0(sK14(sK40),X0) ),
inference(global_subsumption_just,[status(thm)],[c_37576,c_274,c_32676]) ).
cnf(c_38447,plain,
( ~ aSet0(slbdtrb0(sK40))
| sz00 = sK40
| aElementOf0(sK14(sK40),slbdtrb0(sK40)) ),
inference(superposition,[status(thm)],[c_61,c_38444]) ).
cnf(c_39799,plain,
( X0 != sz00
| sK40 != sz00
| X0 = sK40 ),
inference(instantiation,[status(thm)],[c_29286]) ).
cnf(c_45391,plain,
( sz00 != sz00
| sK40 != sz00
| sz00 = sK40 ),
inference(instantiation,[status(thm)],[c_39799]) ).
cnf(c_51401,plain,
( ~ aSet0(slbdtrb0(szszuzczcdt0(X0)))
| ~ aElementOf0(X0,szNzAzT0)
| aElement0(X0) ),
inference(superposition,[status(thm)],[c_141,c_49]) ).
cnf(c_51427,plain,
( ~ aElementOf0(X0,szNzAzT0)
| aElement0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_51401,c_27344,c_27437]) ).
cnf(c_51694,plain,
( ~ aElementOf0(X0,sdtmndt0(X1,X2))
| ~ aElement0(X2)
| ~ aSet0(X1)
| aElementOf0(X0,X1) ),
inference(superposition,[status(thm)],[c_2075,c_84]) ).
cnf(c_51867,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,sK40),X0)
| ~ aSet0(sdtlpdtrp0(xN,sK40))
| ~ isCountable0(sdtlpdtrp0(xN,sK40))
| ~ aSet0(X0)
| aElementOf0(sK41,X0) ),
inference(superposition,[status(thm)],[c_269,c_58]) ).
cnf(c_51888,plain,
( szszuzczcdt0(sK14(sK40)) = sK40
| sz00 = sK40 ),
inference(superposition,[status(thm)],[c_274,c_100]) ).
cnf(c_51929,plain,
( ~ aElementOf0(sK14(sK40),szNzAzT0)
| sz00 = sK40
| aElementOf0(sK14(sK40),slbdtrb0(sK40)) ),
inference(superposition,[status(thm)],[c_51888,c_141]) ).
cnf(c_51939,plain,
( ~ aElementOf0(X0,sdtlpdtrp0(xN,sK14(sK40)))
| ~ aElementOf0(sK14(sK40),szNzAzT0)
| sz00 = sK40
| aElementOf0(X0,szNzAzT0) ),
inference(superposition,[status(thm)],[c_51888,c_2368]) ).
cnf(c_51942,plain,
( ~ aElementOf0(sK14(sK40),szNzAzT0)
| sz00 = sK40
| aSet0(sdtlpdtrp0(xN,sK14(sK40))) ),
inference(superposition,[status(thm)],[c_51888,c_2332]) ).
cnf(c_52010,plain,
( sz00 = sK40
| aElementOf0(sK14(sK40),slbdtrb0(sK40)) ),
inference(global_subsumption_just,[status(thm)],[c_51929,c_27335,c_38447]) ).
cnf(c_52015,plain,
( ~ aElementOf0(sK40,szNzAzT0)
| sz00 = sK40
| aElementOf0(sK14(sK40),szNzAzT0) ),
inference(superposition,[status(thm)],[c_52010,c_137]) ).
cnf(c_52018,plain,
( sz00 = sK40
| aSet0(sdtlpdtrp0(xN,sK14(sK40))) ),
inference(global_subsumption_just,[status(thm)],[c_51942,c_274,c_96,c_27324,c_29951,c_35905,c_45391,c_52015]) ).
cnf(c_52187,plain,
( ~ aElementOf0(X0,sdtlpdtrp0(xN,sK14(sK40)))
| sz00 = sK40
| aElementOf0(X0,szNzAzT0) ),
inference(global_subsumption_just,[status(thm)],[c_51939,c_274,c_29061,c_52015]) ).
cnf(c_52194,plain,
( ~ sP9(sK14(sK40))
| sz00 = sK40
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))),szNzAzT0) ),
inference(superposition,[status(thm)],[c_256,c_52187]) ).
cnf(c_52395,plain,
( sz00 = sK40
| aElementOf0(sK14(sK40),szNzAzT0) ),
inference(global_subsumption_just,[status(thm)],[c_52015,c_274,c_52015]) ).
cnf(c_52428,plain,
( sz00 = sK40
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))),szNzAzT0) ),
inference(global_subsumption_just,[status(thm)],[c_52194,c_274,c_32539,c_52194]) ).
cnf(c_52436,plain,
( sz00 = sK40
| aElement0(szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))) ),
inference(superposition,[status(thm)],[c_52428,c_51427]) ).
cnf(c_52462,plain,
( ~ sP9(sK14(sK40))
| sz00 = sK40
| aSubsetOf0(sdtlpdtrp0(xN,sK40),sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))))) ),
inference(superposition,[status(thm)],[c_51888,c_250]) ).
cnf(c_52546,plain,
( sz00 = sK40
| aSubsetOf0(sdtlpdtrp0(xN,sK40),sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))))) ),
inference(global_subsumption_just,[status(thm)],[c_52462,c_37966]) ).
cnf(c_52550,plain,
( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))))
| ~ aSet0(sdtlpdtrp0(xN,sK40))
| ~ isCountable0(sdtlpdtrp0(xN,sK40))
| sz00 = sK40
| aElementOf0(sK41,sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))))) ),
inference(superposition,[status(thm)],[c_52546,c_51867]) ).
cnf(c_52560,plain,
( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))))
| sz00 = sK40
| aElementOf0(sK41,sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))))) ),
inference(global_subsumption_just,[status(thm)],[c_52550,c_37971]) ).
cnf(c_58051,plain,
( szszuzczcdt0(sK14(sK40)) != sK40
| ~ aElementOf0(X0,sdtlpdtrp0(xN,sK14(sK40)))
| ~ aElementOf0(sK14(sK40),szNzAzT0)
| aElementOf0(X0,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_2368]) ).
cnf(c_70186,plain,
( szszuzczcdt0(sK14(sK40)) != sK40
| ~ aElementOf0(sK41,sdtlpdtrp0(xN,sK14(sK40)))
| ~ aElementOf0(sK14(sK40),szNzAzT0)
| aElementOf0(sK41,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_58051]) ).
cnf(c_75608,plain,
( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))))
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))))
| ~ aSet0(sdtlpdtrp0(xN,sK14(sK40)))
| sz00 = sK40
| aElementOf0(sK41,sdtlpdtrp0(xN,sK14(sK40))) ),
inference(superposition,[status(thm)],[c_52560,c_51694]) ).
cnf(c_79935,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,sK40),X0)
| ~ aSet0(sdtlpdtrp0(xN,sK40))
| ~ isCountable0(sdtlpdtrp0(xN,sK40))
| ~ aSet0(X0)
| aElementOf0(sK41,X0) ),
inference(superposition,[status(thm)],[c_269,c_58]) ).
cnf(c_79955,plain,
( szszuzczcdt0(sK14(sK40)) = sK40
| sz00 = sK40 ),
inference(superposition,[status(thm)],[c_274,c_100]) ).
cnf(c_80429,plain,
( ~ sP9(sK14(sK40))
| sz00 = sK40
| aSubsetOf0(sdtlpdtrp0(xN,sK40),sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))))) ),
inference(superposition,[status(thm)],[c_79955,c_250]) ).
cnf(c_80502,plain,
( sz00 = sK40
| aSubsetOf0(sdtlpdtrp0(xN,sK40),sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))))) ),
inference(global_subsumption_just,[status(thm)],[c_80429,c_37966]) ).
cnf(c_80506,plain,
( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))))
| ~ aSet0(sdtlpdtrp0(xN,sK40))
| ~ isCountable0(sdtlpdtrp0(xN,sK40))
| sz00 = sK40
| aElementOf0(sK41,sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))))) ),
inference(superposition,[status(thm)],[c_80502,c_79935]) ).
cnf(c_80516,plain,
( sz00 = sK40
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))))) ),
inference(global_subsumption_just,[status(thm)],[c_80506,c_28947,c_37540,c_52018,c_52395,c_52436,c_70186,c_75608]) ).
cnf(c_80517,plain,
( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))))
| sz00 = sK40 ),
inference(renaming,[status(thm)],[c_80516]) ).
cnf(c_80518,plain,
( ~ sP9(sK14(sK40))
| sz00 = sK40 ),
inference(superposition,[status(thm)],[c_254,c_80517]) ).
cnf(c_80520,plain,
sz00 = sK40,
inference(global_subsumption_just,[status(thm)],[c_80518,c_274,c_32539,c_80518]) ).
cnf(c_80594,plain,
( ~ aSet0(sdtlpdtrp0(xN,sK40))
| ~ isCountable0(sdtlpdtrp0(xN,sK40))
| aElementOf0(sK41,sdtlpdtrp0(xN,sz00)) ),
inference(superposition,[status(thm)],[c_80520,c_269]) ).
cnf(c_80596,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,sz00),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,sK40)) ),
inference(superposition,[status(thm)],[c_80520,c_267]) ).
cnf(c_80601,plain,
( ~ isCountable0(sdtlpdtrp0(xN,sK40))
| ~ aSubsetOf0(xS,szNzAzT0) ),
inference(superposition,[status(thm)],[c_264,c_80596]) ).
cnf(c_80605,plain,
~ isCountable0(sdtlpdtrp0(xN,sK40)),
inference(global_subsumption_just,[status(thm)],[c_80594,c_196,c_80601]) ).
cnf(c_80607,plain,
~ isCountable0(sdtlpdtrp0(xN,sz00)),
inference(superposition,[status(thm)],[c_80520,c_80605]) ).
cnf(c_80608,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_80607,c_30414,c_195]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM569+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 15:22:02 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 202.80/26.86 % SZS status Started for theBenchmark.p
% 202.80/26.86 % SZS status Theorem for theBenchmark.p
% 202.80/26.86
% 202.80/26.86 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 202.80/26.86
% 202.80/26.86 ------ iProver source info
% 202.80/26.86
% 202.80/26.86 git: date: 2023-05-31 18:12:56 +0000
% 202.80/26.86 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 202.80/26.86 git: non_committed_changes: false
% 202.80/26.86 git: last_make_outside_of_git: false
% 202.80/26.86
% 202.80/26.86 ------ Parsing...
% 202.80/26.86 ------ Clausification by vclausify_rel & Parsing by iProver...
% 202.80/26.86
% 202.80/26.86 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 202.80/26.86
% 202.80/26.86 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 202.80/26.86
% 202.80/26.86 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 202.80/26.86 ------ Proving...
% 202.80/26.86 ------ Problem Properties
% 202.80/26.86
% 202.80/26.86
% 202.80/26.86 clauses 221
% 202.80/26.86 conjectures 4
% 202.80/26.86 EPR 44
% 202.80/26.86 Horn 170
% 202.80/26.86 unary 26
% 202.80/26.86 binary 44
% 202.80/26.86 lits 758
% 202.80/26.86 lits eq 107
% 202.80/26.86 fd_pure 0
% 202.80/26.86 fd_pseudo 0
% 202.80/26.86 fd_cond 10
% 202.80/26.86 fd_pseudo_cond 30
% 202.80/26.86 AC symbols 0
% 202.80/26.86
% 202.80/26.86 ------ Input Options Time Limit: Unbounded
% 202.80/26.86
% 202.80/26.86
% 202.80/26.86 ------
% 202.80/26.86 Current options:
% 202.80/26.86 ------
% 202.80/26.86
% 202.80/26.86
% 202.80/26.86
% 202.80/26.86
% 202.80/26.86 ------ Proving...
% 202.80/26.86
% 202.80/26.86
% 202.80/26.86 % SZS status Theorem for theBenchmark.p
% 202.80/26.86
% 202.80/26.86 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 202.80/26.87
% 202.80/26.88
%------------------------------------------------------------------------------