%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM602+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:52:47 AM UTC 2026
% Result : Theorem 4.45s 4.76s
% Output : Proof 4.54s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(mSetSort,axiom,
! [W0] :
( aSet0(W0)
=> $true ),
file('theBenchmark.p',mSetSort) ).
fof(mElmSort,axiom,
! [W0] :
( aElement0(W0)
=> $true ),
file('theBenchmark.p',mElmSort) ).
fof(mEOfElem,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('theBenchmark.p',mEOfElem) ).
fof(mFinRel,axiom,
! [W0] :
( aSet0(W0)
=> ( isFinite0(W0)
=> $true ) ),
file('theBenchmark.p',mFinRel) ).
fof(mDefEmp,definition,
! [W0] :
( W0 = slcrc0
<=> ( ~ ? [W1] : aElementOf0(W1,W0)
& aSet0(W0) ) ),
file('theBenchmark.p',mDefEmp) ).
fof(mEmpFin,axiom,
isFinite0(slcrc0),
file('theBenchmark.p',mEmpFin) ).
fof(mCntRel,axiom,
! [W0] :
( aSet0(W0)
=> ( isCountable0(W0)
=> $true ) ),
file('theBenchmark.p',mCntRel) ).
fof(mCountNFin,axiom,
! [W0] :
( ( isCountable0(W0)
& aSet0(W0) )
=> ~ isFinite0(W0) ),
file('theBenchmark.p',mCountNFin) ).
fof(mCountNFin_01,axiom,
! [W0] :
( ( isCountable0(W0)
& aSet0(W0) )
=> W0 != slcrc0 ),
file('theBenchmark.p',mCountNFin_01) ).
fof(mDefSub,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& aSet0(W1) ) ) ),
file('theBenchmark.p',mDefSub) ).
fof(mSubFSet,axiom,
! [W0] :
( ( isFinite0(W0)
& aSet0(W0) )
=> ! [W1] :
( aSubsetOf0(W1,W0)
=> isFinite0(W1) ) ),
file('theBenchmark.p',mSubFSet) ).
fof(mSubRefl,axiom,
! [W0] :
( aSet0(W0)
=> aSubsetOf0(W0,W0) ),
file('theBenchmark.p',mSubRefl) ).
fof(mSubASymm,axiom,
! [W0,W1] :
( ( aSet0(W1)
& aSet0(W0) )
=> ( ( aSubsetOf0(W1,W0)
& aSubsetOf0(W0,W1) )
=> W0 = W1 ) ),
file('theBenchmark.p',mSubASymm) ).
fof(mSubTrans,axiom,
! [W0,W1,W2] :
( ( aSet0(W2)
& aSet0(W1)
& aSet0(W0) )
=> ( ( aSubsetOf0(W1,W2)
& aSubsetOf0(W0,W1) )
=> aSubsetOf0(W0,W2) ) ),
file('theBenchmark.p',mSubTrans) ).
fof(mDefCons,definition,
! [W0,W1] :
( ( aElement0(W1)
& aSet0(W0) )
=> ! [W2] :
( W2 = sdtpldt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) ) )
& aSet0(W2) ) ) ),
file('theBenchmark.p',mDefCons) ).
fof(mDefDiff,definition,
! [W0,W1] :
( ( aElement0(W1)
& aSet0(W0) )
=> ! [W2] :
( W2 = sdtmndt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) ) )
& aSet0(W2) ) ) ),
file('theBenchmark.p',mDefDiff) ).
fof(mConsDiff,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ),
file('theBenchmark.p',mConsDiff) ).
fof(mDiffCons,axiom,
! [W0,W1] :
( ( aSet0(W1)
& aElement0(W0) )
=> ( ~ aElementOf0(W0,W1)
=> sdtmndt0(sdtpldt0(W1,W0),W0) = W1 ) ),
file('theBenchmark.p',mDiffCons) ).
fof(mCConsSet,axiom,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( ( isCountable0(W1)
& aSet0(W1) )
=> isCountable0(sdtpldt0(W1,W0)) ) ),
file('theBenchmark.p',mCConsSet) ).
fof(mCDiffSet,axiom,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( ( isCountable0(W1)
& aSet0(W1) )
=> isCountable0(sdtmndt0(W1,W0)) ) ),
file('theBenchmark.p',mCDiffSet) ).
fof(mFConsSet,axiom,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( ( isFinite0(W1)
& aSet0(W1) )
=> isFinite0(sdtpldt0(W1,W0)) ) ),
file('theBenchmark.p',mFConsSet) ).
fof(mFDiffSet,axiom,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( ( isFinite0(W1)
& aSet0(W1) )
=> isFinite0(sdtmndt0(W1,W0)) ) ),
file('theBenchmark.p',mFDiffSet) ).
fof(mNATSet,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('theBenchmark.p',mNATSet) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('theBenchmark.p',mZeroNum) ).
fof(mSuccNum,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( szszuzczcdt0(W0) != sz00
& aElementOf0(szszuzczcdt0(W0),szNzAzT0) ) ),
file('theBenchmark.p',mSuccNum) ).
fof(mSuccEquSucc,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( szszuzczcdt0(W0) = szszuzczcdt0(W1)
=> W0 = W1 ) ),
file('theBenchmark.p',mSuccEquSucc) ).
fof(mNatExtra,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( ? [W1] :
( W0 = szszuzczcdt0(W1)
& aElementOf0(W1,szNzAzT0) )
| W0 = sz00 ) ),
file('theBenchmark.p',mNatExtra) ).
fof(mNatNSucc,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> W0 != szszuzczcdt0(W0) ),
file('theBenchmark.p',mNatNSucc) ).
fof(mLessRel,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( sdtlseqdt0(W0,W1)
=> $true ) ),
file('theBenchmark.p',mLessRel) ).
fof(mZeroLess,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> sdtlseqdt0(sz00,W0) ),
file('theBenchmark.p',mZeroLess) ).
fof(mNoScLessZr,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ~ sdtlseqdt0(szszuzczcdt0(W0),sz00) ),
file('theBenchmark.p',mNoScLessZr) ).
fof(mSuccLess,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( sdtlseqdt0(W0,W1)
<=> sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(W1)) ) ),
file('theBenchmark.p',mSuccLess) ).
fof(mLessSucc,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> sdtlseqdt0(W0,szszuzczcdt0(W0)) ),
file('theBenchmark.p',mLessSucc) ).
fof(mLessRefl,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> sdtlseqdt0(W0,W0) ),
file('theBenchmark.p',mLessRefl) ).
fof(mLessASymm,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( ( sdtlseqdt0(W1,W0)
& sdtlseqdt0(W0,W1) )
=> W0 = W1 ) ),
file('theBenchmark.p',mLessASymm) ).
fof(mLessTrans,axiom,
! [W0,W1,W2] :
( ( aElementOf0(W2,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( ( sdtlseqdt0(W1,W2)
& sdtlseqdt0(W0,W1) )
=> sdtlseqdt0(W0,W2) ) ),
file('theBenchmark.p',mLessTrans) ).
fof(mLessTotal,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( sdtlseqdt0(szszuzczcdt0(W1),W0)
| sdtlseqdt0(W0,W1) ) ),
file('theBenchmark.p',mLessTotal) ).
fof(mIHSort,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( iLess0(W0,W1)
=> $true ) ),
file('theBenchmark.p',mIHSort) ).
fof(mIH,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> iLess0(W0,szszuzczcdt0(W0)) ),
file('theBenchmark.p',mIH) ).
fof(mCardS,axiom,
! [W0] :
( aSet0(W0)
=> aElement0(sbrdtbr0(W0)) ),
file('theBenchmark.p',mCardS) ).
fof(mCardNum,axiom,
! [W0] :
( aSet0(W0)
=> ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
file('theBenchmark.p',mCardNum) ).
fof(mCardEmpty,axiom,
! [W0] :
( aSet0(W0)
=> ( sbrdtbr0(W0) = sz00
<=> W0 = slcrc0 ) ),
file('theBenchmark.p',mCardEmpty) ).
fof(mCardCons,axiom,
! [W0] :
( ( isFinite0(W0)
& aSet0(W0) )
=> ! [W1] :
( aElement0(W1)
=> ( ~ aElementOf0(W1,W0)
=> sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) ),
file('theBenchmark.p',mCardCons) ).
fof(mCardDiff,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( ( aElementOf0(W1,W0)
& isFinite0(W0) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ),
file('theBenchmark.p',mCardDiff) ).
fof(mCardSub,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( ( aSubsetOf0(W1,W0)
& isFinite0(W0) )
=> sdtlseqdt0(sbrdtbr0(W1),sbrdtbr0(W0)) ) ),
file('theBenchmark.p',mCardSub) ).
fof(mCardSubEx,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aSet0(W0) )
=> ( ( sdtlseqdt0(W1,sbrdtbr0(W0))
& isFinite0(W0) )
=> ? [W2] :
( sbrdtbr0(W2) = W1
& aSubsetOf0(W2,W0) ) ) ),
file('theBenchmark.p',mCardSubEx) ).
fof(mDefMin,definition,
! [W0] :
( ( W0 != slcrc0
& aSubsetOf0(W0,szNzAzT0) )
=> ! [W1] :
( W1 = szmzizndt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W0)
=> sdtlseqdt0(W1,W2) )
& aElementOf0(W1,W0) ) ) ),
file('theBenchmark.p',mDefMin) ).
fof(mDefMax,definition,
! [W0] :
( ( W0 != slcrc0
& isFinite0(W0)
& aSubsetOf0(W0,szNzAzT0) )
=> ! [W1] :
( W1 = szmzazxdt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W0)
=> sdtlseqdt0(W2,W1) )
& aElementOf0(W1,W0) ) ) ),
file('theBenchmark.p',mDefMax) ).
fof(mMinMin,axiom,
! [W0,W1] :
( ( W1 != slcrc0
& W0 != slcrc0
& aSubsetOf0(W1,szNzAzT0)
& aSubsetOf0(W0,szNzAzT0) )
=> ( ( aElementOf0(szmzizndt0(W1),W0)
& aElementOf0(szmzizndt0(W0),W1) )
=> szmzizndt0(W0) = szmzizndt0(W1) ) ),
file('theBenchmark.p',mMinMin) ).
fof(mDefSeg,definition,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( W1 = slbdtrb0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ( sdtlseqdt0(szszuzczcdt0(W2),W0)
& aElementOf0(W2,szNzAzT0) ) )
& aSet0(W1) ) ) ),
file('theBenchmark.p',mDefSeg) ).
fof(mSegFin,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> isFinite0(slbdtrb0(W0)) ),
file('theBenchmark.p',mSegFin) ).
fof(mSegZero,axiom,
slbdtrb0(sz00) = slcrc0,
file('theBenchmark.p',mSegZero) ).
fof(mSegSucc,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( aElementOf0(W0,slbdtrb0(szszuzczcdt0(W1)))
<=> ( W0 = W1
| aElementOf0(W0,slbdtrb0(W1)) ) ) ),
file('theBenchmark.p',mSegSucc) ).
fof(mSegLess,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( sdtlseqdt0(W0,W1)
<=> aSubsetOf0(slbdtrb0(W0),slbdtrb0(W1)) ) ),
file('theBenchmark.p',mSegLess) ).
fof(mFinSubSeg,axiom,
! [W0] :
( ( isFinite0(W0)
& aSubsetOf0(W0,szNzAzT0) )
=> ? [W1] :
( aSubsetOf0(W0,slbdtrb0(W1))
& aElementOf0(W1,szNzAzT0) ) ),
file('theBenchmark.p',mFinSubSeg) ).
fof(mCardSeg,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> sbrdtbr0(slbdtrb0(W0)) = W0 ),
file('theBenchmark.p',mCardSeg) ).
fof(mDefSel,definition,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aSet0(W0) )
=> ! [W2] :
( W2 = slbdtsldtrb0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) ) )
& aSet0(W2) ) ) ),
file('theBenchmark.p',mDefSel) ).
fof(mSelFSet,axiom,
! [W0] :
( ( isFinite0(W0)
& aSet0(W0) )
=> ! [W1] :
( aElementOf0(W1,szNzAzT0)
=> isFinite0(slbdtsldtrb0(W0,W1)) ) ),
file('theBenchmark.p',mSelFSet) ).
fof(mSelNSet,axiom,
! [W0] :
( ( ~ isFinite0(W0)
& aSet0(W0) )
=> ! [W1] :
( aElementOf0(W1,szNzAzT0)
=> slbdtsldtrb0(W0,W1) != slcrc0 ) ),
file('theBenchmark.p',mSelNSet) ).
fof(mSelCSet,axiom,
! [W0] :
( ( isCountable0(W0)
& aSet0(W0) )
=> ! [W1] :
( ( W1 != sz00
& aElementOf0(W1,szNzAzT0) )
=> isCountable0(slbdtsldtrb0(W0,W1)) ) ),
file('theBenchmark.p',mSelCSet) ).
fof(mSelSub,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1,W2] :
( ( W0 != sz00
& aSet0(W2)
& aSet0(W1) )
=> ( ( slbdtsldtrb0(W1,W0) != slcrc0
& aSubsetOf0(slbdtsldtrb0(W1,W0),slbdtsldtrb0(W2,W0)) )
=> aSubsetOf0(W1,W2) ) ) ),
file('theBenchmark.p',mSelSub) ).
fof(mSelExtra,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aSet0(W0) )
=> ! [W2] :
( ( isFinite0(W2)
& aSubsetOf0(W2,slbdtsldtrb0(W0,W1)) )
=> ? [W3] :
( aSubsetOf0(W2,slbdtsldtrb0(W3,W1))
& isFinite0(W3)
& aSubsetOf0(W3,W0) ) ) ),
file('theBenchmark.p',mSelExtra) ).
fof(mFunSort,axiom,
! [W0] :
( aFunction0(W0)
=> $true ),
file('theBenchmark.p',mFunSort) ).
fof(mDomSet,axiom,
! [W0] :
( aFunction0(W0)
=> aSet0(szDzozmdt0(W0)) ),
file('theBenchmark.p',mDomSet) ).
fof(mImgElm,axiom,
! [W0] :
( aFunction0(W0)
=> ! [W1] :
( aElementOf0(W1,szDzozmdt0(W0))
=> aElement0(sdtlpdtrp0(W0,W1)) ) ),
file('theBenchmark.p',mImgElm) ).
fof(mDefPtt,definition,
! [W0,W1] :
( ( aElement0(W1)
& aFunction0(W0) )
=> ! [W2] :
( W2 = sdtlbdtrb0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( sdtlpdtrp0(W0,W3) = W1
& aElementOf0(W3,szDzozmdt0(W0)) ) )
& aSet0(W2) ) ) ),
file('theBenchmark.p',mDefPtt) ).
fof(mPttSet,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aFunction0(W0) )
=> aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) ),
file('theBenchmark.p',mPttSet) ).
fof(mDefSImg,definition,
! [W0] :
( aFunction0(W0)
=> ! [W1] :
( aSubsetOf0(W1,szDzozmdt0(W0))
=> ! [W2] :
( W2 = sdtlcdtrc0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ? [W4] :
( sdtlpdtrp0(W0,W4) = W3
& aElementOf0(W4,W1) ) )
& aSet0(W2) ) ) ) ),
file('theBenchmark.p',mDefSImg) ).
fof(mImgRng,axiom,
! [W0] :
( aFunction0(W0)
=> ! [W1] :
( aElementOf0(W1,szDzozmdt0(W0))
=> aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ),
file('theBenchmark.p',mImgRng) ).
fof(mDefRst,definition,
! [W0] :
( aFunction0(W0)
=> ! [W1] :
( aSubsetOf0(W1,szDzozmdt0(W0))
=> ! [W2] :
( W2 = sdtexdt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W1)
=> sdtlpdtrp0(W2,W3) = sdtlpdtrp0(W0,W3) )
& szDzozmdt0(W2) = W1
& aFunction0(W2) ) ) ) ),
file('theBenchmark.p',mDefRst) ).
fof(mImgCount,axiom,
! [W0] :
( aFunction0(W0)
=> ! [W1] :
( ( isCountable0(W1)
& aSubsetOf0(W1,szDzozmdt0(W0)) )
=> ( ! [W2,W3] :
( ( W2 != W3
& aElementOf0(W3,szDzozmdt0(W0))
& aElementOf0(W2,szDzozmdt0(W0)) )
=> sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
=> isCountable0(sdtlcdtrc0(W0,W1)) ) ) ),
file('theBenchmark.p',mImgCount) ).
fof(mDirichlet,axiom,
! [W0] :
( aFunction0(W0)
=> ( ( isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0)))
& isCountable0(szDzozmdt0(W0)) )
=> ( isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0)))
& aElement0(szDzizrdt0(W0)) ) ) ),
file('theBenchmark.p',mDirichlet) ).
fof(m__3291,hypothesis,
( isFinite0(xT)
& aSet0(xT) ),
file('theBenchmark.p',m__3291) ).
fof(m__3418,hypothesis,
aElementOf0(xK,szNzAzT0),
file('theBenchmark.p',m__3418) ).
fof(m__3435,hypothesis,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
file('theBenchmark.p',m__3435) ).
fof(m__3453,hypothesis,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aFunction0(xc) ),
file('theBenchmark.p',m__3453) ).
fof(m__3398,hypothesis,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( ( isCountable0(W1)
& aSubsetOf0(W1,szNzAzT0) )
=> ! [W2] :
( ( aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
& szDzozmdt0(W2) = slbdtsldtrb0(W1,W0)
& aFunction0(W2) )
=> ( iLess0(W0,xK)
=> ? [W3] :
( ? [W4] :
( ! [W5] :
( aElementOf0(W5,slbdtsldtrb0(W4,W0))
=> sdtlpdtrp0(W2,W5) = W3 )
& isCountable0(W4)
& aSubsetOf0(W4,W1) )
& aElementOf0(W3,xT) ) ) ) ) ),
file('theBenchmark.p',m__3398) ).
fof(m__3462,hypothesis,
xK != sz00,
file('theBenchmark.p',m__3462) ).
fof(m__3520,hypothesis,
xK != sz00,
file('theBenchmark.p',m__3520) ).
fof(m__3533,hypothesis,
( szszuzczcdt0(xk) = xK
& aElementOf0(xk,szNzAzT0) ),
file('theBenchmark.p',m__3533) ).
fof(m__3623,hypothesis,
( ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( ( isCountable0(sdtlpdtrp0(xN,W0))
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
=> ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
file('theBenchmark.p',m__3623) ).
fof(m__3671,hypothesis,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( isCountable0(sdtlpdtrp0(xN,W0))
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) ) ),
file('theBenchmark.p',m__3671) ).
fof(m__3754,hypothesis,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( sdtlseqdt0(W1,W0)
=> aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ),
file('theBenchmark.p',m__3754) ).
fof(m__3821,hypothesis,
! [W0,W1] :
( ( W0 != W1
& aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) ),
file('theBenchmark.p',m__3821) ).
fof(m__3965,hypothesis,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
& aSet0(W1) )
=> aElementOf0(sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))),slbdtsldtrb0(xS,xK)) ) ),
file('theBenchmark.p',m__3965) ).
fof(m__4151,hypothesis,
( ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( ! [W1] :
( ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
& aSet0(W1) )
=> sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)
& aFunction0(sdtlpdtrp0(xC,W0)) ) )
& szDzozmdt0(xC) = szNzAzT0
& aFunction0(xC) ),
file('theBenchmark.p',m__4151) ).
fof(m__4182,hypothesis,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,W0),szDzozmdt0(sdtlpdtrp0(xC,W0))),xT) ),
file('theBenchmark.p',m__4182) ).
fof(m__4331,hypothesis,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( ( isCountable0(W1)
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
=> ! [W2] :
( ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
& aSet0(W2) )
=> aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ),
file('theBenchmark.p',m__4331) ).
fof(m__4411,hypothesis,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ? [W1] :
( ? [W2] :
( ! [W3] :
( ( aElementOf0(W3,slbdtsldtrb0(W2,xk))
& aSet0(W3) )
=> sdtlpdtrp0(sdtlpdtrp0(xC,W0),W3) = W1 )
& isCountable0(W2)
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aElementOf0(W1,xT) ) ),
file('theBenchmark.p',m__4411) ).
fof(m__4618,hypothesis,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ? [W1] :
( ! [W2] :
( ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
& aSet0(W2) )
=> sdtlpdtrp0(sdtlpdtrp0(xC,W0),W2) = W1 )
& aElementOf0(W1,xT) ) ),
file('theBenchmark.p',m__4618) ).
fof(m__4660,hypothesis,
( ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
& szDzozmdt0(xe) = szNzAzT0
& aFunction0(xe) ),
file('theBenchmark.p',m__4660) ).
fof(m__4730,hypothesis,
( ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
& aSet0(W1) )
=> sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) )
& szDzozmdt0(xd) = szNzAzT0
& aFunction0(xd) ),
file('theBenchmark.p',m__4730) ).
fof(m__4758,hypothesis,
aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),
file('theBenchmark.p',m__4758) ).
fof(m__4854,hypothesis,
( isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(szDzizrdt0(xd),xT) ),
file('theBenchmark.p',m__4854) ).
fof(m__4891,hypothesis,
( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aSet0(xO) ),
file('theBenchmark.p',m__4891) ).
fof(m__4908,hypothesis,
( isCountable0(xO)
& aSet0(xO) ),
file('theBenchmark.p',m__4908) ).
fof(m__4982,hypothesis,
! [W0] :
( aElementOf0(W0,xO)
=> ? [W1] :
( sdtlpdtrp0(xe,W1) = W0
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(W1,szNzAzT0) ) ),
file('theBenchmark.p',m__4982) ).
fof(m__5009,hypothesis,
aElementOf0(xx,xO),
file('theBenchmark.p',m__5009) ).
fof(m__,conjecture,
? [W0] :
( sdtlpdtrp0(xe,W0) = xx
& aElementOf0(W0,szNzAzT0) ),
file('theBenchmark.p',m__) ).
fof(f_1_1,plain,
! [W0] :
( $true
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mSetSort]) ).
fof(f_1_2,plain,
! [U_0] :
( $true
| ~ aSet0(U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ! [U_0] : ~ aSet0(U_0)
| $true ),
inference(miniscope,[status(thm)],[f_1_2]) ).
cnf(f_1_4,plain,
( ~ aSet0(U_0)
| $true ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
! [W0] :
( $true
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mElmSort]) ).
fof(f_2_2,plain,
! [U_1] :
( $true
| ~ aElement0(U_1) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_1] : ~ aElement0(U_1)
| $true ),
inference(miniscope,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( ~ aElement0(U_1)
| $true ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mEOfElem]) ).
fof(f_3_2,plain,
! [U_3] :
( ! [U_2] :
( aElement0(U_2)
| ~ aElementOf0(U_2,U_3) )
| ~ aSet0(U_3) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( aElement0(U_2)
| ~ aElementOf0(U_2,U_3)
| ~ aSet0(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [W0] :
( $true
| ~ isFinite0(W0)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mFinRel]) ).
fof(f_4_2,plain,
! [U_4] :
( $true
| ~ isFinite0(U_4)
| ~ aSet0(U_4) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( $true
| ~ isFinite0(U_4)
| ~ aSet0(U_4) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [W0] :
( ( W0 = slcrc0
| ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0) )
& ( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(fof_nnf,[status(thm)],[mDefEmp]) ).
fof(f_5_2,plain,
! [U_7] :
( ( U_7 = slcrc0
| ? [U_6] : aElementOf0(U_6,U_7)
| ~ aSet0(U_7) )
& ( ( ! [U_5] : ~ aElementOf0(U_5,U_7)
& aSet0(U_7) )
| U_7 != slcrc0 ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_9] :
( U_9 = slcrc0
| ? [U_6] : aElementOf0(U_6,U_9)
| ~ aSet0(U_9) )
& ! [U_8] :
( ( ! [U_5] : ~ aElementOf0(U_5,U_8)
& aSet0(U_8) )
| U_8 != slcrc0 ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
( ! [U_9] :
( U_9 = slcrc0
| aElementOf0(sK1(U_9),U_9)
| ~ aSet0(U_9) )
& ! [U_8] :
( ( ! [U_5] : ~ aElementOf0(U_5,U_8)
& aSet0(U_8) )
| U_8 != slcrc0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_6,sK1(U_9))],[f_5_3]) ).
cnf(f_5_5,plain,
( aSet0(U_8)
| U_8 != slcrc0 ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_6,plain,
( ~ aElementOf0(U_5,U_8)
| U_8 != slcrc0 ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_7,plain,
( U_9 = slcrc0
| aElementOf0(sK1(U_9),U_9)
| ~ aSet0(U_9) ),
inference(clausify,[status(thm)],[f_5_4]) ).
fof(f_6_1,plain,
isFinite0(slcrc0),
inference(fof_nnf,[status(thm)],[mEmpFin]) ).
cnf(f_6_2,plain,
isFinite0(slcrc0),
inference(clausify,[status(thm)],[f_6_1]) ).
fof(f_7_1,plain,
! [W0] :
( $true
| ~ isCountable0(W0)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mCntRel]) ).
fof(f_7_2,plain,
! [U_10] :
( $true
| ~ isCountable0(U_10)
| ~ aSet0(U_10) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( $true
| ~ isCountable0(U_10)
| ~ aSet0(U_10) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [W0] :
( ~ isFinite0(W0)
| ~ isCountable0(W0)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mCountNFin]) ).
fof(f_8_2,plain,
! [U_11] :
( ~ isFinite0(U_11)
| ~ isCountable0(U_11)
| ~ aSet0(U_11) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( ~ isFinite0(U_11)
| ~ isCountable0(U_11)
| ~ aSet0(U_11) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [W0] :
( W0 != slcrc0
| ~ isCountable0(W0)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mCountNFin_01]) ).
fof(f_9_2,plain,
! [U_12] :
( U_12 != slcrc0
| ~ isCountable0(U_12)
| ~ aSet0(U_12) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( U_12 != slcrc0
| ~ isCountable0(U_12)
| ~ aSet0(U_12) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [W0] :
( ! [W1] :
( ( aSubsetOf0(W1,W0)
| ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1) )
& ( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mDefSub]) ).
fof(f_10_2,plain,
! [U_16] :
( ! [U_15] :
( ( aSubsetOf0(U_15,U_16)
| ? [U_14] :
( ~ aElementOf0(U_14,U_16)
& aElementOf0(U_14,U_15) )
| ~ aSet0(U_15) )
& ( ( ! [U_13] :
( aElementOf0(U_13,U_16)
| ~ aElementOf0(U_13,U_15) )
& aSet0(U_15) )
| ~ aSubsetOf0(U_15,U_16) ) )
| ~ aSet0(U_16) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_16] :
( ( ! [U_18] :
( aSubsetOf0(U_18,U_16)
| ? [U_14] :
( ~ aElementOf0(U_14,U_16)
& aElementOf0(U_14,U_18) )
| ~ aSet0(U_18) )
& ! [U_17] :
( ( ! [U_13] :
( aElementOf0(U_13,U_16)
| ~ aElementOf0(U_13,U_17) )
& aSet0(U_17) )
| ~ aSubsetOf0(U_17,U_16) ) )
| ~ aSet0(U_16) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
fof(f_10_4,plain,
! [U_16] :
( ( ! [U_18] :
( aSubsetOf0(U_18,U_16)
| ( ~ aElementOf0(sK2(U_16,U_18),U_16)
& aElementOf0(sK2(U_16,U_18),U_18) )
| ~ aSet0(U_18) )
& ! [U_17] :
( ( ! [U_13] :
( aElementOf0(U_13,U_16)
| ~ aElementOf0(U_13,U_17) )
& aSet0(U_17) )
| ~ aSubsetOf0(U_17,U_16) ) )
| ~ aSet0(U_16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_14,sK2(U_16,U_18))],[f_10_3]) ).
cnf(f_10_5,plain,
( aSet0(U_17)
| ~ aSubsetOf0(U_17,U_16)
| ~ aSet0(U_16) ),
inference(clausify,[status(thm)],[f_10_4]) ).
cnf(f_10_6,plain,
( aElementOf0(U_13,U_16)
| ~ aElementOf0(U_13,U_17)
| ~ aSubsetOf0(U_17,U_16)
| ~ aSet0(U_16) ),
inference(clausify,[status(thm)],[f_10_4]) ).
cnf(f_10_7,plain,
( aElementOf0(sK2(U_16,U_18),U_18)
| ~ aSet0(U_18)
| aSubsetOf0(U_18,U_16)
| ~ aSet0(U_16) ),
inference(clausify,[status(thm)],[f_10_4]) ).
cnf(f_10_8,plain,
( ~ aElementOf0(sK2(U_16,U_18),U_16)
| ~ aSet0(U_18)
| aSubsetOf0(U_18,U_16)
| ~ aSet0(U_16) ),
inference(clausify,[status(thm)],[f_10_4]) ).
fof(f_11_1,plain,
! [W0] :
( ! [W1] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) )
| ~ isFinite0(W0)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mSubFSet]) ).
fof(f_11_2,plain,
! [U_20] :
( ! [U_19] :
( isFinite0(U_19)
| ~ aSubsetOf0(U_19,U_20) )
| ~ isFinite0(U_20)
| ~ aSet0(U_20) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( isFinite0(U_19)
| ~ aSubsetOf0(U_19,U_20)
| ~ isFinite0(U_20)
| ~ aSet0(U_20) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [W0] :
( aSubsetOf0(W0,W0)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mSubRefl]) ).
fof(f_12_2,plain,
! [U_21] :
( aSubsetOf0(U_21,U_21)
| ~ aSet0(U_21) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( aSubsetOf0(U_21,U_21)
| ~ aSet0(U_21) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [W0,W1] :
( W0 = W1
| ~ aSubsetOf0(W1,W0)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mSubASymm]) ).
fof(f_13_2,plain,
! [U_23,U_22] :
( U_23 = U_22
| ~ aSubsetOf0(U_22,U_23)
| ~ aSubsetOf0(U_23,U_22)
| ~ aSet0(U_22)
| ~ aSet0(U_23) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( U_23 = U_22
| ~ aSubsetOf0(U_22,U_23)
| ~ aSubsetOf0(U_23,U_22)
| ~ aSet0(U_22)
| ~ aSet0(U_23) ),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
! [W0,W1,W2] :
( aSubsetOf0(W0,W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W2)
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mSubTrans]) ).
fof(f_14_2,plain,
! [U_26,U_25,U_24] :
( aSubsetOf0(U_26,U_24)
| ~ aSubsetOf0(U_25,U_24)
| ~ aSubsetOf0(U_26,U_25)
| ~ aSet0(U_24)
| ~ aSet0(U_25)
| ~ aSet0(U_26) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( aSubsetOf0(U_26,U_24)
| ~ aSubsetOf0(U_25,U_24)
| ~ aSubsetOf0(U_26,U_25)
| ~ aSet0(U_24)
| ~ aSet0(U_25)
| ~ aSet0(U_26) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [W0,W1] :
( ! [W2] :
( ( W2 = sdtpldt0(W0,W1)
| ? [W3] :
( ( ~ aElementOf0(W3,W2)
& ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) )
| ( ( ( W3 != W1
& ~ aElementOf0(W3,W0) )
| ~ aElement0(W3) )
& aElementOf0(W3,W2) ) )
| ~ aSet0(W2) )
& ( ( ! [W3] :
( ( aElementOf0(W3,W2)
| ( W3 != W1
& ~ aElementOf0(W3,W0) )
| ~ aElement0(W3) )
& ( ( ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtpldt0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mDefCons]) ).
fof(f_15_2,plain,
! [U_31,U_30] :
( ! [U_29] :
( ( U_29 = sdtpldt0(U_31,U_30)
| ? [U_28] :
( ( ~ aElementOf0(U_28,U_29)
& ( U_28 = U_30
| aElementOf0(U_28,U_31) )
& aElement0(U_28) )
| ( ( ( U_28 != U_30
& ~ aElementOf0(U_28,U_31) )
| ~ aElement0(U_28) )
& aElementOf0(U_28,U_29) ) )
| ~ aSet0(U_29) )
& ( ( ! [U_27] :
( ( aElementOf0(U_27,U_29)
| ( U_27 != U_30
& ~ aElementOf0(U_27,U_31) )
| ~ aElement0(U_27) )
& ( ( ( U_27 = U_30
| aElementOf0(U_27,U_31) )
& aElement0(U_27) )
| ~ aElementOf0(U_27,U_29) ) )
& aSet0(U_29) )
| U_29 != sdtpldt0(U_31,U_30) ) )
| ~ aElement0(U_30)
| ~ aSet0(U_31) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_31,U_30] :
( ( ! [U_37] :
( U_37 = sdtpldt0(U_31,U_30)
| ? [U_35] :
( ~ aElementOf0(U_35,U_37)
& ( U_35 = U_30
| aElementOf0(U_35,U_31) )
& aElement0(U_35) )
| ? [U_34] :
( ( ( U_34 != U_30
& ~ aElementOf0(U_34,U_31) )
| ~ aElement0(U_34) )
& aElementOf0(U_34,U_37) )
| ~ aSet0(U_37) )
& ! [U_36] :
( ( ! [U_33] :
( aElementOf0(U_33,U_36)
| ( U_33 != U_30
& ~ aElementOf0(U_33,U_31) )
| ~ aElement0(U_33) )
& ! [U_32] :
( ( ( U_32 = U_30
| aElementOf0(U_32,U_31) )
& aElement0(U_32) )
| ~ aElementOf0(U_32,U_36) )
& aSet0(U_36) )
| U_36 != sdtpldt0(U_31,U_30) ) )
| ~ aElement0(U_30)
| ~ aSet0(U_31) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
fof(f_15_4,plain,
! [U_31,U_30] :
( ( ! [U_37] :
( U_37 = sdtpldt0(U_31,U_30)
| ? [U_35] :
( ~ aElementOf0(U_35,U_37)
& ( U_35 = U_30
| aElementOf0(U_35,U_31) )
& aElement0(U_35) )
| ( ( ( sK3(U_31,U_30,U_37) != U_30
& ~ aElementOf0(sK3(U_31,U_30,U_37),U_31) )
| ~ aElement0(sK3(U_31,U_30,U_37)) )
& aElementOf0(sK3(U_31,U_30,U_37),U_37) )
| ~ aSet0(U_37) )
& ! [U_36] :
( ( ! [U_33] :
( aElementOf0(U_33,U_36)
| ( U_33 != U_30
& ~ aElementOf0(U_33,U_31) )
| ~ aElement0(U_33) )
& ! [U_32] :
( ( ( U_32 = U_30
| aElementOf0(U_32,U_31) )
& aElement0(U_32) )
| ~ aElementOf0(U_32,U_36) )
& aSet0(U_36) )
| U_36 != sdtpldt0(U_31,U_30) ) )
| ~ aElement0(U_30)
| ~ aSet0(U_31) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_34,sK3(U_31,U_30,U_37))],[f_15_3]) ).
fof(f_15_5,plain,
! [U_31,U_30] :
( ( ! [U_37] :
( U_37 = sdtpldt0(U_31,U_30)
| ( ~ aElementOf0(sK4(U_31,U_30,U_37),U_37)
& ( sK4(U_31,U_30,U_37) = U_30
| aElementOf0(sK4(U_31,U_30,U_37),U_31) )
& aElement0(sK4(U_31,U_30,U_37)) )
| ( ( ( sK3(U_31,U_30,U_37) != U_30
& ~ aElementOf0(sK3(U_31,U_30,U_37),U_31) )
| ~ aElement0(sK3(U_31,U_30,U_37)) )
& aElementOf0(sK3(U_31,U_30,U_37),U_37) )
| ~ aSet0(U_37) )
& ! [U_36] :
( ( ! [U_33] :
( aElementOf0(U_33,U_36)
| ( U_33 != U_30
& ~ aElementOf0(U_33,U_31) )
| ~ aElement0(U_33) )
& ! [U_32] :
( ( ( U_32 = U_30
| aElementOf0(U_32,U_31) )
& aElement0(U_32) )
| ~ aElementOf0(U_32,U_36) )
& aSet0(U_36) )
| U_36 != sdtpldt0(U_31,U_30) ) )
| ~ aElement0(U_30)
| ~ aSet0(U_31) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_35,sK4(U_31,U_30,U_37))],[f_15_4]) ).
cnf(f_15_6,plain,
( aSet0(U_36)
| U_36 != sdtpldt0(U_31,U_30)
| ~ aElement0(U_30)
| ~ aSet0(U_31) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_7,plain,
( aElement0(U_32)
| ~ aElementOf0(U_32,U_36)
| U_36 != sdtpldt0(U_31,U_30)
| ~ aElement0(U_30)
| ~ aSet0(U_31) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_8,plain,
( U_32 = U_30
| aElementOf0(U_32,U_31)
| ~ aElementOf0(U_32,U_36)
| U_36 != sdtpldt0(U_31,U_30)
| ~ aElement0(U_30)
| ~ aSet0(U_31) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_9,plain,
( ~ aElementOf0(U_33,U_31)
| ~ aElement0(U_33)
| aElementOf0(U_33,U_36)
| U_36 != sdtpldt0(U_31,U_30)
| ~ aElement0(U_30)
| ~ aSet0(U_31) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_10,plain,
( U_33 != U_30
| ~ aElement0(U_33)
| aElementOf0(U_33,U_36)
| U_36 != sdtpldt0(U_31,U_30)
| ~ aElement0(U_30)
| ~ aSet0(U_31) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_11,plain,
( aElement0(sK4(U_31,U_30,U_37))
| aElementOf0(sK3(U_31,U_30,U_37),U_37)
| ~ aSet0(U_37)
| U_37 = sdtpldt0(U_31,U_30)
| ~ aElement0(U_30)
| ~ aSet0(U_31) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_12,plain,
( sK4(U_31,U_30,U_37) = U_30
| aElementOf0(sK4(U_31,U_30,U_37),U_31)
| aElementOf0(sK3(U_31,U_30,U_37),U_37)
| ~ aSet0(U_37)
| U_37 = sdtpldt0(U_31,U_30)
| ~ aElement0(U_30)
| ~ aSet0(U_31) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_13,plain,
( ~ aElementOf0(sK4(U_31,U_30,U_37),U_37)
| aElementOf0(sK3(U_31,U_30,U_37),U_37)
| ~ aSet0(U_37)
| U_37 = sdtpldt0(U_31,U_30)
| ~ aElement0(U_30)
| ~ aSet0(U_31) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_14,plain,
( ~ aElementOf0(sK3(U_31,U_30,U_37),U_31)
| ~ aElement0(sK3(U_31,U_30,U_37))
| aElement0(sK4(U_31,U_30,U_37))
| ~ aSet0(U_37)
| U_37 = sdtpldt0(U_31,U_30)
| ~ aElement0(U_30)
| ~ aSet0(U_31) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_15,plain,
( sK3(U_31,U_30,U_37) != U_30
| ~ aElement0(sK3(U_31,U_30,U_37))
| aElement0(sK4(U_31,U_30,U_37))
| ~ aSet0(U_37)
| U_37 = sdtpldt0(U_31,U_30)
| ~ aElement0(U_30)
| ~ aSet0(U_31) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_16,plain,
( ~ aElementOf0(sK3(U_31,U_30,U_37),U_31)
| ~ aElement0(sK3(U_31,U_30,U_37))
| sK4(U_31,U_30,U_37) = U_30
| aElementOf0(sK4(U_31,U_30,U_37),U_31)
| ~ aSet0(U_37)
| U_37 = sdtpldt0(U_31,U_30)
| ~ aElement0(U_30)
| ~ aSet0(U_31) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_17,plain,
( sK3(U_31,U_30,U_37) != U_30
| ~ aElement0(sK3(U_31,U_30,U_37))
| sK4(U_31,U_30,U_37) = U_30
| aElementOf0(sK4(U_31,U_30,U_37),U_31)
| ~ aSet0(U_37)
| U_37 = sdtpldt0(U_31,U_30)
| ~ aElement0(U_30)
| ~ aSet0(U_31) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_18,plain,
( ~ aElementOf0(sK3(U_31,U_30,U_37),U_31)
| ~ aElement0(sK3(U_31,U_30,U_37))
| ~ aElementOf0(sK4(U_31,U_30,U_37),U_37)
| ~ aSet0(U_37)
| U_37 = sdtpldt0(U_31,U_30)
| ~ aElement0(U_30)
| ~ aSet0(U_31) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_19,plain,
( sK3(U_31,U_30,U_37) != U_30
| ~ aElement0(sK3(U_31,U_30,U_37))
| ~ aElementOf0(sK4(U_31,U_30,U_37),U_37)
| ~ aSet0(U_37)
| U_37 = sdtpldt0(U_31,U_30)
| ~ aElement0(U_30)
| ~ aSet0(U_31) ),
inference(clausify,[status(thm)],[f_15_5]) ).
fof(f_16_1,plain,
! [W0,W1] :
( ! [W2] :
( ( W2 = sdtmndt0(W0,W1)
| ? [W3] :
( ( ~ aElementOf0(W3,W2)
& W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) )
| ( ( W3 = W1
| ~ aElementOf0(W3,W0)
| ~ aElement0(W3) )
& aElementOf0(W3,W2) ) )
| ~ aSet0(W2) )
& ( ( ! [W3] :
( ( aElementOf0(W3,W2)
| W3 = W1
| ~ aElementOf0(W3,W0)
| ~ aElement0(W3) )
& ( ( W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtmndt0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mDefDiff]) ).
fof(f_16_2,plain,
! [U_42,U_41] :
( ! [U_40] :
( ( U_40 = sdtmndt0(U_42,U_41)
| ? [U_39] :
( ( ~ aElementOf0(U_39,U_40)
& U_39 != U_41
& aElementOf0(U_39,U_42)
& aElement0(U_39) )
| ( ( U_39 = U_41
| ~ aElementOf0(U_39,U_42)
| ~ aElement0(U_39) )
& aElementOf0(U_39,U_40) ) )
| ~ aSet0(U_40) )
& ( ( ! [U_38] :
( ( aElementOf0(U_38,U_40)
| U_38 = U_41
| ~ aElementOf0(U_38,U_42)
| ~ aElement0(U_38) )
& ( ( U_38 != U_41
& aElementOf0(U_38,U_42)
& aElement0(U_38) )
| ~ aElementOf0(U_38,U_40) ) )
& aSet0(U_40) )
| U_40 != sdtmndt0(U_42,U_41) ) )
| ~ aElement0(U_41)
| ~ aSet0(U_42) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_42,U_41] :
( ( ! [U_48] :
( U_48 = sdtmndt0(U_42,U_41)
| ? [U_46] :
( ~ aElementOf0(U_46,U_48)
& U_46 != U_41
& aElementOf0(U_46,U_42)
& aElement0(U_46) )
| ? [U_45] :
( ( U_45 = U_41
| ~ aElementOf0(U_45,U_42)
| ~ aElement0(U_45) )
& aElementOf0(U_45,U_48) )
| ~ aSet0(U_48) )
& ! [U_47] :
( ( ! [U_44] :
( aElementOf0(U_44,U_47)
| U_44 = U_41
| ~ aElementOf0(U_44,U_42)
| ~ aElement0(U_44) )
& ! [U_43] :
( ( U_43 != U_41
& aElementOf0(U_43,U_42)
& aElement0(U_43) )
| ~ aElementOf0(U_43,U_47) )
& aSet0(U_47) )
| U_47 != sdtmndt0(U_42,U_41) ) )
| ~ aElement0(U_41)
| ~ aSet0(U_42) ),
inference(miniscope,[status(thm)],[f_16_2]) ).
fof(f_16_4,plain,
! [U_42,U_41] :
( ( ! [U_48] :
( U_48 = sdtmndt0(U_42,U_41)
| ? [U_46] :
( ~ aElementOf0(U_46,U_48)
& U_46 != U_41
& aElementOf0(U_46,U_42)
& aElement0(U_46) )
| ( ( sK5(U_42,U_41,U_48) = U_41
| ~ aElementOf0(sK5(U_42,U_41,U_48),U_42)
| ~ aElement0(sK5(U_42,U_41,U_48)) )
& aElementOf0(sK5(U_42,U_41,U_48),U_48) )
| ~ aSet0(U_48) )
& ! [U_47] :
( ( ! [U_44] :
( aElementOf0(U_44,U_47)
| U_44 = U_41
| ~ aElementOf0(U_44,U_42)
| ~ aElement0(U_44) )
& ! [U_43] :
( ( U_43 != U_41
& aElementOf0(U_43,U_42)
& aElement0(U_43) )
| ~ aElementOf0(U_43,U_47) )
& aSet0(U_47) )
| U_47 != sdtmndt0(U_42,U_41) ) )
| ~ aElement0(U_41)
| ~ aSet0(U_42) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_45,sK5(U_42,U_41,U_48))],[f_16_3]) ).
fof(f_16_5,plain,
! [U_42,U_41] :
( ( ! [U_48] :
( U_48 = sdtmndt0(U_42,U_41)
| ( ~ aElementOf0(sK6(U_42,U_41,U_48),U_48)
& sK6(U_42,U_41,U_48) != U_41
& aElementOf0(sK6(U_42,U_41,U_48),U_42)
& aElement0(sK6(U_42,U_41,U_48)) )
| ( ( sK5(U_42,U_41,U_48) = U_41
| ~ aElementOf0(sK5(U_42,U_41,U_48),U_42)
| ~ aElement0(sK5(U_42,U_41,U_48)) )
& aElementOf0(sK5(U_42,U_41,U_48),U_48) )
| ~ aSet0(U_48) )
& ! [U_47] :
( ( ! [U_44] :
( aElementOf0(U_44,U_47)
| U_44 = U_41
| ~ aElementOf0(U_44,U_42)
| ~ aElement0(U_44) )
& ! [U_43] :
( ( U_43 != U_41
& aElementOf0(U_43,U_42)
& aElement0(U_43) )
| ~ aElementOf0(U_43,U_47) )
& aSet0(U_47) )
| U_47 != sdtmndt0(U_42,U_41) ) )
| ~ aElement0(U_41)
| ~ aSet0(U_42) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_46,sK6(U_42,U_41,U_48))],[f_16_4]) ).
cnf(f_16_6,plain,
( aSet0(U_47)
| U_47 != sdtmndt0(U_42,U_41)
| ~ aElement0(U_41)
| ~ aSet0(U_42) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_7,plain,
( aElement0(U_43)
| ~ aElementOf0(U_43,U_47)
| U_47 != sdtmndt0(U_42,U_41)
| ~ aElement0(U_41)
| ~ aSet0(U_42) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_8,plain,
( aElementOf0(U_43,U_42)
| ~ aElementOf0(U_43,U_47)
| U_47 != sdtmndt0(U_42,U_41)
| ~ aElement0(U_41)
| ~ aSet0(U_42) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_9,plain,
( U_43 != U_41
| ~ aElementOf0(U_43,U_47)
| U_47 != sdtmndt0(U_42,U_41)
| ~ aElement0(U_41)
| ~ aSet0(U_42) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_10,plain,
( aElementOf0(U_44,U_47)
| U_44 = U_41
| ~ aElementOf0(U_44,U_42)
| ~ aElement0(U_44)
| U_47 != sdtmndt0(U_42,U_41)
| ~ aElement0(U_41)
| ~ aSet0(U_42) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_11,plain,
( aElement0(sK6(U_42,U_41,U_48))
| aElementOf0(sK5(U_42,U_41,U_48),U_48)
| ~ aSet0(U_48)
| U_48 = sdtmndt0(U_42,U_41)
| ~ aElement0(U_41)
| ~ aSet0(U_42) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_12,plain,
( aElementOf0(sK6(U_42,U_41,U_48),U_42)
| aElementOf0(sK5(U_42,U_41,U_48),U_48)
| ~ aSet0(U_48)
| U_48 = sdtmndt0(U_42,U_41)
| ~ aElement0(U_41)
| ~ aSet0(U_42) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_13,plain,
( sK6(U_42,U_41,U_48) != U_41
| aElementOf0(sK5(U_42,U_41,U_48),U_48)
| ~ aSet0(U_48)
| U_48 = sdtmndt0(U_42,U_41)
| ~ aElement0(U_41)
| ~ aSet0(U_42) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_14,plain,
( ~ aElementOf0(sK6(U_42,U_41,U_48),U_48)
| aElementOf0(sK5(U_42,U_41,U_48),U_48)
| ~ aSet0(U_48)
| U_48 = sdtmndt0(U_42,U_41)
| ~ aElement0(U_41)
| ~ aSet0(U_42) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_15,plain,
( aElement0(sK6(U_42,U_41,U_48))
| sK5(U_42,U_41,U_48) = U_41
| ~ aElementOf0(sK5(U_42,U_41,U_48),U_42)
| ~ aElement0(sK5(U_42,U_41,U_48))
| ~ aSet0(U_48)
| U_48 = sdtmndt0(U_42,U_41)
| ~ aElement0(U_41)
| ~ aSet0(U_42) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_16,plain,
( aElementOf0(sK6(U_42,U_41,U_48),U_42)
| sK5(U_42,U_41,U_48) = U_41
| ~ aElementOf0(sK5(U_42,U_41,U_48),U_42)
| ~ aElement0(sK5(U_42,U_41,U_48))
| ~ aSet0(U_48)
| U_48 = sdtmndt0(U_42,U_41)
| ~ aElement0(U_41)
| ~ aSet0(U_42) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_17,plain,
( sK6(U_42,U_41,U_48) != U_41
| sK5(U_42,U_41,U_48) = U_41
| ~ aElementOf0(sK5(U_42,U_41,U_48),U_42)
| ~ aElement0(sK5(U_42,U_41,U_48))
| ~ aSet0(U_48)
| U_48 = sdtmndt0(U_42,U_41)
| ~ aElement0(U_41)
| ~ aSet0(U_42) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_18,plain,
( ~ aElementOf0(sK6(U_42,U_41,U_48),U_48)
| sK5(U_42,U_41,U_48) = U_41
| ~ aElementOf0(sK5(U_42,U_41,U_48),U_42)
| ~ aElement0(sK5(U_42,U_41,U_48))
| ~ aSet0(U_48)
| U_48 = sdtmndt0(U_42,U_41)
| ~ aElement0(U_41)
| ~ aSet0(U_42) ),
inference(clausify,[status(thm)],[f_16_5]) ).
fof(f_17_1,plain,
! [W0] :
( ! [W1] :
( sdtpldt0(sdtmndt0(W0,W1),W1) = W0
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mConsDiff]) ).
fof(f_17_2,plain,
! [U_50] :
( ! [U_49] :
( sdtpldt0(sdtmndt0(U_50,U_49),U_49) = U_50
| ~ aElementOf0(U_49,U_50) )
| ~ aSet0(U_50) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( sdtpldt0(sdtmndt0(U_50,U_49),U_49) = U_50
| ~ aElementOf0(U_49,U_50)
| ~ aSet0(U_50) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [W0,W1] :
( sdtmndt0(sdtpldt0(W1,W0),W0) = W1
| aElementOf0(W0,W1)
| ~ aSet0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mDiffCons]) ).
fof(f_18_2,plain,
! [U_52,U_51] :
( sdtmndt0(sdtpldt0(U_51,U_52),U_52) = U_51
| aElementOf0(U_52,U_51)
| ~ aSet0(U_51)
| ~ aElement0(U_52) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( sdtmndt0(sdtpldt0(U_51,U_52),U_52) = U_51
| aElementOf0(U_52,U_51)
| ~ aSet0(U_51)
| ~ aElement0(U_52) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [W0] :
( ! [W1] :
( isCountable0(sdtpldt0(W1,W0))
| ~ isCountable0(W1)
| ~ aSet0(W1) )
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mCConsSet]) ).
fof(f_19_2,plain,
! [U_54] :
( ! [U_53] :
( isCountable0(sdtpldt0(U_53,U_54))
| ~ isCountable0(U_53)
| ~ aSet0(U_53) )
| ~ aElement0(U_54) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( isCountable0(sdtpldt0(U_53,U_54))
| ~ isCountable0(U_53)
| ~ aSet0(U_53)
| ~ aElement0(U_54) ),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
! [W0] :
( ! [W1] :
( isCountable0(sdtmndt0(W1,W0))
| ~ isCountable0(W1)
| ~ aSet0(W1) )
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mCDiffSet]) ).
fof(f_20_2,plain,
! [U_56] :
( ! [U_55] :
( isCountable0(sdtmndt0(U_55,U_56))
| ~ isCountable0(U_55)
| ~ aSet0(U_55) )
| ~ aElement0(U_56) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( isCountable0(sdtmndt0(U_55,U_56))
| ~ isCountable0(U_55)
| ~ aSet0(U_55)
| ~ aElement0(U_56) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
! [W0] :
( ! [W1] :
( isFinite0(sdtpldt0(W1,W0))
| ~ isFinite0(W1)
| ~ aSet0(W1) )
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mFConsSet]) ).
fof(f_21_2,plain,
! [U_58] :
( ! [U_57] :
( isFinite0(sdtpldt0(U_57,U_58))
| ~ isFinite0(U_57)
| ~ aSet0(U_57) )
| ~ aElement0(U_58) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
( isFinite0(sdtpldt0(U_57,U_58))
| ~ isFinite0(U_57)
| ~ aSet0(U_57)
| ~ aElement0(U_58) ),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
! [W0] :
( ! [W1] :
( isFinite0(sdtmndt0(W1,W0))
| ~ isFinite0(W1)
| ~ aSet0(W1) )
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mFDiffSet]) ).
fof(f_22_2,plain,
! [U_60] :
( ! [U_59] :
( isFinite0(sdtmndt0(U_59,U_60))
| ~ isFinite0(U_59)
| ~ aSet0(U_59) )
| ~ aElement0(U_60) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( isFinite0(sdtmndt0(U_59,U_60))
| ~ isFinite0(U_59)
| ~ aSet0(U_59)
| ~ aElement0(U_60) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mNATSet]) ).
cnf(f_23_2,plain,
aSet0(szNzAzT0),
inference(clausify,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
isCountable0(szNzAzT0),
inference(clausify,[status(thm)],[f_23_1]) ).
fof(f_24_1,plain,
aElementOf0(sz00,szNzAzT0),
inference(fof_nnf,[status(thm)],[mZeroNum]) ).
cnf(f_24_2,plain,
aElementOf0(sz00,szNzAzT0),
inference(clausify,[status(thm)],[f_24_1]) ).
fof(f_25_1,plain,
! [W0] :
( ( szszuzczcdt0(W0) != sz00
& aElementOf0(szszuzczcdt0(W0),szNzAzT0) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mSuccNum]) ).
fof(f_25_2,plain,
! [U_61] :
( ( szszuzczcdt0(U_61) != sz00
& aElementOf0(szszuzczcdt0(U_61),szNzAzT0) )
| ~ aElementOf0(U_61,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( aElementOf0(szszuzczcdt0(U_61),szNzAzT0)
| ~ aElementOf0(U_61,szNzAzT0) ),
inference(clausify,[status(thm)],[f_25_2]) ).
cnf(f_25_4,plain,
( szszuzczcdt0(U_61) != sz00
| ~ aElementOf0(U_61,szNzAzT0) ),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
! [W0,W1] :
( W0 = W1
| szszuzczcdt0(W0) != szszuzczcdt0(W1)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mSuccEquSucc]) ).
fof(f_26_2,plain,
! [U_63,U_62] :
( U_63 = U_62
| szszuzczcdt0(U_63) != szszuzczcdt0(U_62)
| ~ aElementOf0(U_62,szNzAzT0)
| ~ aElementOf0(U_63,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
( U_63 = U_62
| szszuzczcdt0(U_63) != szszuzczcdt0(U_62)
| ~ aElementOf0(U_62,szNzAzT0)
| ~ aElementOf0(U_63,szNzAzT0) ),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
! [W0] :
( ? [W1] :
( W0 = szszuzczcdt0(W1)
& aElementOf0(W1,szNzAzT0) )
| W0 = sz00
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mNatExtra]) ).
fof(f_27_2,plain,
! [U_65] :
( ? [U_64] :
( U_65 = szszuzczcdt0(U_64)
& aElementOf0(U_64,szNzAzT0) )
| U_65 = sz00
| ~ aElementOf0(U_65,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_65] :
( ( U_65 = szszuzczcdt0(sK7(U_65))
& aElementOf0(sK7(U_65),szNzAzT0) )
| U_65 = sz00
| ~ aElementOf0(U_65,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_64,sK7(U_65))],[f_27_2]) ).
cnf(f_27_4,plain,
( aElementOf0(sK7(U_65),szNzAzT0)
| U_65 = sz00
| ~ aElementOf0(U_65,szNzAzT0) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_5,plain,
( U_65 = szszuzczcdt0(sK7(U_65))
| U_65 = sz00
| ~ aElementOf0(U_65,szNzAzT0) ),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
! [W0] :
( W0 != szszuzczcdt0(W0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mNatNSucc]) ).
fof(f_28_2,plain,
! [U_66] :
( U_66 != szszuzczcdt0(U_66)
| ~ aElementOf0(U_66,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( U_66 != szszuzczcdt0(U_66)
| ~ aElementOf0(U_66,szNzAzT0) ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
! [W0,W1] :
( $true
| ~ sdtlseqdt0(W0,W1)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mLessRel]) ).
fof(f_29_2,plain,
! [U_68,U_67] :
( $true
| ~ sdtlseqdt0(U_68,U_67)
| ~ aElementOf0(U_67,szNzAzT0)
| ~ aElementOf0(U_68,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( $true
| ~ sdtlseqdt0(U_68,U_67)
| ~ aElementOf0(U_67,szNzAzT0)
| ~ aElementOf0(U_68,szNzAzT0) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
! [W0] :
( sdtlseqdt0(sz00,W0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mZeroLess]) ).
fof(f_30_2,plain,
! [U_69] :
( sdtlseqdt0(sz00,U_69)
| ~ aElementOf0(U_69,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( sdtlseqdt0(sz00,U_69)
| ~ aElementOf0(U_69,szNzAzT0) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
! [W0] :
( ~ sdtlseqdt0(szszuzczcdt0(W0),sz00)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mNoScLessZr]) ).
fof(f_31_2,plain,
! [U_70] :
( ~ sdtlseqdt0(szszuzczcdt0(U_70),sz00)
| ~ aElementOf0(U_70,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( ~ sdtlseqdt0(szszuzczcdt0(U_70),sz00)
| ~ aElementOf0(U_70,szNzAzT0) ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
! [W0,W1] :
( ( ( sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(W1)) )
& ( sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(W1))
| ~ sdtlseqdt0(W0,W1) ) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mSuccLess]) ).
fof(f_32_2,plain,
! [U_72,U_71] :
( ( ( sdtlseqdt0(U_72,U_71)
| ~ sdtlseqdt0(szszuzczcdt0(U_72),szszuzczcdt0(U_71)) )
& ( sdtlseqdt0(szszuzczcdt0(U_72),szszuzczcdt0(U_71))
| ~ sdtlseqdt0(U_72,U_71) ) )
| ~ aElementOf0(U_71,szNzAzT0)
| ~ aElementOf0(U_72,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( sdtlseqdt0(szszuzczcdt0(U_72),szszuzczcdt0(U_71))
| ~ sdtlseqdt0(U_72,U_71)
| ~ aElementOf0(U_71,szNzAzT0)
| ~ aElementOf0(U_72,szNzAzT0) ),
inference(clausify,[status(thm)],[f_32_2]) ).
cnf(f_32_4,plain,
( sdtlseqdt0(U_72,U_71)
| ~ sdtlseqdt0(szszuzczcdt0(U_72),szszuzczcdt0(U_71))
| ~ aElementOf0(U_71,szNzAzT0)
| ~ aElementOf0(U_72,szNzAzT0) ),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,plain,
! [W0] :
( sdtlseqdt0(W0,szszuzczcdt0(W0))
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mLessSucc]) ).
fof(f_33_2,plain,
! [U_73] :
( sdtlseqdt0(U_73,szszuzczcdt0(U_73))
| ~ aElementOf0(U_73,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
( sdtlseqdt0(U_73,szszuzczcdt0(U_73))
| ~ aElementOf0(U_73,szNzAzT0) ),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_1,plain,
! [W0] :
( sdtlseqdt0(W0,W0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mLessRefl]) ).
fof(f_34_2,plain,
! [U_74] :
( sdtlseqdt0(U_74,U_74)
| ~ aElementOf0(U_74,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
( sdtlseqdt0(U_74,U_74)
| ~ aElementOf0(U_74,szNzAzT0) ),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_1,plain,
! [W0,W1] :
( W0 = W1
| ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mLessASymm]) ).
fof(f_35_2,plain,
! [U_76,U_75] :
( U_76 = U_75
| ~ sdtlseqdt0(U_75,U_76)
| ~ sdtlseqdt0(U_76,U_75)
| ~ aElementOf0(U_75,szNzAzT0)
| ~ aElementOf0(U_76,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
( U_76 = U_75
| ~ sdtlseqdt0(U_75,U_76)
| ~ sdtlseqdt0(U_76,U_75)
| ~ aElementOf0(U_75,szNzAzT0)
| ~ aElementOf0(U_76,szNzAzT0) ),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_1,plain,
! [W0,W1,W2] :
( sdtlseqdt0(W0,W2)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1)
| ~ aElementOf0(W2,szNzAzT0)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mLessTrans]) ).
fof(f_36_2,plain,
! [U_79,U_78,U_77] :
( sdtlseqdt0(U_79,U_77)
| ~ sdtlseqdt0(U_78,U_77)
| ~ sdtlseqdt0(U_79,U_78)
| ~ aElementOf0(U_77,szNzAzT0)
| ~ aElementOf0(U_78,szNzAzT0)
| ~ aElementOf0(U_79,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
cnf(f_36_3,plain,
( sdtlseqdt0(U_79,U_77)
| ~ sdtlseqdt0(U_78,U_77)
| ~ sdtlseqdt0(U_79,U_78)
| ~ aElementOf0(U_77,szNzAzT0)
| ~ aElementOf0(U_78,szNzAzT0)
| ~ aElementOf0(U_79,szNzAzT0) ),
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,plain,
! [W0,W1] :
( sdtlseqdt0(szszuzczcdt0(W1),W0)
| sdtlseqdt0(W0,W1)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mLessTotal]) ).
fof(f_37_2,plain,
! [U_81,U_80] :
( sdtlseqdt0(szszuzczcdt0(U_80),U_81)
| sdtlseqdt0(U_81,U_80)
| ~ aElementOf0(U_80,szNzAzT0)
| ~ aElementOf0(U_81,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
( sdtlseqdt0(szszuzczcdt0(U_80),U_81)
| sdtlseqdt0(U_81,U_80)
| ~ aElementOf0(U_80,szNzAzT0)
| ~ aElementOf0(U_81,szNzAzT0) ),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_1,plain,
! [W0,W1] :
( $true
| ~ iLess0(W0,W1)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mIHSort]) ).
fof(f_38_2,plain,
! [U_83,U_82] :
( $true
| ~ iLess0(U_83,U_82)
| ~ aElementOf0(U_82,szNzAzT0)
| ~ aElementOf0(U_83,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
cnf(f_38_3,plain,
( $true
| ~ iLess0(U_83,U_82)
| ~ aElementOf0(U_82,szNzAzT0)
| ~ aElementOf0(U_83,szNzAzT0) ),
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_1,plain,
! [W0] :
( iLess0(W0,szszuzczcdt0(W0))
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mIH]) ).
fof(f_39_2,plain,
! [U_84] :
( iLess0(U_84,szszuzczcdt0(U_84))
| ~ aElementOf0(U_84,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
cnf(f_39_3,plain,
( iLess0(U_84,szszuzczcdt0(U_84))
| ~ aElementOf0(U_84,szNzAzT0) ),
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_1,plain,
! [W0] :
( aElement0(sbrdtbr0(W0))
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mCardS]) ).
fof(f_40_2,plain,
! [U_85] :
( aElement0(sbrdtbr0(U_85))
| ~ aSet0(U_85) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
( aElement0(sbrdtbr0(U_85))
| ~ aSet0(U_85) ),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_1,plain,
! [W0] :
( ( ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
| ~ isFinite0(W0) )
& ( isFinite0(W0)
| ~ aElementOf0(sbrdtbr0(W0),szNzAzT0) ) )
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mCardNum]) ).
fof(f_41_2,plain,
! [U_86] :
( ( ( aElementOf0(sbrdtbr0(U_86),szNzAzT0)
| ~ isFinite0(U_86) )
& ( isFinite0(U_86)
| ~ aElementOf0(sbrdtbr0(U_86),szNzAzT0) ) )
| ~ aSet0(U_86) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
cnf(f_41_3,plain,
( isFinite0(U_86)
| ~ aElementOf0(sbrdtbr0(U_86),szNzAzT0)
| ~ aSet0(U_86) ),
inference(clausify,[status(thm)],[f_41_2]) ).
cnf(f_41_4,plain,
( aElementOf0(sbrdtbr0(U_86),szNzAzT0)
| ~ isFinite0(U_86)
| ~ aSet0(U_86) ),
inference(clausify,[status(thm)],[f_41_2]) ).
fof(f_42_1,plain,
! [W0] :
( ( ( sbrdtbr0(W0) = sz00
| W0 != slcrc0 )
& ( W0 = slcrc0
| sbrdtbr0(W0) != sz00 ) )
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mCardEmpty]) ).
fof(f_42_2,plain,
! [U_87] :
( ( ( sbrdtbr0(U_87) = sz00
| U_87 != slcrc0 )
& ( U_87 = slcrc0
| sbrdtbr0(U_87) != sz00 ) )
| ~ aSet0(U_87) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
cnf(f_42_3,plain,
( U_87 = slcrc0
| sbrdtbr0(U_87) != sz00
| ~ aSet0(U_87) ),
inference(clausify,[status(thm)],[f_42_2]) ).
cnf(f_42_4,plain,
( sbrdtbr0(U_87) = sz00
| U_87 != slcrc0
| ~ aSet0(U_87) ),
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_43_1,plain,
! [W0] :
( ! [W1] :
( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0))
| aElementOf0(W1,W0)
| ~ aElement0(W1) )
| ~ isFinite0(W0)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mCardCons]) ).
fof(f_43_2,plain,
! [U_89] :
( ! [U_88] :
( sbrdtbr0(sdtpldt0(U_89,U_88)) = szszuzczcdt0(sbrdtbr0(U_89))
| aElementOf0(U_88,U_89)
| ~ aElement0(U_88) )
| ~ isFinite0(U_89)
| ~ aSet0(U_89) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
cnf(f_43_3,plain,
( sbrdtbr0(sdtpldt0(U_89,U_88)) = szszuzczcdt0(sbrdtbr0(U_89))
| aElementOf0(U_88,U_89)
| ~ aElement0(U_88)
| ~ isFinite0(U_89)
| ~ aSet0(U_89) ),
inference(clausify,[status(thm)],[f_43_2]) ).
fof(f_44_1,plain,
! [W0] :
( ! [W1] :
( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0)
| ~ aElementOf0(W1,W0)
| ~ isFinite0(W0) )
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mCardDiff]) ).
fof(f_44_2,plain,
! [U_91] :
( ! [U_90] :
( szszuzczcdt0(sbrdtbr0(sdtmndt0(U_91,U_90))) = sbrdtbr0(U_91)
| ~ aElementOf0(U_90,U_91)
| ~ isFinite0(U_91) )
| ~ aSet0(U_91) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
cnf(f_44_3,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(U_91,U_90))) = sbrdtbr0(U_91)
| ~ aElementOf0(U_90,U_91)
| ~ isFinite0(U_91)
| ~ aSet0(U_91) ),
inference(clausify,[status(thm)],[f_44_2]) ).
fof(f_45_1,plain,
! [W0] :
( ! [W1] :
( sdtlseqdt0(sbrdtbr0(W1),sbrdtbr0(W0))
| ~ aSubsetOf0(W1,W0)
| ~ isFinite0(W0) )
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mCardSub]) ).
fof(f_45_2,plain,
! [U_93] :
( ! [U_92] :
( sdtlseqdt0(sbrdtbr0(U_92),sbrdtbr0(U_93))
| ~ aSubsetOf0(U_92,U_93)
| ~ isFinite0(U_93) )
| ~ aSet0(U_93) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
cnf(f_45_3,plain,
( sdtlseqdt0(sbrdtbr0(U_92),sbrdtbr0(U_93))
| ~ aSubsetOf0(U_92,U_93)
| ~ isFinite0(U_93)
| ~ aSet0(U_93) ),
inference(clausify,[status(thm)],[f_45_2]) ).
fof(f_46_1,plain,
! [W0,W1] :
( ? [W2] :
( sbrdtbr0(W2) = W1
& aSubsetOf0(W2,W0) )
| ~ sdtlseqdt0(W1,sbrdtbr0(W0))
| ~ isFinite0(W0)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mCardSubEx]) ).
fof(f_46_2,plain,
! [U_96,U_95] :
( ? [U_94] :
( sbrdtbr0(U_94) = U_95
& aSubsetOf0(U_94,U_96) )
| ~ sdtlseqdt0(U_95,sbrdtbr0(U_96))
| ~ isFinite0(U_96)
| ~ aElementOf0(U_95,szNzAzT0)
| ~ aSet0(U_96) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_96,U_95] :
( ( sbrdtbr0(sK8(U_96,U_95)) = U_95
& aSubsetOf0(sK8(U_96,U_95),U_96) )
| ~ sdtlseqdt0(U_95,sbrdtbr0(U_96))
| ~ isFinite0(U_96)
| ~ aElementOf0(U_95,szNzAzT0)
| ~ aSet0(U_96) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_94,sK8(U_96,U_95))],[f_46_2]) ).
cnf(f_46_4,plain,
( aSubsetOf0(sK8(U_96,U_95),U_96)
| ~ sdtlseqdt0(U_95,sbrdtbr0(U_96))
| ~ isFinite0(U_96)
| ~ aElementOf0(U_95,szNzAzT0)
| ~ aSet0(U_96) ),
inference(clausify,[status(thm)],[f_46_3]) ).
cnf(f_46_5,plain,
( sbrdtbr0(sK8(U_96,U_95)) = U_95
| ~ sdtlseqdt0(U_95,sbrdtbr0(U_96))
| ~ isFinite0(U_96)
| ~ aElementOf0(U_95,szNzAzT0)
| ~ aSet0(U_96) ),
inference(clausify,[status(thm)],[f_46_3]) ).
fof(f_47_1,plain,
! [W0] :
( ! [W1] :
( ( W1 = szmzizndt0(W0)
| ? [W2] :
( ~ sdtlseqdt0(W1,W2)
& aElementOf0(W2,W0) )
| ~ aElementOf0(W1,W0) )
& ( ( ! [W2] :
( sdtlseqdt0(W1,W2)
| ~ aElementOf0(W2,W0) )
& aElementOf0(W1,W0) )
| W1 != szmzizndt0(W0) ) )
| W0 = slcrc0
| ~ aSubsetOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mDefMin]) ).
fof(f_47_2,plain,
! [U_100] :
( ! [U_99] :
( ( U_99 = szmzizndt0(U_100)
| ? [U_98] :
( ~ sdtlseqdt0(U_99,U_98)
& aElementOf0(U_98,U_100) )
| ~ aElementOf0(U_99,U_100) )
& ( ( ! [U_97] :
( sdtlseqdt0(U_99,U_97)
| ~ aElementOf0(U_97,U_100) )
& aElementOf0(U_99,U_100) )
| U_99 != szmzizndt0(U_100) ) )
| U_100 = slcrc0
| ~ aSubsetOf0(U_100,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_100] :
( ( ! [U_102] :
( U_102 = szmzizndt0(U_100)
| ? [U_98] :
( ~ sdtlseqdt0(U_102,U_98)
& aElementOf0(U_98,U_100) )
| ~ aElementOf0(U_102,U_100) )
& ! [U_101] :
( ( ! [U_97] :
( sdtlseqdt0(U_101,U_97)
| ~ aElementOf0(U_97,U_100) )
& aElementOf0(U_101,U_100) )
| U_101 != szmzizndt0(U_100) ) )
| U_100 = slcrc0
| ~ aSubsetOf0(U_100,szNzAzT0) ),
inference(miniscope,[status(thm)],[f_47_2]) ).
fof(f_47_4,plain,
! [U_100] :
( ( ! [U_102] :
( U_102 = szmzizndt0(U_100)
| ( ~ sdtlseqdt0(U_102,sK9(U_100,U_102))
& aElementOf0(sK9(U_100,U_102),U_100) )
| ~ aElementOf0(U_102,U_100) )
& ! [U_101] :
( ( ! [U_97] :
( sdtlseqdt0(U_101,U_97)
| ~ aElementOf0(U_97,U_100) )
& aElementOf0(U_101,U_100) )
| U_101 != szmzizndt0(U_100) ) )
| U_100 = slcrc0
| ~ aSubsetOf0(U_100,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_98,sK9(U_100,U_102))],[f_47_3]) ).
cnf(f_47_5,plain,
( aElementOf0(U_101,U_100)
| U_101 != szmzizndt0(U_100)
| U_100 = slcrc0
| ~ aSubsetOf0(U_100,szNzAzT0) ),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_6,plain,
( sdtlseqdt0(U_101,U_97)
| ~ aElementOf0(U_97,U_100)
| U_101 != szmzizndt0(U_100)
| U_100 = slcrc0
| ~ aSubsetOf0(U_100,szNzAzT0) ),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_7,plain,
( aElementOf0(sK9(U_100,U_102),U_100)
| ~ aElementOf0(U_102,U_100)
| U_102 = szmzizndt0(U_100)
| U_100 = slcrc0
| ~ aSubsetOf0(U_100,szNzAzT0) ),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_8,plain,
( ~ sdtlseqdt0(U_102,sK9(U_100,U_102))
| ~ aElementOf0(U_102,U_100)
| U_102 = szmzizndt0(U_100)
| U_100 = slcrc0
| ~ aSubsetOf0(U_100,szNzAzT0) ),
inference(clausify,[status(thm)],[f_47_4]) ).
fof(f_48_1,plain,
! [W0] :
( ! [W1] :
( ( W1 = szmzazxdt0(W0)
| ? [W2] :
( ~ sdtlseqdt0(W2,W1)
& aElementOf0(W2,W0) )
| ~ aElementOf0(W1,W0) )
& ( ( ! [W2] :
( sdtlseqdt0(W2,W1)
| ~ aElementOf0(W2,W0) )
& aElementOf0(W1,W0) )
| W1 != szmzazxdt0(W0) ) )
| W0 = slcrc0
| ~ isFinite0(W0)
| ~ aSubsetOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mDefMax]) ).
fof(f_48_2,plain,
! [U_106] :
( ! [U_105] :
( ( U_105 = szmzazxdt0(U_106)
| ? [U_104] :
( ~ sdtlseqdt0(U_104,U_105)
& aElementOf0(U_104,U_106) )
| ~ aElementOf0(U_105,U_106) )
& ( ( ! [U_103] :
( sdtlseqdt0(U_103,U_105)
| ~ aElementOf0(U_103,U_106) )
& aElementOf0(U_105,U_106) )
| U_105 != szmzazxdt0(U_106) ) )
| U_106 = slcrc0
| ~ isFinite0(U_106)
| ~ aSubsetOf0(U_106,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
! [U_106] :
( ( ! [U_108] :
( U_108 = szmzazxdt0(U_106)
| ? [U_104] :
( ~ sdtlseqdt0(U_104,U_108)
& aElementOf0(U_104,U_106) )
| ~ aElementOf0(U_108,U_106) )
& ! [U_107] :
( ( ! [U_103] :
( sdtlseqdt0(U_103,U_107)
| ~ aElementOf0(U_103,U_106) )
& aElementOf0(U_107,U_106) )
| U_107 != szmzazxdt0(U_106) ) )
| U_106 = slcrc0
| ~ isFinite0(U_106)
| ~ aSubsetOf0(U_106,szNzAzT0) ),
inference(miniscope,[status(thm)],[f_48_2]) ).
fof(f_48_4,plain,
! [U_106] :
( ( ! [U_108] :
( U_108 = szmzazxdt0(U_106)
| ( ~ sdtlseqdt0(sK10(U_106,U_108),U_108)
& aElementOf0(sK10(U_106,U_108),U_106) )
| ~ aElementOf0(U_108,U_106) )
& ! [U_107] :
( ( ! [U_103] :
( sdtlseqdt0(U_103,U_107)
| ~ aElementOf0(U_103,U_106) )
& aElementOf0(U_107,U_106) )
| U_107 != szmzazxdt0(U_106) ) )
| U_106 = slcrc0
| ~ isFinite0(U_106)
| ~ aSubsetOf0(U_106,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_104,sK10(U_106,U_108))],[f_48_3]) ).
cnf(f_48_5,plain,
( aElementOf0(U_107,U_106)
| U_107 != szmzazxdt0(U_106)
| U_106 = slcrc0
| ~ isFinite0(U_106)
| ~ aSubsetOf0(U_106,szNzAzT0) ),
inference(clausify,[status(thm)],[f_48_4]) ).
cnf(f_48_6,plain,
( sdtlseqdt0(U_103,U_107)
| ~ aElementOf0(U_103,U_106)
| U_107 != szmzazxdt0(U_106)
| U_106 = slcrc0
| ~ isFinite0(U_106)
| ~ aSubsetOf0(U_106,szNzAzT0) ),
inference(clausify,[status(thm)],[f_48_4]) ).
cnf(f_48_7,plain,
( aElementOf0(sK10(U_106,U_108),U_106)
| ~ aElementOf0(U_108,U_106)
| U_108 = szmzazxdt0(U_106)
| U_106 = slcrc0
| ~ isFinite0(U_106)
| ~ aSubsetOf0(U_106,szNzAzT0) ),
inference(clausify,[status(thm)],[f_48_4]) ).
cnf(f_48_8,plain,
( ~ sdtlseqdt0(sK10(U_106,U_108),U_108)
| ~ aElementOf0(U_108,U_106)
| U_108 = szmzazxdt0(U_106)
| U_106 = slcrc0
| ~ isFinite0(U_106)
| ~ aSubsetOf0(U_106,szNzAzT0) ),
inference(clausify,[status(thm)],[f_48_4]) ).
fof(f_49_1,plain,
! [W0,W1] :
( szmzizndt0(W0) = szmzizndt0(W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aElementOf0(szmzizndt0(W0),W1)
| W1 = slcrc0
| W0 = slcrc0
| ~ aSubsetOf0(W1,szNzAzT0)
| ~ aSubsetOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mMinMin]) ).
fof(f_49_2,plain,
! [U_110,U_109] :
( szmzizndt0(U_110) = szmzizndt0(U_109)
| ~ aElementOf0(szmzizndt0(U_109),U_110)
| ~ aElementOf0(szmzizndt0(U_110),U_109)
| U_109 = slcrc0
| U_110 = slcrc0
| ~ aSubsetOf0(U_109,szNzAzT0)
| ~ aSubsetOf0(U_110,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
cnf(f_49_3,plain,
( szmzizndt0(U_110) = szmzizndt0(U_109)
| ~ aElementOf0(szmzizndt0(U_109),U_110)
| ~ aElementOf0(szmzizndt0(U_110),U_109)
| U_109 = slcrc0
| U_110 = slcrc0
| ~ aSubsetOf0(U_109,szNzAzT0)
| ~ aSubsetOf0(U_110,szNzAzT0) ),
inference(clausify,[status(thm)],[f_49_2]) ).
fof(f_50_1,plain,
! [W0] :
( ! [W1] :
( ( W1 = slbdtrb0(W0)
| ? [W2] :
( ( ~ aElementOf0(W2,W1)
& sdtlseqdt0(szszuzczcdt0(W2),W0)
& aElementOf0(W2,szNzAzT0) )
| ( ( ~ sdtlseqdt0(szszuzczcdt0(W2),W0)
| ~ aElementOf0(W2,szNzAzT0) )
& aElementOf0(W2,W1) ) )
| ~ aSet0(W1) )
& ( ( ! [W2] :
( ( aElementOf0(W2,W1)
| ~ sdtlseqdt0(szszuzczcdt0(W2),W0)
| ~ aElementOf0(W2,szNzAzT0) )
& ( ( sdtlseqdt0(szszuzczcdt0(W2),W0)
& aElementOf0(W2,szNzAzT0) )
| ~ aElementOf0(W2,W1) ) )
& aSet0(W1) )
| W1 != slbdtrb0(W0) ) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mDefSeg]) ).
fof(f_50_2,plain,
! [U_114] :
( ! [U_113] :
( ( U_113 = slbdtrb0(U_114)
| ? [U_112] :
( ( ~ aElementOf0(U_112,U_113)
& sdtlseqdt0(szszuzczcdt0(U_112),U_114)
& aElementOf0(U_112,szNzAzT0) )
| ( ( ~ sdtlseqdt0(szszuzczcdt0(U_112),U_114)
| ~ aElementOf0(U_112,szNzAzT0) )
& aElementOf0(U_112,U_113) ) )
| ~ aSet0(U_113) )
& ( ( ! [U_111] :
( ( aElementOf0(U_111,U_113)
| ~ sdtlseqdt0(szszuzczcdt0(U_111),U_114)
| ~ aElementOf0(U_111,szNzAzT0) )
& ( ( sdtlseqdt0(szszuzczcdt0(U_111),U_114)
& aElementOf0(U_111,szNzAzT0) )
| ~ aElementOf0(U_111,U_113) ) )
& aSet0(U_113) )
| U_113 != slbdtrb0(U_114) ) )
| ~ aElementOf0(U_114,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
! [U_114] :
( ( ! [U_120] :
( U_120 = slbdtrb0(U_114)
| ? [U_118] :
( ~ aElementOf0(U_118,U_120)
& sdtlseqdt0(szszuzczcdt0(U_118),U_114)
& aElementOf0(U_118,szNzAzT0) )
| ? [U_117] :
( ( ~ sdtlseqdt0(szszuzczcdt0(U_117),U_114)
| ~ aElementOf0(U_117,szNzAzT0) )
& aElementOf0(U_117,U_120) )
| ~ aSet0(U_120) )
& ! [U_119] :
( ( ! [U_116] :
( aElementOf0(U_116,U_119)
| ~ sdtlseqdt0(szszuzczcdt0(U_116),U_114)
| ~ aElementOf0(U_116,szNzAzT0) )
& ! [U_115] :
( ( sdtlseqdt0(szszuzczcdt0(U_115),U_114)
& aElementOf0(U_115,szNzAzT0) )
| ~ aElementOf0(U_115,U_119) )
& aSet0(U_119) )
| U_119 != slbdtrb0(U_114) ) )
| ~ aElementOf0(U_114,szNzAzT0) ),
inference(miniscope,[status(thm)],[f_50_2]) ).
fof(f_50_4,plain,
! [U_114] :
( ( ! [U_120] :
( U_120 = slbdtrb0(U_114)
| ? [U_118] :
( ~ aElementOf0(U_118,U_120)
& sdtlseqdt0(szszuzczcdt0(U_118),U_114)
& aElementOf0(U_118,szNzAzT0) )
| ( ( ~ sdtlseqdt0(szszuzczcdt0(sK11(U_114,U_120)),U_114)
| ~ aElementOf0(sK11(U_114,U_120),szNzAzT0) )
& aElementOf0(sK11(U_114,U_120),U_120) )
| ~ aSet0(U_120) )
& ! [U_119] :
( ( ! [U_116] :
( aElementOf0(U_116,U_119)
| ~ sdtlseqdt0(szszuzczcdt0(U_116),U_114)
| ~ aElementOf0(U_116,szNzAzT0) )
& ! [U_115] :
( ( sdtlseqdt0(szszuzczcdt0(U_115),U_114)
& aElementOf0(U_115,szNzAzT0) )
| ~ aElementOf0(U_115,U_119) )
& aSet0(U_119) )
| U_119 != slbdtrb0(U_114) ) )
| ~ aElementOf0(U_114,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_117,sK11(U_114,U_120))],[f_50_3]) ).
fof(f_50_5,plain,
! [U_114] :
( ( ! [U_120] :
( U_120 = slbdtrb0(U_114)
| ( ~ aElementOf0(sK12(U_114,U_120),U_120)
& sdtlseqdt0(szszuzczcdt0(sK12(U_114,U_120)),U_114)
& aElementOf0(sK12(U_114,U_120),szNzAzT0) )
| ( ( ~ sdtlseqdt0(szszuzczcdt0(sK11(U_114,U_120)),U_114)
| ~ aElementOf0(sK11(U_114,U_120),szNzAzT0) )
& aElementOf0(sK11(U_114,U_120),U_120) )
| ~ aSet0(U_120) )
& ! [U_119] :
( ( ! [U_116] :
( aElementOf0(U_116,U_119)
| ~ sdtlseqdt0(szszuzczcdt0(U_116),U_114)
| ~ aElementOf0(U_116,szNzAzT0) )
& ! [U_115] :
( ( sdtlseqdt0(szszuzczcdt0(U_115),U_114)
& aElementOf0(U_115,szNzAzT0) )
| ~ aElementOf0(U_115,U_119) )
& aSet0(U_119) )
| U_119 != slbdtrb0(U_114) ) )
| ~ aElementOf0(U_114,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_118,sK12(U_114,U_120))],[f_50_4]) ).
cnf(f_50_6,plain,
( aSet0(U_119)
| U_119 != slbdtrb0(U_114)
| ~ aElementOf0(U_114,szNzAzT0) ),
inference(clausify,[status(thm)],[f_50_5]) ).
cnf(f_50_7,plain,
( aElementOf0(U_115,szNzAzT0)
| ~ aElementOf0(U_115,U_119)
| U_119 != slbdtrb0(U_114)
| ~ aElementOf0(U_114,szNzAzT0) ),
inference(clausify,[status(thm)],[f_50_5]) ).
cnf(f_50_8,plain,
( sdtlseqdt0(szszuzczcdt0(U_115),U_114)
| ~ aElementOf0(U_115,U_119)
| U_119 != slbdtrb0(U_114)
| ~ aElementOf0(U_114,szNzAzT0) ),
inference(clausify,[status(thm)],[f_50_5]) ).
cnf(f_50_9,plain,
( aElementOf0(U_116,U_119)
| ~ sdtlseqdt0(szszuzczcdt0(U_116),U_114)
| ~ aElementOf0(U_116,szNzAzT0)
| U_119 != slbdtrb0(U_114)
| ~ aElementOf0(U_114,szNzAzT0) ),
inference(clausify,[status(thm)],[f_50_5]) ).
cnf(f_50_10,plain,
( aElementOf0(sK12(U_114,U_120),szNzAzT0)
| aElementOf0(sK11(U_114,U_120),U_120)
| ~ aSet0(U_120)
| U_120 = slbdtrb0(U_114)
| ~ aElementOf0(U_114,szNzAzT0) ),
inference(clausify,[status(thm)],[f_50_5]) ).
cnf(f_50_11,plain,
( sdtlseqdt0(szszuzczcdt0(sK12(U_114,U_120)),U_114)
| aElementOf0(sK11(U_114,U_120),U_120)
| ~ aSet0(U_120)
| U_120 = slbdtrb0(U_114)
| ~ aElementOf0(U_114,szNzAzT0) ),
inference(clausify,[status(thm)],[f_50_5]) ).
cnf(f_50_12,plain,
( ~ aElementOf0(sK12(U_114,U_120),U_120)
| aElementOf0(sK11(U_114,U_120),U_120)
| ~ aSet0(U_120)
| U_120 = slbdtrb0(U_114)
| ~ aElementOf0(U_114,szNzAzT0) ),
inference(clausify,[status(thm)],[f_50_5]) ).
cnf(f_50_13,plain,
( aElementOf0(sK12(U_114,U_120),szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(sK11(U_114,U_120)),U_114)
| ~ aElementOf0(sK11(U_114,U_120),szNzAzT0)
| ~ aSet0(U_120)
| U_120 = slbdtrb0(U_114)
| ~ aElementOf0(U_114,szNzAzT0) ),
inference(clausify,[status(thm)],[f_50_5]) ).
cnf(f_50_14,plain,
( sdtlseqdt0(szszuzczcdt0(sK12(U_114,U_120)),U_114)
| ~ sdtlseqdt0(szszuzczcdt0(sK11(U_114,U_120)),U_114)
| ~ aElementOf0(sK11(U_114,U_120),szNzAzT0)
| ~ aSet0(U_120)
| U_120 = slbdtrb0(U_114)
| ~ aElementOf0(U_114,szNzAzT0) ),
inference(clausify,[status(thm)],[f_50_5]) ).
cnf(f_50_15,plain,
( ~ aElementOf0(sK12(U_114,U_120),U_120)
| ~ sdtlseqdt0(szszuzczcdt0(sK11(U_114,U_120)),U_114)
| ~ aElementOf0(sK11(U_114,U_120),szNzAzT0)
| ~ aSet0(U_120)
| U_120 = slbdtrb0(U_114)
| ~ aElementOf0(U_114,szNzAzT0) ),
inference(clausify,[status(thm)],[f_50_5]) ).
fof(f_51_1,plain,
! [W0] :
( isFinite0(slbdtrb0(W0))
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mSegFin]) ).
fof(f_51_2,plain,
! [U_121] :
( isFinite0(slbdtrb0(U_121))
| ~ aElementOf0(U_121,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
cnf(f_51_3,plain,
( isFinite0(slbdtrb0(U_121))
| ~ aElementOf0(U_121,szNzAzT0) ),
inference(clausify,[status(thm)],[f_51_2]) ).
fof(f_52_1,plain,
slbdtrb0(sz00) = slcrc0,
inference(fof_nnf,[status(thm)],[mSegZero]) ).
cnf(f_52_2,plain,
slbdtrb0(sz00) = slcrc0,
inference(clausify,[status(thm)],[f_52_1]) ).
fof(f_53_1,plain,
! [W0,W1] :
( ( ( aElementOf0(W0,slbdtrb0(szszuzczcdt0(W1)))
| ( W0 != W1
& ~ aElementOf0(W0,slbdtrb0(W1)) ) )
& ( W0 = W1
| aElementOf0(W0,slbdtrb0(W1))
| ~ aElementOf0(W0,slbdtrb0(szszuzczcdt0(W1))) ) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mSegSucc]) ).
fof(f_53_2,plain,
! [U_123,U_122] :
( ( ( aElementOf0(U_123,slbdtrb0(szszuzczcdt0(U_122)))
| ( U_123 != U_122
& ~ aElementOf0(U_123,slbdtrb0(U_122)) ) )
& ( U_123 = U_122
| aElementOf0(U_123,slbdtrb0(U_122))
| ~ aElementOf0(U_123,slbdtrb0(szszuzczcdt0(U_122))) ) )
| ~ aElementOf0(U_122,szNzAzT0)
| ~ aElementOf0(U_123,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
cnf(f_53_3,plain,
( U_123 = U_122
| aElementOf0(U_123,slbdtrb0(U_122))
| ~ aElementOf0(U_123,slbdtrb0(szszuzczcdt0(U_122)))
| ~ aElementOf0(U_122,szNzAzT0)
| ~ aElementOf0(U_123,szNzAzT0) ),
inference(clausify,[status(thm)],[f_53_2]) ).
cnf(f_53_4,plain,
( ~ aElementOf0(U_123,slbdtrb0(U_122))
| aElementOf0(U_123,slbdtrb0(szszuzczcdt0(U_122)))
| ~ aElementOf0(U_122,szNzAzT0)
| ~ aElementOf0(U_123,szNzAzT0) ),
inference(clausify,[status(thm)],[f_53_2]) ).
cnf(f_53_5,plain,
( U_123 != U_122
| aElementOf0(U_123,slbdtrb0(szszuzczcdt0(U_122)))
| ~ aElementOf0(U_122,szNzAzT0)
| ~ aElementOf0(U_123,szNzAzT0) ),
inference(clausify,[status(thm)],[f_53_2]) ).
fof(f_54_1,plain,
! [W0,W1] :
( ( ( sdtlseqdt0(W0,W1)
| ~ aSubsetOf0(slbdtrb0(W0),slbdtrb0(W1)) )
& ( aSubsetOf0(slbdtrb0(W0),slbdtrb0(W1))
| ~ sdtlseqdt0(W0,W1) ) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mSegLess]) ).
fof(f_54_2,plain,
! [U_125,U_124] :
( ( ( sdtlseqdt0(U_125,U_124)
| ~ aSubsetOf0(slbdtrb0(U_125),slbdtrb0(U_124)) )
& ( aSubsetOf0(slbdtrb0(U_125),slbdtrb0(U_124))
| ~ sdtlseqdt0(U_125,U_124) ) )
| ~ aElementOf0(U_124,szNzAzT0)
| ~ aElementOf0(U_125,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
cnf(f_54_3,plain,
( aSubsetOf0(slbdtrb0(U_125),slbdtrb0(U_124))
| ~ sdtlseqdt0(U_125,U_124)
| ~ aElementOf0(U_124,szNzAzT0)
| ~ aElementOf0(U_125,szNzAzT0) ),
inference(clausify,[status(thm)],[f_54_2]) ).
cnf(f_54_4,plain,
( sdtlseqdt0(U_125,U_124)
| ~ aSubsetOf0(slbdtrb0(U_125),slbdtrb0(U_124))
| ~ aElementOf0(U_124,szNzAzT0)
| ~ aElementOf0(U_125,szNzAzT0) ),
inference(clausify,[status(thm)],[f_54_2]) ).
fof(f_55_1,plain,
! [W0] :
( ? [W1] :
( aSubsetOf0(W0,slbdtrb0(W1))
& aElementOf0(W1,szNzAzT0) )
| ~ isFinite0(W0)
| ~ aSubsetOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mFinSubSeg]) ).
fof(f_55_2,plain,
! [U_127] :
( ? [U_126] :
( aSubsetOf0(U_127,slbdtrb0(U_126))
& aElementOf0(U_126,szNzAzT0) )
| ~ isFinite0(U_127)
| ~ aSubsetOf0(U_127,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
! [U_127] :
( ( aSubsetOf0(U_127,slbdtrb0(sK13(U_127)))
& aElementOf0(sK13(U_127),szNzAzT0) )
| ~ isFinite0(U_127)
| ~ aSubsetOf0(U_127,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_126,sK13(U_127))],[f_55_2]) ).
cnf(f_55_4,plain,
( aElementOf0(sK13(U_127),szNzAzT0)
| ~ isFinite0(U_127)
| ~ aSubsetOf0(U_127,szNzAzT0) ),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_5,plain,
( aSubsetOf0(U_127,slbdtrb0(sK13(U_127)))
| ~ isFinite0(U_127)
| ~ aSubsetOf0(U_127,szNzAzT0) ),
inference(clausify,[status(thm)],[f_55_3]) ).
fof(f_56_1,plain,
! [W0] :
( sbrdtbr0(slbdtrb0(W0)) = W0
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mCardSeg]) ).
fof(f_56_2,plain,
! [U_128] :
( sbrdtbr0(slbdtrb0(U_128)) = U_128
| ~ aElementOf0(U_128,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
cnf(f_56_3,plain,
( sbrdtbr0(slbdtrb0(U_128)) = U_128
| ~ aElementOf0(U_128,szNzAzT0) ),
inference(clausify,[status(thm)],[f_56_2]) ).
fof(f_57_1,plain,
! [W0,W1] :
( ! [W2] :
( ( W2 = slbdtsldtrb0(W0,W1)
| ? [W3] :
( ( ~ aElementOf0(W3,W2)
& sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) )
| ( ( sbrdtbr0(W3) != W1
| ~ aSubsetOf0(W3,W0) )
& aElementOf0(W3,W2) ) )
| ~ aSet0(W2) )
& ( ( ! [W3] :
( ( aElementOf0(W3,W2)
| sbrdtbr0(W3) != W1
| ~ aSubsetOf0(W3,W0) )
& ( ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != slbdtsldtrb0(W0,W1) ) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mDefSel]) ).
fof(f_57_2,plain,
! [U_133,U_132] :
( ! [U_131] :
( ( U_131 = slbdtsldtrb0(U_133,U_132)
| ? [U_130] :
( ( ~ aElementOf0(U_130,U_131)
& sbrdtbr0(U_130) = U_132
& aSubsetOf0(U_130,U_133) )
| ( ( sbrdtbr0(U_130) != U_132
| ~ aSubsetOf0(U_130,U_133) )
& aElementOf0(U_130,U_131) ) )
| ~ aSet0(U_131) )
& ( ( ! [U_129] :
( ( aElementOf0(U_129,U_131)
| sbrdtbr0(U_129) != U_132
| ~ aSubsetOf0(U_129,U_133) )
& ( ( sbrdtbr0(U_129) = U_132
& aSubsetOf0(U_129,U_133) )
| ~ aElementOf0(U_129,U_131) ) )
& aSet0(U_131) )
| U_131 != slbdtsldtrb0(U_133,U_132) ) )
| ~ aElementOf0(U_132,szNzAzT0)
| ~ aSet0(U_133) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
! [U_133,U_132] :
( ( ! [U_139] :
( U_139 = slbdtsldtrb0(U_133,U_132)
| ? [U_137] :
( ~ aElementOf0(U_137,U_139)
& sbrdtbr0(U_137) = U_132
& aSubsetOf0(U_137,U_133) )
| ? [U_136] :
( ( sbrdtbr0(U_136) != U_132
| ~ aSubsetOf0(U_136,U_133) )
& aElementOf0(U_136,U_139) )
| ~ aSet0(U_139) )
& ! [U_138] :
( ( ! [U_135] :
( aElementOf0(U_135,U_138)
| sbrdtbr0(U_135) != U_132
| ~ aSubsetOf0(U_135,U_133) )
& ! [U_134] :
( ( sbrdtbr0(U_134) = U_132
& aSubsetOf0(U_134,U_133) )
| ~ aElementOf0(U_134,U_138) )
& aSet0(U_138) )
| U_138 != slbdtsldtrb0(U_133,U_132) ) )
| ~ aElementOf0(U_132,szNzAzT0)
| ~ aSet0(U_133) ),
inference(miniscope,[status(thm)],[f_57_2]) ).
fof(f_57_4,plain,
! [U_133,U_132] :
( ( ! [U_139] :
( U_139 = slbdtsldtrb0(U_133,U_132)
| ? [U_137] :
( ~ aElementOf0(U_137,U_139)
& sbrdtbr0(U_137) = U_132
& aSubsetOf0(U_137,U_133) )
| ( ( sbrdtbr0(sK14(U_133,U_132,U_139)) != U_132
| ~ aSubsetOf0(sK14(U_133,U_132,U_139),U_133) )
& aElementOf0(sK14(U_133,U_132,U_139),U_139) )
| ~ aSet0(U_139) )
& ! [U_138] :
( ( ! [U_135] :
( aElementOf0(U_135,U_138)
| sbrdtbr0(U_135) != U_132
| ~ aSubsetOf0(U_135,U_133) )
& ! [U_134] :
( ( sbrdtbr0(U_134) = U_132
& aSubsetOf0(U_134,U_133) )
| ~ aElementOf0(U_134,U_138) )
& aSet0(U_138) )
| U_138 != slbdtsldtrb0(U_133,U_132) ) )
| ~ aElementOf0(U_132,szNzAzT0)
| ~ aSet0(U_133) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_136,sK14(U_133,U_132,U_139))],[f_57_3]) ).
fof(f_57_5,plain,
! [U_133,U_132] :
( ( ! [U_139] :
( U_139 = slbdtsldtrb0(U_133,U_132)
| ( ~ aElementOf0(sK15(U_133,U_132,U_139),U_139)
& sbrdtbr0(sK15(U_133,U_132,U_139)) = U_132
& aSubsetOf0(sK15(U_133,U_132,U_139),U_133) )
| ( ( sbrdtbr0(sK14(U_133,U_132,U_139)) != U_132
| ~ aSubsetOf0(sK14(U_133,U_132,U_139),U_133) )
& aElementOf0(sK14(U_133,U_132,U_139),U_139) )
| ~ aSet0(U_139) )
& ! [U_138] :
( ( ! [U_135] :
( aElementOf0(U_135,U_138)
| sbrdtbr0(U_135) != U_132
| ~ aSubsetOf0(U_135,U_133) )
& ! [U_134] :
( ( sbrdtbr0(U_134) = U_132
& aSubsetOf0(U_134,U_133) )
| ~ aElementOf0(U_134,U_138) )
& aSet0(U_138) )
| U_138 != slbdtsldtrb0(U_133,U_132) ) )
| ~ aElementOf0(U_132,szNzAzT0)
| ~ aSet0(U_133) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_137,sK15(U_133,U_132,U_139))],[f_57_4]) ).
cnf(f_57_6,plain,
( aSet0(U_138)
| U_138 != slbdtsldtrb0(U_133,U_132)
| ~ aElementOf0(U_132,szNzAzT0)
| ~ aSet0(U_133) ),
inference(clausify,[status(thm)],[f_57_5]) ).
cnf(f_57_7,plain,
( aSubsetOf0(U_134,U_133)
| ~ aElementOf0(U_134,U_138)
| U_138 != slbdtsldtrb0(U_133,U_132)
| ~ aElementOf0(U_132,szNzAzT0)
| ~ aSet0(U_133) ),
inference(clausify,[status(thm)],[f_57_5]) ).
cnf(f_57_8,plain,
( sbrdtbr0(U_134) = U_132
| ~ aElementOf0(U_134,U_138)
| U_138 != slbdtsldtrb0(U_133,U_132)
| ~ aElementOf0(U_132,szNzAzT0)
| ~ aSet0(U_133) ),
inference(clausify,[status(thm)],[f_57_5]) ).
cnf(f_57_9,plain,
( aElementOf0(U_135,U_138)
| sbrdtbr0(U_135) != U_132
| ~ aSubsetOf0(U_135,U_133)
| U_138 != slbdtsldtrb0(U_133,U_132)
| ~ aElementOf0(U_132,szNzAzT0)
| ~ aSet0(U_133) ),
inference(clausify,[status(thm)],[f_57_5]) ).
cnf(f_57_10,plain,
( aSubsetOf0(sK15(U_133,U_132,U_139),U_133)
| aElementOf0(sK14(U_133,U_132,U_139),U_139)
| ~ aSet0(U_139)
| U_139 = slbdtsldtrb0(U_133,U_132)
| ~ aElementOf0(U_132,szNzAzT0)
| ~ aSet0(U_133) ),
inference(clausify,[status(thm)],[f_57_5]) ).
cnf(f_57_11,plain,
( sbrdtbr0(sK15(U_133,U_132,U_139)) = U_132
| aElementOf0(sK14(U_133,U_132,U_139),U_139)
| ~ aSet0(U_139)
| U_139 = slbdtsldtrb0(U_133,U_132)
| ~ aElementOf0(U_132,szNzAzT0)
| ~ aSet0(U_133) ),
inference(clausify,[status(thm)],[f_57_5]) ).
cnf(f_57_12,plain,
( ~ aElementOf0(sK15(U_133,U_132,U_139),U_139)
| aElementOf0(sK14(U_133,U_132,U_139),U_139)
| ~ aSet0(U_139)
| U_139 = slbdtsldtrb0(U_133,U_132)
| ~ aElementOf0(U_132,szNzAzT0)
| ~ aSet0(U_133) ),
inference(clausify,[status(thm)],[f_57_5]) ).
cnf(f_57_13,plain,
( aSubsetOf0(sK15(U_133,U_132,U_139),U_133)
| sbrdtbr0(sK14(U_133,U_132,U_139)) != U_132
| ~ aSubsetOf0(sK14(U_133,U_132,U_139),U_133)
| ~ aSet0(U_139)
| U_139 = slbdtsldtrb0(U_133,U_132)
| ~ aElementOf0(U_132,szNzAzT0)
| ~ aSet0(U_133) ),
inference(clausify,[status(thm)],[f_57_5]) ).
cnf(f_57_14,plain,
( sbrdtbr0(sK15(U_133,U_132,U_139)) = U_132
| sbrdtbr0(sK14(U_133,U_132,U_139)) != U_132
| ~ aSubsetOf0(sK14(U_133,U_132,U_139),U_133)
| ~ aSet0(U_139)
| U_139 = slbdtsldtrb0(U_133,U_132)
| ~ aElementOf0(U_132,szNzAzT0)
| ~ aSet0(U_133) ),
inference(clausify,[status(thm)],[f_57_5]) ).
cnf(f_57_15,plain,
( ~ aElementOf0(sK15(U_133,U_132,U_139),U_139)
| sbrdtbr0(sK14(U_133,U_132,U_139)) != U_132
| ~ aSubsetOf0(sK14(U_133,U_132,U_139),U_133)
| ~ aSet0(U_139)
| U_139 = slbdtsldtrb0(U_133,U_132)
| ~ aElementOf0(U_132,szNzAzT0)
| ~ aSet0(U_133) ),
inference(clausify,[status(thm)],[f_57_5]) ).
fof(f_58_1,plain,
! [W0] :
( ! [W1] :
( isFinite0(slbdtsldtrb0(W0,W1))
| ~ aElementOf0(W1,szNzAzT0) )
| ~ isFinite0(W0)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mSelFSet]) ).
fof(f_58_2,plain,
! [U_141] :
( ! [U_140] :
( isFinite0(slbdtsldtrb0(U_141,U_140))
| ~ aElementOf0(U_140,szNzAzT0) )
| ~ isFinite0(U_141)
| ~ aSet0(U_141) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
cnf(f_58_3,plain,
( isFinite0(slbdtsldtrb0(U_141,U_140))
| ~ aElementOf0(U_140,szNzAzT0)
| ~ isFinite0(U_141)
| ~ aSet0(U_141) ),
inference(clausify,[status(thm)],[f_58_2]) ).
fof(f_59_1,plain,
! [W0] :
( ! [W1] :
( slbdtsldtrb0(W0,W1) != slcrc0
| ~ aElementOf0(W1,szNzAzT0) )
| isFinite0(W0)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mSelNSet]) ).
fof(f_59_2,plain,
! [U_143] :
( ! [U_142] :
( slbdtsldtrb0(U_143,U_142) != slcrc0
| ~ aElementOf0(U_142,szNzAzT0) )
| isFinite0(U_143)
| ~ aSet0(U_143) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
cnf(f_59_3,plain,
( slbdtsldtrb0(U_143,U_142) != slcrc0
| ~ aElementOf0(U_142,szNzAzT0)
| isFinite0(U_143)
| ~ aSet0(U_143) ),
inference(clausify,[status(thm)],[f_59_2]) ).
fof(f_60_1,plain,
! [W0] :
( ! [W1] :
( isCountable0(slbdtsldtrb0(W0,W1))
| W1 = sz00
| ~ aElementOf0(W1,szNzAzT0) )
| ~ isCountable0(W0)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mSelCSet]) ).
fof(f_60_2,plain,
! [U_145] :
( ! [U_144] :
( isCountable0(slbdtsldtrb0(U_145,U_144))
| U_144 = sz00
| ~ aElementOf0(U_144,szNzAzT0) )
| ~ isCountable0(U_145)
| ~ aSet0(U_145) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
cnf(f_60_3,plain,
( isCountable0(slbdtsldtrb0(U_145,U_144))
| U_144 = sz00
| ~ aElementOf0(U_144,szNzAzT0)
| ~ isCountable0(U_145)
| ~ aSet0(U_145) ),
inference(clausify,[status(thm)],[f_60_2]) ).
fof(f_61_1,plain,
! [W0] :
( ! [W1,W2] :
( aSubsetOf0(W1,W2)
| slbdtsldtrb0(W1,W0) = slcrc0
| ~ aSubsetOf0(slbdtsldtrb0(W1,W0),slbdtsldtrb0(W2,W0))
| W0 = sz00
| ~ aSet0(W2)
| ~ aSet0(W1) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mSelSub]) ).
fof(f_61_2,plain,
! [U_148] :
( ! [U_147,U_146] :
( aSubsetOf0(U_147,U_146)
| slbdtsldtrb0(U_147,U_148) = slcrc0
| ~ aSubsetOf0(slbdtsldtrb0(U_147,U_148),slbdtsldtrb0(U_146,U_148))
| U_148 = sz00
| ~ aSet0(U_146)
| ~ aSet0(U_147) )
| ~ aElementOf0(U_148,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
cnf(f_61_3,plain,
( aSubsetOf0(U_147,U_146)
| slbdtsldtrb0(U_147,U_148) = slcrc0
| ~ aSubsetOf0(slbdtsldtrb0(U_147,U_148),slbdtsldtrb0(U_146,U_148))
| U_148 = sz00
| ~ aSet0(U_146)
| ~ aSet0(U_147)
| ~ aElementOf0(U_148,szNzAzT0) ),
inference(clausify,[status(thm)],[f_61_2]) ).
fof(f_62_1,plain,
! [W0,W1] :
( ! [W2] :
( ? [W3] :
( aSubsetOf0(W2,slbdtsldtrb0(W3,W1))
& isFinite0(W3)
& aSubsetOf0(W3,W0) )
| ~ isFinite0(W2)
| ~ aSubsetOf0(W2,slbdtsldtrb0(W0,W1)) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mSelExtra]) ).
fof(f_62_2,plain,
! [U_152,U_151] :
( ! [U_150] :
( ? [U_149] :
( aSubsetOf0(U_150,slbdtsldtrb0(U_149,U_151))
& isFinite0(U_149)
& aSubsetOf0(U_149,U_152) )
| ~ isFinite0(U_150)
| ~ aSubsetOf0(U_150,slbdtsldtrb0(U_152,U_151)) )
| ~ aElementOf0(U_151,szNzAzT0)
| ~ aSet0(U_152) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
! [U_152,U_151] :
( ! [U_150] :
( ( aSubsetOf0(U_150,slbdtsldtrb0(sK16(U_152,U_151,U_150),U_151))
& isFinite0(sK16(U_152,U_151,U_150))
& aSubsetOf0(sK16(U_152,U_151,U_150),U_152) )
| ~ isFinite0(U_150)
| ~ aSubsetOf0(U_150,slbdtsldtrb0(U_152,U_151)) )
| ~ aElementOf0(U_151,szNzAzT0)
| ~ aSet0(U_152) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_149,sK16(U_152,U_151,U_150))],[f_62_2]) ).
cnf(f_62_4,plain,
( aSubsetOf0(sK16(U_152,U_151,U_150),U_152)
| ~ isFinite0(U_150)
| ~ aSubsetOf0(U_150,slbdtsldtrb0(U_152,U_151))
| ~ aElementOf0(U_151,szNzAzT0)
| ~ aSet0(U_152) ),
inference(clausify,[status(thm)],[f_62_3]) ).
cnf(f_62_5,plain,
( isFinite0(sK16(U_152,U_151,U_150))
| ~ isFinite0(U_150)
| ~ aSubsetOf0(U_150,slbdtsldtrb0(U_152,U_151))
| ~ aElementOf0(U_151,szNzAzT0)
| ~ aSet0(U_152) ),
inference(clausify,[status(thm)],[f_62_3]) ).
cnf(f_62_6,plain,
( aSubsetOf0(U_150,slbdtsldtrb0(sK16(U_152,U_151,U_150),U_151))
| ~ isFinite0(U_150)
| ~ aSubsetOf0(U_150,slbdtsldtrb0(U_152,U_151))
| ~ aElementOf0(U_151,szNzAzT0)
| ~ aSet0(U_152) ),
inference(clausify,[status(thm)],[f_62_3]) ).
fof(f_63_1,plain,
! [W0] :
( $true
| ~ aFunction0(W0) ),
inference(fof_nnf,[status(thm)],[mFunSort]) ).
fof(f_63_2,plain,
! [U_153] :
( $true
| ~ aFunction0(U_153) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
fof(f_63_3,plain,
( ! [U_153] : ~ aFunction0(U_153)
| $true ),
inference(miniscope,[status(thm)],[f_63_2]) ).
cnf(f_63_4,plain,
( ~ aFunction0(U_153)
| $true ),
inference(clausify,[status(thm)],[f_63_3]) ).
fof(f_64_1,plain,
! [W0] :
( aSet0(szDzozmdt0(W0))
| ~ aFunction0(W0) ),
inference(fof_nnf,[status(thm)],[mDomSet]) ).
fof(f_64_2,plain,
! [U_154] :
( aSet0(szDzozmdt0(U_154))
| ~ aFunction0(U_154) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
cnf(f_64_3,plain,
( aSet0(szDzozmdt0(U_154))
| ~ aFunction0(U_154) ),
inference(clausify,[status(thm)],[f_64_2]) ).
fof(f_65_1,plain,
! [W0] :
( ! [W1] :
( aElement0(sdtlpdtrp0(W0,W1))
| ~ aElementOf0(W1,szDzozmdt0(W0)) )
| ~ aFunction0(W0) ),
inference(fof_nnf,[status(thm)],[mImgElm]) ).
fof(f_65_2,plain,
! [U_156] :
( ! [U_155] :
( aElement0(sdtlpdtrp0(U_156,U_155))
| ~ aElementOf0(U_155,szDzozmdt0(U_156)) )
| ~ aFunction0(U_156) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
cnf(f_65_3,plain,
( aElement0(sdtlpdtrp0(U_156,U_155))
| ~ aElementOf0(U_155,szDzozmdt0(U_156))
| ~ aFunction0(U_156) ),
inference(clausify,[status(thm)],[f_65_2]) ).
fof(f_66_1,plain,
! [W0,W1] :
( ! [W2] :
( ( W2 = sdtlbdtrb0(W0,W1)
| ? [W3] :
( ( ~ aElementOf0(W3,W2)
& sdtlpdtrp0(W0,W3) = W1
& aElementOf0(W3,szDzozmdt0(W0)) )
| ( ( sdtlpdtrp0(W0,W3) != W1
| ~ aElementOf0(W3,szDzozmdt0(W0)) )
& aElementOf0(W3,W2) ) )
| ~ aSet0(W2) )
& ( ( ! [W3] :
( ( aElementOf0(W3,W2)
| sdtlpdtrp0(W0,W3) != W1
| ~ aElementOf0(W3,szDzozmdt0(W0)) )
& ( ( sdtlpdtrp0(W0,W3) = W1
& aElementOf0(W3,szDzozmdt0(W0)) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtlbdtrb0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aFunction0(W0) ),
inference(fof_nnf,[status(thm)],[mDefPtt]) ).
fof(f_66_2,plain,
! [U_161,U_160] :
( ! [U_159] :
( ( U_159 = sdtlbdtrb0(U_161,U_160)
| ? [U_158] :
( ( ~ aElementOf0(U_158,U_159)
& sdtlpdtrp0(U_161,U_158) = U_160
& aElementOf0(U_158,szDzozmdt0(U_161)) )
| ( ( sdtlpdtrp0(U_161,U_158) != U_160
| ~ aElementOf0(U_158,szDzozmdt0(U_161)) )
& aElementOf0(U_158,U_159) ) )
| ~ aSet0(U_159) )
& ( ( ! [U_157] :
( ( aElementOf0(U_157,U_159)
| sdtlpdtrp0(U_161,U_157) != U_160
| ~ aElementOf0(U_157,szDzozmdt0(U_161)) )
& ( ( sdtlpdtrp0(U_161,U_157) = U_160
& aElementOf0(U_157,szDzozmdt0(U_161)) )
| ~ aElementOf0(U_157,U_159) ) )
& aSet0(U_159) )
| U_159 != sdtlbdtrb0(U_161,U_160) ) )
| ~ aElement0(U_160)
| ~ aFunction0(U_161) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
! [U_161,U_160] :
( ( ! [U_167] :
( U_167 = sdtlbdtrb0(U_161,U_160)
| ? [U_165] :
( ~ aElementOf0(U_165,U_167)
& sdtlpdtrp0(U_161,U_165) = U_160
& aElementOf0(U_165,szDzozmdt0(U_161)) )
| ? [U_164] :
( ( sdtlpdtrp0(U_161,U_164) != U_160
| ~ aElementOf0(U_164,szDzozmdt0(U_161)) )
& aElementOf0(U_164,U_167) )
| ~ aSet0(U_167) )
& ! [U_166] :
( ( ! [U_163] :
( aElementOf0(U_163,U_166)
| sdtlpdtrp0(U_161,U_163) != U_160
| ~ aElementOf0(U_163,szDzozmdt0(U_161)) )
& ! [U_162] :
( ( sdtlpdtrp0(U_161,U_162) = U_160
& aElementOf0(U_162,szDzozmdt0(U_161)) )
| ~ aElementOf0(U_162,U_166) )
& aSet0(U_166) )
| U_166 != sdtlbdtrb0(U_161,U_160) ) )
| ~ aElement0(U_160)
| ~ aFunction0(U_161) ),
inference(miniscope,[status(thm)],[f_66_2]) ).
fof(f_66_4,plain,
! [U_161,U_160] :
( ( ! [U_167] :
( U_167 = sdtlbdtrb0(U_161,U_160)
| ? [U_165] :
( ~ aElementOf0(U_165,U_167)
& sdtlpdtrp0(U_161,U_165) = U_160
& aElementOf0(U_165,szDzozmdt0(U_161)) )
| ( ( sdtlpdtrp0(U_161,sK17(U_161,U_160,U_167)) != U_160
| ~ aElementOf0(sK17(U_161,U_160,U_167),szDzozmdt0(U_161)) )
& aElementOf0(sK17(U_161,U_160,U_167),U_167) )
| ~ aSet0(U_167) )
& ! [U_166] :
( ( ! [U_163] :
( aElementOf0(U_163,U_166)
| sdtlpdtrp0(U_161,U_163) != U_160
| ~ aElementOf0(U_163,szDzozmdt0(U_161)) )
& ! [U_162] :
( ( sdtlpdtrp0(U_161,U_162) = U_160
& aElementOf0(U_162,szDzozmdt0(U_161)) )
| ~ aElementOf0(U_162,U_166) )
& aSet0(U_166) )
| U_166 != sdtlbdtrb0(U_161,U_160) ) )
| ~ aElement0(U_160)
| ~ aFunction0(U_161) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_164,sK17(U_161,U_160,U_167))],[f_66_3]) ).
fof(f_66_5,plain,
! [U_161,U_160] :
( ( ! [U_167] :
( U_167 = sdtlbdtrb0(U_161,U_160)
| ( ~ aElementOf0(sK18(U_161,U_160,U_167),U_167)
& sdtlpdtrp0(U_161,sK18(U_161,U_160,U_167)) = U_160
& aElementOf0(sK18(U_161,U_160,U_167),szDzozmdt0(U_161)) )
| ( ( sdtlpdtrp0(U_161,sK17(U_161,U_160,U_167)) != U_160
| ~ aElementOf0(sK17(U_161,U_160,U_167),szDzozmdt0(U_161)) )
& aElementOf0(sK17(U_161,U_160,U_167),U_167) )
| ~ aSet0(U_167) )
& ! [U_166] :
( ( ! [U_163] :
( aElementOf0(U_163,U_166)
| sdtlpdtrp0(U_161,U_163) != U_160
| ~ aElementOf0(U_163,szDzozmdt0(U_161)) )
& ! [U_162] :
( ( sdtlpdtrp0(U_161,U_162) = U_160
& aElementOf0(U_162,szDzozmdt0(U_161)) )
| ~ aElementOf0(U_162,U_166) )
& aSet0(U_166) )
| U_166 != sdtlbdtrb0(U_161,U_160) ) )
| ~ aElement0(U_160)
| ~ aFunction0(U_161) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_165,sK18(U_161,U_160,U_167))],[f_66_4]) ).
cnf(f_66_6,plain,
( aSet0(U_166)
| U_166 != sdtlbdtrb0(U_161,U_160)
| ~ aElement0(U_160)
| ~ aFunction0(U_161) ),
inference(clausify,[status(thm)],[f_66_5]) ).
cnf(f_66_7,plain,
( aElementOf0(U_162,szDzozmdt0(U_161))
| ~ aElementOf0(U_162,U_166)
| U_166 != sdtlbdtrb0(U_161,U_160)
| ~ aElement0(U_160)
| ~ aFunction0(U_161) ),
inference(clausify,[status(thm)],[f_66_5]) ).
cnf(f_66_8,plain,
( sdtlpdtrp0(U_161,U_162) = U_160
| ~ aElementOf0(U_162,U_166)
| U_166 != sdtlbdtrb0(U_161,U_160)
| ~ aElement0(U_160)
| ~ aFunction0(U_161) ),
inference(clausify,[status(thm)],[f_66_5]) ).
cnf(f_66_9,plain,
( aElementOf0(U_163,U_166)
| sdtlpdtrp0(U_161,U_163) != U_160
| ~ aElementOf0(U_163,szDzozmdt0(U_161))
| U_166 != sdtlbdtrb0(U_161,U_160)
| ~ aElement0(U_160)
| ~ aFunction0(U_161) ),
inference(clausify,[status(thm)],[f_66_5]) ).
cnf(f_66_10,plain,
( aElementOf0(sK18(U_161,U_160,U_167),szDzozmdt0(U_161))
| aElementOf0(sK17(U_161,U_160,U_167),U_167)
| ~ aSet0(U_167)
| U_167 = sdtlbdtrb0(U_161,U_160)
| ~ aElement0(U_160)
| ~ aFunction0(U_161) ),
inference(clausify,[status(thm)],[f_66_5]) ).
cnf(f_66_11,plain,
( sdtlpdtrp0(U_161,sK18(U_161,U_160,U_167)) = U_160
| aElementOf0(sK17(U_161,U_160,U_167),U_167)
| ~ aSet0(U_167)
| U_167 = sdtlbdtrb0(U_161,U_160)
| ~ aElement0(U_160)
| ~ aFunction0(U_161) ),
inference(clausify,[status(thm)],[f_66_5]) ).
cnf(f_66_12,plain,
( ~ aElementOf0(sK18(U_161,U_160,U_167),U_167)
| aElementOf0(sK17(U_161,U_160,U_167),U_167)
| ~ aSet0(U_167)
| U_167 = sdtlbdtrb0(U_161,U_160)
| ~ aElement0(U_160)
| ~ aFunction0(U_161) ),
inference(clausify,[status(thm)],[f_66_5]) ).
cnf(f_66_13,plain,
( aElementOf0(sK18(U_161,U_160,U_167),szDzozmdt0(U_161))
| sdtlpdtrp0(U_161,sK17(U_161,U_160,U_167)) != U_160
| ~ aElementOf0(sK17(U_161,U_160,U_167),szDzozmdt0(U_161))
| ~ aSet0(U_167)
| U_167 = sdtlbdtrb0(U_161,U_160)
| ~ aElement0(U_160)
| ~ aFunction0(U_161) ),
inference(clausify,[status(thm)],[f_66_5]) ).
cnf(f_66_14,plain,
( sdtlpdtrp0(U_161,sK18(U_161,U_160,U_167)) = U_160
| sdtlpdtrp0(U_161,sK17(U_161,U_160,U_167)) != U_160
| ~ aElementOf0(sK17(U_161,U_160,U_167),szDzozmdt0(U_161))
| ~ aSet0(U_167)
| U_167 = sdtlbdtrb0(U_161,U_160)
| ~ aElement0(U_160)
| ~ aFunction0(U_161) ),
inference(clausify,[status(thm)],[f_66_5]) ).
cnf(f_66_15,plain,
( ~ aElementOf0(sK18(U_161,U_160,U_167),U_167)
| sdtlpdtrp0(U_161,sK17(U_161,U_160,U_167)) != U_160
| ~ aElementOf0(sK17(U_161,U_160,U_167),szDzozmdt0(U_161))
| ~ aSet0(U_167)
| U_167 = sdtlbdtrb0(U_161,U_160)
| ~ aElement0(U_160)
| ~ aFunction0(U_161) ),
inference(clausify,[status(thm)],[f_66_5]) ).
fof(f_67_1,plain,
! [W0,W1] :
( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) ),
inference(fof_nnf,[status(thm)],[mPttSet]) ).
fof(f_67_2,plain,
! [U_169,U_168] :
( aSubsetOf0(sdtlbdtrb0(U_169,U_168),szDzozmdt0(U_169))
| ~ aElement0(U_168)
| ~ aFunction0(U_169) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
cnf(f_67_3,plain,
( aSubsetOf0(sdtlbdtrb0(U_169,U_168),szDzozmdt0(U_169))
| ~ aElement0(U_168)
| ~ aFunction0(U_169) ),
inference(clausify,[status(thm)],[f_67_2]) ).
fof(f_68_1,plain,
! [W0] :
( ! [W1] :
( ! [W2] :
( ( W2 = sdtlcdtrc0(W0,W1)
| ? [W3] :
( ( ~ aElementOf0(W3,W2)
& ? [W4] :
( sdtlpdtrp0(W0,W4) = W3
& aElementOf0(W4,W1) ) )
| ( ! [W4] :
( sdtlpdtrp0(W0,W4) != W3
| ~ aElementOf0(W4,W1) )
& aElementOf0(W3,W2) ) )
| ~ aSet0(W2) )
& ( ( ! [W3] :
( ( aElementOf0(W3,W2)
| ! [W4] :
( sdtlpdtrp0(W0,W4) != W3
| ~ aElementOf0(W4,W1) ) )
& ( ? [W4] :
( sdtlpdtrp0(W0,W4) = W3
& aElementOf0(W4,W1) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtlcdtrc0(W0,W1) ) )
| ~ aSubsetOf0(W1,szDzozmdt0(W0)) )
| ~ aFunction0(W0) ),
inference(fof_nnf,[status(thm)],[mDefSImg]) ).
fof(f_68_2,plain,
! [U_178] :
( ! [U_177] :
( ! [U_176] :
( ( U_176 = sdtlcdtrc0(U_178,U_177)
| ? [U_175] :
( ( ~ aElementOf0(U_175,U_176)
& ? [U_174] :
( sdtlpdtrp0(U_178,U_174) = U_175
& aElementOf0(U_174,U_177) ) )
| ( ! [U_173] :
( sdtlpdtrp0(U_178,U_173) != U_175
| ~ aElementOf0(U_173,U_177) )
& aElementOf0(U_175,U_176) ) )
| ~ aSet0(U_176) )
& ( ( ! [U_172] :
( ( aElementOf0(U_172,U_176)
| ! [U_171] :
( sdtlpdtrp0(U_178,U_171) != U_172
| ~ aElementOf0(U_171,U_177) ) )
& ( ? [U_170] :
( sdtlpdtrp0(U_178,U_170) = U_172
& aElementOf0(U_170,U_177) )
| ~ aElementOf0(U_172,U_176) ) )
& aSet0(U_176) )
| U_176 != sdtlcdtrc0(U_178,U_177) ) )
| ~ aSubsetOf0(U_177,szDzozmdt0(U_178)) )
| ~ aFunction0(U_178) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
fof(f_68_3,plain,
! [U_178] :
( ! [U_177] :
( ( ! [U_184] :
( U_184 = sdtlcdtrc0(U_178,U_177)
| ? [U_182] :
( ~ aElementOf0(U_182,U_184)
& ? [U_174] :
( sdtlpdtrp0(U_178,U_174) = U_182
& aElementOf0(U_174,U_177) ) )
| ? [U_181] :
( ! [U_173] :
( sdtlpdtrp0(U_178,U_173) != U_181
| ~ aElementOf0(U_173,U_177) )
& aElementOf0(U_181,U_184) )
| ~ aSet0(U_184) )
& ! [U_183] :
( ( ! [U_180] :
( aElementOf0(U_180,U_183)
| ! [U_171] :
( sdtlpdtrp0(U_178,U_171) != U_180
| ~ aElementOf0(U_171,U_177) ) )
& ! [U_179] :
( ? [U_170] :
( sdtlpdtrp0(U_178,U_170) = U_179
& aElementOf0(U_170,U_177) )
| ~ aElementOf0(U_179,U_183) )
& aSet0(U_183) )
| U_183 != sdtlcdtrc0(U_178,U_177) ) )
| ~ aSubsetOf0(U_177,szDzozmdt0(U_178)) )
| ~ aFunction0(U_178) ),
inference(miniscope,[status(thm)],[f_68_2]) ).
fof(f_68_4,plain,
! [U_178] :
( ! [U_177] :
( ( ! [U_184] :
( U_184 = sdtlcdtrc0(U_178,U_177)
| ? [U_182] :
( ~ aElementOf0(U_182,U_184)
& ? [U_174] :
( sdtlpdtrp0(U_178,U_174) = U_182
& aElementOf0(U_174,U_177) ) )
| ? [U_181] :
( ! [U_173] :
( sdtlpdtrp0(U_178,U_173) != U_181
| ~ aElementOf0(U_173,U_177) )
& aElementOf0(U_181,U_184) )
| ~ aSet0(U_184) )
& ! [U_183] :
( ( ! [U_180] :
( aElementOf0(U_180,U_183)
| ! [U_171] :
( sdtlpdtrp0(U_178,U_171) != U_180
| ~ aElementOf0(U_171,U_177) ) )
& ! [U_179] :
( ( sdtlpdtrp0(U_178,sK19(U_178,U_177,U_183,U_179)) = U_179
& aElementOf0(sK19(U_178,U_177,U_183,U_179),U_177) )
| ~ aElementOf0(U_179,U_183) )
& aSet0(U_183) )
| U_183 != sdtlcdtrc0(U_178,U_177) ) )
| ~ aSubsetOf0(U_177,szDzozmdt0(U_178)) )
| ~ aFunction0(U_178) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_170,sK19(U_178,U_177,U_183,U_179))],[f_68_3]) ).
fof(f_68_5,plain,
! [U_178] :
( ! [U_177] :
( ( ! [U_184] :
( U_184 = sdtlcdtrc0(U_178,U_177)
| ? [U_182] :
( ~ aElementOf0(U_182,U_184)
& ? [U_174] :
( sdtlpdtrp0(U_178,U_174) = U_182
& aElementOf0(U_174,U_177) ) )
| ( ! [U_173] :
( sdtlpdtrp0(U_178,U_173) != sK20(U_178,U_177,U_184)
| ~ aElementOf0(U_173,U_177) )
& aElementOf0(sK20(U_178,U_177,U_184),U_184) )
| ~ aSet0(U_184) )
& ! [U_183] :
( ( ! [U_180] :
( aElementOf0(U_180,U_183)
| ! [U_171] :
( sdtlpdtrp0(U_178,U_171) != U_180
| ~ aElementOf0(U_171,U_177) ) )
& ! [U_179] :
( ( sdtlpdtrp0(U_178,sK19(U_178,U_177,U_183,U_179)) = U_179
& aElementOf0(sK19(U_178,U_177,U_183,U_179),U_177) )
| ~ aElementOf0(U_179,U_183) )
& aSet0(U_183) )
| U_183 != sdtlcdtrc0(U_178,U_177) ) )
| ~ aSubsetOf0(U_177,szDzozmdt0(U_178)) )
| ~ aFunction0(U_178) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_181,sK20(U_178,U_177,U_184))],[f_68_4]) ).
fof(f_68_6,plain,
! [U_178] :
( ! [U_177] :
( ( ! [U_184] :
( U_184 = sdtlcdtrc0(U_178,U_177)
| ( ~ aElementOf0(sK21(U_178,U_177,U_184),U_184)
& ? [U_174] :
( sdtlpdtrp0(U_178,U_174) = sK21(U_178,U_177,U_184)
& aElementOf0(U_174,U_177) ) )
| ( ! [U_173] :
( sdtlpdtrp0(U_178,U_173) != sK20(U_178,U_177,U_184)
| ~ aElementOf0(U_173,U_177) )
& aElementOf0(sK20(U_178,U_177,U_184),U_184) )
| ~ aSet0(U_184) )
& ! [U_183] :
( ( ! [U_180] :
( aElementOf0(U_180,U_183)
| ! [U_171] :
( sdtlpdtrp0(U_178,U_171) != U_180
| ~ aElementOf0(U_171,U_177) ) )
& ! [U_179] :
( ( sdtlpdtrp0(U_178,sK19(U_178,U_177,U_183,U_179)) = U_179
& aElementOf0(sK19(U_178,U_177,U_183,U_179),U_177) )
| ~ aElementOf0(U_179,U_183) )
& aSet0(U_183) )
| U_183 != sdtlcdtrc0(U_178,U_177) ) )
| ~ aSubsetOf0(U_177,szDzozmdt0(U_178)) )
| ~ aFunction0(U_178) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_182,sK21(U_178,U_177,U_184))],[f_68_5]) ).
fof(f_68_7,plain,
! [U_178] :
( ! [U_177] :
( ( ! [U_184] :
( U_184 = sdtlcdtrc0(U_178,U_177)
| ( ~ aElementOf0(sK21(U_178,U_177,U_184),U_184)
& sdtlpdtrp0(U_178,sK22(U_178,U_177,U_184)) = sK21(U_178,U_177,U_184)
& aElementOf0(sK22(U_178,U_177,U_184),U_177) )
| ( ! [U_173] :
( sdtlpdtrp0(U_178,U_173) != sK20(U_178,U_177,U_184)
| ~ aElementOf0(U_173,U_177) )
& aElementOf0(sK20(U_178,U_177,U_184),U_184) )
| ~ aSet0(U_184) )
& ! [U_183] :
( ( ! [U_180] :
( aElementOf0(U_180,U_183)
| ! [U_171] :
( sdtlpdtrp0(U_178,U_171) != U_180
| ~ aElementOf0(U_171,U_177) ) )
& ! [U_179] :
( ( sdtlpdtrp0(U_178,sK19(U_178,U_177,U_183,U_179)) = U_179
& aElementOf0(sK19(U_178,U_177,U_183,U_179),U_177) )
| ~ aElementOf0(U_179,U_183) )
& aSet0(U_183) )
| U_183 != sdtlcdtrc0(U_178,U_177) ) )
| ~ aSubsetOf0(U_177,szDzozmdt0(U_178)) )
| ~ aFunction0(U_178) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_174,sK22(U_178,U_177,U_184))],[f_68_6]) ).
cnf(f_68_8,plain,
( aSet0(U_183)
| U_183 != sdtlcdtrc0(U_178,U_177)
| ~ aSubsetOf0(U_177,szDzozmdt0(U_178))
| ~ aFunction0(U_178) ),
inference(clausify,[status(thm)],[f_68_7]) ).
cnf(f_68_9,plain,
( aElementOf0(sK19(U_178,U_177,U_183,U_179),U_177)
| ~ aElementOf0(U_179,U_183)
| U_183 != sdtlcdtrc0(U_178,U_177)
| ~ aSubsetOf0(U_177,szDzozmdt0(U_178))
| ~ aFunction0(U_178) ),
inference(clausify,[status(thm)],[f_68_7]) ).
cnf(f_68_10,plain,
( sdtlpdtrp0(U_178,sK19(U_178,U_177,U_183,U_179)) = U_179
| ~ aElementOf0(U_179,U_183)
| U_183 != sdtlcdtrc0(U_178,U_177)
| ~ aSubsetOf0(U_177,szDzozmdt0(U_178))
| ~ aFunction0(U_178) ),
inference(clausify,[status(thm)],[f_68_7]) ).
cnf(f_68_11,plain,
( aElementOf0(U_180,U_183)
| sdtlpdtrp0(U_178,U_171) != U_180
| ~ aElementOf0(U_171,U_177)
| U_183 != sdtlcdtrc0(U_178,U_177)
| ~ aSubsetOf0(U_177,szDzozmdt0(U_178))
| ~ aFunction0(U_178) ),
inference(clausify,[status(thm)],[f_68_7]) ).
cnf(f_68_12,plain,
( aElementOf0(sK22(U_178,U_177,U_184),U_177)
| aElementOf0(sK20(U_178,U_177,U_184),U_184)
| ~ aSet0(U_184)
| U_184 = sdtlcdtrc0(U_178,U_177)
| ~ aSubsetOf0(U_177,szDzozmdt0(U_178))
| ~ aFunction0(U_178) ),
inference(clausify,[status(thm)],[f_68_7]) ).
cnf(f_68_13,plain,
( sdtlpdtrp0(U_178,sK22(U_178,U_177,U_184)) = sK21(U_178,U_177,U_184)
| aElementOf0(sK20(U_178,U_177,U_184),U_184)
| ~ aSet0(U_184)
| U_184 = sdtlcdtrc0(U_178,U_177)
| ~ aSubsetOf0(U_177,szDzozmdt0(U_178))
| ~ aFunction0(U_178) ),
inference(clausify,[status(thm)],[f_68_7]) ).
cnf(f_68_14,plain,
( ~ aElementOf0(sK21(U_178,U_177,U_184),U_184)
| aElementOf0(sK20(U_178,U_177,U_184),U_184)
| ~ aSet0(U_184)
| U_184 = sdtlcdtrc0(U_178,U_177)
| ~ aSubsetOf0(U_177,szDzozmdt0(U_178))
| ~ aFunction0(U_178) ),
inference(clausify,[status(thm)],[f_68_7]) ).
cnf(f_68_15,plain,
( aElementOf0(sK22(U_178,U_177,U_184),U_177)
| sdtlpdtrp0(U_178,U_173) != sK20(U_178,U_177,U_184)
| ~ aElementOf0(U_173,U_177)
| ~ aSet0(U_184)
| U_184 = sdtlcdtrc0(U_178,U_177)
| ~ aSubsetOf0(U_177,szDzozmdt0(U_178))
| ~ aFunction0(U_178) ),
inference(clausify,[status(thm)],[f_68_7]) ).
cnf(f_68_16,plain,
( sdtlpdtrp0(U_178,sK22(U_178,U_177,U_184)) = sK21(U_178,U_177,U_184)
| sdtlpdtrp0(U_178,U_173) != sK20(U_178,U_177,U_184)
| ~ aElementOf0(U_173,U_177)
| ~ aSet0(U_184)
| U_184 = sdtlcdtrc0(U_178,U_177)
| ~ aSubsetOf0(U_177,szDzozmdt0(U_178))
| ~ aFunction0(U_178) ),
inference(clausify,[status(thm)],[f_68_7]) ).
cnf(f_68_17,plain,
( ~ aElementOf0(sK21(U_178,U_177,U_184),U_184)
| sdtlpdtrp0(U_178,U_173) != sK20(U_178,U_177,U_184)
| ~ aElementOf0(U_173,U_177)
| ~ aSet0(U_184)
| U_184 = sdtlcdtrc0(U_178,U_177)
| ~ aSubsetOf0(U_177,szDzozmdt0(U_178))
| ~ aFunction0(U_178) ),
inference(clausify,[status(thm)],[f_68_7]) ).
fof(f_69_1,plain,
! [W0] :
( ! [W1] :
( aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0)))
| ~ aElementOf0(W1,szDzozmdt0(W0)) )
| ~ aFunction0(W0) ),
inference(fof_nnf,[status(thm)],[mImgRng]) ).
fof(f_69_2,plain,
! [U_186] :
( ! [U_185] :
( aElementOf0(sdtlpdtrp0(U_186,U_185),sdtlcdtrc0(U_186,szDzozmdt0(U_186)))
| ~ aElementOf0(U_185,szDzozmdt0(U_186)) )
| ~ aFunction0(U_186) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
cnf(f_69_3,plain,
( aElementOf0(sdtlpdtrp0(U_186,U_185),sdtlcdtrc0(U_186,szDzozmdt0(U_186)))
| ~ aElementOf0(U_185,szDzozmdt0(U_186))
| ~ aFunction0(U_186) ),
inference(clausify,[status(thm)],[f_69_2]) ).
fof(f_70_1,plain,
! [W0] :
( ! [W1] :
( ! [W2] :
( ( W2 = sdtexdt0(W0,W1)
| ? [W3] :
( sdtlpdtrp0(W2,W3) != sdtlpdtrp0(W0,W3)
& aElementOf0(W3,W1) )
| szDzozmdt0(W2) != W1
| ~ aFunction0(W2) )
& ( ( ! [W3] :
( sdtlpdtrp0(W2,W3) = sdtlpdtrp0(W0,W3)
| ~ aElementOf0(W3,W1) )
& szDzozmdt0(W2) = W1
& aFunction0(W2) )
| W2 != sdtexdt0(W0,W1) ) )
| ~ aSubsetOf0(W1,szDzozmdt0(W0)) )
| ~ aFunction0(W0) ),
inference(fof_nnf,[status(thm)],[mDefRst]) ).
fof(f_70_2,plain,
! [U_191] :
( ! [U_190] :
( ! [U_189] :
( ( U_189 = sdtexdt0(U_191,U_190)
| ? [U_188] :
( sdtlpdtrp0(U_189,U_188) != sdtlpdtrp0(U_191,U_188)
& aElementOf0(U_188,U_190) )
| szDzozmdt0(U_189) != U_190
| ~ aFunction0(U_189) )
& ( ( ! [U_187] :
( sdtlpdtrp0(U_189,U_187) = sdtlpdtrp0(U_191,U_187)
| ~ aElementOf0(U_187,U_190) )
& szDzozmdt0(U_189) = U_190
& aFunction0(U_189) )
| U_189 != sdtexdt0(U_191,U_190) ) )
| ~ aSubsetOf0(U_190,szDzozmdt0(U_191)) )
| ~ aFunction0(U_191) ),
inference(variable_rename,[status(thm)],[f_70_1]) ).
fof(f_70_3,plain,
! [U_191] :
( ! [U_190] :
( ( ! [U_193] :
( U_193 = sdtexdt0(U_191,U_190)
| ? [U_188] :
( sdtlpdtrp0(U_193,U_188) != sdtlpdtrp0(U_191,U_188)
& aElementOf0(U_188,U_190) )
| szDzozmdt0(U_193) != U_190
| ~ aFunction0(U_193) )
& ! [U_192] :
( ( ! [U_187] :
( sdtlpdtrp0(U_192,U_187) = sdtlpdtrp0(U_191,U_187)
| ~ aElementOf0(U_187,U_190) )
& szDzozmdt0(U_192) = U_190
& aFunction0(U_192) )
| U_192 != sdtexdt0(U_191,U_190) ) )
| ~ aSubsetOf0(U_190,szDzozmdt0(U_191)) )
| ~ aFunction0(U_191) ),
inference(miniscope,[status(thm)],[f_70_2]) ).
fof(f_70_4,plain,
! [U_191] :
( ! [U_190] :
( ( ! [U_193] :
( U_193 = sdtexdt0(U_191,U_190)
| ( sdtlpdtrp0(U_193,sK23(U_191,U_190,U_193)) != sdtlpdtrp0(U_191,sK23(U_191,U_190,U_193))
& aElementOf0(sK23(U_191,U_190,U_193),U_190) )
| szDzozmdt0(U_193) != U_190
| ~ aFunction0(U_193) )
& ! [U_192] :
( ( ! [U_187] :
( sdtlpdtrp0(U_192,U_187) = sdtlpdtrp0(U_191,U_187)
| ~ aElementOf0(U_187,U_190) )
& szDzozmdt0(U_192) = U_190
& aFunction0(U_192) )
| U_192 != sdtexdt0(U_191,U_190) ) )
| ~ aSubsetOf0(U_190,szDzozmdt0(U_191)) )
| ~ aFunction0(U_191) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_188,sK23(U_191,U_190,U_193))],[f_70_3]) ).
cnf(f_70_5,plain,
( aFunction0(U_192)
| U_192 != sdtexdt0(U_191,U_190)
| ~ aSubsetOf0(U_190,szDzozmdt0(U_191))
| ~ aFunction0(U_191) ),
inference(clausify,[status(thm)],[f_70_4]) ).
cnf(f_70_6,plain,
( szDzozmdt0(U_192) = U_190
| U_192 != sdtexdt0(U_191,U_190)
| ~ aSubsetOf0(U_190,szDzozmdt0(U_191))
| ~ aFunction0(U_191) ),
inference(clausify,[status(thm)],[f_70_4]) ).
cnf(f_70_7,plain,
( sdtlpdtrp0(U_192,U_187) = sdtlpdtrp0(U_191,U_187)
| ~ aElementOf0(U_187,U_190)
| U_192 != sdtexdt0(U_191,U_190)
| ~ aSubsetOf0(U_190,szDzozmdt0(U_191))
| ~ aFunction0(U_191) ),
inference(clausify,[status(thm)],[f_70_4]) ).
cnf(f_70_8,plain,
( aElementOf0(sK23(U_191,U_190,U_193),U_190)
| szDzozmdt0(U_193) != U_190
| ~ aFunction0(U_193)
| U_193 = sdtexdt0(U_191,U_190)
| ~ aSubsetOf0(U_190,szDzozmdt0(U_191))
| ~ aFunction0(U_191) ),
inference(clausify,[status(thm)],[f_70_4]) ).
cnf(f_70_9,plain,
( sdtlpdtrp0(U_193,sK23(U_191,U_190,U_193)) != sdtlpdtrp0(U_191,sK23(U_191,U_190,U_193))
| szDzozmdt0(U_193) != U_190
| ~ aFunction0(U_193)
| U_193 = sdtexdt0(U_191,U_190)
| ~ aSubsetOf0(U_190,szDzozmdt0(U_191))
| ~ aFunction0(U_191) ),
inference(clausify,[status(thm)],[f_70_4]) ).
fof(f_71_1,plain,
! [W0] :
( ! [W1] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ? [W2,W3] :
( sdtlpdtrp0(W0,W2) = sdtlpdtrp0(W0,W3)
& W2 != W3
& aElementOf0(W3,szDzozmdt0(W0))
& aElementOf0(W2,szDzozmdt0(W0)) )
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(W0)) )
| ~ aFunction0(W0) ),
inference(fof_nnf,[status(thm)],[mImgCount]) ).
fof(f_71_2,plain,
! [U_197] :
( ! [U_196] :
( isCountable0(sdtlcdtrc0(U_197,U_196))
| ? [U_195,U_194] :
( sdtlpdtrp0(U_197,U_195) = sdtlpdtrp0(U_197,U_194)
& U_195 != U_194
& aElementOf0(U_194,szDzozmdt0(U_197))
& aElementOf0(U_195,szDzozmdt0(U_197)) )
| ~ isCountable0(U_196)
| ~ aSubsetOf0(U_196,szDzozmdt0(U_197)) )
| ~ aFunction0(U_197) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
fof(f_71_3,plain,
! [U_197] :
( ! [U_196] :
( isCountable0(sdtlcdtrc0(U_197,U_196))
| ? [U_194] :
( sdtlpdtrp0(U_197,sK24(U_197,U_196)) = sdtlpdtrp0(U_197,U_194)
& sK24(U_197,U_196) != U_194
& aElementOf0(U_194,szDzozmdt0(U_197))
& aElementOf0(sK24(U_197,U_196),szDzozmdt0(U_197)) )
| ~ isCountable0(U_196)
| ~ aSubsetOf0(U_196,szDzozmdt0(U_197)) )
| ~ aFunction0(U_197) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_195,sK24(U_197,U_196))],[f_71_2]) ).
fof(f_71_4,plain,
! [U_197] :
( ! [U_196] :
( isCountable0(sdtlcdtrc0(U_197,U_196))
| ( sdtlpdtrp0(U_197,sK24(U_197,U_196)) = sdtlpdtrp0(U_197,sK25(U_197,U_196))
& sK24(U_197,U_196) != sK25(U_197,U_196)
& aElementOf0(sK25(U_197,U_196),szDzozmdt0(U_197))
& aElementOf0(sK24(U_197,U_196),szDzozmdt0(U_197)) )
| ~ isCountable0(U_196)
| ~ aSubsetOf0(U_196,szDzozmdt0(U_197)) )
| ~ aFunction0(U_197) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_194,sK25(U_197,U_196))],[f_71_3]) ).
cnf(f_71_5,plain,
( aElementOf0(sK24(U_197,U_196),szDzozmdt0(U_197))
| isCountable0(sdtlcdtrc0(U_197,U_196))
| ~ isCountable0(U_196)
| ~ aSubsetOf0(U_196,szDzozmdt0(U_197))
| ~ aFunction0(U_197) ),
inference(clausify,[status(thm)],[f_71_4]) ).
cnf(f_71_6,plain,
( aElementOf0(sK25(U_197,U_196),szDzozmdt0(U_197))
| isCountable0(sdtlcdtrc0(U_197,U_196))
| ~ isCountable0(U_196)
| ~ aSubsetOf0(U_196,szDzozmdt0(U_197))
| ~ aFunction0(U_197) ),
inference(clausify,[status(thm)],[f_71_4]) ).
cnf(f_71_7,plain,
( sK24(U_197,U_196) != sK25(U_197,U_196)
| isCountable0(sdtlcdtrc0(U_197,U_196))
| ~ isCountable0(U_196)
| ~ aSubsetOf0(U_196,szDzozmdt0(U_197))
| ~ aFunction0(U_197) ),
inference(clausify,[status(thm)],[f_71_4]) ).
cnf(f_71_8,plain,
( sdtlpdtrp0(U_197,sK24(U_197,U_196)) = sdtlpdtrp0(U_197,sK25(U_197,U_196))
| isCountable0(sdtlcdtrc0(U_197,U_196))
| ~ isCountable0(U_196)
| ~ aSubsetOf0(U_196,szDzozmdt0(U_197))
| ~ aFunction0(U_197) ),
inference(clausify,[status(thm)],[f_71_4]) ).
fof(f_72_1,plain,
! [W0] :
( ( isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0)))
& aElement0(szDzizrdt0(W0)) )
| ~ isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0)))
| ~ isCountable0(szDzozmdt0(W0))
| ~ aFunction0(W0) ),
inference(fof_nnf,[status(thm)],[mDirichlet]) ).
fof(f_72_2,plain,
! [U_198] :
( ( isCountable0(sdtlbdtrb0(U_198,szDzizrdt0(U_198)))
& aElement0(szDzizrdt0(U_198)) )
| ~ isFinite0(sdtlcdtrc0(U_198,szDzozmdt0(U_198)))
| ~ isCountable0(szDzozmdt0(U_198))
| ~ aFunction0(U_198) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
cnf(f_72_3,plain,
( aElement0(szDzizrdt0(U_198))
| ~ isFinite0(sdtlcdtrc0(U_198,szDzozmdt0(U_198)))
| ~ isCountable0(szDzozmdt0(U_198))
| ~ aFunction0(U_198) ),
inference(clausify,[status(thm)],[f_72_2]) ).
cnf(f_72_4,plain,
( isCountable0(sdtlbdtrb0(U_198,szDzizrdt0(U_198)))
| ~ isFinite0(sdtlcdtrc0(U_198,szDzozmdt0(U_198)))
| ~ isCountable0(szDzozmdt0(U_198))
| ~ aFunction0(U_198) ),
inference(clausify,[status(thm)],[f_72_2]) ).
fof(f_73_1,plain,
( isFinite0(xT)
& aSet0(xT) ),
inference(fof_nnf,[status(thm)],[m__3291]) ).
cnf(f_73_2,plain,
aSet0(xT),
inference(clausify,[status(thm)],[f_73_1]) ).
cnf(f_73_3,plain,
isFinite0(xT),
inference(clausify,[status(thm)],[f_73_1]) ).
fof(f_74_1,plain,
aElementOf0(xK,szNzAzT0),
inference(fof_nnf,[status(thm)],[m__3418]) ).
cnf(f_74_2,plain,
aElementOf0(xK,szNzAzT0),
inference(clausify,[status(thm)],[f_74_1]) ).
fof(f_75_1,plain,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[m__3435]) ).
cnf(f_75_2,plain,
aSubsetOf0(xS,szNzAzT0),
inference(clausify,[status(thm)],[f_75_1]) ).
cnf(f_75_3,plain,
isCountable0(xS),
inference(clausify,[status(thm)],[f_75_1]) ).
fof(f_76_1,plain,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aFunction0(xc) ),
inference(fof_nnf,[status(thm)],[m__3453]) ).
cnf(f_76_2,plain,
aFunction0(xc),
inference(clausify,[status(thm)],[f_76_1]) ).
cnf(f_76_3,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(clausify,[status(thm)],[f_76_1]) ).
cnf(f_76_4,plain,
aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),
inference(clausify,[status(thm)],[f_76_1]) ).
fof(f_77_1,plain,
! [W0] :
( ! [W1] :
( ! [W2] :
( ? [W3] :
( ? [W4] :
( ! [W5] :
( sdtlpdtrp0(W2,W5) = W3
| ~ aElementOf0(W5,slbdtsldtrb0(W4,W0)) )
& isCountable0(W4)
& aSubsetOf0(W4,W1) )
& aElementOf0(W3,xT) )
| ~ iLess0(W0,xK)
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| szDzozmdt0(W2) != slbdtsldtrb0(W1,W0)
| ~ aFunction0(W2) )
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szNzAzT0) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[m__3398]) ).
fof(f_77_2,plain,
! [U_204] :
( ! [U_203] :
( ! [U_202] :
( ? [U_201] :
( ? [U_200] :
( ! [U_199] :
( sdtlpdtrp0(U_202,U_199) = U_201
| ~ aElementOf0(U_199,slbdtsldtrb0(U_200,U_204)) )
& isCountable0(U_200)
& aSubsetOf0(U_200,U_203) )
& aElementOf0(U_201,xT) )
| ~ iLess0(U_204,xK)
| ~ aSubsetOf0(sdtlcdtrc0(U_202,szDzozmdt0(U_202)),xT)
| szDzozmdt0(U_202) != slbdtsldtrb0(U_203,U_204)
| ~ aFunction0(U_202) )
| ~ isCountable0(U_203)
| ~ aSubsetOf0(U_203,szNzAzT0) )
| ~ aElementOf0(U_204,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_77_1]) ).
fof(f_77_3,plain,
! [U_204] :
( ! [U_203] :
( ! [U_202] :
( ( ? [U_200] :
( ! [U_199] :
( sdtlpdtrp0(U_202,U_199) = sK26(U_204,U_203,U_202)
| ~ aElementOf0(U_199,slbdtsldtrb0(U_200,U_204)) )
& isCountable0(U_200)
& aSubsetOf0(U_200,U_203) )
& aElementOf0(sK26(U_204,U_203,U_202),xT) )
| ~ iLess0(U_204,xK)
| ~ aSubsetOf0(sdtlcdtrc0(U_202,szDzozmdt0(U_202)),xT)
| szDzozmdt0(U_202) != slbdtsldtrb0(U_203,U_204)
| ~ aFunction0(U_202) )
| ~ isCountable0(U_203)
| ~ aSubsetOf0(U_203,szNzAzT0) )
| ~ aElementOf0(U_204,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_201,sK26(U_204,U_203,U_202))],[f_77_2]) ).
fof(f_77_4,plain,
! [U_204] :
( ! [U_203] :
( ! [U_202] :
( ( ! [U_199] :
( sdtlpdtrp0(U_202,U_199) = sK26(U_204,U_203,U_202)
| ~ aElementOf0(U_199,slbdtsldtrb0(sK27(U_204,U_203,U_202),U_204)) )
& isCountable0(sK27(U_204,U_203,U_202))
& aSubsetOf0(sK27(U_204,U_203,U_202),U_203)
& aElementOf0(sK26(U_204,U_203,U_202),xT) )
| ~ iLess0(U_204,xK)
| ~ aSubsetOf0(sdtlcdtrc0(U_202,szDzozmdt0(U_202)),xT)
| szDzozmdt0(U_202) != slbdtsldtrb0(U_203,U_204)
| ~ aFunction0(U_202) )
| ~ isCountable0(U_203)
| ~ aSubsetOf0(U_203,szNzAzT0) )
| ~ aElementOf0(U_204,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_200,sK27(U_204,U_203,U_202))],[f_77_3]) ).
cnf(f_77_5,plain,
( aElementOf0(sK26(U_204,U_203,U_202),xT)
| ~ iLess0(U_204,xK)
| ~ aSubsetOf0(sdtlcdtrc0(U_202,szDzozmdt0(U_202)),xT)
| szDzozmdt0(U_202) != slbdtsldtrb0(U_203,U_204)
| ~ aFunction0(U_202)
| ~ isCountable0(U_203)
| ~ aSubsetOf0(U_203,szNzAzT0)
| ~ aElementOf0(U_204,szNzAzT0) ),
inference(clausify,[status(thm)],[f_77_4]) ).
cnf(f_77_6,plain,
( aSubsetOf0(sK27(U_204,U_203,U_202),U_203)
| ~ iLess0(U_204,xK)
| ~ aSubsetOf0(sdtlcdtrc0(U_202,szDzozmdt0(U_202)),xT)
| szDzozmdt0(U_202) != slbdtsldtrb0(U_203,U_204)
| ~ aFunction0(U_202)
| ~ isCountable0(U_203)
| ~ aSubsetOf0(U_203,szNzAzT0)
| ~ aElementOf0(U_204,szNzAzT0) ),
inference(clausify,[status(thm)],[f_77_4]) ).
cnf(f_77_7,plain,
( isCountable0(sK27(U_204,U_203,U_202))
| ~ iLess0(U_204,xK)
| ~ aSubsetOf0(sdtlcdtrc0(U_202,szDzozmdt0(U_202)),xT)
| szDzozmdt0(U_202) != slbdtsldtrb0(U_203,U_204)
| ~ aFunction0(U_202)
| ~ isCountable0(U_203)
| ~ aSubsetOf0(U_203,szNzAzT0)
| ~ aElementOf0(U_204,szNzAzT0) ),
inference(clausify,[status(thm)],[f_77_4]) ).
cnf(f_77_8,plain,
( sdtlpdtrp0(U_202,U_199) = sK26(U_204,U_203,U_202)
| ~ aElementOf0(U_199,slbdtsldtrb0(sK27(U_204,U_203,U_202),U_204))
| ~ iLess0(U_204,xK)
| ~ aSubsetOf0(sdtlcdtrc0(U_202,szDzozmdt0(U_202)),xT)
| szDzozmdt0(U_202) != slbdtsldtrb0(U_203,U_204)
| ~ aFunction0(U_202)
| ~ isCountable0(U_203)
| ~ aSubsetOf0(U_203,szNzAzT0)
| ~ aElementOf0(U_204,szNzAzT0) ),
inference(clausify,[status(thm)],[f_77_4]) ).
fof(f_78_1,plain,
xK != sz00,
inference(fof_nnf,[status(thm)],[m__3462]) ).
cnf(f_78_2,plain,
xK != sz00,
inference(clausify,[status(thm)],[f_78_1]) ).
fof(f_79_1,plain,
xK != sz00,
inference(fof_nnf,[status(thm)],[m__3520]) ).
cnf(f_79_2,plain,
xK != sz00,
inference(clausify,[status(thm)],[f_79_1]) ).
fof(f_80_1,plain,
( szszuzczcdt0(xk) = xK
& aElementOf0(xk,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[m__3533]) ).
cnf(f_80_2,plain,
aElementOf0(xk,szNzAzT0),
inference(clausify,[status(thm)],[f_80_1]) ).
cnf(f_80_3,plain,
szszuzczcdt0(xk) = xK,
inference(clausify,[status(thm)],[f_80_1]) ).
fof(f_81_1,plain,
( ! [W0] :
( ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(fof_nnf,[status(thm)],[m__3623]) ).
fof(f_81_2,plain,
( ! [U_205] :
( ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(U_205)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(U_205)),sdtmndt0(sdtlpdtrp0(xN,U_205),szmzizndt0(sdtlpdtrp0(xN,U_205)))) )
| ~ isCountable0(sdtlpdtrp0(xN,U_205))
| ~ aSubsetOf0(sdtlpdtrp0(xN,U_205),szNzAzT0)
| ~ aElementOf0(U_205,szNzAzT0) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
cnf(f_81_3,plain,
aFunction0(xN),
inference(clausify,[status(thm)],[f_81_2]) ).
cnf(f_81_4,plain,
szDzozmdt0(xN) = szNzAzT0,
inference(clausify,[status(thm)],[f_81_2]) ).
cnf(f_81_5,plain,
sdtlpdtrp0(xN,sz00) = xS,
inference(clausify,[status(thm)],[f_81_2]) ).
cnf(f_81_6,plain,
( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(U_205)),sdtmndt0(sdtlpdtrp0(xN,U_205),szmzizndt0(sdtlpdtrp0(xN,U_205))))
| ~ isCountable0(sdtlpdtrp0(xN,U_205))
| ~ aSubsetOf0(sdtlpdtrp0(xN,U_205),szNzAzT0)
| ~ aElementOf0(U_205,szNzAzT0) ),
inference(clausify,[status(thm)],[f_81_2]) ).
cnf(f_81_7,plain,
( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(U_205)))
| ~ isCountable0(sdtlpdtrp0(xN,U_205))
| ~ aSubsetOf0(sdtlpdtrp0(xN,U_205),szNzAzT0)
| ~ aElementOf0(U_205,szNzAzT0) ),
inference(clausify,[status(thm)],[f_81_2]) ).
fof(f_82_1,plain,
! [W0] :
( ( isCountable0(sdtlpdtrp0(xN,W0))
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[m__3671]) ).
fof(f_82_2,plain,
! [U_206] :
( ( isCountable0(sdtlpdtrp0(xN,U_206))
& aSubsetOf0(sdtlpdtrp0(xN,U_206),szNzAzT0) )
| ~ aElementOf0(U_206,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
cnf(f_82_3,plain,
( aSubsetOf0(sdtlpdtrp0(xN,U_206),szNzAzT0)
| ~ aElementOf0(U_206,szNzAzT0) ),
inference(clausify,[status(thm)],[f_82_2]) ).
cnf(f_82_4,plain,
( isCountable0(sdtlpdtrp0(xN,U_206))
| ~ aElementOf0(U_206,szNzAzT0) ),
inference(clausify,[status(thm)],[f_82_2]) ).
fof(f_83_1,plain,
! [W0,W1] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[m__3754]) ).
fof(f_83_2,plain,
! [U_208,U_207] :
( aSubsetOf0(sdtlpdtrp0(xN,U_208),sdtlpdtrp0(xN,U_207))
| ~ sdtlseqdt0(U_207,U_208)
| ~ aElementOf0(U_207,szNzAzT0)
| ~ aElementOf0(U_208,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
cnf(f_83_3,plain,
( aSubsetOf0(sdtlpdtrp0(xN,U_208),sdtlpdtrp0(xN,U_207))
| ~ sdtlseqdt0(U_207,U_208)
| ~ aElementOf0(U_207,szNzAzT0)
| ~ aElementOf0(U_208,szNzAzT0) ),
inference(clausify,[status(thm)],[f_83_2]) ).
fof(f_84_1,plain,
! [W0,W1] :
( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1))
| W0 = W1
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[m__3821]) ).
fof(f_84_2,plain,
! [U_210,U_209] :
( szmzizndt0(sdtlpdtrp0(xN,U_210)) != szmzizndt0(sdtlpdtrp0(xN,U_209))
| U_210 = U_209
| ~ aElementOf0(U_209,szNzAzT0)
| ~ aElementOf0(U_210,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_84_1]) ).
cnf(f_84_3,plain,
( szmzizndt0(sdtlpdtrp0(xN,U_210)) != szmzizndt0(sdtlpdtrp0(xN,U_209))
| U_210 = U_209
| ~ aElementOf0(U_209,szNzAzT0)
| ~ aElementOf0(U_210,szNzAzT0) ),
inference(clausify,[status(thm)],[f_84_2]) ).
fof(f_85_1,plain,
! [W0] :
( ! [W1] :
( aElementOf0(sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))),slbdtsldtrb0(xS,xK))
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
| ~ aSet0(W1) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[m__3965]) ).
fof(f_85_2,plain,
! [U_212] :
( ! [U_211] :
( aElementOf0(sdtpldt0(U_211,szmzizndt0(sdtlpdtrp0(xN,U_212))),slbdtsldtrb0(xS,xK))
| ~ aElementOf0(U_211,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,U_212),szmzizndt0(sdtlpdtrp0(xN,U_212))),xk))
| ~ aSet0(U_211) )
| ~ aElementOf0(U_212,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
cnf(f_85_3,plain,
( aElementOf0(sdtpldt0(U_211,szmzizndt0(sdtlpdtrp0(xN,U_212))),slbdtsldtrb0(xS,xK))
| ~ aElementOf0(U_211,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,U_212),szmzizndt0(sdtlpdtrp0(xN,U_212))),xk))
| ~ aSet0(U_211)
| ~ aElementOf0(U_212,szNzAzT0) ),
inference(clausify,[status(thm)],[f_85_2]) ).
fof(f_86_1,plain,
( ! [W0] :
( ( ! [W1] :
( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
| ~ aSet0(W1) )
& szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)
& aFunction0(sdtlpdtrp0(xC,W0)) )
| ~ aElementOf0(W0,szNzAzT0) )
& szDzozmdt0(xC) = szNzAzT0
& aFunction0(xC) ),
inference(fof_nnf,[status(thm)],[m__4151]) ).
fof(f_86_2,plain,
( ! [U_214] :
( ( ! [U_213] :
( sdtlpdtrp0(sdtlpdtrp0(xC,U_214),U_213) = sdtlpdtrp0(xc,sdtpldt0(U_213,szmzizndt0(sdtlpdtrp0(xN,U_214))))
| ~ aElementOf0(U_213,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,U_214),szmzizndt0(sdtlpdtrp0(xN,U_214))),xk))
| ~ aSet0(U_213) )
& szDzozmdt0(sdtlpdtrp0(xC,U_214)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,U_214),szmzizndt0(sdtlpdtrp0(xN,U_214))),xk)
& aFunction0(sdtlpdtrp0(xC,U_214)) )
| ~ aElementOf0(U_214,szNzAzT0) )
& szDzozmdt0(xC) = szNzAzT0
& aFunction0(xC) ),
inference(variable_rename,[status(thm)],[f_86_1]) ).
cnf(f_86_3,plain,
aFunction0(xC),
inference(clausify,[status(thm)],[f_86_2]) ).
cnf(f_86_4,plain,
szDzozmdt0(xC) = szNzAzT0,
inference(clausify,[status(thm)],[f_86_2]) ).
cnf(f_86_5,plain,
( aFunction0(sdtlpdtrp0(xC,U_214))
| ~ aElementOf0(U_214,szNzAzT0) ),
inference(clausify,[status(thm)],[f_86_2]) ).
cnf(f_86_6,plain,
( szDzozmdt0(sdtlpdtrp0(xC,U_214)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,U_214),szmzizndt0(sdtlpdtrp0(xN,U_214))),xk)
| ~ aElementOf0(U_214,szNzAzT0) ),
inference(clausify,[status(thm)],[f_86_2]) ).
cnf(f_86_7,plain,
( sdtlpdtrp0(sdtlpdtrp0(xC,U_214),U_213) = sdtlpdtrp0(xc,sdtpldt0(U_213,szmzizndt0(sdtlpdtrp0(xN,U_214))))
| ~ aElementOf0(U_213,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,U_214),szmzizndt0(sdtlpdtrp0(xN,U_214))),xk))
| ~ aSet0(U_213)
| ~ aElementOf0(U_214,szNzAzT0) ),
inference(clausify,[status(thm)],[f_86_2]) ).
fof(f_87_1,plain,
! [W0] :
( aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,W0),szDzozmdt0(sdtlpdtrp0(xC,W0))),xT)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[m__4182]) ).
fof(f_87_2,plain,
! [U_215] :
( aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,U_215),szDzozmdt0(sdtlpdtrp0(xC,U_215))),xT)
| ~ aElementOf0(U_215,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_87_1]) ).
cnf(f_87_3,plain,
( aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,U_215),szDzozmdt0(sdtlpdtrp0(xC,U_215))),xT)
| ~ aElementOf0(U_215,szNzAzT0) ),
inference(clausify,[status(thm)],[f_87_2]) ).
fof(f_88_1,plain,
! [W0] :
( ! [W1] :
( ! [W2] :
( aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
| ~ aElementOf0(W2,slbdtsldtrb0(W1,xk))
| ~ aSet0(W2) )
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[m__4331]) ).
fof(f_88_2,plain,
! [U_218] :
( ! [U_217] :
( ! [U_216] :
( aElementOf0(U_216,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,U_218),szmzizndt0(sdtlpdtrp0(xN,U_218))),xk))
| ~ aElementOf0(U_216,slbdtsldtrb0(U_217,xk))
| ~ aSet0(U_216) )
| ~ isCountable0(U_217)
| ~ aSubsetOf0(U_217,sdtmndt0(sdtlpdtrp0(xN,U_218),szmzizndt0(sdtlpdtrp0(xN,U_218)))) )
| ~ aElementOf0(U_218,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
cnf(f_88_3,plain,
( aElementOf0(U_216,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,U_218),szmzizndt0(sdtlpdtrp0(xN,U_218))),xk))
| ~ aElementOf0(U_216,slbdtsldtrb0(U_217,xk))
| ~ aSet0(U_216)
| ~ isCountable0(U_217)
| ~ aSubsetOf0(U_217,sdtmndt0(sdtlpdtrp0(xN,U_218),szmzizndt0(sdtlpdtrp0(xN,U_218))))
| ~ aElementOf0(U_218,szNzAzT0) ),
inference(clausify,[status(thm)],[f_88_2]) ).
fof(f_89_1,plain,
! [W0] :
( ? [W1] :
( ? [W2] :
( ! [W3] :
( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W3) = W1
| ~ aElementOf0(W3,slbdtsldtrb0(W2,xk))
| ~ aSet0(W3) )
& isCountable0(W2)
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aElementOf0(W1,xT) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[m__4411]) ).
fof(f_89_2,plain,
! [U_222] :
( ? [U_221] :
( ? [U_220] :
( ! [U_219] :
( sdtlpdtrp0(sdtlpdtrp0(xC,U_222),U_219) = U_221
| ~ aElementOf0(U_219,slbdtsldtrb0(U_220,xk))
| ~ aSet0(U_219) )
& isCountable0(U_220)
& aSubsetOf0(U_220,sdtmndt0(sdtlpdtrp0(xN,U_222),szmzizndt0(sdtlpdtrp0(xN,U_222)))) )
& aElementOf0(U_221,xT) )
| ~ aElementOf0(U_222,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_89_1]) ).
fof(f_89_3,plain,
! [U_222] :
( ( ? [U_220] :
( ! [U_219] :
( sdtlpdtrp0(sdtlpdtrp0(xC,U_222),U_219) = sK28(U_222)
| ~ aElementOf0(U_219,slbdtsldtrb0(U_220,xk))
| ~ aSet0(U_219) )
& isCountable0(U_220)
& aSubsetOf0(U_220,sdtmndt0(sdtlpdtrp0(xN,U_222),szmzizndt0(sdtlpdtrp0(xN,U_222)))) )
& aElementOf0(sK28(U_222),xT) )
| ~ aElementOf0(U_222,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_221,sK28(U_222))],[f_89_2]) ).
fof(f_89_4,plain,
! [U_222] :
( ( ! [U_219] :
( sdtlpdtrp0(sdtlpdtrp0(xC,U_222),U_219) = sK28(U_222)
| ~ aElementOf0(U_219,slbdtsldtrb0(sK29(U_222),xk))
| ~ aSet0(U_219) )
& isCountable0(sK29(U_222))
& aSubsetOf0(sK29(U_222),sdtmndt0(sdtlpdtrp0(xN,U_222),szmzizndt0(sdtlpdtrp0(xN,U_222))))
& aElementOf0(sK28(U_222),xT) )
| ~ aElementOf0(U_222,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_220,sK29(U_222))],[f_89_3]) ).
cnf(f_89_5,plain,
( aElementOf0(sK28(U_222),xT)
| ~ aElementOf0(U_222,szNzAzT0) ),
inference(clausify,[status(thm)],[f_89_4]) ).
cnf(f_89_6,plain,
( aSubsetOf0(sK29(U_222),sdtmndt0(sdtlpdtrp0(xN,U_222),szmzizndt0(sdtlpdtrp0(xN,U_222))))
| ~ aElementOf0(U_222,szNzAzT0) ),
inference(clausify,[status(thm)],[f_89_4]) ).
cnf(f_89_7,plain,
( isCountable0(sK29(U_222))
| ~ aElementOf0(U_222,szNzAzT0) ),
inference(clausify,[status(thm)],[f_89_4]) ).
cnf(f_89_8,plain,
( sdtlpdtrp0(sdtlpdtrp0(xC,U_222),U_219) = sK28(U_222)
| ~ aElementOf0(U_219,slbdtsldtrb0(sK29(U_222),xk))
| ~ aSet0(U_219)
| ~ aElementOf0(U_222,szNzAzT0) ),
inference(clausify,[status(thm)],[f_89_4]) ).
fof(f_90_1,plain,
! [W0] :
( ? [W1] :
( ! [W2] :
( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W2) = W1
| ~ aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ~ aSet0(W2) )
& aElementOf0(W1,xT) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[m__4618]) ).
fof(f_90_2,plain,
! [U_225] :
( ? [U_224] :
( ! [U_223] :
( sdtlpdtrp0(sdtlpdtrp0(xC,U_225),U_223) = U_224
| ~ aElementOf0(U_223,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(U_225)),xk))
| ~ aSet0(U_223) )
& aElementOf0(U_224,xT) )
| ~ aElementOf0(U_225,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_90_1]) ).
fof(f_90_3,plain,
! [U_225] :
( ( ! [U_223] :
( sdtlpdtrp0(sdtlpdtrp0(xC,U_225),U_223) = sK30(U_225)
| ~ aElementOf0(U_223,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(U_225)),xk))
| ~ aSet0(U_223) )
& aElementOf0(sK30(U_225),xT) )
| ~ aElementOf0(U_225,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_224,sK30(U_225))],[f_90_2]) ).
cnf(f_90_4,plain,
( aElementOf0(sK30(U_225),xT)
| ~ aElementOf0(U_225,szNzAzT0) ),
inference(clausify,[status(thm)],[f_90_3]) ).
cnf(f_90_5,plain,
( sdtlpdtrp0(sdtlpdtrp0(xC,U_225),U_223) = sK30(U_225)
| ~ aElementOf0(U_223,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(U_225)),xk))
| ~ aSet0(U_223)
| ~ aElementOf0(U_225,szNzAzT0) ),
inference(clausify,[status(thm)],[f_90_3]) ).
fof(f_91_1,plain,
( ! [W0] :
( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0))
| ~ aElementOf0(W0,szNzAzT0) )
& szDzozmdt0(xe) = szNzAzT0
& aFunction0(xe) ),
inference(fof_nnf,[status(thm)],[m__4660]) ).
fof(f_91_2,plain,
( ! [U_226] :
( sdtlpdtrp0(xe,U_226) = szmzizndt0(sdtlpdtrp0(xN,U_226))
| ~ aElementOf0(U_226,szNzAzT0) )
& szDzozmdt0(xe) = szNzAzT0
& aFunction0(xe) ),
inference(variable_rename,[status(thm)],[f_91_1]) ).
cnf(f_91_3,plain,
aFunction0(xe),
inference(clausify,[status(thm)],[f_91_2]) ).
cnf(f_91_4,plain,
szDzozmdt0(xe) = szNzAzT0,
inference(clausify,[status(thm)],[f_91_2]) ).
cnf(f_91_5,plain,
( sdtlpdtrp0(xe,U_226) = szmzizndt0(sdtlpdtrp0(xN,U_226))
| ~ aElementOf0(U_226,szNzAzT0) ),
inference(clausify,[status(thm)],[f_91_2]) ).
fof(f_92_1,plain,
( ! [W0] :
( ! [W1] :
( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1)
| ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ~ aSet0(W1) )
| ~ aElementOf0(W0,szNzAzT0) )
& szDzozmdt0(xd) = szNzAzT0
& aFunction0(xd) ),
inference(fof_nnf,[status(thm)],[m__4730]) ).
fof(f_92_2,plain,
( ! [U_228] :
( ! [U_227] :
( sdtlpdtrp0(xd,U_228) = sdtlpdtrp0(sdtlpdtrp0(xC,U_228),U_227)
| ~ aElementOf0(U_227,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(U_228)),xk))
| ~ aSet0(U_227) )
| ~ aElementOf0(U_228,szNzAzT0) )
& szDzozmdt0(xd) = szNzAzT0
& aFunction0(xd) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
cnf(f_92_3,plain,
aFunction0(xd),
inference(clausify,[status(thm)],[f_92_2]) ).
cnf(f_92_4,plain,
szDzozmdt0(xd) = szNzAzT0,
inference(clausify,[status(thm)],[f_92_2]) ).
cnf(f_92_5,plain,
( sdtlpdtrp0(xd,U_228) = sdtlpdtrp0(sdtlpdtrp0(xC,U_228),U_227)
| ~ aElementOf0(U_227,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(U_228)),xk))
| ~ aSet0(U_227)
| ~ aElementOf0(U_228,szNzAzT0) ),
inference(clausify,[status(thm)],[f_92_2]) ).
fof(f_93_1,plain,
aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),
inference(fof_nnf,[status(thm)],[m__4758]) ).
cnf(f_93_2,plain,
aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),
inference(clausify,[status(thm)],[f_93_1]) ).
fof(f_94_1,plain,
( isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(szDzizrdt0(xd),xT) ),
inference(fof_nnf,[status(thm)],[m__4854]) ).
cnf(f_94_2,plain,
aElementOf0(szDzizrdt0(xd),xT),
inference(clausify,[status(thm)],[f_94_1]) ).
cnf(f_94_3,plain,
isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(clausify,[status(thm)],[f_94_1]) ).
fof(f_95_1,plain,
( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aSet0(xO) ),
inference(fof_nnf,[status(thm)],[m__4891]) ).
cnf(f_95_2,plain,
aSet0(xO),
inference(clausify,[status(thm)],[f_95_1]) ).
cnf(f_95_3,plain,
xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(clausify,[status(thm)],[f_95_1]) ).
fof(f_96_1,plain,
( isCountable0(xO)
& aSet0(xO) ),
inference(fof_nnf,[status(thm)],[m__4908]) ).
cnf(f_96_2,plain,
aSet0(xO),
inference(clausify,[status(thm)],[f_96_1]) ).
cnf(f_96_3,plain,
isCountable0(xO),
inference(clausify,[status(thm)],[f_96_1]) ).
fof(f_97_1,plain,
! [W0] :
( ? [W1] :
( sdtlpdtrp0(xe,W1) = W0
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(W1,szNzAzT0) )
| ~ aElementOf0(W0,xO) ),
inference(fof_nnf,[status(thm)],[m__4982]) ).
fof(f_97_2,plain,
! [U_230] :
( ? [U_229] :
( sdtlpdtrp0(xe,U_229) = U_230
& aElementOf0(U_229,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(U_229,szNzAzT0) )
| ~ aElementOf0(U_230,xO) ),
inference(variable_rename,[status(thm)],[f_97_1]) ).
fof(f_97_3,plain,
! [U_230] :
( ( sdtlpdtrp0(xe,sK31(U_230)) = U_230
& aElementOf0(sK31(U_230),sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(sK31(U_230),szNzAzT0) )
| ~ aElementOf0(U_230,xO) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_229,sK31(U_230))],[f_97_2]) ).
cnf(f_97_4,plain,
( aElementOf0(sK31(U_230),szNzAzT0)
| ~ aElementOf0(U_230,xO) ),
inference(clausify,[status(thm)],[f_97_3]) ).
cnf(f_97_5,plain,
( aElementOf0(sK31(U_230),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aElementOf0(U_230,xO) ),
inference(clausify,[status(thm)],[f_97_3]) ).
cnf(f_97_6,plain,
( sdtlpdtrp0(xe,sK31(U_230)) = U_230
| ~ aElementOf0(U_230,xO) ),
inference(clausify,[status(thm)],[f_97_3]) ).
fof(f_98_1,plain,
aElementOf0(xx,xO),
inference(fof_nnf,[status(thm)],[m__5009]) ).
cnf(f_98_2,plain,
aElementOf0(xx,xO),
inference(clausify,[status(thm)],[f_98_1]) ).
fof(f_99_1,negated_conjecture,
~ ? [W0] :
( sdtlpdtrp0(xe,W0) = xx
& aElementOf0(W0,szNzAzT0) ),
inference(negate,[status(cth)],[m__]) ).
fof(f_99_2,negated_conjecture,
! [W0] :
( sdtlpdtrp0(xe,W0) != xx
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[f_99_1]) ).
fof(f_99_3,negated_conjecture,
! [U_231] :
( sdtlpdtrp0(xe,U_231) != xx
| ~ aElementOf0(U_231,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_99_2]) ).
fof(f_99_4,negated_conjecture,
! [U_231] :
( sdtlpdtrp0(xe,U_231) != xx
| ~ aElementOf0(U_231,szNzAzT0) ),
inference(definitional_conversion,[status(esa)],[f_99_3]) ).
cnf(f_99_5,negated_conjecture,
( sdtlpdtrp0(xe,U_231) != xx
| ~ aElementOf0(U_231,szNzAzT0) ),
inference(clausify,[status(thm)],[f_99_4]) ).
cnf(f_1_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1_4]) ).
cnf(f_2_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_2_4]) ).
cnf(f_4_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_3]) ).
cnf(f_7_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_3]) ).
cnf(f_29_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_29_3]) ).
cnf(f_38_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_38_3]) ).
cnf(f_63_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_63_4]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( sdtpldt0(Eq_x_0,Eq_x_1) = sdtpldt0(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( sdtmndt0(Eq_x_0,Eq_x_1) = sdtmndt0(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( szszuzczcdt0(Eq_x_0) = szszuzczcdt0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sbrdtbr0(Eq_x_0) = sbrdtbr0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( szmzizndt0(Eq_x_0) = szmzizndt0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( szmzazxdt0(Eq_x_0) = szmzazxdt0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( slbdtrb0(Eq_x_0) = slbdtrb0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( slbdtsldtrb0(Eq_x_0,Eq_x_1) = slbdtsldtrb0(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( szDzozmdt0(Eq_x_0) = szDzozmdt0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sdtlpdtrp0(Eq_x_0,Eq_x_1) = sdtlpdtrp0(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sdtlbdtrb0(Eq_x_0,Eq_x_1) = sdtlbdtrb0(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sdtlcdtrc0(Eq_x_0,Eq_x_1) = sdtlcdtrc0(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sdtexdt0(Eq_x_0,Eq_x_1) = sdtexdt0(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( szDzizrdt0(Eq_x_0) = szDzizrdt0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( sK1(Eq_x_0) = sK1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( sK2(Eq_x_0,Eq_x_1) = sK2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( sK3(Eq_x_0,Eq_x_1,Eq_x_2) = sK3(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( sK4(Eq_x_0,Eq_x_1,Eq_x_2) = sK4(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( sK5(Eq_x_0,Eq_x_1,Eq_x_2) = sK5(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( sK6(Eq_x_0,Eq_x_1,Eq_x_2) = sK6(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_24,axiom,
( sK7(Eq_x_0) = sK7(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,axiom,
( sK8(Eq_x_0,Eq_x_1) = sK8(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,axiom,
( sK9(Eq_x_0,Eq_x_1) = sK9(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_27,axiom,
( sK10(Eq_x_0,Eq_x_1) = sK10(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_28,axiom,
( sK11(Eq_x_0,Eq_x_1) = sK11(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_29,axiom,
( sK12(Eq_x_0,Eq_x_1) = sK12(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_30,axiom,
( sK13(Eq_x_0) = sK13(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_31,axiom,
( sK14(Eq_x_0,Eq_x_1,Eq_x_2) = sK14(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_32,axiom,
( sK15(Eq_x_0,Eq_x_1,Eq_x_2) = sK15(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_33,axiom,
( sK16(Eq_x_0,Eq_x_1,Eq_x_2) = sK16(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_34,axiom,
( sK17(Eq_x_0,Eq_x_1,Eq_x_2) = sK17(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_35,axiom,
( sK18(Eq_x_0,Eq_x_1,Eq_x_2) = sK18(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_36,axiom,
( sK19(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK19(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_37,axiom,
( sK20(Eq_x_0,Eq_x_1,Eq_x_2) = sK20(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_38,axiom,
( sK21(Eq_x_0,Eq_x_1,Eq_x_2) = sK21(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_39,axiom,
( sK22(Eq_x_0,Eq_x_1,Eq_x_2) = sK22(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_40,axiom,
( sK23(Eq_x_0,Eq_x_1,Eq_x_2) = sK23(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_41,axiom,
( sK24(Eq_x_0,Eq_x_1) = sK24(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_42,axiom,
( sK25(Eq_x_0,Eq_x_1) = sK25(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_43,axiom,
( sK26(Eq_x_0,Eq_x_1,Eq_x_2) = sK26(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_44,axiom,
( sK27(Eq_x_0,Eq_x_1,Eq_x_2) = sK27(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_45,axiom,
( sK28(Eq_x_0) = sK28(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_46,axiom,
( sK29(Eq_x_0) = sK29(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_47,axiom,
( sK30(Eq_x_0) = sK30(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_48,axiom,
( sK31(Eq_x_0) = sK31(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_49,axiom,
( aSet0(Eq_y_0)
| ~ aSet0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_50,axiom,
( aElement0(Eq_y_0)
| ~ aElement0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_51,axiom,
( aElementOf0(Eq_y_0,Eq_y_1)
| ~ aElementOf0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_52,axiom,
( isFinite0(Eq_y_0)
| ~ isFinite0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_53,axiom,
( isCountable0(Eq_y_0)
| ~ isCountable0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_54,axiom,
( aSubsetOf0(Eq_y_0,Eq_y_1)
| ~ aSubsetOf0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_55,axiom,
( sdtlseqdt0(Eq_y_0,Eq_y_1)
| ~ sdtlseqdt0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_56,axiom,
( iLess0(Eq_y_0,Eq_y_1)
| ~ iLess0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_57,axiom,
( aFunction0(Eq_y_0)
| ~ aFunction0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM602+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 19 18:56:20 UTC 2026
% 0.11/0.37 % CPUTime :
% 4.45/4.76 % SZS status Theorem for theBenchmark
% 4.45/4.76 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------