%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM541+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/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 08:52:34 AM UTC 2026
% Result : Theorem 37.78s 38.09s
% Output : Proof 37.90s
% 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(m__1936,hypothesis,
( aElementOf0(xn,szNzAzT0)
& aElementOf0(xm,szNzAzT0) ),
file('theBenchmark.p',m__1936) ).
fof(m__,conjecture,
( ( ( xm = xn
| ( aElementOf0(xm,slbdtrb0(xn))
& sdtlseqdt0(szszuzczcdt0(xm),xn) ) )
=> ( aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
| sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) ) )
& ( ( aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
& sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) )
=> ( xm = xn
| aElementOf0(xm,slbdtrb0(xn))
| sdtlseqdt0(szszuzczcdt0(xm),xn) ) ) ),
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]) ).
fof(f_1_4,plain,
! [U_0] :
( ~ aSet0(U_0)
| $true ),
inference(definitional_conversion,[status(esa)],[f_1_3]) ).
cnf(f_1_5,plain,
( ~ aSet0(U_0)
| $true ),
inference(clausify,[status(thm)],[f_1_4]) ).
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]) ).
fof(f_2_4,plain,
! [U_1] :
( ~ aElement0(U_1)
| $true ),
inference(definitional_conversion,[status(esa)],[f_2_3]) ).
cnf(f_2_5,plain,
( ~ aElement0(U_1)
| $true ),
inference(clausify,[status(thm)],[f_2_4]) ).
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]) ).
fof(f_3_3,plain,
! [U_3,U_2] :
( aElement0(U_2)
| ~ aElementOf0(U_2,U_3)
| ~ aSet0(U_3) ),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
( aElement0(U_2)
| ~ aElementOf0(U_2,U_3)
| ~ aSet0(U_3) ),
inference(clausify,[status(thm)],[f_3_3]) ).
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]) ).
fof(f_4_3,plain,
! [U_4] :
( $true
| ~ isFinite0(U_4)
| ~ aSet0(U_4) ),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
( $true
| ~ isFinite0(U_4)
| ~ aSet0(U_4) ),
inference(clausify,[status(thm)],[f_4_3]) ).
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]) ).
fof(f_5_5,plain,
( ! [U_8,U_5] :
( ~ aElementOf0(U_5,U_8)
| ~ sP0(U_8,U_5) )
& ! [U_8,U_5] :
( aSet0(U_8)
| ~ sP0(U_8,U_5) )
& ! [U_9] :
( U_9 = slcrc0
| aElementOf0(sK1(U_9),U_9)
| ~ aSet0(U_9) )
& ! [U_8,U_5] :
( sP0(U_8,U_5)
| U_8 != slcrc0 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_5_4]) ).
cnf(f_5_6,plain,
( sP0(U_8,U_5)
| U_8 != slcrc0 ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_7,plain,
( U_9 = slcrc0
| aElementOf0(sK1(U_9),U_9)
| ~ aSet0(U_9) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_8,plain,
( aSet0(U_8)
| ~ sP0(U_8,U_5) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_9,plain,
( ~ aElementOf0(U_5,U_8)
| ~ sP0(U_8,U_5) ),
inference(clausify,[status(thm)],[f_5_5]) ).
fof(f_6_1,plain,
isFinite0(slcrc0),
inference(fof_nnf,[status(thm)],[mEmpFin]) ).
fof(f_6_2,plain,
isFinite0(slcrc0),
inference(definitional_conversion,[status(esa)],[f_6_1]) ).
cnf(f_6_3,plain,
isFinite0(slcrc0),
inference(clausify,[status(thm)],[f_6_2]) ).
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]) ).
fof(f_7_3,plain,
! [U_10] :
( $true
| ~ isCountable0(U_10)
| ~ aSet0(U_10) ),
inference(definitional_conversion,[status(esa)],[f_7_2]) ).
cnf(f_7_4,plain,
( $true
| ~ isCountable0(U_10)
| ~ aSet0(U_10) ),
inference(clausify,[status(thm)],[f_7_3]) ).
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]) ).
fof(f_8_3,plain,
! [U_11] :
( ~ isFinite0(U_11)
| ~ isCountable0(U_11)
| ~ aSet0(U_11) ),
inference(definitional_conversion,[status(esa)],[f_8_2]) ).
cnf(f_8_4,plain,
( ~ isFinite0(U_11)
| ~ isCountable0(U_11)
| ~ aSet0(U_11) ),
inference(clausify,[status(thm)],[f_8_3]) ).
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]) ).
fof(f_9_3,plain,
! [U_12] :
( U_12 != slcrc0
| ~ isCountable0(U_12)
| ~ aSet0(U_12) ),
inference(definitional_conversion,[status(esa)],[f_9_2]) ).
cnf(f_9_4,plain,
( U_12 != slcrc0
| ~ isCountable0(U_12)
| ~ aSet0(U_12) ),
inference(clausify,[status(thm)],[f_9_3]) ).
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]) ).
fof(f_10_5,plain,
( ! [U_16,U_18] :
( ~ aElementOf0(sK2(U_16,U_18),U_16)
| ~ sP2(U_16,U_18) )
& ! [U_16,U_18] :
( aElementOf0(sK2(U_16,U_18),U_18)
| ~ sP2(U_16,U_18) )
& ! [U_13,U_16,U_17] :
( aElementOf0(U_13,U_16)
| ~ aElementOf0(U_13,U_17)
| ~ sP1(U_13,U_16,U_17) )
& ! [U_13,U_16,U_17] :
( aSet0(U_17)
| ~ sP1(U_13,U_16,U_17) )
& ! [U_13,U_16,U_17,U_18] :
( aSubsetOf0(U_18,U_16)
| sP2(U_16,U_18)
| ~ aSet0(U_18)
| ~ sP3(U_13,U_16,U_17,U_18) )
& ! [U_13,U_16,U_17,U_18] :
( sP1(U_13,U_16,U_17)
| ~ aSubsetOf0(U_17,U_16)
| ~ sP3(U_13,U_16,U_17,U_18) )
& ! [U_13,U_16,U_17,U_18] :
( sP3(U_13,U_16,U_17,U_18)
| ~ aSet0(U_16) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1,sP2,sP3])],[f_10_4]) ).
cnf(f_10_6,plain,
( sP3(U_13,U_16,U_17,U_18)
| ~ aSet0(U_16) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_7,plain,
( sP1(U_13,U_16,U_17)
| ~ aSubsetOf0(U_17,U_16)
| ~ sP3(U_13,U_16,U_17,U_18) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_8,plain,
( aSubsetOf0(U_18,U_16)
| sP2(U_16,U_18)
| ~ aSet0(U_18)
| ~ sP3(U_13,U_16,U_17,U_18) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_9,plain,
( aSet0(U_17)
| ~ sP1(U_13,U_16,U_17) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_10,plain,
( aElementOf0(U_13,U_16)
| ~ aElementOf0(U_13,U_17)
| ~ sP1(U_13,U_16,U_17) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_11,plain,
( aElementOf0(sK2(U_16,U_18),U_18)
| ~ sP2(U_16,U_18) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_12,plain,
( ~ aElementOf0(sK2(U_16,U_18),U_16)
| ~ sP2(U_16,U_18) ),
inference(clausify,[status(thm)],[f_10_5]) ).
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]) ).
fof(f_11_3,plain,
! [U_19,U_20] :
( isFinite0(U_19)
| ~ aSubsetOf0(U_19,U_20)
| ~ isFinite0(U_20)
| ~ aSet0(U_20) ),
inference(definitional_conversion,[status(esa)],[f_11_2]) ).
cnf(f_11_4,plain,
( isFinite0(U_19)
| ~ aSubsetOf0(U_19,U_20)
| ~ isFinite0(U_20)
| ~ aSet0(U_20) ),
inference(clausify,[status(thm)],[f_11_3]) ).
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]) ).
fof(f_12_3,plain,
! [U_21] :
( aSubsetOf0(U_21,U_21)
| ~ aSet0(U_21) ),
inference(definitional_conversion,[status(esa)],[f_12_2]) ).
cnf(f_12_4,plain,
( aSubsetOf0(U_21,U_21)
| ~ aSet0(U_21) ),
inference(clausify,[status(thm)],[f_12_3]) ).
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]) ).
fof(f_13_3,plain,
! [U_22,U_23] :
( U_23 = U_22
| ~ aSubsetOf0(U_22,U_23)
| ~ aSubsetOf0(U_23,U_22)
| ~ aSet0(U_22)
| ~ aSet0(U_23) ),
inference(definitional_conversion,[status(esa)],[f_13_2]) ).
cnf(f_13_4,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_3]) ).
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]) ).
fof(f_14_3,plain,
! [U_25,U_26,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(definitional_conversion,[status(esa)],[f_14_2]) ).
cnf(f_14_4,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_3]) ).
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]) ).
fof(f_15_6,plain,
( ! [U_31,U_37,U_30] :
( ~ aElementOf0(sK4(U_31,U_30,U_37),U_37)
| ~ sP9(U_31,U_37,U_30) )
& ! [U_31,U_37,U_30] :
( sK4(U_31,U_30,U_37) = U_30
| aElementOf0(sK4(U_31,U_30,U_37),U_31)
| ~ sP9(U_31,U_37,U_30) )
& ! [U_31,U_37,U_30] :
( aElement0(sK4(U_31,U_30,U_37))
| ~ sP9(U_31,U_37,U_30) )
& ! [U_31,U_37,U_30] :
( sK3(U_31,U_30,U_37) != U_30
| ~ sP7(U_31,U_37,U_30) )
& ! [U_31,U_37,U_30] :
( ~ aElementOf0(sK3(U_31,U_30,U_37),U_31)
| ~ sP7(U_31,U_37,U_30) )
& ! [U_31,U_37,U_30] :
( sP7(U_31,U_37,U_30)
| ~ aElement0(sK3(U_31,U_30,U_37))
| ~ sP8(U_31,U_37,U_30) )
& ! [U_31,U_37,U_30] :
( aElementOf0(sK3(U_31,U_30,U_37),U_37)
| ~ sP8(U_31,U_37,U_30) )
& ! [U_33,U_31,U_30] :
( U_33 != U_30
| ~ sP5(U_33,U_31,U_30) )
& ! [U_33,U_31,U_30] :
( ~ aElementOf0(U_33,U_31)
| ~ sP5(U_33,U_31,U_30) )
& ! [U_31,U_32,U_30] :
( U_32 = U_30
| aElementOf0(U_32,U_31)
| ~ sP4(U_31,U_32,U_30) )
& ! [U_31,U_32,U_30] :
( aElement0(U_32)
| ~ sP4(U_31,U_32,U_30) )
& ! [U_33,U_31,U_32,U_30,U_36] :
( aElementOf0(U_33,U_36)
| sP5(U_33,U_31,U_30)
| ~ aElement0(U_33)
| ~ sP6(U_33,U_31,U_32,U_30,U_36) )
& ! [U_33,U_31,U_32,U_30,U_36] :
( sP4(U_31,U_32,U_30)
| ~ aElementOf0(U_32,U_36)
| ~ sP6(U_33,U_31,U_32,U_30,U_36) )
& ! [U_33,U_31,U_32,U_30,U_36] :
( aSet0(U_36)
| ~ sP6(U_33,U_31,U_32,U_30,U_36) )
& ! [U_33,U_31,U_32,U_37,U_30,U_36] :
( U_37 = sdtpldt0(U_31,U_30)
| sP9(U_31,U_37,U_30)
| sP8(U_31,U_37,U_30)
| ~ aSet0(U_37)
| ~ sP10(U_33,U_31,U_32,U_37,U_30,U_36) )
& ! [U_33,U_31,U_32,U_37,U_30,U_36] :
( sP6(U_33,U_31,U_32,U_30,U_36)
| U_36 != sdtpldt0(U_31,U_30)
| ~ sP10(U_33,U_31,U_32,U_37,U_30,U_36) )
& ! [U_33,U_31,U_32,U_37,U_30,U_36] :
( sP10(U_33,U_31,U_32,U_37,U_30,U_36)
| ~ aElement0(U_30)
| ~ aSet0(U_31) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4,sP5,sP6,sP7,sP8,sP9,sP10])],[f_15_5]) ).
cnf(f_15_7,plain,
( sP10(U_33,U_31,U_32,U_37,U_30,U_36)
| ~ aElement0(U_30)
| ~ aSet0(U_31) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_8,plain,
( sP6(U_33,U_31,U_32,U_30,U_36)
| U_36 != sdtpldt0(U_31,U_30)
| ~ sP10(U_33,U_31,U_32,U_37,U_30,U_36) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_9,plain,
( U_37 = sdtpldt0(U_31,U_30)
| sP9(U_31,U_37,U_30)
| sP8(U_31,U_37,U_30)
| ~ aSet0(U_37)
| ~ sP10(U_33,U_31,U_32,U_37,U_30,U_36) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_10,plain,
( aSet0(U_36)
| ~ sP6(U_33,U_31,U_32,U_30,U_36) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_11,plain,
( sP4(U_31,U_32,U_30)
| ~ aElementOf0(U_32,U_36)
| ~ sP6(U_33,U_31,U_32,U_30,U_36) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_12,plain,
( aElementOf0(U_33,U_36)
| sP5(U_33,U_31,U_30)
| ~ aElement0(U_33)
| ~ sP6(U_33,U_31,U_32,U_30,U_36) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_13,plain,
( aElement0(U_32)
| ~ sP4(U_31,U_32,U_30) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_14,plain,
( U_32 = U_30
| aElementOf0(U_32,U_31)
| ~ sP4(U_31,U_32,U_30) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_15,plain,
( ~ aElementOf0(U_33,U_31)
| ~ sP5(U_33,U_31,U_30) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_16,plain,
( U_33 != U_30
| ~ sP5(U_33,U_31,U_30) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_17,plain,
( aElementOf0(sK3(U_31,U_30,U_37),U_37)
| ~ sP8(U_31,U_37,U_30) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_18,plain,
( sP7(U_31,U_37,U_30)
| ~ aElement0(sK3(U_31,U_30,U_37))
| ~ sP8(U_31,U_37,U_30) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_19,plain,
( ~ aElementOf0(sK3(U_31,U_30,U_37),U_31)
| ~ sP7(U_31,U_37,U_30) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_20,plain,
( sK3(U_31,U_30,U_37) != U_30
| ~ sP7(U_31,U_37,U_30) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_21,plain,
( aElement0(sK4(U_31,U_30,U_37))
| ~ sP9(U_31,U_37,U_30) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_22,plain,
( sK4(U_31,U_30,U_37) = U_30
| aElementOf0(sK4(U_31,U_30,U_37),U_31)
| ~ sP9(U_31,U_37,U_30) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_23,plain,
( ~ aElementOf0(sK4(U_31,U_30,U_37),U_37)
| ~ sP9(U_31,U_37,U_30) ),
inference(clausify,[status(thm)],[f_15_6]) ).
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]) ).
fof(f_16_6,plain,
( ! [U_42,U_48,U_41] :
( ~ aElementOf0(sK6(U_42,U_41,U_48),U_48)
| ~ sP14(U_42,U_48,U_41) )
& ! [U_42,U_48,U_41] :
( sK6(U_42,U_41,U_48) != U_41
| ~ sP14(U_42,U_48,U_41) )
& ! [U_42,U_48,U_41] :
( aElementOf0(sK6(U_42,U_41,U_48),U_42)
| ~ sP14(U_42,U_48,U_41) )
& ! [U_42,U_48,U_41] :
( aElement0(sK6(U_42,U_41,U_48))
| ~ sP14(U_42,U_48,U_41) )
& ! [U_42,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))
| ~ sP13(U_42,U_48,U_41) )
& ! [U_42,U_48,U_41] :
( aElementOf0(sK5(U_42,U_41,U_48),U_48)
| ~ sP13(U_42,U_48,U_41) )
& ! [U_42,U_43,U_41] :
( U_43 != U_41
| ~ sP11(U_42,U_43,U_41) )
& ! [U_42,U_43,U_41] :
( aElementOf0(U_43,U_42)
| ~ sP11(U_42,U_43,U_41) )
& ! [U_42,U_43,U_41] :
( aElement0(U_43)
| ~ sP11(U_42,U_43,U_41) )
& ! [U_42,U_43,U_47,U_41,U_44] :
( aElementOf0(U_44,U_47)
| U_44 = U_41
| ~ aElementOf0(U_44,U_42)
| ~ aElement0(U_44)
| ~ sP12(U_42,U_43,U_47,U_41,U_44) )
& ! [U_42,U_43,U_47,U_41,U_44] :
( sP11(U_42,U_43,U_41)
| ~ aElementOf0(U_43,U_47)
| ~ sP12(U_42,U_43,U_47,U_41,U_44) )
& ! [U_42,U_43,U_47,U_41,U_44] :
( aSet0(U_47)
| ~ sP12(U_42,U_43,U_47,U_41,U_44) )
& ! [U_42,U_43,U_47,U_48,U_41,U_44] :
( U_48 = sdtmndt0(U_42,U_41)
| sP14(U_42,U_48,U_41)
| sP13(U_42,U_48,U_41)
| ~ aSet0(U_48)
| ~ sP15(U_42,U_43,U_47,U_48,U_41,U_44) )
& ! [U_42,U_43,U_47,U_48,U_41,U_44] :
( sP12(U_42,U_43,U_47,U_41,U_44)
| U_47 != sdtmndt0(U_42,U_41)
| ~ sP15(U_42,U_43,U_47,U_48,U_41,U_44) )
& ! [U_42,U_43,U_47,U_48,U_41,U_44] :
( sP15(U_42,U_43,U_47,U_48,U_41,U_44)
| ~ aElement0(U_41)
| ~ aSet0(U_42) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP11,sP12,sP13,sP14,sP15])],[f_16_5]) ).
cnf(f_16_7,plain,
( sP15(U_42,U_43,U_47,U_48,U_41,U_44)
| ~ aElement0(U_41)
| ~ aSet0(U_42) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_8,plain,
( sP12(U_42,U_43,U_47,U_41,U_44)
| U_47 != sdtmndt0(U_42,U_41)
| ~ sP15(U_42,U_43,U_47,U_48,U_41,U_44) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_9,plain,
( U_48 = sdtmndt0(U_42,U_41)
| sP14(U_42,U_48,U_41)
| sP13(U_42,U_48,U_41)
| ~ aSet0(U_48)
| ~ sP15(U_42,U_43,U_47,U_48,U_41,U_44) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_10,plain,
( aSet0(U_47)
| ~ sP12(U_42,U_43,U_47,U_41,U_44) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_11,plain,
( sP11(U_42,U_43,U_41)
| ~ aElementOf0(U_43,U_47)
| ~ sP12(U_42,U_43,U_47,U_41,U_44) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_12,plain,
( aElementOf0(U_44,U_47)
| U_44 = U_41
| ~ aElementOf0(U_44,U_42)
| ~ aElement0(U_44)
| ~ sP12(U_42,U_43,U_47,U_41,U_44) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_13,plain,
( aElement0(U_43)
| ~ sP11(U_42,U_43,U_41) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_14,plain,
( aElementOf0(U_43,U_42)
| ~ sP11(U_42,U_43,U_41) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_15,plain,
( U_43 != U_41
| ~ sP11(U_42,U_43,U_41) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_16,plain,
( aElementOf0(sK5(U_42,U_41,U_48),U_48)
| ~ sP13(U_42,U_48,U_41) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_17,plain,
( 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))
| ~ sP13(U_42,U_48,U_41) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_18,plain,
( aElement0(sK6(U_42,U_41,U_48))
| ~ sP14(U_42,U_48,U_41) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_19,plain,
( aElementOf0(sK6(U_42,U_41,U_48),U_42)
| ~ sP14(U_42,U_48,U_41) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_20,plain,
( sK6(U_42,U_41,U_48) != U_41
| ~ sP14(U_42,U_48,U_41) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_21,plain,
( ~ aElementOf0(sK6(U_42,U_41,U_48),U_48)
| ~ sP14(U_42,U_48,U_41) ),
inference(clausify,[status(thm)],[f_16_6]) ).
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]) ).
fof(f_17_3,plain,
! [U_50,U_49] :
( sdtpldt0(sdtmndt0(U_50,U_49),U_49) = U_50
| ~ aElementOf0(U_49,U_50)
| ~ aSet0(U_50) ),
inference(definitional_conversion,[status(esa)],[f_17_2]) ).
cnf(f_17_4,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_3]) ).
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]) ).
fof(f_18_3,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(definitional_conversion,[status(esa)],[f_18_2]) ).
cnf(f_18_4,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_3]) ).
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]) ).
fof(f_19_3,plain,
! [U_53,U_54] :
( isCountable0(sdtpldt0(U_53,U_54))
| ~ isCountable0(U_53)
| ~ aSet0(U_53)
| ~ aElement0(U_54) ),
inference(definitional_conversion,[status(esa)],[f_19_2]) ).
cnf(f_19_4,plain,
( isCountable0(sdtpldt0(U_53,U_54))
| ~ isCountable0(U_53)
| ~ aSet0(U_53)
| ~ aElement0(U_54) ),
inference(clausify,[status(thm)],[f_19_3]) ).
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]) ).
fof(f_20_3,plain,
! [U_55,U_56] :
( isCountable0(sdtmndt0(U_55,U_56))
| ~ isCountable0(U_55)
| ~ aSet0(U_55)
| ~ aElement0(U_56) ),
inference(definitional_conversion,[status(esa)],[f_20_2]) ).
cnf(f_20_4,plain,
( isCountable0(sdtmndt0(U_55,U_56))
| ~ isCountable0(U_55)
| ~ aSet0(U_55)
| ~ aElement0(U_56) ),
inference(clausify,[status(thm)],[f_20_3]) ).
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]) ).
fof(f_21_3,plain,
! [U_57,U_58] :
( isFinite0(sdtpldt0(U_57,U_58))
| ~ isFinite0(U_57)
| ~ aSet0(U_57)
| ~ aElement0(U_58) ),
inference(definitional_conversion,[status(esa)],[f_21_2]) ).
cnf(f_21_4,plain,
( isFinite0(sdtpldt0(U_57,U_58))
| ~ isFinite0(U_57)
| ~ aSet0(U_57)
| ~ aElement0(U_58) ),
inference(clausify,[status(thm)],[f_21_3]) ).
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]) ).
fof(f_22_3,plain,
! [U_60,U_59] :
( isFinite0(sdtmndt0(U_59,U_60))
| ~ isFinite0(U_59)
| ~ aSet0(U_59)
| ~ aElement0(U_60) ),
inference(definitional_conversion,[status(esa)],[f_22_2]) ).
cnf(f_22_4,plain,
( isFinite0(sdtmndt0(U_59,U_60))
| ~ isFinite0(U_59)
| ~ aSet0(U_59)
| ~ aElement0(U_60) ),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mNATSet]) ).
fof(f_23_2,plain,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
inference(definitional_conversion,[status(esa)],[f_23_1]) ).
cnf(f_23_3,plain,
aSet0(szNzAzT0),
inference(clausify,[status(thm)],[f_23_2]) ).
cnf(f_23_4,plain,
isCountable0(szNzAzT0),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
aElementOf0(sz00,szNzAzT0),
inference(fof_nnf,[status(thm)],[mZeroNum]) ).
fof(f_24_2,plain,
aElementOf0(sz00,szNzAzT0),
inference(definitional_conversion,[status(esa)],[f_24_1]) ).
cnf(f_24_3,plain,
aElementOf0(sz00,szNzAzT0),
inference(clausify,[status(thm)],[f_24_2]) ).
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]) ).
fof(f_25_3,plain,
( ! [U_61] :
( szszuzczcdt0(U_61) != sz00
| ~ sP16(U_61) )
& ! [U_61] :
( aElementOf0(szszuzczcdt0(U_61),szNzAzT0)
| ~ sP16(U_61) )
& ! [U_61] :
( sP16(U_61)
| ~ aElementOf0(U_61,szNzAzT0) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP16])],[f_25_2]) ).
cnf(f_25_4,plain,
( sP16(U_61)
| ~ aElementOf0(U_61,szNzAzT0) ),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_5,plain,
( aElementOf0(szszuzczcdt0(U_61),szNzAzT0)
| ~ sP16(U_61) ),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_6,plain,
( szszuzczcdt0(U_61) != sz00
| ~ sP16(U_61) ),
inference(clausify,[status(thm)],[f_25_3]) ).
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]) ).
fof(f_26_3,plain,
! [U_63,U_62] :
( U_63 = U_62
| szszuzczcdt0(U_63) != szszuzczcdt0(U_62)
| ~ aElementOf0(U_62,szNzAzT0)
| ~ aElementOf0(U_63,szNzAzT0) ),
inference(definitional_conversion,[status(esa)],[f_26_2]) ).
cnf(f_26_4,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_3]) ).
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]) ).
fof(f_27_4,plain,
( ! [U_65] :
( U_65 = szszuzczcdt0(sK7(U_65))
| ~ sP17(U_65) )
& ! [U_65] :
( aElementOf0(sK7(U_65),szNzAzT0)
| ~ sP17(U_65) )
& ! [U_65] :
( sP17(U_65)
| U_65 = sz00
| ~ aElementOf0(U_65,szNzAzT0) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP17])],[f_27_3]) ).
cnf(f_27_5,plain,
( sP17(U_65)
| U_65 = sz00
| ~ aElementOf0(U_65,szNzAzT0) ),
inference(clausify,[status(thm)],[f_27_4]) ).
cnf(f_27_6,plain,
( aElementOf0(sK7(U_65),szNzAzT0)
| ~ sP17(U_65) ),
inference(clausify,[status(thm)],[f_27_4]) ).
cnf(f_27_7,plain,
( U_65 = szszuzczcdt0(sK7(U_65))
| ~ sP17(U_65) ),
inference(clausify,[status(thm)],[f_27_4]) ).
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]) ).
fof(f_28_3,plain,
! [U_66] :
( U_66 != szszuzczcdt0(U_66)
| ~ aElementOf0(U_66,szNzAzT0) ),
inference(definitional_conversion,[status(esa)],[f_28_2]) ).
cnf(f_28_4,plain,
( U_66 != szszuzczcdt0(U_66)
| ~ aElementOf0(U_66,szNzAzT0) ),
inference(clausify,[status(thm)],[f_28_3]) ).
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]) ).
fof(f_29_3,plain,
! [U_67,U_68] :
( $true
| ~ sdtlseqdt0(U_68,U_67)
| ~ aElementOf0(U_67,szNzAzT0)
| ~ aElementOf0(U_68,szNzAzT0) ),
inference(definitional_conversion,[status(esa)],[f_29_2]) ).
cnf(f_29_4,plain,
( $true
| ~ sdtlseqdt0(U_68,U_67)
| ~ aElementOf0(U_67,szNzAzT0)
| ~ aElementOf0(U_68,szNzAzT0) ),
inference(clausify,[status(thm)],[f_29_3]) ).
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]) ).
fof(f_30_3,plain,
! [U_69] :
( sdtlseqdt0(sz00,U_69)
| ~ aElementOf0(U_69,szNzAzT0) ),
inference(definitional_conversion,[status(esa)],[f_30_2]) ).
cnf(f_30_4,plain,
( sdtlseqdt0(sz00,U_69)
| ~ aElementOf0(U_69,szNzAzT0) ),
inference(clausify,[status(thm)],[f_30_3]) ).
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]) ).
fof(f_31_3,plain,
! [U_70] :
( ~ sdtlseqdt0(szszuzczcdt0(U_70),sz00)
| ~ aElementOf0(U_70,szNzAzT0) ),
inference(definitional_conversion,[status(esa)],[f_31_2]) ).
cnf(f_31_4,plain,
( ~ sdtlseqdt0(szszuzczcdt0(U_70),sz00)
| ~ aElementOf0(U_70,szNzAzT0) ),
inference(clausify,[status(thm)],[f_31_3]) ).
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]) ).
fof(f_32_3,plain,
( ! [U_72,U_71] :
( sdtlseqdt0(U_72,U_71)
| ~ sdtlseqdt0(szszuzczcdt0(U_72),szszuzczcdt0(U_71))
| ~ sP18(U_72,U_71) )
& ! [U_72,U_71] :
( sdtlseqdt0(szszuzczcdt0(U_72),szszuzczcdt0(U_71))
| ~ sdtlseqdt0(U_72,U_71)
| ~ sP18(U_72,U_71) )
& ! [U_72,U_71] :
( sP18(U_72,U_71)
| ~ aElementOf0(U_71,szNzAzT0)
| ~ aElementOf0(U_72,szNzAzT0) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP18])],[f_32_2]) ).
cnf(f_32_4,plain,
( sP18(U_72,U_71)
| ~ aElementOf0(U_71,szNzAzT0)
| ~ aElementOf0(U_72,szNzAzT0) ),
inference(clausify,[status(thm)],[f_32_3]) ).
cnf(f_32_5,plain,
( sdtlseqdt0(szszuzczcdt0(U_72),szszuzczcdt0(U_71))
| ~ sdtlseqdt0(U_72,U_71)
| ~ sP18(U_72,U_71) ),
inference(clausify,[status(thm)],[f_32_3]) ).
cnf(f_32_6,plain,
( sdtlseqdt0(U_72,U_71)
| ~ sdtlseqdt0(szszuzczcdt0(U_72),szszuzczcdt0(U_71))
| ~ sP18(U_72,U_71) ),
inference(clausify,[status(thm)],[f_32_3]) ).
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]) ).
fof(f_33_3,plain,
! [U_73] :
( sdtlseqdt0(U_73,szszuzczcdt0(U_73))
| ~ aElementOf0(U_73,szNzAzT0) ),
inference(definitional_conversion,[status(esa)],[f_33_2]) ).
cnf(f_33_4,plain,
( sdtlseqdt0(U_73,szszuzczcdt0(U_73))
| ~ aElementOf0(U_73,szNzAzT0) ),
inference(clausify,[status(thm)],[f_33_3]) ).
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]) ).
fof(f_34_3,plain,
! [U_74] :
( sdtlseqdt0(U_74,U_74)
| ~ aElementOf0(U_74,szNzAzT0) ),
inference(definitional_conversion,[status(esa)],[f_34_2]) ).
cnf(f_34_4,plain,
( sdtlseqdt0(U_74,U_74)
| ~ aElementOf0(U_74,szNzAzT0) ),
inference(clausify,[status(thm)],[f_34_3]) ).
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]) ).
fof(f_35_3,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(definitional_conversion,[status(esa)],[f_35_2]) ).
cnf(f_35_4,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_3]) ).
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]) ).
fof(f_36_3,plain,
! [U_77,U_78,U_79] :
( 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(definitional_conversion,[status(esa)],[f_36_2]) ).
cnf(f_36_4,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_3]) ).
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]) ).
fof(f_37_3,plain,
! [U_80,U_81] :
( sdtlseqdt0(szszuzczcdt0(U_80),U_81)
| sdtlseqdt0(U_81,U_80)
| ~ aElementOf0(U_80,szNzAzT0)
| ~ aElementOf0(U_81,szNzAzT0) ),
inference(definitional_conversion,[status(esa)],[f_37_2]) ).
cnf(f_37_4,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_3]) ).
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]) ).
fof(f_38_3,plain,
! [U_83,U_82] :
( $true
| ~ iLess0(U_83,U_82)
| ~ aElementOf0(U_82,szNzAzT0)
| ~ aElementOf0(U_83,szNzAzT0) ),
inference(definitional_conversion,[status(esa)],[f_38_2]) ).
cnf(f_38_4,plain,
( $true
| ~ iLess0(U_83,U_82)
| ~ aElementOf0(U_82,szNzAzT0)
| ~ aElementOf0(U_83,szNzAzT0) ),
inference(clausify,[status(thm)],[f_38_3]) ).
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]) ).
fof(f_39_3,plain,
! [U_84] :
( iLess0(U_84,szszuzczcdt0(U_84))
| ~ aElementOf0(U_84,szNzAzT0) ),
inference(definitional_conversion,[status(esa)],[f_39_2]) ).
cnf(f_39_4,plain,
( iLess0(U_84,szszuzczcdt0(U_84))
| ~ aElementOf0(U_84,szNzAzT0) ),
inference(clausify,[status(thm)],[f_39_3]) ).
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]) ).
fof(f_40_3,plain,
! [U_85] :
( aElement0(sbrdtbr0(U_85))
| ~ aSet0(U_85) ),
inference(definitional_conversion,[status(esa)],[f_40_2]) ).
cnf(f_40_4,plain,
( aElement0(sbrdtbr0(U_85))
| ~ aSet0(U_85) ),
inference(clausify,[status(thm)],[f_40_3]) ).
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]) ).
fof(f_41_3,plain,
( ! [U_86] :
( aElementOf0(sbrdtbr0(U_86),szNzAzT0)
| ~ isFinite0(U_86)
| ~ sP19(U_86) )
& ! [U_86] :
( isFinite0(U_86)
| ~ aElementOf0(sbrdtbr0(U_86),szNzAzT0)
| ~ sP19(U_86) )
& ! [U_86] :
( sP19(U_86)
| ~ aSet0(U_86) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP19])],[f_41_2]) ).
cnf(f_41_4,plain,
( sP19(U_86)
| ~ aSet0(U_86) ),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_5,plain,
( isFinite0(U_86)
| ~ aElementOf0(sbrdtbr0(U_86),szNzAzT0)
| ~ sP19(U_86) ),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_6,plain,
( aElementOf0(sbrdtbr0(U_86),szNzAzT0)
| ~ isFinite0(U_86)
| ~ sP19(U_86) ),
inference(clausify,[status(thm)],[f_41_3]) ).
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]) ).
fof(f_42_3,plain,
( ! [U_87] :
( sbrdtbr0(U_87) = sz00
| U_87 != slcrc0
| ~ sP20(U_87) )
& ! [U_87] :
( U_87 = slcrc0
| sbrdtbr0(U_87) != sz00
| ~ sP20(U_87) )
& ! [U_87] :
( sP20(U_87)
| ~ aSet0(U_87) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP20])],[f_42_2]) ).
cnf(f_42_4,plain,
( sP20(U_87)
| ~ aSet0(U_87) ),
inference(clausify,[status(thm)],[f_42_3]) ).
cnf(f_42_5,plain,
( U_87 = slcrc0
| sbrdtbr0(U_87) != sz00
| ~ sP20(U_87) ),
inference(clausify,[status(thm)],[f_42_3]) ).
cnf(f_42_6,plain,
( sbrdtbr0(U_87) = sz00
| U_87 != slcrc0
| ~ sP20(U_87) ),
inference(clausify,[status(thm)],[f_42_3]) ).
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]) ).
fof(f_43_3,plain,
! [U_88,U_89] :
( 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(definitional_conversion,[status(esa)],[f_43_2]) ).
cnf(f_43_4,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_3]) ).
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]) ).
fof(f_44_3,plain,
! [U_90,U_91] :
( szszuzczcdt0(sbrdtbr0(sdtmndt0(U_91,U_90))) = sbrdtbr0(U_91)
| ~ aElementOf0(U_90,U_91)
| ~ isFinite0(U_91)
| ~ aSet0(U_91) ),
inference(definitional_conversion,[status(esa)],[f_44_2]) ).
cnf(f_44_4,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_3]) ).
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]) ).
fof(f_45_3,plain,
! [U_93,U_92] :
( sdtlseqdt0(sbrdtbr0(U_92),sbrdtbr0(U_93))
| ~ aSubsetOf0(U_92,U_93)
| ~ isFinite0(U_93)
| ~ aSet0(U_93) ),
inference(definitional_conversion,[status(esa)],[f_45_2]) ).
cnf(f_45_4,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_3]) ).
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]) ).
fof(f_46_4,plain,
( ! [U_95,U_96] :
( sbrdtbr0(sK8(U_96,U_95)) = U_95
| ~ sP21(U_95,U_96) )
& ! [U_95,U_96] :
( aSubsetOf0(sK8(U_96,U_95),U_96)
| ~ sP21(U_95,U_96) )
& ! [U_95,U_96] :
( sP21(U_95,U_96)
| ~ sdtlseqdt0(U_95,sbrdtbr0(U_96))
| ~ isFinite0(U_96)
| ~ aElementOf0(U_95,szNzAzT0)
| ~ aSet0(U_96) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP21])],[f_46_3]) ).
cnf(f_46_5,plain,
( sP21(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_4]) ).
cnf(f_46_6,plain,
( aSubsetOf0(sK8(U_96,U_95),U_96)
| ~ sP21(U_95,U_96) ),
inference(clausify,[status(thm)],[f_46_4]) ).
cnf(f_46_7,plain,
( sbrdtbr0(sK8(U_96,U_95)) = U_95
| ~ sP21(U_95,U_96) ),
inference(clausify,[status(thm)],[f_46_4]) ).
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]) ).
fof(f_47_5,plain,
( ! [U_100,U_102] :
( ~ sdtlseqdt0(U_102,sK9(U_100,U_102))
| ~ sP23(U_100,U_102) )
& ! [U_100,U_102] :
( aElementOf0(sK9(U_100,U_102),U_100)
| ~ sP23(U_100,U_102) )
& ! [U_100,U_97,U_101] :
( sdtlseqdt0(U_101,U_97)
| ~ aElementOf0(U_97,U_100)
| ~ sP22(U_100,U_97,U_101) )
& ! [U_100,U_97,U_101] :
( aElementOf0(U_101,U_100)
| ~ sP22(U_100,U_97,U_101) )
& ! [U_100,U_97,U_101,U_102] :
( U_102 = szmzizndt0(U_100)
| sP23(U_100,U_102)
| ~ aElementOf0(U_102,U_100)
| ~ sP24(U_100,U_97,U_101,U_102) )
& ! [U_100,U_97,U_101,U_102] :
( sP22(U_100,U_97,U_101)
| U_101 != szmzizndt0(U_100)
| ~ sP24(U_100,U_97,U_101,U_102) )
& ! [U_100,U_97,U_101,U_102] :
( sP24(U_100,U_97,U_101,U_102)
| U_100 = slcrc0
| ~ aSubsetOf0(U_100,szNzAzT0) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP22,sP23,sP24])],[f_47_4]) ).
cnf(f_47_6,plain,
( sP24(U_100,U_97,U_101,U_102)
| U_100 = slcrc0
| ~ aSubsetOf0(U_100,szNzAzT0) ),
inference(clausify,[status(thm)],[f_47_5]) ).
cnf(f_47_7,plain,
( sP22(U_100,U_97,U_101)
| U_101 != szmzizndt0(U_100)
| ~ sP24(U_100,U_97,U_101,U_102) ),
inference(clausify,[status(thm)],[f_47_5]) ).
cnf(f_47_8,plain,
( U_102 = szmzizndt0(U_100)
| sP23(U_100,U_102)
| ~ aElementOf0(U_102,U_100)
| ~ sP24(U_100,U_97,U_101,U_102) ),
inference(clausify,[status(thm)],[f_47_5]) ).
cnf(f_47_9,plain,
( aElementOf0(U_101,U_100)
| ~ sP22(U_100,U_97,U_101) ),
inference(clausify,[status(thm)],[f_47_5]) ).
cnf(f_47_10,plain,
( sdtlseqdt0(U_101,U_97)
| ~ aElementOf0(U_97,U_100)
| ~ sP22(U_100,U_97,U_101) ),
inference(clausify,[status(thm)],[f_47_5]) ).
cnf(f_47_11,plain,
( aElementOf0(sK9(U_100,U_102),U_100)
| ~ sP23(U_100,U_102) ),
inference(clausify,[status(thm)],[f_47_5]) ).
cnf(f_47_12,plain,
( ~ sdtlseqdt0(U_102,sK9(U_100,U_102))
| ~ sP23(U_100,U_102) ),
inference(clausify,[status(thm)],[f_47_5]) ).
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]) ).
fof(f_48_5,plain,
( ! [U_108,U_106] :
( ~ sdtlseqdt0(sK10(U_106,U_108),U_108)
| ~ sP26(U_108,U_106) )
& ! [U_108,U_106] :
( aElementOf0(sK10(U_106,U_108),U_106)
| ~ sP26(U_108,U_106) )
& ! [U_107,U_106,U_103] :
( sdtlseqdt0(U_103,U_107)
| ~ aElementOf0(U_103,U_106)
| ~ sP25(U_107,U_106,U_103) )
& ! [U_107,U_106,U_103] :
( aElementOf0(U_107,U_106)
| ~ sP25(U_107,U_106,U_103) )
& ! [U_108,U_107,U_106,U_103] :
( U_108 = szmzazxdt0(U_106)
| sP26(U_108,U_106)
| ~ aElementOf0(U_108,U_106)
| ~ sP27(U_108,U_107,U_106,U_103) )
& ! [U_108,U_107,U_106,U_103] :
( sP25(U_107,U_106,U_103)
| U_107 != szmzazxdt0(U_106)
| ~ sP27(U_108,U_107,U_106,U_103) )
& ! [U_108,U_107,U_106,U_103] :
( sP27(U_108,U_107,U_106,U_103)
| U_106 = slcrc0
| ~ isFinite0(U_106)
| ~ aSubsetOf0(U_106,szNzAzT0) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP25,sP26,sP27])],[f_48_4]) ).
cnf(f_48_6,plain,
( sP27(U_108,U_107,U_106,U_103)
| U_106 = slcrc0
| ~ isFinite0(U_106)
| ~ aSubsetOf0(U_106,szNzAzT0) ),
inference(clausify,[status(thm)],[f_48_5]) ).
cnf(f_48_7,plain,
( sP25(U_107,U_106,U_103)
| U_107 != szmzazxdt0(U_106)
| ~ sP27(U_108,U_107,U_106,U_103) ),
inference(clausify,[status(thm)],[f_48_5]) ).
cnf(f_48_8,plain,
( U_108 = szmzazxdt0(U_106)
| sP26(U_108,U_106)
| ~ aElementOf0(U_108,U_106)
| ~ sP27(U_108,U_107,U_106,U_103) ),
inference(clausify,[status(thm)],[f_48_5]) ).
cnf(f_48_9,plain,
( aElementOf0(U_107,U_106)
| ~ sP25(U_107,U_106,U_103) ),
inference(clausify,[status(thm)],[f_48_5]) ).
cnf(f_48_10,plain,
( sdtlseqdt0(U_103,U_107)
| ~ aElementOf0(U_103,U_106)
| ~ sP25(U_107,U_106,U_103) ),
inference(clausify,[status(thm)],[f_48_5]) ).
cnf(f_48_11,plain,
( aElementOf0(sK10(U_106,U_108),U_106)
| ~ sP26(U_108,U_106) ),
inference(clausify,[status(thm)],[f_48_5]) ).
cnf(f_48_12,plain,
( ~ sdtlseqdt0(sK10(U_106,U_108),U_108)
| ~ sP26(U_108,U_106) ),
inference(clausify,[status(thm)],[f_48_5]) ).
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]) ).
fof(f_49_3,plain,
! [U_109,U_110] :
( 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(definitional_conversion,[status(esa)],[f_49_2]) ).
cnf(f_49_4,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_3]) ).
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]) ).
fof(f_50_6,plain,
( ! [U_114,U_120] :
( ~ aElementOf0(sK12(U_114,U_120),U_120)
| ~ sP31(U_114,U_120) )
& ! [U_114,U_120] :
( sdtlseqdt0(szszuzczcdt0(sK12(U_114,U_120)),U_114)
| ~ sP31(U_114,U_120) )
& ! [U_114,U_120] :
( aElementOf0(sK12(U_114,U_120),szNzAzT0)
| ~ sP31(U_114,U_120) )
& ! [U_114,U_120] :
( ~ sdtlseqdt0(szszuzczcdt0(sK11(U_114,U_120)),U_114)
| ~ aElementOf0(sK11(U_114,U_120),szNzAzT0)
| ~ sP30(U_114,U_120) )
& ! [U_114,U_120] :
( aElementOf0(sK11(U_114,U_120),U_120)
| ~ sP30(U_114,U_120) )
& ! [U_114,U_115] :
( sdtlseqdt0(szszuzczcdt0(U_115),U_114)
| ~ sP28(U_114,U_115) )
& ! [U_114,U_115] :
( aElementOf0(U_115,szNzAzT0)
| ~ sP28(U_114,U_115) )
& ! [U_116,U_114,U_119,U_115] :
( aElementOf0(U_116,U_119)
| ~ sdtlseqdt0(szszuzczcdt0(U_116),U_114)
| ~ aElementOf0(U_116,szNzAzT0)
| ~ sP29(U_116,U_114,U_119,U_115) )
& ! [U_116,U_114,U_119,U_115] :
( sP28(U_114,U_115)
| ~ aElementOf0(U_115,U_119)
| ~ sP29(U_116,U_114,U_119,U_115) )
& ! [U_116,U_114,U_119,U_115] :
( aSet0(U_119)
| ~ sP29(U_116,U_114,U_119,U_115) )
& ! [U_116,U_114,U_120,U_119,U_115] :
( U_120 = slbdtrb0(U_114)
| sP31(U_114,U_120)
| sP30(U_114,U_120)
| ~ aSet0(U_120)
| ~ sP32(U_116,U_114,U_120,U_119,U_115) )
& ! [U_116,U_114,U_120,U_119,U_115] :
( sP29(U_116,U_114,U_119,U_115)
| U_119 != slbdtrb0(U_114)
| ~ sP32(U_116,U_114,U_120,U_119,U_115) )
& ! [U_116,U_114,U_120,U_119,U_115] :
( sP32(U_116,U_114,U_120,U_119,U_115)
| ~ aElementOf0(U_114,szNzAzT0) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP28,sP29,sP30,sP31,sP32])],[f_50_5]) ).
cnf(f_50_7,plain,
( sP32(U_116,U_114,U_120,U_119,U_115)
| ~ aElementOf0(U_114,szNzAzT0) ),
inference(clausify,[status(thm)],[f_50_6]) ).
cnf(f_50_8,plain,
( sP29(U_116,U_114,U_119,U_115)
| U_119 != slbdtrb0(U_114)
| ~ sP32(U_116,U_114,U_120,U_119,U_115) ),
inference(clausify,[status(thm)],[f_50_6]) ).
cnf(f_50_9,plain,
( U_120 = slbdtrb0(U_114)
| sP31(U_114,U_120)
| sP30(U_114,U_120)
| ~ aSet0(U_120)
| ~ sP32(U_116,U_114,U_120,U_119,U_115) ),
inference(clausify,[status(thm)],[f_50_6]) ).
cnf(f_50_10,plain,
( aSet0(U_119)
| ~ sP29(U_116,U_114,U_119,U_115) ),
inference(clausify,[status(thm)],[f_50_6]) ).
cnf(f_50_11,plain,
( sP28(U_114,U_115)
| ~ aElementOf0(U_115,U_119)
| ~ sP29(U_116,U_114,U_119,U_115) ),
inference(clausify,[status(thm)],[f_50_6]) ).
cnf(f_50_12,plain,
( aElementOf0(U_116,U_119)
| ~ sdtlseqdt0(szszuzczcdt0(U_116),U_114)
| ~ aElementOf0(U_116,szNzAzT0)
| ~ sP29(U_116,U_114,U_119,U_115) ),
inference(clausify,[status(thm)],[f_50_6]) ).
cnf(f_50_13,plain,
( aElementOf0(U_115,szNzAzT0)
| ~ sP28(U_114,U_115) ),
inference(clausify,[status(thm)],[f_50_6]) ).
cnf(f_50_14,plain,
( sdtlseqdt0(szszuzczcdt0(U_115),U_114)
| ~ sP28(U_114,U_115) ),
inference(clausify,[status(thm)],[f_50_6]) ).
cnf(f_50_15,plain,
( aElementOf0(sK11(U_114,U_120),U_120)
| ~ sP30(U_114,U_120) ),
inference(clausify,[status(thm)],[f_50_6]) ).
cnf(f_50_16,plain,
( ~ sdtlseqdt0(szszuzczcdt0(sK11(U_114,U_120)),U_114)
| ~ aElementOf0(sK11(U_114,U_120),szNzAzT0)
| ~ sP30(U_114,U_120) ),
inference(clausify,[status(thm)],[f_50_6]) ).
cnf(f_50_17,plain,
( aElementOf0(sK12(U_114,U_120),szNzAzT0)
| ~ sP31(U_114,U_120) ),
inference(clausify,[status(thm)],[f_50_6]) ).
cnf(f_50_18,plain,
( sdtlseqdt0(szszuzczcdt0(sK12(U_114,U_120)),U_114)
| ~ sP31(U_114,U_120) ),
inference(clausify,[status(thm)],[f_50_6]) ).
cnf(f_50_19,plain,
( ~ aElementOf0(sK12(U_114,U_120),U_120)
| ~ sP31(U_114,U_120) ),
inference(clausify,[status(thm)],[f_50_6]) ).
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]) ).
fof(f_51_3,plain,
! [U_121] :
( isFinite0(slbdtrb0(U_121))
| ~ aElementOf0(U_121,szNzAzT0) ),
inference(definitional_conversion,[status(esa)],[f_51_2]) ).
cnf(f_51_4,plain,
( isFinite0(slbdtrb0(U_121))
| ~ aElementOf0(U_121,szNzAzT0) ),
inference(clausify,[status(thm)],[f_51_3]) ).
fof(f_52_1,plain,
slbdtrb0(sz00) = slcrc0,
inference(fof_nnf,[status(thm)],[mSegZero]) ).
fof(f_52_2,plain,
slbdtrb0(sz00) = slcrc0,
inference(definitional_conversion,[status(esa)],[f_52_1]) ).
cnf(f_52_3,plain,
slbdtrb0(sz00) = slcrc0,
inference(clausify,[status(thm)],[f_52_2]) ).
fof(f_53_1,plain,
( aElementOf0(xn,szNzAzT0)
& aElementOf0(xm,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[m__1936]) ).
fof(f_53_2,plain,
( aElementOf0(xn,szNzAzT0)
& aElementOf0(xm,szNzAzT0) ),
inference(definitional_conversion,[status(esa)],[f_53_1]) ).
cnf(f_53_3,plain,
aElementOf0(xm,szNzAzT0),
inference(clausify,[status(thm)],[f_53_2]) ).
cnf(f_53_4,plain,
aElementOf0(xn,szNzAzT0),
inference(clausify,[status(thm)],[f_53_2]) ).
fof(f_54_1,negated_conjecture,
~ ( ( ( xm = xn
| ( aElementOf0(xm,slbdtrb0(xn))
& sdtlseqdt0(szszuzczcdt0(xm),xn) ) )
=> ( aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
| sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) ) )
& ( ( aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
& sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) )
=> ( xm = xn
| aElementOf0(xm,slbdtrb0(xn))
| sdtlseqdt0(szszuzczcdt0(xm),xn) ) ) ),
inference(negate,[status(cth)],[m__]) ).
fof(f_54_2,negated_conjecture,
( ( ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
& ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
& ( xm = xn
| ( aElementOf0(xm,slbdtrb0(xn))
& sdtlseqdt0(szszuzczcdt0(xm),xn) ) ) )
| ( xm != xn
& ~ aElementOf0(xm,slbdtrb0(xn))
& ~ sdtlseqdt0(szszuzczcdt0(xm),xn)
& aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
& sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) ) ),
inference(fof_nnf,[status(thm)],[f_54_1]) ).
fof(f_54_3,negated_conjecture,
( ( aElementOf0(xm,slbdtrb0(xn))
| ~ sP34 )
& ( sdtlseqdt0(szszuzczcdt0(xm),xn)
| ~ sP34 )
& ( ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
| ~ sP35 )
& ( ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| ~ sP35 )
& ( xm = xn
| sP34
| ~ sP35 )
& ( xm != xn
| ~ sP33 )
& ( ~ aElementOf0(xm,slbdtrb0(xn))
| ~ sP33 )
& ( ~ sdtlseqdt0(szszuzczcdt0(xm),xn)
| ~ sP33 )
& ( aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
| ~ sP33 )
& ( sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| ~ sP33 )
& ( sP35
| sP33 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP33,sP34,sP35])],[f_54_2]) ).
cnf(f_54_4,negated_conjecture,
( sP35
| sP33 ),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_5,negated_conjecture,
( sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| ~ sP33 ),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_6,negated_conjecture,
( aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
| ~ sP33 ),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_7,negated_conjecture,
( ~ sdtlseqdt0(szszuzczcdt0(xm),xn)
| ~ sP33 ),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_8,negated_conjecture,
( ~ aElementOf0(xm,slbdtrb0(xn))
| ~ sP33 ),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_9,negated_conjecture,
( xm != xn
| ~ sP33 ),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_10,negated_conjecture,
( xm = xn
| sP34
| ~ sP35 ),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_11,negated_conjecture,
( ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| ~ sP35 ),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_12,negated_conjecture,
( ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
| ~ sP35 ),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_13,negated_conjecture,
( sdtlseqdt0(szszuzczcdt0(xm),xn)
| ~ sP34 ),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_14,negated_conjecture,
( aElementOf0(xm,slbdtrb0(xn))
| ~ sP34 ),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_1_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1_5]) ).
cnf(f_2_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_2_5]) ).
cnf(f_4_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_4]) ).
cnf(f_7_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_4]) ).
cnf(f_29_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_29_4]) ).
cnf(f_38_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_38_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,
( sK1(Eq_x_0) = sK1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,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_13,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_14,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_15,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_16,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_17,axiom,
( sK7(Eq_x_0) = sK7(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,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_19,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_20,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_21,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_22,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_23,axiom,
( aSet0(Eq_y_0)
| ~ aSet0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( aElement0(Eq_y_0)
| ~ aElement0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,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_26,axiom,
( isFinite0(Eq_y_0)
| ~ isFinite0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( isCountable0(Eq_y_0)
| ~ isCountable0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,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_29,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_30,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_31,axiom,
( sP0(Eq_y_0,Eq_y_1)
| ~ sP0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_32,axiom,
( sP1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP1(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,axiom,
( sP2(Eq_y_0,Eq_y_1)
| ~ sP2(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_34,axiom,
( sP3(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP3(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_35,axiom,
( sP4(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP4(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_36,axiom,
( sP5(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP5(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_37,axiom,
( sP6(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP6(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(equality_38,axiom,
( sP7(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP7(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_39,axiom,
( sP8(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP8(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_40,axiom,
( sP9(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP9(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_41,axiom,
( sP10(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP10(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(equality_42,axiom,
( sP11(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP11(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_43,axiom,
( sP12(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP12(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(equality_44,axiom,
( sP13(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP13(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_45,axiom,
( sP14(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP14(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_46,axiom,
( sP15(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP15(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(equality_47,axiom,
( sP16(Eq_y_0)
| ~ sP16(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_48,axiom,
( sP17(Eq_y_0)
| ~ sP17(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_49,axiom,
( sP18(Eq_y_0,Eq_y_1)
| ~ sP18(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_50,axiom,
( sP19(Eq_y_0)
| ~ sP19(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_51,axiom,
( sP20(Eq_y_0)
| ~ sP20(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_52,axiom,
( sP21(Eq_y_0,Eq_y_1)
| ~ sP21(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_53,axiom,
( sP22(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP22(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_54,axiom,
( sP23(Eq_y_0,Eq_y_1)
| ~ sP23(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,
( sP24(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP24(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_56,axiom,
( sP25(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP25(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_57,axiom,
( sP26(Eq_y_0,Eq_y_1)
| ~ sP26(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_58,axiom,
( sP27(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP27(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_59,axiom,
( sP28(Eq_y_0,Eq_y_1)
| ~ sP28(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_60,axiom,
( sP29(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP29(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_61,axiom,
( sP30(Eq_y_0,Eq_y_1)
| ~ sP30(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_62,axiom,
( sP31(Eq_y_0,Eq_y_1)
| ~ sP31(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_63,axiom,
( sP32(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP32(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM541+2 : 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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 19 18:45:21 UTC 2026
% 0.10/0.36 % CPUTime :
% 37.78/38.09 % SZS status Theorem for theBenchmark
% 37.78/38.09 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------