%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM455+6 : 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 : n026.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 08:52:17 AM UTC 2026
% Result : Theorem 8.87s 9.17s
% Output : Proof 8.94s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(mIntegers,axiom,
! [W0] :
( aInteger0(W0)
=> $true ),
file('theBenchmark.p',mIntegers) ).
fof(mIntZero,axiom,
aInteger0(sz00),
file('theBenchmark.p',mIntZero) ).
fof(mIntOne,axiom,
aInteger0(sz10),
file('theBenchmark.p',mIntOne) ).
fof(mIntNeg,axiom,
! [W0] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ),
file('theBenchmark.p',mIntNeg) ).
fof(mIntPlus,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> aInteger0(sdtpldt0(W0,W1)) ),
file('theBenchmark.p',mIntPlus) ).
fof(mIntMult,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> aInteger0(sdtasdt0(W0,W1)) ),
file('theBenchmark.p',mIntMult) ).
fof(mAddAsso,axiom,
! [W0,W1,W2] :
( ( aInteger0(W2)
& aInteger0(W1)
& aInteger0(W0) )
=> sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ),
file('theBenchmark.p',mAddAsso) ).
fof(mAddComm,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
file('theBenchmark.p',mAddComm) ).
fof(mAddZero,axiom,
! [W0] :
( aInteger0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
file('theBenchmark.p',mAddZero) ).
fof(mAddNeg,axiom,
! [W0] :
( aInteger0(W0)
=> ( sz00 = sdtpldt0(smndt0(W0),W0)
& sdtpldt0(W0,smndt0(W0)) = sz00 ) ),
file('theBenchmark.p',mAddNeg) ).
fof(mMulAsso,axiom,
! [W0,W1,W2] :
( ( aInteger0(W2)
& aInteger0(W1)
& aInteger0(W0) )
=> sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ),
file('theBenchmark.p',mMulAsso) ).
fof(mMulComm,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('theBenchmark.p',mMulComm) ).
fof(mMulOne,axiom,
! [W0] :
( aInteger0(W0)
=> ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 ) ),
file('theBenchmark.p',mMulOne) ).
fof(mDistrib,axiom,
! [W0,W1,W2] :
( ( aInteger0(W2)
& aInteger0(W1)
& aInteger0(W0) )
=> ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) ) ),
file('theBenchmark.p',mDistrib) ).
fof(mMulZero,axiom,
! [W0] :
( aInteger0(W0)
=> ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 ) ),
file('theBenchmark.p',mMulZero) ).
fof(mMulMinOne,axiom,
! [W0] :
( aInteger0(W0)
=> ( smndt0(W0) = sdtasdt0(W0,smndt0(sz10))
& sdtasdt0(smndt0(sz10),W0) = smndt0(W0) ) ),
file('theBenchmark.p',mMulMinOne) ).
fof(mZeroDiv,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> ( sdtasdt0(W0,W1) = sz00
=> ( W1 = sz00
| W0 = sz00 ) ) ),
file('theBenchmark.p',mZeroDiv) ).
fof(mDivisor,definition,
! [W0] :
( aInteger0(W0)
=> ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) ) ) ),
file('theBenchmark.p',mDivisor) ).
fof(mEquMod,definition,
! [W0,W1,W2] :
( ( W2 != sz00
& aInteger0(W2)
& aInteger0(W1)
& aInteger0(W0) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ),
file('theBenchmark.p',mEquMod) ).
fof(mEquModRef,axiom,
! [W0,W1] :
( ( W1 != sz00
& aInteger0(W1)
& aInteger0(W0) )
=> sdteqdtlpzmzozddtrp0(W0,W0,W1) ),
file('theBenchmark.p',mEquModRef) ).
fof(mEquModSym,axiom,
! [W0,W1,W2] :
( ( W2 != sz00
& aInteger0(W2)
& aInteger0(W1)
& aInteger0(W0) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
=> sdteqdtlpzmzozddtrp0(W1,W0,W2) ) ),
file('theBenchmark.p',mEquModSym) ).
fof(mEquModTrn,axiom,
! [W0,W1,W2,W3] :
( ( aInteger0(W3)
& W2 != sz00
& aInteger0(W2)
& aInteger0(W1)
& aInteger0(W0) )
=> ( ( sdteqdtlpzmzozddtrp0(W1,W3,W2)
& sdteqdtlpzmzozddtrp0(W0,W1,W2) )
=> sdteqdtlpzmzozddtrp0(W0,W3,W2) ) ),
file('theBenchmark.p',mEquModTrn) ).
fof(mEquModMul,axiom,
! [W0,W1,W2,W3] :
( ( W3 != sz00
& aInteger0(W3)
& W2 != sz00
& aInteger0(W2)
& aInteger0(W1)
& aInteger0(W0) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,sdtasdt0(W2,W3))
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W3)
& sdteqdtlpzmzozddtrp0(W0,W1,W2) ) ) ),
file('theBenchmark.p',mEquModMul) ).
fof(mPrime,axiom,
! [W0] :
( ( W0 != sz00
& aInteger0(W0) )
=> ( isPrime0(W0)
=> $true ) ),
file('theBenchmark.p',mPrime) ).
fof(mPrimeDivisor,axiom,
! [W0] :
( aInteger0(W0)
=> ( ? [W1] :
( isPrime0(W1)
& aDivisorOf0(W1,W0) )
<=> ( W0 != smndt0(sz10)
& W0 != sz10 ) ) ),
file('theBenchmark.p',mPrimeDivisor) ).
fof(mSets,axiom,
! [W0] :
( aSet0(W0)
=> $true ),
file('theBenchmark.p',mSets) ).
fof(mElements,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> $true ) ),
file('theBenchmark.p',mElements) ).
fof(mSubset,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& aSet0(W1) ) ) ),
file('theBenchmark.p',mSubset) ).
fof(mFinSet,axiom,
! [W0] :
( aSet0(W0)
=> ( isFinite0(W0)
=> $true ) ),
file('theBenchmark.p',mFinSet) ).
fof(mUnion,definition,
! [W0,W1] :
( ( aSubsetOf0(W1,cS1395)
& aSubsetOf0(W0,cS1395) )
=> ! [W2] :
( W2 = sdtbsmnsldt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( ( aElementOf0(W3,W1)
| aElementOf0(W3,W0) )
& aInteger0(W3) ) )
& aSet0(W2) ) ) ),
file('theBenchmark.p',mUnion) ).
fof(mIntersection,definition,
! [W0,W1] :
( ( aSubsetOf0(W1,cS1395)
& aSubsetOf0(W0,cS1395) )
=> ! [W2] :
( W2 = sdtslmnbsdt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( aElementOf0(W3,W1)
& aElementOf0(W3,W0)
& aInteger0(W3) ) )
& aSet0(W2) ) ) ),
file('theBenchmark.p',mIntersection) ).
fof(mUnionSet,definition,
! [W0] :
( ( ! [W1] :
( aElementOf0(W1,W0)
=> aSubsetOf0(W1,cS1395) )
& aSet0(W0) )
=> ! [W1] :
( W1 = sbsmnsldt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ( ? [W3] :
( aElementOf0(W2,W3)
& aElementOf0(W3,W0) )
& aInteger0(W2) ) )
& aSet0(W1) ) ) ),
file('theBenchmark.p',mUnionSet) ).
fof(mComplement,definition,
! [W0] :
( aSubsetOf0(W0,cS1395)
=> ! [W1] :
( W1 = stldt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ( ~ aElementOf0(W2,W0)
& aInteger0(W2) ) )
& aSet0(W1) ) ) ),
file('theBenchmark.p',mComplement) ).
fof(mArSeq,definition,
! [W0,W1] :
( ( W1 != sz00
& aInteger0(W1)
& aInteger0(W0) )
=> ! [W2] :
( W2 = szAzrzSzezqlpdtcmdtrp0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( sdteqdtlpzmzozddtrp0(W3,W0,W1)
& aInteger0(W3) ) )
& aSet0(W2) ) ) ),
file('theBenchmark.p',mArSeq) ).
fof(mOpen,definition,
! [W0] :
( aSubsetOf0(W0,cS1395)
=> ( isOpen0(W0)
<=> ! [W1] :
( aElementOf0(W1,W0)
=> ? [W2] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1,W2),W0)
& W2 != sz00
& aInteger0(W2) ) ) ) ),
file('theBenchmark.p',mOpen) ).
fof(mClosed,definition,
! [W0] :
( aSubsetOf0(W0,cS1395)
=> ( isClosed0(W0)
<=> isOpen0(stldt0(W0)) ) ),
file('theBenchmark.p',mClosed) ).
fof(mUnionOpen,axiom,
! [W0] :
( ( ! [W1] :
( aElementOf0(W1,W0)
=> ( isOpen0(W1)
& aSubsetOf0(W1,cS1395) ) )
& aSet0(W0) )
=> isOpen0(sbsmnsldt0(W0)) ),
file('theBenchmark.p',mUnionOpen) ).
fof(mInterOpen,axiom,
! [W0,W1] :
( ( isOpen0(W1)
& isOpen0(W0)
& aSubsetOf0(W1,cS1395)
& aSubsetOf0(W0,cS1395) )
=> isOpen0(sdtslmnbsdt0(W0,W1)) ),
file('theBenchmark.p',mInterOpen) ).
fof(mUnionClosed,axiom,
! [W0,W1] :
( ( isClosed0(W1)
& isClosed0(W0)
& aSubsetOf0(W1,cS1395)
& aSubsetOf0(W0,cS1395) )
=> isClosed0(sdtbsmnsldt0(W0,W1)) ),
file('theBenchmark.p',mUnionClosed) ).
fof(mUnionSClosed,axiom,
! [W0] :
( ( ! [W1] :
( aElementOf0(W1,W0)
=> ( isClosed0(W1)
& aSubsetOf0(W1,cS1395) ) )
& isFinite0(W0)
& aSet0(W0) )
=> isClosed0(sbsmnsldt0(W0)) ),
file('theBenchmark.p',mUnionSClosed) ).
fof(mArSeqClosed,axiom,
! [W0,W1] :
( ( W1 != sz00
& aInteger0(W1)
& aInteger0(W0) )
=> ( isClosed0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),cS1395) ) ),
file('theBenchmark.p',mArSeqClosed) ).
fof(m__2046,hypothesis,
( xS = cS2043
& ! [W0] :
( ( ? [W1] :
( ( ( ! [W2] :
( ( ( ( sdteqdtlpzmzozddtrp0(W2,sz00,W1)
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(sz00)))
| ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(sz00))
& aInteger0(W3) ) )
& aInteger0(W2) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,W1)) )
& ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,W1))
=> ( sdteqdtlpzmzozddtrp0(W2,sz00,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(sz00)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(sz00))
& aInteger0(W3) )
& aInteger0(W2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,W1)) )
=> szAzrzSzezqlpdtcmdtrp0(sz00,W1) = W0 )
& isPrime0(W1)
& W1 != sz00
& aInteger0(W1) )
=> aElementOf0(W0,xS) )
& ( aElementOf0(W0,xS)
=> ? [W1] :
( szAzrzSzezqlpdtcmdtrp0(sz00,W1) = W0
& ! [W2] :
( ( ( ( sdteqdtlpzmzozddtrp0(W2,sz00,W1)
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(sz00)))
| ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(sz00))
& aInteger0(W3) ) )
& aInteger0(W2) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,W1)) )
& ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,W1))
=> ( sdteqdtlpzmzozddtrp0(W2,sz00,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(sz00)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(sz00))
& aInteger0(W3) )
& aInteger0(W2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,W1))
& isPrime0(W1)
& W1 != sz00
& aInteger0(W1) ) ) )
& aSet0(xS) ),
file('theBenchmark.p',m__2046) ).
fof(m__2079,hypothesis,
( stldt0(sbsmnsldt0(xS)) = cS2076
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
<=> ( W0 = smndt0(sz10)
| W0 = sz10 ) )
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(W0,sbsmnsldt0(xS))
& aInteger0(W0) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [W0] :
( aElementOf0(W0,sbsmnsldt0(xS))
<=> ( ? [W1] :
( aElementOf0(W0,W1)
& aElementOf0(W1,xS) )
& aInteger0(W0) ) )
& aSet0(sbsmnsldt0(xS)) ),
file('theBenchmark.p',m__2079) ).
fof(m__2117,hypothesis,
isFinite0(xS),
file('theBenchmark.p',m__2117) ).
fof(m__2144,hypothesis,
( ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
=> ? [W1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(sbsmnsldt0(xS)))
& ! [W2] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> aElementOf0(W2,stldt0(sbsmnsldt0(xS))) )
& ! [W2] :
( ( ( ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
| ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) ) )
& aInteger0(W2) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) )
& aInteger0(W2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& W1 != sz00
& aInteger0(W1) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(W0,sbsmnsldt0(xS))
& aInteger0(W0) ) )
& ! [W0] :
( aElementOf0(W0,sbsmnsldt0(xS))
<=> ( ? [W1] :
( aElementOf0(W0,W1)
& aElementOf0(W1,xS) )
& aInteger0(W0) ) )
& aSet0(sbsmnsldt0(xS))
& isClosed0(sbsmnsldt0(xS))
& isOpen0(stldt0(sbsmnsldt0(xS)))
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
=> ? [W1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(sbsmnsldt0(xS)))
& ! [W2] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> aElementOf0(W2,stldt0(sbsmnsldt0(xS))) )
& ! [W2] :
( ( ( ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
| ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) ) )
& aInteger0(W2) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) )
& aInteger0(W2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& W1 != sz00
& aInteger0(W1) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(W0,sbsmnsldt0(xS))
& aInteger0(W0) ) )
& ! [W0] :
( aElementOf0(W0,sbsmnsldt0(xS))
<=> ( ? [W1] :
( aElementOf0(W0,W1)
& aElementOf0(W1,xS) )
& aInteger0(W0) ) )
& aSet0(sbsmnsldt0(xS)) ),
file('theBenchmark.p',m__2144) ).
fof(m__2171,hypothesis,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [W0] :
( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> aElementOf0(W0,stldt0(sbsmnsldt0(xS))) )
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(W0,sbsmnsldt0(xS))
& aInteger0(W0) ) )
& ! [W0] :
( aElementOf0(W0,sbsmnsldt0(xS))
<=> ( ? [W1] :
( aElementOf0(W0,W1)
& aElementOf0(W1,xS) )
& aInteger0(W0) ) )
& aSet0(sbsmnsldt0(xS))
& ! [W0] :
( ( ( ( sdteqdtlpzmzozddtrp0(W0,sz10,xp)
| aDivisorOf0(xp,sdtpldt0(W0,smndt0(sz10)))
| ? [W1] :
( sdtasdt0(xp,W1) = sdtpldt0(W0,smndt0(sz10))
& aInteger0(W1) ) )
& aInteger0(W0) )
=> aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> ( sdteqdtlpzmzozddtrp0(W0,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(W0,smndt0(sz10)))
& ? [W1] :
( sdtasdt0(xp,W1) = sdtpldt0(W0,smndt0(sz10))
& aInteger0(W1) )
& aInteger0(W0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
file('theBenchmark.p',m__2171) ).
fof(m__2232,hypothesis,
( aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
& ? [W0] :
( sdtasdt0(xp,W0) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
& aInteger0(W0) )
& aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp)
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
& ? [W0] :
( sdtasdt0(xp,W0) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))
& aInteger0(W0) ) ),
file('theBenchmark.p',m__2232) ).
fof(m__2258,hypothesis,
( sdtpldt0(sz10,smndt0(xp)) != sz10
& sdtpldt0(sz10,xp) != sz10 ),
file('theBenchmark.p',m__2258) ).
fof(m__2286,hypothesis,
( sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10)
| sdtpldt0(sz10,xp) != smndt0(sz10) ),
file('theBenchmark.p',m__2286) ).
fof(m__,conjecture,
? [W0] :
( ~ ( aElementOf0(W0,cS2200)
& ( W0 = smndt0(sz10)
| W0 = sz10 ) )
& ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ( ( sdteqdtlpzmzozddtrp0(W0,sz10,xp)
| aDivisorOf0(xp,sdtpldt0(W0,smndt0(sz10)))
| ? [W1] :
( sdtasdt0(xp,W1) = sdtpldt0(W0,smndt0(sz10))
& aInteger0(W1) ) )
& aInteger0(W0) ) ) ),
file('theBenchmark.p',m__) ).
fof(f_1_1,plain,
! [W0] :
( $true
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mIntegers]) ).
fof(f_1_2,plain,
! [U_0] :
( $true
| ~ aInteger0(U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ! [U_0] : ~ aInteger0(U_0)
| $true ),
inference(miniscope,[status(thm)],[f_1_2]) ).
cnf(f_1_4,plain,
( ~ aInteger0(U_0)
| $true ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
aInteger0(sz00),
inference(fof_nnf,[status(thm)],[mIntZero]) ).
cnf(f_2_2,plain,
aInteger0(sz00),
inference(clausify,[status(thm)],[f_2_1]) ).
fof(f_3_1,plain,
aInteger0(sz10),
inference(fof_nnf,[status(thm)],[mIntOne]) ).
cnf(f_3_2,plain,
aInteger0(sz10),
inference(clausify,[status(thm)],[f_3_1]) ).
fof(f_4_1,plain,
! [W0] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mIntNeg]) ).
fof(f_4_2,plain,
! [U_1] :
( aInteger0(smndt0(U_1))
| ~ aInteger0(U_1) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( aInteger0(smndt0(U_1))
| ~ aInteger0(U_1) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [W0,W1] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mIntPlus]) ).
fof(f_5_2,plain,
! [U_3,U_2] :
( aInteger0(sdtpldt0(U_3,U_2))
| ~ aInteger0(U_2)
| ~ aInteger0(U_3) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( aInteger0(sdtpldt0(U_3,U_2))
| ~ aInteger0(U_2)
| ~ aInteger0(U_3) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [W0,W1] :
( aInteger0(sdtasdt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mIntMult]) ).
fof(f_6_2,plain,
! [U_5,U_4] :
( aInteger0(sdtasdt0(U_5,U_4))
| ~ aInteger0(U_4)
| ~ aInteger0(U_5) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( aInteger0(sdtasdt0(U_5,U_4))
| ~ aInteger0(U_4)
| ~ aInteger0(U_5) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [W0,W1,W2] :
( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mAddAsso]) ).
fof(f_7_2,plain,
! [U_8,U_7,U_6] :
( sdtpldt0(U_8,sdtpldt0(U_7,U_6)) = sdtpldt0(sdtpldt0(U_8,U_7),U_6)
| ~ aInteger0(U_6)
| ~ aInteger0(U_7)
| ~ aInteger0(U_8) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( sdtpldt0(U_8,sdtpldt0(U_7,U_6)) = sdtpldt0(sdtpldt0(U_8,U_7),U_6)
| ~ aInteger0(U_6)
| ~ aInteger0(U_7)
| ~ aInteger0(U_8) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [W0,W1] :
( sdtpldt0(W0,W1) = sdtpldt0(W1,W0)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mAddComm]) ).
fof(f_8_2,plain,
! [U_10,U_9] :
( sdtpldt0(U_10,U_9) = sdtpldt0(U_9,U_10)
| ~ aInteger0(U_9)
| ~ aInteger0(U_10) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( sdtpldt0(U_10,U_9) = sdtpldt0(U_9,U_10)
| ~ aInteger0(U_9)
| ~ aInteger0(U_10) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [W0] :
( ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 )
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mAddZero]) ).
fof(f_9_2,plain,
! [U_11] :
( ( U_11 = sdtpldt0(sz00,U_11)
& sdtpldt0(U_11,sz00) = U_11 )
| ~ aInteger0(U_11) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( sdtpldt0(U_11,sz00) = U_11
| ~ aInteger0(U_11) ),
inference(clausify,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( U_11 = sdtpldt0(sz00,U_11)
| ~ aInteger0(U_11) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [W0] :
( ( sz00 = sdtpldt0(smndt0(W0),W0)
& sdtpldt0(W0,smndt0(W0)) = sz00 )
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mAddNeg]) ).
fof(f_10_2,plain,
! [U_12] :
( ( sz00 = sdtpldt0(smndt0(U_12),U_12)
& sdtpldt0(U_12,smndt0(U_12)) = sz00 )
| ~ aInteger0(U_12) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( sdtpldt0(U_12,smndt0(U_12)) = sz00
| ~ aInteger0(U_12) ),
inference(clausify,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
( sz00 = sdtpldt0(smndt0(U_12),U_12)
| ~ aInteger0(U_12) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [W0,W1,W2] :
( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mMulAsso]) ).
fof(f_11_2,plain,
! [U_15,U_14,U_13] :
( sdtasdt0(U_15,sdtasdt0(U_14,U_13)) = sdtasdt0(sdtasdt0(U_15,U_14),U_13)
| ~ aInteger0(U_13)
| ~ aInteger0(U_14)
| ~ aInteger0(U_15) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( sdtasdt0(U_15,sdtasdt0(U_14,U_13)) = sdtasdt0(sdtasdt0(U_15,U_14),U_13)
| ~ aInteger0(U_13)
| ~ aInteger0(U_14)
| ~ aInteger0(U_15) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [W0,W1] :
( sdtasdt0(W0,W1) = sdtasdt0(W1,W0)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mMulComm]) ).
fof(f_12_2,plain,
! [U_17,U_16] :
( sdtasdt0(U_17,U_16) = sdtasdt0(U_16,U_17)
| ~ aInteger0(U_16)
| ~ aInteger0(U_17) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( sdtasdt0(U_17,U_16) = sdtasdt0(U_16,U_17)
| ~ aInteger0(U_16)
| ~ aInteger0(U_17) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [W0] :
( ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 )
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mMulOne]) ).
fof(f_13_2,plain,
! [U_18] :
( ( U_18 = sdtasdt0(sz10,U_18)
& sdtasdt0(U_18,sz10) = U_18 )
| ~ aInteger0(U_18) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( sdtasdt0(U_18,sz10) = U_18
| ~ aInteger0(U_18) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
( U_18 = sdtasdt0(sz10,U_18)
| ~ aInteger0(U_18) ),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
! [W0,W1,W2] :
( ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mDistrib]) ).
fof(f_14_2,plain,
! [U_21,U_20,U_19] :
( ( sdtasdt0(sdtpldt0(U_21,U_20),U_19) = sdtpldt0(sdtasdt0(U_21,U_19),sdtasdt0(U_20,U_19))
& sdtasdt0(U_21,sdtpldt0(U_20,U_19)) = sdtpldt0(sdtasdt0(U_21,U_20),sdtasdt0(U_21,U_19)) )
| ~ aInteger0(U_19)
| ~ aInteger0(U_20)
| ~ aInteger0(U_21) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( sdtasdt0(U_21,sdtpldt0(U_20,U_19)) = sdtpldt0(sdtasdt0(U_21,U_20),sdtasdt0(U_21,U_19))
| ~ aInteger0(U_19)
| ~ aInteger0(U_20)
| ~ aInteger0(U_21) ),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( sdtasdt0(sdtpldt0(U_21,U_20),U_19) = sdtpldt0(sdtasdt0(U_21,U_19),sdtasdt0(U_20,U_19))
| ~ aInteger0(U_19)
| ~ aInteger0(U_20)
| ~ aInteger0(U_21) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [W0] :
( ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 )
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mMulZero]) ).
fof(f_15_2,plain,
! [U_22] :
( ( sz00 = sdtasdt0(sz00,U_22)
& sdtasdt0(U_22,sz00) = sz00 )
| ~ aInteger0(U_22) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( sdtasdt0(U_22,sz00) = sz00
| ~ aInteger0(U_22) ),
inference(clausify,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
( sz00 = sdtasdt0(sz00,U_22)
| ~ aInteger0(U_22) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [W0] :
( ( smndt0(W0) = sdtasdt0(W0,smndt0(sz10))
& sdtasdt0(smndt0(sz10),W0) = smndt0(W0) )
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mMulMinOne]) ).
fof(f_16_2,plain,
! [U_23] :
( ( smndt0(U_23) = sdtasdt0(U_23,smndt0(sz10))
& sdtasdt0(smndt0(sz10),U_23) = smndt0(U_23) )
| ~ aInteger0(U_23) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( sdtasdt0(smndt0(sz10),U_23) = smndt0(U_23)
| ~ aInteger0(U_23) ),
inference(clausify,[status(thm)],[f_16_2]) ).
cnf(f_16_4,plain,
( smndt0(U_23) = sdtasdt0(U_23,smndt0(sz10))
| ~ aInteger0(U_23) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [W0,W1] :
( W1 = sz00
| W0 = sz00
| sdtasdt0(W0,W1) != sz00
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mZeroDiv]) ).
fof(f_17_2,plain,
! [U_25,U_24] :
( U_24 = sz00
| U_25 = sz00
| sdtasdt0(U_25,U_24) != sz00
| ~ aInteger0(U_24)
| ~ aInteger0(U_25) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( U_24 = sz00
| U_25 = sz00
| sdtasdt0(U_25,U_24) != sz00
| ~ aInteger0(U_24)
| ~ aInteger0(U_25) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [W0] :
( ! [W1] :
( ( aDivisorOf0(W1,W0)
| ! [W2] :
( sdtasdt0(W1,W2) != W0
| ~ aInteger0(W2) )
| W1 = sz00
| ~ aInteger0(W1) )
& ( ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) )
| ~ aDivisorOf0(W1,W0) ) )
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mDivisor]) ).
fof(f_18_2,plain,
! [U_29] :
( ! [U_28] :
( ( aDivisorOf0(U_28,U_29)
| ! [U_27] :
( sdtasdt0(U_28,U_27) != U_29
| ~ aInteger0(U_27) )
| U_28 = sz00
| ~ aInteger0(U_28) )
& ( ( ? [U_26] :
( sdtasdt0(U_28,U_26) = U_29
& aInteger0(U_26) )
& U_28 != sz00
& aInteger0(U_28) )
| ~ aDivisorOf0(U_28,U_29) ) )
| ~ aInteger0(U_29) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_29] :
( ( ! [U_31] :
( aDivisorOf0(U_31,U_29)
| ! [U_27] :
( sdtasdt0(U_31,U_27) != U_29
| ~ aInteger0(U_27) )
| U_31 = sz00
| ~ aInteger0(U_31) )
& ! [U_30] :
( ( ? [U_26] :
( sdtasdt0(U_30,U_26) = U_29
& aInteger0(U_26) )
& U_30 != sz00
& aInteger0(U_30) )
| ~ aDivisorOf0(U_30,U_29) ) )
| ~ aInteger0(U_29) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
fof(f_18_4,plain,
! [U_29] :
( ( ! [U_31] :
( aDivisorOf0(U_31,U_29)
| ! [U_27] :
( sdtasdt0(U_31,U_27) != U_29
| ~ aInteger0(U_27) )
| U_31 = sz00
| ~ aInteger0(U_31) )
& ! [U_30] :
( ( sdtasdt0(U_30,sK1(U_29,U_30)) = U_29
& aInteger0(sK1(U_29,U_30))
& U_30 != sz00
& aInteger0(U_30) )
| ~ aDivisorOf0(U_30,U_29) ) )
| ~ aInteger0(U_29) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_26,sK1(U_29,U_30))],[f_18_3]) ).
cnf(f_18_5,plain,
( aInteger0(U_30)
| ~ aDivisorOf0(U_30,U_29)
| ~ aInteger0(U_29) ),
inference(clausify,[status(thm)],[f_18_4]) ).
cnf(f_18_6,plain,
( U_30 != sz00
| ~ aDivisorOf0(U_30,U_29)
| ~ aInteger0(U_29) ),
inference(clausify,[status(thm)],[f_18_4]) ).
cnf(f_18_7,plain,
( aInteger0(sK1(U_29,U_30))
| ~ aDivisorOf0(U_30,U_29)
| ~ aInteger0(U_29) ),
inference(clausify,[status(thm)],[f_18_4]) ).
cnf(f_18_8,plain,
( sdtasdt0(U_30,sK1(U_29,U_30)) = U_29
| ~ aDivisorOf0(U_30,U_29)
| ~ aInteger0(U_29) ),
inference(clausify,[status(thm)],[f_18_4]) ).
cnf(f_18_9,plain,
( aDivisorOf0(U_31,U_29)
| sdtasdt0(U_31,U_27) != U_29
| ~ aInteger0(U_27)
| U_31 = sz00
| ~ aInteger0(U_31)
| ~ aInteger0(U_29) ),
inference(clausify,[status(thm)],[f_18_4]) ).
fof(f_19_1,plain,
! [W0,W1,W2] :
( ( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) )
& ( aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1)))
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2) ) )
| W2 = sz00
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mEquMod]) ).
fof(f_19_2,plain,
! [U_34,U_33,U_32] :
( ( ( sdteqdtlpzmzozddtrp0(U_34,U_33,U_32)
| ~ aDivisorOf0(U_32,sdtpldt0(U_34,smndt0(U_33))) )
& ( aDivisorOf0(U_32,sdtpldt0(U_34,smndt0(U_33)))
| ~ sdteqdtlpzmzozddtrp0(U_34,U_33,U_32) ) )
| U_32 = sz00
| ~ aInteger0(U_32)
| ~ aInteger0(U_33)
| ~ aInteger0(U_34) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( aDivisorOf0(U_32,sdtpldt0(U_34,smndt0(U_33)))
| ~ sdteqdtlpzmzozddtrp0(U_34,U_33,U_32)
| U_32 = sz00
| ~ aInteger0(U_32)
| ~ aInteger0(U_33)
| ~ aInteger0(U_34) ),
inference(clausify,[status(thm)],[f_19_2]) ).
cnf(f_19_4,plain,
( sdteqdtlpzmzozddtrp0(U_34,U_33,U_32)
| ~ aDivisorOf0(U_32,sdtpldt0(U_34,smndt0(U_33)))
| U_32 = sz00
| ~ aInteger0(U_32)
| ~ aInteger0(U_33)
| ~ aInteger0(U_34) ),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
! [W0,W1] :
( sdteqdtlpzmzozddtrp0(W0,W0,W1)
| W1 = sz00
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mEquModRef]) ).
fof(f_20_2,plain,
! [U_36,U_35] :
( sdteqdtlpzmzozddtrp0(U_36,U_36,U_35)
| U_35 = sz00
| ~ aInteger0(U_35)
| ~ aInteger0(U_36) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( sdteqdtlpzmzozddtrp0(U_36,U_36,U_35)
| U_35 = sz00
| ~ aInteger0(U_35)
| ~ aInteger0(U_36) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
! [W0,W1,W2] :
( sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| W2 = sz00
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mEquModSym]) ).
fof(f_21_2,plain,
! [U_39,U_38,U_37] :
( sdteqdtlpzmzozddtrp0(U_38,U_39,U_37)
| ~ sdteqdtlpzmzozddtrp0(U_39,U_38,U_37)
| U_37 = sz00
| ~ aInteger0(U_37)
| ~ aInteger0(U_38)
| ~ aInteger0(U_39) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
( sdteqdtlpzmzozddtrp0(U_38,U_39,U_37)
| ~ sdteqdtlpzmzozddtrp0(U_39,U_38,U_37)
| U_37 = sz00
| ~ aInteger0(U_37)
| ~ aInteger0(U_38)
| ~ aInteger0(U_39) ),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
! [W0,W1,W2,W3] :
( sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ sdteqdtlpzmzozddtrp0(W1,W3,W2)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ aInteger0(W3)
| W2 = sz00
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mEquModTrn]) ).
fof(f_22_2,plain,
! [U_43,U_42,U_41,U_40] :
( sdteqdtlpzmzozddtrp0(U_43,U_40,U_41)
| ~ sdteqdtlpzmzozddtrp0(U_42,U_40,U_41)
| ~ sdteqdtlpzmzozddtrp0(U_43,U_42,U_41)
| ~ aInteger0(U_40)
| U_41 = sz00
| ~ aInteger0(U_41)
| ~ aInteger0(U_42)
| ~ aInteger0(U_43) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( sdteqdtlpzmzozddtrp0(U_43,U_40,U_41)
| ~ sdteqdtlpzmzozddtrp0(U_42,U_40,U_41)
| ~ sdteqdtlpzmzozddtrp0(U_43,U_42,U_41)
| ~ aInteger0(U_40)
| U_41 = sz00
| ~ aInteger0(U_41)
| ~ aInteger0(U_42)
| ~ aInteger0(U_43) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
! [W0,W1,W2,W3] :
( ( sdteqdtlpzmzozddtrp0(W0,W1,W3)
& sdteqdtlpzmzozddtrp0(W0,W1,W2) )
| ~ sdteqdtlpzmzozddtrp0(W0,W1,sdtasdt0(W2,W3))
| W3 = sz00
| ~ aInteger0(W3)
| W2 = sz00
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mEquModMul]) ).
fof(f_23_2,plain,
! [U_47,U_46,U_45,U_44] :
( ( sdteqdtlpzmzozddtrp0(U_47,U_46,U_44)
& sdteqdtlpzmzozddtrp0(U_47,U_46,U_45) )
| ~ sdteqdtlpzmzozddtrp0(U_47,U_46,sdtasdt0(U_45,U_44))
| U_44 = sz00
| ~ aInteger0(U_44)
| U_45 = sz00
| ~ aInteger0(U_45)
| ~ aInteger0(U_46)
| ~ aInteger0(U_47) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
( sdteqdtlpzmzozddtrp0(U_47,U_46,U_45)
| ~ sdteqdtlpzmzozddtrp0(U_47,U_46,sdtasdt0(U_45,U_44))
| U_44 = sz00
| ~ aInteger0(U_44)
| U_45 = sz00
| ~ aInteger0(U_45)
| ~ aInteger0(U_46)
| ~ aInteger0(U_47) ),
inference(clausify,[status(thm)],[f_23_2]) ).
cnf(f_23_4,plain,
( sdteqdtlpzmzozddtrp0(U_47,U_46,U_44)
| ~ sdteqdtlpzmzozddtrp0(U_47,U_46,sdtasdt0(U_45,U_44))
| U_44 = sz00
| ~ aInteger0(U_44)
| U_45 = sz00
| ~ aInteger0(U_45)
| ~ aInteger0(U_46)
| ~ aInteger0(U_47) ),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
! [W0] :
( $true
| ~ isPrime0(W0)
| W0 = sz00
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mPrime]) ).
fof(f_24_2,plain,
! [U_48] :
( $true
| ~ isPrime0(U_48)
| U_48 = sz00
| ~ aInteger0(U_48) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
( $true
| ~ isPrime0(U_48)
| U_48 = sz00
| ~ aInteger0(U_48) ),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,plain,
! [W0] :
( ( ( ? [W1] :
( isPrime0(W1)
& aDivisorOf0(W1,W0) )
| W0 = smndt0(sz10)
| W0 = sz10 )
& ( ( W0 != smndt0(sz10)
& W0 != sz10 )
| ! [W1] :
( ~ isPrime0(W1)
| ~ aDivisorOf0(W1,W0) ) ) )
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mPrimeDivisor]) ).
fof(f_25_2,plain,
! [U_51] :
( ( ( ? [U_50] :
( isPrime0(U_50)
& aDivisorOf0(U_50,U_51) )
| U_51 = smndt0(sz10)
| U_51 = sz10 )
& ( ( U_51 != smndt0(sz10)
& U_51 != sz10 )
| ! [U_49] :
( ~ isPrime0(U_49)
| ~ aDivisorOf0(U_49,U_51) ) ) )
| ~ aInteger0(U_51) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_51] :
( ( ( ( isPrime0(sK2(U_51))
& aDivisorOf0(sK2(U_51),U_51) )
| U_51 = smndt0(sz10)
| U_51 = sz10 )
& ( ( U_51 != smndt0(sz10)
& U_51 != sz10 )
| ! [U_49] :
( ~ isPrime0(U_49)
| ~ aDivisorOf0(U_49,U_51) ) ) )
| ~ aInteger0(U_51) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_50,sK2(U_51))],[f_25_2]) ).
cnf(f_25_4,plain,
( U_51 != sz10
| ~ isPrime0(U_49)
| ~ aDivisorOf0(U_49,U_51)
| ~ aInteger0(U_51) ),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_5,plain,
( U_51 != smndt0(sz10)
| ~ isPrime0(U_49)
| ~ aDivisorOf0(U_49,U_51)
| ~ aInteger0(U_51) ),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_6,plain,
( aDivisorOf0(sK2(U_51),U_51)
| U_51 = smndt0(sz10)
| U_51 = sz10
| ~ aInteger0(U_51) ),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_7,plain,
( isPrime0(sK2(U_51))
| U_51 = smndt0(sz10)
| U_51 = sz10
| ~ aInteger0(U_51) ),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
! [W0] :
( $true
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mSets]) ).
fof(f_26_2,plain,
! [U_52] :
( $true
| ~ aSet0(U_52) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( ! [U_52] : ~ aSet0(U_52)
| $true ),
inference(miniscope,[status(thm)],[f_26_2]) ).
cnf(f_26_4,plain,
( ~ aSet0(U_52)
| $true ),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [W0] :
( ! [W1] :
( $true
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mElements]) ).
fof(f_27_2,plain,
! [U_54] :
( ! [U_53] :
( $true
| ~ aElementOf0(U_53,U_54) )
| ~ aSet0(U_54) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_54] :
( ! [U_53] : ~ aElementOf0(U_53,U_54)
| $true
| ~ aSet0(U_54) ),
inference(miniscope,[status(thm)],[f_27_2]) ).
cnf(f_27_4,plain,
( ~ aElementOf0(U_53,U_54)
| $true
| ~ aSet0(U_54) ),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_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)],[mSubset]) ).
fof(f_28_2,plain,
! [U_58] :
( ! [U_57] :
( ( aSubsetOf0(U_57,U_58)
| ? [U_56] :
( ~ aElementOf0(U_56,U_58)
& aElementOf0(U_56,U_57) )
| ~ aSet0(U_57) )
& ( ( ! [U_55] :
( aElementOf0(U_55,U_58)
| ~ aElementOf0(U_55,U_57) )
& aSet0(U_57) )
| ~ aSubsetOf0(U_57,U_58) ) )
| ~ aSet0(U_58) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_58] :
( ( ! [U_60] :
( aSubsetOf0(U_60,U_58)
| ? [U_56] :
( ~ aElementOf0(U_56,U_58)
& aElementOf0(U_56,U_60) )
| ~ aSet0(U_60) )
& ! [U_59] :
( ( ! [U_55] :
( aElementOf0(U_55,U_58)
| ~ aElementOf0(U_55,U_59) )
& aSet0(U_59) )
| ~ aSubsetOf0(U_59,U_58) ) )
| ~ aSet0(U_58) ),
inference(miniscope,[status(thm)],[f_28_2]) ).
fof(f_28_4,plain,
! [U_58] :
( ( ! [U_60] :
( aSubsetOf0(U_60,U_58)
| ( ~ aElementOf0(sK3(U_58,U_60),U_58)
& aElementOf0(sK3(U_58,U_60),U_60) )
| ~ aSet0(U_60) )
& ! [U_59] :
( ( ! [U_55] :
( aElementOf0(U_55,U_58)
| ~ aElementOf0(U_55,U_59) )
& aSet0(U_59) )
| ~ aSubsetOf0(U_59,U_58) ) )
| ~ aSet0(U_58) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_56,sK3(U_58,U_60))],[f_28_3]) ).
cnf(f_28_5,plain,
( aSet0(U_59)
| ~ aSubsetOf0(U_59,U_58)
| ~ aSet0(U_58) ),
inference(clausify,[status(thm)],[f_28_4]) ).
cnf(f_28_6,plain,
( aElementOf0(U_55,U_58)
| ~ aElementOf0(U_55,U_59)
| ~ aSubsetOf0(U_59,U_58)
| ~ aSet0(U_58) ),
inference(clausify,[status(thm)],[f_28_4]) ).
cnf(f_28_7,plain,
( aElementOf0(sK3(U_58,U_60),U_60)
| ~ aSet0(U_60)
| aSubsetOf0(U_60,U_58)
| ~ aSet0(U_58) ),
inference(clausify,[status(thm)],[f_28_4]) ).
cnf(f_28_8,plain,
( ~ aElementOf0(sK3(U_58,U_60),U_58)
| ~ aSet0(U_60)
| aSubsetOf0(U_60,U_58)
| ~ aSet0(U_58) ),
inference(clausify,[status(thm)],[f_28_4]) ).
fof(f_29_1,plain,
! [W0] :
( $true
| ~ isFinite0(W0)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mFinSet]) ).
fof(f_29_2,plain,
! [U_61] :
( $true
| ~ isFinite0(U_61)
| ~ aSet0(U_61) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( $true
| ~ isFinite0(U_61)
| ~ aSet0(U_61) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
! [W0,W1] :
( ! [W2] :
( ( W2 = sdtbsmnsldt0(W0,W1)
| ? [W3] :
( ( ~ aElementOf0(W3,W2)
& ( aElementOf0(W3,W1)
| aElementOf0(W3,W0) )
& aInteger0(W3) )
| ( ( ( ~ aElementOf0(W3,W1)
& ~ aElementOf0(W3,W0) )
| ~ aInteger0(W3) )
& aElementOf0(W3,W2) ) )
| ~ aSet0(W2) )
& ( ( ! [W3] :
( ( aElementOf0(W3,W2)
| ( ~ aElementOf0(W3,W1)
& ~ aElementOf0(W3,W0) )
| ~ aInteger0(W3) )
& ( ( ( aElementOf0(W3,W1)
| aElementOf0(W3,W0) )
& aInteger0(W3) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtbsmnsldt0(W0,W1) ) )
| ~ aSubsetOf0(W1,cS1395)
| ~ aSubsetOf0(W0,cS1395) ),
inference(fof_nnf,[status(thm)],[mUnion]) ).
fof(f_30_2,plain,
! [U_66,U_65] :
( ! [U_64] :
( ( U_64 = sdtbsmnsldt0(U_66,U_65)
| ? [U_63] :
( ( ~ aElementOf0(U_63,U_64)
& ( aElementOf0(U_63,U_65)
| aElementOf0(U_63,U_66) )
& aInteger0(U_63) )
| ( ( ( ~ aElementOf0(U_63,U_65)
& ~ aElementOf0(U_63,U_66) )
| ~ aInteger0(U_63) )
& aElementOf0(U_63,U_64) ) )
| ~ aSet0(U_64) )
& ( ( ! [U_62] :
( ( aElementOf0(U_62,U_64)
| ( ~ aElementOf0(U_62,U_65)
& ~ aElementOf0(U_62,U_66) )
| ~ aInteger0(U_62) )
& ( ( ( aElementOf0(U_62,U_65)
| aElementOf0(U_62,U_66) )
& aInteger0(U_62) )
| ~ aElementOf0(U_62,U_64) ) )
& aSet0(U_64) )
| U_64 != sdtbsmnsldt0(U_66,U_65) ) )
| ~ aSubsetOf0(U_65,cS1395)
| ~ aSubsetOf0(U_66,cS1395) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_66,U_65] :
( ( ! [U_72] :
( U_72 = sdtbsmnsldt0(U_66,U_65)
| ? [U_70] :
( ~ aElementOf0(U_70,U_72)
& ( aElementOf0(U_70,U_65)
| aElementOf0(U_70,U_66) )
& aInteger0(U_70) )
| ? [U_69] :
( ( ( ~ aElementOf0(U_69,U_65)
& ~ aElementOf0(U_69,U_66) )
| ~ aInteger0(U_69) )
& aElementOf0(U_69,U_72) )
| ~ aSet0(U_72) )
& ! [U_71] :
( ( ! [U_68] :
( aElementOf0(U_68,U_71)
| ( ~ aElementOf0(U_68,U_65)
& ~ aElementOf0(U_68,U_66) )
| ~ aInteger0(U_68) )
& ! [U_67] :
( ( ( aElementOf0(U_67,U_65)
| aElementOf0(U_67,U_66) )
& aInteger0(U_67) )
| ~ aElementOf0(U_67,U_71) )
& aSet0(U_71) )
| U_71 != sdtbsmnsldt0(U_66,U_65) ) )
| ~ aSubsetOf0(U_65,cS1395)
| ~ aSubsetOf0(U_66,cS1395) ),
inference(miniscope,[status(thm)],[f_30_2]) ).
fof(f_30_4,plain,
! [U_66,U_65] :
( ( ! [U_72] :
( U_72 = sdtbsmnsldt0(U_66,U_65)
| ? [U_70] :
( ~ aElementOf0(U_70,U_72)
& ( aElementOf0(U_70,U_65)
| aElementOf0(U_70,U_66) )
& aInteger0(U_70) )
| ( ( ( ~ aElementOf0(sK4(U_66,U_65,U_72),U_65)
& ~ aElementOf0(sK4(U_66,U_65,U_72),U_66) )
| ~ aInteger0(sK4(U_66,U_65,U_72)) )
& aElementOf0(sK4(U_66,U_65,U_72),U_72) )
| ~ aSet0(U_72) )
& ! [U_71] :
( ( ! [U_68] :
( aElementOf0(U_68,U_71)
| ( ~ aElementOf0(U_68,U_65)
& ~ aElementOf0(U_68,U_66) )
| ~ aInteger0(U_68) )
& ! [U_67] :
( ( ( aElementOf0(U_67,U_65)
| aElementOf0(U_67,U_66) )
& aInteger0(U_67) )
| ~ aElementOf0(U_67,U_71) )
& aSet0(U_71) )
| U_71 != sdtbsmnsldt0(U_66,U_65) ) )
| ~ aSubsetOf0(U_65,cS1395)
| ~ aSubsetOf0(U_66,cS1395) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_69,sK4(U_66,U_65,U_72))],[f_30_3]) ).
fof(f_30_5,plain,
! [U_66,U_65] :
( ( ! [U_72] :
( U_72 = sdtbsmnsldt0(U_66,U_65)
| ( ~ aElementOf0(sK5(U_66,U_65,U_72),U_72)
& ( aElementOf0(sK5(U_66,U_65,U_72),U_65)
| aElementOf0(sK5(U_66,U_65,U_72),U_66) )
& aInteger0(sK5(U_66,U_65,U_72)) )
| ( ( ( ~ aElementOf0(sK4(U_66,U_65,U_72),U_65)
& ~ aElementOf0(sK4(U_66,U_65,U_72),U_66) )
| ~ aInteger0(sK4(U_66,U_65,U_72)) )
& aElementOf0(sK4(U_66,U_65,U_72),U_72) )
| ~ aSet0(U_72) )
& ! [U_71] :
( ( ! [U_68] :
( aElementOf0(U_68,U_71)
| ( ~ aElementOf0(U_68,U_65)
& ~ aElementOf0(U_68,U_66) )
| ~ aInteger0(U_68) )
& ! [U_67] :
( ( ( aElementOf0(U_67,U_65)
| aElementOf0(U_67,U_66) )
& aInteger0(U_67) )
| ~ aElementOf0(U_67,U_71) )
& aSet0(U_71) )
| U_71 != sdtbsmnsldt0(U_66,U_65) ) )
| ~ aSubsetOf0(U_65,cS1395)
| ~ aSubsetOf0(U_66,cS1395) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_70,sK5(U_66,U_65,U_72))],[f_30_4]) ).
cnf(f_30_6,plain,
( aSet0(U_71)
| U_71 != sdtbsmnsldt0(U_66,U_65)
| ~ aSubsetOf0(U_65,cS1395)
| ~ aSubsetOf0(U_66,cS1395) ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_7,plain,
( aInteger0(U_67)
| ~ aElementOf0(U_67,U_71)
| U_71 != sdtbsmnsldt0(U_66,U_65)
| ~ aSubsetOf0(U_65,cS1395)
| ~ aSubsetOf0(U_66,cS1395) ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_8,plain,
( aElementOf0(U_67,U_65)
| aElementOf0(U_67,U_66)
| ~ aElementOf0(U_67,U_71)
| U_71 != sdtbsmnsldt0(U_66,U_65)
| ~ aSubsetOf0(U_65,cS1395)
| ~ aSubsetOf0(U_66,cS1395) ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_9,plain,
( ~ aElementOf0(U_68,U_66)
| ~ aInteger0(U_68)
| aElementOf0(U_68,U_71)
| U_71 != sdtbsmnsldt0(U_66,U_65)
| ~ aSubsetOf0(U_65,cS1395)
| ~ aSubsetOf0(U_66,cS1395) ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_10,plain,
( ~ aElementOf0(U_68,U_65)
| ~ aInteger0(U_68)
| aElementOf0(U_68,U_71)
| U_71 != sdtbsmnsldt0(U_66,U_65)
| ~ aSubsetOf0(U_65,cS1395)
| ~ aSubsetOf0(U_66,cS1395) ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_11,plain,
( aInteger0(sK5(U_66,U_65,U_72))
| aElementOf0(sK4(U_66,U_65,U_72),U_72)
| ~ aSet0(U_72)
| U_72 = sdtbsmnsldt0(U_66,U_65)
| ~ aSubsetOf0(U_65,cS1395)
| ~ aSubsetOf0(U_66,cS1395) ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_12,plain,
( aElementOf0(sK5(U_66,U_65,U_72),U_65)
| aElementOf0(sK5(U_66,U_65,U_72),U_66)
| aElementOf0(sK4(U_66,U_65,U_72),U_72)
| ~ aSet0(U_72)
| U_72 = sdtbsmnsldt0(U_66,U_65)
| ~ aSubsetOf0(U_65,cS1395)
| ~ aSubsetOf0(U_66,cS1395) ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_13,plain,
( ~ aElementOf0(sK5(U_66,U_65,U_72),U_72)
| aElementOf0(sK4(U_66,U_65,U_72),U_72)
| ~ aSet0(U_72)
| U_72 = sdtbsmnsldt0(U_66,U_65)
| ~ aSubsetOf0(U_65,cS1395)
| ~ aSubsetOf0(U_66,cS1395) ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_14,plain,
( ~ aElementOf0(sK4(U_66,U_65,U_72),U_66)
| ~ aInteger0(sK4(U_66,U_65,U_72))
| aInteger0(sK5(U_66,U_65,U_72))
| ~ aSet0(U_72)
| U_72 = sdtbsmnsldt0(U_66,U_65)
| ~ aSubsetOf0(U_65,cS1395)
| ~ aSubsetOf0(U_66,cS1395) ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_15,plain,
( ~ aElementOf0(sK4(U_66,U_65,U_72),U_65)
| ~ aInteger0(sK4(U_66,U_65,U_72))
| aInteger0(sK5(U_66,U_65,U_72))
| ~ aSet0(U_72)
| U_72 = sdtbsmnsldt0(U_66,U_65)
| ~ aSubsetOf0(U_65,cS1395)
| ~ aSubsetOf0(U_66,cS1395) ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_16,plain,
( ~ aElementOf0(sK4(U_66,U_65,U_72),U_66)
| ~ aInteger0(sK4(U_66,U_65,U_72))
| aElementOf0(sK5(U_66,U_65,U_72),U_65)
| aElementOf0(sK5(U_66,U_65,U_72),U_66)
| ~ aSet0(U_72)
| U_72 = sdtbsmnsldt0(U_66,U_65)
| ~ aSubsetOf0(U_65,cS1395)
| ~ aSubsetOf0(U_66,cS1395) ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_17,plain,
( ~ aElementOf0(sK4(U_66,U_65,U_72),U_65)
| ~ aInteger0(sK4(U_66,U_65,U_72))
| aElementOf0(sK5(U_66,U_65,U_72),U_65)
| aElementOf0(sK5(U_66,U_65,U_72),U_66)
| ~ aSet0(U_72)
| U_72 = sdtbsmnsldt0(U_66,U_65)
| ~ aSubsetOf0(U_65,cS1395)
| ~ aSubsetOf0(U_66,cS1395) ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_18,plain,
( ~ aElementOf0(sK4(U_66,U_65,U_72),U_66)
| ~ aInteger0(sK4(U_66,U_65,U_72))
| ~ aElementOf0(sK5(U_66,U_65,U_72),U_72)
| ~ aSet0(U_72)
| U_72 = sdtbsmnsldt0(U_66,U_65)
| ~ aSubsetOf0(U_65,cS1395)
| ~ aSubsetOf0(U_66,cS1395) ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_19,plain,
( ~ aElementOf0(sK4(U_66,U_65,U_72),U_65)
| ~ aInteger0(sK4(U_66,U_65,U_72))
| ~ aElementOf0(sK5(U_66,U_65,U_72),U_72)
| ~ aSet0(U_72)
| U_72 = sdtbsmnsldt0(U_66,U_65)
| ~ aSubsetOf0(U_65,cS1395)
| ~ aSubsetOf0(U_66,cS1395) ),
inference(clausify,[status(thm)],[f_30_5]) ).
fof(f_31_1,plain,
! [W0,W1] :
( ! [W2] :
( ( W2 = sdtslmnbsdt0(W0,W1)
| ? [W3] :
( ( ~ aElementOf0(W3,W2)
& aElementOf0(W3,W1)
& aElementOf0(W3,W0)
& aInteger0(W3) )
| ( ( ~ aElementOf0(W3,W1)
| ~ aElementOf0(W3,W0)
| ~ aInteger0(W3) )
& aElementOf0(W3,W2) ) )
| ~ aSet0(W2) )
& ( ( ! [W3] :
( ( aElementOf0(W3,W2)
| ~ aElementOf0(W3,W1)
| ~ aElementOf0(W3,W0)
| ~ aInteger0(W3) )
& ( ( aElementOf0(W3,W1)
& aElementOf0(W3,W0)
& aInteger0(W3) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtslmnbsdt0(W0,W1) ) )
| ~ aSubsetOf0(W1,cS1395)
| ~ aSubsetOf0(W0,cS1395) ),
inference(fof_nnf,[status(thm)],[mIntersection]) ).
fof(f_31_2,plain,
! [U_77,U_76] :
( ! [U_75] :
( ( U_75 = sdtslmnbsdt0(U_77,U_76)
| ? [U_74] :
( ( ~ aElementOf0(U_74,U_75)
& aElementOf0(U_74,U_76)
& aElementOf0(U_74,U_77)
& aInteger0(U_74) )
| ( ( ~ aElementOf0(U_74,U_76)
| ~ aElementOf0(U_74,U_77)
| ~ aInteger0(U_74) )
& aElementOf0(U_74,U_75) ) )
| ~ aSet0(U_75) )
& ( ( ! [U_73] :
( ( aElementOf0(U_73,U_75)
| ~ aElementOf0(U_73,U_76)
| ~ aElementOf0(U_73,U_77)
| ~ aInteger0(U_73) )
& ( ( aElementOf0(U_73,U_76)
& aElementOf0(U_73,U_77)
& aInteger0(U_73) )
| ~ aElementOf0(U_73,U_75) ) )
& aSet0(U_75) )
| U_75 != sdtslmnbsdt0(U_77,U_76) ) )
| ~ aSubsetOf0(U_76,cS1395)
| ~ aSubsetOf0(U_77,cS1395) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_77,U_76] :
( ( ! [U_83] :
( U_83 = sdtslmnbsdt0(U_77,U_76)
| ? [U_81] :
( ~ aElementOf0(U_81,U_83)
& aElementOf0(U_81,U_76)
& aElementOf0(U_81,U_77)
& aInteger0(U_81) )
| ? [U_80] :
( ( ~ aElementOf0(U_80,U_76)
| ~ aElementOf0(U_80,U_77)
| ~ aInteger0(U_80) )
& aElementOf0(U_80,U_83) )
| ~ aSet0(U_83) )
& ! [U_82] :
( ( ! [U_79] :
( aElementOf0(U_79,U_82)
| ~ aElementOf0(U_79,U_76)
| ~ aElementOf0(U_79,U_77)
| ~ aInteger0(U_79) )
& ! [U_78] :
( ( aElementOf0(U_78,U_76)
& aElementOf0(U_78,U_77)
& aInteger0(U_78) )
| ~ aElementOf0(U_78,U_82) )
& aSet0(U_82) )
| U_82 != sdtslmnbsdt0(U_77,U_76) ) )
| ~ aSubsetOf0(U_76,cS1395)
| ~ aSubsetOf0(U_77,cS1395) ),
inference(miniscope,[status(thm)],[f_31_2]) ).
fof(f_31_4,plain,
! [U_77,U_76] :
( ( ! [U_83] :
( U_83 = sdtslmnbsdt0(U_77,U_76)
| ? [U_81] :
( ~ aElementOf0(U_81,U_83)
& aElementOf0(U_81,U_76)
& aElementOf0(U_81,U_77)
& aInteger0(U_81) )
| ( ( ~ aElementOf0(sK6(U_77,U_76,U_83),U_76)
| ~ aElementOf0(sK6(U_77,U_76,U_83),U_77)
| ~ aInteger0(sK6(U_77,U_76,U_83)) )
& aElementOf0(sK6(U_77,U_76,U_83),U_83) )
| ~ aSet0(U_83) )
& ! [U_82] :
( ( ! [U_79] :
( aElementOf0(U_79,U_82)
| ~ aElementOf0(U_79,U_76)
| ~ aElementOf0(U_79,U_77)
| ~ aInteger0(U_79) )
& ! [U_78] :
( ( aElementOf0(U_78,U_76)
& aElementOf0(U_78,U_77)
& aInteger0(U_78) )
| ~ aElementOf0(U_78,U_82) )
& aSet0(U_82) )
| U_82 != sdtslmnbsdt0(U_77,U_76) ) )
| ~ aSubsetOf0(U_76,cS1395)
| ~ aSubsetOf0(U_77,cS1395) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_80,sK6(U_77,U_76,U_83))],[f_31_3]) ).
fof(f_31_5,plain,
! [U_77,U_76] :
( ( ! [U_83] :
( U_83 = sdtslmnbsdt0(U_77,U_76)
| ( ~ aElementOf0(sK7(U_77,U_76,U_83),U_83)
& aElementOf0(sK7(U_77,U_76,U_83),U_76)
& aElementOf0(sK7(U_77,U_76,U_83),U_77)
& aInteger0(sK7(U_77,U_76,U_83)) )
| ( ( ~ aElementOf0(sK6(U_77,U_76,U_83),U_76)
| ~ aElementOf0(sK6(U_77,U_76,U_83),U_77)
| ~ aInteger0(sK6(U_77,U_76,U_83)) )
& aElementOf0(sK6(U_77,U_76,U_83),U_83) )
| ~ aSet0(U_83) )
& ! [U_82] :
( ( ! [U_79] :
( aElementOf0(U_79,U_82)
| ~ aElementOf0(U_79,U_76)
| ~ aElementOf0(U_79,U_77)
| ~ aInteger0(U_79) )
& ! [U_78] :
( ( aElementOf0(U_78,U_76)
& aElementOf0(U_78,U_77)
& aInteger0(U_78) )
| ~ aElementOf0(U_78,U_82) )
& aSet0(U_82) )
| U_82 != sdtslmnbsdt0(U_77,U_76) ) )
| ~ aSubsetOf0(U_76,cS1395)
| ~ aSubsetOf0(U_77,cS1395) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_81,sK7(U_77,U_76,U_83))],[f_31_4]) ).
cnf(f_31_6,plain,
( aSet0(U_82)
| U_82 != sdtslmnbsdt0(U_77,U_76)
| ~ aSubsetOf0(U_76,cS1395)
| ~ aSubsetOf0(U_77,cS1395) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_7,plain,
( aInteger0(U_78)
| ~ aElementOf0(U_78,U_82)
| U_82 != sdtslmnbsdt0(U_77,U_76)
| ~ aSubsetOf0(U_76,cS1395)
| ~ aSubsetOf0(U_77,cS1395) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_8,plain,
( aElementOf0(U_78,U_77)
| ~ aElementOf0(U_78,U_82)
| U_82 != sdtslmnbsdt0(U_77,U_76)
| ~ aSubsetOf0(U_76,cS1395)
| ~ aSubsetOf0(U_77,cS1395) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_9,plain,
( aElementOf0(U_78,U_76)
| ~ aElementOf0(U_78,U_82)
| U_82 != sdtslmnbsdt0(U_77,U_76)
| ~ aSubsetOf0(U_76,cS1395)
| ~ aSubsetOf0(U_77,cS1395) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_10,plain,
( aElementOf0(U_79,U_82)
| ~ aElementOf0(U_79,U_76)
| ~ aElementOf0(U_79,U_77)
| ~ aInteger0(U_79)
| U_82 != sdtslmnbsdt0(U_77,U_76)
| ~ aSubsetOf0(U_76,cS1395)
| ~ aSubsetOf0(U_77,cS1395) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_11,plain,
( aInteger0(sK7(U_77,U_76,U_83))
| aElementOf0(sK6(U_77,U_76,U_83),U_83)
| ~ aSet0(U_83)
| U_83 = sdtslmnbsdt0(U_77,U_76)
| ~ aSubsetOf0(U_76,cS1395)
| ~ aSubsetOf0(U_77,cS1395) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_12,plain,
( aElementOf0(sK7(U_77,U_76,U_83),U_77)
| aElementOf0(sK6(U_77,U_76,U_83),U_83)
| ~ aSet0(U_83)
| U_83 = sdtslmnbsdt0(U_77,U_76)
| ~ aSubsetOf0(U_76,cS1395)
| ~ aSubsetOf0(U_77,cS1395) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_13,plain,
( aElementOf0(sK7(U_77,U_76,U_83),U_76)
| aElementOf0(sK6(U_77,U_76,U_83),U_83)
| ~ aSet0(U_83)
| U_83 = sdtslmnbsdt0(U_77,U_76)
| ~ aSubsetOf0(U_76,cS1395)
| ~ aSubsetOf0(U_77,cS1395) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_14,plain,
( ~ aElementOf0(sK7(U_77,U_76,U_83),U_83)
| aElementOf0(sK6(U_77,U_76,U_83),U_83)
| ~ aSet0(U_83)
| U_83 = sdtslmnbsdt0(U_77,U_76)
| ~ aSubsetOf0(U_76,cS1395)
| ~ aSubsetOf0(U_77,cS1395) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_15,plain,
( aInteger0(sK7(U_77,U_76,U_83))
| ~ aElementOf0(sK6(U_77,U_76,U_83),U_76)
| ~ aElementOf0(sK6(U_77,U_76,U_83),U_77)
| ~ aInteger0(sK6(U_77,U_76,U_83))
| ~ aSet0(U_83)
| U_83 = sdtslmnbsdt0(U_77,U_76)
| ~ aSubsetOf0(U_76,cS1395)
| ~ aSubsetOf0(U_77,cS1395) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_16,plain,
( aElementOf0(sK7(U_77,U_76,U_83),U_77)
| ~ aElementOf0(sK6(U_77,U_76,U_83),U_76)
| ~ aElementOf0(sK6(U_77,U_76,U_83),U_77)
| ~ aInteger0(sK6(U_77,U_76,U_83))
| ~ aSet0(U_83)
| U_83 = sdtslmnbsdt0(U_77,U_76)
| ~ aSubsetOf0(U_76,cS1395)
| ~ aSubsetOf0(U_77,cS1395) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_17,plain,
( aElementOf0(sK7(U_77,U_76,U_83),U_76)
| ~ aElementOf0(sK6(U_77,U_76,U_83),U_76)
| ~ aElementOf0(sK6(U_77,U_76,U_83),U_77)
| ~ aInteger0(sK6(U_77,U_76,U_83))
| ~ aSet0(U_83)
| U_83 = sdtslmnbsdt0(U_77,U_76)
| ~ aSubsetOf0(U_76,cS1395)
| ~ aSubsetOf0(U_77,cS1395) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_18,plain,
( ~ aElementOf0(sK7(U_77,U_76,U_83),U_83)
| ~ aElementOf0(sK6(U_77,U_76,U_83),U_76)
| ~ aElementOf0(sK6(U_77,U_76,U_83),U_77)
| ~ aInteger0(sK6(U_77,U_76,U_83))
| ~ aSet0(U_83)
| U_83 = sdtslmnbsdt0(U_77,U_76)
| ~ aSubsetOf0(U_76,cS1395)
| ~ aSubsetOf0(U_77,cS1395) ),
inference(clausify,[status(thm)],[f_31_5]) ).
fof(f_32_1,plain,
! [W0] :
( ! [W1] :
( ( W1 = sbsmnsldt0(W0)
| ? [W2] :
( ( ~ aElementOf0(W2,W1)
& ? [W3] :
( aElementOf0(W2,W3)
& aElementOf0(W3,W0) )
& aInteger0(W2) )
| ( ( ! [W3] :
( ~ aElementOf0(W2,W3)
| ~ aElementOf0(W3,W0) )
| ~ aInteger0(W2) )
& aElementOf0(W2,W1) ) )
| ~ aSet0(W1) )
& ( ( ! [W2] :
( ( aElementOf0(W2,W1)
| ! [W3] :
( ~ aElementOf0(W2,W3)
| ~ aElementOf0(W3,W0) )
| ~ aInteger0(W2) )
& ( ( ? [W3] :
( aElementOf0(W2,W3)
& aElementOf0(W3,W0) )
& aInteger0(W2) )
| ~ aElementOf0(W2,W1) ) )
& aSet0(W1) )
| W1 != sbsmnsldt0(W0) ) )
| ? [W1] :
( ~ aSubsetOf0(W1,cS1395)
& aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mUnionSet]) ).
fof(f_32_2,plain,
! [U_92] :
( ! [U_91] :
( ( U_91 = sbsmnsldt0(U_92)
| ? [U_90] :
( ( ~ aElementOf0(U_90,U_91)
& ? [U_89] :
( aElementOf0(U_90,U_89)
& aElementOf0(U_89,U_92) )
& aInteger0(U_90) )
| ( ( ! [U_88] :
( ~ aElementOf0(U_90,U_88)
| ~ aElementOf0(U_88,U_92) )
| ~ aInteger0(U_90) )
& aElementOf0(U_90,U_91) ) )
| ~ aSet0(U_91) )
& ( ( ! [U_87] :
( ( aElementOf0(U_87,U_91)
| ! [U_86] :
( ~ aElementOf0(U_87,U_86)
| ~ aElementOf0(U_86,U_92) )
| ~ aInteger0(U_87) )
& ( ( ? [U_85] :
( aElementOf0(U_87,U_85)
& aElementOf0(U_85,U_92) )
& aInteger0(U_87) )
| ~ aElementOf0(U_87,U_91) ) )
& aSet0(U_91) )
| U_91 != sbsmnsldt0(U_92) ) )
| ? [U_84] :
( ~ aSubsetOf0(U_84,cS1395)
& aElementOf0(U_84,U_92) )
| ~ aSet0(U_92) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_92] :
( ( ! [U_98] :
( U_98 = sbsmnsldt0(U_92)
| ? [U_96] :
( ~ aElementOf0(U_96,U_98)
& ? [U_89] :
( aElementOf0(U_96,U_89)
& aElementOf0(U_89,U_92) )
& aInteger0(U_96) )
| ? [U_95] :
( ( ! [U_88] :
( ~ aElementOf0(U_95,U_88)
| ~ aElementOf0(U_88,U_92) )
| ~ aInteger0(U_95) )
& aElementOf0(U_95,U_98) )
| ~ aSet0(U_98) )
& ! [U_97] :
( ( ! [U_94] :
( aElementOf0(U_94,U_97)
| ! [U_86] :
( ~ aElementOf0(U_94,U_86)
| ~ aElementOf0(U_86,U_92) )
| ~ aInteger0(U_94) )
& ! [U_93] :
( ( ? [U_85] :
( aElementOf0(U_93,U_85)
& aElementOf0(U_85,U_92) )
& aInteger0(U_93) )
| ~ aElementOf0(U_93,U_97) )
& aSet0(U_97) )
| U_97 != sbsmnsldt0(U_92) ) )
| ? [U_84] :
( ~ aSubsetOf0(U_84,cS1395)
& aElementOf0(U_84,U_92) )
| ~ aSet0(U_92) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
fof(f_32_4,plain,
! [U_92] :
( ( ! [U_98] :
( U_98 = sbsmnsldt0(U_92)
| ? [U_96] :
( ~ aElementOf0(U_96,U_98)
& ? [U_89] :
( aElementOf0(U_96,U_89)
& aElementOf0(U_89,U_92) )
& aInteger0(U_96) )
| ? [U_95] :
( ( ! [U_88] :
( ~ aElementOf0(U_95,U_88)
| ~ aElementOf0(U_88,U_92) )
| ~ aInteger0(U_95) )
& aElementOf0(U_95,U_98) )
| ~ aSet0(U_98) )
& ! [U_97] :
( ( ! [U_94] :
( aElementOf0(U_94,U_97)
| ! [U_86] :
( ~ aElementOf0(U_94,U_86)
| ~ aElementOf0(U_86,U_92) )
| ~ aInteger0(U_94) )
& ! [U_93] :
( ( ? [U_85] :
( aElementOf0(U_93,U_85)
& aElementOf0(U_85,U_92) )
& aInteger0(U_93) )
| ~ aElementOf0(U_93,U_97) )
& aSet0(U_97) )
| U_97 != sbsmnsldt0(U_92) ) )
| ( ~ aSubsetOf0(sK8(U_92),cS1395)
& aElementOf0(sK8(U_92),U_92) )
| ~ aSet0(U_92) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_84,sK8(U_92))],[f_32_3]) ).
fof(f_32_5,plain,
! [U_92] :
( ( ! [U_98] :
( U_98 = sbsmnsldt0(U_92)
| ? [U_96] :
( ~ aElementOf0(U_96,U_98)
& ? [U_89] :
( aElementOf0(U_96,U_89)
& aElementOf0(U_89,U_92) )
& aInteger0(U_96) )
| ? [U_95] :
( ( ! [U_88] :
( ~ aElementOf0(U_95,U_88)
| ~ aElementOf0(U_88,U_92) )
| ~ aInteger0(U_95) )
& aElementOf0(U_95,U_98) )
| ~ aSet0(U_98) )
& ! [U_97] :
( ( ! [U_94] :
( aElementOf0(U_94,U_97)
| ! [U_86] :
( ~ aElementOf0(U_94,U_86)
| ~ aElementOf0(U_86,U_92) )
| ~ aInteger0(U_94) )
& ! [U_93] :
( ( aElementOf0(U_93,sK9(U_92,U_97,U_93))
& aElementOf0(sK9(U_92,U_97,U_93),U_92)
& aInteger0(U_93) )
| ~ aElementOf0(U_93,U_97) )
& aSet0(U_97) )
| U_97 != sbsmnsldt0(U_92) ) )
| ( ~ aSubsetOf0(sK8(U_92),cS1395)
& aElementOf0(sK8(U_92),U_92) )
| ~ aSet0(U_92) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_85,sK9(U_92,U_97,U_93))],[f_32_4]) ).
fof(f_32_6,plain,
! [U_92] :
( ( ! [U_98] :
( U_98 = sbsmnsldt0(U_92)
| ? [U_96] :
( ~ aElementOf0(U_96,U_98)
& ? [U_89] :
( aElementOf0(U_96,U_89)
& aElementOf0(U_89,U_92) )
& aInteger0(U_96) )
| ( ( ! [U_88] :
( ~ aElementOf0(sK10(U_92,U_98),U_88)
| ~ aElementOf0(U_88,U_92) )
| ~ aInteger0(sK10(U_92,U_98)) )
& aElementOf0(sK10(U_92,U_98),U_98) )
| ~ aSet0(U_98) )
& ! [U_97] :
( ( ! [U_94] :
( aElementOf0(U_94,U_97)
| ! [U_86] :
( ~ aElementOf0(U_94,U_86)
| ~ aElementOf0(U_86,U_92) )
| ~ aInteger0(U_94) )
& ! [U_93] :
( ( aElementOf0(U_93,sK9(U_92,U_97,U_93))
& aElementOf0(sK9(U_92,U_97,U_93),U_92)
& aInteger0(U_93) )
| ~ aElementOf0(U_93,U_97) )
& aSet0(U_97) )
| U_97 != sbsmnsldt0(U_92) ) )
| ( ~ aSubsetOf0(sK8(U_92),cS1395)
& aElementOf0(sK8(U_92),U_92) )
| ~ aSet0(U_92) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_95,sK10(U_92,U_98))],[f_32_5]) ).
fof(f_32_7,plain,
! [U_92] :
( ( ! [U_98] :
( U_98 = sbsmnsldt0(U_92)
| ( ~ aElementOf0(sK11(U_92,U_98),U_98)
& ? [U_89] :
( aElementOf0(sK11(U_92,U_98),U_89)
& aElementOf0(U_89,U_92) )
& aInteger0(sK11(U_92,U_98)) )
| ( ( ! [U_88] :
( ~ aElementOf0(sK10(U_92,U_98),U_88)
| ~ aElementOf0(U_88,U_92) )
| ~ aInteger0(sK10(U_92,U_98)) )
& aElementOf0(sK10(U_92,U_98),U_98) )
| ~ aSet0(U_98) )
& ! [U_97] :
( ( ! [U_94] :
( aElementOf0(U_94,U_97)
| ! [U_86] :
( ~ aElementOf0(U_94,U_86)
| ~ aElementOf0(U_86,U_92) )
| ~ aInteger0(U_94) )
& ! [U_93] :
( ( aElementOf0(U_93,sK9(U_92,U_97,U_93))
& aElementOf0(sK9(U_92,U_97,U_93),U_92)
& aInteger0(U_93) )
| ~ aElementOf0(U_93,U_97) )
& aSet0(U_97) )
| U_97 != sbsmnsldt0(U_92) ) )
| ( ~ aSubsetOf0(sK8(U_92),cS1395)
& aElementOf0(sK8(U_92),U_92) )
| ~ aSet0(U_92) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_96,sK11(U_92,U_98))],[f_32_6]) ).
fof(f_32_8,plain,
! [U_92] :
( ( ! [U_98] :
( U_98 = sbsmnsldt0(U_92)
| ( ~ aElementOf0(sK11(U_92,U_98),U_98)
& aElementOf0(sK11(U_92,U_98),sK12(U_92,U_98))
& aElementOf0(sK12(U_92,U_98),U_92)
& aInteger0(sK11(U_92,U_98)) )
| ( ( ! [U_88] :
( ~ aElementOf0(sK10(U_92,U_98),U_88)
| ~ aElementOf0(U_88,U_92) )
| ~ aInteger0(sK10(U_92,U_98)) )
& aElementOf0(sK10(U_92,U_98),U_98) )
| ~ aSet0(U_98) )
& ! [U_97] :
( ( ! [U_94] :
( aElementOf0(U_94,U_97)
| ! [U_86] :
( ~ aElementOf0(U_94,U_86)
| ~ aElementOf0(U_86,U_92) )
| ~ aInteger0(U_94) )
& ! [U_93] :
( ( aElementOf0(U_93,sK9(U_92,U_97,U_93))
& aElementOf0(sK9(U_92,U_97,U_93),U_92)
& aInteger0(U_93) )
| ~ aElementOf0(U_93,U_97) )
& aSet0(U_97) )
| U_97 != sbsmnsldt0(U_92) ) )
| ( ~ aSubsetOf0(sK8(U_92),cS1395)
& aElementOf0(sK8(U_92),U_92) )
| ~ aSet0(U_92) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_89,sK12(U_92,U_98))],[f_32_7]) ).
cnf(f_32_9,plain,
( aSet0(U_97)
| U_97 != sbsmnsldt0(U_92)
| aElementOf0(sK8(U_92),U_92)
| ~ aSet0(U_92) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_10,plain,
( aInteger0(U_93)
| ~ aElementOf0(U_93,U_97)
| U_97 != sbsmnsldt0(U_92)
| aElementOf0(sK8(U_92),U_92)
| ~ aSet0(U_92) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_11,plain,
( aElementOf0(sK9(U_92,U_97,U_93),U_92)
| ~ aElementOf0(U_93,U_97)
| U_97 != sbsmnsldt0(U_92)
| aElementOf0(sK8(U_92),U_92)
| ~ aSet0(U_92) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_12,plain,
( aElementOf0(U_93,sK9(U_92,U_97,U_93))
| ~ aElementOf0(U_93,U_97)
| U_97 != sbsmnsldt0(U_92)
| aElementOf0(sK8(U_92),U_92)
| ~ aSet0(U_92) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_13,plain,
( aElementOf0(U_94,U_97)
| ~ aElementOf0(U_94,U_86)
| ~ aElementOf0(U_86,U_92)
| ~ aInteger0(U_94)
| U_97 != sbsmnsldt0(U_92)
| aElementOf0(sK8(U_92),U_92)
| ~ aSet0(U_92) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_14,plain,
( aSet0(U_97)
| U_97 != sbsmnsldt0(U_92)
| ~ aSubsetOf0(sK8(U_92),cS1395)
| ~ aSet0(U_92) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_15,plain,
( aInteger0(U_93)
| ~ aElementOf0(U_93,U_97)
| U_97 != sbsmnsldt0(U_92)
| ~ aSubsetOf0(sK8(U_92),cS1395)
| ~ aSet0(U_92) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_16,plain,
( aElementOf0(sK9(U_92,U_97,U_93),U_92)
| ~ aElementOf0(U_93,U_97)
| U_97 != sbsmnsldt0(U_92)
| ~ aSubsetOf0(sK8(U_92),cS1395)
| ~ aSet0(U_92) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_17,plain,
( aElementOf0(U_93,sK9(U_92,U_97,U_93))
| ~ aElementOf0(U_93,U_97)
| U_97 != sbsmnsldt0(U_92)
| ~ aSubsetOf0(sK8(U_92),cS1395)
| ~ aSet0(U_92) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_18,plain,
( aElementOf0(U_94,U_97)
| ~ aElementOf0(U_94,U_86)
| ~ aElementOf0(U_86,U_92)
| ~ aInteger0(U_94)
| U_97 != sbsmnsldt0(U_92)
| ~ aSubsetOf0(sK8(U_92),cS1395)
| ~ aSet0(U_92) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_19,plain,
( aInteger0(sK11(U_92,U_98))
| aElementOf0(sK10(U_92,U_98),U_98)
| ~ aSet0(U_98)
| U_98 = sbsmnsldt0(U_92)
| aElementOf0(sK8(U_92),U_92)
| ~ aSet0(U_92) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_20,plain,
( aElementOf0(sK12(U_92,U_98),U_92)
| aElementOf0(sK10(U_92,U_98),U_98)
| ~ aSet0(U_98)
| U_98 = sbsmnsldt0(U_92)
| aElementOf0(sK8(U_92),U_92)
| ~ aSet0(U_92) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_21,plain,
( aElementOf0(sK11(U_92,U_98),sK12(U_92,U_98))
| aElementOf0(sK10(U_92,U_98),U_98)
| ~ aSet0(U_98)
| U_98 = sbsmnsldt0(U_92)
| aElementOf0(sK8(U_92),U_92)
| ~ aSet0(U_92) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_22,plain,
( ~ aElementOf0(sK11(U_92,U_98),U_98)
| aElementOf0(sK10(U_92,U_98),U_98)
| ~ aSet0(U_98)
| U_98 = sbsmnsldt0(U_92)
| aElementOf0(sK8(U_92),U_92)
| ~ aSet0(U_92) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_23,plain,
( aInteger0(sK11(U_92,U_98))
| ~ aElementOf0(sK10(U_92,U_98),U_88)
| ~ aElementOf0(U_88,U_92)
| ~ aInteger0(sK10(U_92,U_98))
| ~ aSet0(U_98)
| U_98 = sbsmnsldt0(U_92)
| aElementOf0(sK8(U_92),U_92)
| ~ aSet0(U_92) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_24,plain,
( aElementOf0(sK12(U_92,U_98),U_92)
| ~ aElementOf0(sK10(U_92,U_98),U_88)
| ~ aElementOf0(U_88,U_92)
| ~ aInteger0(sK10(U_92,U_98))
| ~ aSet0(U_98)
| U_98 = sbsmnsldt0(U_92)
| aElementOf0(sK8(U_92),U_92)
| ~ aSet0(U_92) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_25,plain,
( aElementOf0(sK11(U_92,U_98),sK12(U_92,U_98))
| ~ aElementOf0(sK10(U_92,U_98),U_88)
| ~ aElementOf0(U_88,U_92)
| ~ aInteger0(sK10(U_92,U_98))
| ~ aSet0(U_98)
| U_98 = sbsmnsldt0(U_92)
| aElementOf0(sK8(U_92),U_92)
| ~ aSet0(U_92) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_26,plain,
( ~ aElementOf0(sK11(U_92,U_98),U_98)
| ~ aElementOf0(sK10(U_92,U_98),U_88)
| ~ aElementOf0(U_88,U_92)
| ~ aInteger0(sK10(U_92,U_98))
| ~ aSet0(U_98)
| U_98 = sbsmnsldt0(U_92)
| aElementOf0(sK8(U_92),U_92)
| ~ aSet0(U_92) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_27,plain,
( aInteger0(sK11(U_92,U_98))
| aElementOf0(sK10(U_92,U_98),U_98)
| ~ aSet0(U_98)
| U_98 = sbsmnsldt0(U_92)
| ~ aSubsetOf0(sK8(U_92),cS1395)
| ~ aSet0(U_92) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_28,plain,
( aElementOf0(sK12(U_92,U_98),U_92)
| aElementOf0(sK10(U_92,U_98),U_98)
| ~ aSet0(U_98)
| U_98 = sbsmnsldt0(U_92)
| ~ aSubsetOf0(sK8(U_92),cS1395)
| ~ aSet0(U_92) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_29,plain,
( aElementOf0(sK11(U_92,U_98),sK12(U_92,U_98))
| aElementOf0(sK10(U_92,U_98),U_98)
| ~ aSet0(U_98)
| U_98 = sbsmnsldt0(U_92)
| ~ aSubsetOf0(sK8(U_92),cS1395)
| ~ aSet0(U_92) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_30,plain,
( ~ aElementOf0(sK11(U_92,U_98),U_98)
| aElementOf0(sK10(U_92,U_98),U_98)
| ~ aSet0(U_98)
| U_98 = sbsmnsldt0(U_92)
| ~ aSubsetOf0(sK8(U_92),cS1395)
| ~ aSet0(U_92) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_31,plain,
( aInteger0(sK11(U_92,U_98))
| ~ aElementOf0(sK10(U_92,U_98),U_88)
| ~ aElementOf0(U_88,U_92)
| ~ aInteger0(sK10(U_92,U_98))
| ~ aSet0(U_98)
| U_98 = sbsmnsldt0(U_92)
| ~ aSubsetOf0(sK8(U_92),cS1395)
| ~ aSet0(U_92) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_32,plain,
( aElementOf0(sK12(U_92,U_98),U_92)
| ~ aElementOf0(sK10(U_92,U_98),U_88)
| ~ aElementOf0(U_88,U_92)
| ~ aInteger0(sK10(U_92,U_98))
| ~ aSet0(U_98)
| U_98 = sbsmnsldt0(U_92)
| ~ aSubsetOf0(sK8(U_92),cS1395)
| ~ aSet0(U_92) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_33,plain,
( aElementOf0(sK11(U_92,U_98),sK12(U_92,U_98))
| ~ aElementOf0(sK10(U_92,U_98),U_88)
| ~ aElementOf0(U_88,U_92)
| ~ aInteger0(sK10(U_92,U_98))
| ~ aSet0(U_98)
| U_98 = sbsmnsldt0(U_92)
| ~ aSubsetOf0(sK8(U_92),cS1395)
| ~ aSet0(U_92) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_34,plain,
( ~ aElementOf0(sK11(U_92,U_98),U_98)
| ~ aElementOf0(sK10(U_92,U_98),U_88)
| ~ aElementOf0(U_88,U_92)
| ~ aInteger0(sK10(U_92,U_98))
| ~ aSet0(U_98)
| U_98 = sbsmnsldt0(U_92)
| ~ aSubsetOf0(sK8(U_92),cS1395)
| ~ aSet0(U_92) ),
inference(clausify,[status(thm)],[f_32_8]) ).
fof(f_33_1,plain,
! [W0] :
( ! [W1] :
( ( W1 = stldt0(W0)
| ? [W2] :
( ( ~ aElementOf0(W2,W1)
& ~ aElementOf0(W2,W0)
& aInteger0(W2) )
| ( ( aElementOf0(W2,W0)
| ~ aInteger0(W2) )
& aElementOf0(W2,W1) ) )
| ~ aSet0(W1) )
& ( ( ! [W2] :
( ( aElementOf0(W2,W1)
| aElementOf0(W2,W0)
| ~ aInteger0(W2) )
& ( ( ~ aElementOf0(W2,W0)
& aInteger0(W2) )
| ~ aElementOf0(W2,W1) ) )
& aSet0(W1) )
| W1 != stldt0(W0) ) )
| ~ aSubsetOf0(W0,cS1395) ),
inference(fof_nnf,[status(thm)],[mComplement]) ).
fof(f_33_2,plain,
! [U_102] :
( ! [U_101] :
( ( U_101 = stldt0(U_102)
| ? [U_100] :
( ( ~ aElementOf0(U_100,U_101)
& ~ aElementOf0(U_100,U_102)
& aInteger0(U_100) )
| ( ( aElementOf0(U_100,U_102)
| ~ aInteger0(U_100) )
& aElementOf0(U_100,U_101) ) )
| ~ aSet0(U_101) )
& ( ( ! [U_99] :
( ( aElementOf0(U_99,U_101)
| aElementOf0(U_99,U_102)
| ~ aInteger0(U_99) )
& ( ( ~ aElementOf0(U_99,U_102)
& aInteger0(U_99) )
| ~ aElementOf0(U_99,U_101) ) )
& aSet0(U_101) )
| U_101 != stldt0(U_102) ) )
| ~ aSubsetOf0(U_102,cS1395) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_102] :
( ( ! [U_108] :
( U_108 = stldt0(U_102)
| ? [U_106] :
( ~ aElementOf0(U_106,U_108)
& ~ aElementOf0(U_106,U_102)
& aInteger0(U_106) )
| ? [U_105] :
( ( aElementOf0(U_105,U_102)
| ~ aInteger0(U_105) )
& aElementOf0(U_105,U_108) )
| ~ aSet0(U_108) )
& ! [U_107] :
( ( ! [U_104] :
( aElementOf0(U_104,U_107)
| aElementOf0(U_104,U_102)
| ~ aInteger0(U_104) )
& ! [U_103] :
( ( ~ aElementOf0(U_103,U_102)
& aInteger0(U_103) )
| ~ aElementOf0(U_103,U_107) )
& aSet0(U_107) )
| U_107 != stldt0(U_102) ) )
| ~ aSubsetOf0(U_102,cS1395) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
fof(f_33_4,plain,
! [U_102] :
( ( ! [U_108] :
( U_108 = stldt0(U_102)
| ? [U_106] :
( ~ aElementOf0(U_106,U_108)
& ~ aElementOf0(U_106,U_102)
& aInteger0(U_106) )
| ( ( aElementOf0(sK13(U_102,U_108),U_102)
| ~ aInteger0(sK13(U_102,U_108)) )
& aElementOf0(sK13(U_102,U_108),U_108) )
| ~ aSet0(U_108) )
& ! [U_107] :
( ( ! [U_104] :
( aElementOf0(U_104,U_107)
| aElementOf0(U_104,U_102)
| ~ aInteger0(U_104) )
& ! [U_103] :
( ( ~ aElementOf0(U_103,U_102)
& aInteger0(U_103) )
| ~ aElementOf0(U_103,U_107) )
& aSet0(U_107) )
| U_107 != stldt0(U_102) ) )
| ~ aSubsetOf0(U_102,cS1395) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_105,sK13(U_102,U_108))],[f_33_3]) ).
fof(f_33_5,plain,
! [U_102] :
( ( ! [U_108] :
( U_108 = stldt0(U_102)
| ( ~ aElementOf0(sK14(U_102,U_108),U_108)
& ~ aElementOf0(sK14(U_102,U_108),U_102)
& aInteger0(sK14(U_102,U_108)) )
| ( ( aElementOf0(sK13(U_102,U_108),U_102)
| ~ aInteger0(sK13(U_102,U_108)) )
& aElementOf0(sK13(U_102,U_108),U_108) )
| ~ aSet0(U_108) )
& ! [U_107] :
( ( ! [U_104] :
( aElementOf0(U_104,U_107)
| aElementOf0(U_104,U_102)
| ~ aInteger0(U_104) )
& ! [U_103] :
( ( ~ aElementOf0(U_103,U_102)
& aInteger0(U_103) )
| ~ aElementOf0(U_103,U_107) )
& aSet0(U_107) )
| U_107 != stldt0(U_102) ) )
| ~ aSubsetOf0(U_102,cS1395) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_106,sK14(U_102,U_108))],[f_33_4]) ).
cnf(f_33_6,plain,
( aSet0(U_107)
| U_107 != stldt0(U_102)
| ~ aSubsetOf0(U_102,cS1395) ),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_7,plain,
( aInteger0(U_103)
| ~ aElementOf0(U_103,U_107)
| U_107 != stldt0(U_102)
| ~ aSubsetOf0(U_102,cS1395) ),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_8,plain,
( ~ aElementOf0(U_103,U_102)
| ~ aElementOf0(U_103,U_107)
| U_107 != stldt0(U_102)
| ~ aSubsetOf0(U_102,cS1395) ),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_9,plain,
( aElementOf0(U_104,U_107)
| aElementOf0(U_104,U_102)
| ~ aInteger0(U_104)
| U_107 != stldt0(U_102)
| ~ aSubsetOf0(U_102,cS1395) ),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_10,plain,
( aInteger0(sK14(U_102,U_108))
| aElementOf0(sK13(U_102,U_108),U_108)
| ~ aSet0(U_108)
| U_108 = stldt0(U_102)
| ~ aSubsetOf0(U_102,cS1395) ),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_11,plain,
( ~ aElementOf0(sK14(U_102,U_108),U_102)
| aElementOf0(sK13(U_102,U_108),U_108)
| ~ aSet0(U_108)
| U_108 = stldt0(U_102)
| ~ aSubsetOf0(U_102,cS1395) ),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_12,plain,
( ~ aElementOf0(sK14(U_102,U_108),U_108)
| aElementOf0(sK13(U_102,U_108),U_108)
| ~ aSet0(U_108)
| U_108 = stldt0(U_102)
| ~ aSubsetOf0(U_102,cS1395) ),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_13,plain,
( aInteger0(sK14(U_102,U_108))
| aElementOf0(sK13(U_102,U_108),U_102)
| ~ aInteger0(sK13(U_102,U_108))
| ~ aSet0(U_108)
| U_108 = stldt0(U_102)
| ~ aSubsetOf0(U_102,cS1395) ),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_14,plain,
( ~ aElementOf0(sK14(U_102,U_108),U_102)
| aElementOf0(sK13(U_102,U_108),U_102)
| ~ aInteger0(sK13(U_102,U_108))
| ~ aSet0(U_108)
| U_108 = stldt0(U_102)
| ~ aSubsetOf0(U_102,cS1395) ),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_15,plain,
( ~ aElementOf0(sK14(U_102,U_108),U_108)
| aElementOf0(sK13(U_102,U_108),U_102)
| ~ aInteger0(sK13(U_102,U_108))
| ~ aSet0(U_108)
| U_108 = stldt0(U_102)
| ~ aSubsetOf0(U_102,cS1395) ),
inference(clausify,[status(thm)],[f_33_5]) ).
fof(f_34_1,plain,
! [W0,W1] :
( ! [W2] :
( ( W2 = szAzrzSzezqlpdtcmdtrp0(W0,W1)
| ? [W3] :
( ( ~ aElementOf0(W3,W2)
& sdteqdtlpzmzozddtrp0(W3,W0,W1)
& aInteger0(W3) )
| ( ( ~ sdteqdtlpzmzozddtrp0(W3,W0,W1)
| ~ aInteger0(W3) )
& aElementOf0(W3,W2) ) )
| ~ aSet0(W2) )
& ( ( ! [W3] :
( ( aElementOf0(W3,W2)
| ~ sdteqdtlpzmzozddtrp0(W3,W0,W1)
| ~ aInteger0(W3) )
& ( ( sdteqdtlpzmzozddtrp0(W3,W0,W1)
& aInteger0(W3) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != szAzrzSzezqlpdtcmdtrp0(W0,W1) ) )
| W1 = sz00
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mArSeq]) ).
fof(f_34_2,plain,
! [U_113,U_112] :
( ! [U_111] :
( ( U_111 = szAzrzSzezqlpdtcmdtrp0(U_113,U_112)
| ? [U_110] :
( ( ~ aElementOf0(U_110,U_111)
& sdteqdtlpzmzozddtrp0(U_110,U_113,U_112)
& aInteger0(U_110) )
| ( ( ~ sdteqdtlpzmzozddtrp0(U_110,U_113,U_112)
| ~ aInteger0(U_110) )
& aElementOf0(U_110,U_111) ) )
| ~ aSet0(U_111) )
& ( ( ! [U_109] :
( ( aElementOf0(U_109,U_111)
| ~ sdteqdtlpzmzozddtrp0(U_109,U_113,U_112)
| ~ aInteger0(U_109) )
& ( ( sdteqdtlpzmzozddtrp0(U_109,U_113,U_112)
& aInteger0(U_109) )
| ~ aElementOf0(U_109,U_111) ) )
& aSet0(U_111) )
| U_111 != szAzrzSzezqlpdtcmdtrp0(U_113,U_112) ) )
| U_112 = sz00
| ~ aInteger0(U_112)
| ~ aInteger0(U_113) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_113,U_112] :
( ( ! [U_119] :
( U_119 = szAzrzSzezqlpdtcmdtrp0(U_113,U_112)
| ? [U_117] :
( ~ aElementOf0(U_117,U_119)
& sdteqdtlpzmzozddtrp0(U_117,U_113,U_112)
& aInteger0(U_117) )
| ? [U_116] :
( ( ~ sdteqdtlpzmzozddtrp0(U_116,U_113,U_112)
| ~ aInteger0(U_116) )
& aElementOf0(U_116,U_119) )
| ~ aSet0(U_119) )
& ! [U_118] :
( ( ! [U_115] :
( aElementOf0(U_115,U_118)
| ~ sdteqdtlpzmzozddtrp0(U_115,U_113,U_112)
| ~ aInteger0(U_115) )
& ! [U_114] :
( ( sdteqdtlpzmzozddtrp0(U_114,U_113,U_112)
& aInteger0(U_114) )
| ~ aElementOf0(U_114,U_118) )
& aSet0(U_118) )
| U_118 != szAzrzSzezqlpdtcmdtrp0(U_113,U_112) ) )
| U_112 = sz00
| ~ aInteger0(U_112)
| ~ aInteger0(U_113) ),
inference(miniscope,[status(thm)],[f_34_2]) ).
fof(f_34_4,plain,
! [U_113,U_112] :
( ( ! [U_119] :
( U_119 = szAzrzSzezqlpdtcmdtrp0(U_113,U_112)
| ? [U_117] :
( ~ aElementOf0(U_117,U_119)
& sdteqdtlpzmzozddtrp0(U_117,U_113,U_112)
& aInteger0(U_117) )
| ( ( ~ sdteqdtlpzmzozddtrp0(sK15(U_113,U_112,U_119),U_113,U_112)
| ~ aInteger0(sK15(U_113,U_112,U_119)) )
& aElementOf0(sK15(U_113,U_112,U_119),U_119) )
| ~ aSet0(U_119) )
& ! [U_118] :
( ( ! [U_115] :
( aElementOf0(U_115,U_118)
| ~ sdteqdtlpzmzozddtrp0(U_115,U_113,U_112)
| ~ aInteger0(U_115) )
& ! [U_114] :
( ( sdteqdtlpzmzozddtrp0(U_114,U_113,U_112)
& aInteger0(U_114) )
| ~ aElementOf0(U_114,U_118) )
& aSet0(U_118) )
| U_118 != szAzrzSzezqlpdtcmdtrp0(U_113,U_112) ) )
| U_112 = sz00
| ~ aInteger0(U_112)
| ~ aInteger0(U_113) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_116,sK15(U_113,U_112,U_119))],[f_34_3]) ).
fof(f_34_5,plain,
! [U_113,U_112] :
( ( ! [U_119] :
( U_119 = szAzrzSzezqlpdtcmdtrp0(U_113,U_112)
| ( ~ aElementOf0(sK16(U_113,U_112,U_119),U_119)
& sdteqdtlpzmzozddtrp0(sK16(U_113,U_112,U_119),U_113,U_112)
& aInteger0(sK16(U_113,U_112,U_119)) )
| ( ( ~ sdteqdtlpzmzozddtrp0(sK15(U_113,U_112,U_119),U_113,U_112)
| ~ aInteger0(sK15(U_113,U_112,U_119)) )
& aElementOf0(sK15(U_113,U_112,U_119),U_119) )
| ~ aSet0(U_119) )
& ! [U_118] :
( ( ! [U_115] :
( aElementOf0(U_115,U_118)
| ~ sdteqdtlpzmzozddtrp0(U_115,U_113,U_112)
| ~ aInteger0(U_115) )
& ! [U_114] :
( ( sdteqdtlpzmzozddtrp0(U_114,U_113,U_112)
& aInteger0(U_114) )
| ~ aElementOf0(U_114,U_118) )
& aSet0(U_118) )
| U_118 != szAzrzSzezqlpdtcmdtrp0(U_113,U_112) ) )
| U_112 = sz00
| ~ aInteger0(U_112)
| ~ aInteger0(U_113) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_117,sK16(U_113,U_112,U_119))],[f_34_4]) ).
cnf(f_34_6,plain,
( aSet0(U_118)
| U_118 != szAzrzSzezqlpdtcmdtrp0(U_113,U_112)
| U_112 = sz00
| ~ aInteger0(U_112)
| ~ aInteger0(U_113) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_7,plain,
( aInteger0(U_114)
| ~ aElementOf0(U_114,U_118)
| U_118 != szAzrzSzezqlpdtcmdtrp0(U_113,U_112)
| U_112 = sz00
| ~ aInteger0(U_112)
| ~ aInteger0(U_113) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_8,plain,
( sdteqdtlpzmzozddtrp0(U_114,U_113,U_112)
| ~ aElementOf0(U_114,U_118)
| U_118 != szAzrzSzezqlpdtcmdtrp0(U_113,U_112)
| U_112 = sz00
| ~ aInteger0(U_112)
| ~ aInteger0(U_113) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_9,plain,
( aElementOf0(U_115,U_118)
| ~ sdteqdtlpzmzozddtrp0(U_115,U_113,U_112)
| ~ aInteger0(U_115)
| U_118 != szAzrzSzezqlpdtcmdtrp0(U_113,U_112)
| U_112 = sz00
| ~ aInteger0(U_112)
| ~ aInteger0(U_113) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_10,plain,
( aInteger0(sK16(U_113,U_112,U_119))
| aElementOf0(sK15(U_113,U_112,U_119),U_119)
| ~ aSet0(U_119)
| U_119 = szAzrzSzezqlpdtcmdtrp0(U_113,U_112)
| U_112 = sz00
| ~ aInteger0(U_112)
| ~ aInteger0(U_113) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_11,plain,
( sdteqdtlpzmzozddtrp0(sK16(U_113,U_112,U_119),U_113,U_112)
| aElementOf0(sK15(U_113,U_112,U_119),U_119)
| ~ aSet0(U_119)
| U_119 = szAzrzSzezqlpdtcmdtrp0(U_113,U_112)
| U_112 = sz00
| ~ aInteger0(U_112)
| ~ aInteger0(U_113) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_12,plain,
( ~ aElementOf0(sK16(U_113,U_112,U_119),U_119)
| aElementOf0(sK15(U_113,U_112,U_119),U_119)
| ~ aSet0(U_119)
| U_119 = szAzrzSzezqlpdtcmdtrp0(U_113,U_112)
| U_112 = sz00
| ~ aInteger0(U_112)
| ~ aInteger0(U_113) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_13,plain,
( aInteger0(sK16(U_113,U_112,U_119))
| ~ sdteqdtlpzmzozddtrp0(sK15(U_113,U_112,U_119),U_113,U_112)
| ~ aInteger0(sK15(U_113,U_112,U_119))
| ~ aSet0(U_119)
| U_119 = szAzrzSzezqlpdtcmdtrp0(U_113,U_112)
| U_112 = sz00
| ~ aInteger0(U_112)
| ~ aInteger0(U_113) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_14,plain,
( sdteqdtlpzmzozddtrp0(sK16(U_113,U_112,U_119),U_113,U_112)
| ~ sdteqdtlpzmzozddtrp0(sK15(U_113,U_112,U_119),U_113,U_112)
| ~ aInteger0(sK15(U_113,U_112,U_119))
| ~ aSet0(U_119)
| U_119 = szAzrzSzezqlpdtcmdtrp0(U_113,U_112)
| U_112 = sz00
| ~ aInteger0(U_112)
| ~ aInteger0(U_113) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_15,plain,
( ~ aElementOf0(sK16(U_113,U_112,U_119),U_119)
| ~ sdteqdtlpzmzozddtrp0(sK15(U_113,U_112,U_119),U_113,U_112)
| ~ aInteger0(sK15(U_113,U_112,U_119))
| ~ aSet0(U_119)
| U_119 = szAzrzSzezqlpdtcmdtrp0(U_113,U_112)
| U_112 = sz00
| ~ aInteger0(U_112)
| ~ aInteger0(U_113) ),
inference(clausify,[status(thm)],[f_34_5]) ).
fof(f_35_1,plain,
! [W0] :
( ( ( isOpen0(W0)
| ? [W1] :
( ! [W2] :
( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1,W2),W0)
| W2 = sz00
| ~ aInteger0(W2) )
& aElementOf0(W1,W0) ) )
& ( ! [W1] :
( ? [W2] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1,W2),W0)
& W2 != sz00
& aInteger0(W2) )
| ~ aElementOf0(W1,W0) )
| ~ isOpen0(W0) ) )
| ~ aSubsetOf0(W0,cS1395) ),
inference(fof_nnf,[status(thm)],[mOpen]) ).
fof(f_35_2,plain,
! [U_124] :
( ( ( isOpen0(U_124)
| ? [U_123] :
( ! [U_122] :
( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(U_123,U_122),U_124)
| U_122 = sz00
| ~ aInteger0(U_122) )
& aElementOf0(U_123,U_124) ) )
& ( ! [U_121] :
( ? [U_120] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(U_121,U_120),U_124)
& U_120 != sz00
& aInteger0(U_120) )
| ~ aElementOf0(U_121,U_124) )
| ~ isOpen0(U_124) ) )
| ~ aSubsetOf0(U_124,cS1395) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_124] :
( ( ( isOpen0(U_124)
| ? [U_123] :
( ! [U_122] :
( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(U_123,U_122),U_124)
| U_122 = sz00
| ~ aInteger0(U_122) )
& aElementOf0(U_123,U_124) ) )
& ( ! [U_121] :
( ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(U_121,sK17(U_124,U_121)),U_124)
& sK17(U_124,U_121) != sz00
& aInteger0(sK17(U_124,U_121)) )
| ~ aElementOf0(U_121,U_124) )
| ~ isOpen0(U_124) ) )
| ~ aSubsetOf0(U_124,cS1395) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_120,sK17(U_124,U_121))],[f_35_2]) ).
fof(f_35_4,plain,
! [U_124] :
( ( ( isOpen0(U_124)
| ( ! [U_122] :
( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sK18(U_124),U_122),U_124)
| U_122 = sz00
| ~ aInteger0(U_122) )
& aElementOf0(sK18(U_124),U_124) ) )
& ( ! [U_121] :
( ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(U_121,sK17(U_124,U_121)),U_124)
& sK17(U_124,U_121) != sz00
& aInteger0(sK17(U_124,U_121)) )
| ~ aElementOf0(U_121,U_124) )
| ~ isOpen0(U_124) ) )
| ~ aSubsetOf0(U_124,cS1395) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_123,sK18(U_124))],[f_35_3]) ).
cnf(f_35_5,plain,
( aInteger0(sK17(U_124,U_121))
| ~ aElementOf0(U_121,U_124)
| ~ isOpen0(U_124)
| ~ aSubsetOf0(U_124,cS1395) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_6,plain,
( sK17(U_124,U_121) != sz00
| ~ aElementOf0(U_121,U_124)
| ~ isOpen0(U_124)
| ~ aSubsetOf0(U_124,cS1395) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_7,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(U_121,sK17(U_124,U_121)),U_124)
| ~ aElementOf0(U_121,U_124)
| ~ isOpen0(U_124)
| ~ aSubsetOf0(U_124,cS1395) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_8,plain,
( aElementOf0(sK18(U_124),U_124)
| isOpen0(U_124)
| ~ aSubsetOf0(U_124,cS1395) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_9,plain,
( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sK18(U_124),U_122),U_124)
| U_122 = sz00
| ~ aInteger0(U_122)
| isOpen0(U_124)
| ~ aSubsetOf0(U_124,cS1395) ),
inference(clausify,[status(thm)],[f_35_4]) ).
fof(f_36_1,plain,
! [W0] :
( ( ( isClosed0(W0)
| ~ isOpen0(stldt0(W0)) )
& ( isOpen0(stldt0(W0))
| ~ isClosed0(W0) ) )
| ~ aSubsetOf0(W0,cS1395) ),
inference(fof_nnf,[status(thm)],[mClosed]) ).
fof(f_36_2,plain,
! [U_125] :
( ( ( isClosed0(U_125)
| ~ isOpen0(stldt0(U_125)) )
& ( isOpen0(stldt0(U_125))
| ~ isClosed0(U_125) ) )
| ~ aSubsetOf0(U_125,cS1395) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
cnf(f_36_3,plain,
( isOpen0(stldt0(U_125))
| ~ isClosed0(U_125)
| ~ aSubsetOf0(U_125,cS1395) ),
inference(clausify,[status(thm)],[f_36_2]) ).
cnf(f_36_4,plain,
( isClosed0(U_125)
| ~ isOpen0(stldt0(U_125))
| ~ aSubsetOf0(U_125,cS1395) ),
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,plain,
! [W0] :
( isOpen0(sbsmnsldt0(W0))
| ? [W1] :
( ( ~ isOpen0(W1)
| ~ aSubsetOf0(W1,cS1395) )
& aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mUnionOpen]) ).
fof(f_37_2,plain,
! [U_127] :
( isOpen0(sbsmnsldt0(U_127))
| ? [U_126] :
( ( ~ isOpen0(U_126)
| ~ aSubsetOf0(U_126,cS1395) )
& aElementOf0(U_126,U_127) )
| ~ aSet0(U_127) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_127] :
( isOpen0(sbsmnsldt0(U_127))
| ( ( ~ isOpen0(sK19(U_127))
| ~ aSubsetOf0(sK19(U_127),cS1395) )
& aElementOf0(sK19(U_127),U_127) )
| ~ aSet0(U_127) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_126,sK19(U_127))],[f_37_2]) ).
cnf(f_37_4,plain,
( aElementOf0(sK19(U_127),U_127)
| ~ aSet0(U_127)
| isOpen0(sbsmnsldt0(U_127)) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_5,plain,
( ~ isOpen0(sK19(U_127))
| ~ aSubsetOf0(sK19(U_127),cS1395)
| ~ aSet0(U_127)
| isOpen0(sbsmnsldt0(U_127)) ),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
! [W0,W1] :
( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ isOpen0(W1)
| ~ isOpen0(W0)
| ~ aSubsetOf0(W1,cS1395)
| ~ aSubsetOf0(W0,cS1395) ),
inference(fof_nnf,[status(thm)],[mInterOpen]) ).
fof(f_38_2,plain,
! [U_129,U_128] :
( isOpen0(sdtslmnbsdt0(U_129,U_128))
| ~ isOpen0(U_128)
| ~ isOpen0(U_129)
| ~ aSubsetOf0(U_128,cS1395)
| ~ aSubsetOf0(U_129,cS1395) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
cnf(f_38_3,plain,
( isOpen0(sdtslmnbsdt0(U_129,U_128))
| ~ isOpen0(U_128)
| ~ isOpen0(U_129)
| ~ aSubsetOf0(U_128,cS1395)
| ~ aSubsetOf0(U_129,cS1395) ),
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_1,plain,
! [W0,W1] :
( isClosed0(sdtbsmnsldt0(W0,W1))
| ~ isClosed0(W1)
| ~ isClosed0(W0)
| ~ aSubsetOf0(W1,cS1395)
| ~ aSubsetOf0(W0,cS1395) ),
inference(fof_nnf,[status(thm)],[mUnionClosed]) ).
fof(f_39_2,plain,
! [U_131,U_130] :
( isClosed0(sdtbsmnsldt0(U_131,U_130))
| ~ isClosed0(U_130)
| ~ isClosed0(U_131)
| ~ aSubsetOf0(U_130,cS1395)
| ~ aSubsetOf0(U_131,cS1395) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
cnf(f_39_3,plain,
( isClosed0(sdtbsmnsldt0(U_131,U_130))
| ~ isClosed0(U_130)
| ~ isClosed0(U_131)
| ~ aSubsetOf0(U_130,cS1395)
| ~ aSubsetOf0(U_131,cS1395) ),
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_1,plain,
! [W0] :
( isClosed0(sbsmnsldt0(W0))
| ? [W1] :
( ( ~ isClosed0(W1)
| ~ aSubsetOf0(W1,cS1395) )
& aElementOf0(W1,W0) )
| ~ isFinite0(W0)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mUnionSClosed]) ).
fof(f_40_2,plain,
! [U_133] :
( isClosed0(sbsmnsldt0(U_133))
| ? [U_132] :
( ( ~ isClosed0(U_132)
| ~ aSubsetOf0(U_132,cS1395) )
& aElementOf0(U_132,U_133) )
| ~ isFinite0(U_133)
| ~ aSet0(U_133) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_133] :
( isClosed0(sbsmnsldt0(U_133))
| ( ( ~ isClosed0(sK20(U_133))
| ~ aSubsetOf0(sK20(U_133),cS1395) )
& aElementOf0(sK20(U_133),U_133) )
| ~ isFinite0(U_133)
| ~ aSet0(U_133) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_132,sK20(U_133))],[f_40_2]) ).
cnf(f_40_4,plain,
( aElementOf0(sK20(U_133),U_133)
| ~ isFinite0(U_133)
| ~ aSet0(U_133)
| isClosed0(sbsmnsldt0(U_133)) ),
inference(clausify,[status(thm)],[f_40_3]) ).
cnf(f_40_5,plain,
( ~ isClosed0(sK20(U_133))
| ~ aSubsetOf0(sK20(U_133),cS1395)
| ~ isFinite0(U_133)
| ~ aSet0(U_133)
| isClosed0(sbsmnsldt0(U_133)) ),
inference(clausify,[status(thm)],[f_40_3]) ).
fof(f_41_1,plain,
! [W0,W1] :
( ( isClosed0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),cS1395) )
| W1 = sz00
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mArSeqClosed]) ).
fof(f_41_2,plain,
! [U_135,U_134] :
( ( isClosed0(szAzrzSzezqlpdtcmdtrp0(U_135,U_134))
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(U_135,U_134),cS1395) )
| U_134 = sz00
| ~ aInteger0(U_134)
| ~ aInteger0(U_135) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
cnf(f_41_3,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(U_135,U_134),cS1395)
| U_134 = sz00
| ~ aInteger0(U_134)
| ~ aInteger0(U_135) ),
inference(clausify,[status(thm)],[f_41_2]) ).
cnf(f_41_4,plain,
( isClosed0(szAzrzSzezqlpdtcmdtrp0(U_135,U_134))
| U_134 = sz00
| ~ aInteger0(U_134)
| ~ aInteger0(U_135) ),
inference(clausify,[status(thm)],[f_41_2]) ).
fof(f_42_1,plain,
( xS = cS2043
& ! [W0] :
( ( aElementOf0(W0,xS)
| ! [W1] :
( ( szAzrzSzezqlpdtcmdtrp0(sz00,W1) != W0
& ! [W2] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,W1))
| ( ~ sdteqdtlpzmzozddtrp0(W2,sz00,W1)
& ~ aDivisorOf0(W1,sdtpldt0(W2,smndt0(sz00)))
& ! [W3] :
( sdtasdt0(W1,W3) != sdtpldt0(W2,smndt0(sz00))
| ~ aInteger0(W3) ) )
| ~ aInteger0(W2) )
& ( ( sdteqdtlpzmzozddtrp0(W2,sz00,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(sz00)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(sz00))
& aInteger0(W3) )
& aInteger0(W2) )
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,W1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,W1)) )
| ~ isPrime0(W1)
| W1 = sz00
| ~ aInteger0(W1) ) )
& ( ? [W1] :
( szAzrzSzezqlpdtcmdtrp0(sz00,W1) = W0
& ! [W2] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,W1))
| ( ~ sdteqdtlpzmzozddtrp0(W2,sz00,W1)
& ~ aDivisorOf0(W1,sdtpldt0(W2,smndt0(sz00)))
& ! [W3] :
( sdtasdt0(W1,W3) != sdtpldt0(W2,smndt0(sz00))
| ~ aInteger0(W3) ) )
| ~ aInteger0(W2) )
& ( ( sdteqdtlpzmzozddtrp0(W2,sz00,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(sz00)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(sz00))
& aInteger0(W3) )
& aInteger0(W2) )
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,W1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,W1))
& isPrime0(W1)
& W1 != sz00
& aInteger0(W1) )
| ~ aElementOf0(W0,xS) ) )
& aSet0(xS) ),
inference(fof_nnf,[status(thm)],[m__2046]) ).
fof(f_42_2,plain,
( xS = cS2043
& ! [U_144] :
( ( aElementOf0(U_144,xS)
| ! [U_143] :
( ( szAzrzSzezqlpdtcmdtrp0(sz00,U_143) != U_144
& ! [U_142] :
( ( aElementOf0(U_142,szAzrzSzezqlpdtcmdtrp0(sz00,U_143))
| ( ~ sdteqdtlpzmzozddtrp0(U_142,sz00,U_143)
& ~ aDivisorOf0(U_143,sdtpldt0(U_142,smndt0(sz00)))
& ! [U_141] :
( sdtasdt0(U_143,U_141) != sdtpldt0(U_142,smndt0(sz00))
| ~ aInteger0(U_141) ) )
| ~ aInteger0(U_142) )
& ( ( sdteqdtlpzmzozddtrp0(U_142,sz00,U_143)
& aDivisorOf0(U_143,sdtpldt0(U_142,smndt0(sz00)))
& ? [U_140] :
( sdtasdt0(U_143,U_140) = sdtpldt0(U_142,smndt0(sz00))
& aInteger0(U_140) )
& aInteger0(U_142) )
| ~ aElementOf0(U_142,szAzrzSzezqlpdtcmdtrp0(sz00,U_143)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,U_143)) )
| ~ isPrime0(U_143)
| U_143 = sz00
| ~ aInteger0(U_143) ) )
& ( ? [U_139] :
( szAzrzSzezqlpdtcmdtrp0(sz00,U_139) = U_144
& ! [U_138] :
( ( aElementOf0(U_138,szAzrzSzezqlpdtcmdtrp0(sz00,U_139))
| ( ~ sdteqdtlpzmzozddtrp0(U_138,sz00,U_139)
& ~ aDivisorOf0(U_139,sdtpldt0(U_138,smndt0(sz00)))
& ! [U_137] :
( sdtasdt0(U_139,U_137) != sdtpldt0(U_138,smndt0(sz00))
| ~ aInteger0(U_137) ) )
| ~ aInteger0(U_138) )
& ( ( sdteqdtlpzmzozddtrp0(U_138,sz00,U_139)
& aDivisorOf0(U_139,sdtpldt0(U_138,smndt0(sz00)))
& ? [U_136] :
( sdtasdt0(U_139,U_136) = sdtpldt0(U_138,smndt0(sz00))
& aInteger0(U_136) )
& aInteger0(U_138) )
| ~ aElementOf0(U_138,szAzrzSzezqlpdtcmdtrp0(sz00,U_139)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,U_139))
& isPrime0(U_139)
& U_139 != sz00
& aInteger0(U_139) )
| ~ aElementOf0(U_144,xS) ) )
& aSet0(xS) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
( xS = cS2043
& ! [U_150] :
( aElementOf0(U_150,xS)
| ! [U_143] :
( ( szAzrzSzezqlpdtcmdtrp0(sz00,U_143) != U_150
& ! [U_148] :
( aElementOf0(U_148,szAzrzSzezqlpdtcmdtrp0(sz00,U_143))
| ( ~ sdteqdtlpzmzozddtrp0(U_148,sz00,U_143)
& ~ aDivisorOf0(U_143,sdtpldt0(U_148,smndt0(sz00)))
& ! [U_141] :
( sdtasdt0(U_143,U_141) != sdtpldt0(U_148,smndt0(sz00))
| ~ aInteger0(U_141) ) )
| ~ aInteger0(U_148) )
& ! [U_147] :
( ( sdteqdtlpzmzozddtrp0(U_147,sz00,U_143)
& aDivisorOf0(U_143,sdtpldt0(U_147,smndt0(sz00)))
& ? [U_140] :
( sdtasdt0(U_143,U_140) = sdtpldt0(U_147,smndt0(sz00))
& aInteger0(U_140) )
& aInteger0(U_147) )
| ~ aElementOf0(U_147,szAzrzSzezqlpdtcmdtrp0(sz00,U_143)) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,U_143)) )
| ~ isPrime0(U_143)
| U_143 = sz00
| ~ aInteger0(U_143) ) )
& ! [U_149] :
( ? [U_139] :
( szAzrzSzezqlpdtcmdtrp0(sz00,U_139) = U_149
& ! [U_146] :
( aElementOf0(U_146,szAzrzSzezqlpdtcmdtrp0(sz00,U_139))
| ( ~ sdteqdtlpzmzozddtrp0(U_146,sz00,U_139)
& ~ aDivisorOf0(U_139,sdtpldt0(U_146,smndt0(sz00)))
& ! [U_137] :
( sdtasdt0(U_139,U_137) != sdtpldt0(U_146,smndt0(sz00))
| ~ aInteger0(U_137) ) )
| ~ aInteger0(U_146) )
& ! [U_145] :
( ( sdteqdtlpzmzozddtrp0(U_145,sz00,U_139)
& aDivisorOf0(U_139,sdtpldt0(U_145,smndt0(sz00)))
& ? [U_136] :
( sdtasdt0(U_139,U_136) = sdtpldt0(U_145,smndt0(sz00))
& aInteger0(U_136) )
& aInteger0(U_145) )
| ~ aElementOf0(U_145,szAzrzSzezqlpdtcmdtrp0(sz00,U_139)) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,U_139))
& isPrime0(U_139)
& U_139 != sz00
& aInteger0(U_139) )
| ~ aElementOf0(U_149,xS) )
& aSet0(xS) ),
inference(miniscope,[status(thm)],[f_42_2]) ).
fof(f_42_4,plain,
( xS = cS2043
& ! [U_150] :
( aElementOf0(U_150,xS)
| ! [U_143] :
( ( szAzrzSzezqlpdtcmdtrp0(sz00,U_143) != U_150
& ! [U_148] :
( aElementOf0(U_148,szAzrzSzezqlpdtcmdtrp0(sz00,U_143))
| ( ~ sdteqdtlpzmzozddtrp0(U_148,sz00,U_143)
& ~ aDivisorOf0(U_143,sdtpldt0(U_148,smndt0(sz00)))
& ! [U_141] :
( sdtasdt0(U_143,U_141) != sdtpldt0(U_148,smndt0(sz00))
| ~ aInteger0(U_141) ) )
| ~ aInteger0(U_148) )
& ! [U_147] :
( ( sdteqdtlpzmzozddtrp0(U_147,sz00,U_143)
& aDivisorOf0(U_143,sdtpldt0(U_147,smndt0(sz00)))
& ? [U_140] :
( sdtasdt0(U_143,U_140) = sdtpldt0(U_147,smndt0(sz00))
& aInteger0(U_140) )
& aInteger0(U_147) )
| ~ aElementOf0(U_147,szAzrzSzezqlpdtcmdtrp0(sz00,U_143)) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,U_143)) )
| ~ isPrime0(U_143)
| U_143 = sz00
| ~ aInteger0(U_143) ) )
& ! [U_149] :
( ( szAzrzSzezqlpdtcmdtrp0(sz00,sK21(U_149)) = U_149
& ! [U_146] :
( aElementOf0(U_146,szAzrzSzezqlpdtcmdtrp0(sz00,sK21(U_149)))
| ( ~ sdteqdtlpzmzozddtrp0(U_146,sz00,sK21(U_149))
& ~ aDivisorOf0(sK21(U_149),sdtpldt0(U_146,smndt0(sz00)))
& ! [U_137] :
( sdtasdt0(sK21(U_149),U_137) != sdtpldt0(U_146,smndt0(sz00))
| ~ aInteger0(U_137) ) )
| ~ aInteger0(U_146) )
& ! [U_145] :
( ( sdteqdtlpzmzozddtrp0(U_145,sz00,sK21(U_149))
& aDivisorOf0(sK21(U_149),sdtpldt0(U_145,smndt0(sz00)))
& ? [U_136] :
( sdtasdt0(sK21(U_149),U_136) = sdtpldt0(U_145,smndt0(sz00))
& aInteger0(U_136) )
& aInteger0(U_145) )
| ~ aElementOf0(U_145,szAzrzSzezqlpdtcmdtrp0(sz00,sK21(U_149))) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,sK21(U_149)))
& isPrime0(sK21(U_149))
& sK21(U_149) != sz00
& aInteger0(sK21(U_149)) )
| ~ aElementOf0(U_149,xS) )
& aSet0(xS) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_139,sK21(U_149))],[f_42_3]) ).
fof(f_42_5,plain,
( xS = cS2043
& ! [U_150] :
( aElementOf0(U_150,xS)
| ! [U_143] :
( ( szAzrzSzezqlpdtcmdtrp0(sz00,U_143) != U_150
& ! [U_148] :
( aElementOf0(U_148,szAzrzSzezqlpdtcmdtrp0(sz00,U_143))
| ( ~ sdteqdtlpzmzozddtrp0(U_148,sz00,U_143)
& ~ aDivisorOf0(U_143,sdtpldt0(U_148,smndt0(sz00)))
& ! [U_141] :
( sdtasdt0(U_143,U_141) != sdtpldt0(U_148,smndt0(sz00))
| ~ aInteger0(U_141) ) )
| ~ aInteger0(U_148) )
& ! [U_147] :
( ( sdteqdtlpzmzozddtrp0(U_147,sz00,U_143)
& aDivisorOf0(U_143,sdtpldt0(U_147,smndt0(sz00)))
& ? [U_140] :
( sdtasdt0(U_143,U_140) = sdtpldt0(U_147,smndt0(sz00))
& aInteger0(U_140) )
& aInteger0(U_147) )
| ~ aElementOf0(U_147,szAzrzSzezqlpdtcmdtrp0(sz00,U_143)) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,U_143)) )
| ~ isPrime0(U_143)
| U_143 = sz00
| ~ aInteger0(U_143) ) )
& ! [U_149] :
( ( szAzrzSzezqlpdtcmdtrp0(sz00,sK21(U_149)) = U_149
& ! [U_146] :
( aElementOf0(U_146,szAzrzSzezqlpdtcmdtrp0(sz00,sK21(U_149)))
| ( ~ sdteqdtlpzmzozddtrp0(U_146,sz00,sK21(U_149))
& ~ aDivisorOf0(sK21(U_149),sdtpldt0(U_146,smndt0(sz00)))
& ! [U_137] :
( sdtasdt0(sK21(U_149),U_137) != sdtpldt0(U_146,smndt0(sz00))
| ~ aInteger0(U_137) ) )
| ~ aInteger0(U_146) )
& ! [U_145] :
( ( sdteqdtlpzmzozddtrp0(U_145,sz00,sK21(U_149))
& aDivisorOf0(sK21(U_149),sdtpldt0(U_145,smndt0(sz00)))
& sdtasdt0(sK21(U_149),sK22(U_149,U_145)) = sdtpldt0(U_145,smndt0(sz00))
& aInteger0(sK22(U_149,U_145))
& aInteger0(U_145) )
| ~ aElementOf0(U_145,szAzrzSzezqlpdtcmdtrp0(sz00,sK21(U_149))) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,sK21(U_149)))
& isPrime0(sK21(U_149))
& sK21(U_149) != sz00
& aInteger0(sK21(U_149)) )
| ~ aElementOf0(U_149,xS) )
& aSet0(xS) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_136,sK22(U_149,U_145))],[f_42_4]) ).
fof(f_42_6,plain,
( xS = cS2043
& ! [U_150] :
( aElementOf0(U_150,xS)
| ! [U_143] :
( ( szAzrzSzezqlpdtcmdtrp0(sz00,U_143) != U_150
& ! [U_148] :
( aElementOf0(U_148,szAzrzSzezqlpdtcmdtrp0(sz00,U_143))
| ( ~ sdteqdtlpzmzozddtrp0(U_148,sz00,U_143)
& ~ aDivisorOf0(U_143,sdtpldt0(U_148,smndt0(sz00)))
& ! [U_141] :
( sdtasdt0(U_143,U_141) != sdtpldt0(U_148,smndt0(sz00))
| ~ aInteger0(U_141) ) )
| ~ aInteger0(U_148) )
& ! [U_147] :
( ( sdteqdtlpzmzozddtrp0(U_147,sz00,U_143)
& aDivisorOf0(U_143,sdtpldt0(U_147,smndt0(sz00)))
& sdtasdt0(U_143,sK23(U_150,U_143,U_147)) = sdtpldt0(U_147,smndt0(sz00))
& aInteger0(sK23(U_150,U_143,U_147))
& aInteger0(U_147) )
| ~ aElementOf0(U_147,szAzrzSzezqlpdtcmdtrp0(sz00,U_143)) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,U_143)) )
| ~ isPrime0(U_143)
| U_143 = sz00
| ~ aInteger0(U_143) ) )
& ! [U_149] :
( ( szAzrzSzezqlpdtcmdtrp0(sz00,sK21(U_149)) = U_149
& ! [U_146] :
( aElementOf0(U_146,szAzrzSzezqlpdtcmdtrp0(sz00,sK21(U_149)))
| ( ~ sdteqdtlpzmzozddtrp0(U_146,sz00,sK21(U_149))
& ~ aDivisorOf0(sK21(U_149),sdtpldt0(U_146,smndt0(sz00)))
& ! [U_137] :
( sdtasdt0(sK21(U_149),U_137) != sdtpldt0(U_146,smndt0(sz00))
| ~ aInteger0(U_137) ) )
| ~ aInteger0(U_146) )
& ! [U_145] :
( ( sdteqdtlpzmzozddtrp0(U_145,sz00,sK21(U_149))
& aDivisorOf0(sK21(U_149),sdtpldt0(U_145,smndt0(sz00)))
& sdtasdt0(sK21(U_149),sK22(U_149,U_145)) = sdtpldt0(U_145,smndt0(sz00))
& aInteger0(sK22(U_149,U_145))
& aInteger0(U_145) )
| ~ aElementOf0(U_145,szAzrzSzezqlpdtcmdtrp0(sz00,sK21(U_149))) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,sK21(U_149)))
& isPrime0(sK21(U_149))
& sK21(U_149) != sz00
& aInteger0(sK21(U_149)) )
| ~ aElementOf0(U_149,xS) )
& aSet0(xS) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_140,sK23(U_150,U_143,U_147))],[f_42_5]) ).
cnf(f_42_7,plain,
aSet0(xS),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_8,plain,
( aInteger0(sK21(U_149))
| ~ aElementOf0(U_149,xS) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_9,plain,
( sK21(U_149) != sz00
| ~ aElementOf0(U_149,xS) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_10,plain,
( isPrime0(sK21(U_149))
| ~ aElementOf0(U_149,xS) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_11,plain,
( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,sK21(U_149)))
| ~ aElementOf0(U_149,xS) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_12,plain,
( aInteger0(U_145)
| ~ aElementOf0(U_145,szAzrzSzezqlpdtcmdtrp0(sz00,sK21(U_149)))
| ~ aElementOf0(U_149,xS) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_13,plain,
( aInteger0(sK22(U_149,U_145))
| ~ aElementOf0(U_145,szAzrzSzezqlpdtcmdtrp0(sz00,sK21(U_149)))
| ~ aElementOf0(U_149,xS) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_14,plain,
( sdtasdt0(sK21(U_149),sK22(U_149,U_145)) = sdtpldt0(U_145,smndt0(sz00))
| ~ aElementOf0(U_145,szAzrzSzezqlpdtcmdtrp0(sz00,sK21(U_149)))
| ~ aElementOf0(U_149,xS) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_15,plain,
( aDivisorOf0(sK21(U_149),sdtpldt0(U_145,smndt0(sz00)))
| ~ aElementOf0(U_145,szAzrzSzezqlpdtcmdtrp0(sz00,sK21(U_149)))
| ~ aElementOf0(U_149,xS) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_16,plain,
( sdteqdtlpzmzozddtrp0(U_145,sz00,sK21(U_149))
| ~ aElementOf0(U_145,szAzrzSzezqlpdtcmdtrp0(sz00,sK21(U_149)))
| ~ aElementOf0(U_149,xS) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_17,plain,
( sdtasdt0(sK21(U_149),U_137) != sdtpldt0(U_146,smndt0(sz00))
| ~ aInteger0(U_137)
| ~ aInteger0(U_146)
| aElementOf0(U_146,szAzrzSzezqlpdtcmdtrp0(sz00,sK21(U_149)))
| ~ aElementOf0(U_149,xS) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_18,plain,
( ~ aDivisorOf0(sK21(U_149),sdtpldt0(U_146,smndt0(sz00)))
| ~ aInteger0(U_146)
| aElementOf0(U_146,szAzrzSzezqlpdtcmdtrp0(sz00,sK21(U_149)))
| ~ aElementOf0(U_149,xS) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_19,plain,
( ~ sdteqdtlpzmzozddtrp0(U_146,sz00,sK21(U_149))
| ~ aInteger0(U_146)
| aElementOf0(U_146,szAzrzSzezqlpdtcmdtrp0(sz00,sK21(U_149)))
| ~ aElementOf0(U_149,xS) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_20,plain,
( szAzrzSzezqlpdtcmdtrp0(sz00,sK21(U_149)) = U_149
| ~ aElementOf0(U_149,xS) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_21,plain,
( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,U_143))
| ~ isPrime0(U_143)
| U_143 = sz00
| ~ aInteger0(U_143)
| aElementOf0(U_150,xS) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_22,plain,
( aInteger0(U_147)
| ~ aElementOf0(U_147,szAzrzSzezqlpdtcmdtrp0(sz00,U_143))
| ~ isPrime0(U_143)
| U_143 = sz00
| ~ aInteger0(U_143)
| aElementOf0(U_150,xS) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_23,plain,
( aInteger0(sK23(U_150,U_143,U_147))
| ~ aElementOf0(U_147,szAzrzSzezqlpdtcmdtrp0(sz00,U_143))
| ~ isPrime0(U_143)
| U_143 = sz00
| ~ aInteger0(U_143)
| aElementOf0(U_150,xS) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_24,plain,
( sdtasdt0(U_143,sK23(U_150,U_143,U_147)) = sdtpldt0(U_147,smndt0(sz00))
| ~ aElementOf0(U_147,szAzrzSzezqlpdtcmdtrp0(sz00,U_143))
| ~ isPrime0(U_143)
| U_143 = sz00
| ~ aInteger0(U_143)
| aElementOf0(U_150,xS) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_25,plain,
( aDivisorOf0(U_143,sdtpldt0(U_147,smndt0(sz00)))
| ~ aElementOf0(U_147,szAzrzSzezqlpdtcmdtrp0(sz00,U_143))
| ~ isPrime0(U_143)
| U_143 = sz00
| ~ aInteger0(U_143)
| aElementOf0(U_150,xS) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_26,plain,
( sdteqdtlpzmzozddtrp0(U_147,sz00,U_143)
| ~ aElementOf0(U_147,szAzrzSzezqlpdtcmdtrp0(sz00,U_143))
| ~ isPrime0(U_143)
| U_143 = sz00
| ~ aInteger0(U_143)
| aElementOf0(U_150,xS) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_27,plain,
( sdtasdt0(U_143,U_141) != sdtpldt0(U_148,smndt0(sz00))
| ~ aInteger0(U_141)
| ~ aInteger0(U_148)
| aElementOf0(U_148,szAzrzSzezqlpdtcmdtrp0(sz00,U_143))
| ~ isPrime0(U_143)
| U_143 = sz00
| ~ aInteger0(U_143)
| aElementOf0(U_150,xS) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_28,plain,
( ~ aDivisorOf0(U_143,sdtpldt0(U_148,smndt0(sz00)))
| ~ aInteger0(U_148)
| aElementOf0(U_148,szAzrzSzezqlpdtcmdtrp0(sz00,U_143))
| ~ isPrime0(U_143)
| U_143 = sz00
| ~ aInteger0(U_143)
| aElementOf0(U_150,xS) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_29,plain,
( ~ sdteqdtlpzmzozddtrp0(U_148,sz00,U_143)
| ~ aInteger0(U_148)
| aElementOf0(U_148,szAzrzSzezqlpdtcmdtrp0(sz00,U_143))
| ~ isPrime0(U_143)
| U_143 = sz00
| ~ aInteger0(U_143)
| aElementOf0(U_150,xS) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_30,plain,
( szAzrzSzezqlpdtcmdtrp0(sz00,U_143) != U_150
| ~ isPrime0(U_143)
| U_143 = sz00
| ~ aInteger0(U_143)
| aElementOf0(U_150,xS) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_31,plain,
xS = cS2043,
inference(clausify,[status(thm)],[f_42_6]) ).
fof(f_43_1,plain,
( stldt0(sbsmnsldt0(xS)) = cS2076
& ! [W0] :
( ( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
| ( W0 != smndt0(sz10)
& W0 != sz10 ) )
& ( W0 = smndt0(sz10)
| W0 = sz10
| ~ aElementOf0(W0,stldt0(sbsmnsldt0(xS))) ) )
& ! [W0] :
( ( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
| aElementOf0(W0,sbsmnsldt0(xS))
| ~ aInteger0(W0) )
& ( ( ~ aElementOf0(W0,sbsmnsldt0(xS))
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(sbsmnsldt0(xS))) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [W0] :
( ( aElementOf0(W0,sbsmnsldt0(xS))
| ! [W1] :
( ~ aElementOf0(W0,W1)
| ~ aElementOf0(W1,xS) )
| ~ aInteger0(W0) )
& ( ( ? [W1] :
( aElementOf0(W0,W1)
& aElementOf0(W1,xS) )
& aInteger0(W0) )
| ~ aElementOf0(W0,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(fof_nnf,[status(thm)],[m__2079]) ).
fof(f_43_2,plain,
( stldt0(sbsmnsldt0(xS)) = cS2076
& ! [U_155] :
( ( aElementOf0(U_155,stldt0(sbsmnsldt0(xS)))
| ( U_155 != smndt0(sz10)
& U_155 != sz10 ) )
& ( U_155 = smndt0(sz10)
| U_155 = sz10
| ~ aElementOf0(U_155,stldt0(sbsmnsldt0(xS))) ) )
& ! [U_154] :
( ( aElementOf0(U_154,stldt0(sbsmnsldt0(xS)))
| aElementOf0(U_154,sbsmnsldt0(xS))
| ~ aInteger0(U_154) )
& ( ( ~ aElementOf0(U_154,sbsmnsldt0(xS))
& aInteger0(U_154) )
| ~ aElementOf0(U_154,stldt0(sbsmnsldt0(xS))) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [U_153] :
( ( aElementOf0(U_153,sbsmnsldt0(xS))
| ! [U_152] :
( ~ aElementOf0(U_153,U_152)
| ~ aElementOf0(U_152,xS) )
| ~ aInteger0(U_153) )
& ( ( ? [U_151] :
( aElementOf0(U_153,U_151)
& aElementOf0(U_151,xS) )
& aInteger0(U_153) )
| ~ aElementOf0(U_153,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
( stldt0(sbsmnsldt0(xS)) = cS2076
& ! [U_161] :
( aElementOf0(U_161,stldt0(sbsmnsldt0(xS)))
| ( U_161 != smndt0(sz10)
& U_161 != sz10 ) )
& ! [U_160] :
( U_160 = smndt0(sz10)
| U_160 = sz10
| ~ aElementOf0(U_160,stldt0(sbsmnsldt0(xS))) )
& ! [U_159] :
( aElementOf0(U_159,stldt0(sbsmnsldt0(xS)))
| aElementOf0(U_159,sbsmnsldt0(xS))
| ~ aInteger0(U_159) )
& ! [U_158] :
( ( ~ aElementOf0(U_158,sbsmnsldt0(xS))
& aInteger0(U_158) )
| ~ aElementOf0(U_158,stldt0(sbsmnsldt0(xS))) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [U_157] :
( aElementOf0(U_157,sbsmnsldt0(xS))
| ! [U_152] :
( ~ aElementOf0(U_157,U_152)
| ~ aElementOf0(U_152,xS) )
| ~ aInteger0(U_157) )
& ! [U_156] :
( ( ? [U_151] :
( aElementOf0(U_156,U_151)
& aElementOf0(U_151,xS) )
& aInteger0(U_156) )
| ~ aElementOf0(U_156,sbsmnsldt0(xS)) )
& aSet0(sbsmnsldt0(xS)) ),
inference(miniscope,[status(thm)],[f_43_2]) ).
fof(f_43_4,plain,
( stldt0(sbsmnsldt0(xS)) = cS2076
& ! [U_161] :
( aElementOf0(U_161,stldt0(sbsmnsldt0(xS)))
| ( U_161 != smndt0(sz10)
& U_161 != sz10 ) )
& ! [U_160] :
( U_160 = smndt0(sz10)
| U_160 = sz10
| ~ aElementOf0(U_160,stldt0(sbsmnsldt0(xS))) )
& ! [U_159] :
( aElementOf0(U_159,stldt0(sbsmnsldt0(xS)))
| aElementOf0(U_159,sbsmnsldt0(xS))
| ~ aInteger0(U_159) )
& ! [U_158] :
( ( ~ aElementOf0(U_158,sbsmnsldt0(xS))
& aInteger0(U_158) )
| ~ aElementOf0(U_158,stldt0(sbsmnsldt0(xS))) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [U_157] :
( aElementOf0(U_157,sbsmnsldt0(xS))
| ! [U_152] :
( ~ aElementOf0(U_157,U_152)
| ~ aElementOf0(U_152,xS) )
| ~ aInteger0(U_157) )
& ! [U_156] :
( ( aElementOf0(U_156,sK24(U_156))
& aElementOf0(sK24(U_156),xS)
& aInteger0(U_156) )
| ~ aElementOf0(U_156,sbsmnsldt0(xS)) )
& aSet0(sbsmnsldt0(xS)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_151,sK24(U_156))],[f_43_3]) ).
cnf(f_43_5,plain,
aSet0(sbsmnsldt0(xS)),
inference(clausify,[status(thm)],[f_43_4]) ).
cnf(f_43_6,plain,
( aInteger0(U_156)
| ~ aElementOf0(U_156,sbsmnsldt0(xS)) ),
inference(clausify,[status(thm)],[f_43_4]) ).
cnf(f_43_7,plain,
( aElementOf0(sK24(U_156),xS)
| ~ aElementOf0(U_156,sbsmnsldt0(xS)) ),
inference(clausify,[status(thm)],[f_43_4]) ).
cnf(f_43_8,plain,
( aElementOf0(U_156,sK24(U_156))
| ~ aElementOf0(U_156,sbsmnsldt0(xS)) ),
inference(clausify,[status(thm)],[f_43_4]) ).
cnf(f_43_9,plain,
( aElementOf0(U_157,sbsmnsldt0(xS))
| ~ aElementOf0(U_157,U_152)
| ~ aElementOf0(U_152,xS)
| ~ aInteger0(U_157) ),
inference(clausify,[status(thm)],[f_43_4]) ).
cnf(f_43_10,plain,
aSet0(stldt0(sbsmnsldt0(xS))),
inference(clausify,[status(thm)],[f_43_4]) ).
cnf(f_43_11,plain,
( aInteger0(U_158)
| ~ aElementOf0(U_158,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_43_4]) ).
cnf(f_43_12,plain,
( ~ aElementOf0(U_158,sbsmnsldt0(xS))
| ~ aElementOf0(U_158,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_43_4]) ).
cnf(f_43_13,plain,
( aElementOf0(U_159,stldt0(sbsmnsldt0(xS)))
| aElementOf0(U_159,sbsmnsldt0(xS))
| ~ aInteger0(U_159) ),
inference(clausify,[status(thm)],[f_43_4]) ).
cnf(f_43_14,plain,
( U_160 = smndt0(sz10)
| U_160 = sz10
| ~ aElementOf0(U_160,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_43_4]) ).
cnf(f_43_15,plain,
( U_161 != sz10
| aElementOf0(U_161,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_43_4]) ).
cnf(f_43_16,plain,
( U_161 != smndt0(sz10)
| aElementOf0(U_161,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_43_4]) ).
cnf(f_43_17,plain,
stldt0(sbsmnsldt0(xS)) = cS2076,
inference(clausify,[status(thm)],[f_43_4]) ).
fof(f_44_1,plain,
isFinite0(xS),
inference(fof_nnf,[status(thm)],[m__2117]) ).
cnf(f_44_2,plain,
isFinite0(xS),
inference(clausify,[status(thm)],[f_44_1]) ).
fof(f_45_1,plain,
( ! [W0] :
( ? [W1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(sbsmnsldt0(xS)))
& ! [W2] :
( aElementOf0(W2,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& ! [W2] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
| ( ~ sdteqdtlpzmzozddtrp0(W2,W0,W1)
& ~ aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ! [W3] :
( sdtasdt0(W1,W3) != sdtpldt0(W2,smndt0(W0))
| ~ aInteger0(W3) ) )
| ~ aInteger0(W2) )
& ( ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) )
& aInteger0(W2) )
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& W1 != sz00
& aInteger0(W1) )
| ~ aElementOf0(W0,stldt0(sbsmnsldt0(xS))) )
& ! [W0] :
( ( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
| aElementOf0(W0,sbsmnsldt0(xS))
| ~ aInteger0(W0) )
& ( ( ~ aElementOf0(W0,sbsmnsldt0(xS))
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(sbsmnsldt0(xS))) ) )
& ! [W0] :
( ( aElementOf0(W0,sbsmnsldt0(xS))
| ! [W1] :
( ~ aElementOf0(W0,W1)
| ~ aElementOf0(W1,xS) )
| ~ aInteger0(W0) )
& ( ( ? [W1] :
( aElementOf0(W0,W1)
& aElementOf0(W1,xS) )
& aInteger0(W0) )
| ~ aElementOf0(W0,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS))
& isClosed0(sbsmnsldt0(xS))
& isOpen0(stldt0(sbsmnsldt0(xS)))
& ! [W0] :
( ? [W1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(sbsmnsldt0(xS)))
& ! [W2] :
( aElementOf0(W2,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& ! [W2] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
| ( ~ sdteqdtlpzmzozddtrp0(W2,W0,W1)
& ~ aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ! [W3] :
( sdtasdt0(W1,W3) != sdtpldt0(W2,smndt0(W0))
| ~ aInteger0(W3) ) )
| ~ aInteger0(W2) )
& ( ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) )
& aInteger0(W2) )
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& W1 != sz00
& aInteger0(W1) )
| ~ aElementOf0(W0,stldt0(sbsmnsldt0(xS))) )
& ! [W0] :
( ( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
| aElementOf0(W0,sbsmnsldt0(xS))
| ~ aInteger0(W0) )
& ( ( ~ aElementOf0(W0,sbsmnsldt0(xS))
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(sbsmnsldt0(xS))) ) )
& ! [W0] :
( ( aElementOf0(W0,sbsmnsldt0(xS))
| ! [W1] :
( ~ aElementOf0(W0,W1)
| ~ aElementOf0(W1,xS) )
| ~ aInteger0(W0) )
& ( ( ? [W1] :
( aElementOf0(W0,W1)
& aElementOf0(W1,xS) )
& aInteger0(W0) )
| ~ aElementOf0(W0,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(fof_nnf,[status(thm)],[m__2144]) ).
fof(f_45_2,plain,
( ! [U_181] :
( ? [U_180] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(U_181,U_180),stldt0(sbsmnsldt0(xS)))
& ! [U_179] :
( aElementOf0(U_179,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(U_179,szAzrzSzezqlpdtcmdtrp0(U_181,U_180)) )
& ! [U_178] :
( ( aElementOf0(U_178,szAzrzSzezqlpdtcmdtrp0(U_181,U_180))
| ( ~ sdteqdtlpzmzozddtrp0(U_178,U_181,U_180)
& ~ aDivisorOf0(U_180,sdtpldt0(U_178,smndt0(U_181)))
& ! [U_177] :
( sdtasdt0(U_180,U_177) != sdtpldt0(U_178,smndt0(U_181))
| ~ aInteger0(U_177) ) )
| ~ aInteger0(U_178) )
& ( ( sdteqdtlpzmzozddtrp0(U_178,U_181,U_180)
& aDivisorOf0(U_180,sdtpldt0(U_178,smndt0(U_181)))
& ? [U_176] :
( sdtasdt0(U_180,U_176) = sdtpldt0(U_178,smndt0(U_181))
& aInteger0(U_176) )
& aInteger0(U_178) )
| ~ aElementOf0(U_178,szAzrzSzezqlpdtcmdtrp0(U_181,U_180)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(U_181,U_180))
& U_180 != sz00
& aInteger0(U_180) )
| ~ aElementOf0(U_181,stldt0(sbsmnsldt0(xS))) )
& ! [U_175] :
( ( aElementOf0(U_175,stldt0(sbsmnsldt0(xS)))
| aElementOf0(U_175,sbsmnsldt0(xS))
| ~ aInteger0(U_175) )
& ( ( ~ aElementOf0(U_175,sbsmnsldt0(xS))
& aInteger0(U_175) )
| ~ aElementOf0(U_175,stldt0(sbsmnsldt0(xS))) ) )
& ! [U_174] :
( ( aElementOf0(U_174,sbsmnsldt0(xS))
| ! [U_173] :
( ~ aElementOf0(U_174,U_173)
| ~ aElementOf0(U_173,xS) )
| ~ aInteger0(U_174) )
& ( ( ? [U_172] :
( aElementOf0(U_174,U_172)
& aElementOf0(U_172,xS) )
& aInteger0(U_174) )
| ~ aElementOf0(U_174,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS))
& isClosed0(sbsmnsldt0(xS))
& isOpen0(stldt0(sbsmnsldt0(xS)))
& ! [U_171] :
( ? [U_170] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(U_171,U_170),stldt0(sbsmnsldt0(xS)))
& ! [U_169] :
( aElementOf0(U_169,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(U_169,szAzrzSzezqlpdtcmdtrp0(U_171,U_170)) )
& ! [U_168] :
( ( aElementOf0(U_168,szAzrzSzezqlpdtcmdtrp0(U_171,U_170))
| ( ~ sdteqdtlpzmzozddtrp0(U_168,U_171,U_170)
& ~ aDivisorOf0(U_170,sdtpldt0(U_168,smndt0(U_171)))
& ! [U_167] :
( sdtasdt0(U_170,U_167) != sdtpldt0(U_168,smndt0(U_171))
| ~ aInteger0(U_167) ) )
| ~ aInteger0(U_168) )
& ( ( sdteqdtlpzmzozddtrp0(U_168,U_171,U_170)
& aDivisorOf0(U_170,sdtpldt0(U_168,smndt0(U_171)))
& ? [U_166] :
( sdtasdt0(U_170,U_166) = sdtpldt0(U_168,smndt0(U_171))
& aInteger0(U_166) )
& aInteger0(U_168) )
| ~ aElementOf0(U_168,szAzrzSzezqlpdtcmdtrp0(U_171,U_170)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(U_171,U_170))
& U_170 != sz00
& aInteger0(U_170) )
| ~ aElementOf0(U_171,stldt0(sbsmnsldt0(xS))) )
& ! [U_165] :
( ( aElementOf0(U_165,stldt0(sbsmnsldt0(xS)))
| aElementOf0(U_165,sbsmnsldt0(xS))
| ~ aInteger0(U_165) )
& ( ( ~ aElementOf0(U_165,sbsmnsldt0(xS))
& aInteger0(U_165) )
| ~ aElementOf0(U_165,stldt0(sbsmnsldt0(xS))) ) )
& ! [U_164] :
( ( aElementOf0(U_164,sbsmnsldt0(xS))
| ! [U_163] :
( ~ aElementOf0(U_164,U_163)
| ~ aElementOf0(U_163,xS) )
| ~ aInteger0(U_164) )
& ( ( ? [U_162] :
( aElementOf0(U_164,U_162)
& aElementOf0(U_162,xS) )
& aInteger0(U_164) )
| ~ aElementOf0(U_164,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
( ! [U_181] :
( ? [U_180] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(U_181,U_180),stldt0(sbsmnsldt0(xS)))
& ! [U_179] :
( aElementOf0(U_179,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(U_179,szAzrzSzezqlpdtcmdtrp0(U_181,U_180)) )
& ! [U_193] :
( aElementOf0(U_193,szAzrzSzezqlpdtcmdtrp0(U_181,U_180))
| ( ~ sdteqdtlpzmzozddtrp0(U_193,U_181,U_180)
& ~ aDivisorOf0(U_180,sdtpldt0(U_193,smndt0(U_181)))
& ! [U_177] :
( sdtasdt0(U_180,U_177) != sdtpldt0(U_193,smndt0(U_181))
| ~ aInteger0(U_177) ) )
| ~ aInteger0(U_193) )
& ! [U_192] :
( ( sdteqdtlpzmzozddtrp0(U_192,U_181,U_180)
& aDivisorOf0(U_180,sdtpldt0(U_192,smndt0(U_181)))
& ? [U_176] :
( sdtasdt0(U_180,U_176) = sdtpldt0(U_192,smndt0(U_181))
& aInteger0(U_176) )
& aInteger0(U_192) )
| ~ aElementOf0(U_192,szAzrzSzezqlpdtcmdtrp0(U_181,U_180)) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(U_181,U_180))
& U_180 != sz00
& aInteger0(U_180) )
| ~ aElementOf0(U_181,stldt0(sbsmnsldt0(xS))) )
& ! [U_191] :
( aElementOf0(U_191,stldt0(sbsmnsldt0(xS)))
| aElementOf0(U_191,sbsmnsldt0(xS))
| ~ aInteger0(U_191) )
& ! [U_190] :
( ( ~ aElementOf0(U_190,sbsmnsldt0(xS))
& aInteger0(U_190) )
| ~ aElementOf0(U_190,stldt0(sbsmnsldt0(xS))) )
& ! [U_189] :
( aElementOf0(U_189,sbsmnsldt0(xS))
| ! [U_173] :
( ~ aElementOf0(U_189,U_173)
| ~ aElementOf0(U_173,xS) )
| ~ aInteger0(U_189) )
& ! [U_188] :
( ( ? [U_172] :
( aElementOf0(U_188,U_172)
& aElementOf0(U_172,xS) )
& aInteger0(U_188) )
| ~ aElementOf0(U_188,sbsmnsldt0(xS)) )
& aSet0(sbsmnsldt0(xS))
& isClosed0(sbsmnsldt0(xS))
& isOpen0(stldt0(sbsmnsldt0(xS)))
& ! [U_171] :
( ? [U_170] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(U_171,U_170),stldt0(sbsmnsldt0(xS)))
& ! [U_169] :
( aElementOf0(U_169,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(U_169,szAzrzSzezqlpdtcmdtrp0(U_171,U_170)) )
& ! [U_187] :
( aElementOf0(U_187,szAzrzSzezqlpdtcmdtrp0(U_171,U_170))
| ( ~ sdteqdtlpzmzozddtrp0(U_187,U_171,U_170)
& ~ aDivisorOf0(U_170,sdtpldt0(U_187,smndt0(U_171)))
& ! [U_167] :
( sdtasdt0(U_170,U_167) != sdtpldt0(U_187,smndt0(U_171))
| ~ aInteger0(U_167) ) )
| ~ aInteger0(U_187) )
& ! [U_186] :
( ( sdteqdtlpzmzozddtrp0(U_186,U_171,U_170)
& aDivisorOf0(U_170,sdtpldt0(U_186,smndt0(U_171)))
& ? [U_166] :
( sdtasdt0(U_170,U_166) = sdtpldt0(U_186,smndt0(U_171))
& aInteger0(U_166) )
& aInteger0(U_186) )
| ~ aElementOf0(U_186,szAzrzSzezqlpdtcmdtrp0(U_171,U_170)) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(U_171,U_170))
& U_170 != sz00
& aInteger0(U_170) )
| ~ aElementOf0(U_171,stldt0(sbsmnsldt0(xS))) )
& ! [U_185] :
( aElementOf0(U_185,stldt0(sbsmnsldt0(xS)))
| aElementOf0(U_185,sbsmnsldt0(xS))
| ~ aInteger0(U_185) )
& ! [U_184] :
( ( ~ aElementOf0(U_184,sbsmnsldt0(xS))
& aInteger0(U_184) )
| ~ aElementOf0(U_184,stldt0(sbsmnsldt0(xS))) )
& ! [U_183] :
( aElementOf0(U_183,sbsmnsldt0(xS))
| ! [U_163] :
( ~ aElementOf0(U_183,U_163)
| ~ aElementOf0(U_163,xS) )
| ~ aInteger0(U_183) )
& ! [U_182] :
( ( ? [U_162] :
( aElementOf0(U_182,U_162)
& aElementOf0(U_162,xS) )
& aInteger0(U_182) )
| ~ aElementOf0(U_182,sbsmnsldt0(xS)) )
& aSet0(sbsmnsldt0(xS)) ),
inference(miniscope,[status(thm)],[f_45_2]) ).
fof(f_45_4,plain,
( ! [U_181] :
( ? [U_180] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(U_181,U_180),stldt0(sbsmnsldt0(xS)))
& ! [U_179] :
( aElementOf0(U_179,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(U_179,szAzrzSzezqlpdtcmdtrp0(U_181,U_180)) )
& ! [U_193] :
( aElementOf0(U_193,szAzrzSzezqlpdtcmdtrp0(U_181,U_180))
| ( ~ sdteqdtlpzmzozddtrp0(U_193,U_181,U_180)
& ~ aDivisorOf0(U_180,sdtpldt0(U_193,smndt0(U_181)))
& ! [U_177] :
( sdtasdt0(U_180,U_177) != sdtpldt0(U_193,smndt0(U_181))
| ~ aInteger0(U_177) ) )
| ~ aInteger0(U_193) )
& ! [U_192] :
( ( sdteqdtlpzmzozddtrp0(U_192,U_181,U_180)
& aDivisorOf0(U_180,sdtpldt0(U_192,smndt0(U_181)))
& ? [U_176] :
( sdtasdt0(U_180,U_176) = sdtpldt0(U_192,smndt0(U_181))
& aInteger0(U_176) )
& aInteger0(U_192) )
| ~ aElementOf0(U_192,szAzrzSzezqlpdtcmdtrp0(U_181,U_180)) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(U_181,U_180))
& U_180 != sz00
& aInteger0(U_180) )
| ~ aElementOf0(U_181,stldt0(sbsmnsldt0(xS))) )
& ! [U_191] :
( aElementOf0(U_191,stldt0(sbsmnsldt0(xS)))
| aElementOf0(U_191,sbsmnsldt0(xS))
| ~ aInteger0(U_191) )
& ! [U_190] :
( ( ~ aElementOf0(U_190,sbsmnsldt0(xS))
& aInteger0(U_190) )
| ~ aElementOf0(U_190,stldt0(sbsmnsldt0(xS))) )
& ! [U_189] :
( aElementOf0(U_189,sbsmnsldt0(xS))
| ! [U_173] :
( ~ aElementOf0(U_189,U_173)
| ~ aElementOf0(U_173,xS) )
| ~ aInteger0(U_189) )
& ! [U_188] :
( ( ? [U_172] :
( aElementOf0(U_188,U_172)
& aElementOf0(U_172,xS) )
& aInteger0(U_188) )
| ~ aElementOf0(U_188,sbsmnsldt0(xS)) )
& aSet0(sbsmnsldt0(xS))
& isClosed0(sbsmnsldt0(xS))
& isOpen0(stldt0(sbsmnsldt0(xS)))
& ! [U_171] :
( ? [U_170] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(U_171,U_170),stldt0(sbsmnsldt0(xS)))
& ! [U_169] :
( aElementOf0(U_169,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(U_169,szAzrzSzezqlpdtcmdtrp0(U_171,U_170)) )
& ! [U_187] :
( aElementOf0(U_187,szAzrzSzezqlpdtcmdtrp0(U_171,U_170))
| ( ~ sdteqdtlpzmzozddtrp0(U_187,U_171,U_170)
& ~ aDivisorOf0(U_170,sdtpldt0(U_187,smndt0(U_171)))
& ! [U_167] :
( sdtasdt0(U_170,U_167) != sdtpldt0(U_187,smndt0(U_171))
| ~ aInteger0(U_167) ) )
| ~ aInteger0(U_187) )
& ! [U_186] :
( ( sdteqdtlpzmzozddtrp0(U_186,U_171,U_170)
& aDivisorOf0(U_170,sdtpldt0(U_186,smndt0(U_171)))
& ? [U_166] :
( sdtasdt0(U_170,U_166) = sdtpldt0(U_186,smndt0(U_171))
& aInteger0(U_166) )
& aInteger0(U_186) )
| ~ aElementOf0(U_186,szAzrzSzezqlpdtcmdtrp0(U_171,U_170)) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(U_171,U_170))
& U_170 != sz00
& aInteger0(U_170) )
| ~ aElementOf0(U_171,stldt0(sbsmnsldt0(xS))) )
& ! [U_185] :
( aElementOf0(U_185,stldt0(sbsmnsldt0(xS)))
| aElementOf0(U_185,sbsmnsldt0(xS))
| ~ aInteger0(U_185) )
& ! [U_184] :
( ( ~ aElementOf0(U_184,sbsmnsldt0(xS))
& aInteger0(U_184) )
| ~ aElementOf0(U_184,stldt0(sbsmnsldt0(xS))) )
& ! [U_183] :
( aElementOf0(U_183,sbsmnsldt0(xS))
| ! [U_163] :
( ~ aElementOf0(U_183,U_163)
| ~ aElementOf0(U_163,xS) )
| ~ aInteger0(U_183) )
& ! [U_182] :
( ( aElementOf0(U_182,sK25(U_182))
& aElementOf0(sK25(U_182),xS)
& aInteger0(U_182) )
| ~ aElementOf0(U_182,sbsmnsldt0(xS)) )
& aSet0(sbsmnsldt0(xS)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_162,sK25(U_182))],[f_45_3]) ).
fof(f_45_5,plain,
( ! [U_181] :
( ? [U_180] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(U_181,U_180),stldt0(sbsmnsldt0(xS)))
& ! [U_179] :
( aElementOf0(U_179,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(U_179,szAzrzSzezqlpdtcmdtrp0(U_181,U_180)) )
& ! [U_193] :
( aElementOf0(U_193,szAzrzSzezqlpdtcmdtrp0(U_181,U_180))
| ( ~ sdteqdtlpzmzozddtrp0(U_193,U_181,U_180)
& ~ aDivisorOf0(U_180,sdtpldt0(U_193,smndt0(U_181)))
& ! [U_177] :
( sdtasdt0(U_180,U_177) != sdtpldt0(U_193,smndt0(U_181))
| ~ aInteger0(U_177) ) )
| ~ aInteger0(U_193) )
& ! [U_192] :
( ( sdteqdtlpzmzozddtrp0(U_192,U_181,U_180)
& aDivisorOf0(U_180,sdtpldt0(U_192,smndt0(U_181)))
& ? [U_176] :
( sdtasdt0(U_180,U_176) = sdtpldt0(U_192,smndt0(U_181))
& aInteger0(U_176) )
& aInteger0(U_192) )
| ~ aElementOf0(U_192,szAzrzSzezqlpdtcmdtrp0(U_181,U_180)) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(U_181,U_180))
& U_180 != sz00
& aInteger0(U_180) )
| ~ aElementOf0(U_181,stldt0(sbsmnsldt0(xS))) )
& ! [U_191] :
( aElementOf0(U_191,stldt0(sbsmnsldt0(xS)))
| aElementOf0(U_191,sbsmnsldt0(xS))
| ~ aInteger0(U_191) )
& ! [U_190] :
( ( ~ aElementOf0(U_190,sbsmnsldt0(xS))
& aInteger0(U_190) )
| ~ aElementOf0(U_190,stldt0(sbsmnsldt0(xS))) )
& ! [U_189] :
( aElementOf0(U_189,sbsmnsldt0(xS))
| ! [U_173] :
( ~ aElementOf0(U_189,U_173)
| ~ aElementOf0(U_173,xS) )
| ~ aInteger0(U_189) )
& ! [U_188] :
( ( ? [U_172] :
( aElementOf0(U_188,U_172)
& aElementOf0(U_172,xS) )
& aInteger0(U_188) )
| ~ aElementOf0(U_188,sbsmnsldt0(xS)) )
& aSet0(sbsmnsldt0(xS))
& isClosed0(sbsmnsldt0(xS))
& isOpen0(stldt0(sbsmnsldt0(xS)))
& ! [U_171] :
( ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171)),stldt0(sbsmnsldt0(xS)))
& ! [U_169] :
( aElementOf0(U_169,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(U_169,szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171))) )
& ! [U_187] :
( aElementOf0(U_187,szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171)))
| ( ~ sdteqdtlpzmzozddtrp0(U_187,U_171,sK26(U_171))
& ~ aDivisorOf0(sK26(U_171),sdtpldt0(U_187,smndt0(U_171)))
& ! [U_167] :
( sdtasdt0(sK26(U_171),U_167) != sdtpldt0(U_187,smndt0(U_171))
| ~ aInteger0(U_167) ) )
| ~ aInteger0(U_187) )
& ! [U_186] :
( ( sdteqdtlpzmzozddtrp0(U_186,U_171,sK26(U_171))
& aDivisorOf0(sK26(U_171),sdtpldt0(U_186,smndt0(U_171)))
& ? [U_166] :
( sdtasdt0(sK26(U_171),U_166) = sdtpldt0(U_186,smndt0(U_171))
& aInteger0(U_166) )
& aInteger0(U_186) )
| ~ aElementOf0(U_186,szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171))) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171)))
& sK26(U_171) != sz00
& aInteger0(sK26(U_171)) )
| ~ aElementOf0(U_171,stldt0(sbsmnsldt0(xS))) )
& ! [U_185] :
( aElementOf0(U_185,stldt0(sbsmnsldt0(xS)))
| aElementOf0(U_185,sbsmnsldt0(xS))
| ~ aInteger0(U_185) )
& ! [U_184] :
( ( ~ aElementOf0(U_184,sbsmnsldt0(xS))
& aInteger0(U_184) )
| ~ aElementOf0(U_184,stldt0(sbsmnsldt0(xS))) )
& ! [U_183] :
( aElementOf0(U_183,sbsmnsldt0(xS))
| ! [U_163] :
( ~ aElementOf0(U_183,U_163)
| ~ aElementOf0(U_163,xS) )
| ~ aInteger0(U_183) )
& ! [U_182] :
( ( aElementOf0(U_182,sK25(U_182))
& aElementOf0(sK25(U_182),xS)
& aInteger0(U_182) )
| ~ aElementOf0(U_182,sbsmnsldt0(xS)) )
& aSet0(sbsmnsldt0(xS)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_170,sK26(U_171))],[f_45_4]) ).
fof(f_45_6,plain,
( ! [U_181] :
( ? [U_180] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(U_181,U_180),stldt0(sbsmnsldt0(xS)))
& ! [U_179] :
( aElementOf0(U_179,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(U_179,szAzrzSzezqlpdtcmdtrp0(U_181,U_180)) )
& ! [U_193] :
( aElementOf0(U_193,szAzrzSzezqlpdtcmdtrp0(U_181,U_180))
| ( ~ sdteqdtlpzmzozddtrp0(U_193,U_181,U_180)
& ~ aDivisorOf0(U_180,sdtpldt0(U_193,smndt0(U_181)))
& ! [U_177] :
( sdtasdt0(U_180,U_177) != sdtpldt0(U_193,smndt0(U_181))
| ~ aInteger0(U_177) ) )
| ~ aInteger0(U_193) )
& ! [U_192] :
( ( sdteqdtlpzmzozddtrp0(U_192,U_181,U_180)
& aDivisorOf0(U_180,sdtpldt0(U_192,smndt0(U_181)))
& ? [U_176] :
( sdtasdt0(U_180,U_176) = sdtpldt0(U_192,smndt0(U_181))
& aInteger0(U_176) )
& aInteger0(U_192) )
| ~ aElementOf0(U_192,szAzrzSzezqlpdtcmdtrp0(U_181,U_180)) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(U_181,U_180))
& U_180 != sz00
& aInteger0(U_180) )
| ~ aElementOf0(U_181,stldt0(sbsmnsldt0(xS))) )
& ! [U_191] :
( aElementOf0(U_191,stldt0(sbsmnsldt0(xS)))
| aElementOf0(U_191,sbsmnsldt0(xS))
| ~ aInteger0(U_191) )
& ! [U_190] :
( ( ~ aElementOf0(U_190,sbsmnsldt0(xS))
& aInteger0(U_190) )
| ~ aElementOf0(U_190,stldt0(sbsmnsldt0(xS))) )
& ! [U_189] :
( aElementOf0(U_189,sbsmnsldt0(xS))
| ! [U_173] :
( ~ aElementOf0(U_189,U_173)
| ~ aElementOf0(U_173,xS) )
| ~ aInteger0(U_189) )
& ! [U_188] :
( ( ? [U_172] :
( aElementOf0(U_188,U_172)
& aElementOf0(U_172,xS) )
& aInteger0(U_188) )
| ~ aElementOf0(U_188,sbsmnsldt0(xS)) )
& aSet0(sbsmnsldt0(xS))
& isClosed0(sbsmnsldt0(xS))
& isOpen0(stldt0(sbsmnsldt0(xS)))
& ! [U_171] :
( ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171)),stldt0(sbsmnsldt0(xS)))
& ! [U_169] :
( aElementOf0(U_169,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(U_169,szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171))) )
& ! [U_187] :
( aElementOf0(U_187,szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171)))
| ( ~ sdteqdtlpzmzozddtrp0(U_187,U_171,sK26(U_171))
& ~ aDivisorOf0(sK26(U_171),sdtpldt0(U_187,smndt0(U_171)))
& ! [U_167] :
( sdtasdt0(sK26(U_171),U_167) != sdtpldt0(U_187,smndt0(U_171))
| ~ aInteger0(U_167) ) )
| ~ aInteger0(U_187) )
& ! [U_186] :
( ( sdteqdtlpzmzozddtrp0(U_186,U_171,sK26(U_171))
& aDivisorOf0(sK26(U_171),sdtpldt0(U_186,smndt0(U_171)))
& sdtasdt0(sK26(U_171),sK27(U_171,U_186)) = sdtpldt0(U_186,smndt0(U_171))
& aInteger0(sK27(U_171,U_186))
& aInteger0(U_186) )
| ~ aElementOf0(U_186,szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171))) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171)))
& sK26(U_171) != sz00
& aInteger0(sK26(U_171)) )
| ~ aElementOf0(U_171,stldt0(sbsmnsldt0(xS))) )
& ! [U_185] :
( aElementOf0(U_185,stldt0(sbsmnsldt0(xS)))
| aElementOf0(U_185,sbsmnsldt0(xS))
| ~ aInteger0(U_185) )
& ! [U_184] :
( ( ~ aElementOf0(U_184,sbsmnsldt0(xS))
& aInteger0(U_184) )
| ~ aElementOf0(U_184,stldt0(sbsmnsldt0(xS))) )
& ! [U_183] :
( aElementOf0(U_183,sbsmnsldt0(xS))
| ! [U_163] :
( ~ aElementOf0(U_183,U_163)
| ~ aElementOf0(U_163,xS) )
| ~ aInteger0(U_183) )
& ! [U_182] :
( ( aElementOf0(U_182,sK25(U_182))
& aElementOf0(sK25(U_182),xS)
& aInteger0(U_182) )
| ~ aElementOf0(U_182,sbsmnsldt0(xS)) )
& aSet0(sbsmnsldt0(xS)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_166,sK27(U_171,U_186))],[f_45_5]) ).
fof(f_45_7,plain,
( ! [U_181] :
( ? [U_180] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(U_181,U_180),stldt0(sbsmnsldt0(xS)))
& ! [U_179] :
( aElementOf0(U_179,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(U_179,szAzrzSzezqlpdtcmdtrp0(U_181,U_180)) )
& ! [U_193] :
( aElementOf0(U_193,szAzrzSzezqlpdtcmdtrp0(U_181,U_180))
| ( ~ sdteqdtlpzmzozddtrp0(U_193,U_181,U_180)
& ~ aDivisorOf0(U_180,sdtpldt0(U_193,smndt0(U_181)))
& ! [U_177] :
( sdtasdt0(U_180,U_177) != sdtpldt0(U_193,smndt0(U_181))
| ~ aInteger0(U_177) ) )
| ~ aInteger0(U_193) )
& ! [U_192] :
( ( sdteqdtlpzmzozddtrp0(U_192,U_181,U_180)
& aDivisorOf0(U_180,sdtpldt0(U_192,smndt0(U_181)))
& ? [U_176] :
( sdtasdt0(U_180,U_176) = sdtpldt0(U_192,smndt0(U_181))
& aInteger0(U_176) )
& aInteger0(U_192) )
| ~ aElementOf0(U_192,szAzrzSzezqlpdtcmdtrp0(U_181,U_180)) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(U_181,U_180))
& U_180 != sz00
& aInteger0(U_180) )
| ~ aElementOf0(U_181,stldt0(sbsmnsldt0(xS))) )
& ! [U_191] :
( aElementOf0(U_191,stldt0(sbsmnsldt0(xS)))
| aElementOf0(U_191,sbsmnsldt0(xS))
| ~ aInteger0(U_191) )
& ! [U_190] :
( ( ~ aElementOf0(U_190,sbsmnsldt0(xS))
& aInteger0(U_190) )
| ~ aElementOf0(U_190,stldt0(sbsmnsldt0(xS))) )
& ! [U_189] :
( aElementOf0(U_189,sbsmnsldt0(xS))
| ! [U_173] :
( ~ aElementOf0(U_189,U_173)
| ~ aElementOf0(U_173,xS) )
| ~ aInteger0(U_189) )
& ! [U_188] :
( ( aElementOf0(U_188,sK28(U_188))
& aElementOf0(sK28(U_188),xS)
& aInteger0(U_188) )
| ~ aElementOf0(U_188,sbsmnsldt0(xS)) )
& aSet0(sbsmnsldt0(xS))
& isClosed0(sbsmnsldt0(xS))
& isOpen0(stldt0(sbsmnsldt0(xS)))
& ! [U_171] :
( ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171)),stldt0(sbsmnsldt0(xS)))
& ! [U_169] :
( aElementOf0(U_169,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(U_169,szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171))) )
& ! [U_187] :
( aElementOf0(U_187,szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171)))
| ( ~ sdteqdtlpzmzozddtrp0(U_187,U_171,sK26(U_171))
& ~ aDivisorOf0(sK26(U_171),sdtpldt0(U_187,smndt0(U_171)))
& ! [U_167] :
( sdtasdt0(sK26(U_171),U_167) != sdtpldt0(U_187,smndt0(U_171))
| ~ aInteger0(U_167) ) )
| ~ aInteger0(U_187) )
& ! [U_186] :
( ( sdteqdtlpzmzozddtrp0(U_186,U_171,sK26(U_171))
& aDivisorOf0(sK26(U_171),sdtpldt0(U_186,smndt0(U_171)))
& sdtasdt0(sK26(U_171),sK27(U_171,U_186)) = sdtpldt0(U_186,smndt0(U_171))
& aInteger0(sK27(U_171,U_186))
& aInteger0(U_186) )
| ~ aElementOf0(U_186,szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171))) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171)))
& sK26(U_171) != sz00
& aInteger0(sK26(U_171)) )
| ~ aElementOf0(U_171,stldt0(sbsmnsldt0(xS))) )
& ! [U_185] :
( aElementOf0(U_185,stldt0(sbsmnsldt0(xS)))
| aElementOf0(U_185,sbsmnsldt0(xS))
| ~ aInteger0(U_185) )
& ! [U_184] :
( ( ~ aElementOf0(U_184,sbsmnsldt0(xS))
& aInteger0(U_184) )
| ~ aElementOf0(U_184,stldt0(sbsmnsldt0(xS))) )
& ! [U_183] :
( aElementOf0(U_183,sbsmnsldt0(xS))
| ! [U_163] :
( ~ aElementOf0(U_183,U_163)
| ~ aElementOf0(U_163,xS) )
| ~ aInteger0(U_183) )
& ! [U_182] :
( ( aElementOf0(U_182,sK25(U_182))
& aElementOf0(sK25(U_182),xS)
& aInteger0(U_182) )
| ~ aElementOf0(U_182,sbsmnsldt0(xS)) )
& aSet0(sbsmnsldt0(xS)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_172,sK28(U_188))],[f_45_6]) ).
fof(f_45_8,plain,
( ! [U_181] :
( ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(U_181,sK29(U_181)),stldt0(sbsmnsldt0(xS)))
& ! [U_179] :
( aElementOf0(U_179,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(U_179,szAzrzSzezqlpdtcmdtrp0(U_181,sK29(U_181))) )
& ! [U_193] :
( aElementOf0(U_193,szAzrzSzezqlpdtcmdtrp0(U_181,sK29(U_181)))
| ( ~ sdteqdtlpzmzozddtrp0(U_193,U_181,sK29(U_181))
& ~ aDivisorOf0(sK29(U_181),sdtpldt0(U_193,smndt0(U_181)))
& ! [U_177] :
( sdtasdt0(sK29(U_181),U_177) != sdtpldt0(U_193,smndt0(U_181))
| ~ aInteger0(U_177) ) )
| ~ aInteger0(U_193) )
& ! [U_192] :
( ( sdteqdtlpzmzozddtrp0(U_192,U_181,sK29(U_181))
& aDivisorOf0(sK29(U_181),sdtpldt0(U_192,smndt0(U_181)))
& ? [U_176] :
( sdtasdt0(sK29(U_181),U_176) = sdtpldt0(U_192,smndt0(U_181))
& aInteger0(U_176) )
& aInteger0(U_192) )
| ~ aElementOf0(U_192,szAzrzSzezqlpdtcmdtrp0(U_181,sK29(U_181))) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(U_181,sK29(U_181)))
& sK29(U_181) != sz00
& aInteger0(sK29(U_181)) )
| ~ aElementOf0(U_181,stldt0(sbsmnsldt0(xS))) )
& ! [U_191] :
( aElementOf0(U_191,stldt0(sbsmnsldt0(xS)))
| aElementOf0(U_191,sbsmnsldt0(xS))
| ~ aInteger0(U_191) )
& ! [U_190] :
( ( ~ aElementOf0(U_190,sbsmnsldt0(xS))
& aInteger0(U_190) )
| ~ aElementOf0(U_190,stldt0(sbsmnsldt0(xS))) )
& ! [U_189] :
( aElementOf0(U_189,sbsmnsldt0(xS))
| ! [U_173] :
( ~ aElementOf0(U_189,U_173)
| ~ aElementOf0(U_173,xS) )
| ~ aInteger0(U_189) )
& ! [U_188] :
( ( aElementOf0(U_188,sK28(U_188))
& aElementOf0(sK28(U_188),xS)
& aInteger0(U_188) )
| ~ aElementOf0(U_188,sbsmnsldt0(xS)) )
& aSet0(sbsmnsldt0(xS))
& isClosed0(sbsmnsldt0(xS))
& isOpen0(stldt0(sbsmnsldt0(xS)))
& ! [U_171] :
( ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171)),stldt0(sbsmnsldt0(xS)))
& ! [U_169] :
( aElementOf0(U_169,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(U_169,szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171))) )
& ! [U_187] :
( aElementOf0(U_187,szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171)))
| ( ~ sdteqdtlpzmzozddtrp0(U_187,U_171,sK26(U_171))
& ~ aDivisorOf0(sK26(U_171),sdtpldt0(U_187,smndt0(U_171)))
& ! [U_167] :
( sdtasdt0(sK26(U_171),U_167) != sdtpldt0(U_187,smndt0(U_171))
| ~ aInteger0(U_167) ) )
| ~ aInteger0(U_187) )
& ! [U_186] :
( ( sdteqdtlpzmzozddtrp0(U_186,U_171,sK26(U_171))
& aDivisorOf0(sK26(U_171),sdtpldt0(U_186,smndt0(U_171)))
& sdtasdt0(sK26(U_171),sK27(U_171,U_186)) = sdtpldt0(U_186,smndt0(U_171))
& aInteger0(sK27(U_171,U_186))
& aInteger0(U_186) )
| ~ aElementOf0(U_186,szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171))) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171)))
& sK26(U_171) != sz00
& aInteger0(sK26(U_171)) )
| ~ aElementOf0(U_171,stldt0(sbsmnsldt0(xS))) )
& ! [U_185] :
( aElementOf0(U_185,stldt0(sbsmnsldt0(xS)))
| aElementOf0(U_185,sbsmnsldt0(xS))
| ~ aInteger0(U_185) )
& ! [U_184] :
( ( ~ aElementOf0(U_184,sbsmnsldt0(xS))
& aInteger0(U_184) )
| ~ aElementOf0(U_184,stldt0(sbsmnsldt0(xS))) )
& ! [U_183] :
( aElementOf0(U_183,sbsmnsldt0(xS))
| ! [U_163] :
( ~ aElementOf0(U_183,U_163)
| ~ aElementOf0(U_163,xS) )
| ~ aInteger0(U_183) )
& ! [U_182] :
( ( aElementOf0(U_182,sK25(U_182))
& aElementOf0(sK25(U_182),xS)
& aInteger0(U_182) )
| ~ aElementOf0(U_182,sbsmnsldt0(xS)) )
& aSet0(sbsmnsldt0(xS)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_180,sK29(U_181))],[f_45_7]) ).
fof(f_45_9,plain,
( ! [U_181] :
( ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(U_181,sK29(U_181)),stldt0(sbsmnsldt0(xS)))
& ! [U_179] :
( aElementOf0(U_179,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(U_179,szAzrzSzezqlpdtcmdtrp0(U_181,sK29(U_181))) )
& ! [U_193] :
( aElementOf0(U_193,szAzrzSzezqlpdtcmdtrp0(U_181,sK29(U_181)))
| ( ~ sdteqdtlpzmzozddtrp0(U_193,U_181,sK29(U_181))
& ~ aDivisorOf0(sK29(U_181),sdtpldt0(U_193,smndt0(U_181)))
& ! [U_177] :
( sdtasdt0(sK29(U_181),U_177) != sdtpldt0(U_193,smndt0(U_181))
| ~ aInteger0(U_177) ) )
| ~ aInteger0(U_193) )
& ! [U_192] :
( ( sdteqdtlpzmzozddtrp0(U_192,U_181,sK29(U_181))
& aDivisorOf0(sK29(U_181),sdtpldt0(U_192,smndt0(U_181)))
& sdtasdt0(sK29(U_181),sK30(U_181,U_192)) = sdtpldt0(U_192,smndt0(U_181))
& aInteger0(sK30(U_181,U_192))
& aInteger0(U_192) )
| ~ aElementOf0(U_192,szAzrzSzezqlpdtcmdtrp0(U_181,sK29(U_181))) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(U_181,sK29(U_181)))
& sK29(U_181) != sz00
& aInteger0(sK29(U_181)) )
| ~ aElementOf0(U_181,stldt0(sbsmnsldt0(xS))) )
& ! [U_191] :
( aElementOf0(U_191,stldt0(sbsmnsldt0(xS)))
| aElementOf0(U_191,sbsmnsldt0(xS))
| ~ aInteger0(U_191) )
& ! [U_190] :
( ( ~ aElementOf0(U_190,sbsmnsldt0(xS))
& aInteger0(U_190) )
| ~ aElementOf0(U_190,stldt0(sbsmnsldt0(xS))) )
& ! [U_189] :
( aElementOf0(U_189,sbsmnsldt0(xS))
| ! [U_173] :
( ~ aElementOf0(U_189,U_173)
| ~ aElementOf0(U_173,xS) )
| ~ aInteger0(U_189) )
& ! [U_188] :
( ( aElementOf0(U_188,sK28(U_188))
& aElementOf0(sK28(U_188),xS)
& aInteger0(U_188) )
| ~ aElementOf0(U_188,sbsmnsldt0(xS)) )
& aSet0(sbsmnsldt0(xS))
& isClosed0(sbsmnsldt0(xS))
& isOpen0(stldt0(sbsmnsldt0(xS)))
& ! [U_171] :
( ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171)),stldt0(sbsmnsldt0(xS)))
& ! [U_169] :
( aElementOf0(U_169,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(U_169,szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171))) )
& ! [U_187] :
( aElementOf0(U_187,szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171)))
| ( ~ sdteqdtlpzmzozddtrp0(U_187,U_171,sK26(U_171))
& ~ aDivisorOf0(sK26(U_171),sdtpldt0(U_187,smndt0(U_171)))
& ! [U_167] :
( sdtasdt0(sK26(U_171),U_167) != sdtpldt0(U_187,smndt0(U_171))
| ~ aInteger0(U_167) ) )
| ~ aInteger0(U_187) )
& ! [U_186] :
( ( sdteqdtlpzmzozddtrp0(U_186,U_171,sK26(U_171))
& aDivisorOf0(sK26(U_171),sdtpldt0(U_186,smndt0(U_171)))
& sdtasdt0(sK26(U_171),sK27(U_171,U_186)) = sdtpldt0(U_186,smndt0(U_171))
& aInteger0(sK27(U_171,U_186))
& aInteger0(U_186) )
| ~ aElementOf0(U_186,szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171))) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171)))
& sK26(U_171) != sz00
& aInteger0(sK26(U_171)) )
| ~ aElementOf0(U_171,stldt0(sbsmnsldt0(xS))) )
& ! [U_185] :
( aElementOf0(U_185,stldt0(sbsmnsldt0(xS)))
| aElementOf0(U_185,sbsmnsldt0(xS))
| ~ aInteger0(U_185) )
& ! [U_184] :
( ( ~ aElementOf0(U_184,sbsmnsldt0(xS))
& aInteger0(U_184) )
| ~ aElementOf0(U_184,stldt0(sbsmnsldt0(xS))) )
& ! [U_183] :
( aElementOf0(U_183,sbsmnsldt0(xS))
| ! [U_163] :
( ~ aElementOf0(U_183,U_163)
| ~ aElementOf0(U_163,xS) )
| ~ aInteger0(U_183) )
& ! [U_182] :
( ( aElementOf0(U_182,sK25(U_182))
& aElementOf0(sK25(U_182),xS)
& aInteger0(U_182) )
| ~ aElementOf0(U_182,sbsmnsldt0(xS)) )
& aSet0(sbsmnsldt0(xS)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_176,sK30(U_181,U_192))],[f_45_8]) ).
cnf(f_45_10,plain,
aSet0(sbsmnsldt0(xS)),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_11,plain,
( aInteger0(U_182)
| ~ aElementOf0(U_182,sbsmnsldt0(xS)) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_12,plain,
( aElementOf0(sK25(U_182),xS)
| ~ aElementOf0(U_182,sbsmnsldt0(xS)) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_13,plain,
( aElementOf0(U_182,sK25(U_182))
| ~ aElementOf0(U_182,sbsmnsldt0(xS)) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_14,plain,
( aElementOf0(U_183,sbsmnsldt0(xS))
| ~ aElementOf0(U_183,U_163)
| ~ aElementOf0(U_163,xS)
| ~ aInteger0(U_183) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_15,plain,
( aInteger0(U_184)
| ~ aElementOf0(U_184,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_16,plain,
( ~ aElementOf0(U_184,sbsmnsldt0(xS))
| ~ aElementOf0(U_184,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_17,plain,
( aElementOf0(U_185,stldt0(sbsmnsldt0(xS)))
| aElementOf0(U_185,sbsmnsldt0(xS))
| ~ aInteger0(U_185) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_18,plain,
( aInteger0(sK26(U_171))
| ~ aElementOf0(U_171,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_19,plain,
( sK26(U_171) != sz00
| ~ aElementOf0(U_171,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_20,plain,
( aSet0(szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171)))
| ~ aElementOf0(U_171,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_21,plain,
( aInteger0(U_186)
| ~ aElementOf0(U_186,szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171)))
| ~ aElementOf0(U_171,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_22,plain,
( aInteger0(sK27(U_171,U_186))
| ~ aElementOf0(U_186,szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171)))
| ~ aElementOf0(U_171,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_23,plain,
( sdtasdt0(sK26(U_171),sK27(U_171,U_186)) = sdtpldt0(U_186,smndt0(U_171))
| ~ aElementOf0(U_186,szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171)))
| ~ aElementOf0(U_171,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_24,plain,
( aDivisorOf0(sK26(U_171),sdtpldt0(U_186,smndt0(U_171)))
| ~ aElementOf0(U_186,szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171)))
| ~ aElementOf0(U_171,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_25,plain,
( sdteqdtlpzmzozddtrp0(U_186,U_171,sK26(U_171))
| ~ aElementOf0(U_186,szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171)))
| ~ aElementOf0(U_171,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_26,plain,
( sdtasdt0(sK26(U_171),U_167) != sdtpldt0(U_187,smndt0(U_171))
| ~ aInteger0(U_167)
| ~ aInteger0(U_187)
| aElementOf0(U_187,szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171)))
| ~ aElementOf0(U_171,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_27,plain,
( ~ aDivisorOf0(sK26(U_171),sdtpldt0(U_187,smndt0(U_171)))
| ~ aInteger0(U_187)
| aElementOf0(U_187,szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171)))
| ~ aElementOf0(U_171,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_28,plain,
( ~ sdteqdtlpzmzozddtrp0(U_187,U_171,sK26(U_171))
| ~ aInteger0(U_187)
| aElementOf0(U_187,szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171)))
| ~ aElementOf0(U_171,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_29,plain,
( aElementOf0(U_169,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(U_169,szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171)))
| ~ aElementOf0(U_171,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_30,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(U_171,sK26(U_171)),stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(U_171,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_31,plain,
isOpen0(stldt0(sbsmnsldt0(xS))),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_32,plain,
isClosed0(sbsmnsldt0(xS)),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_33,plain,
aSet0(sbsmnsldt0(xS)),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_34,plain,
( aInteger0(U_188)
| ~ aElementOf0(U_188,sbsmnsldt0(xS)) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_35,plain,
( aElementOf0(sK28(U_188),xS)
| ~ aElementOf0(U_188,sbsmnsldt0(xS)) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_36,plain,
( aElementOf0(U_188,sK28(U_188))
| ~ aElementOf0(U_188,sbsmnsldt0(xS)) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_37,plain,
( aElementOf0(U_189,sbsmnsldt0(xS))
| ~ aElementOf0(U_189,U_173)
| ~ aElementOf0(U_173,xS)
| ~ aInteger0(U_189) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_38,plain,
( aInteger0(U_190)
| ~ aElementOf0(U_190,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_39,plain,
( ~ aElementOf0(U_190,sbsmnsldt0(xS))
| ~ aElementOf0(U_190,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_40,plain,
( aElementOf0(U_191,stldt0(sbsmnsldt0(xS)))
| aElementOf0(U_191,sbsmnsldt0(xS))
| ~ aInteger0(U_191) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_41,plain,
( aInteger0(sK29(U_181))
| ~ aElementOf0(U_181,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_42,plain,
( sK29(U_181) != sz00
| ~ aElementOf0(U_181,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_43,plain,
( aSet0(szAzrzSzezqlpdtcmdtrp0(U_181,sK29(U_181)))
| ~ aElementOf0(U_181,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_44,plain,
( aInteger0(U_192)
| ~ aElementOf0(U_192,szAzrzSzezqlpdtcmdtrp0(U_181,sK29(U_181)))
| ~ aElementOf0(U_181,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_45,plain,
( aInteger0(sK30(U_181,U_192))
| ~ aElementOf0(U_192,szAzrzSzezqlpdtcmdtrp0(U_181,sK29(U_181)))
| ~ aElementOf0(U_181,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_46,plain,
( sdtasdt0(sK29(U_181),sK30(U_181,U_192)) = sdtpldt0(U_192,smndt0(U_181))
| ~ aElementOf0(U_192,szAzrzSzezqlpdtcmdtrp0(U_181,sK29(U_181)))
| ~ aElementOf0(U_181,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_47,plain,
( aDivisorOf0(sK29(U_181),sdtpldt0(U_192,smndt0(U_181)))
| ~ aElementOf0(U_192,szAzrzSzezqlpdtcmdtrp0(U_181,sK29(U_181)))
| ~ aElementOf0(U_181,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_48,plain,
( sdteqdtlpzmzozddtrp0(U_192,U_181,sK29(U_181))
| ~ aElementOf0(U_192,szAzrzSzezqlpdtcmdtrp0(U_181,sK29(U_181)))
| ~ aElementOf0(U_181,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_49,plain,
( sdtasdt0(sK29(U_181),U_177) != sdtpldt0(U_193,smndt0(U_181))
| ~ aInteger0(U_177)
| ~ aInteger0(U_193)
| aElementOf0(U_193,szAzrzSzezqlpdtcmdtrp0(U_181,sK29(U_181)))
| ~ aElementOf0(U_181,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_50,plain,
( ~ aDivisorOf0(sK29(U_181),sdtpldt0(U_193,smndt0(U_181)))
| ~ aInteger0(U_193)
| aElementOf0(U_193,szAzrzSzezqlpdtcmdtrp0(U_181,sK29(U_181)))
| ~ aElementOf0(U_181,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_51,plain,
( ~ sdteqdtlpzmzozddtrp0(U_193,U_181,sK29(U_181))
| ~ aInteger0(U_193)
| aElementOf0(U_193,szAzrzSzezqlpdtcmdtrp0(U_181,sK29(U_181)))
| ~ aElementOf0(U_181,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_52,plain,
( aElementOf0(U_179,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(U_179,szAzrzSzezqlpdtcmdtrp0(U_181,sK29(U_181)))
| ~ aElementOf0(U_181,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_53,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(U_181,sK29(U_181)),stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(U_181,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_45_9]) ).
fof(f_46_1,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ! [W0] :
( ( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
| aElementOf0(W0,sbsmnsldt0(xS))
| ~ aInteger0(W0) )
& ( ( ~ aElementOf0(W0,sbsmnsldt0(xS))
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(sbsmnsldt0(xS))) ) )
& ! [W0] :
( ( aElementOf0(W0,sbsmnsldt0(xS))
| ! [W1] :
( ~ aElementOf0(W0,W1)
| ~ aElementOf0(W1,xS) )
| ~ aInteger0(W0) )
& ( ( ? [W1] :
( aElementOf0(W0,W1)
& aElementOf0(W1,xS) )
& aInteger0(W0) )
| ~ aElementOf0(W0,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [W0] :
( ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ( ~ sdteqdtlpzmzozddtrp0(W0,sz10,xp)
& ~ aDivisorOf0(xp,sdtpldt0(W0,smndt0(sz10)))
& ! [W1] :
( sdtasdt0(xp,W1) != sdtpldt0(W0,smndt0(sz10))
| ~ aInteger0(W1) ) )
| ~ aInteger0(W0) )
& ( ( sdteqdtlpzmzozddtrp0(W0,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(W0,smndt0(sz10)))
& ? [W1] :
( sdtasdt0(xp,W1) = sdtpldt0(W0,smndt0(sz10))
& aInteger0(W1) )
& aInteger0(W0) )
| ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
inference(fof_nnf,[status(thm)],[m__2171]) ).
fof(f_46_2,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [U_201] :
( aElementOf0(U_201,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(U_201,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ! [U_200] :
( ( aElementOf0(U_200,stldt0(sbsmnsldt0(xS)))
| aElementOf0(U_200,sbsmnsldt0(xS))
| ~ aInteger0(U_200) )
& ( ( ~ aElementOf0(U_200,sbsmnsldt0(xS))
& aInteger0(U_200) )
| ~ aElementOf0(U_200,stldt0(sbsmnsldt0(xS))) ) )
& ! [U_199] :
( ( aElementOf0(U_199,sbsmnsldt0(xS))
| ! [U_198] :
( ~ aElementOf0(U_199,U_198)
| ~ aElementOf0(U_198,xS) )
| ~ aInteger0(U_199) )
& ( ( ? [U_197] :
( aElementOf0(U_199,U_197)
& aElementOf0(U_197,xS) )
& aInteger0(U_199) )
| ~ aElementOf0(U_199,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [U_196] :
( ( aElementOf0(U_196,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ( ~ sdteqdtlpzmzozddtrp0(U_196,sz10,xp)
& ~ aDivisorOf0(xp,sdtpldt0(U_196,smndt0(sz10)))
& ! [U_195] :
( sdtasdt0(xp,U_195) != sdtpldt0(U_196,smndt0(sz10))
| ~ aInteger0(U_195) ) )
| ~ aInteger0(U_196) )
& ( ( sdteqdtlpzmzozddtrp0(U_196,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(U_196,smndt0(sz10)))
& ? [U_194] :
( sdtasdt0(xp,U_194) = sdtpldt0(U_196,smndt0(sz10))
& aInteger0(U_194) )
& aInteger0(U_196) )
| ~ aElementOf0(U_196,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [U_201] :
( aElementOf0(U_201,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(U_201,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ! [U_207] :
( aElementOf0(U_207,stldt0(sbsmnsldt0(xS)))
| aElementOf0(U_207,sbsmnsldt0(xS))
| ~ aInteger0(U_207) )
& ! [U_206] :
( ( ~ aElementOf0(U_206,sbsmnsldt0(xS))
& aInteger0(U_206) )
| ~ aElementOf0(U_206,stldt0(sbsmnsldt0(xS))) )
& ! [U_205] :
( aElementOf0(U_205,sbsmnsldt0(xS))
| ! [U_198] :
( ~ aElementOf0(U_205,U_198)
| ~ aElementOf0(U_198,xS) )
| ~ aInteger0(U_205) )
& ! [U_204] :
( ( ? [U_197] :
( aElementOf0(U_204,U_197)
& aElementOf0(U_197,xS) )
& aInteger0(U_204) )
| ~ aElementOf0(U_204,sbsmnsldt0(xS)) )
& aSet0(sbsmnsldt0(xS))
& ! [U_203] :
( aElementOf0(U_203,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ( ~ sdteqdtlpzmzozddtrp0(U_203,sz10,xp)
& ~ aDivisorOf0(xp,sdtpldt0(U_203,smndt0(sz10)))
& ! [U_195] :
( sdtasdt0(xp,U_195) != sdtpldt0(U_203,smndt0(sz10))
| ~ aInteger0(U_195) ) )
| ~ aInteger0(U_203) )
& ! [U_202] :
( ( sdteqdtlpzmzozddtrp0(U_202,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(U_202,smndt0(sz10)))
& ? [U_194] :
( sdtasdt0(xp,U_194) = sdtpldt0(U_202,smndt0(sz10))
& aInteger0(U_194) )
& aInteger0(U_202) )
| ~ aElementOf0(U_202,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
inference(miniscope,[status(thm)],[f_46_2]) ).
fof(f_46_4,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [U_201] :
( aElementOf0(U_201,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(U_201,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ! [U_207] :
( aElementOf0(U_207,stldt0(sbsmnsldt0(xS)))
| aElementOf0(U_207,sbsmnsldt0(xS))
| ~ aInteger0(U_207) )
& ! [U_206] :
( ( ~ aElementOf0(U_206,sbsmnsldt0(xS))
& aInteger0(U_206) )
| ~ aElementOf0(U_206,stldt0(sbsmnsldt0(xS))) )
& ! [U_205] :
( aElementOf0(U_205,sbsmnsldt0(xS))
| ! [U_198] :
( ~ aElementOf0(U_205,U_198)
| ~ aElementOf0(U_198,xS) )
| ~ aInteger0(U_205) )
& ! [U_204] :
( ( ? [U_197] :
( aElementOf0(U_204,U_197)
& aElementOf0(U_197,xS) )
& aInteger0(U_204) )
| ~ aElementOf0(U_204,sbsmnsldt0(xS)) )
& aSet0(sbsmnsldt0(xS))
& ! [U_203] :
( aElementOf0(U_203,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ( ~ sdteqdtlpzmzozddtrp0(U_203,sz10,xp)
& ~ aDivisorOf0(xp,sdtpldt0(U_203,smndt0(sz10)))
& ! [U_195] :
( sdtasdt0(xp,U_195) != sdtpldt0(U_203,smndt0(sz10))
| ~ aInteger0(U_195) ) )
| ~ aInteger0(U_203) )
& ! [U_202] :
( ( sdteqdtlpzmzozddtrp0(U_202,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(U_202,smndt0(sz10)))
& sdtasdt0(xp,sK31(U_202)) = sdtpldt0(U_202,smndt0(sz10))
& aInteger0(sK31(U_202))
& aInteger0(U_202) )
| ~ aElementOf0(U_202,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_194,sK31(U_202))],[f_46_3]) ).
fof(f_46_5,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [U_201] :
( aElementOf0(U_201,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(U_201,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ! [U_207] :
( aElementOf0(U_207,stldt0(sbsmnsldt0(xS)))
| aElementOf0(U_207,sbsmnsldt0(xS))
| ~ aInteger0(U_207) )
& ! [U_206] :
( ( ~ aElementOf0(U_206,sbsmnsldt0(xS))
& aInteger0(U_206) )
| ~ aElementOf0(U_206,stldt0(sbsmnsldt0(xS))) )
& ! [U_205] :
( aElementOf0(U_205,sbsmnsldt0(xS))
| ! [U_198] :
( ~ aElementOf0(U_205,U_198)
| ~ aElementOf0(U_198,xS) )
| ~ aInteger0(U_205) )
& ! [U_204] :
( ( aElementOf0(U_204,sK32(U_204))
& aElementOf0(sK32(U_204),xS)
& aInteger0(U_204) )
| ~ aElementOf0(U_204,sbsmnsldt0(xS)) )
& aSet0(sbsmnsldt0(xS))
& ! [U_203] :
( aElementOf0(U_203,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ( ~ sdteqdtlpzmzozddtrp0(U_203,sz10,xp)
& ~ aDivisorOf0(xp,sdtpldt0(U_203,smndt0(sz10)))
& ! [U_195] :
( sdtasdt0(xp,U_195) != sdtpldt0(U_203,smndt0(sz10))
| ~ aInteger0(U_195) ) )
| ~ aInteger0(U_203) )
& ! [U_202] :
( ( sdteqdtlpzmzozddtrp0(U_202,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(U_202,smndt0(sz10)))
& sdtasdt0(xp,sK31(U_202)) = sdtpldt0(U_202,smndt0(sz10))
& aInteger0(sK31(U_202))
& aInteger0(U_202) )
| ~ aElementOf0(U_202,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_197,sK32(U_204))],[f_46_4]) ).
cnf(f_46_6,plain,
aInteger0(xp),
inference(clausify,[status(thm)],[f_46_5]) ).
cnf(f_46_7,plain,
xp != sz00,
inference(clausify,[status(thm)],[f_46_5]) ).
cnf(f_46_8,plain,
aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(clausify,[status(thm)],[f_46_5]) ).
cnf(f_46_9,plain,
( aInteger0(U_202)
| ~ aElementOf0(U_202,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(clausify,[status(thm)],[f_46_5]) ).
cnf(f_46_10,plain,
( aInteger0(sK31(U_202))
| ~ aElementOf0(U_202,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(clausify,[status(thm)],[f_46_5]) ).
cnf(f_46_11,plain,
( sdtasdt0(xp,sK31(U_202)) = sdtpldt0(U_202,smndt0(sz10))
| ~ aElementOf0(U_202,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(clausify,[status(thm)],[f_46_5]) ).
cnf(f_46_12,plain,
( aDivisorOf0(xp,sdtpldt0(U_202,smndt0(sz10)))
| ~ aElementOf0(U_202,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(clausify,[status(thm)],[f_46_5]) ).
cnf(f_46_13,plain,
( sdteqdtlpzmzozddtrp0(U_202,sz10,xp)
| ~ aElementOf0(U_202,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(clausify,[status(thm)],[f_46_5]) ).
cnf(f_46_14,plain,
( sdtasdt0(xp,U_195) != sdtpldt0(U_203,smndt0(sz10))
| ~ aInteger0(U_195)
| ~ aInteger0(U_203)
| aElementOf0(U_203,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(clausify,[status(thm)],[f_46_5]) ).
cnf(f_46_15,plain,
( ~ aDivisorOf0(xp,sdtpldt0(U_203,smndt0(sz10)))
| ~ aInteger0(U_203)
| aElementOf0(U_203,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(clausify,[status(thm)],[f_46_5]) ).
cnf(f_46_16,plain,
( ~ sdteqdtlpzmzozddtrp0(U_203,sz10,xp)
| ~ aInteger0(U_203)
| aElementOf0(U_203,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(clausify,[status(thm)],[f_46_5]) ).
cnf(f_46_17,plain,
aSet0(sbsmnsldt0(xS)),
inference(clausify,[status(thm)],[f_46_5]) ).
cnf(f_46_18,plain,
( aInteger0(U_204)
| ~ aElementOf0(U_204,sbsmnsldt0(xS)) ),
inference(clausify,[status(thm)],[f_46_5]) ).
cnf(f_46_19,plain,
( aElementOf0(sK32(U_204),xS)
| ~ aElementOf0(U_204,sbsmnsldt0(xS)) ),
inference(clausify,[status(thm)],[f_46_5]) ).
cnf(f_46_20,plain,
( aElementOf0(U_204,sK32(U_204))
| ~ aElementOf0(U_204,sbsmnsldt0(xS)) ),
inference(clausify,[status(thm)],[f_46_5]) ).
cnf(f_46_21,plain,
( aElementOf0(U_205,sbsmnsldt0(xS))
| ~ aElementOf0(U_205,U_198)
| ~ aElementOf0(U_198,xS)
| ~ aInteger0(U_205) ),
inference(clausify,[status(thm)],[f_46_5]) ).
cnf(f_46_22,plain,
( aInteger0(U_206)
| ~ aElementOf0(U_206,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_46_5]) ).
cnf(f_46_23,plain,
( ~ aElementOf0(U_206,sbsmnsldt0(xS))
| ~ aElementOf0(U_206,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[f_46_5]) ).
cnf(f_46_24,plain,
( aElementOf0(U_207,stldt0(sbsmnsldt0(xS)))
| aElementOf0(U_207,sbsmnsldt0(xS))
| ~ aInteger0(U_207) ),
inference(clausify,[status(thm)],[f_46_5]) ).
cnf(f_46_25,plain,
( aElementOf0(U_201,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(U_201,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(clausify,[status(thm)],[f_46_5]) ).
cnf(f_46_26,plain,
aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))),
inference(clausify,[status(thm)],[f_46_5]) ).
fof(f_47_1,plain,
( aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
& ? [W0] :
( sdtasdt0(xp,W0) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
& aInteger0(W0) )
& aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp)
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
& ? [W0] :
( sdtasdt0(xp,W0) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))
& aInteger0(W0) ) ),
inference(fof_nnf,[status(thm)],[m__2232]) ).
fof(f_47_2,plain,
( aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
& ? [U_209] :
( sdtasdt0(xp,U_209) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
& aInteger0(U_209) )
& aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp)
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
& ? [U_208] :
( sdtasdt0(xp,U_208) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))
& aInteger0(U_208) ) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
( aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
& ? [U_209] :
( sdtasdt0(xp,U_209) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
& aInteger0(U_209) )
& aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp)
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
& sdtasdt0(xp,sK33) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))
& aInteger0(sK33) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_208,sK33)],[f_47_2]) ).
fof(f_47_4,plain,
( aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
& sdtasdt0(xp,sK34) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
& aInteger0(sK34)
& aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp)
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
& sdtasdt0(xp,sK33) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))
& aInteger0(sK33) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_209,sK34)],[f_47_3]) ).
cnf(f_47_5,plain,
aInteger0(sK33),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_6,plain,
sdtasdt0(xp,sK33) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_7,plain,
aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_8,plain,
sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_9,plain,
aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_10,plain,
aInteger0(sK34),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_11,plain,
sdtasdt0(xp,sK34) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_12,plain,
aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_13,plain,
sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_14,plain,
aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(clausify,[status(thm)],[f_47_4]) ).
fof(f_48_1,plain,
( sdtpldt0(sz10,smndt0(xp)) != sz10
& sdtpldt0(sz10,xp) != sz10 ),
inference(fof_nnf,[status(thm)],[m__2258]) ).
cnf(f_48_2,plain,
sdtpldt0(sz10,xp) != sz10,
inference(clausify,[status(thm)],[f_48_1]) ).
cnf(f_48_3,plain,
sdtpldt0(sz10,smndt0(xp)) != sz10,
inference(clausify,[status(thm)],[f_48_1]) ).
fof(f_49_1,plain,
( sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10)
| sdtpldt0(sz10,xp) != smndt0(sz10) ),
inference(fof_nnf,[status(thm)],[m__2286]) ).
cnf(f_49_2,plain,
( sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10)
| sdtpldt0(sz10,xp) != smndt0(sz10) ),
inference(clausify,[status(thm)],[f_49_1]) ).
fof(f_50_1,negated_conjecture,
~ ? [W0] :
( ~ ( aElementOf0(W0,cS2200)
& ( W0 = smndt0(sz10)
| W0 = sz10 ) )
& ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ( ( sdteqdtlpzmzozddtrp0(W0,sz10,xp)
| aDivisorOf0(xp,sdtpldt0(W0,smndt0(sz10)))
| ? [W1] :
( sdtasdt0(xp,W1) = sdtpldt0(W0,smndt0(sz10))
& aInteger0(W1) ) )
& aInteger0(W0) ) ) ),
inference(negate,[status(cth)],[m__]) ).
fof(f_50_2,negated_conjecture,
! [W0] :
( ( aElementOf0(W0,cS2200)
& ( W0 = smndt0(sz10)
| W0 = sz10 ) )
| ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ( ( ~ sdteqdtlpzmzozddtrp0(W0,sz10,xp)
& ~ aDivisorOf0(xp,sdtpldt0(W0,smndt0(sz10)))
& ! [W1] :
( sdtasdt0(xp,W1) != sdtpldt0(W0,smndt0(sz10))
| ~ aInteger0(W1) ) )
| ~ aInteger0(W0) ) ) ),
inference(fof_nnf,[status(thm)],[f_50_1]) ).
fof(f_50_3,negated_conjecture,
! [U_211] :
( ( aElementOf0(U_211,cS2200)
& ( U_211 = smndt0(sz10)
| U_211 = sz10 ) )
| ( ~ aElementOf0(U_211,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ( ( ~ sdteqdtlpzmzozddtrp0(U_211,sz10,xp)
& ~ aDivisorOf0(xp,sdtpldt0(U_211,smndt0(sz10)))
& ! [U_210] :
( sdtasdt0(xp,U_210) != sdtpldt0(U_211,smndt0(sz10))
| ~ aInteger0(U_210) ) )
| ~ aInteger0(U_211) ) ) ),
inference(variable_rename,[status(thm)],[f_50_2]) ).
fof(f_50_4,negated_conjecture,
( ! [U_211] :
( aElementOf0(U_211,cS2200)
| ~ sP2(U_211) )
& ! [U_211] :
( U_211 = smndt0(sz10)
| U_211 = sz10
| ~ sP2(U_211) )
& ! [U_211,U_210] :
( ~ sdteqdtlpzmzozddtrp0(U_211,sz10,xp)
| ~ sP0(U_211,U_210) )
& ! [U_211,U_210] :
( ~ aDivisorOf0(xp,sdtpldt0(U_211,smndt0(sz10)))
| ~ sP0(U_211,U_210) )
& ! [U_211,U_210] :
( sdtasdt0(xp,U_210) != sdtpldt0(U_211,smndt0(sz10))
| ~ aInteger0(U_210)
| ~ sP0(U_211,U_210) )
& ! [U_211,U_210] :
( ~ aElementOf0(U_211,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ sP1(U_211,U_210) )
& ! [U_211,U_210] :
( sP0(U_211,U_210)
| ~ aInteger0(U_211)
| ~ sP1(U_211,U_210) )
& ! [U_211,U_210] :
( sP2(U_211)
| sP1(U_211,U_210) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1,sP2])],[f_50_3]) ).
cnf(f_50_5,negated_conjecture,
( sP2(U_211)
| sP1(U_211,U_210) ),
inference(clausify,[status(thm)],[f_50_4]) ).
cnf(f_50_6,negated_conjecture,
( sP0(U_211,U_210)
| ~ aInteger0(U_211)
| ~ sP1(U_211,U_210) ),
inference(clausify,[status(thm)],[f_50_4]) ).
cnf(f_50_7,negated_conjecture,
( ~ aElementOf0(U_211,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ sP1(U_211,U_210) ),
inference(clausify,[status(thm)],[f_50_4]) ).
cnf(f_50_8,negated_conjecture,
( sdtasdt0(xp,U_210) != sdtpldt0(U_211,smndt0(sz10))
| ~ aInteger0(U_210)
| ~ sP0(U_211,U_210) ),
inference(clausify,[status(thm)],[f_50_4]) ).
cnf(f_50_9,negated_conjecture,
( ~ aDivisorOf0(xp,sdtpldt0(U_211,smndt0(sz10)))
| ~ sP0(U_211,U_210) ),
inference(clausify,[status(thm)],[f_50_4]) ).
cnf(f_50_10,negated_conjecture,
( ~ sdteqdtlpzmzozddtrp0(U_211,sz10,xp)
| ~ sP0(U_211,U_210) ),
inference(clausify,[status(thm)],[f_50_4]) ).
cnf(f_50_11,negated_conjecture,
( U_211 = smndt0(sz10)
| U_211 = sz10
| ~ sP2(U_211) ),
inference(clausify,[status(thm)],[f_50_4]) ).
cnf(f_50_12,negated_conjecture,
( aElementOf0(U_211,cS2200)
| ~ sP2(U_211) ),
inference(clausify,[status(thm)],[f_50_4]) ).
cnf(f_1_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1_4]) ).
cnf(f_24_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_24_3]) ).
cnf(f_26_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_26_4]) ).
cnf(f_27_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_27_4]) ).
cnf(f_29_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_29_3]) ).
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,
( smndt0(Eq_x_0) = smndt0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,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_6,axiom,
( sdtasdt0(Eq_x_0,Eq_x_1) = sdtasdt0(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sdtbsmnsldt0(Eq_x_0,Eq_x_1) = sdtbsmnsldt0(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sdtslmnbsdt0(Eq_x_0,Eq_x_1) = sdtslmnbsdt0(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sbsmnsldt0(Eq_x_0) = sbsmnsldt0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( stldt0(Eq_x_0) = stldt0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( szAzrzSzezqlpdtcmdtrp0(Eq_x_0,Eq_x_1) = szAzrzSzezqlpdtcmdtrp0(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,
( sK1(Eq_x_0,Eq_x_1) = sK1(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,
( sK2(Eq_x_0) = sK2(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK3(Eq_x_0,Eq_x_1) = sK3(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,
( 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_16,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_17,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_18,axiom,
( sK7(Eq_x_0,Eq_x_1,Eq_x_2) = sK7(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_19,axiom,
( sK8(Eq_x_0) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( sK9(Eq_x_0,Eq_x_1,Eq_x_2) = sK9(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,
( 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_22,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_23,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_24,axiom,
( sK13(Eq_x_0,Eq_x_1) = sK13(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,axiom,
( sK14(Eq_x_0,Eq_x_1) = sK14(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,
( 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_27,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_28,axiom,
( sK17(Eq_x_0,Eq_x_1) = sK17(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,
( sK18(Eq_x_0) = sK18(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_30,axiom,
( sK19(Eq_x_0) = sK19(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_31,axiom,
( sK20(Eq_x_0) = sK20(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_32,axiom,
( sK21(Eq_x_0) = sK21(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_33,axiom,
( sK22(Eq_x_0,Eq_x_1) = sK22(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_34,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_35,axiom,
( sK24(Eq_x_0) = sK24(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_36,axiom,
( sK25(Eq_x_0) = sK25(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_37,axiom,
( sK26(Eq_x_0) = sK26(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_38,axiom,
( sK27(Eq_x_0,Eq_x_1) = sK27(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_39,axiom,
( sK28(Eq_x_0) = sK28(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_40,axiom,
( sK29(Eq_x_0) = sK29(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_41,axiom,
( sK30(Eq_x_0,Eq_x_1) = sK30(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,
( sK31(Eq_x_0) = sK31(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_43,axiom,
( sK32(Eq_x_0) = sK32(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_44,axiom,
( aInteger0(Eq_y_0)
| ~ aInteger0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_45,axiom,
( aDivisorOf0(Eq_y_0,Eq_y_1)
| ~ aDivisorOf0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_46,axiom,
( sdteqdtlpzmzozddtrp0(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sdteqdtlpzmzozddtrp0(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_47,axiom,
( isPrime0(Eq_y_0)
| ~ isPrime0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_48,axiom,
( aSet0(Eq_y_0)
| ~ aSet0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_49,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_50,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_51,axiom,
( isFinite0(Eq_y_0)
| ~ isFinite0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_52,axiom,
( isOpen0(Eq_y_0)
| ~ isOpen0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_53,axiom,
( isClosed0(Eq_y_0)
| ~ isClosed0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_54,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_55,axiom,
( sP1(Eq_y_0,Eq_y_1)
| ~ sP1(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,
( sP2(Eq_y_0)
| ~ sP2(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
% 0.00/0.02 % Problem : NUM455+6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 This is a FOF_CAX_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n026.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sat Sep 19 18:31:50 UTC 2026
% 0.08/0.37 % CPUTime :
% 8.87/9.17 % SZS status Theorem for theBenchmark
% 8.87/9.17 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------