%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM453+6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 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 : Fri Sep 25 02:24:30 PM UTC 2026
% Result : Theorem 54.72s 15.06s
% Output : CNFRefutation 54.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 53
% Syntax : Number of formulae : 687 ( 63 unt; 10 def)
% Number of atoms : 3850 ( 550 equ)
% Maximal formula atoms : 56 ( 5 avg)
% Number of connectives : 4971 (1808 ~;1870 |;1126 &)
% ( 86 <=>; 81 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 22 ( 20 usr; 1 prp; 0-3 aty)
% Number of functors : 44 ( 44 usr; 9 con; 0-3 aty)
% Number of variables : 1619 ( 0 sgn1466 !; 153 ?; 381 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntZero) ).
fof(f3,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntOne) ).
fof(f4,axiom,
! [X0] :
( aInteger0(X0)
=> aInteger0(smndt0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).
fof(f5,axiom,
! [X0,X1] :
( ( aInteger0(X1)
& aInteger0(X0) )
=> aInteger0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntPlus) ).
fof(f6,axiom,
! [X0,X1] :
( ( aInteger0(X1)
& aInteger0(X0) )
=> aInteger0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntMult) ).
fof(f7,axiom,
! [X0,X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1)
& aInteger0(X0) )
=> sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(f8,axiom,
! [X0,X1] :
( ( aInteger0(X1)
& aInteger0(X0) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(f9,axiom,
! [X0] :
( aInteger0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(f10,axiom,
! [X0] :
( aInteger0(X0)
=> ( sz00 = sdtpldt0(smndt0(X0),X0)
& sdtpldt0(X0,smndt0(X0)) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).
fof(f11,axiom,
! [X0,X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1)
& aInteger0(X0) )
=> sdtasdt0(X0,sdtasdt0(X1,X2)) = sdtasdt0(sdtasdt0(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(f12,axiom,
! [X0,X1] :
( ( aInteger0(X1)
& aInteger0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(f13,axiom,
! [X0] :
( aInteger0(X0)
=> ( X0 = sdtasdt0(sz10,X0)
& sdtasdt0(X0,sz10) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulOne) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1)
& aInteger0(X0) )
=> ( sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDistrib) ).
fof(f15,axiom,
! [X0] :
( aInteger0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
fof(f16,axiom,
! [X0] :
( aInteger0(X0)
=> ( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
& sdtasdt0(smndt0(sz10),X0) = smndt0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulMinOne) ).
fof(f17,axiom,
! [X0,X1] :
( ( aInteger0(X1)
& aInteger0(X0) )
=> ( sdtasdt0(X0,X1) = sz00
=> ( X1 = sz00
| X0 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroDiv) ).
fof(f18,axiom,
! [X0] :
( aInteger0(X0)
=> ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& X1 != sz00
& aInteger0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivisor) ).
fof(f19,axiom,
! [X0,X1,X2] :
( ( X2 != sz00
& aInteger0(X2)
& aInteger0(X1)
& aInteger0(X0) )
=> ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquMod) ).
fof(f20,axiom,
! [X0,X1] :
( ( X1 != sz00
& aInteger0(X1)
& aInteger0(X0) )
=> sdteqdtlpzmzozddtrp0(X0,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModRef) ).
fof(f21,axiom,
! [X0,X1,X2] :
( ( X2 != sz00
& aInteger0(X2)
& aInteger0(X1)
& aInteger0(X0) )
=> ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
=> sdteqdtlpzmzozddtrp0(X1,X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModSym) ).
fof(f22,axiom,
! [X0,X1,X2,X3] :
( ( aInteger0(X3)
& X2 != sz00
& aInteger0(X2)
& aInteger0(X1)
& aInteger0(X0) )
=> ( ( sdteqdtlpzmzozddtrp0(X1,X3,X2)
& sdteqdtlpzmzozddtrp0(X0,X1,X2) )
=> sdteqdtlpzmzozddtrp0(X0,X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModTrn) ).
fof(f23,axiom,
! [X0,X1,X2,X3] :
( ( X3 != sz00
& aInteger0(X3)
& X2 != sz00
& aInteger0(X2)
& aInteger0(X1)
& aInteger0(X0) )
=> ( sdteqdtlpzmzozddtrp0(X0,X1,sdtasdt0(X2,X3))
=> ( sdteqdtlpzmzozddtrp0(X0,X1,X3)
& sdteqdtlpzmzozddtrp0(X0,X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModMul) ).
fof(f25,axiom,
! [X0] :
( aInteger0(X0)
=> ( ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,X0) )
<=> ( X0 != smndt0(sz10)
& X0 != sz10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPrimeDivisor) ).
fof(f28,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubset) ).
fof(f30,axiom,
! [X0,X1] :
( ( aSubsetOf0(X1,cS1395)
& aSubsetOf0(X0,cS1395) )
=> ! [X2] :
( X2 = sdtbsmnsldt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( ( aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aInteger0(X3) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mUnion) ).
fof(f31,axiom,
! [X0,X1] :
( ( aSubsetOf0(X1,cS1395)
& aSubsetOf0(X0,cS1395) )
=> ! [X2] :
( X2 = sdtslmnbsdt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,X1)
& aElementOf0(X3,X0)
& aInteger0(X3) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntersection) ).
fof(f32,axiom,
! [X0] :
( ( ! [X1] :
( aElementOf0(X1,X0)
=> aSubsetOf0(X1,cS1395) )
& aSet0(X0) )
=> ! [X1] :
( X1 = sbsmnsldt0(X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ( ? [X3] :
( aElementOf0(X2,X3)
& aElementOf0(X3,X0) )
& aInteger0(X2) ) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mUnionSet) ).
fof(f33,axiom,
! [X0] :
( aSubsetOf0(X0,cS1395)
=> ! [X1] :
( X1 = stldt0(X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ( ~ aElementOf0(X2,X0)
& aInteger0(X2) ) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mComplement) ).
fof(f34,axiom,
! [X0,X1] :
( ( X1 != sz00
& aInteger0(X1)
& aInteger0(X0) )
=> ! [X2] :
( X2 = szAzrzSzezqlpdtcmdtrp0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aInteger0(X3) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mArSeq) ).
fof(f35,axiom,
! [X0] :
( aSubsetOf0(X0,cS1395)
=> ( isOpen0(X0)
<=> ! [X1] :
( aElementOf0(X1,X0)
=> ? [X2] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),X0)
& X2 != sz00
& aInteger0(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mOpen) ).
fof(f36,axiom,
! [X0] :
( aSubsetOf0(X0,cS1395)
=> ( isClosed0(X0)
<=> isOpen0(stldt0(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mClosed) ).
fof(f37,axiom,
! [X0] :
( ( ! [X1] :
( aElementOf0(X1,X0)
=> ( isOpen0(X1)
& aSubsetOf0(X1,cS1395) ) )
& aSet0(X0) )
=> isOpen0(sbsmnsldt0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mUnionOpen) ).
fof(f38,axiom,
! [X0,X1] :
( ( isOpen0(X1)
& isOpen0(X0)
& aSubsetOf0(X1,cS1395)
& aSubsetOf0(X0,cS1395) )
=> isOpen0(sdtslmnbsdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mInterOpen) ).
fof(f39,axiom,
! [X0,X1] :
( ( isClosed0(X1)
& isClosed0(X0)
& aSubsetOf0(X1,cS1395)
& aSubsetOf0(X0,cS1395) )
=> isClosed0(sdtbsmnsldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mUnionClosed) ).
fof(f40,axiom,
! [X0] :
( ( ! [X1] :
( aElementOf0(X1,X0)
=> ( isClosed0(X1)
& aSubsetOf0(X1,cS1395) ) )
& isFinite0(X0)
& aSet0(X0) )
=> isClosed0(sbsmnsldt0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mUnionSClosed) ).
fof(f41,axiom,
! [X0,X1] :
( ( X1 != sz00
& aInteger0(X1)
& aInteger0(X0) )
=> ( isClosed0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),cS1395) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mArSeqClosed) ).
fof(f42,axiom,
( xS = cS2043
& ! [X0] :
( ( ? [X1] :
( ( ( ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
| ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00))
& aInteger0(X3) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
=> ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
=> szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0 )
& isPrime0(X1)
& X1 != sz00
& aInteger0(X1) )
=> aElementOf0(X0,xS) )
& ( aElementOf0(X0,xS)
=> ? [X1] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0
& ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
| ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00))
& aInteger0(X3) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
=> ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
& isPrime0(X1)
& X1 != sz00
& aInteger0(X1) ) ) )
& aSet0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2046) ).
fof(f43,axiom,
( stldt0(sbsmnsldt0(xS)) = cS2076
& ! [X0] :
( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
<=> ( X0 = smndt0(sz10)
| X0 = sz10 ) )
& ! [X0] :
( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X0,sbsmnsldt0(xS))
& aInteger0(X0) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) ) )
& aSet0(sbsmnsldt0(xS)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2079) ).
fof(f44,axiom,
isFinite0(xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2117) ).
fof(f45,axiom,
( ! [X0] :
( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
=> ? [X1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(sbsmnsldt0(xS)))
& ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> aElementOf0(X2,stldt0(sbsmnsldt0(xS))) )
& ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
| ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& X1 != sz00
& aInteger0(X1) ) )
& ! [X0] :
( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X0,sbsmnsldt0(xS))
& aInteger0(X0) ) )
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) ) )
& aSet0(sbsmnsldt0(xS))
& isClosed0(sbsmnsldt0(xS))
& isOpen0(stldt0(sbsmnsldt0(xS)))
& ! [X0] :
( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
=> ? [X1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(sbsmnsldt0(xS)))
& ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> aElementOf0(X2,stldt0(sbsmnsldt0(xS))) )
& ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
| ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& X1 != sz00
& aInteger0(X1) ) )
& ! [X0] :
( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X0,sbsmnsldt0(xS))
& aInteger0(X0) ) )
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) ) )
& aSet0(sbsmnsldt0(xS)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2144) ).
fof(f46,axiom,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [X0] :
( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> aElementOf0(X0,stldt0(sbsmnsldt0(xS))) )
& ! [X0] :
( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X0,sbsmnsldt0(xS))
& aInteger0(X0) ) )
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( ( ( sdteqdtlpzmzozddtrp0(X0,sz10,xp)
| aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
| ? [X1] :
( sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10))
& aInteger0(X1) ) )
& aInteger0(X0) )
=> aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> ( sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ? [X1] :
( sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10))
& aInteger0(X1) )
& aInteger0(X0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2171) ).
fof(f47,axiom,
( aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
& ? [X0] :
( sdtasdt0(xp,X0) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
& aInteger0(X0) )
& aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp)
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
& ? [X0] :
( sdtasdt0(xp,X0) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))
& aInteger0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2232) ).
fof(f48,conjecture,
( sdtpldt0(sz10,smndt0(xp)) != sz10
& sdtpldt0(sz10,xp) != sz10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f49,negated_conjecture,
~ ( sdtpldt0(sz10,smndt0(xp)) != sz10
& sdtpldt0(sz10,xp) != sz10 ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f55,plain,
! [X0] :
( ( ! [X1] :
( aElementOf0(X1,X0)
=> aSubsetOf0(X1,cS1395) )
& aSet0(X0) )
=> ! [X2] :
( sbsmnsldt0(X0) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( ? [X4] :
( aElementOf0(X3,X4)
& aElementOf0(X4,X0) )
& aInteger0(X3) ) )
& aSet0(X2) ) ) ),
inference(rectify,[],[f32]) ).
fof(f56,plain,
( xS = cS2043
& ! [X0] :
( ( ? [X5] :
( ( ( ! [X6] :
( ( ( ( sdteqdtlpzmzozddtrp0(X6,sz00,X5)
| aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
| ? [X8] :
( sdtpldt0(X6,smndt0(sz00)) = sdtasdt0(X5,X8)
& aInteger0(X8) ) )
& aInteger0(X6) )
=> aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5)) )
& ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
=> ( sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ? [X7] :
( sdtasdt0(X5,X7) = sdtpldt0(X6,smndt0(sz00))
& aInteger0(X7) )
& aInteger0(X6) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5)) )
=> szAzrzSzezqlpdtcmdtrp0(sz00,X5) = X0 )
& isPrime0(X5)
& sz00 != X5
& aInteger0(X5) )
=> aElementOf0(X0,xS) )
& ( aElementOf0(X0,xS)
=> ? [X1] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0
& ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
| ? [X4] :
( sdtpldt0(X2,smndt0(sz00)) = sdtasdt0(X1,X4)
& aInteger0(X4) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
=> ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
& isPrime0(X1)
& X1 != sz00
& aInteger0(X1) ) ) )
& aSet0(xS) ),
inference(rectify,[],[f42]) ).
fof(f57,plain,
( stldt0(sbsmnsldt0(xS)) = cS2076
& ! [X3] :
( aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
<=> ( smndt0(sz10) = X3
| sz10 = X3 ) )
& ! [X2] :
( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X2,sbsmnsldt0(xS))
& aInteger0(X2) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(rectify,[],[f43]) ).
fof(f58,plain,
( ! [X12] :
( aElementOf0(X12,stldt0(sbsmnsldt0(xS)))
=> ? [X13] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X12,X13),stldt0(sbsmnsldt0(xS)))
& ! [X17] :
( aElementOf0(X17,szAzrzSzezqlpdtcmdtrp0(X12,X13))
=> aElementOf0(X17,stldt0(sbsmnsldt0(xS))) )
& ! [X14] :
( ( ( ( sdteqdtlpzmzozddtrp0(X14,X12,X13)
| aDivisorOf0(X13,sdtpldt0(X14,smndt0(X12)))
| ? [X16] :
( sdtpldt0(X14,smndt0(X12)) = sdtasdt0(X13,X16)
& aInteger0(X16) ) )
& aInteger0(X14) )
=> aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(X12,X13)) )
& ( aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(X12,X13))
=> ( sdteqdtlpzmzozddtrp0(X14,X12,X13)
& aDivisorOf0(X13,sdtpldt0(X14,smndt0(X12)))
& ? [X15] :
( sdtasdt0(X13,X15) = sdtpldt0(X14,smndt0(X12))
& aInteger0(X15) )
& aInteger0(X14) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X12,X13))
& sz00 != X13
& aInteger0(X13) ) )
& ! [X11] :
( aElementOf0(X11,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X11,sbsmnsldt0(xS))
& aInteger0(X11) ) )
& ! [X9] :
( aElementOf0(X9,sbsmnsldt0(xS))
<=> ( ? [X10] :
( aElementOf0(X9,X10)
& aElementOf0(X10,xS) )
& aInteger0(X9) ) )
& aSet0(sbsmnsldt0(xS))
& isClosed0(sbsmnsldt0(xS))
& isOpen0(stldt0(sbsmnsldt0(xS)))
& ! [X3] :
( aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
=> ? [X4] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),stldt0(sbsmnsldt0(xS)))
& ! [X8] :
( aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(X3,X4))
=> aElementOf0(X8,stldt0(sbsmnsldt0(xS))) )
& ! [X5] :
( ( ( ( sdteqdtlpzmzozddtrp0(X5,X3,X4)
| aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
| ? [X7] :
( sdtpldt0(X5,smndt0(X3)) = sdtasdt0(X4,X7)
& aInteger0(X7) ) )
& aInteger0(X5) )
=> aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& ( aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4))
=> ( sdteqdtlpzmzozddtrp0(X5,X3,X4)
& aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& ? [X6] :
( sdtasdt0(X4,X6) = sdtpldt0(X5,smndt0(X3))
& aInteger0(X6) )
& aInteger0(X5) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X3,X4))
& sz00 != X4
& aInteger0(X4) ) )
& ! [X2] :
( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X2,sbsmnsldt0(xS))
& aInteger0(X2) ) )
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(rectify,[],[f45]) ).
fof(f59,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [X6] :
( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> aElementOf0(X6,stldt0(sbsmnsldt0(xS))) )
& ! [X5] :
( aElementOf0(X5,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X5,sbsmnsldt0(xS))
& aInteger0(X5) ) )
& ! [X3] :
( aElementOf0(X3,sbsmnsldt0(xS))
<=> ( ? [X4] :
( aElementOf0(X3,X4)
& aElementOf0(X4,xS) )
& aInteger0(X3) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( ( ( sdteqdtlpzmzozddtrp0(X0,sz10,xp)
| aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
| ? [X2] :
( sdtpldt0(X0,smndt0(sz10)) = sdtasdt0(xp,X2)
& aInteger0(X2) ) )
& aInteger0(X0) )
=> aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> ( sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ? [X1] :
( sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10))
& aInteger0(X1) )
& aInteger0(X0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
inference(rectify,[],[f46]) ).
fof(f60,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)))
& ? [X1] :
( sdtasdt0(xp,X1) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
& aInteger0(X1) )
& aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp)
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
& ? [X0] :
( sdtasdt0(xp,X0) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))
& aInteger0(X0) ) ),
inference(rectify,[],[f47]) ).
fof(f61,plain,
! [X0] :
( ~ aInteger0(X0)
| aInteger0(smndt0(X0)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f62,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| aInteger0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f63,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| aInteger0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| aInteger0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f65,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| aInteger0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2) ),
inference(ennf_transformation,[],[f7]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2) ),
inference(flattening,[],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f69,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(flattening,[],[f68]) ).
fof(f70,plain,
! [X0] :
( ~ aInteger0(X0)
| ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f71,plain,
! [X0] :
( ~ aInteger0(X0)
| ( sz00 = sdtpldt0(smndt0(X0),X0)
& sdtpldt0(X0,smndt0(X0)) = sz00 ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdtasdt0(X0,sdtasdt0(X1,X2)) = sdtasdt0(sdtasdt0(X0,X1),X2) ),
inference(ennf_transformation,[],[f11]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdtasdt0(X0,sdtasdt0(X1,X2)) = sdtasdt0(sdtasdt0(X0,X1),X2) ),
inference(flattening,[],[f72]) ).
fof(f74,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f75,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
! [X0] :
( ~ aInteger0(X0)
| ( X0 = sdtasdt0(sz10,X0)
& sdtasdt0(X0,sz10) = X0 ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ( sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ( sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
! [X0] :
( ~ aInteger0(X0)
| ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f80,plain,
! [X0] :
( ~ aInteger0(X0)
| ( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
& sdtasdt0(smndt0(sz10),X0) = smndt0(X0) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f81,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| sz00 != sdtasdt0(X0,X1)
| X1 = sz00
| X0 = sz00 ),
inference(ennf_transformation,[],[f17]) ).
fof(f82,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| sz00 != sdtasdt0(X0,X1)
| X1 = sz00
| X0 = sz00 ),
inference(flattening,[],[f81]) ).
fof(f83,plain,
! [X0] :
( ~ aInteger0(X0)
| ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& X1 != sz00
& aInteger0(X1) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f84,plain,
! [X0,X1,X2] :
( sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f85,plain,
! [X0,X1,X2] :
( sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ) ),
inference(flattening,[],[f84]) ).
fof(f86,plain,
! [X0,X1] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdteqdtlpzmzozddtrp0(X0,X0,X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f87,plain,
! [X0,X1] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdteqdtlpzmzozddtrp0(X0,X0,X1) ),
inference(flattening,[],[f86]) ).
fof(f88,plain,
! [X0,X1,X2] :
( sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| sdteqdtlpzmzozddtrp0(X1,X0,X2) ),
inference(ennf_transformation,[],[f21]) ).
fof(f89,plain,
! [X0,X1,X2] :
( sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| sdteqdtlpzmzozddtrp0(X1,X0,X2) ),
inference(flattening,[],[f88]) ).
fof(f90,plain,
! [X0,X1,X2,X3] :
( ~ aInteger0(X3)
| sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X1,X3,X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| sdteqdtlpzmzozddtrp0(X0,X3,X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f91,plain,
! [X0,X1,X2,X3] :
( ~ aInteger0(X3)
| sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X1,X3,X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| sdteqdtlpzmzozddtrp0(X0,X3,X2) ),
inference(flattening,[],[f90]) ).
fof(f92,plain,
! [X0,X1,X2,X3] :
( sz00 = X3
| ~ aInteger0(X3)
| sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,sdtasdt0(X2,X3))
| ( sdteqdtlpzmzozddtrp0(X0,X1,X3)
& sdteqdtlpzmzozddtrp0(X0,X1,X2) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f93,plain,
! [X0,X1,X2,X3] :
( sz00 = X3
| ~ aInteger0(X3)
| sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,sdtasdt0(X2,X3))
| ( sdteqdtlpzmzozddtrp0(X0,X1,X3)
& sdteqdtlpzmzozddtrp0(X0,X1,X2) ) ),
inference(flattening,[],[f92]) ).
fof(f94,plain,
! [X0] :
( ~ aInteger0(X0)
| ( ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,X0) )
<=> ( X0 != smndt0(sz10)
& X0 != sz10 ) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f95,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f96,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395)
| ! [X2] :
( X2 = sdtbsmnsldt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( ( aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aInteger0(X3) ) )
& aSet0(X2) ) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f97,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395)
| ! [X2] :
( X2 = sdtbsmnsldt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( ( aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aInteger0(X3) ) )
& aSet0(X2) ) ) ),
inference(flattening,[],[f96]) ).
fof(f98,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395)
| ! [X2] :
( X2 = sdtslmnbsdt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,X1)
& aElementOf0(X3,X0)
& aInteger0(X3) ) )
& aSet0(X2) ) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f99,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395)
| ! [X2] :
( X2 = sdtslmnbsdt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,X1)
& aElementOf0(X3,X0)
& aInteger0(X3) ) )
& aSet0(X2) ) ) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0] :
( ? [X1] :
( aElementOf0(X1,X0)
& ~ aSubsetOf0(X1,cS1395) )
| ~ aSet0(X0)
| ! [X2] :
( sbsmnsldt0(X0) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( ? [X4] :
( aElementOf0(X3,X4)
& aElementOf0(X4,X0) )
& aInteger0(X3) ) )
& aSet0(X2) ) ) ),
inference(ennf_transformation,[],[f55]) ).
fof(f101,plain,
! [X0] :
( ? [X1] :
( aElementOf0(X1,X0)
& ~ aSubsetOf0(X1,cS1395) )
| ~ aSet0(X0)
| ! [X2] :
( sbsmnsldt0(X0) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( ? [X4] :
( aElementOf0(X3,X4)
& aElementOf0(X4,X0) )
& aInteger0(X3) ) )
& aSet0(X2) ) ) ),
inference(flattening,[],[f100]) ).
fof(f102,plain,
! [X0] :
( ~ aSubsetOf0(X0,cS1395)
| ! [X1] :
( X1 = stldt0(X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ( ~ aElementOf0(X2,X0)
& aInteger0(X2) ) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f103,plain,
! [X0,X1] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ! [X2] :
( X2 = szAzrzSzezqlpdtcmdtrp0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aInteger0(X3) ) )
& aSet0(X2) ) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f104,plain,
! [X0,X1] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ! [X2] :
( X2 = szAzrzSzezqlpdtcmdtrp0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aInteger0(X3) ) )
& aSet0(X2) ) ) ),
inference(flattening,[],[f103]) ).
fof(f105,plain,
! [X0] :
( ~ aSubsetOf0(X0,cS1395)
| ( isOpen0(X0)
<=> ! [X1] :
( ~ aElementOf0(X1,X0)
| ? [X2] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),X0)
& X2 != sz00
& aInteger0(X2) ) ) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f106,plain,
! [X0] :
( ~ aSubsetOf0(X0,cS1395)
| ( isClosed0(X0)
<=> isOpen0(stldt0(X0)) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f107,plain,
! [X0] :
( ? [X1] :
( aElementOf0(X1,X0)
& ( ~ isOpen0(X1)
| ~ aSubsetOf0(X1,cS1395) ) )
| ~ aSet0(X0)
| isOpen0(sbsmnsldt0(X0)) ),
inference(ennf_transformation,[],[f37]) ).
fof(f108,plain,
! [X0] :
( ? [X1] :
( aElementOf0(X1,X0)
& ( ~ isOpen0(X1)
| ~ aSubsetOf0(X1,cS1395) ) )
| ~ aSet0(X0)
| isOpen0(sbsmnsldt0(X0)) ),
inference(flattening,[],[f107]) ).
fof(f109,plain,
! [X0,X1] :
( ~ isOpen0(X1)
| ~ isOpen0(X0)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395)
| isOpen0(sdtslmnbsdt0(X0,X1)) ),
inference(ennf_transformation,[],[f38]) ).
fof(f110,plain,
! [X0,X1] :
( ~ isOpen0(X1)
| ~ isOpen0(X0)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395)
| isOpen0(sdtslmnbsdt0(X0,X1)) ),
inference(flattening,[],[f109]) ).
fof(f111,plain,
! [X0,X1] :
( ~ isClosed0(X1)
| ~ isClosed0(X0)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395)
| isClosed0(sdtbsmnsldt0(X0,X1)) ),
inference(ennf_transformation,[],[f39]) ).
fof(f112,plain,
! [X0,X1] :
( ~ isClosed0(X1)
| ~ isClosed0(X0)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395)
| isClosed0(sdtbsmnsldt0(X0,X1)) ),
inference(flattening,[],[f111]) ).
fof(f113,plain,
! [X0] :
( ? [X1] :
( aElementOf0(X1,X0)
& ( ~ isClosed0(X1)
| ~ aSubsetOf0(X1,cS1395) ) )
| ~ isFinite0(X0)
| ~ aSet0(X0)
| isClosed0(sbsmnsldt0(X0)) ),
inference(ennf_transformation,[],[f40]) ).
fof(f114,plain,
! [X0] :
( ? [X1] :
( aElementOf0(X1,X0)
& ( ~ isClosed0(X1)
| ~ aSubsetOf0(X1,cS1395) ) )
| ~ isFinite0(X0)
| ~ aSet0(X0)
| isClosed0(sbsmnsldt0(X0)) ),
inference(flattening,[],[f113]) ).
fof(f115,plain,
! [X0,X1] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ( isClosed0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),cS1395) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f116,plain,
! [X0,X1] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ( isClosed0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),cS1395) ) ),
inference(flattening,[],[f115]) ).
fof(f117,plain,
( xS = cS2043
& ! [X0] :
( ( ! [X5] :
( ( ! [X6] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& ~ aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ! [X8] :
( sdtpldt0(X6,smndt0(sz00)) != sdtasdt0(X5,X8)
| ~ aInteger0(X8) ) )
| ~ aInteger0(X6)
| aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5)) )
& ( ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
| ( sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ? [X7] :
( sdtasdt0(X5,X7) = sdtpldt0(X6,smndt0(sz00))
& aInteger0(X7) )
& aInteger0(X6) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5))
& szAzrzSzezqlpdtcmdtrp0(sz00,X5) != X0 )
| ~ isPrime0(X5)
| sz00 = X5
| ~ aInteger0(X5) )
| aElementOf0(X0,xS) )
& ( ~ aElementOf0(X0,xS)
| ? [X1] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0
& ! [X2] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X2,sz00,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ! [X4] :
( sdtpldt0(X2,smndt0(sz00)) != sdtasdt0(X1,X4)
| ~ aInteger0(X4) ) )
| ~ aInteger0(X2)
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
& ( ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
& isPrime0(X1)
& X1 != sz00
& aInteger0(X1) ) ) )
& aSet0(xS) ),
inference(ennf_transformation,[],[f56]) ).
fof(f118,plain,
( xS = cS2043
& ! [X0] :
( ( ! [X5] :
( ( ! [X6] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& ~ aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ! [X8] :
( sdtpldt0(X6,smndt0(sz00)) != sdtasdt0(X5,X8)
| ~ aInteger0(X8) ) )
| ~ aInteger0(X6)
| aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5)) )
& ( ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
| ( sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ? [X7] :
( sdtasdt0(X5,X7) = sdtpldt0(X6,smndt0(sz00))
& aInteger0(X7) )
& aInteger0(X6) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5))
& szAzrzSzezqlpdtcmdtrp0(sz00,X5) != X0 )
| ~ isPrime0(X5)
| sz00 = X5
| ~ aInteger0(X5) )
| aElementOf0(X0,xS) )
& ( ~ aElementOf0(X0,xS)
| ? [X1] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0
& ! [X2] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X2,sz00,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ! [X4] :
( sdtpldt0(X2,smndt0(sz00)) != sdtasdt0(X1,X4)
| ~ aInteger0(X4) ) )
| ~ aInteger0(X2)
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
& ( ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
& isPrime0(X1)
& X1 != sz00
& aInteger0(X1) ) ) )
& aSet0(xS) ),
inference(flattening,[],[f117]) ).
fof(f119,plain,
( ! [X12] :
( ~ aElementOf0(X12,stldt0(sbsmnsldt0(xS)))
| ? [X13] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X12,X13),stldt0(sbsmnsldt0(xS)))
& ! [X17] :
( ~ aElementOf0(X17,szAzrzSzezqlpdtcmdtrp0(X12,X13))
| aElementOf0(X17,stldt0(sbsmnsldt0(xS))) )
& ! [X14] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X14,X12,X13)
& ~ aDivisorOf0(X13,sdtpldt0(X14,smndt0(X12)))
& ! [X16] :
( sdtpldt0(X14,smndt0(X12)) != sdtasdt0(X13,X16)
| ~ aInteger0(X16) ) )
| ~ aInteger0(X14)
| aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(X12,X13)) )
& ( ~ aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(X12,X13))
| ( sdteqdtlpzmzozddtrp0(X14,X12,X13)
& aDivisorOf0(X13,sdtpldt0(X14,smndt0(X12)))
& ? [X15] :
( sdtasdt0(X13,X15) = sdtpldt0(X14,smndt0(X12))
& aInteger0(X15) )
& aInteger0(X14) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X12,X13))
& sz00 != X13
& aInteger0(X13) ) )
& ! [X11] :
( aElementOf0(X11,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X11,sbsmnsldt0(xS))
& aInteger0(X11) ) )
& ! [X9] :
( aElementOf0(X9,sbsmnsldt0(xS))
<=> ( ? [X10] :
( aElementOf0(X9,X10)
& aElementOf0(X10,xS) )
& aInteger0(X9) ) )
& aSet0(sbsmnsldt0(xS))
& isClosed0(sbsmnsldt0(xS))
& isOpen0(stldt0(sbsmnsldt0(xS)))
& ! [X3] :
( ~ aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
| ? [X4] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),stldt0(sbsmnsldt0(xS)))
& ! [X8] :
( ~ aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(X3,X4))
| aElementOf0(X8,stldt0(sbsmnsldt0(xS))) )
& ! [X5] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X5,X3,X4)
& ~ aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& ! [X7] :
( sdtpldt0(X5,smndt0(X3)) != sdtasdt0(X4,X7)
| ~ aInteger0(X7) ) )
| ~ aInteger0(X5)
| aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& ( ~ aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4))
| ( sdteqdtlpzmzozddtrp0(X5,X3,X4)
& aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& ? [X6] :
( sdtasdt0(X4,X6) = sdtpldt0(X5,smndt0(X3))
& aInteger0(X6) )
& aInteger0(X5) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X3,X4))
& sz00 != X4
& aInteger0(X4) ) )
& ! [X2] :
( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X2,sbsmnsldt0(xS))
& aInteger0(X2) ) )
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(ennf_transformation,[],[f58]) ).
fof(f120,plain,
( ! [X12] :
( ~ aElementOf0(X12,stldt0(sbsmnsldt0(xS)))
| ? [X13] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X12,X13),stldt0(sbsmnsldt0(xS)))
& ! [X17] :
( ~ aElementOf0(X17,szAzrzSzezqlpdtcmdtrp0(X12,X13))
| aElementOf0(X17,stldt0(sbsmnsldt0(xS))) )
& ! [X14] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X14,X12,X13)
& ~ aDivisorOf0(X13,sdtpldt0(X14,smndt0(X12)))
& ! [X16] :
( sdtpldt0(X14,smndt0(X12)) != sdtasdt0(X13,X16)
| ~ aInteger0(X16) ) )
| ~ aInteger0(X14)
| aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(X12,X13)) )
& ( ~ aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(X12,X13))
| ( sdteqdtlpzmzozddtrp0(X14,X12,X13)
& aDivisorOf0(X13,sdtpldt0(X14,smndt0(X12)))
& ? [X15] :
( sdtasdt0(X13,X15) = sdtpldt0(X14,smndt0(X12))
& aInteger0(X15) )
& aInteger0(X14) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X12,X13))
& sz00 != X13
& aInteger0(X13) ) )
& ! [X11] :
( aElementOf0(X11,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X11,sbsmnsldt0(xS))
& aInteger0(X11) ) )
& ! [X9] :
( aElementOf0(X9,sbsmnsldt0(xS))
<=> ( ? [X10] :
( aElementOf0(X9,X10)
& aElementOf0(X10,xS) )
& aInteger0(X9) ) )
& aSet0(sbsmnsldt0(xS))
& isClosed0(sbsmnsldt0(xS))
& isOpen0(stldt0(sbsmnsldt0(xS)))
& ! [X3] :
( ~ aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
| ? [X4] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),stldt0(sbsmnsldt0(xS)))
& ! [X8] :
( ~ aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(X3,X4))
| aElementOf0(X8,stldt0(sbsmnsldt0(xS))) )
& ! [X5] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X5,X3,X4)
& ~ aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& ! [X7] :
( sdtpldt0(X5,smndt0(X3)) != sdtasdt0(X4,X7)
| ~ aInteger0(X7) ) )
| ~ aInteger0(X5)
| aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& ( ~ aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4))
| ( sdteqdtlpzmzozddtrp0(X5,X3,X4)
& aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& ? [X6] :
( sdtasdt0(X4,X6) = sdtpldt0(X5,smndt0(X3))
& aInteger0(X6) )
& aInteger0(X5) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X3,X4))
& sz00 != X4
& aInteger0(X4) ) )
& ! [X2] :
( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X2,sbsmnsldt0(xS))
& aInteger0(X2) ) )
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(flattening,[],[f119]) ).
fof(f121,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [X6] :
( ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aElementOf0(X6,stldt0(sbsmnsldt0(xS))) )
& ! [X5] :
( aElementOf0(X5,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X5,sbsmnsldt0(xS))
& aInteger0(X5) ) )
& ! [X3] :
( aElementOf0(X3,sbsmnsldt0(xS))
<=> ( ? [X4] :
( aElementOf0(X3,X4)
& aElementOf0(X4,xS) )
& aInteger0(X3) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& ~ aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ! [X2] :
( sdtpldt0(X0,smndt0(sz10)) != sdtasdt0(xp,X2)
| ~ aInteger0(X2) ) )
| ~ aInteger0(X0)
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ( sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ? [X1] :
( sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10))
& aInteger0(X1) )
& aInteger0(X0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
inference(ennf_transformation,[],[f59]) ).
fof(f122,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [X6] :
( ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aElementOf0(X6,stldt0(sbsmnsldt0(xS))) )
& ! [X5] :
( aElementOf0(X5,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X5,sbsmnsldt0(xS))
& aInteger0(X5) ) )
& ! [X3] :
( aElementOf0(X3,sbsmnsldt0(xS))
<=> ( ? [X4] :
( aElementOf0(X3,X4)
& aElementOf0(X4,xS) )
& aInteger0(X3) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& ~ aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ! [X2] :
( sdtpldt0(X0,smndt0(sz10)) != sdtasdt0(xp,X2)
| ~ aInteger0(X2) ) )
| ~ aInteger0(X0)
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ( sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ? [X1] :
( sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10))
& aInteger0(X1) )
& aInteger0(X0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
inference(flattening,[],[f121]) ).
fof(f123,plain,
( sz10 = sdtpldt0(sz10,smndt0(xp))
| sz10 = sdtpldt0(sz10,xp) ),
inference(ennf_transformation,[],[f49]) ).
fof(f139,plain,
! [X0] :
( ~ aInteger0(X0)
| ! [X1] :
( ( ~ aDivisorOf0(X1,X0)
| ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& X1 != sz00
& aInteger0(X1) ) )
& ( ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1)
| aDivisorOf0(X1,X0) ) ) ),
inference(nnf_transformation,[],[f83]) ).
fof(f140,plain,
! [X0] :
( ~ aInteger0(X0)
| ! [X1] :
( ( ~ aDivisorOf0(X1,X0)
| ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& X1 != sz00
& aInteger0(X1) ) )
& ( ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1)
| aDivisorOf0(X1,X0) ) ) ),
inference(flattening,[],[f139]) ).
fof(f141,plain,
! [X0] :
( ~ aInteger0(X0)
| ! [X1] :
( ( ~ aDivisorOf0(X1,X0)
| ( ? [X3] :
( sdtasdt0(X1,X3) = X0
& aInteger0(X3) )
& X1 != sz00
& aInteger0(X1) ) )
& ( ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1)
| aDivisorOf0(X1,X0) ) ) ),
inference(rectify,[],[f140]) ).
fof(f142,plain,
! [X0] :
( ~ aInteger0(X0)
| ! [X1] :
( ( ~ aDivisorOf0(X1,X0)
| ( sdtasdt0(X1,sK10(X0,X1)) = X0
& aInteger0(sK10(X0,X1))
& X1 != sz00
& aInteger0(X1) ) )
& ( ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1)
| aDivisorOf0(X1,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X3,sK10(X0,X1))],[f141]) ).
fof(f143,plain,
! [X0,X1,X2] :
( sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ( ( ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
& ( ~ aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
| sdteqdtlpzmzozddtrp0(X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f85]) ).
fof(f144,plain,
! [X0] :
( ~ aInteger0(X0)
| ( ( ! [X1] :
( ~ isPrime0(X1)
| ~ aDivisorOf0(X1,X0) )
| ( X0 != smndt0(sz10)
& X0 != sz10 ) )
& ( smndt0(sz10) = X0
| sz10 = X0
| ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,X0) ) ) ) ),
inference(nnf_transformation,[],[f94]) ).
fof(f145,plain,
! [X0] :
( ~ aInteger0(X0)
| ( ( ! [X1] :
( ~ isPrime0(X1)
| ~ aDivisorOf0(X1,X0) )
| ( X0 != smndt0(sz10)
& X0 != sz10 ) )
& ( smndt0(sz10) = X0
| sz10 = X0
| ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,X0) ) ) ) ),
inference(flattening,[],[f144]) ).
fof(f146,plain,
! [X0] :
( ~ aInteger0(X0)
| ( ( ! [X2] :
( ~ isPrime0(X2)
| ~ aDivisorOf0(X2,X0) )
| ( X0 != smndt0(sz10)
& X0 != sz10 ) )
& ( smndt0(sz10) = X0
| sz10 = X0
| ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,X0) ) ) ) ),
inference(rectify,[],[f145]) ).
fof(f147,plain,
! [X0] :
( ~ aInteger0(X0)
| ( ( ! [X2] :
( ~ isPrime0(X2)
| ~ aDivisorOf0(X2,X0) )
| ( X0 != smndt0(sz10)
& X0 != sz10 ) )
& ( smndt0(sz10) = X0
| sz10 = X0
| ( isPrime0(sK11(X0))
& aDivisorOf0(sK11(X0),X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X1,sK11(X0))],[f146]) ).
fof(f148,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(nnf_transformation,[],[f95]) ).
fof(f149,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(flattening,[],[f148]) ).
fof(f150,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X3] :
( ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(rectify,[],[f149]) ).
fof(f151,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X3] :
( ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aSet0(X1) ) )
& ( ( aElementOf0(sK12(X0,X1),X1)
& ~ aElementOf0(sK12(X0,X1),X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X2,sK12(X0,X1))],[f150]) ).
fof(f152,plain,
! [X1,X0] :
( ~ sP1(X1,X0)
| ! [X2] :
( ( sdtbsmnsldt0(X0,X1) != X2
| sP0(X2,X0,X1) )
& ( ~ sP0(X2,X0,X1)
| X2 = sdtbsmnsldt0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f125]) ).
fof(f153,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| ! [X2] :
( ( sdtbsmnsldt0(X1,X0) != X2
| sP0(X2,X1,X0) )
& ( ~ sP0(X2,X1,X0)
| sdtbsmnsldt0(X1,X0) = X2 ) ) ),
inference(rectify,[],[f152]) ).
fof(f158,plain,
! [X1,X0] :
( ~ sP3(X1,X0)
| ! [X2] :
( ( sdtslmnbsdt0(X0,X1) != X2
| sP2(X2,X0,X1) )
& ( ~ sP2(X2,X0,X1)
| X2 = sdtslmnbsdt0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f128]) ).
fof(f159,plain,
! [X0,X1] :
( ~ sP3(X0,X1)
| ! [X2] :
( ( sdtslmnbsdt0(X1,X0) != X2
| sP2(X2,X1,X0) )
& ( ~ sP2(X2,X1,X0)
| sdtslmnbsdt0(X1,X0) = X2 ) ) ),
inference(rectify,[],[f158]) ).
fof(f164,plain,
! [X0] :
( ~ sP5(X0)
| ! [X2] :
( ( sbsmnsldt0(X0) != X2
| sP4(X2,X0) )
& ( ~ sP4(X2,X0)
| sbsmnsldt0(X0) = X2 ) ) ),
inference(nnf_transformation,[],[f131]) ).
fof(f165,plain,
! [X0] :
( ~ sP5(X0)
| ! [X1] :
( ( sbsmnsldt0(X0) != X1
| sP4(X1,X0) )
& ( ~ sP4(X1,X0)
| sbsmnsldt0(X0) = X1 ) ) ),
inference(rectify,[],[f164]) ).
fof(f170,plain,
! [X0] :
( ( aElementOf0(sK18(X0),X0)
& ~ aSubsetOf0(sK18(X0),cS1395) )
| ~ aSet0(X0)
| sP5(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(X1,sK18(X0))],[f132]) ).
fof(f171,plain,
! [X0] :
( ~ aSubsetOf0(X0,cS1395)
| ! [X1] :
( ( stldt0(X0) != X1
| ( ! [X2] :
( ( ~ aElementOf0(X2,X1)
| ( ~ aElementOf0(X2,X0)
& aInteger0(X2) ) )
& ( aElementOf0(X2,X0)
| ~ aInteger0(X2)
| aElementOf0(X2,X1) ) )
& aSet0(X1) ) )
& ( ? [X2] :
( ( aElementOf0(X2,X1)
| ( ~ aElementOf0(X2,X0)
& aInteger0(X2) ) )
& ( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0)
| ~ aInteger0(X2) ) )
| ~ aSet0(X1)
| X1 = stldt0(X0) ) ) ),
inference(nnf_transformation,[],[f102]) ).
fof(f172,plain,
! [X0] :
( ~ aSubsetOf0(X0,cS1395)
| ! [X1] :
( ( stldt0(X0) != X1
| ( ! [X2] :
( ( ~ aElementOf0(X2,X1)
| ( ~ aElementOf0(X2,X0)
& aInteger0(X2) ) )
& ( aElementOf0(X2,X0)
| ~ aInteger0(X2)
| aElementOf0(X2,X1) ) )
& aSet0(X1) ) )
& ( ? [X2] :
( ( aElementOf0(X2,X1)
| ( ~ aElementOf0(X2,X0)
& aInteger0(X2) ) )
& ( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0)
| ~ aInteger0(X2) ) )
| ~ aSet0(X1)
| X1 = stldt0(X0) ) ) ),
inference(flattening,[],[f171]) ).
fof(f173,plain,
! [X0] :
( ~ aSubsetOf0(X0,cS1395)
| ! [X1] :
( ( stldt0(X0) != X1
| ( ! [X3] :
( ( ~ aElementOf0(X3,X1)
| ( ~ aElementOf0(X3,X0)
& aInteger0(X3) ) )
& ( aElementOf0(X3,X0)
| ~ aInteger0(X3)
| aElementOf0(X3,X1) ) )
& aSet0(X1) ) )
& ( ? [X2] :
( ( aElementOf0(X2,X1)
| ( ~ aElementOf0(X2,X0)
& aInteger0(X2) ) )
& ( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0)
| ~ aInteger0(X2) ) )
| ~ aSet0(X1)
| X1 = stldt0(X0) ) ) ),
inference(rectify,[],[f172]) ).
fof(f174,plain,
! [X0] :
( ~ aSubsetOf0(X0,cS1395)
| ! [X1] :
( ( stldt0(X0) != X1
| ( ! [X3] :
( ( ~ aElementOf0(X3,X1)
| ( ~ aElementOf0(X3,X0)
& aInteger0(X3) ) )
& ( aElementOf0(X3,X0)
| ~ aInteger0(X3)
| aElementOf0(X3,X1) ) )
& aSet0(X1) ) )
& ( ( ( aElementOf0(sK19(X0,X1),X1)
| ( ~ aElementOf0(sK19(X0,X1),X0)
& aInteger0(sK19(X0,X1)) ) )
& ( ~ aElementOf0(sK19(X0,X1),X1)
| aElementOf0(sK19(X0,X1),X0)
| ~ aInteger0(sK19(X0,X1)) ) )
| ~ aSet0(X1)
| X1 = stldt0(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X2,sK19(X0,X1))],[f173]) ).
fof(f175,plain,
! [X0,X1] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ! [X2] :
( ( szAzrzSzezqlpdtcmdtrp0(X0,X1) != X2
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aInteger0(X3) ) )
& ( ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
| ~ aInteger0(X3)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aInteger0(X3) ) )
& ( ~ aElementOf0(X3,X2)
| ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
| ~ aInteger0(X3) ) )
| ~ aSet0(X2)
| X2 = szAzrzSzezqlpdtcmdtrp0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f104]) ).
fof(f176,plain,
! [X0,X1] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ! [X2] :
( ( szAzrzSzezqlpdtcmdtrp0(X0,X1) != X2
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aInteger0(X3) ) )
& ( ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
| ~ aInteger0(X3)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aInteger0(X3) ) )
& ( ~ aElementOf0(X3,X2)
| ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
| ~ aInteger0(X3) ) )
| ~ aSet0(X2)
| X2 = szAzrzSzezqlpdtcmdtrp0(X0,X1) ) ) ),
inference(flattening,[],[f175]) ).
fof(f177,plain,
! [X0,X1] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ! [X2] :
( ( szAzrzSzezqlpdtcmdtrp0(X0,X1) != X2
| ( ! [X4] :
( ( ~ aElementOf0(X4,X2)
| ( sdteqdtlpzmzozddtrp0(X4,X0,X1)
& aInteger0(X4) ) )
& ( ~ sdteqdtlpzmzozddtrp0(X4,X0,X1)
| ~ aInteger0(X4)
| aElementOf0(X4,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aInteger0(X3) ) )
& ( ~ aElementOf0(X3,X2)
| ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
| ~ aInteger0(X3) ) )
| ~ aSet0(X2)
| X2 = szAzrzSzezqlpdtcmdtrp0(X0,X1) ) ) ),
inference(rectify,[],[f176]) ).
fof(f178,plain,
! [X0,X1] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ! [X2] :
( ( szAzrzSzezqlpdtcmdtrp0(X0,X1) != X2
| ( ! [X4] :
( ( ~ aElementOf0(X4,X2)
| ( sdteqdtlpzmzozddtrp0(X4,X0,X1)
& aInteger0(X4) ) )
& ( ~ sdteqdtlpzmzozddtrp0(X4,X0,X1)
| ~ aInteger0(X4)
| aElementOf0(X4,X2) ) )
& aSet0(X2) ) )
& ( ( ( aElementOf0(sK20(X0,X1,X2),X2)
| ( sdteqdtlpzmzozddtrp0(sK20(X0,X1,X2),X0,X1)
& aInteger0(sK20(X0,X1,X2)) ) )
& ( ~ aElementOf0(sK20(X0,X1,X2),X2)
| ~ sdteqdtlpzmzozddtrp0(sK20(X0,X1,X2),X0,X1)
| ~ aInteger0(sK20(X0,X1,X2)) ) )
| ~ aSet0(X2)
| X2 = szAzrzSzezqlpdtcmdtrp0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X3,sK20(X0,X1,X2))],[f177]) ).
fof(f179,plain,
! [X0] :
( ~ aSubsetOf0(X0,cS1395)
| ( ( ~ isOpen0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| ? [X2] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),X0)
& X2 != sz00
& aInteger0(X2) ) ) )
& ( ? [X1] :
( aElementOf0(X1,X0)
& ! [X2] :
( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),X0)
| sz00 = X2
| ~ aInteger0(X2) ) )
| isOpen0(X0) ) ) ),
inference(nnf_transformation,[],[f105]) ).
fof(f180,plain,
! [X0] :
( ~ aSubsetOf0(X0,cS1395)
| ( ( ~ isOpen0(X0)
| ! [X3] :
( ~ aElementOf0(X3,X0)
| ? [X4] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),X0)
& sz00 != X4
& aInteger0(X4) ) ) )
& ( ? [X1] :
( aElementOf0(X1,X0)
& ! [X2] :
( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),X0)
| sz00 = X2
| ~ aInteger0(X2) ) )
| isOpen0(X0) ) ) ),
inference(rectify,[],[f179]) ).
fof(f181,plain,
! [X0] :
( ~ aSubsetOf0(X0,cS1395)
| ( ( ~ isOpen0(X0)
| ! [X3] :
( ~ aElementOf0(X3,X0)
| ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,sK22(X0,X3)),X0)
& sz00 != sK22(X0,X3)
& aInteger0(sK22(X0,X3)) ) ) )
& ( ( aElementOf0(sK21(X0),X0)
& ! [X2] :
( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sK21(X0),X2),X0)
| sz00 = X2
| ~ aInteger0(X2) ) )
| isOpen0(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21,sK22]),skolemize(X1,sK21(X0)),skolemize(X4,sK22(X0,X3))],[f180]) ).
fof(f182,plain,
! [X0] :
( ~ aSubsetOf0(X0,cS1395)
| ( ( ~ isClosed0(X0)
| isOpen0(stldt0(X0)) )
& ( ~ isOpen0(stldt0(X0))
| isClosed0(X0) ) ) ),
inference(nnf_transformation,[],[f106]) ).
fof(f183,plain,
! [X0] :
( ( aElementOf0(sK23(X0),X0)
& ( ~ isOpen0(sK23(X0))
| ~ aSubsetOf0(sK23(X0),cS1395) ) )
| ~ aSet0(X0)
| isOpen0(sbsmnsldt0(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(X1,sK23(X0))],[f108]) ).
fof(f184,plain,
! [X0] :
( ( aElementOf0(sK24(X0),X0)
& ( ~ isClosed0(sK24(X0))
| ~ aSubsetOf0(sK24(X0),cS1395) ) )
| ~ isFinite0(X0)
| ~ aSet0(X0)
| isClosed0(sbsmnsldt0(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(X1,sK24(X0))],[f114]) ).
fof(f185,plain,
! [X1] :
( ~ sP7(X1)
| ! [X2] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X2,sz00,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ! [X4] :
( sdtpldt0(X2,smndt0(sz00)) != sdtasdt0(X1,X4)
| ~ aInteger0(X4) ) )
| ~ aInteger0(X2)
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
& ( ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00))
& aInteger0(X3) )
& aInteger0(X2) ) ) ) ),
inference(nnf_transformation,[],[f134]) ).
fof(f186,plain,
! [X0] :
( ~ sP7(X0)
| ! [X1] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X1,sz00,X0)
& ~ aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
& ! [X3] :
( sdtpldt0(X1,smndt0(sz00)) != sdtasdt0(X0,X3)
| ~ aInteger0(X3) ) )
| ~ aInteger0(X1)
| aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0)) )
& ( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| ( sdteqdtlpzmzozddtrp0(X1,sz00,X0)
& aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
& ? [X2] :
( sdtasdt0(X0,X2) = sdtpldt0(X1,smndt0(sz00))
& aInteger0(X2) )
& aInteger0(X1) ) ) ) ),
inference(rectify,[],[f185]) ).
fof(f187,plain,
! [X0] :
( ~ sP7(X0)
| ! [X1] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X1,sz00,X0)
& ~ aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
& ! [X3] :
( sdtpldt0(X1,smndt0(sz00)) != sdtasdt0(X0,X3)
| ~ aInteger0(X3) ) )
| ~ aInteger0(X1)
| aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0)) )
& ( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| ( sdteqdtlpzmzozddtrp0(X1,sz00,X0)
& aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
& sdtpldt0(X1,smndt0(sz00)) = sdtasdt0(X0,sK25(X0,X1))
& aInteger0(sK25(X0,X1))
& aInteger0(X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(X2,sK25(X0,X1))],[f186]) ).
fof(f191,plain,
( xS = cS2043
& ! [X0] :
( ( ! [X2] :
( ( sP6(X2)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
& szAzrzSzezqlpdtcmdtrp0(sz00,X2) != X0 )
| ~ isPrime0(X2)
| sz00 = X2
| ~ aInteger0(X2) )
| aElementOf0(X0,xS) )
& ( ~ aElementOf0(X0,xS)
| ? [X1] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0
& sP7(X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
& isPrime0(X1)
& X1 != sz00
& aInteger0(X1) ) ) )
& aSet0(xS) ),
inference(rectify,[],[f135]) ).
fof(f192,plain,
( xS = cS2043
& ! [X0] :
( ( ! [X2] :
( ( sP6(X2)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
& szAzrzSzezqlpdtcmdtrp0(sz00,X2) != X0 )
| ~ isPrime0(X2)
| sz00 = X2
| ~ aInteger0(X2) )
| aElementOf0(X0,xS) )
& ( ~ aElementOf0(X0,xS)
| ( szAzrzSzezqlpdtcmdtrp0(sz00,sK27(X0)) = X0
& sP7(sK27(X0))
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,sK27(X0)))
& isPrime0(sK27(X0))
& sz00 != sK27(X0)
& aInteger0(sK27(X0)) ) ) )
& aSet0(xS) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(X1,sK27(X0))],[f191]) ).
fof(f193,plain,
( stldt0(sbsmnsldt0(xS)) = cS2076
& ! [X3] :
( ( ~ aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
| smndt0(sz10) = X3
| sz10 = X3 )
& ( ( smndt0(sz10) != X3
& sz10 != X3 )
| aElementOf0(X3,stldt0(sbsmnsldt0(xS))) ) )
& ! [X2] :
( ( ~ aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
| ( ~ aElementOf0(X2,sbsmnsldt0(xS))
& aInteger0(X2) ) )
& ( aElementOf0(X2,sbsmnsldt0(xS))
| ~ aInteger0(X2)
| aElementOf0(X2,stldt0(sbsmnsldt0(xS))) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X0] :
( ( ~ aElementOf0(X0,sbsmnsldt0(xS))
| ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) ) )
& ( ! [X1] :
( ~ aElementOf0(X0,X1)
| ~ aElementOf0(X1,xS) )
| ~ aInteger0(X0)
| aElementOf0(X0,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(nnf_transformation,[],[f57]) ).
fof(f194,plain,
( stldt0(sbsmnsldt0(xS)) = cS2076
& ! [X3] :
( ( ~ aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
| smndt0(sz10) = X3
| sz10 = X3 )
& ( ( smndt0(sz10) != X3
& sz10 != X3 )
| aElementOf0(X3,stldt0(sbsmnsldt0(xS))) ) )
& ! [X2] :
( ( ~ aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
| ( ~ aElementOf0(X2,sbsmnsldt0(xS))
& aInteger0(X2) ) )
& ( aElementOf0(X2,sbsmnsldt0(xS))
| ~ aInteger0(X2)
| aElementOf0(X2,stldt0(sbsmnsldt0(xS))) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X0] :
( ( ~ aElementOf0(X0,sbsmnsldt0(xS))
| ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) ) )
& ( ! [X1] :
( ~ aElementOf0(X0,X1)
| ~ aElementOf0(X1,xS) )
| ~ aInteger0(X0)
| aElementOf0(X0,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(flattening,[],[f193]) ).
fof(f195,plain,
( stldt0(sbsmnsldt0(xS)) = cS2076
& ! [X4] :
( ( ~ aElementOf0(X4,stldt0(sbsmnsldt0(xS)))
| smndt0(sz10) = X4
| sz10 = X4 )
& ( ( smndt0(sz10) != X4
& sz10 != X4 )
| aElementOf0(X4,stldt0(sbsmnsldt0(xS))) ) )
& ! [X3] :
( ( ~ aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
| ( ~ aElementOf0(X3,sbsmnsldt0(xS))
& aInteger0(X3) ) )
& ( aElementOf0(X3,sbsmnsldt0(xS))
| ~ aInteger0(X3)
| aElementOf0(X3,stldt0(sbsmnsldt0(xS))) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X0] :
( ( ~ aElementOf0(X0,sbsmnsldt0(xS))
| ( ? [X2] :
( aElementOf0(X0,X2)
& aElementOf0(X2,xS) )
& aInteger0(X0) ) )
& ( ! [X1] :
( ~ aElementOf0(X0,X1)
| ~ aElementOf0(X1,xS) )
| ~ aInteger0(X0)
| aElementOf0(X0,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(rectify,[],[f194]) ).
fof(f196,plain,
( stldt0(sbsmnsldt0(xS)) = cS2076
& ! [X4] :
( ( ~ aElementOf0(X4,stldt0(sbsmnsldt0(xS)))
| smndt0(sz10) = X4
| sz10 = X4 )
& ( ( smndt0(sz10) != X4
& sz10 != X4 )
| aElementOf0(X4,stldt0(sbsmnsldt0(xS))) ) )
& ! [X3] :
( ( ~ aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
| ( ~ aElementOf0(X3,sbsmnsldt0(xS))
& aInteger0(X3) ) )
& ( aElementOf0(X3,sbsmnsldt0(xS))
| ~ aInteger0(X3)
| aElementOf0(X3,stldt0(sbsmnsldt0(xS))) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X0] :
( ( ~ aElementOf0(X0,sbsmnsldt0(xS))
| ( aElementOf0(X0,sK28(X0))
& aElementOf0(sK28(X0),xS)
& aInteger0(X0) ) )
& ( ! [X1] :
( ~ aElementOf0(X0,X1)
| ~ aElementOf0(X1,xS) )
| ~ aInteger0(X0)
| aElementOf0(X0,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(X2,sK28(X0))],[f195]) ).
fof(f197,plain,
! [X3,X4] :
( ~ sP9(X3,X4)
| ! [X5] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X5,X3,X4)
& ~ aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& ! [X7] :
( sdtpldt0(X5,smndt0(X3)) != sdtasdt0(X4,X7)
| ~ aInteger0(X7) ) )
| ~ aInteger0(X5)
| aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& ( ~ aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4))
| ( sdteqdtlpzmzozddtrp0(X5,X3,X4)
& aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& ? [X6] :
( sdtasdt0(X4,X6) = sdtpldt0(X5,smndt0(X3))
& aInteger0(X6) )
& aInteger0(X5) ) ) ) ),
inference(nnf_transformation,[],[f137]) ).
fof(f198,plain,
! [X0,X1] :
( ~ sP9(X0,X1)
| ! [X2] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X2,X0,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& ! [X4] :
( sdtpldt0(X2,smndt0(X0)) != sdtasdt0(X1,X4)
| ~ aInteger0(X4) ) )
| ~ aInteger0(X2)
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ( ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) )
& aInteger0(X2) ) ) ) ),
inference(rectify,[],[f197]) ).
fof(f199,plain,
! [X0,X1] :
( ~ sP9(X0,X1)
| ! [X2] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X2,X0,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& ! [X4] :
( sdtpldt0(X2,smndt0(X0)) != sdtasdt0(X1,X4)
| ~ aInteger0(X4) ) )
| ~ aInteger0(X2)
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ( ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& sdtpldt0(X2,smndt0(X0)) = sdtasdt0(X1,sK29(X0,X1,X2))
& aInteger0(sK29(X0,X1,X2))
& aInteger0(X2) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(X3,sK29(X0,X1,X2))],[f198]) ).
fof(f203,plain,
( ! [X12] :
( ~ aElementOf0(X12,stldt0(sbsmnsldt0(xS)))
| ? [X13] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X12,X13),stldt0(sbsmnsldt0(xS)))
& ! [X17] :
( ~ aElementOf0(X17,szAzrzSzezqlpdtcmdtrp0(X12,X13))
| aElementOf0(X17,stldt0(sbsmnsldt0(xS))) )
& sP8(X12,X13)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X12,X13))
& sz00 != X13
& aInteger0(X13) ) )
& ! [X11] :
( ( ~ aElementOf0(X11,stldt0(sbsmnsldt0(xS)))
| ( ~ aElementOf0(X11,sbsmnsldt0(xS))
& aInteger0(X11) ) )
& ( aElementOf0(X11,sbsmnsldt0(xS))
| ~ aInteger0(X11)
| aElementOf0(X11,stldt0(sbsmnsldt0(xS))) ) )
& ! [X9] :
( ( ~ aElementOf0(X9,sbsmnsldt0(xS))
| ( ? [X10] :
( aElementOf0(X9,X10)
& aElementOf0(X10,xS) )
& aInteger0(X9) ) )
& ( ! [X10] :
( ~ aElementOf0(X9,X10)
| ~ aElementOf0(X10,xS) )
| ~ aInteger0(X9)
| aElementOf0(X9,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS))
& isClosed0(sbsmnsldt0(xS))
& isOpen0(stldt0(sbsmnsldt0(xS)))
& ! [X3] :
( ~ aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
| ? [X4] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),stldt0(sbsmnsldt0(xS)))
& ! [X8] :
( ~ aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(X3,X4))
| aElementOf0(X8,stldt0(sbsmnsldt0(xS))) )
& sP9(X3,X4)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X3,X4))
& sz00 != X4
& aInteger0(X4) ) )
& ! [X2] :
( ( ~ aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
| ( ~ aElementOf0(X2,sbsmnsldt0(xS))
& aInteger0(X2) ) )
& ( aElementOf0(X2,sbsmnsldt0(xS))
| ~ aInteger0(X2)
| aElementOf0(X2,stldt0(sbsmnsldt0(xS))) ) )
& ! [X0] :
( ( ~ aElementOf0(X0,sbsmnsldt0(xS))
| ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) ) )
& ( ! [X1] :
( ~ aElementOf0(X0,X1)
| ~ aElementOf0(X1,xS) )
| ~ aInteger0(X0)
| aElementOf0(X0,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(nnf_transformation,[],[f138]) ).
fof(f204,plain,
( ! [X12] :
( ~ aElementOf0(X12,stldt0(sbsmnsldt0(xS)))
| ? [X13] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X12,X13),stldt0(sbsmnsldt0(xS)))
& ! [X17] :
( ~ aElementOf0(X17,szAzrzSzezqlpdtcmdtrp0(X12,X13))
| aElementOf0(X17,stldt0(sbsmnsldt0(xS))) )
& sP8(X12,X13)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X12,X13))
& sz00 != X13
& aInteger0(X13) ) )
& ! [X11] :
( ( ~ aElementOf0(X11,stldt0(sbsmnsldt0(xS)))
| ( ~ aElementOf0(X11,sbsmnsldt0(xS))
& aInteger0(X11) ) )
& ( aElementOf0(X11,sbsmnsldt0(xS))
| ~ aInteger0(X11)
| aElementOf0(X11,stldt0(sbsmnsldt0(xS))) ) )
& ! [X9] :
( ( ~ aElementOf0(X9,sbsmnsldt0(xS))
| ( ? [X10] :
( aElementOf0(X9,X10)
& aElementOf0(X10,xS) )
& aInteger0(X9) ) )
& ( ! [X10] :
( ~ aElementOf0(X9,X10)
| ~ aElementOf0(X10,xS) )
| ~ aInteger0(X9)
| aElementOf0(X9,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS))
& isClosed0(sbsmnsldt0(xS))
& isOpen0(stldt0(sbsmnsldt0(xS)))
& ! [X3] :
( ~ aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
| ? [X4] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),stldt0(sbsmnsldt0(xS)))
& ! [X8] :
( ~ aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(X3,X4))
| aElementOf0(X8,stldt0(sbsmnsldt0(xS))) )
& sP9(X3,X4)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X3,X4))
& sz00 != X4
& aInteger0(X4) ) )
& ! [X2] :
( ( ~ aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
| ( ~ aElementOf0(X2,sbsmnsldt0(xS))
& aInteger0(X2) ) )
& ( aElementOf0(X2,sbsmnsldt0(xS))
| ~ aInteger0(X2)
| aElementOf0(X2,stldt0(sbsmnsldt0(xS))) ) )
& ! [X0] :
( ( ~ aElementOf0(X0,sbsmnsldt0(xS))
| ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) ) )
& ( ! [X1] :
( ~ aElementOf0(X0,X1)
| ~ aElementOf0(X1,xS) )
| ~ aInteger0(X0)
| aElementOf0(X0,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(flattening,[],[f203]) ).
fof(f205,plain,
( ! [X11] :
( ~ aElementOf0(X11,stldt0(sbsmnsldt0(xS)))
| ? [X12] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X11,X12),stldt0(sbsmnsldt0(xS)))
& ! [X13] :
( ~ aElementOf0(X13,szAzrzSzezqlpdtcmdtrp0(X11,X12))
| aElementOf0(X13,stldt0(sbsmnsldt0(xS))) )
& sP8(X11,X12)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X11,X12))
& sz00 != X12
& aInteger0(X12) ) )
& ! [X10] :
( ( ~ aElementOf0(X10,stldt0(sbsmnsldt0(xS)))
| ( ~ aElementOf0(X10,sbsmnsldt0(xS))
& aInteger0(X10) ) )
& ( aElementOf0(X10,sbsmnsldt0(xS))
| ~ aInteger0(X10)
| aElementOf0(X10,stldt0(sbsmnsldt0(xS))) ) )
& ! [X7] :
( ( ~ aElementOf0(X7,sbsmnsldt0(xS))
| ( ? [X9] :
( aElementOf0(X7,X9)
& aElementOf0(X9,xS) )
& aInteger0(X7) ) )
& ( ! [X8] :
( ~ aElementOf0(X7,X8)
| ~ aElementOf0(X8,xS) )
| ~ aInteger0(X7)
| aElementOf0(X7,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS))
& isClosed0(sbsmnsldt0(xS))
& isOpen0(stldt0(sbsmnsldt0(xS)))
& ! [X4] :
( ~ aElementOf0(X4,stldt0(sbsmnsldt0(xS)))
| ? [X5] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X4,X5),stldt0(sbsmnsldt0(xS)))
& ! [X6] :
( ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(X4,X5))
| aElementOf0(X6,stldt0(sbsmnsldt0(xS))) )
& sP9(X4,X5)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X4,X5))
& sz00 != X5
& aInteger0(X5) ) )
& ! [X3] :
( ( ~ aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
| ( ~ aElementOf0(X3,sbsmnsldt0(xS))
& aInteger0(X3) ) )
& ( aElementOf0(X3,sbsmnsldt0(xS))
| ~ aInteger0(X3)
| aElementOf0(X3,stldt0(sbsmnsldt0(xS))) ) )
& ! [X0] :
( ( ~ aElementOf0(X0,sbsmnsldt0(xS))
| ( ? [X2] :
( aElementOf0(X0,X2)
& aElementOf0(X2,xS) )
& aInteger0(X0) ) )
& ( ! [X1] :
( ~ aElementOf0(X0,X1)
| ~ aElementOf0(X1,xS) )
| ~ aInteger0(X0)
| aElementOf0(X0,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(rectify,[],[f204]) ).
fof(f206,plain,
( ! [X11] :
( ~ aElementOf0(X11,stldt0(sbsmnsldt0(xS)))
| ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X11,sK34(X11)),stldt0(sbsmnsldt0(xS)))
& ! [X13] :
( ~ aElementOf0(X13,szAzrzSzezqlpdtcmdtrp0(X11,sK34(X11)))
| aElementOf0(X13,stldt0(sbsmnsldt0(xS))) )
& sP8(X11,sK34(X11))
& aSet0(szAzrzSzezqlpdtcmdtrp0(X11,sK34(X11)))
& sz00 != sK34(X11)
& aInteger0(sK34(X11)) ) )
& ! [X10] :
( ( ~ aElementOf0(X10,stldt0(sbsmnsldt0(xS)))
| ( ~ aElementOf0(X10,sbsmnsldt0(xS))
& aInteger0(X10) ) )
& ( aElementOf0(X10,sbsmnsldt0(xS))
| ~ aInteger0(X10)
| aElementOf0(X10,stldt0(sbsmnsldt0(xS))) ) )
& ! [X7] :
( ( ~ aElementOf0(X7,sbsmnsldt0(xS))
| ( aElementOf0(X7,sK33(X7))
& aElementOf0(sK33(X7),xS)
& aInteger0(X7) ) )
& ( ! [X8] :
( ~ aElementOf0(X7,X8)
| ~ aElementOf0(X8,xS) )
| ~ aInteger0(X7)
| aElementOf0(X7,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS))
& isClosed0(sbsmnsldt0(xS))
& isOpen0(stldt0(sbsmnsldt0(xS)))
& ! [X4] :
( ~ aElementOf0(X4,stldt0(sbsmnsldt0(xS)))
| ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X4,sK32(X4)),stldt0(sbsmnsldt0(xS)))
& ! [X6] :
( ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(X4,sK32(X4)))
| aElementOf0(X6,stldt0(sbsmnsldt0(xS))) )
& sP9(X4,sK32(X4))
& aSet0(szAzrzSzezqlpdtcmdtrp0(X4,sK32(X4)))
& sz00 != sK32(X4)
& aInteger0(sK32(X4)) ) )
& ! [X3] :
( ( ~ aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
| ( ~ aElementOf0(X3,sbsmnsldt0(xS))
& aInteger0(X3) ) )
& ( aElementOf0(X3,sbsmnsldt0(xS))
| ~ aInteger0(X3)
| aElementOf0(X3,stldt0(sbsmnsldt0(xS))) ) )
& ! [X0] :
( ( ~ aElementOf0(X0,sbsmnsldt0(xS))
| ( aElementOf0(X0,sK31(X0))
& aElementOf0(sK31(X0),xS)
& aInteger0(X0) ) )
& ( ! [X1] :
( ~ aElementOf0(X0,X1)
| ~ aElementOf0(X1,xS) )
| ~ aInteger0(X0)
| aElementOf0(X0,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31,sK32,sK33,sK34]),skolemize(X2,sK31(X0)),skolemize(X5,sK32(X4)),skolemize(X9,sK33(X7)),skolemize(X12,sK34(X11))],[f205]) ).
fof(f207,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [X6] :
( ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aElementOf0(X6,stldt0(sbsmnsldt0(xS))) )
& ! [X5] :
( ( ~ aElementOf0(X5,stldt0(sbsmnsldt0(xS)))
| ( ~ aElementOf0(X5,sbsmnsldt0(xS))
& aInteger0(X5) ) )
& ( aElementOf0(X5,sbsmnsldt0(xS))
| ~ aInteger0(X5)
| aElementOf0(X5,stldt0(sbsmnsldt0(xS))) ) )
& ! [X3] :
( ( ~ aElementOf0(X3,sbsmnsldt0(xS))
| ( ? [X4] :
( aElementOf0(X3,X4)
& aElementOf0(X4,xS) )
& aInteger0(X3) ) )
& ( ! [X4] :
( ~ aElementOf0(X3,X4)
| ~ aElementOf0(X4,xS) )
| ~ aInteger0(X3)
| aElementOf0(X3,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& ~ aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ! [X2] :
( sdtpldt0(X0,smndt0(sz10)) != sdtasdt0(xp,X2)
| ~ aInteger0(X2) ) )
| ~ aInteger0(X0)
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ( sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ? [X1] :
( sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10))
& aInteger0(X1) )
& aInteger0(X0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
inference(nnf_transformation,[],[f122]) ).
fof(f208,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [X6] :
( ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aElementOf0(X6,stldt0(sbsmnsldt0(xS))) )
& ! [X5] :
( ( ~ aElementOf0(X5,stldt0(sbsmnsldt0(xS)))
| ( ~ aElementOf0(X5,sbsmnsldt0(xS))
& aInteger0(X5) ) )
& ( aElementOf0(X5,sbsmnsldt0(xS))
| ~ aInteger0(X5)
| aElementOf0(X5,stldt0(sbsmnsldt0(xS))) ) )
& ! [X3] :
( ( ~ aElementOf0(X3,sbsmnsldt0(xS))
| ( ? [X4] :
( aElementOf0(X3,X4)
& aElementOf0(X4,xS) )
& aInteger0(X3) ) )
& ( ! [X4] :
( ~ aElementOf0(X3,X4)
| ~ aElementOf0(X4,xS) )
| ~ aInteger0(X3)
| aElementOf0(X3,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& ~ aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ! [X2] :
( sdtpldt0(X0,smndt0(sz10)) != sdtasdt0(xp,X2)
| ~ aInteger0(X2) ) )
| ~ aInteger0(X0)
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ( sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ? [X1] :
( sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10))
& aInteger0(X1) )
& aInteger0(X0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
inference(flattening,[],[f207]) ).
fof(f209,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [X7] :
( ~ aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aElementOf0(X7,stldt0(sbsmnsldt0(xS))) )
& ! [X6] :
( ( ~ aElementOf0(X6,stldt0(sbsmnsldt0(xS)))
| ( ~ aElementOf0(X6,sbsmnsldt0(xS))
& aInteger0(X6) ) )
& ( aElementOf0(X6,sbsmnsldt0(xS))
| ~ aInteger0(X6)
| aElementOf0(X6,stldt0(sbsmnsldt0(xS))) ) )
& ! [X3] :
( ( ~ aElementOf0(X3,sbsmnsldt0(xS))
| ( ? [X5] :
( aElementOf0(X3,X5)
& aElementOf0(X5,xS) )
& aInteger0(X3) ) )
& ( ! [X4] :
( ~ aElementOf0(X3,X4)
| ~ aElementOf0(X4,xS) )
| ~ aInteger0(X3)
| aElementOf0(X3,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& ~ aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ! [X2] :
( sdtpldt0(X0,smndt0(sz10)) != sdtasdt0(xp,X2)
| ~ aInteger0(X2) ) )
| ~ aInteger0(X0)
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ( sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ? [X1] :
( sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10))
& aInteger0(X1) )
& aInteger0(X0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
inference(rectify,[],[f208]) ).
fof(f210,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [X7] :
( ~ aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aElementOf0(X7,stldt0(sbsmnsldt0(xS))) )
& ! [X6] :
( ( ~ aElementOf0(X6,stldt0(sbsmnsldt0(xS)))
| ( ~ aElementOf0(X6,sbsmnsldt0(xS))
& aInteger0(X6) ) )
& ( aElementOf0(X6,sbsmnsldt0(xS))
| ~ aInteger0(X6)
| aElementOf0(X6,stldt0(sbsmnsldt0(xS))) ) )
& ! [X3] :
( ( ~ aElementOf0(X3,sbsmnsldt0(xS))
| ( aElementOf0(X3,sK36(X3))
& aElementOf0(sK36(X3),xS)
& aInteger0(X3) ) )
& ( ! [X4] :
( ~ aElementOf0(X3,X4)
| ~ aElementOf0(X4,xS) )
| ~ aInteger0(X3)
| aElementOf0(X3,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& ~ aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ! [X2] :
( sdtpldt0(X0,smndt0(sz10)) != sdtasdt0(xp,X2)
| ~ aInteger0(X2) ) )
| ~ aInteger0(X0)
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ( sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& sdtpldt0(X0,smndt0(sz10)) = sdtasdt0(xp,sK35(X0))
& aInteger0(sK35(X0))
& aInteger0(X0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35,sK36]),skolemize(X1,sK35(X0)),skolemize(X5,sK36(X3))],[f209]) ).
fof(f211,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)))
& sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)) = sdtasdt0(xp,sK38)
& aInteger0(sK38)
& aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp)
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
& sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) = sdtasdt0(xp,sK37)
& aInteger0(sK37) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37,sK38]),skolemize(X0,sK37),skolemize(X1,sK38)],[f60]) ).
fof(f212,plain,
aInteger0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f213,plain,
aInteger0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f214,plain,
! [X0] :
( ~ aInteger0(X0)
| aInteger0(smndt0(X0)) ),
inference(cnf_transformation,[],[f61]) ).
fof(f215,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| aInteger0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f216,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| aInteger0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f217,plain,
! [X2,X0,X1] :
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2) ),
inference(cnf_transformation,[],[f67]) ).
fof(f218,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f219,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f70]) ).
fof(f220,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f70]) ).
fof(f221,plain,
! [X0] :
( ~ aInteger0(X0)
| sz00 = sdtpldt0(smndt0(X0),X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f222,plain,
! [X0] :
( ~ aInteger0(X0)
| sz00 = sdtpldt0(X0,smndt0(X0)) ),
inference(cnf_transformation,[],[f71]) ).
fof(f223,plain,
! [X2,X0,X1] :
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdtasdt0(X0,sdtasdt0(X1,X2)) = sdtasdt0(sdtasdt0(X0,X1),X2) ),
inference(cnf_transformation,[],[f73]) ).
fof(f224,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f225,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtasdt0(sz10,X0) = X0 ),
inference(cnf_transformation,[],[f76]) ).
fof(f226,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f76]) ).
fof(f227,plain,
! [X2,X0,X1] :
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2)) ),
inference(cnf_transformation,[],[f78]) ).
fof(f228,plain,
! [X2,X0,X1] :
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ),
inference(cnf_transformation,[],[f78]) ).
fof(f229,plain,
! [X0] :
( ~ aInteger0(X0)
| sz00 = sdtasdt0(sz00,X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f230,plain,
! [X0] :
( ~ aInteger0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(cnf_transformation,[],[f79]) ).
fof(f231,plain,
! [X0] :
( ~ aInteger0(X0)
| smndt0(X0) = sdtasdt0(X0,smndt0(sz10)) ),
inference(cnf_transformation,[],[f80]) ).
fof(f232,plain,
! [X0] :
( ~ aInteger0(X0)
| smndt0(X0) = sdtasdt0(smndt0(sz10),X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f233,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| sz00 != sdtasdt0(X0,X1)
| sz00 = X1
| sz00 = X0 ),
inference(cnf_transformation,[],[f82]) ).
fof(f234,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ aDivisorOf0(X1,X0)
| sdtasdt0(X1,sK10(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f142]) ).
fof(f235,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ aDivisorOf0(X1,X0)
| aInteger0(sK10(X0,X1)) ),
inference(cnf_transformation,[],[f142]) ).
fof(f236,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ aDivisorOf0(X1,X0)
| sz00 != X1 ),
inference(cnf_transformation,[],[f142]) ).
fof(f237,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ aDivisorOf0(X1,X0)
| aInteger0(X1) ),
inference(cnf_transformation,[],[f142]) ).
fof(f238,plain,
! [X2,X0,X1] :
( ~ aInteger0(X0)
| sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2)
| sz00 = X1
| ~ aInteger0(X1)
| aDivisorOf0(X1,X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f239,plain,
! [X2,X0,X1] :
( sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ),
inference(cnf_transformation,[],[f143]) ).
fof(f240,plain,
! [X2,X0,X1] :
( sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
| sdteqdtlpzmzozddtrp0(X0,X1,X2) ),
inference(cnf_transformation,[],[f143]) ).
fof(f241,plain,
! [X0,X1] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdteqdtlpzmzozddtrp0(X0,X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f242,plain,
! [X2,X0,X1] :
( sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| sdteqdtlpzmzozddtrp0(X1,X0,X2) ),
inference(cnf_transformation,[],[f89]) ).
fof(f243,plain,
! [X2,X3,X0,X1] :
( ~ aInteger0(X3)
| sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X1,X3,X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| sdteqdtlpzmzozddtrp0(X0,X3,X2) ),
inference(cnf_transformation,[],[f91]) ).
fof(f244,plain,
! [X2,X3,X0,X1] :
( sz00 = X3
| ~ aInteger0(X3)
| sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,sdtasdt0(X2,X3))
| sdteqdtlpzmzozddtrp0(X0,X1,X3) ),
inference(cnf_transformation,[],[f93]) ).
fof(f245,plain,
! [X2,X3,X0,X1] :
( sz00 = X3
| ~ aInteger0(X3)
| sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,sdtasdt0(X2,X3))
| sdteqdtlpzmzozddtrp0(X0,X1,X2) ),
inference(cnf_transformation,[],[f93]) ).
fof(f246,plain,
! [X2,X0] :
( ~ aInteger0(X0)
| ~ isPrime0(X2)
| ~ aDivisorOf0(X2,X0)
| smndt0(sz10) != X0 ),
inference(cnf_transformation,[],[f147]) ).
fof(f247,plain,
! [X2,X0] :
( ~ aInteger0(X0)
| ~ isPrime0(X2)
| ~ aDivisorOf0(X2,X0)
| sz10 != X0 ),
inference(cnf_transformation,[],[f147]) ).
fof(f248,plain,
! [X0] :
( ~ aInteger0(X0)
| smndt0(sz10) = X0
| sz10 = X0
| isPrime0(sK11(X0)) ),
inference(cnf_transformation,[],[f147]) ).
fof(f249,plain,
! [X0] :
( ~ aInteger0(X0)
| smndt0(sz10) = X0
| sz10 = X0
| aDivisorOf0(sK11(X0),X0) ),
inference(cnf_transformation,[],[f147]) ).
fof(f250,plain,
! [X3,X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) ),
inference(cnf_transformation,[],[f151]) ).
fof(f251,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| aSet0(X1) ),
inference(cnf_transformation,[],[f151]) ).
fof(f252,plain,
! [X0,X1] :
( ~ aSet0(X0)
| aElementOf0(sK12(X0,X1),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ),
inference(cnf_transformation,[],[f151]) ).
fof(f253,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(sK12(X0,X1),X0)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ),
inference(cnf_transformation,[],[f151]) ).
fof(f254,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1)
| sdtbsmnsldt0(X1,X0) != X2
| sP0(X2,X1,X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f255,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1)
| ~ sP0(X2,X1,X0)
| sdtbsmnsldt0(X1,X0) = X2 ),
inference(cnf_transformation,[],[f153]) ).
fof(f265,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395)
| sP1(X1,X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f266,plain,
! [X2,X0,X1] :
( ~ sP3(X0,X1)
| sdtslmnbsdt0(X1,X0) != X2
| sP2(X2,X1,X0) ),
inference(cnf_transformation,[],[f159]) ).
fof(f267,plain,
! [X2,X0,X1] :
( ~ sP3(X0,X1)
| ~ sP2(X2,X1,X0)
| sdtslmnbsdt0(X1,X0) = X2 ),
inference(cnf_transformation,[],[f159]) ).
fof(f277,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395)
| sP3(X1,X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f278,plain,
! [X0,X1] :
( ~ sP5(X0)
| sbsmnsldt0(X0) != X1
| sP4(X1,X0) ),
inference(cnf_transformation,[],[f165]) ).
fof(f279,plain,
! [X0,X1] :
( ~ sP5(X0)
| ~ sP4(X1,X0)
| sbsmnsldt0(X0) = X1 ),
inference(cnf_transformation,[],[f165]) ).
fof(f289,plain,
! [X0] :
( aElementOf0(sK18(X0),X0)
| ~ aSet0(X0)
| sP5(X0) ),
inference(cnf_transformation,[],[f170]) ).
fof(f290,plain,
! [X0] :
( ~ aSubsetOf0(sK18(X0),cS1395)
| ~ aSet0(X0)
| sP5(X0) ),
inference(cnf_transformation,[],[f170]) ).
fof(f291,plain,
! [X3,X0,X1] :
( ~ aSubsetOf0(X0,cS1395)
| stldt0(X0) != X1
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0) ),
inference(cnf_transformation,[],[f174]) ).
fof(f292,plain,
! [X3,X0,X1] :
( ~ aSubsetOf0(X0,cS1395)
| stldt0(X0) != X1
| ~ aElementOf0(X3,X1)
| aInteger0(X3) ),
inference(cnf_transformation,[],[f174]) ).
fof(f293,plain,
! [X3,X0,X1] :
( ~ aSubsetOf0(X0,cS1395)
| stldt0(X0) != X1
| aElementOf0(X3,X0)
| ~ aInteger0(X3)
| aElementOf0(X3,X1) ),
inference(cnf_transformation,[],[f174]) ).
fof(f294,plain,
! [X0,X1] :
( ~ aSubsetOf0(X0,cS1395)
| stldt0(X0) != X1
| aSet0(X1) ),
inference(cnf_transformation,[],[f174]) ).
fof(f295,plain,
! [X0,X1] :
( ~ aSubsetOf0(X0,cS1395)
| aElementOf0(sK19(X0,X1),X1)
| ~ aElementOf0(sK19(X0,X1),X0)
| ~ aSet0(X1)
| stldt0(X0) = X1 ),
inference(cnf_transformation,[],[f174]) ).
fof(f296,plain,
! [X0,X1] :
( ~ aSubsetOf0(X0,cS1395)
| aElementOf0(sK19(X0,X1),X1)
| aInteger0(sK19(X0,X1))
| ~ aSet0(X1)
| stldt0(X0) = X1 ),
inference(cnf_transformation,[],[f174]) ).
fof(f297,plain,
! [X0,X1] :
( ~ aSubsetOf0(X0,cS1395)
| ~ aElementOf0(sK19(X0,X1),X1)
| aElementOf0(sK19(X0,X1),X0)
| ~ aInteger0(sK19(X0,X1))
| ~ aSet0(X1)
| stldt0(X0) = X1 ),
inference(cnf_transformation,[],[f174]) ).
fof(f298,plain,
! [X2,X0,X1,X4] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| szAzrzSzezqlpdtcmdtrp0(X0,X1) != X2
| ~ aElementOf0(X4,X2)
| sdteqdtlpzmzozddtrp0(X4,X0,X1) ),
inference(cnf_transformation,[],[f178]) ).
fof(f299,plain,
! [X2,X0,X1,X4] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| szAzrzSzezqlpdtcmdtrp0(X0,X1) != X2
| ~ aElementOf0(X4,X2)
| aInteger0(X4) ),
inference(cnf_transformation,[],[f178]) ).
fof(f300,plain,
! [X2,X0,X1,X4] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| szAzrzSzezqlpdtcmdtrp0(X0,X1) != X2
| ~ sdteqdtlpzmzozddtrp0(X4,X0,X1)
| ~ aInteger0(X4)
| aElementOf0(X4,X2) ),
inference(cnf_transformation,[],[f178]) ).
fof(f301,plain,
! [X2,X0,X1] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| szAzrzSzezqlpdtcmdtrp0(X0,X1) != X2
| aSet0(X2) ),
inference(cnf_transformation,[],[f178]) ).
fof(f302,plain,
! [X2,X0,X1] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| aElementOf0(sK20(X0,X1,X2),X2)
| sdteqdtlpzmzozddtrp0(sK20(X0,X1,X2),X0,X1)
| ~ aSet0(X2)
| szAzrzSzezqlpdtcmdtrp0(X0,X1) = X2 ),
inference(cnf_transformation,[],[f178]) ).
fof(f303,plain,
! [X2,X0,X1] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| aElementOf0(sK20(X0,X1,X2),X2)
| aInteger0(sK20(X0,X1,X2))
| ~ aSet0(X2)
| szAzrzSzezqlpdtcmdtrp0(X0,X1) = X2 ),
inference(cnf_transformation,[],[f178]) ).
fof(f304,plain,
! [X2,X0,X1] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ aElementOf0(sK20(X0,X1,X2),X2)
| ~ sdteqdtlpzmzozddtrp0(sK20(X0,X1,X2),X0,X1)
| ~ aInteger0(sK20(X0,X1,X2))
| ~ aSet0(X2)
| szAzrzSzezqlpdtcmdtrp0(X0,X1) = X2 ),
inference(cnf_transformation,[],[f178]) ).
fof(f305,plain,
! [X3,X0] :
( ~ aSubsetOf0(X0,cS1395)
| ~ isOpen0(X0)
| ~ aElementOf0(X3,X0)
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,sK22(X0,X3)),X0) ),
inference(cnf_transformation,[],[f181]) ).
fof(f306,plain,
! [X3,X0] :
( ~ aSubsetOf0(X0,cS1395)
| ~ isOpen0(X0)
| ~ aElementOf0(X3,X0)
| sz00 != sK22(X0,X3) ),
inference(cnf_transformation,[],[f181]) ).
fof(f307,plain,
! [X3,X0] :
( ~ aSubsetOf0(X0,cS1395)
| ~ isOpen0(X0)
| ~ aElementOf0(X3,X0)
| aInteger0(sK22(X0,X3)) ),
inference(cnf_transformation,[],[f181]) ).
fof(f308,plain,
! [X0] :
( ~ aSubsetOf0(X0,cS1395)
| aElementOf0(sK21(X0),X0)
| isOpen0(X0) ),
inference(cnf_transformation,[],[f181]) ).
fof(f309,plain,
! [X2,X0] :
( ~ aSubsetOf0(X0,cS1395)
| ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sK21(X0),X2),X0)
| sz00 = X2
| ~ aInteger0(X2)
| isOpen0(X0) ),
inference(cnf_transformation,[],[f181]) ).
fof(f310,plain,
! [X0] :
( ~ aSubsetOf0(X0,cS1395)
| ~ isClosed0(X0)
| isOpen0(stldt0(X0)) ),
inference(cnf_transformation,[],[f182]) ).
fof(f311,plain,
! [X0] :
( ~ aSubsetOf0(X0,cS1395)
| ~ isOpen0(stldt0(X0))
| isClosed0(X0) ),
inference(cnf_transformation,[],[f182]) ).
fof(f312,plain,
! [X0] :
( aElementOf0(sK23(X0),X0)
| ~ aSet0(X0)
| isOpen0(sbsmnsldt0(X0)) ),
inference(cnf_transformation,[],[f183]) ).
fof(f313,plain,
! [X0] :
( ~ isOpen0(sK23(X0))
| ~ aSubsetOf0(sK23(X0),cS1395)
| ~ aSet0(X0)
| isOpen0(sbsmnsldt0(X0)) ),
inference(cnf_transformation,[],[f183]) ).
fof(f314,plain,
! [X0,X1] :
( ~ isOpen0(X1)
| ~ isOpen0(X0)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395)
| isOpen0(sdtslmnbsdt0(X0,X1)) ),
inference(cnf_transformation,[],[f110]) ).
fof(f315,plain,
! [X0,X1] :
( ~ isClosed0(X1)
| ~ isClosed0(X0)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395)
| isClosed0(sdtbsmnsldt0(X0,X1)) ),
inference(cnf_transformation,[],[f112]) ).
fof(f316,plain,
! [X0] :
( aElementOf0(sK24(X0),X0)
| ~ isFinite0(X0)
| ~ aSet0(X0)
| isClosed0(sbsmnsldt0(X0)) ),
inference(cnf_transformation,[],[f184]) ).
fof(f317,plain,
! [X0] :
( ~ isClosed0(sK24(X0))
| ~ aSubsetOf0(sK24(X0),cS1395)
| ~ isFinite0(X0)
| ~ aSet0(X0)
| isClosed0(sbsmnsldt0(X0)) ),
inference(cnf_transformation,[],[f184]) ).
fof(f318,plain,
! [X0,X1] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| isClosed0(szAzrzSzezqlpdtcmdtrp0(X0,X1)) ),
inference(cnf_transformation,[],[f116]) ).
fof(f319,plain,
! [X0,X1] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),cS1395) ),
inference(cnf_transformation,[],[f116]) ).
fof(f320,plain,
! [X0,X1] :
( ~ sP7(X0)
| ~ sdteqdtlpzmzozddtrp0(X1,sz00,X0)
| ~ aInteger0(X1)
| aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0)) ),
inference(cnf_transformation,[],[f187]) ).
fof(f321,plain,
! [X0,X1] :
( ~ sP7(X0)
| ~ aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
| ~ aInteger0(X1)
| aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0)) ),
inference(cnf_transformation,[],[f187]) ).
fof(f322,plain,
! [X3,X0,X1] :
( ~ sP7(X0)
| sdtpldt0(X1,smndt0(sz00)) != sdtasdt0(X0,X3)
| ~ aInteger0(X3)
| ~ aInteger0(X1)
| aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0)) ),
inference(cnf_transformation,[],[f187]) ).
fof(f323,plain,
! [X0,X1] :
( ~ sP7(X0)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| sdteqdtlpzmzozddtrp0(X1,sz00,X0) ),
inference(cnf_transformation,[],[f187]) ).
fof(f324,plain,
! [X0,X1] :
( ~ sP7(X0)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00))) ),
inference(cnf_transformation,[],[f187]) ).
fof(f325,plain,
! [X0,X1] :
( ~ sP7(X0)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| sdtpldt0(X1,smndt0(sz00)) = sdtasdt0(X0,sK25(X0,X1)) ),
inference(cnf_transformation,[],[f187]) ).
fof(f326,plain,
! [X0,X1] :
( ~ sP7(X0)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| aInteger0(sK25(X0,X1)) ),
inference(cnf_transformation,[],[f187]) ).
fof(f327,plain,
! [X0,X1] :
( ~ sP7(X0)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| aInteger0(X1) ),
inference(cnf_transformation,[],[f187]) ).
fof(f336,plain,
xS = cS2043,
inference(cnf_transformation,[],[f192]) ).
fof(f337,plain,
! [X2,X0] :
( sP6(X2)
| ~ isPrime0(X2)
| sz00 = X2
| ~ aInteger0(X2)
| aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f192]) ).
fof(f338,plain,
! [X2,X0] :
( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
| ~ isPrime0(X2)
| sz00 = X2
| ~ aInteger0(X2)
| aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f192]) ).
fof(f339,plain,
! [X2,X0] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X2) != X0
| ~ isPrime0(X2)
| sz00 = X2
| ~ aInteger0(X2)
| aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f192]) ).
fof(f340,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| szAzrzSzezqlpdtcmdtrp0(sz00,sK27(X0)) = X0 ),
inference(cnf_transformation,[],[f192]) ).
fof(f341,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| sP7(sK27(X0)) ),
inference(cnf_transformation,[],[f192]) ).
fof(f342,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,sK27(X0))) ),
inference(cnf_transformation,[],[f192]) ).
fof(f343,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| isPrime0(sK27(X0)) ),
inference(cnf_transformation,[],[f192]) ).
fof(f344,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| sz00 != sK27(X0) ),
inference(cnf_transformation,[],[f192]) ).
fof(f345,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| aInteger0(sK27(X0)) ),
inference(cnf_transformation,[],[f192]) ).
fof(f346,plain,
aSet0(xS),
inference(cnf_transformation,[],[f192]) ).
fof(f347,plain,
stldt0(sbsmnsldt0(xS)) = cS2076,
inference(cnf_transformation,[],[f196]) ).
fof(f348,plain,
! [X4] :
( ~ aElementOf0(X4,stldt0(sbsmnsldt0(xS)))
| smndt0(sz10) = X4
| sz10 = X4 ),
inference(cnf_transformation,[],[f196]) ).
fof(f349,plain,
! [X4] :
( smndt0(sz10) != X4
| aElementOf0(X4,stldt0(sbsmnsldt0(xS))) ),
inference(cnf_transformation,[],[f196]) ).
fof(f350,plain,
! [X4] :
( sz10 != X4
| aElementOf0(X4,stldt0(sbsmnsldt0(xS))) ),
inference(cnf_transformation,[],[f196]) ).
fof(f354,plain,
aSet0(stldt0(sbsmnsldt0(xS))),
inference(cnf_transformation,[],[f196]) ).
fof(f355,plain,
! [X0] :
( ~ aElementOf0(X0,sbsmnsldt0(xS))
| aElementOf0(X0,sK28(X0)) ),
inference(cnf_transformation,[],[f196]) ).
fof(f356,plain,
! [X0] :
( ~ aElementOf0(X0,sbsmnsldt0(xS))
| aElementOf0(sK28(X0),xS) ),
inference(cnf_transformation,[],[f196]) ).
fof(f360,plain,
isFinite0(xS),
inference(cnf_transformation,[],[f44]) ).
fof(f361,plain,
! [X2,X0,X1] :
( ~ sP9(X0,X1)
| ~ sdteqdtlpzmzozddtrp0(X2,X0,X1)
| ~ aInteger0(X2)
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) ),
inference(cnf_transformation,[],[f199]) ).
fof(f362,plain,
! [X2,X0,X1] :
( ~ sP9(X0,X1)
| ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
| ~ aInteger0(X2)
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) ),
inference(cnf_transformation,[],[f199]) ).
fof(f363,plain,
! [X2,X0,X1,X4] :
( ~ sP9(X0,X1)
| sdtpldt0(X2,smndt0(X0)) != sdtasdt0(X1,X4)
| ~ aInteger0(X4)
| ~ aInteger0(X2)
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) ),
inference(cnf_transformation,[],[f199]) ).
fof(f364,plain,
! [X2,X0,X1] :
( ~ sP9(X0,X1)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| sdteqdtlpzmzozddtrp0(X2,X0,X1) ),
inference(cnf_transformation,[],[f199]) ).
fof(f365,plain,
! [X2,X0,X1] :
( ~ sP9(X0,X1)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0))) ),
inference(cnf_transformation,[],[f199]) ).
fof(f366,plain,
! [X2,X0,X1] :
( ~ sP9(X0,X1)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| sdtpldt0(X2,smndt0(X0)) = sdtasdt0(X1,sK29(X0,X1,X2)) ),
inference(cnf_transformation,[],[f199]) ).
fof(f367,plain,
! [X2,X0,X1] :
( ~ sP9(X0,X1)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| aInteger0(sK29(X0,X1,X2)) ),
inference(cnf_transformation,[],[f199]) ).
fof(f368,plain,
! [X2,X0,X1] :
( ~ sP9(X0,X1)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| aInteger0(X2) ),
inference(cnf_transformation,[],[f199]) ).
fof(f377,plain,
! [X11] :
( ~ aElementOf0(X11,stldt0(sbsmnsldt0(xS)))
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X11,sK34(X11)),stldt0(sbsmnsldt0(xS))) ),
inference(cnf_transformation,[],[f206]) ).
fof(f378,plain,
! [X11,X13] :
( ~ aElementOf0(X11,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X13,szAzrzSzezqlpdtcmdtrp0(X11,sK34(X11)))
| aElementOf0(X13,stldt0(sbsmnsldt0(xS))) ),
inference(cnf_transformation,[],[f206]) ).
fof(f379,plain,
! [X11] :
( ~ aElementOf0(X11,stldt0(sbsmnsldt0(xS)))
| sP8(X11,sK34(X11)) ),
inference(cnf_transformation,[],[f206]) ).
fof(f380,plain,
! [X11] :
( ~ aElementOf0(X11,stldt0(sbsmnsldt0(xS)))
| aSet0(szAzrzSzezqlpdtcmdtrp0(X11,sK34(X11))) ),
inference(cnf_transformation,[],[f206]) ).
fof(f381,plain,
! [X11] :
( ~ aElementOf0(X11,stldt0(sbsmnsldt0(xS)))
| sz00 != sK34(X11) ),
inference(cnf_transformation,[],[f206]) ).
fof(f382,plain,
! [X11] :
( ~ aElementOf0(X11,stldt0(sbsmnsldt0(xS)))
| aInteger0(sK34(X11)) ),
inference(cnf_transformation,[],[f206]) ).
fof(f386,plain,
! [X7] :
( ~ aElementOf0(X7,sbsmnsldt0(xS))
| aElementOf0(X7,sK33(X7)) ),
inference(cnf_transformation,[],[f206]) ).
fof(f387,plain,
! [X7] :
( ~ aElementOf0(X7,sbsmnsldt0(xS))
| aElementOf0(sK33(X7),xS) ),
inference(cnf_transformation,[],[f206]) ).
fof(f391,plain,
isClosed0(sbsmnsldt0(xS)),
inference(cnf_transformation,[],[f206]) ).
fof(f392,plain,
isOpen0(stldt0(sbsmnsldt0(xS))),
inference(cnf_transformation,[],[f206]) ).
fof(f393,plain,
! [X4] :
( ~ aElementOf0(X4,stldt0(sbsmnsldt0(xS)))
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X4,sK32(X4)),stldt0(sbsmnsldt0(xS))) ),
inference(cnf_transformation,[],[f206]) ).
fof(f394,plain,
! [X6,X4] :
( ~ aElementOf0(X4,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(X4,sK32(X4)))
| aElementOf0(X6,stldt0(sbsmnsldt0(xS))) ),
inference(cnf_transformation,[],[f206]) ).
fof(f395,plain,
! [X4] :
( ~ aElementOf0(X4,stldt0(sbsmnsldt0(xS)))
| sP9(X4,sK32(X4)) ),
inference(cnf_transformation,[],[f206]) ).
fof(f396,plain,
! [X4] :
( ~ aElementOf0(X4,stldt0(sbsmnsldt0(xS)))
| aSet0(szAzrzSzezqlpdtcmdtrp0(X4,sK32(X4))) ),
inference(cnf_transformation,[],[f206]) ).
fof(f397,plain,
! [X4] :
( ~ aElementOf0(X4,stldt0(sbsmnsldt0(xS)))
| sz00 != sK32(X4) ),
inference(cnf_transformation,[],[f206]) ).
fof(f398,plain,
! [X4] :
( ~ aElementOf0(X4,stldt0(sbsmnsldt0(xS)))
| aInteger0(sK32(X4)) ),
inference(cnf_transformation,[],[f206]) ).
fof(f402,plain,
! [X0] :
( ~ aElementOf0(X0,sbsmnsldt0(xS))
| aElementOf0(X0,sK31(X0)) ),
inference(cnf_transformation,[],[f206]) ).
fof(f403,plain,
! [X0] :
( ~ aElementOf0(X0,sbsmnsldt0(xS))
| aElementOf0(sK31(X0),xS) ),
inference(cnf_transformation,[],[f206]) ).
fof(f407,plain,
aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))),
inference(cnf_transformation,[],[f210]) ).
fof(f408,plain,
! [X7] :
( ~ aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aElementOf0(X7,stldt0(sbsmnsldt0(xS))) ),
inference(cnf_transformation,[],[f210]) ).
fof(f409,plain,
! [X6] :
( ~ aElementOf0(X6,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X6,sbsmnsldt0(xS)) ),
inference(cnf_transformation,[],[f210]) ).
fof(f410,plain,
! [X6] :
( ~ aElementOf0(X6,stldt0(sbsmnsldt0(xS)))
| aInteger0(X6) ),
inference(cnf_transformation,[],[f210]) ).
fof(f411,plain,
! [X6] :
( aElementOf0(X6,sbsmnsldt0(xS))
| ~ aInteger0(X6)
| aElementOf0(X6,stldt0(sbsmnsldt0(xS))) ),
inference(cnf_transformation,[],[f210]) ).
fof(f412,plain,
! [X3] :
( ~ aElementOf0(X3,sbsmnsldt0(xS))
| aElementOf0(X3,sK36(X3)) ),
inference(cnf_transformation,[],[f210]) ).
fof(f413,plain,
! [X3] :
( ~ aElementOf0(X3,sbsmnsldt0(xS))
| aElementOf0(sK36(X3),xS) ),
inference(cnf_transformation,[],[f210]) ).
fof(f414,plain,
! [X3] :
( ~ aElementOf0(X3,sbsmnsldt0(xS))
| aInteger0(X3) ),
inference(cnf_transformation,[],[f210]) ).
fof(f415,plain,
! [X3,X4] :
( ~ aElementOf0(X3,X4)
| ~ aElementOf0(X4,xS)
| ~ aInteger0(X3)
| aElementOf0(X3,sbsmnsldt0(xS)) ),
inference(cnf_transformation,[],[f210]) ).
fof(f416,plain,
aSet0(sbsmnsldt0(xS)),
inference(cnf_transformation,[],[f210]) ).
fof(f417,plain,
! [X0] :
( ~ sdteqdtlpzmzozddtrp0(X0,sz10,xp)
| ~ aInteger0(X0)
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(cnf_transformation,[],[f210]) ).
fof(f418,plain,
! [X0] :
( ~ aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
| ~ aInteger0(X0)
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(cnf_transformation,[],[f210]) ).
fof(f419,plain,
! [X2,X0] :
( sdtpldt0(X0,smndt0(sz10)) != sdtasdt0(xp,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X0)
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(cnf_transformation,[],[f210]) ).
fof(f420,plain,
! [X0] :
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| sdteqdtlpzmzozddtrp0(X0,sz10,xp) ),
inference(cnf_transformation,[],[f210]) ).
fof(f421,plain,
! [X0] :
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10))) ),
inference(cnf_transformation,[],[f210]) ).
fof(f422,plain,
! [X0] :
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| sdtpldt0(X0,smndt0(sz10)) = sdtasdt0(xp,sK35(X0)) ),
inference(cnf_transformation,[],[f210]) ).
fof(f423,plain,
! [X0] :
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aInteger0(sK35(X0)) ),
inference(cnf_transformation,[],[f210]) ).
fof(f424,plain,
! [X0] :
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aInteger0(X0) ),
inference(cnf_transformation,[],[f210]) ).
fof(f425,plain,
aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(cnf_transformation,[],[f210]) ).
fof(f426,plain,
sz00 != xp,
inference(cnf_transformation,[],[f210]) ).
fof(f427,plain,
aInteger0(xp),
inference(cnf_transformation,[],[f210]) ).
fof(f428,plain,
aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(cnf_transformation,[],[f211]) ).
fof(f429,plain,
sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp),
inference(cnf_transformation,[],[f211]) ).
fof(f430,plain,
aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))),
inference(cnf_transformation,[],[f211]) ).
fof(f431,plain,
sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)) = sdtasdt0(xp,sK38),
inference(cnf_transformation,[],[f211]) ).
fof(f432,plain,
aInteger0(sK38),
inference(cnf_transformation,[],[f211]) ).
fof(f433,plain,
aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(cnf_transformation,[],[f211]) ).
fof(f434,plain,
sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp),
inference(cnf_transformation,[],[f211]) ).
fof(f435,plain,
aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))),
inference(cnf_transformation,[],[f211]) ).
fof(f436,plain,
sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) = sdtasdt0(xp,sK37),
inference(cnf_transformation,[],[f211]) ).
fof(f437,plain,
aInteger0(sK37),
inference(cnf_transformation,[],[f211]) ).
fof(f438,plain,
( sz10 = sdtpldt0(sz10,smndt0(xp))
| sz10 = sdtpldt0(sz10,xp) ),
inference(cnf_transformation,[],[f123]) ).
fof(f439,plain,
aSet0(cS2043),
inference(definition_unfolding,[],[f346,f336]) ).
fof(f440,plain,
! [X0] :
( ~ aElementOf0(X0,cS2043)
| aInteger0(sK27(X0)) ),
inference(definition_unfolding,[],[f345,f336]) ).
fof(f441,plain,
! [X0] :
( ~ aElementOf0(X0,cS2043)
| sz00 != sK27(X0) ),
inference(definition_unfolding,[],[f344,f336]) ).
fof(f442,plain,
! [X0] :
( ~ aElementOf0(X0,cS2043)
| isPrime0(sK27(X0)) ),
inference(definition_unfolding,[],[f343,f336]) ).
fof(f443,plain,
! [X0] :
( ~ aElementOf0(X0,cS2043)
| aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,sK27(X0))) ),
inference(definition_unfolding,[],[f342,f336]) ).
fof(f444,plain,
! [X0] :
( ~ aElementOf0(X0,cS2043)
| sP7(sK27(X0)) ),
inference(definition_unfolding,[],[f341,f336]) ).
fof(f445,plain,
! [X0] :
( ~ aElementOf0(X0,cS2043)
| szAzrzSzezqlpdtcmdtrp0(sz00,sK27(X0)) = X0 ),
inference(definition_unfolding,[],[f340,f336]) ).
fof(f446,plain,
! [X2,X0] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X2) != X0
| ~ isPrime0(X2)
| sz00 = X2
| ~ aInteger0(X2)
| aElementOf0(X0,cS2043) ),
inference(definition_unfolding,[],[f339,f336]) ).
fof(f447,plain,
! [X2,X0] :
( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
| ~ isPrime0(X2)
| sz00 = X2
| ~ aInteger0(X2)
| aElementOf0(X0,cS2043) ),
inference(definition_unfolding,[],[f338,f336]) ).
fof(f448,plain,
! [X2,X0] :
( sP6(X2)
| ~ isPrime0(X2)
| sz00 = X2
| ~ aInteger0(X2)
| aElementOf0(X0,cS2043) ),
inference(definition_unfolding,[],[f337,f336]) ).
fof(f452,plain,
! [X0] :
( ~ aElementOf0(X0,sbsmnsldt0(cS2043))
| aElementOf0(sK28(X0),cS2043) ),
inference(definition_unfolding,[],[f356,f336,f336]) ).
fof(f453,plain,
! [X0] :
( ~ aElementOf0(X0,sbsmnsldt0(cS2043))
| aElementOf0(X0,sK28(X0)) ),
inference(definition_unfolding,[],[f355,f336]) ).
fof(f454,plain,
aSet0(stldt0(sbsmnsldt0(cS2043))),
inference(definition_unfolding,[],[f354,f336]) ).
fof(f458,plain,
! [X4] :
( sz10 != X4
| aElementOf0(X4,stldt0(sbsmnsldt0(cS2043))) ),
inference(definition_unfolding,[],[f350,f336]) ).
fof(f459,plain,
! [X4] :
( smndt0(sz10) != X4
| aElementOf0(X4,stldt0(sbsmnsldt0(cS2043))) ),
inference(definition_unfolding,[],[f349,f336]) ).
fof(f460,plain,
! [X4] :
( ~ aElementOf0(X4,stldt0(sbsmnsldt0(cS2043)))
| smndt0(sz10) = X4
| sz10 = X4 ),
inference(definition_unfolding,[],[f348,f336]) ).
fof(f461,plain,
cS2076 = stldt0(sbsmnsldt0(cS2043)),
inference(definition_unfolding,[],[f347,f336]) ).
fof(f462,plain,
isFinite0(cS2043),
inference(definition_unfolding,[],[f360,f336]) ).
fof(f466,plain,
! [X0] :
( ~ aElementOf0(X0,sbsmnsldt0(cS2043))
| aElementOf0(sK31(X0),cS2043) ),
inference(definition_unfolding,[],[f403,f336,f336]) ).
fof(f467,plain,
! [X0] :
( ~ aElementOf0(X0,sbsmnsldt0(cS2043))
| aElementOf0(X0,sK31(X0)) ),
inference(definition_unfolding,[],[f402,f336]) ).
fof(f471,plain,
! [X4] :
( ~ aElementOf0(X4,stldt0(sbsmnsldt0(cS2043)))
| aInteger0(sK32(X4)) ),
inference(definition_unfolding,[],[f398,f336]) ).
fof(f472,plain,
! [X4] :
( ~ aElementOf0(X4,stldt0(sbsmnsldt0(cS2043)))
| sz00 != sK32(X4) ),
inference(definition_unfolding,[],[f397,f336]) ).
fof(f473,plain,
! [X4] :
( ~ aElementOf0(X4,stldt0(sbsmnsldt0(cS2043)))
| aSet0(szAzrzSzezqlpdtcmdtrp0(X4,sK32(X4))) ),
inference(definition_unfolding,[],[f396,f336]) ).
fof(f474,plain,
! [X4] :
( ~ aElementOf0(X4,stldt0(sbsmnsldt0(cS2043)))
| sP9(X4,sK32(X4)) ),
inference(definition_unfolding,[],[f395,f336]) ).
fof(f475,plain,
! [X6,X4] :
( ~ aElementOf0(X4,stldt0(sbsmnsldt0(cS2043)))
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(X4,sK32(X4)))
| aElementOf0(X6,stldt0(sbsmnsldt0(cS2043))) ),
inference(definition_unfolding,[],[f394,f336,f336]) ).
fof(f476,plain,
! [X4] :
( ~ aElementOf0(X4,stldt0(sbsmnsldt0(cS2043)))
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X4,sK32(X4)),stldt0(sbsmnsldt0(cS2043))) ),
inference(definition_unfolding,[],[f393,f336,f336]) ).
fof(f477,plain,
isOpen0(stldt0(sbsmnsldt0(cS2043))),
inference(definition_unfolding,[],[f392,f336]) ).
fof(f478,plain,
isClosed0(sbsmnsldt0(cS2043)),
inference(definition_unfolding,[],[f391,f336]) ).
fof(f482,plain,
! [X7] :
( ~ aElementOf0(X7,sbsmnsldt0(cS2043))
| aElementOf0(sK33(X7),cS2043) ),
inference(definition_unfolding,[],[f387,f336,f336]) ).
fof(f483,plain,
! [X7] :
( ~ aElementOf0(X7,sbsmnsldt0(cS2043))
| aElementOf0(X7,sK33(X7)) ),
inference(definition_unfolding,[],[f386,f336]) ).
fof(f487,plain,
! [X11] :
( ~ aElementOf0(X11,stldt0(sbsmnsldt0(cS2043)))
| aInteger0(sK34(X11)) ),
inference(definition_unfolding,[],[f382,f336]) ).
fof(f488,plain,
! [X11] :
( ~ aElementOf0(X11,stldt0(sbsmnsldt0(cS2043)))
| sz00 != sK34(X11) ),
inference(definition_unfolding,[],[f381,f336]) ).
fof(f489,plain,
! [X11] :
( ~ aElementOf0(X11,stldt0(sbsmnsldt0(cS2043)))
| aSet0(szAzrzSzezqlpdtcmdtrp0(X11,sK34(X11))) ),
inference(definition_unfolding,[],[f380,f336]) ).
fof(f490,plain,
! [X11] :
( ~ aElementOf0(X11,stldt0(sbsmnsldt0(cS2043)))
| sP8(X11,sK34(X11)) ),
inference(definition_unfolding,[],[f379,f336]) ).
fof(f491,plain,
! [X11,X13] :
( ~ aElementOf0(X11,stldt0(sbsmnsldt0(cS2043)))
| ~ aElementOf0(X13,szAzrzSzezqlpdtcmdtrp0(X11,sK34(X11)))
| aElementOf0(X13,stldt0(sbsmnsldt0(cS2043))) ),
inference(definition_unfolding,[],[f378,f336,f336]) ).
fof(f492,plain,
! [X11] :
( ~ aElementOf0(X11,stldt0(sbsmnsldt0(cS2043)))
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X11,sK34(X11)),stldt0(sbsmnsldt0(cS2043))) ),
inference(definition_unfolding,[],[f377,f336,f336]) ).
fof(f493,plain,
aSet0(sbsmnsldt0(cS2043)),
inference(definition_unfolding,[],[f416,f336]) ).
fof(f494,plain,
! [X3,X4] :
( ~ aElementOf0(X3,X4)
| ~ aElementOf0(X4,cS2043)
| ~ aInteger0(X3)
| aElementOf0(X3,sbsmnsldt0(cS2043)) ),
inference(definition_unfolding,[],[f415,f336,f336]) ).
fof(f495,plain,
! [X3] :
( ~ aElementOf0(X3,sbsmnsldt0(cS2043))
| aInteger0(X3) ),
inference(definition_unfolding,[],[f414,f336]) ).
fof(f496,plain,
! [X3] :
( ~ aElementOf0(X3,sbsmnsldt0(cS2043))
| aElementOf0(sK36(X3),cS2043) ),
inference(definition_unfolding,[],[f413,f336,f336]) ).
fof(f497,plain,
! [X3] :
( ~ aElementOf0(X3,sbsmnsldt0(cS2043))
| aElementOf0(X3,sK36(X3)) ),
inference(definition_unfolding,[],[f412,f336]) ).
fof(f498,plain,
! [X6] :
( aElementOf0(X6,sbsmnsldt0(cS2043))
| ~ aInteger0(X6)
| aElementOf0(X6,stldt0(sbsmnsldt0(cS2043))) ),
inference(definition_unfolding,[],[f411,f336,f336]) ).
fof(f499,plain,
! [X6] :
( ~ aElementOf0(X6,stldt0(sbsmnsldt0(cS2043)))
| aInteger0(X6) ),
inference(definition_unfolding,[],[f410,f336]) ).
fof(f500,plain,
! [X6] :
( ~ aElementOf0(X6,stldt0(sbsmnsldt0(cS2043)))
| ~ aElementOf0(X6,sbsmnsldt0(cS2043)) ),
inference(definition_unfolding,[],[f409,f336,f336]) ).
fof(f501,plain,
! [X7] :
( ~ aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aElementOf0(X7,stldt0(sbsmnsldt0(cS2043))) ),
inference(definition_unfolding,[],[f408,f336]) ).
fof(f502,plain,
aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(cS2043))),
inference(definition_unfolding,[],[f407,f336]) ).
fof(f503,plain,
! [X2,X1] :
( ~ aInteger0(sdtasdt0(X1,X2))
| ~ aInteger0(X2)
| sz00 = X1
| ~ aInteger0(X1)
| aDivisorOf0(X1,sdtasdt0(X1,X2)) ),
inference(equality_resolution,[],[f238]) ).
fof(f504,plain,
! [X0] :
( ~ aInteger0(X0)
| ~ aDivisorOf0(sz00,X0) ),
inference(equality_resolution,[],[f236]) ).
fof(f505,plain,
! [X2] :
( ~ aInteger0(sz10)
| ~ isPrime0(X2)
| ~ aDivisorOf0(X2,sz10) ),
inference(equality_resolution,[],[f247]) ).
fof(f506,plain,
! [X2] :
( ~ aInteger0(smndt0(sz10))
| ~ isPrime0(X2)
| ~ aDivisorOf0(X2,smndt0(sz10)) ),
inference(equality_resolution,[],[f246]) ).
fof(f507,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| sP0(sdtbsmnsldt0(X1,X0),X1,X0) ),
inference(equality_resolution,[],[f254]) ).
fof(f508,plain,
! [X0,X1] :
( ~ sP3(X0,X1)
| sP2(sdtslmnbsdt0(X1,X0),X1,X0) ),
inference(equality_resolution,[],[f266]) ).
fof(f509,plain,
! [X0] :
( ~ sP5(X0)
| sP4(sbsmnsldt0(X0),X0) ),
inference(equality_resolution,[],[f278]) ).
fof(f510,plain,
! [X0] :
( ~ aSubsetOf0(X0,cS1395)
| aSet0(stldt0(X0)) ),
inference(equality_resolution,[],[f294]) ).
fof(f511,plain,
! [X3,X0] :
( ~ aSubsetOf0(X0,cS1395)
| aElementOf0(X3,X0)
| ~ aInteger0(X3)
| aElementOf0(X3,stldt0(X0)) ),
inference(equality_resolution,[],[f293]) ).
fof(f512,plain,
! [X3,X0] :
( ~ aSubsetOf0(X0,cS1395)
| ~ aElementOf0(X3,stldt0(X0))
| aInteger0(X3) ),
inference(equality_resolution,[],[f292]) ).
fof(f513,plain,
! [X3,X0] :
( ~ aSubsetOf0(X0,cS1395)
| ~ aElementOf0(X3,stldt0(X0))
| ~ aElementOf0(X3,X0) ),
inference(equality_resolution,[],[f291]) ).
fof(f514,plain,
! [X0,X1] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1)) ),
inference(equality_resolution,[],[f301]) ).
fof(f515,plain,
! [X0,X1,X4] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X4,X0,X1)
| ~ aInteger0(X4)
| aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X0,X1)) ),
inference(equality_resolution,[],[f300]) ).
fof(f516,plain,
! [X0,X1,X4] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| aInteger0(X4) ),
inference(equality_resolution,[],[f299]) ).
fof(f517,plain,
! [X0,X1,X4] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| sdteqdtlpzmzozddtrp0(X4,X0,X1) ),
inference(equality_resolution,[],[f298]) ).
fof(f518,plain,
! [X2] :
( ~ isPrime0(X2)
| sz00 = X2
| ~ aInteger0(X2)
| aElementOf0(szAzrzSzezqlpdtcmdtrp0(sz00,X2),cS2043) ),
inference(equality_resolution,[],[f446]) ).
fof(f519,plain,
aElementOf0(sz10,stldt0(sbsmnsldt0(cS2043))),
inference(equality_resolution,[],[f458]) ).
fof(f520,plain,
aElementOf0(smndt0(sz10),stldt0(sbsmnsldt0(cS2043))),
inference(equality_resolution,[],[f459]) ).
tcf(c_49,plain,
aInteger0(sz00),
inference(cnf_transformation,[],[f212]) ).
tcf(c_50,plain,
aInteger0(sz10),
inference(cnf_transformation,[],[f213]) ).
tcf(c_51,plain,
! [X0: $i] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f214]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( aInteger0(sdtpldt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f216]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) )
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0) )
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_56,plain,
! [X0: $i] :
( ( sdtpldt0(X0,sz00) = X0 )
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f220]) ).
tcf(c_57,plain,
! [X0: $i] :
( ( sdtpldt0(sz00,X0) = X0 )
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_58,plain,
! [X0: $i] :
( ( sdtpldt0(X0,smndt0(X0)) = sz00 )
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f222]) ).
tcf(c_59,plain,
! [X0: $i] :
( ( sdtpldt0(smndt0(X0),X0) = sz00 )
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f221]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) )
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f223]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f224]) ).
tcf(c_62,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sz10) = X0 )
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f226]) ).
tcf(c_63,plain,
! [X0: $i] :
( ( sdtasdt0(sz10,X0) = X0 )
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f225]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) = sdtasdt0(X0,sdtpldt0(X1,X2)) )
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f228]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2)) = sdtasdt0(sdtpldt0(X0,X1),X2) )
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f227]) ).
tcf(c_66,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sz00) = sz00 )
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f230]) ).
tcf(c_67,plain,
! [X0: $i] :
( ( sdtasdt0(sz00,X0) = sz00 )
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f229]) ).
tcf(c_68,plain,
! [X0: $i] :
( ( sdtasdt0(smndt0(sz10),X0) = smndt0(X0) )
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f232]) ).
tcf(c_69,plain,
! [X0: $i] :
( ( sdtasdt0(X0,smndt0(sz10)) = smndt0(X0) )
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f231]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ( X0 = sz00 )
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ( sdtasdt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f233]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( aDivisorOf0(X0,sdtasdt0(X0,X1))
| ( X0 = sz00 )
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ aInteger0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f503]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( aInteger0(X0)
| ~ aInteger0(X1)
| ~ aDivisorOf0(X0,X1) ),
inference(cnf_transformation,[],[f237]) ).
tcf(c_73,plain,
! [X0: $i] :
( ~ aInteger0(X0)
| ~ aDivisorOf0(sz00,X0) ),
inference(cnf_transformation,[],[f504]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( aInteger0(sK10(X1,X0))
| ~ aInteger0(X1)
| ~ aDivisorOf0(X0,X1) ),
inference(cnf_transformation,[],[f235]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,sK10(X1,X0)) = X1 )
| ~ aInteger0(X1)
| ~ aDivisorOf0(X0,X1) ),
inference(cnf_transformation,[],[f234]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdteqdtlpzmzozddtrp0(X1,X2,X0)
| ( X0 = sz00 )
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ aDivisorOf0(X0,sdtpldt0(X1,smndt0(X2))) ),
inference(cnf_transformation,[],[f240]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i] :
( aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
| ( X2 = sz00 )
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2) ),
inference(cnf_transformation,[],[f239]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( sdteqdtlpzmzozddtrp0(X0,X0,X1)
| ( X1 = sz00 )
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f241]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdteqdtlpzmzozddtrp0(X1,X0,X2)
| ( X2 = sz00 )
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2) ),
inference(cnf_transformation,[],[f242]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdteqdtlpzmzozddtrp0(X0,X3,X2)
| ( X2 = sz00 )
| ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X1,X3,X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2) ),
inference(cnf_transformation,[],[f243]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ( X3 = sz00 )
| ( X2 = sz00 )
| ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,sdtasdt0(X2,X3)) ),
inference(cnf_transformation,[],[f245]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdteqdtlpzmzozddtrp0(X0,X1,X3)
| ( X3 = sz00 )
| ( X2 = sz00 )
| ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,sdtasdt0(X2,X3)) ),
inference(cnf_transformation,[],[f244]) ).
tcf(c_83,plain,
! [X0: $i] :
( aDivisorOf0(sK11(X0),X0)
| ( X0 = sz10 )
| ( smndt0(sz10) = X0 )
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f249]) ).
tcf(c_84,plain,
! [X0: $i] :
( isPrime0(sK11(X0))
| ( X0 = sz10 )
| ( smndt0(sz10) = X0 )
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f248]) ).
tcf(c_85,plain,
! [X0: $i] :
( ~ aInteger0(sz10)
| ~ isPrime0(X0)
| ~ aDivisorOf0(X0,sz10) ),
inference(cnf_transformation,[],[f505]) ).
tcf(c_86,plain,
! [X0: $i] :
( ~ isPrime0(X0)
| ~ aInteger0(smndt0(sz10))
| ~ aDivisorOf0(X0,smndt0(sz10)) ),
inference(cnf_transformation,[],[f506]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aElementOf0(sK12(X0,X1),X0) ),
inference(cnf_transformation,[],[f253]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(X1,X0)
| aElementOf0(sK12(X0,X1),X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f252]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] :
( aSet0(X0)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f251]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X2,X1)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X0)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f250]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtbsmnsldt0(X1,X2) = X0 )
| ~ sP1(X2,X1)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f255]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] :
( sP0(sdtbsmnsldt0(X1,X0),X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f507]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i] :
( sP1(X1,X0)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[],[f265]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtslmnbsdt0(X1,X2) = X0 )
| ~ sP3(X2,X1)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f267]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i] :
( sP2(sdtslmnbsdt0(X1,X0),X1,X0)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f508]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i] :
( sP3(X1,X0)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[],[f277]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i] :
( ( sbsmnsldt0(X1) = X0 )
| ~ sP5(X1)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f279]) ).
tcf(c_116,plain,
! [X0: $i] :
( sP4(sbsmnsldt0(X0),X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f509]) ).
tcf(c_126,plain,
! [X0: $i] :
( sP5(X0)
| ~ aSet0(X0)
| ~ aSubsetOf0(sK18(X0),cS1395) ),
inference(cnf_transformation,[],[f290]) ).
tcf(c_127,plain,
! [X0: $i] :
( sP5(X0)
| aElementOf0(sK18(X0),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f289]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sK19(X0,X1),X0)
| ( stldt0(X0) = X1 )
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,cS1395)
| ~ aInteger0(sK19(X0,X1))
| ~ aElementOf0(sK19(X0,X1),X1) ),
inference(cnf_transformation,[],[f297]) ).
tcf(c_129,plain,
! [X0: $i,X1: $i] :
( aInteger0(sK19(X0,X1))
| aElementOf0(sK19(X0,X1),X1)
| ( stldt0(X0) = X1 )
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[],[f296]) ).
tcf(c_130,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sK19(X0,X1),X1)
| ( stldt0(X0) = X1 )
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,cS1395)
| ~ aElementOf0(sK19(X0,X1),X0) ),
inference(cnf_transformation,[],[f295]) ).
tcf(c_131,plain,
! [X0: $i] :
( aSet0(stldt0(X0))
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[],[f510]) ).
tcf(c_132,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X1,X0)
| aElementOf0(X1,stldt0(X0))
| ~ aInteger0(X1)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[],[f511]) ).
tcf(c_133,plain,
! [X0: $i,X1: $i] :
( aInteger0(X0)
| ~ aSubsetOf0(X1,cS1395)
| ~ aElementOf0(X0,stldt0(X1)) ),
inference(cnf_transformation,[],[f512]) ).
tcf(c_134,plain,
! [X0: $i,X1: $i] :
( ~ aSubsetOf0(X1,cS1395)
| ~ aElementOf0(X0,X1)
| ~ aElementOf0(X0,stldt0(X1)) ),
inference(cnf_transformation,[],[f513]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = sz00 )
| ( szAzrzSzezqlpdtcmdtrp0(X0,X1) = X2 )
| ~ aSet0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ aInteger0(sK20(X0,X1,X2))
| ~ aElementOf0(sK20(X0,X1,X2),X2)
| ~ sdteqdtlpzmzozddtrp0(sK20(X0,X1,X2),X0,X1) ),
inference(cnf_transformation,[],[f304]) ).
tcf(c_136,plain,
! [X0: $i,X1: $i,X2: $i] :
( aInteger0(sK20(X0,X1,X2))
| aElementOf0(sK20(X0,X1,X2),X2)
| ( X1 = sz00 )
| ( szAzrzSzezqlpdtcmdtrp0(X0,X1) = X2 )
| ~ aSet0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f303]) ).
tcf(c_137,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(sK20(X0,X1,X2),X2)
| sdteqdtlpzmzozddtrp0(sK20(X0,X1,X2),X0,X1)
| ( X1 = sz00 )
| ( szAzrzSzezqlpdtcmdtrp0(X0,X1) = X2 )
| ~ aSet0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f302]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] :
( aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
| ( X1 = sz00 )
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f514]) ).
tcf(c_139,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(X1,X2))
| ( X2 = sz00 )
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2) ),
inference(cnf_transformation,[],[f515]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i,X2: $i] :
( aInteger0(X0)
| ( X2 = sz00 )
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ),
inference(cnf_transformation,[],[f516]) ).
tcf(c_141,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ( X2 = sz00 )
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ),
inference(cnf_transformation,[],[f517]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i] :
( isOpen0(X0)
| ( X1 = sz00 )
| ~ aInteger0(X1)
| ~ aSubsetOf0(X0,cS1395)
| ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sK21(X0),X1),X0) ),
inference(cnf_transformation,[],[f309]) ).
tcf(c_143,plain,
! [X0: $i] :
( isOpen0(X0)
| aElementOf0(sK21(X0),X0)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[],[f308]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i] :
( aInteger0(sK22(X1,X0))
| ~ isOpen0(X1)
| ~ aSubsetOf0(X1,cS1395)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f307]) ).
tcf(c_145,plain,
! [X0: $i,X1: $i] :
( ~ isOpen0(X0)
| ~ aSubsetOf0(X0,cS1395)
| ~ aElementOf0(X1,X0)
| ( sK22(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f306]) ).
tcf(c_146,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,sK22(X1,X0)),X1)
| ~ isOpen0(X1)
| ~ aSubsetOf0(X1,cS1395)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f305]) ).
tcf(c_147,plain,
! [X0: $i] :
( isClosed0(X0)
| ~ isOpen0(stldt0(X0))
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[],[f311]) ).
tcf(c_148,plain,
! [X0: $i] :
( isOpen0(stldt0(X0))
| ~ isClosed0(X0)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[],[f310]) ).
tcf(c_149,plain,
! [X0: $i] :
( isOpen0(sbsmnsldt0(X0))
| ~ aSet0(X0)
| ~ isOpen0(sK23(X0))
| ~ aSubsetOf0(sK23(X0),cS1395) ),
inference(cnf_transformation,[],[f313]) ).
tcf(c_150,plain,
! [X0: $i] :
( isOpen0(sbsmnsldt0(X0))
| aElementOf0(sK23(X0),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f312]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i] :
( isOpen0(sdtslmnbsdt0(X0,X1))
| ~ isOpen0(X1)
| ~ isOpen0(X0)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[],[f314]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i] :
( isClosed0(sdtbsmnsldt0(X0,X1))
| ~ isClosed0(X1)
| ~ isClosed0(X0)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[],[f315]) ).
tcf(c_153,plain,
! [X0: $i] :
( isClosed0(sbsmnsldt0(X0))
| ~ isFinite0(X0)
| ~ aSet0(X0)
| ~ isClosed0(sK24(X0))
| ~ aSubsetOf0(sK24(X0),cS1395) ),
inference(cnf_transformation,[],[f317]) ).
tcf(c_154,plain,
! [X0: $i] :
( isClosed0(sbsmnsldt0(X0))
| aElementOf0(sK24(X0),X0)
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f316]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),cS1395)
| ( X1 = sz00 )
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f319]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i] :
( isClosed0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
| ( X1 = sz00 )
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f318]) ).
tcf(c_157,plain,
! [X0: $i,X1: $i] :
( aInteger0(X0)
| ~ sP7(X1)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ),
inference(cnf_transformation,[],[f327]) ).
tcf(c_158,plain,
! [X0: $i,X1: $i] :
( aInteger0(sK25(X1,X0))
| ~ sP7(X1)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ),
inference(cnf_transformation,[],[f326]) ).
tcf(c_159,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X1,sK25(X1,X0)) = sdtpldt0(X0,smndt0(sz00)) )
| ~ sP7(X1)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ),
inference(cnf_transformation,[],[f325]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i] :
( aDivisorOf0(X1,sdtpldt0(X0,smndt0(sz00)))
| ~ sP7(X1)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ),
inference(cnf_transformation,[],[f324]) ).
tcf(c_161,plain,
! [X0: $i,X1: $i] :
( sdteqdtlpzmzozddtrp0(X0,sz00,X1)
| ~ sP7(X1)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ),
inference(cnf_transformation,[],[f323]) ).
tcf(c_162,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ~ sP7(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X0)
| ( sdtpldt0(X0,smndt0(sz00)) != sdtasdt0(X1,X2) ) ),
inference(cnf_transformation,[],[f322]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| ~ sP7(X0)
| ~ aInteger0(X1)
| ~ aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00))) ),
inference(cnf_transformation,[],[f321]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ~ sP7(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,sz00,X1) ),
inference(cnf_transformation,[],[f320]) ).
tcf(c_173,plain,
aSet0(cS2043),
inference(cnf_transformation,[],[f439]) ).
tcf(c_174,plain,
! [X0: $i] :
( aInteger0(sK27(X0))
| ~ aElementOf0(X0,cS2043) ),
inference(cnf_transformation,[],[f440]) ).
tcf(c_175,plain,
! [X0: $i] :
( ~ aElementOf0(X0,cS2043)
| ( sK27(X0) != sz00 ) ),
inference(cnf_transformation,[],[f441]) ).
tcf(c_176,plain,
! [X0: $i] :
( isPrime0(sK27(X0))
| ~ aElementOf0(X0,cS2043) ),
inference(cnf_transformation,[],[f442]) ).
tcf(c_177,plain,
! [X0: $i] :
( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,sK27(X0)))
| ~ aElementOf0(X0,cS2043) ),
inference(cnf_transformation,[],[f443]) ).
tcf(c_178,plain,
! [X0: $i] :
( sP7(sK27(X0))
| ~ aElementOf0(X0,cS2043) ),
inference(cnf_transformation,[],[f444]) ).
tcf(c_179,plain,
! [X0: $i] :
( ( szAzrzSzezqlpdtcmdtrp0(sz00,sK27(X0)) = X0 )
| ~ aElementOf0(X0,cS2043) ),
inference(cnf_transformation,[],[f445]) ).
tcf(c_180,plain,
! [X0: $i] :
( aElementOf0(szAzrzSzezqlpdtcmdtrp0(sz00,X0),cS2043)
| ( X0 = sz00 )
| ~ isPrime0(X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f518]) ).
tcf(c_181,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X1,cS2043)
| aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| ( X0 = sz00 )
| ~ isPrime0(X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f447]) ).
tcf(c_182,plain,
! [X0: $i,X1: $i] :
( sP6(X0)
| aElementOf0(X1,cS2043)
| ( X0 = sz00 )
| ~ isPrime0(X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f448]) ).
tcf(c_186,plain,
! [X0: $i] :
( aElementOf0(sK28(X0),cS2043)
| ~ aElementOf0(X0,sbsmnsldt0(cS2043)) ),
inference(cnf_transformation,[],[f452]) ).
tcf(c_187,plain,
! [X0: $i] :
( aElementOf0(X0,sK28(X0))
| ~ aElementOf0(X0,sbsmnsldt0(cS2043)) ),
inference(cnf_transformation,[],[f453]) ).
tcf(c_188,plain,
aSet0(stldt0(sbsmnsldt0(cS2043))),
inference(cnf_transformation,[],[f454]) ).
tcf(c_192,plain,
aElementOf0(sz10,stldt0(sbsmnsldt0(cS2043))),
inference(cnf_transformation,[],[f519]) ).
tcf(c_193,plain,
aElementOf0(smndt0(sz10),stldt0(sbsmnsldt0(cS2043))),
inference(cnf_transformation,[],[f520]) ).
tcf(c_194,plain,
! [X0: $i] :
( ( X0 = sz10 )
| ( smndt0(sz10) = X0 )
| ~ aElementOf0(X0,stldt0(sbsmnsldt0(cS2043))) ),
inference(cnf_transformation,[],[f460]) ).
tcf(c_195,plain,
stldt0(sbsmnsldt0(cS2043)) = cS2076,
inference(cnf_transformation,[],[f461]) ).
tcf(c_196,plain,
isFinite0(cS2043),
inference(cnf_transformation,[],[f462]) ).
tcf(c_197,plain,
! [X0: $i,X1: $i,X2: $i] :
( aInteger0(X0)
| ~ sP9(X1,X2)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ),
inference(cnf_transformation,[],[f368]) ).
tcf(c_198,plain,
! [X0: $i,X1: $i,X2: $i] :
( aInteger0(sK29(X1,X2,X0))
| ~ sP9(X1,X2)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ),
inference(cnf_transformation,[],[f367]) ).
tcf(c_199,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(X2,sK29(X1,X2,X0)) = sdtpldt0(X0,smndt0(X1)) )
| ~ sP9(X1,X2)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ),
inference(cnf_transformation,[],[f366]) ).
tcf(c_200,plain,
! [X0: $i,X1: $i,X2: $i] :
( aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
| ~ sP9(X1,X2)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ),
inference(cnf_transformation,[],[f365]) ).
tcf(c_201,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ sP9(X1,X2)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ),
inference(cnf_transformation,[],[f364]) ).
tcf(c_202,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(X1,X2))
| ~ aInteger0(X3)
| ~ aInteger0(X0)
| ~ sP9(X1,X2)
| ( sdtpldt0(X0,smndt0(X1)) != sdtasdt0(X2,X3) ) ),
inference(cnf_transformation,[],[f363]) ).
tcf(c_203,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(X2,X0))
| ~ aInteger0(X1)
| ~ sP9(X2,X0)
| ~ aDivisorOf0(X0,sdtpldt0(X1,smndt0(X2))) ),
inference(cnf_transformation,[],[f362]) ).
tcf(c_204,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(X1,X2))
| ~ aInteger0(X0)
| ~ sP9(X1,X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2) ),
inference(cnf_transformation,[],[f361]) ).
tcf(c_216,plain,
! [X0: $i] :
( aElementOf0(sK31(X0),cS2043)
| ~ aElementOf0(X0,sbsmnsldt0(cS2043)) ),
inference(cnf_transformation,[],[f466]) ).
tcf(c_217,plain,
! [X0: $i] :
( aElementOf0(X0,sK31(X0))
| ~ aElementOf0(X0,sbsmnsldt0(cS2043)) ),
inference(cnf_transformation,[],[f467]) ).
tcf(c_221,plain,
! [X0: $i] :
( aInteger0(sK32(X0))
| ~ aElementOf0(X0,stldt0(sbsmnsldt0(cS2043))) ),
inference(cnf_transformation,[],[f471]) ).
tcf(c_222,plain,
! [X0: $i] :
( ~ aElementOf0(X0,stldt0(sbsmnsldt0(cS2043)))
| ( sK32(X0) != sz00 ) ),
inference(cnf_transformation,[],[f472]) ).
tcf(c_223,plain,
! [X0: $i] :
( aSet0(szAzrzSzezqlpdtcmdtrp0(X0,sK32(X0)))
| ~ aElementOf0(X0,stldt0(sbsmnsldt0(cS2043))) ),
inference(cnf_transformation,[],[f473]) ).
tcf(c_224,plain,
! [X0: $i] :
( sP9(X0,sK32(X0))
| ~ aElementOf0(X0,stldt0(sbsmnsldt0(cS2043))) ),
inference(cnf_transformation,[],[f474]) ).
tcf(c_225,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,stldt0(sbsmnsldt0(cS2043)))
| ~ aElementOf0(X1,stldt0(sbsmnsldt0(cS2043)))
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(X1,sK32(X1))) ),
inference(cnf_transformation,[],[f475]) ).
tcf(c_226,plain,
! [X0: $i] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,sK32(X0)),stldt0(sbsmnsldt0(cS2043)))
| ~ aElementOf0(X0,stldt0(sbsmnsldt0(cS2043))) ),
inference(cnf_transformation,[],[f476]) ).
tcf(c_227,plain,
isOpen0(stldt0(sbsmnsldt0(cS2043))),
inference(cnf_transformation,[],[f477]) ).
tcf(c_228,plain,
isClosed0(sbsmnsldt0(cS2043)),
inference(cnf_transformation,[],[f478]) ).
tcf(c_232,plain,
! [X0: $i] :
( aElementOf0(sK33(X0),cS2043)
| ~ aElementOf0(X0,sbsmnsldt0(cS2043)) ),
inference(cnf_transformation,[],[f482]) ).
tcf(c_233,plain,
! [X0: $i] :
( aElementOf0(X0,sK33(X0))
| ~ aElementOf0(X0,sbsmnsldt0(cS2043)) ),
inference(cnf_transformation,[],[f483]) ).
tcf(c_237,plain,
! [X0: $i] :
( aInteger0(sK34(X0))
| ~ aElementOf0(X0,stldt0(sbsmnsldt0(cS2043))) ),
inference(cnf_transformation,[],[f487]) ).
tcf(c_238,plain,
! [X0: $i] :
( ~ aElementOf0(X0,stldt0(sbsmnsldt0(cS2043)))
| ( sK34(X0) != sz00 ) ),
inference(cnf_transformation,[],[f488]) ).
tcf(c_239,plain,
! [X0: $i] :
( aSet0(szAzrzSzezqlpdtcmdtrp0(X0,sK34(X0)))
| ~ aElementOf0(X0,stldt0(sbsmnsldt0(cS2043))) ),
inference(cnf_transformation,[],[f489]) ).
tcf(c_240,plain,
! [X0: $i] :
( sP8(X0,sK34(X0))
| ~ aElementOf0(X0,stldt0(sbsmnsldt0(cS2043))) ),
inference(cnf_transformation,[],[f490]) ).
tcf(c_241,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,stldt0(sbsmnsldt0(cS2043)))
| ~ aElementOf0(X1,stldt0(sbsmnsldt0(cS2043)))
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(X1,sK34(X1))) ),
inference(cnf_transformation,[],[f491]) ).
tcf(c_242,plain,
! [X0: $i] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,sK34(X0)),stldt0(sbsmnsldt0(cS2043)))
| ~ aElementOf0(X0,stldt0(sbsmnsldt0(cS2043))) ),
inference(cnf_transformation,[],[f492]) ).
tcf(c_243,plain,
aInteger0(xp),
inference(cnf_transformation,[],[f427]) ).
tcf(c_244,plain,
sz00 != xp,
inference(cnf_transformation,[],[f426]) ).
tcf(c_245,plain,
aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(cnf_transformation,[],[f425]) ).
tcf(c_246,plain,
! [X0: $i] :
( aInteger0(X0)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(cnf_transformation,[],[f424]) ).
tcf(c_247,plain,
! [X0: $i] :
( aInteger0(sK35(X0))
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(cnf_transformation,[],[f423]) ).
tcf(c_248,plain,
! [X0: $i] :
( ( sdtpldt0(X0,smndt0(sz10)) = sdtasdt0(xp,sK35(X0)) )
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(cnf_transformation,[],[f422]) ).
tcf(c_249,plain,
! [X0: $i] :
( aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(cnf_transformation,[],[f421]) ).
tcf(c_250,plain,
! [X0: $i] :
( sdteqdtlpzmzozddtrp0(X0,sz10,xp)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(cnf_transformation,[],[f420]) ).
tcf(c_251,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ( sdtpldt0(X0,smndt0(sz10)) != sdtasdt0(xp,X1) ) ),
inference(cnf_transformation,[],[f419]) ).
tcf(c_252,plain,
! [X0: $i] :
( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aInteger0(X0)
| ~ aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10))) ),
inference(cnf_transformation,[],[f418]) ).
tcf(c_253,plain,
! [X0: $i] :
( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,sz10,xp) ),
inference(cnf_transformation,[],[f417]) ).
tcf(c_254,plain,
aSet0(sbsmnsldt0(cS2043)),
inference(cnf_transformation,[],[f493]) ).
tcf(c_255,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,sbsmnsldt0(cS2043))
| ~ aInteger0(X0)
| ~ aElementOf0(X1,cS2043)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f494]) ).
tcf(c_256,plain,
! [X0: $i] :
( aInteger0(X0)
| ~ aElementOf0(X0,sbsmnsldt0(cS2043)) ),
inference(cnf_transformation,[],[f495]) ).
tcf(c_257,plain,
! [X0: $i] :
( aElementOf0(sK36(X0),cS2043)
| ~ aElementOf0(X0,sbsmnsldt0(cS2043)) ),
inference(cnf_transformation,[],[f496]) ).
tcf(c_258,plain,
! [X0: $i] :
( aElementOf0(X0,sK36(X0))
| ~ aElementOf0(X0,sbsmnsldt0(cS2043)) ),
inference(cnf_transformation,[],[f497]) ).
tcf(c_259,plain,
! [X0: $i] :
( aElementOf0(X0,sbsmnsldt0(cS2043))
| aElementOf0(X0,stldt0(sbsmnsldt0(cS2043)))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f498]) ).
tcf(c_260,plain,
! [X0: $i] :
( aInteger0(X0)
| ~ aElementOf0(X0,stldt0(sbsmnsldt0(cS2043))) ),
inference(cnf_transformation,[],[f499]) ).
tcf(c_261,plain,
! [X0: $i] :
( ~ aElementOf0(X0,sbsmnsldt0(cS2043))
| ~ aElementOf0(X0,stldt0(sbsmnsldt0(cS2043))) ),
inference(cnf_transformation,[],[f500]) ).
tcf(c_262,plain,
! [X0: $i] :
( aElementOf0(X0,stldt0(sbsmnsldt0(cS2043)))
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(cnf_transformation,[],[f501]) ).
tcf(c_263,plain,
aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(cS2043))),
inference(cnf_transformation,[],[f502]) ).
tcf(c_264,plain,
aInteger0(sK37),
inference(cnf_transformation,[],[f437]) ).
tcf(c_265,plain,
sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) = sdtasdt0(xp,sK37),
inference(cnf_transformation,[],[f436]) ).
tcf(c_266,plain,
aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))),
inference(cnf_transformation,[],[f435]) ).
tcf(c_267,plain,
sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp),
inference(cnf_transformation,[],[f434]) ).
tcf(c_268,plain,
aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(cnf_transformation,[],[f433]) ).
tcf(c_269,plain,
aInteger0(sK38),
inference(cnf_transformation,[],[f432]) ).
tcf(c_270,plain,
sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)) = sdtasdt0(xp,sK38),
inference(cnf_transformation,[],[f431]) ).
tcf(c_271,plain,
aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))),
inference(cnf_transformation,[],[f430]) ).
tcf(c_272,plain,
sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp),
inference(cnf_transformation,[],[f429]) ).
tcf(c_273,plain,
aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(cnf_transformation,[],[f428]) ).
tcf(c_274,negated_conjecture,
( ( sdtpldt0(sz10,xp) = sz10 )
| ( sdtpldt0(sz10,smndt0(xp)) = sz10 ) ),
inference(cnf_transformation,[],[f438]) ).
tcf(c_430,plain,
! [X0: $i] :
( ~ aDivisorOf0(X0,sz10)
| ~ isPrime0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_85,c_50,c_85]) ).
tcf(c_431,plain,
! [X0: $i] :
( ~ isPrime0(X0)
| ~ aDivisorOf0(X0,sz10) ),
inference(renaming,[status(thm)],[c_430]) ).
tcf(c_433,plain,
! [X0: $i,X1: $i] :
( aDivisorOf0(X0,sdtasdt0(X0,X1))
| ( X0 = sz00 )
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_71,c_53,c_71]) ).
tcf(c_14337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(sK20(X0,sdtasdt0(X1,X2),X3),X3)
| sdteqdtlpzmzozddtrp0(sK20(X0,sdtasdt0(X1,X2),X3),X0,X1)
| ( X2 = sz00 )
| ( X1 = sz00 )
| ( sdtasdt0(X1,X2) = sz00 )
| ( szAzrzSzezqlpdtcmdtrp0(X0,sdtasdt0(X1,X2)) = X3 )
| ~ aSet0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ aInteger0(sdtasdt0(X1,X2))
| ~ aInteger0(sK20(X0,sdtasdt0(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_137,c_81]) ).
fof(f124,definition,
! [X2,X0,X1] :
( sP0(X2,X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( ( aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aInteger0(X3) ) )
& aSet0(X2) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f125,definition,
! [X1,X0] :
( ~ sP1(X1,X0)
| ! [X2] :
( X2 = sdtbsmnsldt0(X0,X1)
<=> sP0(X2,X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f126,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395)
| sP1(X1,X0) ),
inference(definition_folding,[],[f97,f125,f124]) ).
fof(f127,definition,
! [X2,X0,X1] :
( sP2(X2,X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,X1)
& aElementOf0(X3,X0)
& aInteger0(X3) ) )
& aSet0(X2) ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f128,definition,
! [X1,X0] :
( ~ sP3(X1,X0)
| ! [X2] :
( X2 = sdtslmnbsdt0(X0,X1)
<=> sP2(X2,X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f129,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395)
| sP3(X1,X0) ),
inference(definition_folding,[],[f99,f128,f127]) ).
fof(f130,definition,
! [X2,X0] :
( sP4(X2,X0)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( ? [X4] :
( aElementOf0(X3,X4)
& aElementOf0(X4,X0) )
& aInteger0(X3) ) )
& aSet0(X2) ) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f131,definition,
! [X0] :
( ~ sP5(X0)
| ! [X2] :
( sbsmnsldt0(X0) = X2
<=> sP4(X2,X0) ) ),
introduced(definition,[new_symbols(definition,[sP5])],[predicate_definition_introduction]) ).
fof(f132,plain,
! [X0] :
( ? [X1] :
( aElementOf0(X1,X0)
& ~ aSubsetOf0(X1,cS1395) )
| ~ aSet0(X0)
| sP5(X0) ),
inference(definition_folding,[],[f101,f131,f130]) ).
fof(f133,definition,
! [X5] :
( ~ sP6(X5)
| ! [X6] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& ~ aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ! [X8] :
( sdtpldt0(X6,smndt0(sz00)) != sdtasdt0(X5,X8)
| ~ aInteger0(X8) ) )
| ~ aInteger0(X6)
| aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5)) )
& ( ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
| ( sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ? [X7] :
( sdtasdt0(X5,X7) = sdtpldt0(X6,smndt0(sz00))
& aInteger0(X7) )
& aInteger0(X6) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])],[predicate_definition_introduction]) ).
fof(f134,definition,
! [X1] :
( ~ sP7(X1)
| ! [X2] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X2,sz00,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ! [X4] :
( sdtpldt0(X2,smndt0(sz00)) != sdtasdt0(X1,X4)
| ~ aInteger0(X4) ) )
| ~ aInteger0(X2)
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
& ( ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00))
& aInteger0(X3) )
& aInteger0(X2) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])],[predicate_definition_introduction]) ).
fof(f135,plain,
( xS = cS2043
& ! [X0] :
( ( ! [X5] :
( ( sP6(X5)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5))
& szAzrzSzezqlpdtcmdtrp0(sz00,X5) != X0 )
| ~ isPrime0(X5)
| sz00 = X5
| ~ aInteger0(X5) )
| aElementOf0(X0,xS) )
& ( ~ aElementOf0(X0,xS)
| ? [X1] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0
& sP7(X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
& isPrime0(X1)
& X1 != sz00
& aInteger0(X1) ) ) )
& aSet0(xS) ),
inference(definition_folding,[],[f118,f134,f133]) ).
fof(f136,definition,
! [X12,X13] :
( ~ sP8(X12,X13)
| ! [X14] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X14,X12,X13)
& ~ aDivisorOf0(X13,sdtpldt0(X14,smndt0(X12)))
& ! [X16] :
( sdtpldt0(X14,smndt0(X12)) != sdtasdt0(X13,X16)
| ~ aInteger0(X16) ) )
| ~ aInteger0(X14)
| aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(X12,X13)) )
& ( ~ aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(X12,X13))
| ( sdteqdtlpzmzozddtrp0(X14,X12,X13)
& aDivisorOf0(X13,sdtpldt0(X14,smndt0(X12)))
& ? [X15] :
( sdtasdt0(X13,X15) = sdtpldt0(X14,smndt0(X12))
& aInteger0(X15) )
& aInteger0(X14) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f137,definition,
! [X3,X4] :
( ~ sP9(X3,X4)
| ! [X5] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X5,X3,X4)
& ~ aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& ! [X7] :
( sdtpldt0(X5,smndt0(X3)) != sdtasdt0(X4,X7)
| ~ aInteger0(X7) ) )
| ~ aInteger0(X5)
| aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& ( ~ aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4))
| ( sdteqdtlpzmzozddtrp0(X5,X3,X4)
& aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& ? [X6] :
( sdtasdt0(X4,X6) = sdtpldt0(X5,smndt0(X3))
& aInteger0(X6) )
& aInteger0(X5) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])],[predicate_definition_introduction]) ).
fof(f138,plain,
( ! [X12] :
( ~ aElementOf0(X12,stldt0(sbsmnsldt0(xS)))
| ? [X13] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X12,X13),stldt0(sbsmnsldt0(xS)))
& ! [X17] :
( ~ aElementOf0(X17,szAzrzSzezqlpdtcmdtrp0(X12,X13))
| aElementOf0(X17,stldt0(sbsmnsldt0(xS))) )
& sP8(X12,X13)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X12,X13))
& sz00 != X13
& aInteger0(X13) ) )
& ! [X11] :
( aElementOf0(X11,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X11,sbsmnsldt0(xS))
& aInteger0(X11) ) )
& ! [X9] :
( aElementOf0(X9,sbsmnsldt0(xS))
<=> ( ? [X10] :
( aElementOf0(X9,X10)
& aElementOf0(X10,xS) )
& aInteger0(X9) ) )
& aSet0(sbsmnsldt0(xS))
& isClosed0(sbsmnsldt0(xS))
& isOpen0(stldt0(sbsmnsldt0(xS)))
& ! [X3] :
( ~ aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
| ? [X4] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),stldt0(sbsmnsldt0(xS)))
& ! [X8] :
( ~ aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(X3,X4))
| aElementOf0(X8,stldt0(sbsmnsldt0(xS))) )
& sP9(X3,X4)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X3,X4))
& sz00 != X4
& aInteger0(X4) ) )
& ! [X2] :
( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X2,sbsmnsldt0(xS))
& aInteger0(X2) ) )
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(definition_folding,[],[f120,f137,f136]) ).
fof(f154,plain,
! [X2,X0,X1] :
( ( ~ sP0(X2,X0,X1)
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( ( aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aInteger0(X3) ) )
& ( ( ~ aElementOf0(X3,X1)
& ~ aElementOf0(X3,X0) )
| ~ aInteger0(X3)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( ( aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aInteger0(X3) ) )
& ( ~ aElementOf0(X3,X2)
| ( ~ aElementOf0(X3,X1)
& ~ aElementOf0(X3,X0) )
| ~ aInteger0(X3) ) )
| ~ aSet0(X2)
| sP0(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f124]) ).
fof(f155,plain,
! [X2,X0,X1] :
( ( ~ sP0(X2,X0,X1)
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( ( aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aInteger0(X3) ) )
& ( ( ~ aElementOf0(X3,X1)
& ~ aElementOf0(X3,X0) )
| ~ aInteger0(X3)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( ( aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aInteger0(X3) ) )
& ( ~ aElementOf0(X3,X2)
| ( ~ aElementOf0(X3,X1)
& ~ aElementOf0(X3,X0) )
| ~ aInteger0(X3) ) )
| ~ aSet0(X2)
| sP0(X2,X0,X1) ) ),
inference(flattening,[],[f154]) ).
fof(f156,plain,
! [X0,X1,X2] :
( ( ~ sP0(X0,X1,X2)
| ( ! [X4] :
( ( ~ aElementOf0(X4,X0)
| ( ( aElementOf0(X4,X2)
| aElementOf0(X4,X1) )
& aInteger0(X4) ) )
& ( ( ~ aElementOf0(X4,X2)
& ~ aElementOf0(X4,X1) )
| ~ aInteger0(X4)
| aElementOf0(X4,X0) ) )
& aSet0(X0) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X0)
| ( ( aElementOf0(X3,X2)
| aElementOf0(X3,X1) )
& aInteger0(X3) ) )
& ( ~ aElementOf0(X3,X0)
| ( ~ aElementOf0(X3,X2)
& ~ aElementOf0(X3,X1) )
| ~ aInteger0(X3) ) )
| ~ aSet0(X0)
| sP0(X0,X1,X2) ) ),
inference(rectify,[],[f155]) ).
fof(f157,plain,
! [X0,X1,X2] :
( ( ~ sP0(X0,X1,X2)
| ( ! [X4] :
( ( ~ aElementOf0(X4,X0)
| ( ( aElementOf0(X4,X2)
| aElementOf0(X4,X1) )
& aInteger0(X4) ) )
& ( ( ~ aElementOf0(X4,X2)
& ~ aElementOf0(X4,X1) )
| ~ aInteger0(X4)
| aElementOf0(X4,X0) ) )
& aSet0(X0) ) )
& ( ( ( aElementOf0(sK13(X0,X1,X2),X0)
| ( ( aElementOf0(sK13(X0,X1,X2),X2)
| aElementOf0(sK13(X0,X1,X2),X1) )
& aInteger0(sK13(X0,X1,X2)) ) )
& ( ~ aElementOf0(sK13(X0,X1,X2),X0)
| ( ~ aElementOf0(sK13(X0,X1,X2),X2)
& ~ aElementOf0(sK13(X0,X1,X2),X1) )
| ~ aInteger0(sK13(X0,X1,X2)) ) )
| ~ aSet0(X0)
| sP0(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X3,sK13(X0,X1,X2))],[f156]) ).
fof(f160,plain,
! [X2,X0,X1] :
( ( ~ sP2(X2,X0,X1)
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( aElementOf0(X3,X1)
& aElementOf0(X3,X0)
& aInteger0(X3) ) )
& ( ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0)
| ~ aInteger0(X3)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( aElementOf0(X3,X1)
& aElementOf0(X3,X0)
& aInteger0(X3) ) )
& ( ~ aElementOf0(X3,X2)
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0)
| ~ aInteger0(X3) ) )
| ~ aSet0(X2)
| sP2(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f127]) ).
fof(f161,plain,
! [X2,X0,X1] :
( ( ~ sP2(X2,X0,X1)
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( aElementOf0(X3,X1)
& aElementOf0(X3,X0)
& aInteger0(X3) ) )
& ( ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0)
| ~ aInteger0(X3)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( aElementOf0(X3,X1)
& aElementOf0(X3,X0)
& aInteger0(X3) ) )
& ( ~ aElementOf0(X3,X2)
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0)
| ~ aInteger0(X3) ) )
| ~ aSet0(X2)
| sP2(X2,X0,X1) ) ),
inference(flattening,[],[f160]) ).
fof(f162,plain,
! [X0,X1,X2] :
( ( ~ sP2(X0,X1,X2)
| ( ! [X4] :
( ( ~ aElementOf0(X4,X0)
| ( aElementOf0(X4,X2)
& aElementOf0(X4,X1)
& aInteger0(X4) ) )
& ( ~ aElementOf0(X4,X2)
| ~ aElementOf0(X4,X1)
| ~ aInteger0(X4)
| aElementOf0(X4,X0) ) )
& aSet0(X0) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X0)
| ( aElementOf0(X3,X2)
& aElementOf0(X3,X1)
& aInteger0(X3) ) )
& ( ~ aElementOf0(X3,X0)
| ~ aElementOf0(X3,X2)
| ~ aElementOf0(X3,X1)
| ~ aInteger0(X3) ) )
| ~ aSet0(X0)
| sP2(X0,X1,X2) ) ),
inference(rectify,[],[f161]) ).
fof(f163,plain,
! [X0,X1,X2] :
( ( ~ sP2(X0,X1,X2)
| ( ! [X4] :
( ( ~ aElementOf0(X4,X0)
| ( aElementOf0(X4,X2)
& aElementOf0(X4,X1)
& aInteger0(X4) ) )
& ( ~ aElementOf0(X4,X2)
| ~ aElementOf0(X4,X1)
| ~ aInteger0(X4)
| aElementOf0(X4,X0) ) )
& aSet0(X0) ) )
& ( ( ( aElementOf0(sK14(X0,X1,X2),X0)
| ( aElementOf0(sK14(X0,X1,X2),X2)
& aElementOf0(sK14(X0,X1,X2),X1)
& aInteger0(sK14(X0,X1,X2)) ) )
& ( ~ aElementOf0(sK14(X0,X1,X2),X0)
| ~ aElementOf0(sK14(X0,X1,X2),X2)
| ~ aElementOf0(sK14(X0,X1,X2),X1)
| ~ aInteger0(sK14(X0,X1,X2)) ) )
| ~ aSet0(X0)
| sP2(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X3,sK14(X0,X1,X2))],[f162]) ).
fof(f166,plain,
! [X2,X0] :
( ( ~ sP4(X2,X0)
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( ? [X4] :
( aElementOf0(X3,X4)
& aElementOf0(X4,X0) )
& aInteger0(X3) ) )
& ( ! [X4] :
( ~ aElementOf0(X3,X4)
| ~ aElementOf0(X4,X0) )
| ~ aInteger0(X3)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( ? [X4] :
( aElementOf0(X3,X4)
& aElementOf0(X4,X0) )
& aInteger0(X3) ) )
& ( ~ aElementOf0(X3,X2)
| ! [X4] :
( ~ aElementOf0(X3,X4)
| ~ aElementOf0(X4,X0) )
| ~ aInteger0(X3) ) )
| ~ aSet0(X2)
| sP4(X2,X0) ) ),
inference(nnf_transformation,[],[f130]) ).
fof(f167,plain,
! [X2,X0] :
( ( ~ sP4(X2,X0)
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( ? [X4] :
( aElementOf0(X3,X4)
& aElementOf0(X4,X0) )
& aInteger0(X3) ) )
& ( ! [X4] :
( ~ aElementOf0(X3,X4)
| ~ aElementOf0(X4,X0) )
| ~ aInteger0(X3)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( ? [X4] :
( aElementOf0(X3,X4)
& aElementOf0(X4,X0) )
& aInteger0(X3) ) )
& ( ~ aElementOf0(X3,X2)
| ! [X4] :
( ~ aElementOf0(X3,X4)
| ~ aElementOf0(X4,X0) )
| ~ aInteger0(X3) ) )
| ~ aSet0(X2)
| sP4(X2,X0) ) ),
inference(flattening,[],[f166]) ).
fof(f168,plain,
! [X0,X1] :
( ( ~ sP4(X0,X1)
| ( ! [X5] :
( ( ~ aElementOf0(X5,X0)
| ( ? [X7] :
( aElementOf0(X5,X7)
& aElementOf0(X7,X1) )
& aInteger0(X5) ) )
& ( ! [X6] :
( ~ aElementOf0(X5,X6)
| ~ aElementOf0(X6,X1) )
| ~ aInteger0(X5)
| aElementOf0(X5,X0) ) )
& aSet0(X0) ) )
& ( ? [X2] :
( ( aElementOf0(X2,X0)
| ( ? [X4] :
( aElementOf0(X2,X4)
& aElementOf0(X4,X1) )
& aInteger0(X2) ) )
& ( ~ aElementOf0(X2,X0)
| ! [X3] :
( ~ aElementOf0(X2,X3)
| ~ aElementOf0(X3,X1) )
| ~ aInteger0(X2) ) )
| ~ aSet0(X0)
| sP4(X0,X1) ) ),
inference(rectify,[],[f167]) ).
fof(f169,plain,
! [X0,X1] :
( ( ~ sP4(X0,X1)
| ( ! [X5] :
( ( ~ aElementOf0(X5,X0)
| ( aElementOf0(X5,sK17(X1,X5))
& aElementOf0(sK17(X1,X5),X1)
& aInteger0(X5) ) )
& ( ! [X6] :
( ~ aElementOf0(X5,X6)
| ~ aElementOf0(X6,X1) )
| ~ aInteger0(X5)
| aElementOf0(X5,X0) ) )
& aSet0(X0) ) )
& ( ( ( aElementOf0(sK15(X0,X1),X0)
| ( aElementOf0(sK15(X0,X1),sK16(X0,X1))
& aElementOf0(sK16(X0,X1),X1)
& aInteger0(sK15(X0,X1)) ) )
& ( ~ aElementOf0(sK15(X0,X1),X0)
| ! [X3] :
( ~ aElementOf0(sK15(X0,X1),X3)
| ~ aElementOf0(X3,X1) )
| ~ aInteger0(sK15(X0,X1)) ) )
| ~ aSet0(X0)
| sP4(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16,sK17]),skolemize(X2,sK15(X0,X1)),skolemize(X4,sK16(X0,X1)),skolemize(X7,sK17(X1,X5))],[f168]) ).
fof(f188,plain,
! [X5] :
( ~ sP6(X5)
| ! [X6] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& ~ aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ! [X8] :
( sdtpldt0(X6,smndt0(sz00)) != sdtasdt0(X5,X8)
| ~ aInteger0(X8) ) )
| ~ aInteger0(X6)
| aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5)) )
& ( ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
| ( sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ? [X7] :
( sdtasdt0(X5,X7) = sdtpldt0(X6,smndt0(sz00))
& aInteger0(X7) )
& aInteger0(X6) ) ) ) ),
inference(nnf_transformation,[],[f133]) ).
fof(f189,plain,
! [X0] :
( ~ sP6(X0)
| ! [X1] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X1,sz00,X0)
& ~ aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
& ! [X3] :
( sdtpldt0(X1,smndt0(sz00)) != sdtasdt0(X0,X3)
| ~ aInteger0(X3) ) )
| ~ aInteger0(X1)
| aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0)) )
& ( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| ( sdteqdtlpzmzozddtrp0(X1,sz00,X0)
& aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
& ? [X2] :
( sdtasdt0(X0,X2) = sdtpldt0(X1,smndt0(sz00))
& aInteger0(X2) )
& aInteger0(X1) ) ) ) ),
inference(rectify,[],[f188]) ).
fof(f190,plain,
! [X0] :
( ~ sP6(X0)
| ! [X1] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X1,sz00,X0)
& ~ aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
& ! [X3] :
( sdtpldt0(X1,smndt0(sz00)) != sdtasdt0(X0,X3)
| ~ aInteger0(X3) ) )
| ~ aInteger0(X1)
| aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0)) )
& ( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| ( sdteqdtlpzmzozddtrp0(X1,sz00,X0)
& aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
& sdtpldt0(X1,smndt0(sz00)) = sdtasdt0(X0,sK26(X0,X1))
& aInteger0(sK26(X0,X1))
& aInteger0(X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(X2,sK26(X0,X1))],[f189]) ).
fof(f200,plain,
! [X12,X13] :
( ~ sP8(X12,X13)
| ! [X14] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X14,X12,X13)
& ~ aDivisorOf0(X13,sdtpldt0(X14,smndt0(X12)))
& ! [X16] :
( sdtpldt0(X14,smndt0(X12)) != sdtasdt0(X13,X16)
| ~ aInteger0(X16) ) )
| ~ aInteger0(X14)
| aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(X12,X13)) )
& ( ~ aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(X12,X13))
| ( sdteqdtlpzmzozddtrp0(X14,X12,X13)
& aDivisorOf0(X13,sdtpldt0(X14,smndt0(X12)))
& ? [X15] :
( sdtasdt0(X13,X15) = sdtpldt0(X14,smndt0(X12))
& aInteger0(X15) )
& aInteger0(X14) ) ) ) ),
inference(nnf_transformation,[],[f136]) ).
fof(f201,plain,
! [X0,X1] :
( ~ sP8(X0,X1)
| ! [X2] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X2,X0,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& ! [X4] :
( sdtpldt0(X2,smndt0(X0)) != sdtasdt0(X1,X4)
| ~ aInteger0(X4) ) )
| ~ aInteger0(X2)
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ( ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) )
& aInteger0(X2) ) ) ) ),
inference(rectify,[],[f200]) ).
fof(f202,plain,
! [X0,X1] :
( ~ sP8(X0,X1)
| ! [X2] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X2,X0,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& ! [X4] :
( sdtpldt0(X2,smndt0(X0)) != sdtasdt0(X1,X4)
| ~ aInteger0(X4) ) )
| ~ aInteger0(X2)
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ( ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& sdtpldt0(X2,smndt0(X0)) = sdtasdt0(X1,sK30(X0,X1,X2))
& aInteger0(sK30(X0,X1,X2))
& aInteger0(X2) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(X3,sK30(X0,X1,X2))],[f201]) ).
fof(f256,plain,
! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ aElementOf0(X4,X0)
| aElementOf0(X4,X2)
| aElementOf0(X4,X1) ),
inference(cnf_transformation,[],[f157]) ).
fof(f257,plain,
! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ aElementOf0(X4,X0)
| aInteger0(X4) ),
inference(cnf_transformation,[],[f157]) ).
fof(f258,plain,
! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ aElementOf0(X4,X2)
| ~ aInteger0(X4)
| aElementOf0(X4,X0) ),
inference(cnf_transformation,[],[f157]) ).
fof(f259,plain,
! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ aElementOf0(X4,X1)
| ~ aInteger0(X4)
| aElementOf0(X4,X0) ),
inference(cnf_transformation,[],[f157]) ).
fof(f260,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| aSet0(X0) ),
inference(cnf_transformation,[],[f157]) ).
fof(f261,plain,
! [X2,X0,X1] :
( aElementOf0(sK13(X0,X1,X2),X0)
| aElementOf0(sK13(X0,X1,X2),X2)
| aElementOf0(sK13(X0,X1,X2),X1)
| ~ aSet0(X0)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f157]) ).
fof(f262,plain,
! [X2,X0,X1] :
( aElementOf0(sK13(X0,X1,X2),X0)
| aInteger0(sK13(X0,X1,X2))
| ~ aSet0(X0)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f157]) ).
fof(f263,plain,
! [X2,X0,X1] :
( ~ aElementOf0(sK13(X0,X1,X2),X0)
| ~ aElementOf0(sK13(X0,X1,X2),X2)
| ~ aInteger0(sK13(X0,X1,X2))
| ~ aSet0(X0)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f157]) ).
fof(f264,plain,
! [X2,X0,X1] :
( ~ aElementOf0(sK13(X0,X1,X2),X0)
| ~ aElementOf0(sK13(X0,X1,X2),X1)
| ~ aInteger0(sK13(X0,X1,X2))
| ~ aSet0(X0)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f157]) ).
fof(f268,plain,
! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ aElementOf0(X4,X0)
| aElementOf0(X4,X2) ),
inference(cnf_transformation,[],[f163]) ).
fof(f269,plain,
! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ aElementOf0(X4,X0)
| aElementOf0(X4,X1) ),
inference(cnf_transformation,[],[f163]) ).
fof(f270,plain,
! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ aElementOf0(X4,X0)
| aInteger0(X4) ),
inference(cnf_transformation,[],[f163]) ).
fof(f271,plain,
! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ aElementOf0(X4,X2)
| ~ aElementOf0(X4,X1)
| ~ aInteger0(X4)
| aElementOf0(X4,X0) ),
inference(cnf_transformation,[],[f163]) ).
fof(f272,plain,
! [X2,X0,X1] :
( ~ sP2(X0,X1,X2)
| aSet0(X0) ),
inference(cnf_transformation,[],[f163]) ).
fof(f273,plain,
! [X2,X0,X1] :
( aElementOf0(sK14(X0,X1,X2),X0)
| aElementOf0(sK14(X0,X1,X2),X2)
| ~ aSet0(X0)
| sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f163]) ).
fof(f274,plain,
! [X2,X0,X1] :
( aElementOf0(sK14(X0,X1,X2),X0)
| aElementOf0(sK14(X0,X1,X2),X1)
| ~ aSet0(X0)
| sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f163]) ).
fof(f275,plain,
! [X2,X0,X1] :
( aElementOf0(sK14(X0,X1,X2),X0)
| aInteger0(sK14(X0,X1,X2))
| ~ aSet0(X0)
| sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f163]) ).
fof(f276,plain,
! [X2,X0,X1] :
( ~ aElementOf0(sK14(X0,X1,X2),X0)
| ~ aElementOf0(sK14(X0,X1,X2),X2)
| ~ aElementOf0(sK14(X0,X1,X2),X1)
| ~ aInteger0(sK14(X0,X1,X2))
| ~ aSet0(X0)
| sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f163]) ).
fof(f280,plain,
! [X0,X1,X5] :
( ~ sP4(X0,X1)
| ~ aElementOf0(X5,X0)
| aElementOf0(X5,sK17(X1,X5)) ),
inference(cnf_transformation,[],[f169]) ).
fof(f281,plain,
! [X0,X1,X5] :
( ~ sP4(X0,X1)
| ~ aElementOf0(X5,X0)
| aElementOf0(sK17(X1,X5),X1) ),
inference(cnf_transformation,[],[f169]) ).
fof(f282,plain,
! [X0,X1,X5] :
( ~ sP4(X0,X1)
| ~ aElementOf0(X5,X0)
| aInteger0(X5) ),
inference(cnf_transformation,[],[f169]) ).
fof(f283,plain,
! [X0,X1,X6,X5] :
( ~ sP4(X0,X1)
| ~ aElementOf0(X5,X6)
| ~ aElementOf0(X6,X1)
| ~ aInteger0(X5)
| aElementOf0(X5,X0) ),
inference(cnf_transformation,[],[f169]) ).
fof(f284,plain,
! [X0,X1] :
( ~ sP4(X0,X1)
| aSet0(X0) ),
inference(cnf_transformation,[],[f169]) ).
fof(f285,plain,
! [X0,X1] :
( aElementOf0(sK15(X0,X1),X0)
| aElementOf0(sK15(X0,X1),sK16(X0,X1))
| ~ aSet0(X0)
| sP4(X0,X1) ),
inference(cnf_transformation,[],[f169]) ).
fof(f286,plain,
! [X0,X1] :
( aElementOf0(sK15(X0,X1),X0)
| aElementOf0(sK16(X0,X1),X1)
| ~ aSet0(X0)
| sP4(X0,X1) ),
inference(cnf_transformation,[],[f169]) ).
fof(f287,plain,
! [X0,X1] :
( aElementOf0(sK15(X0,X1),X0)
| aInteger0(sK15(X0,X1))
| ~ aSet0(X0)
| sP4(X0,X1) ),
inference(cnf_transformation,[],[f169]) ).
fof(f288,plain,
! [X3,X0,X1] :
( ~ aElementOf0(sK15(X0,X1),X0)
| ~ aElementOf0(sK15(X0,X1),X3)
| ~ aElementOf0(X3,X1)
| ~ aInteger0(sK15(X0,X1))
| ~ aSet0(X0)
| sP4(X0,X1) ),
inference(cnf_transformation,[],[f169]) ).
fof(f328,plain,
! [X0,X1] :
( ~ sP6(X0)
| ~ sdteqdtlpzmzozddtrp0(X1,sz00,X0)
| ~ aInteger0(X1)
| aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0)) ),
inference(cnf_transformation,[],[f190]) ).
fof(f329,plain,
! [X0,X1] :
( ~ sP6(X0)
| ~ aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
| ~ aInteger0(X1)
| aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0)) ),
inference(cnf_transformation,[],[f190]) ).
fof(f330,plain,
! [X3,X0,X1] :
( ~ sP6(X0)
| sdtpldt0(X1,smndt0(sz00)) != sdtasdt0(X0,X3)
| ~ aInteger0(X3)
| ~ aInteger0(X1)
| aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0)) ),
inference(cnf_transformation,[],[f190]) ).
fof(f331,plain,
! [X0,X1] :
( ~ sP6(X0)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| sdteqdtlpzmzozddtrp0(X1,sz00,X0) ),
inference(cnf_transformation,[],[f190]) ).
fof(f332,plain,
! [X0,X1] :
( ~ sP6(X0)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00))) ),
inference(cnf_transformation,[],[f190]) ).
fof(f333,plain,
! [X0,X1] :
( ~ sP6(X0)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| sdtpldt0(X1,smndt0(sz00)) = sdtasdt0(X0,sK26(X0,X1)) ),
inference(cnf_transformation,[],[f190]) ).
fof(f334,plain,
! [X0,X1] :
( ~ sP6(X0)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| aInteger0(sK26(X0,X1)) ),
inference(cnf_transformation,[],[f190]) ).
fof(f335,plain,
! [X0,X1] :
( ~ sP6(X0)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| aInteger0(X1) ),
inference(cnf_transformation,[],[f190]) ).
fof(f369,plain,
! [X2,X0,X1] :
( ~ sP8(X0,X1)
| ~ sdteqdtlpzmzozddtrp0(X2,X0,X1)
| ~ aInteger0(X2)
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) ),
inference(cnf_transformation,[],[f202]) ).
fof(f370,plain,
! [X2,X0,X1] :
( ~ sP8(X0,X1)
| ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
| ~ aInteger0(X2)
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) ),
inference(cnf_transformation,[],[f202]) ).
fof(f371,plain,
! [X2,X0,X1,X4] :
( ~ sP8(X0,X1)
| sdtpldt0(X2,smndt0(X0)) != sdtasdt0(X1,X4)
| ~ aInteger0(X4)
| ~ aInteger0(X2)
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) ),
inference(cnf_transformation,[],[f202]) ).
fof(f372,plain,
! [X2,X0,X1] :
( ~ sP8(X0,X1)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| sdteqdtlpzmzozddtrp0(X2,X0,X1) ),
inference(cnf_transformation,[],[f202]) ).
fof(f373,plain,
! [X2,X0,X1] :
( ~ sP8(X0,X1)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0))) ),
inference(cnf_transformation,[],[f202]) ).
fof(f374,plain,
! [X2,X0,X1] :
( ~ sP8(X0,X1)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| sdtpldt0(X2,smndt0(X0)) = sdtasdt0(X1,sK30(X0,X1,X2)) ),
inference(cnf_transformation,[],[f202]) ).
fof(f375,plain,
! [X2,X0,X1] :
( ~ sP8(X0,X1)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| aInteger0(sK30(X0,X1,X2)) ),
inference(cnf_transformation,[],[f202]) ).
fof(f376,plain,
! [X2,X0,X1] :
( ~ sP8(X0,X1)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| aInteger0(X2) ),
inference(cnf_transformation,[],[f202]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1,X2)
| ~ aSet0(X0)
| ~ aInteger0(sK13(X0,X1,X2))
| ~ aElementOf0(sK13(X0,X1,X2),X1)
| ~ aElementOf0(sK13(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f264]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1,X2)
| ~ aSet0(X0)
| ~ aInteger0(sK13(X0,X1,X2))
| ~ aElementOf0(sK13(X0,X1,X2),X2)
| ~ aElementOf0(sK13(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f263]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1,X2)
| aInteger0(sK13(X0,X1,X2))
| aElementOf0(sK13(X0,X1,X2),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f262]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1,X2)
| aElementOf0(sK13(X0,X1,X2),X2)
| aElementOf0(sK13(X0,X1,X2),X1)
| aElementOf0(sK13(X0,X1,X2),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f261]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i] :
( aSet0(X0)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f260]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X3,X0)
| ~ aInteger0(X3)
| ~ aElementOf0(X3,X1)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f259]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X3,X0)
| ~ aInteger0(X3)
| ~ aElementOf0(X3,X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f258]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aInteger0(X3)
| ~ aElementOf0(X3,X0)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f257]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X3,X2)
| aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f256]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP2(X0,X1,X2)
| ~ aSet0(X0)
| ~ aInteger0(sK14(X0,X1,X2))
| ~ aElementOf0(sK14(X0,X1,X2),X2)
| ~ aElementOf0(sK14(X0,X1,X2),X1)
| ~ aElementOf0(sK14(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f276]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP2(X0,X1,X2)
| aInteger0(sK14(X0,X1,X2))
| aElementOf0(sK14(X0,X1,X2),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f275]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP2(X0,X1,X2)
| aElementOf0(sK14(X0,X1,X2),X1)
| aElementOf0(sK14(X0,X1,X2),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f274]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP2(X0,X1,X2)
| aElementOf0(sK14(X0,X1,X2),X2)
| aElementOf0(sK14(X0,X1,X2),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f273]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i,X2: $i] :
( aSet0(X0)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f272]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X3,X0)
| ~ aInteger0(X3)
| ~ aElementOf0(X3,X2)
| ~ aElementOf0(X3,X1)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f271]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aInteger0(X3)
| ~ aElementOf0(X3,X0)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f270]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f269]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X3,X2)
| ~ aElementOf0(X3,X0)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f268]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP4(X0,X1)
| ~ aSet0(X0)
| ~ aElementOf0(X2,X1)
| ~ aInteger0(sK15(X0,X1))
| ~ aElementOf0(sK15(X0,X1),X2)
| ~ aElementOf0(sK15(X0,X1),X0) ),
inference(cnf_transformation,[],[f288]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i] :
( sP4(X0,X1)
| aInteger0(sK15(X0,X1))
| aElementOf0(sK15(X0,X1),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f287]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i] :
( sP4(X0,X1)
| aElementOf0(sK16(X0,X1),X1)
| aElementOf0(sK15(X0,X1),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f286]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i] :
( sP4(X0,X1)
| aElementOf0(sK15(X0,X1),X0)
| aElementOf0(sK15(X0,X1),sK16(X0,X1))
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f285]) ).
tcf(c_121,plain,
! [X0: $i,X1: $i] :
( aSet0(X0)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f284]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X0,X3)
| ~ aInteger0(X0)
| ~ sP4(X3,X2)
| ~ aElementOf0(X1,X2)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f283]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i,X2: $i] :
( aInteger0(X0)
| ~ sP4(X1,X2)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f282]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(sK17(X2,X0),X2)
| ~ sP4(X1,X2)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f281]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,sK17(X2,X0))
| ~ sP4(X1,X2)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f280]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i] :
( aInteger0(X0)
| ~ sP6(X1)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ),
inference(cnf_transformation,[],[f335]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i] :
( aInteger0(sK26(X1,X0))
| ~ sP6(X1)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ),
inference(cnf_transformation,[],[f334]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X1,sK26(X1,X0)) = sdtpldt0(X0,smndt0(sz00)) )
| ~ sP6(X1)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ),
inference(cnf_transformation,[],[f333]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i] :
( aDivisorOf0(X1,sdtpldt0(X0,smndt0(sz00)))
| ~ sP6(X1)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ),
inference(cnf_transformation,[],[f332]) ).
tcf(c_169,plain,
! [X0: $i,X1: $i] :
( sdteqdtlpzmzozddtrp0(X0,sz00,X1)
| ~ sP6(X1)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ),
inference(cnf_transformation,[],[f331]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ~ sP6(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X0)
| ( sdtpldt0(X0,smndt0(sz00)) != sdtasdt0(X1,X2) ) ),
inference(cnf_transformation,[],[f330]) ).
tcf(c_171,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| ~ sP6(X0)
| ~ aInteger0(X1)
| ~ aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00))) ),
inference(cnf_transformation,[],[f329]) ).
tcf(c_172,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ~ sP6(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,sz00,X1) ),
inference(cnf_transformation,[],[f328]) ).
tcf(c_205,plain,
! [X0: $i,X1: $i,X2: $i] :
( aInteger0(X0)
| ~ sP8(X1,X2)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ),
inference(cnf_transformation,[],[f376]) ).
tcf(c_206,plain,
! [X0: $i,X1: $i,X2: $i] :
( aInteger0(sK30(X1,X2,X0))
| ~ sP8(X1,X2)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ),
inference(cnf_transformation,[],[f375]) ).
tcf(c_207,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(X2,sK30(X1,X2,X0)) = sdtpldt0(X0,smndt0(X1)) )
| ~ sP8(X1,X2)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ),
inference(cnf_transformation,[],[f374]) ).
tcf(c_208,plain,
! [X0: $i,X1: $i,X2: $i] :
( aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
| ~ sP8(X1,X2)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ),
inference(cnf_transformation,[],[f373]) ).
tcf(c_209,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ sP8(X1,X2)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ),
inference(cnf_transformation,[],[f372]) ).
tcf(c_210,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(X1,X2))
| ~ aInteger0(X3)
| ~ aInteger0(X0)
| ~ sP8(X1,X2)
| ( sdtpldt0(X0,smndt0(X1)) != sdtasdt0(X2,X3) ) ),
inference(cnf_transformation,[],[f371]) ).
tcf(c_211,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(X2,X0))
| ~ aInteger0(X1)
| ~ sP8(X2,X0)
| ~ aDivisorOf0(X0,sdtpldt0(X1,smndt0(X2))) ),
inference(cnf_transformation,[],[f370]) ).
tcf(c_212,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(X1,X2))
| ~ aInteger0(X0)
| ~ sP8(X1,X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2) ),
inference(cnf_transformation,[],[f369]) ).
tcf(c_25244,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_14337,c_433,c_431,c_274,c_273,c_272,c_271,c_270,c_269,c_268,c_267,c_266,c_265,c_264,c_263,c_262,c_258,c_257,c_253,c_252,c_251,c_250,c_249,c_248,c_247,c_246,c_245,c_244,c_243,c_242,c_241,c_240,c_239,c_238,c_237,c_233,c_232,c_228,c_227,c_226,c_225,c_224,c_223,c_222,c_221,c_217,c_216,c_212,c_211,c_210,c_209,c_208,c_207,c_206,c_205,c_204,c_203,c_202,c_201,c_200,c_199,c_198,c_197,c_196,c_195,c_194,c_193,c_192,c_261,c_260,c_259,c_188,c_187,c_186,c_256,c_255,c_254,c_182,c_181,c_180,c_179,c_178,c_177,c_176,c_175,c_174,c_173,c_172,c_171,c_170,c_169,c_168,c_167,c_166,c_165,c_164,c_163,c_162,c_161,c_160,c_159,c_158,c_157,c_156,c_155,c_154,c_153,c_152,c_151,c_150,c_149,c_148,c_147,c_146,c_145,c_144,c_143,c_142,c_141,c_140,c_139,c_138,c_137,c_136,c_135,c_134,c_133,c_132,c_131,c_130,c_129,c_128,c_127,c_126,c_125,c_124,c_123,c_122,c_121,c_120,c_119,c_118,c_117,c_116,c_115,c_114,c_113,c_112,c_111,c_110,c_109,c_108,c_107,c_106,c_105,c_104,c_103,c_102,c_101,c_100,c_99,c_98,c_97,c_96,c_95,c_94,c_93,c_92,c_91,c_90,c_89,c_88,c_87,c_86,c_84,c_83,c_82,c_81,c_80,c_79,c_78,c_77,c_76,c_75,c_74,c_73,c_72,c_70,c_69,c_68,c_67,c_66,c_65,c_64,c_63,c_62,c_61,c_60,c_59,c_58,c_57,c_56,c_55,c_54,c_53,c_52,c_51,c_50,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM453+6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.42 % Computer : n026.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Thu Sep 24 04:06:08 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.23/0.49 Running first-order theorem proving
% 0.23/0.49 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.50
% 0.23/0.50 % ======== iProver multi-core TPTP/SMT =========
% 0.23/0.50
% 0.23/0.50 % Detected problem language: tptp
% 0.23/0.52 % Proving...
% 54.72/15.06 % SZS status Started for theBenchmark.p
% 54.72/15.06 % SZS status Theorem for theBenchmark.p
% 54.72/15.06
% 54.72/15.06 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 54.72/15.06
% 54.72/15.06 % ------ iProver source info
% 54.72/15.06
% 54.72/15.06 % git: date: 2026-07-19 20:42:38 +0200
% 54.72/15.06 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 54.72/15.06 % git: non_committed_changes: false
% 54.72/15.06
% 54.72/15.06 % ------ Parsing...
% 54.72/15.06 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 54.72/15.06
% 54.72/15.06 % ------ Preprocessing...%
% 54.72/15.06
% 54.72/15.06 % ------ Preprocessing...%
% 54.72/15.06
% 54.72/15.06 % ------ Preprocessing...
% 54.72/15.06 % ------ Proving...
% 54.72/15.06 % ------ Problem Properties
% 54.72/15.06
% 54.72/15.06 %
% 54.72/15.06 % clauses 208
% 54.72/15.06 % conjectures 1
% 54.72/15.06 % EPR 32
% 54.72/15.06 % Horn 163
% 54.72/15.06 % unary 25
% 54.72/15.06 % binary 54
% 54.72/15.06 % lits 650
% 54.72/15.06 % lits eq 79
% 54.72/15.06 % fd_pure 0
% 54.72/15.06 % fd_pseudo 0
% 54.72/15.06 % fd_cond 22
% 54.72/15.06 % fd_pseudo_cond 9
% 54.72/15.06 % AC symbols 0
% 54.72/15.06
% 54.72/15.06 % ------ Input Options Time Limit: Unbounded
% 54.72/15.06
% 54.72/15.06
% 54.72/15.06 % ------
% 54.72/15.06 % Current options:
% 54.72/15.06 % ------
% 54.72/15.06
% 54.72/15.06
% 54.72/15.06 %
% 54.72/15.06
% 54.72/15.06 % ------ Proving...
% 54.72/15.06 %
% 54.72/15.06
% 54.72/15.06 % SZS status Theorem for theBenchmark.p
% 54.72/15.06
% 54.72/15.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 54.72/15.07
% 54.72/15.07
%------------------------------------------------------------------------------