TSTP Solution File: NUM447+5 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : NUM447+5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 12:52:18 EDT 2024
% Result : Theorem 61.41s 9.23s
% Output : CNFRefutation 61.41s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).
fof(f3,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntOne) ).
fof(f4,axiom,
! [X0] :
( aInteger0(X0)
=> aInteger0(smndt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).
fof(f6,axiom,
! [X0,X1] :
( ( aInteger0(X1)
& aInteger0(X0) )
=> aInteger0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(f8,axiom,
! [X0,X1] :
( ( aInteger0(X1)
& aInteger0(X0) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(f9,axiom,
! [X0] :
( aInteger0(X0)
=> ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(f10,axiom,
! [X0] :
( aInteger0(X0)
=> ( sz00 = sdtpldt0(smndt0(X0),X0)
& sz00 = sdtpldt0(X0,smndt0(X0)) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(f12,axiom,
! [X0,X1] :
( ( aInteger0(X1)
& aInteger0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f15,axiom,
! [X0] :
( aInteger0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
fof(f16,axiom,
! [X0] :
( aInteger0(X0)
=> ( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
& smndt0(X0) = sdtasdt0(smndt0(sz10),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulMinOne) ).
fof(f18,axiom,
! [X0] :
( aInteger0(X0)
=> ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& sz00 != X1
& aInteger0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivisor) ).
fof(f19,axiom,
! [X0,X1,X2] :
( ( sz00 != X2
& aInteger0(X2)
& aInteger0(X1)
& aInteger0(X0) )
=> ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquMod) ).
fof(f21,axiom,
! [X0,X1,X2] :
( ( sz00 != X2
& aInteger0(X2)
& aInteger0(X1)
& aInteger0(X0) )
=> ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
=> sdteqdtlpzmzozddtrp0(X1,X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquModSym) ).
fof(f25,axiom,
! [X0] :
( aInteger0(X0)
=> ( ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,X0) )
<=> ( smndt0(sz10) != X0
& sz10 != X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPrimeDivisor) ).
fof(f34,axiom,
! [X0,X1] :
( ( sz00 != X1
& aInteger0(X1)
& aInteger0(X0) )
=> ! [X2] :
( szAzrzSzezqlpdtcmdtrp0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aInteger0(X3) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mArSeq) ).
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)
& sz00 != X1
& 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)
& sz00 != X1
& aInteger0(X1) ) ) )
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2046) ).
fof(f43,axiom,
aInteger0(xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2106) ).
fof(f44,conjecture,
( ( ? [X0] :
( isPrime0(X0)
& aDivisorOf0(X0,xn)
& ? [X1] :
( sdtasdt0(X0,X1) = xn
& aInteger0(X1) )
& sz00 != X0
& aInteger0(X0) )
=> ( aElementOf0(xn,sbsmnsldt0(xS))
| ? [X0] :
( aElementOf0(xn,X0)
& aElementOf0(X0,xS) ) ) )
& ( ( aElementOf0(xn,sbsmnsldt0(xS))
& ? [X0] :
( aElementOf0(xn,X0)
& aElementOf0(X0,xS) ) )
=> ? [X0] :
( isPrime0(X0)
& ( aDivisorOf0(X0,xn)
| ( ? [X1] :
( sdtasdt0(X0,X1) = xn
& aInteger0(X1) )
& sz00 != X0
& aInteger0(X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f45,negated_conjecture,
~ ( ( ? [X0] :
( isPrime0(X0)
& aDivisorOf0(X0,xn)
& ? [X1] :
( sdtasdt0(X0,X1) = xn
& aInteger0(X1) )
& sz00 != X0
& aInteger0(X0) )
=> ( aElementOf0(xn,sbsmnsldt0(xS))
| ? [X0] :
( aElementOf0(xn,X0)
& aElementOf0(X0,xS) ) ) )
& ( ( aElementOf0(xn,sbsmnsldt0(xS))
& ? [X0] :
( aElementOf0(xn,X0)
& aElementOf0(X0,xS) ) )
=> ? [X0] :
( isPrime0(X0)
& ( aDivisorOf0(X0,xn)
| ( ? [X1] :
( sdtasdt0(X0,X1) = xn
& aInteger0(X1) )
& sz00 != X0
& aInteger0(X0) ) ) ) ) ),
inference(negated_conjecture,[],[f44]) ).
fof(f52,plain,
( 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)))
& ? [X4] :
( sdtpldt0(X2,smndt0(sz00)) = sdtasdt0(X1,X4)
& aInteger0(X4) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
=> szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0 )
& isPrime0(X1)
& sz00 != X1
& aInteger0(X1) )
=> aElementOf0(X0,xS) )
& ( aElementOf0(X0,xS)
=> ? [X5] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X5) = X0
& ! [X6] :
( ( ( ( sdteqdtlpzmzozddtrp0(X6,sz00,X5)
| aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
| ? [X7] :
( sdtpldt0(X6,smndt0(sz00)) = sdtasdt0(X5,X7)
& aInteger0(X7) ) )
& aInteger0(X6) )
=> aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5)) )
& ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
=> ( sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ? [X8] :
( sdtpldt0(X6,smndt0(sz00)) = sdtasdt0(X5,X8)
& aInteger0(X8) )
& aInteger0(X6) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5))
& isPrime0(X5)
& sz00 != X5
& aInteger0(X5) ) ) )
& aSet0(xS) ),
inference(rectify,[],[f42]) ).
fof(f53,plain,
~ ( ( ? [X0] :
( isPrime0(X0)
& aDivisorOf0(X0,xn)
& ? [X1] :
( sdtasdt0(X0,X1) = xn
& aInteger0(X1) )
& sz00 != X0
& aInteger0(X0) )
=> ( aElementOf0(xn,sbsmnsldt0(xS))
| ? [X2] :
( aElementOf0(xn,X2)
& aElementOf0(X2,xS) ) ) )
& ( ( aElementOf0(xn,sbsmnsldt0(xS))
& ? [X3] :
( aElementOf0(xn,X3)
& aElementOf0(X3,xS) ) )
=> ? [X4] :
( isPrime0(X4)
& ( aDivisorOf0(X4,xn)
| ( ? [X5] :
( xn = sdtasdt0(X4,X5)
& aInteger0(X5) )
& sz00 != X4
& aInteger0(X4) ) ) ) ) ),
inference(rectify,[],[f45]) ).
fof(f55,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f58,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f59,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(flattening,[],[f58]) ).
fof(f60,plain,
! [X0,X1,X2] :
( sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f61,plain,
! [X0,X1,X2] :
( sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(flattening,[],[f60]) ).
fof(f62,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f63,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
! [X0] :
( ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f65,plain,
! [X0] :
( ( sz00 = sdtpldt0(smndt0(X0),X0)
& sz00 = sdtpldt0(X0,smndt0(X0)) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f66,plain,
! [X0,X1,X2] :
( sdtasdt0(X0,sdtasdt0(X1,X2)) = sdtasdt0(sdtasdt0(X0,X1),X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f67,plain,
! [X0,X1,X2] :
( sdtasdt0(X0,sdtasdt0(X1,X2)) = sdtasdt0(sdtasdt0(X0,X1),X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(flattening,[],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f69,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(flattening,[],[f68]) ).
fof(f73,plain,
! [X0] :
( ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f74,plain,
! [X0] :
( ( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
& smndt0(X0) = sdtasdt0(smndt0(sz10),X0) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f77,plain,
! [X0] :
( ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& sz00 != X1
& aInteger0(X1) ) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
| sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
| sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(flattening,[],[f78]) ).
fof(f82,plain,
! [X0,X1,X2] :
( sdteqdtlpzmzozddtrp0(X1,X0,X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f83,plain,
! [X0,X1,X2] :
( sdteqdtlpzmzozddtrp0(X1,X0,X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(flattening,[],[f82]) ).
fof(f88,plain,
! [X0] :
( ( ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,X0) )
<=> ( smndt0(sz10) != X0
& sz10 != X0 ) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f97,plain,
! [X0,X1] :
( ! [X2] :
( szAzrzSzezqlpdtcmdtrp0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aInteger0(X3) ) )
& aSet0(X2) ) )
| sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f98,plain,
! [X0,X1] :
( ! [X2] :
( szAzrzSzezqlpdtcmdtrp0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aInteger0(X3) ) )
& aSet0(X2) ) )
| sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(flattening,[],[f97]) ).
fof(f109,plain,
( xS = cS2043
& ! [X0] :
( ( aElementOf0(X0,xS)
| ! [X1] :
( ( szAzrzSzezqlpdtcmdtrp0(sz00,X1) != X0
& ! [X2] :
( ( 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) )
& ( ( 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)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
| ~ isPrime0(X1)
| sz00 = X1
| ~ aInteger0(X1) ) )
& ( ? [X5] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X5) = X0
& ! [X6] :
( ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
| ( ~ sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& ~ aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ! [X7] :
( sdtpldt0(X6,smndt0(sz00)) != sdtasdt0(X5,X7)
| ~ aInteger0(X7) ) )
| ~ aInteger0(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)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5))
& isPrime0(X5)
& sz00 != X5
& aInteger0(X5) )
| ~ aElementOf0(X0,xS) ) )
& aSet0(xS) ),
inference(ennf_transformation,[],[f52]) ).
fof(f110,plain,
( xS = cS2043
& ! [X0] :
( ( aElementOf0(X0,xS)
| ! [X1] :
( ( szAzrzSzezqlpdtcmdtrp0(sz00,X1) != X0
& ! [X2] :
( ( 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) )
& ( ( 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)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
| ~ isPrime0(X1)
| sz00 = X1
| ~ aInteger0(X1) ) )
& ( ? [X5] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X5) = X0
& ! [X6] :
( ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
| ( ~ sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& ~ aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ! [X7] :
( sdtpldt0(X6,smndt0(sz00)) != sdtasdt0(X5,X7)
| ~ aInteger0(X7) ) )
| ~ aInteger0(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)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5))
& isPrime0(X5)
& sz00 != X5
& aInteger0(X5) )
| ~ aElementOf0(X0,xS) ) )
& aSet0(xS) ),
inference(flattening,[],[f109]) ).
fof(f111,plain,
( ( ~ aElementOf0(xn,sbsmnsldt0(xS))
& ! [X2] :
( ~ aElementOf0(xn,X2)
| ~ aElementOf0(X2,xS) )
& ? [X0] :
( isPrime0(X0)
& aDivisorOf0(X0,xn)
& ? [X1] :
( sdtasdt0(X0,X1) = xn
& aInteger0(X1) )
& sz00 != X0
& aInteger0(X0) ) )
| ( ! [X4] :
( ~ isPrime0(X4)
| ( ~ aDivisorOf0(X4,xn)
& ( ! [X5] :
( xn != sdtasdt0(X4,X5)
| ~ aInteger0(X5) )
| sz00 = X4
| ~ aInteger0(X4) ) ) )
& aElementOf0(xn,sbsmnsldt0(xS))
& ? [X3] :
( aElementOf0(xn,X3)
& aElementOf0(X3,xS) ) ) ),
inference(ennf_transformation,[],[f53]) ).
fof(f112,plain,
( ( ~ aElementOf0(xn,sbsmnsldt0(xS))
& ! [X2] :
( ~ aElementOf0(xn,X2)
| ~ aElementOf0(X2,xS) )
& ? [X0] :
( isPrime0(X0)
& aDivisorOf0(X0,xn)
& ? [X1] :
( sdtasdt0(X0,X1) = xn
& aInteger0(X1) )
& sz00 != X0
& aInteger0(X0) ) )
| ( ! [X4] :
( ~ isPrime0(X4)
| ( ~ aDivisorOf0(X4,xn)
& ( ! [X5] :
( xn != sdtasdt0(X4,X5)
| ~ aInteger0(X5) )
| sz00 = X4
| ~ aInteger0(X4) ) ) )
& aElementOf0(xn,sbsmnsldt0(xS))
& ? [X3] :
( aElementOf0(xn,X3)
& aElementOf0(X3,xS) ) ) ),
inference(flattening,[],[f111]) ).
fof(f119,plain,
! [X0,X2] :
( sP4(X0,X2)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( ? [X4] :
( aElementOf0(X3,X4)
& aElementOf0(X4,X0) )
& aInteger0(X3) ) )
& aSet0(X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f122,plain,
! [X5] :
( ! [X6] :
( ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
| ( ~ sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& ~ aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ! [X7] :
( sdtpldt0(X6,smndt0(sz00)) != sdtasdt0(X5,X7)
| ~ aInteger0(X7) ) )
| ~ aInteger0(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)) ) )
| ~ sP6(X5) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f123,plain,
! [X1] :
( ! [X2] :
( ( 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) )
& ( ( 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)) ) )
| ~ sP7(X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f124,plain,
( xS = cS2043
& ! [X0] :
( ( aElementOf0(X0,xS)
| ! [X1] :
( ( szAzrzSzezqlpdtcmdtrp0(sz00,X1) != X0
& sP7(X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
| ~ isPrime0(X1)
| sz00 = X1
| ~ aInteger0(X1) ) )
& ( ? [X5] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X5) = X0
& sP6(X5)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5))
& isPrime0(X5)
& sz00 != X5
& aInteger0(X5) )
| ~ aElementOf0(X0,xS) ) )
& aSet0(xS) ),
inference(definition_folding,[],[f110,f123,f122]) ).
fof(f125,plain,
( ( ~ aElementOf0(xn,sbsmnsldt0(xS))
& ! [X2] :
( ~ aElementOf0(xn,X2)
| ~ aElementOf0(X2,xS) )
& ? [X0] :
( isPrime0(X0)
& aDivisorOf0(X0,xn)
& ? [X1] :
( sdtasdt0(X0,X1) = xn
& aInteger0(X1) )
& sz00 != X0
& aInteger0(X0) ) )
| ~ sP8 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f126,plain,
( sP8
| ( ! [X4] :
( ~ isPrime0(X4)
| ( ~ aDivisorOf0(X4,xn)
& ( ! [X5] :
( xn != sdtasdt0(X4,X5)
| ~ aInteger0(X5) )
| sz00 = X4
| ~ aInteger0(X4) ) ) )
& aElementOf0(xn,sbsmnsldt0(xS))
& ? [X3] :
( aElementOf0(xn,X3)
& aElementOf0(X3,xS) ) ) ),
inference(definition_folding,[],[f112,f125]) ).
fof(f127,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1) )
& ( ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& sz00 != X1
& aInteger0(X1) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(nnf_transformation,[],[f77]) ).
fof(f128,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1) )
& ( ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& sz00 != X1
& aInteger0(X1) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(flattening,[],[f127]) ).
fof(f129,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1) )
& ( ( ? [X3] :
( sdtasdt0(X1,X3) = X0
& aInteger0(X3) )
& sz00 != X1
& aInteger0(X1) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(rectify,[],[f128]) ).
fof(f130,plain,
! [X0,X1] :
( ? [X3] :
( sdtasdt0(X1,X3) = X0
& aInteger0(X3) )
=> ( sdtasdt0(X1,sK9(X0,X1)) = X0
& aInteger0(sK9(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f131,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1) )
& ( ( sdtasdt0(X1,sK9(X0,X1)) = X0
& aInteger0(sK9(X0,X1))
& sz00 != X1
& aInteger0(X1) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f129,f130]) ).
fof(f132,plain,
! [X0,X1,X2] :
( ( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
& ( aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2) ) )
| sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(nnf_transformation,[],[f79]) ).
fof(f133,plain,
! [X0] :
( ( ( ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,X0) )
| smndt0(sz10) = X0
| sz10 = X0 )
& ( ( smndt0(sz10) != X0
& sz10 != X0 )
| ! [X1] :
( ~ isPrime0(X1)
| ~ aDivisorOf0(X1,X0) ) ) )
| ~ aInteger0(X0) ),
inference(nnf_transformation,[],[f88]) ).
fof(f134,plain,
! [X0] :
( ( ( ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,X0) )
| smndt0(sz10) = X0
| sz10 = X0 )
& ( ( smndt0(sz10) != X0
& sz10 != X0 )
| ! [X1] :
( ~ isPrime0(X1)
| ~ aDivisorOf0(X1,X0) ) ) )
| ~ aInteger0(X0) ),
inference(flattening,[],[f133]) ).
fof(f135,plain,
! [X0] :
( ( ( ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,X0) )
| smndt0(sz10) = X0
| sz10 = X0 )
& ( ( smndt0(sz10) != X0
& sz10 != X0 )
| ! [X2] :
( ~ isPrime0(X2)
| ~ aDivisorOf0(X2,X0) ) ) )
| ~ aInteger0(X0) ),
inference(rectify,[],[f134]) ).
fof(f136,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,X0) )
=> ( isPrime0(sK10(X0))
& aDivisorOf0(sK10(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f137,plain,
! [X0] :
( ( ( ( isPrime0(sK10(X0))
& aDivisorOf0(sK10(X0),X0) )
| smndt0(sz10) = X0
| sz10 = X0 )
& ( ( smndt0(sz10) != X0
& sz10 != X0 )
| ! [X2] :
( ~ isPrime0(X2)
| ~ aDivisorOf0(X2,X0) ) ) )
| ~ aInteger0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f135,f136]) ).
fof(f157,plain,
! [X0,X2] :
( ( sP4(X0,X2)
| ? [X3] :
( ( ! [X4] :
( ~ aElementOf0(X3,X4)
| ~ aElementOf0(X4,X0) )
| ~ aInteger0(X3)
| ~ aElementOf0(X3,X2) )
& ( ( ? [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) )
& ( ( ? [X4] :
( aElementOf0(X3,X4)
& aElementOf0(X4,X0) )
& aInteger0(X3) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| ~ sP4(X0,X2) ) ),
inference(nnf_transformation,[],[f119]) ).
fof(f158,plain,
! [X0,X2] :
( ( sP4(X0,X2)
| ? [X3] :
( ( ! [X4] :
( ~ aElementOf0(X3,X4)
| ~ aElementOf0(X4,X0) )
| ~ aInteger0(X3)
| ~ aElementOf0(X3,X2) )
& ( ( ? [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) )
& ( ( ? [X4] :
( aElementOf0(X3,X4)
& aElementOf0(X4,X0) )
& aInteger0(X3) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| ~ sP4(X0,X2) ) ),
inference(flattening,[],[f157]) ).
fof(f159,plain,
! [X0,X1] :
( ( sP4(X0,X1)
| ? [X2] :
( ( ! [X3] :
( ~ aElementOf0(X2,X3)
| ~ aElementOf0(X3,X0) )
| ~ aInteger0(X2)
| ~ aElementOf0(X2,X1) )
& ( ( ? [X4] :
( aElementOf0(X2,X4)
& aElementOf0(X4,X0) )
& aInteger0(X2) )
| aElementOf0(X2,X1) ) )
| ~ aSet0(X1) )
& ( ( ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( ~ aElementOf0(X5,X6)
| ~ aElementOf0(X6,X0) )
| ~ aInteger0(X5) )
& ( ( ? [X7] :
( aElementOf0(X5,X7)
& aElementOf0(X7,X0) )
& aInteger0(X5) )
| ~ aElementOf0(X5,X1) ) )
& aSet0(X1) )
| ~ sP4(X0,X1) ) ),
inference(rectify,[],[f158]) ).
fof(f160,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] :
( ~ aElementOf0(X2,X3)
| ~ aElementOf0(X3,X0) )
| ~ aInteger0(X2)
| ~ aElementOf0(X2,X1) )
& ( ( ? [X4] :
( aElementOf0(X2,X4)
& aElementOf0(X4,X0) )
& aInteger0(X2) )
| aElementOf0(X2,X1) ) )
=> ( ( ! [X3] :
( ~ aElementOf0(sK14(X0,X1),X3)
| ~ aElementOf0(X3,X0) )
| ~ aInteger0(sK14(X0,X1))
| ~ aElementOf0(sK14(X0,X1),X1) )
& ( ( ? [X4] :
( aElementOf0(sK14(X0,X1),X4)
& aElementOf0(X4,X0) )
& aInteger0(sK14(X0,X1)) )
| aElementOf0(sK14(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f161,plain,
! [X0,X1] :
( ? [X4] :
( aElementOf0(sK14(X0,X1),X4)
& aElementOf0(X4,X0) )
=> ( aElementOf0(sK14(X0,X1),sK15(X0,X1))
& aElementOf0(sK15(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f162,plain,
! [X0,X5] :
( ? [X7] :
( aElementOf0(X5,X7)
& aElementOf0(X7,X0) )
=> ( aElementOf0(X5,sK16(X0,X5))
& aElementOf0(sK16(X0,X5),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f163,plain,
! [X0,X1] :
( ( sP4(X0,X1)
| ( ( ! [X3] :
( ~ aElementOf0(sK14(X0,X1),X3)
| ~ aElementOf0(X3,X0) )
| ~ aInteger0(sK14(X0,X1))
| ~ aElementOf0(sK14(X0,X1),X1) )
& ( ( aElementOf0(sK14(X0,X1),sK15(X0,X1))
& aElementOf0(sK15(X0,X1),X0)
& aInteger0(sK14(X0,X1)) )
| aElementOf0(sK14(X0,X1),X1) ) )
| ~ aSet0(X1) )
& ( ( ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( ~ aElementOf0(X5,X6)
| ~ aElementOf0(X6,X0) )
| ~ aInteger0(X5) )
& ( ( aElementOf0(X5,sK16(X0,X5))
& aElementOf0(sK16(X0,X5),X0)
& aInteger0(X5) )
| ~ aElementOf0(X5,X1) ) )
& aSet0(X1) )
| ~ sP4(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16])],[f159,f162,f161,f160]) ).
fof(f171,plain,
! [X0,X1] :
( ! [X2] :
( ( szAzrzSzezqlpdtcmdtrp0(X0,X1) = X2
| ? [X3] :
( ( ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
| ~ aInteger0(X3)
| ~ aElementOf0(X3,X2) )
& ( ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aInteger0(X3) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
| ~ aInteger0(X3) )
& ( ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aInteger0(X3) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| szAzrzSzezqlpdtcmdtrp0(X0,X1) != X2 ) )
| sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(nnf_transformation,[],[f98]) ).
fof(f172,plain,
! [X0,X1] :
( ! [X2] :
( ( szAzrzSzezqlpdtcmdtrp0(X0,X1) = X2
| ? [X3] :
( ( ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
| ~ aInteger0(X3)
| ~ aElementOf0(X3,X2) )
& ( ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aInteger0(X3) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
| ~ aInteger0(X3) )
& ( ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aInteger0(X3) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| szAzrzSzezqlpdtcmdtrp0(X0,X1) != X2 ) )
| sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(flattening,[],[f171]) ).
fof(f173,plain,
! [X0,X1] :
( ! [X2] :
( ( szAzrzSzezqlpdtcmdtrp0(X0,X1) = X2
| ? [X3] :
( ( ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
| ~ aInteger0(X3)
| ~ aElementOf0(X3,X2) )
& ( ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aInteger0(X3) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X4] :
( ( aElementOf0(X4,X2)
| ~ sdteqdtlpzmzozddtrp0(X4,X0,X1)
| ~ aInteger0(X4) )
& ( ( sdteqdtlpzmzozddtrp0(X4,X0,X1)
& aInteger0(X4) )
| ~ aElementOf0(X4,X2) ) )
& aSet0(X2) )
| szAzrzSzezqlpdtcmdtrp0(X0,X1) != X2 ) )
| sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(rectify,[],[f172]) ).
fof(f174,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
| ~ aInteger0(X3)
| ~ aElementOf0(X3,X2) )
& ( ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aInteger0(X3) )
| aElementOf0(X3,X2) ) )
=> ( ( ~ sdteqdtlpzmzozddtrp0(sK19(X0,X1,X2),X0,X1)
| ~ aInteger0(sK19(X0,X1,X2))
| ~ aElementOf0(sK19(X0,X1,X2),X2) )
& ( ( sdteqdtlpzmzozddtrp0(sK19(X0,X1,X2),X0,X1)
& aInteger0(sK19(X0,X1,X2)) )
| aElementOf0(sK19(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f175,plain,
! [X0,X1] :
( ! [X2] :
( ( szAzrzSzezqlpdtcmdtrp0(X0,X1) = X2
| ( ( ~ sdteqdtlpzmzozddtrp0(sK19(X0,X1,X2),X0,X1)
| ~ aInteger0(sK19(X0,X1,X2))
| ~ aElementOf0(sK19(X0,X1,X2),X2) )
& ( ( sdteqdtlpzmzozddtrp0(sK19(X0,X1,X2),X0,X1)
& aInteger0(sK19(X0,X1,X2)) )
| aElementOf0(sK19(X0,X1,X2),X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X4] :
( ( aElementOf0(X4,X2)
| ~ sdteqdtlpzmzozddtrp0(X4,X0,X1)
| ~ aInteger0(X4) )
& ( ( sdteqdtlpzmzozddtrp0(X4,X0,X1)
& aInteger0(X4) )
| ~ aElementOf0(X4,X2) ) )
& aSet0(X2) )
| szAzrzSzezqlpdtcmdtrp0(X0,X1) != X2 ) )
| sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f173,f174]) ).
fof(f184,plain,
! [X1] :
( ! [X2] :
( ( 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) )
& ( ( 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)) ) )
| ~ sP7(X1) ),
inference(nnf_transformation,[],[f123]) ).
fof(f185,plain,
! [X0] :
( ! [X1] :
( ( 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) )
& ( ( 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)) ) )
| ~ sP7(X0) ),
inference(rectify,[],[f184]) ).
fof(f186,plain,
! [X0,X1] :
( ? [X3] :
( sdtpldt0(X1,smndt0(sz00)) = sdtasdt0(X0,X3)
& aInteger0(X3) )
=> ( sdtpldt0(X1,smndt0(sz00)) = sdtasdt0(X0,sK23(X0,X1))
& aInteger0(sK23(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f187,plain,
! [X0] :
( ! [X1] :
( ( 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) )
& ( ( sdteqdtlpzmzozddtrp0(X1,sz00,X0)
& aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
& sdtpldt0(X1,smndt0(sz00)) = sdtasdt0(X0,sK23(X0,X1))
& aInteger0(sK23(X0,X1))
& aInteger0(X1) )
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0)) ) )
| ~ sP7(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f185,f186]) ).
fof(f188,plain,
! [X5] :
( ! [X6] :
( ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
| ( ~ sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& ~ aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ! [X7] :
( sdtpldt0(X6,smndt0(sz00)) != sdtasdt0(X5,X7)
| ~ aInteger0(X7) ) )
| ~ aInteger0(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)) ) )
| ~ sP6(X5) ),
inference(nnf_transformation,[],[f122]) ).
fof(f189,plain,
! [X0] :
( ! [X1] :
( ( 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) )
& ( ( 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)) ) )
| ~ sP6(X0) ),
inference(rectify,[],[f188]) ).
fof(f190,plain,
! [X0,X1] :
( ? [X3] :
( sdtpldt0(X1,smndt0(sz00)) = sdtasdt0(X0,X3)
& aInteger0(X3) )
=> ( sdtpldt0(X1,smndt0(sz00)) = sdtasdt0(X0,sK24(X0,X1))
& aInteger0(sK24(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f191,plain,
! [X0] :
( ! [X1] :
( ( 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) )
& ( ( sdteqdtlpzmzozddtrp0(X1,sz00,X0)
& aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
& sdtpldt0(X1,smndt0(sz00)) = sdtasdt0(X0,sK24(X0,X1))
& aInteger0(sK24(X0,X1))
& aInteger0(X1) )
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0)) ) )
| ~ sP6(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f189,f190]) ).
fof(f192,plain,
( xS = cS2043
& ! [X0] :
( ( aElementOf0(X0,xS)
| ! [X1] :
( ( szAzrzSzezqlpdtcmdtrp0(sz00,X1) != X0
& sP7(X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
| ~ isPrime0(X1)
| sz00 = X1
| ~ aInteger0(X1) ) )
& ( ? [X2] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X2) = X0
& sP6(X2)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
& isPrime0(X2)
& sz00 != X2
& aInteger0(X2) )
| ~ aElementOf0(X0,xS) ) )
& aSet0(xS) ),
inference(rectify,[],[f124]) ).
fof(f193,plain,
! [X0] :
( ? [X2] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X2) = X0
& sP6(X2)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
& isPrime0(X2)
& sz00 != X2
& aInteger0(X2) )
=> ( szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X0)) = X0
& sP6(sK25(X0))
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X0)))
& isPrime0(sK25(X0))
& sz00 != sK25(X0)
& aInteger0(sK25(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f194,plain,
( xS = cS2043
& ! [X0] :
( ( aElementOf0(X0,xS)
| ! [X1] :
( ( szAzrzSzezqlpdtcmdtrp0(sz00,X1) != X0
& sP7(X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
| ~ isPrime0(X1)
| sz00 = X1
| ~ aInteger0(X1) ) )
& ( ( szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X0)) = X0
& sP6(sK25(X0))
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X0)))
& isPrime0(sK25(X0))
& sz00 != sK25(X0)
& aInteger0(sK25(X0)) )
| ~ aElementOf0(X0,xS) ) )
& aSet0(xS) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f192,f193]) ).
fof(f195,plain,
( ( ~ aElementOf0(xn,sbsmnsldt0(xS))
& ! [X2] :
( ~ aElementOf0(xn,X2)
| ~ aElementOf0(X2,xS) )
& ? [X0] :
( isPrime0(X0)
& aDivisorOf0(X0,xn)
& ? [X1] :
( sdtasdt0(X0,X1) = xn
& aInteger0(X1) )
& sz00 != X0
& aInteger0(X0) ) )
| ~ sP8 ),
inference(nnf_transformation,[],[f125]) ).
fof(f196,plain,
( ( ~ aElementOf0(xn,sbsmnsldt0(xS))
& ! [X0] :
( ~ aElementOf0(xn,X0)
| ~ aElementOf0(X0,xS) )
& ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,xn)
& ? [X2] :
( sdtasdt0(X1,X2) = xn
& aInteger0(X2) )
& sz00 != X1
& aInteger0(X1) ) )
| ~ sP8 ),
inference(rectify,[],[f195]) ).
fof(f197,plain,
( ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,xn)
& ? [X2] :
( sdtasdt0(X1,X2) = xn
& aInteger0(X2) )
& sz00 != X1
& aInteger0(X1) )
=> ( isPrime0(sK26)
& aDivisorOf0(sK26,xn)
& ? [X2] :
( xn = sdtasdt0(sK26,X2)
& aInteger0(X2) )
& sz00 != sK26
& aInteger0(sK26) ) ),
introduced(choice_axiom,[]) ).
fof(f198,plain,
( ? [X2] :
( xn = sdtasdt0(sK26,X2)
& aInteger0(X2) )
=> ( xn = sdtasdt0(sK26,sK27)
& aInteger0(sK27) ) ),
introduced(choice_axiom,[]) ).
fof(f199,plain,
( ( ~ aElementOf0(xn,sbsmnsldt0(xS))
& ! [X0] :
( ~ aElementOf0(xn,X0)
| ~ aElementOf0(X0,xS) )
& isPrime0(sK26)
& aDivisorOf0(sK26,xn)
& xn = sdtasdt0(sK26,sK27)
& aInteger0(sK27)
& sz00 != sK26
& aInteger0(sK26) )
| ~ sP8 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26,sK27])],[f196,f198,f197]) ).
fof(f200,plain,
( sP8
| ( ! [X0] :
( ~ isPrime0(X0)
| ( ~ aDivisorOf0(X0,xn)
& ( ! [X1] :
( sdtasdt0(X0,X1) != xn
| ~ aInteger0(X1) )
| sz00 = X0
| ~ aInteger0(X0) ) ) )
& aElementOf0(xn,sbsmnsldt0(xS))
& ? [X2] :
( aElementOf0(xn,X2)
& aElementOf0(X2,xS) ) ) ),
inference(rectify,[],[f126]) ).
fof(f201,plain,
( ? [X2] :
( aElementOf0(xn,X2)
& aElementOf0(X2,xS) )
=> ( aElementOf0(xn,sK28)
& aElementOf0(sK28,xS) ) ),
introduced(choice_axiom,[]) ).
fof(f202,plain,
( sP8
| ( ! [X0] :
( ~ isPrime0(X0)
| ( ~ aDivisorOf0(X0,xn)
& ( ! [X1] :
( sdtasdt0(X0,X1) != xn
| ~ aInteger0(X1) )
| sz00 = X0
| ~ aInteger0(X0) ) ) )
& aElementOf0(xn,sbsmnsldt0(xS))
& aElementOf0(xn,sK28)
& aElementOf0(sK28,xS) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f200,f201]) ).
fof(f203,plain,
aInteger0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f204,plain,
aInteger0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f205,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f207,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f208,plain,
! [X2,X0,X1] :
( sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f209,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f210,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f211,plain,
! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f212,plain,
! [X0] :
( sz00 = sdtpldt0(X0,smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f214,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,sdtasdt0(X1,X2)) = sdtasdt0(sdtasdt0(X0,X1),X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f215,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f220,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f222,plain,
! [X0] :
( smndt0(X0) = sdtasdt0(smndt0(sz10),X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f223,plain,
! [X0] :
( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f227,plain,
! [X0,X1] :
( aInteger0(sK9(X0,X1))
| ~ aDivisorOf0(X1,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f228,plain,
! [X0,X1] :
( sdtasdt0(X1,sK9(X0,X1)) = X0
| ~ aDivisorOf0(X1,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f230,plain,
! [X2,X0,X1] :
( aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f233,plain,
! [X2,X0,X1] :
( sdteqdtlpzmzozddtrp0(X1,X0,X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f237,plain,
! [X2,X0] :
( sz10 != X0
| ~ isPrime0(X2)
| ~ aDivisorOf0(X2,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f238,plain,
! [X2,X0] :
( smndt0(sz10) != X0
| ~ isPrime0(X2)
| ~ aDivisorOf0(X2,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f239,plain,
! [X0] :
( aDivisorOf0(sK10(X0),X0)
| smndt0(sz10) = X0
| sz10 = X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f240,plain,
! [X0] :
( isPrime0(sK10(X0))
| smndt0(sz10) = X0
| sz10 = X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f273,plain,
! [X0,X1,X5] :
( aElementOf0(sK16(X0,X5),X0)
| ~ aElementOf0(X5,X1)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f163]) ).
fof(f275,plain,
! [X0,X1,X6,X5] :
( aElementOf0(X5,X1)
| ~ aElementOf0(X5,X6)
| ~ aElementOf0(X6,X0)
| ~ aInteger0(X5)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f163]) ).
fof(f291,plain,
! [X2,X0,X1,X4] :
( sdteqdtlpzmzozddtrp0(X4,X0,X1)
| ~ aElementOf0(X4,X2)
| szAzrzSzezqlpdtcmdtrp0(X0,X1) != X2
| sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f175]) ).
fof(f312,plain,
! [X0,X1] :
( aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| ~ sP7(X0) ),
inference(cnf_transformation,[],[f187]) ).
fof(f313,plain,
! [X0,X1] :
( sdteqdtlpzmzozddtrp0(X1,sz00,X0)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| ~ sP7(X0) ),
inference(cnf_transformation,[],[f187]) ).
fof(f314,plain,
! [X2,X0,X1] :
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| sdtasdt0(X0,X2) != sdtpldt0(X1,smndt0(sz00))
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ sP7(X0) ),
inference(cnf_transformation,[],[f187]) ).
fof(f317,plain,
! [X0,X1] :
( aInteger0(X1)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| ~ sP6(X0) ),
inference(cnf_transformation,[],[f191]) ).
fof(f326,plain,
! [X0] :
( aInteger0(sK25(X0))
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f194]) ).
fof(f327,plain,
! [X0] :
( sz00 != sK25(X0)
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f194]) ).
fof(f328,plain,
! [X0] :
( isPrime0(sK25(X0))
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f194]) ).
fof(f330,plain,
! [X0] :
( sP6(sK25(X0))
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f194]) ).
fof(f331,plain,
! [X0] :
( szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X0)) = X0
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f194]) ).
fof(f332,plain,
! [X0,X1] :
( aElementOf0(X0,xS)
| aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ~ isPrime0(X1)
| sz00 = X1
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f194]) ).
fof(f333,plain,
! [X0,X1] :
( aElementOf0(X0,xS)
| sP7(X1)
| ~ isPrime0(X1)
| sz00 = X1
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f194]) ).
fof(f334,plain,
! [X0,X1] :
( aElementOf0(X0,xS)
| szAzrzSzezqlpdtcmdtrp0(sz00,X1) != X0
| ~ isPrime0(X1)
| sz00 = X1
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f194]) ).
fof(f335,plain,
xS = cS2043,
inference(cnf_transformation,[],[f194]) ).
fof(f336,plain,
aInteger0(xn),
inference(cnf_transformation,[],[f43]) ).
fof(f337,plain,
( aInteger0(sK26)
| ~ sP8 ),
inference(cnf_transformation,[],[f199]) ).
fof(f338,plain,
( sz00 != sK26
| ~ sP8 ),
inference(cnf_transformation,[],[f199]) ).
fof(f339,plain,
( aInteger0(sK27)
| ~ sP8 ),
inference(cnf_transformation,[],[f199]) ).
fof(f340,plain,
( xn = sdtasdt0(sK26,sK27)
| ~ sP8 ),
inference(cnf_transformation,[],[f199]) ).
fof(f341,plain,
( aDivisorOf0(sK26,xn)
| ~ sP8 ),
inference(cnf_transformation,[],[f199]) ).
fof(f342,plain,
( isPrime0(sK26)
| ~ sP8 ),
inference(cnf_transformation,[],[f199]) ).
fof(f343,plain,
! [X0] :
( ~ aElementOf0(xn,X0)
| ~ aElementOf0(X0,xS)
| ~ sP8 ),
inference(cnf_transformation,[],[f199]) ).
fof(f345,plain,
( sP8
| aElementOf0(sK28,xS) ),
inference(cnf_transformation,[],[f202]) ).
fof(f346,plain,
( sP8
| aElementOf0(xn,sK28) ),
inference(cnf_transformation,[],[f202]) ).
fof(f347,plain,
( sP8
| aElementOf0(xn,sbsmnsldt0(xS)) ),
inference(cnf_transformation,[],[f202]) ).
fof(f348,plain,
! [X0,X1] :
( sP8
| ~ isPrime0(X0)
| sdtasdt0(X0,X1) != xn
| ~ aInteger0(X1)
| sz00 = X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f202]) ).
fof(f349,plain,
! [X0] :
( sP8
| ~ isPrime0(X0)
| ~ aDivisorOf0(X0,xn) ),
inference(cnf_transformation,[],[f202]) ).
fof(f350,plain,
! [X0,X1] :
( aElementOf0(X0,cS2043)
| szAzrzSzezqlpdtcmdtrp0(sz00,X1) != X0
| ~ isPrime0(X1)
| sz00 = X1
| ~ aInteger0(X1) ),
inference(definition_unfolding,[],[f334,f335]) ).
fof(f351,plain,
! [X0,X1] :
( aElementOf0(X0,cS2043)
| sP7(X1)
| ~ isPrime0(X1)
| sz00 = X1
| ~ aInteger0(X1) ),
inference(definition_unfolding,[],[f333,f335]) ).
fof(f352,plain,
! [X0,X1] :
( aElementOf0(X0,cS2043)
| aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ~ isPrime0(X1)
| sz00 = X1
| ~ aInteger0(X1) ),
inference(definition_unfolding,[],[f332,f335]) ).
fof(f353,plain,
! [X0] :
( szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X0)) = X0
| ~ aElementOf0(X0,cS2043) ),
inference(definition_unfolding,[],[f331,f335]) ).
fof(f354,plain,
! [X0] :
( sP6(sK25(X0))
| ~ aElementOf0(X0,cS2043) ),
inference(definition_unfolding,[],[f330,f335]) ).
fof(f356,plain,
! [X0] :
( isPrime0(sK25(X0))
| ~ aElementOf0(X0,cS2043) ),
inference(definition_unfolding,[],[f328,f335]) ).
fof(f357,plain,
! [X0] :
( sz00 != sK25(X0)
| ~ aElementOf0(X0,cS2043) ),
inference(definition_unfolding,[],[f327,f335]) ).
fof(f358,plain,
! [X0] :
( aInteger0(sK25(X0))
| ~ aElementOf0(X0,cS2043) ),
inference(definition_unfolding,[],[f326,f335]) ).
fof(f361,plain,
! [X0] :
( ~ aElementOf0(xn,X0)
| ~ aElementOf0(X0,cS2043)
| ~ sP8 ),
inference(definition_unfolding,[],[f343,f335]) ).
fof(f362,plain,
( sP8
| aElementOf0(xn,sbsmnsldt0(cS2043)) ),
inference(definition_unfolding,[],[f347,f335]) ).
fof(f363,plain,
( sP8
| aElementOf0(sK28,cS2043) ),
inference(definition_unfolding,[],[f345,f335]) ).
fof(f366,plain,
! [X2] :
( ~ isPrime0(X2)
| ~ aDivisorOf0(X2,smndt0(sz10))
| ~ aInteger0(smndt0(sz10)) ),
inference(equality_resolution,[],[f238]) ).
fof(f367,plain,
! [X2] :
( ~ isPrime0(X2)
| ~ aDivisorOf0(X2,sz10)
| ~ aInteger0(sz10) ),
inference(equality_resolution,[],[f237]) ).
fof(f376,plain,
! [X0,X1,X4] :
( sdteqdtlpzmzozddtrp0(X4,X0,X1)
| ~ aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(equality_resolution,[],[f291]) ).
fof(f379,plain,
! [X1] :
( aElementOf0(szAzrzSzezqlpdtcmdtrp0(sz00,X1),cS2043)
| ~ isPrime0(X1)
| sz00 = X1
| ~ aInteger0(X1) ),
inference(equality_resolution,[],[f350]) ).
cnf(c_49,plain,
aInteger0(sz00),
inference(cnf_transformation,[],[f203]) ).
cnf(c_50,plain,
aInteger0(sz10),
inference(cnf_transformation,[],[f204]) ).
cnf(c_51,plain,
( ~ aInteger0(X0)
| aInteger0(smndt0(X0)) ),
inference(cnf_transformation,[],[f205]) ).
cnf(c_53,plain,
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| aInteger0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f207]) ).
cnf(c_54,plain,
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
inference(cnf_transformation,[],[f208]) ).
cnf(c_55,plain,
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[],[f209]) ).
cnf(c_56,plain,
( ~ aInteger0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f211]) ).
cnf(c_57,plain,
( ~ aInteger0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f210]) ).
cnf(c_59,plain,
( ~ aInteger0(X0)
| sdtpldt0(X0,smndt0(X0)) = sz00 ),
inference(cnf_transformation,[],[f212]) ).
cnf(c_60,plain,
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
inference(cnf_transformation,[],[f214]) ).
cnf(c_61,plain,
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f215]) ).
cnf(c_67,plain,
( ~ aInteger0(X0)
| sdtasdt0(X0,sz00) = sz00 ),
inference(cnf_transformation,[],[f220]) ).
cnf(c_68,plain,
( ~ aInteger0(X0)
| sdtasdt0(X0,smndt0(sz10)) = smndt0(X0) ),
inference(cnf_transformation,[],[f223]) ).
cnf(c_69,plain,
( ~ aInteger0(X0)
| sdtasdt0(smndt0(sz10),X0) = smndt0(X0) ),
inference(cnf_transformation,[],[f222]) ).
cnf(c_72,plain,
( ~ aDivisorOf0(X0,X1)
| ~ aInteger0(X1)
| sdtasdt0(X0,sK9(X1,X0)) = X1 ),
inference(cnf_transformation,[],[f228]) ).
cnf(c_73,plain,
( ~ aDivisorOf0(X0,X1)
| ~ aInteger0(X1)
| aInteger0(sK9(X1,X0)) ),
inference(cnf_transformation,[],[f227]) ).
cnf(c_77,plain,
( ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| X2 = sz00
| aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ),
inference(cnf_transformation,[],[f230]) ).
cnf(c_79,plain,
( ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| X2 = sz00
| sdteqdtlpzmzozddtrp0(X1,X0,X2) ),
inference(cnf_transformation,[],[f233]) ).
cnf(c_83,plain,
( ~ aInteger0(X0)
| smndt0(sz10) = X0
| X0 = sz10
| isPrime0(sK10(X0)) ),
inference(cnf_transformation,[],[f240]) ).
cnf(c_84,plain,
( ~ aInteger0(X0)
| smndt0(sz10) = X0
| X0 = sz10
| aDivisorOf0(sK10(X0),X0) ),
inference(cnf_transformation,[],[f239]) ).
cnf(c_85,plain,
( ~ aDivisorOf0(X0,smndt0(sz10))
| ~ aInteger0(smndt0(sz10))
| ~ isPrime0(X0) ),
inference(cnf_transformation,[],[f366]) ).
cnf(c_86,plain,
( ~ aDivisorOf0(X0,sz10)
| ~ isPrime0(X0)
| ~ aInteger0(sz10) ),
inference(cnf_transformation,[],[f367]) ).
cnf(c_121,plain,
( ~ aElementOf0(X0,X1)
| ~ aElementOf0(X1,X2)
| ~ sP4(X2,X3)
| ~ aInteger0(X0)
| aElementOf0(X0,X3) ),
inference(cnf_transformation,[],[f275]) ).
cnf(c_123,plain,
( ~ aElementOf0(X0,X1)
| ~ sP4(X2,X1)
| aElementOf0(sK16(X2,X0),X2) ),
inference(cnf_transformation,[],[f273]) ).
cnf(c_139,plain,
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| X2 = sz00
| sdteqdtlpzmzozddtrp0(X0,X1,X2) ),
inference(cnf_transformation,[],[f376]) ).
cnf(c_157,plain,
( sdtpldt0(X0,smndt0(sz00)) != sdtasdt0(X1,X2)
| ~ aInteger0(X0)
| ~ aInteger0(X2)
| ~ sP7(X1)
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ),
inference(cnf_transformation,[],[f314]) ).
cnf(c_158,plain,
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ~ sP7(X1)
| sdteqdtlpzmzozddtrp0(X0,sz00,X1) ),
inference(cnf_transformation,[],[f313]) ).
cnf(c_159,plain,
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ~ sP7(X1)
| aDivisorOf0(X1,sdtpldt0(X0,smndt0(sz00))) ),
inference(cnf_transformation,[],[f312]) ).
cnf(c_170,plain,
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ~ sP6(X1)
| aInteger0(X0) ),
inference(cnf_transformation,[],[f317]) ).
cnf(c_171,plain,
( ~ aInteger0(X0)
| ~ isPrime0(X0)
| X0 = sz00
| aElementOf0(szAzrzSzezqlpdtcmdtrp0(sz00,X0),cS2043) ),
inference(cnf_transformation,[],[f379]) ).
cnf(c_172,plain,
( ~ aInteger0(X0)
| ~ isPrime0(X0)
| X0 = sz00
| aElementOf0(X1,cS2043)
| sP7(X0) ),
inference(cnf_transformation,[],[f351]) ).
cnf(c_173,plain,
( ~ aInteger0(X0)
| ~ isPrime0(X0)
| X0 = sz00
| aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| aElementOf0(X1,cS2043) ),
inference(cnf_transformation,[],[f352]) ).
cnf(c_174,plain,
( ~ aElementOf0(X0,cS2043)
| szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X0)) = X0 ),
inference(cnf_transformation,[],[f353]) ).
cnf(c_175,plain,
( ~ aElementOf0(X0,cS2043)
| sP6(sK25(X0)) ),
inference(cnf_transformation,[],[f354]) ).
cnf(c_177,plain,
( ~ aElementOf0(X0,cS2043)
| isPrime0(sK25(X0)) ),
inference(cnf_transformation,[],[f356]) ).
cnf(c_178,plain,
( sK25(X0) != sz00
| ~ aElementOf0(X0,cS2043) ),
inference(cnf_transformation,[],[f357]) ).
cnf(c_179,plain,
( ~ aElementOf0(X0,cS2043)
| aInteger0(sK25(X0)) ),
inference(cnf_transformation,[],[f358]) ).
cnf(c_181,plain,
aInteger0(xn),
inference(cnf_transformation,[],[f336]) ).
cnf(c_183,plain,
( ~ aElementOf0(X0,cS2043)
| ~ aElementOf0(xn,X0)
| ~ sP8 ),
inference(cnf_transformation,[],[f361]) ).
cnf(c_184,plain,
( ~ sP8
| isPrime0(sK26) ),
inference(cnf_transformation,[],[f342]) ).
cnf(c_185,plain,
( ~ sP8
| aDivisorOf0(sK26,xn) ),
inference(cnf_transformation,[],[f341]) ).
cnf(c_186,plain,
( ~ sP8
| sdtasdt0(sK26,sK27) = xn ),
inference(cnf_transformation,[],[f340]) ).
cnf(c_187,plain,
( ~ sP8
| aInteger0(sK27) ),
inference(cnf_transformation,[],[f339]) ).
cnf(c_188,plain,
( sz00 != sK26
| ~ sP8 ),
inference(cnf_transformation,[],[f338]) ).
cnf(c_189,plain,
( ~ sP8
| aInteger0(sK26) ),
inference(cnf_transformation,[],[f337]) ).
cnf(c_190,negated_conjecture,
( ~ aDivisorOf0(X0,xn)
| ~ isPrime0(X0)
| sP8 ),
inference(cnf_transformation,[],[f349]) ).
cnf(c_191,negated_conjecture,
( sdtasdt0(X0,X1) != xn
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ isPrime0(X0)
| X0 = sz00
| sP8 ),
inference(cnf_transformation,[],[f348]) ).
cnf(c_192,negated_conjecture,
( aElementOf0(xn,sbsmnsldt0(cS2043))
| sP8 ),
inference(cnf_transformation,[],[f362]) ).
cnf(c_193,negated_conjecture,
( aElementOf0(xn,sK28)
| sP8 ),
inference(cnf_transformation,[],[f346]) ).
cnf(c_194,negated_conjecture,
( aElementOf0(sK28,cS2043)
| sP8 ),
inference(cnf_transformation,[],[f363]) ).
cnf(c_196,plain,
( ~ aInteger0(sz00)
| aInteger0(smndt0(sz00)) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_333,plain,
( ~ isPrime0(X0)
| ~ aDivisorOf0(X0,sz10) ),
inference(prop_impl_just,[status(thm)],[c_50,c_86]) ).
cnf(c_334,plain,
( ~ aDivisorOf0(X0,sz10)
| ~ isPrime0(X0) ),
inference(renaming,[status(thm)],[c_333]) ).
cnf(c_359,plain,
( ~ aElementOf0(X0,cS2043)
| sP6(sK25(X0)) ),
inference(prop_impl_just,[status(thm)],[c_175]) ).
cnf(c_373,plain,
( ~ sP8
| aDivisorOf0(sK26,xn) ),
inference(prop_impl_just,[status(thm)],[c_185]) ).
cnf(c_2881,plain,
( sK25(X0) != X1
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ~ aElementOf0(X0,cS2043)
| aInteger0(X2) ),
inference(resolution_lifted,[status(thm)],[c_170,c_359]) ).
cnf(c_2882,plain,
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X1)))
| ~ aElementOf0(X1,cS2043)
| aInteger0(X0) ),
inference(unflattening,[status(thm)],[c_2881]) ).
cnf(c_6340,plain,
( X0 != sK26
| X1 != xn
| ~ aInteger0(X1)
| ~ sP8
| aInteger0(sK9(X1,X0)) ),
inference(resolution_lifted,[status(thm)],[c_73,c_373]) ).
cnf(c_6341,plain,
( ~ aInteger0(xn)
| ~ sP8
| aInteger0(sK9(xn,sK26)) ),
inference(unflattening,[status(thm)],[c_6340]) ).
cnf(c_6778,plain,
( smndt0(sz10) != xn
| X0 != sK26
| ~ aInteger0(smndt0(sz10))
| ~ isPrime0(X0)
| ~ sP8 ),
inference(resolution_lifted,[status(thm)],[c_85,c_373]) ).
cnf(c_6779,plain,
( smndt0(sz10) != xn
| ~ aInteger0(smndt0(sz10))
| ~ isPrime0(sK26)
| ~ sP8 ),
inference(unflattening,[status(thm)],[c_6778]) ).
cnf(c_6780,plain,
( ~ aInteger0(smndt0(sz10))
| smndt0(sz10) != xn
| ~ sP8 ),
inference(global_subsumption_just,[status(thm)],[c_6779,c_184,c_6779]) ).
cnf(c_6781,plain,
( smndt0(sz10) != xn
| ~ aInteger0(smndt0(sz10))
| ~ sP8 ),
inference(renaming,[status(thm)],[c_6780]) ).
cnf(c_6825,plain,
( X0 != sK26
| sz10 != xn
| ~ isPrime0(X0)
| ~ sP8 ),
inference(resolution_lifted,[status(thm)],[c_334,c_373]) ).
cnf(c_6826,plain,
( sz10 != xn
| ~ isPrime0(sK26)
| ~ sP8 ),
inference(unflattening,[status(thm)],[c_6825]) ).
cnf(c_6827,plain,
( sz10 != xn
| ~ sP8 ),
inference(global_subsumption_just,[status(thm)],[c_6826,c_184,c_6826]) ).
cnf(c_13763,plain,
( aElementOf0(X0,cS2043)
| ~ sP0_iProver_def ),
inference(splitting,[splitting(split),new_symbols(definition,[sP0_iProver_def])],[c_173]) ).
cnf(c_13766,plain,
( sP7(X0)
| ~ isPrime0(X0)
| ~ aInteger0(X0)
| X0 = sz00
| ~ sP2_iProver_def ),
inference(splitting,[splitting(split),new_symbols(definition,[sP2_iProver_def])],[c_172]) ).
cnf(c_13767,plain,
( sP0_iProver_def
| sP2_iProver_def ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_172]) ).
cnf(c_13768,plain,
sbsmnsldt0(cS2043) = sP3_iProver_def,
definition ).
cnf(c_13769,negated_conjecture,
( aElementOf0(sK28,cS2043)
| sP8 ),
inference(demodulation,[status(thm)],[c_194]) ).
cnf(c_13770,negated_conjecture,
( aElementOf0(xn,sK28)
| sP8 ),
inference(demodulation,[status(thm)],[c_193]) ).
cnf(c_13771,negated_conjecture,
( aElementOf0(xn,sP3_iProver_def)
| sP8 ),
inference(demodulation,[status(thm)],[c_192,c_13768]) ).
cnf(c_13772,negated_conjecture,
( sdtasdt0(X0,X1) != xn
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ isPrime0(X0)
| X0 = sz00
| sP8 ),
inference(demodulation,[status(thm)],[c_191]) ).
cnf(c_13773,negated_conjecture,
( ~ aDivisorOf0(X0,xn)
| ~ isPrime0(X0)
| sP8 ),
inference(demodulation,[status(thm)],[c_190]) ).
cnf(c_16229,plain,
( ~ sP0_iProver_def
| isPrime0(sK25(X0)) ),
inference(superposition,[status(thm)],[c_13763,c_177]) ).
cnf(c_16230,plain,
( isPrime0(sK25(sK28))
| sP8 ),
inference(superposition,[status(thm)],[c_13769,c_177]) ).
cnf(c_16241,plain,
( aInteger0(sK25(sK28))
| sP8 ),
inference(superposition,[status(thm)],[c_13769,c_179]) ).
cnf(c_16331,plain,
sdtpldt0(xn,sz00) = xn,
inference(superposition,[status(thm)],[c_181,c_57]) ).
cnf(c_16891,plain,
sdtpldt0(sz00,smndt0(sz00)) = sz00,
inference(superposition,[status(thm)],[c_49,c_59]) ).
cnf(c_17130,plain,
( ~ aInteger0(sz10)
| aInteger0(smndt0(sz10)) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_17270,plain,
( ~ aInteger0(sK25(X0))
| ~ isPrime0(sK25(X0))
| ~ sP2_iProver_def
| sK25(X0) = sz00
| sP7(sK25(X0)) ),
inference(instantiation,[status(thm)],[c_13766]) ).
cnf(c_17296,plain,
( ~ aElementOf0(xn,X0)
| ~ sP8
| ~ sP0_iProver_def ),
inference(superposition,[status(thm)],[c_13763,c_183]) ).
cnf(c_17323,plain,
sdtasdt0(sz00,smndt0(sz10)) = smndt0(sz00),
inference(superposition,[status(thm)],[c_49,c_68]) ).
cnf(c_17329,plain,
sdtasdt0(xn,smndt0(sz10)) = smndt0(xn),
inference(superposition,[status(thm)],[c_181,c_68]) ).
cnf(c_18176,plain,
( ~ sP0_iProver_def
| szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X0)) = X0 ),
inference(superposition,[status(thm)],[c_13763,c_174]) ).
cnf(c_18177,plain,
( szAzrzSzezqlpdtcmdtrp0(sz00,sK25(sK28)) = sK28
| sP8 ),
inference(superposition,[status(thm)],[c_13769,c_174]) ).
cnf(c_18305,plain,
( ~ sP8
| ~ sP0_iProver_def ),
inference(superposition,[status(thm)],[c_13763,c_17296]) ).
cnf(c_18581,plain,
( ~ sP4(X0,sK28)
| aElementOf0(sK16(X0,xn),X0)
| sP8 ),
inference(superposition,[status(thm)],[c_13770,c_123]) ).
cnf(c_18700,plain,
( ~ aInteger0(smndt0(sz10))
| ~ aInteger0(sz00)
| aInteger0(smndt0(sz00)) ),
inference(superposition,[status(thm)],[c_17323,c_53]) ).
cnf(c_18703,plain,
( ~ aInteger0(smndt0(sz10))
| aInteger0(smndt0(sz00)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18700,c_49]) ).
cnf(c_18706,plain,
aInteger0(smndt0(sz00)),
inference(global_subsumption_just,[status(thm)],[c_18703,c_49,c_196]) ).
cnf(c_18717,plain,
sdtpldt0(sz00,smndt0(sz00)) = smndt0(sz00),
inference(superposition,[status(thm)],[c_18706,c_56]) ).
cnf(c_18718,plain,
smndt0(sz00) = sz00,
inference(light_normalisation,[status(thm)],[c_18717,c_16891]) ).
cnf(c_20229,plain,
( ~ aInteger0(smndt0(sz10))
| ~ aInteger0(xn)
| aInteger0(smndt0(xn)) ),
inference(superposition,[status(thm)],[c_17329,c_53]) ).
cnf(c_20232,plain,
( ~ aInteger0(smndt0(sz10))
| aInteger0(smndt0(xn)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20229,c_181]) ).
cnf(c_20261,plain,
aInteger0(smndt0(xn)),
inference(global_subsumption_just,[status(thm)],[c_20232,c_50,c_17130,c_20232]) ).
cnf(c_20274,plain,
sdtpldt0(sz00,smndt0(xn)) = smndt0(xn),
inference(superposition,[status(thm)],[c_20261,c_56]) ).
cnf(c_23393,plain,
( sK25(sK28) != sz00
| ~ aElementOf0(sK28,cS2043) ),
inference(instantiation,[status(thm)],[c_178]) ).
cnf(c_23806,plain,
( ~ aElementOf0(xn,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| ~ aInteger0(X0)
| ~ isPrime0(X0)
| ~ sP8
| X0 = sz00 ),
inference(superposition,[status(thm)],[c_171,c_183]) ).
cnf(c_23943,plain,
( ~ isPrime0(sK10(xn))
| ~ aInteger0(xn)
| smndt0(sz10) = xn
| sz10 = xn
| sP8 ),
inference(superposition,[status(thm)],[c_84,c_13773]) ).
cnf(c_23948,plain,
( ~ isPrime0(sK10(xn))
| smndt0(sz10) = xn
| sz10 = xn
| sP8 ),
inference(forward_subsumption_resolution,[status(thm)],[c_23943,c_181]) ).
cnf(c_24439,plain,
( ~ aInteger0(xn)
| smndt0(sz10) = xn
| sz10 = xn
| sP8 ),
inference(superposition,[status(thm)],[c_83,c_23948]) ).
cnf(c_24440,plain,
( smndt0(sz10) = xn
| sz10 = xn
| sP8 ),
inference(forward_subsumption_resolution,[status(thm)],[c_24439,c_181]) ).
cnf(c_26310,plain,
( ~ aInteger0(sK25(sK28))
| ~ isPrime0(sK25(sK28))
| ~ sP2_iProver_def
| sK25(sK28) = sz00
| sP7(sK25(sK28)) ),
inference(instantiation,[status(thm)],[c_17270]) ).
cnf(c_27114,plain,
( ~ aInteger0(sK16(X0,xn))
| ~ aElementOf0(X0,X1)
| ~ sP4(X1,X2)
| ~ sP4(X0,sK28)
| aElementOf0(sK16(X0,xn),X2)
| sP8 ),
inference(superposition,[status(thm)],[c_18581,c_121]) ).
cnf(c_30860,plain,
( ~ aInteger0(sK16(xn,xn))
| ~ sP4(sK28,X0)
| ~ sP4(xn,sK28)
| aElementOf0(sK16(xn,xn),X0)
| sP8 ),
inference(superposition,[status(thm)],[c_13770,c_27114]) ).
cnf(c_30862,plain,
( ~ aInteger0(sK16(xn,xn))
| ~ sP4(sP3_iProver_def,X0)
| ~ sP4(xn,sK28)
| aElementOf0(sK16(xn,xn),X0)
| sP8 ),
inference(superposition,[status(thm)],[c_13771,c_27114]) ).
cnf(c_31878,plain,
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| sdtasdt0(sdtasdt0(sK25(sK28),X0),X1) = sdtasdt0(sK25(sK28),sdtasdt0(X0,X1))
| sP8 ),
inference(superposition,[status(thm)],[c_16241,c_60]) ).
cnf(c_32840,plain,
( ~ aInteger0(sK16(xn,xn))
| ~ aElementOf0(X0,X1)
| ~ sP4(X1,X2)
| ~ sP4(sP3_iProver_def,X0)
| ~ sP4(xn,sK28)
| aElementOf0(sK16(xn,xn),X2)
| sP8 ),
inference(superposition,[status(thm)],[c_30862,c_121]) ).
cnf(c_37697,plain,
( ~ sdteqdtlpzmzozddtrp0(sz00,xn,X0)
| ~ aInteger0(X0)
| ~ aInteger0(sz00)
| ~ aInteger0(xn)
| X0 = sz00
| aDivisorOf0(X0,smndt0(xn)) ),
inference(superposition,[status(thm)],[c_20274,c_77]) ).
cnf(c_37718,plain,
( ~ sdteqdtlpzmzozddtrp0(sz00,xn,X0)
| ~ aInteger0(X0)
| X0 = sz00
| aDivisorOf0(X0,smndt0(xn)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_37697,c_181,c_49]) ).
cnf(c_40354,plain,
( sdtasdt0(X0,X1) != sdtpldt0(X2,sz00)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ sP7(X0)
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X0)) ),
inference(light_normalisation,[status(thm)],[c_157,c_18718]) ).
cnf(c_40409,plain,
( sdtasdt0(X0,X1) != xn
| ~ aInteger0(X1)
| ~ sP7(X0)
| ~ aInteger0(xn)
| aElementOf0(xn,szAzrzSzezqlpdtcmdtrp0(sz00,X0)) ),
inference(superposition,[status(thm)],[c_16331,c_40354]) ).
cnf(c_40415,plain,
( sdtasdt0(X0,X1) != xn
| ~ aInteger0(X1)
| ~ sP7(X0)
| aElementOf0(xn,szAzrzSzezqlpdtcmdtrp0(sz00,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40409,c_181]) ).
cnf(c_88120,plain,
( X0 = sz00
| ~ isPrime0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdtasdt0(X0,X1) != xn ),
inference(global_subsumption_just,[status(thm)],[c_13772,c_191,c_13766,c_13767,c_18305,c_23806,c_40415]) ).
cnf(c_88121,negated_conjecture,
( sdtasdt0(X0,X1) != xn
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ isPrime0(X0)
| X0 = sz00 ),
inference(renaming,[status(thm)],[c_88120]) ).
cnf(c_88219,plain,
( isPrime0(sK25(sK28))
| sP8 ),
inference(superposition,[status(thm)],[c_13769,c_177]) ).
cnf(c_88322,plain,
sdtpldt0(xn,sz00) = xn,
inference(superposition,[status(thm)],[c_181,c_57]) ).
cnf(c_88500,plain,
( ~ aInteger0(X0)
| sdtasdt0(smndt0(X0),sz00) = sz00 ),
inference(superposition,[status(thm)],[c_51,c_67]) ).
cnf(c_88788,plain,
sdtasdt0(smndt0(sz00),sz00) = sz00,
inference(superposition,[status(thm)],[c_49,c_88500]) ).
cnf(c_88815,plain,
( sz00 != xn
| ~ aInteger0(smndt0(sz00))
| ~ isPrime0(smndt0(sz00))
| ~ aInteger0(sz00)
| smndt0(sz00) = sz00 ),
inference(superposition,[status(thm)],[c_88788,c_88121]) ).
cnf(c_88816,plain,
( sz00 != xn
| ~ aInteger0(smndt0(sz00))
| ~ isPrime0(smndt0(sz00))
| smndt0(sz00) = sz00 ),
inference(forward_subsumption_resolution,[status(thm)],[c_88815,c_49]) ).
cnf(c_88849,plain,
smndt0(sz00) = sz00,
inference(global_subsumption_just,[status(thm)],[c_88816,c_18718]) ).
cnf(c_89654,plain,
( szAzrzSzezqlpdtcmdtrp0(sz00,sK25(sK28)) = sK28
| sP8 ),
inference(superposition,[status(thm)],[c_13769,c_174]) ).
cnf(c_91121,plain,
( ~ aInteger0(X0)
| ~ sP8
| sdtpldt0(X0,sK26) = sdtpldt0(sK26,X0) ),
inference(superposition,[status(thm)],[c_189,c_55]) ).
cnf(c_91892,plain,
( ~ aInteger0(xn)
| ~ sP8
| sdtasdt0(sK26,sK9(xn,sK26)) = xn ),
inference(superposition,[status(thm)],[c_185,c_72]) ).
cnf(c_91893,plain,
( ~ sP8
| sdtasdt0(sK26,sK9(xn,sK26)) = xn ),
inference(forward_subsumption_resolution,[status(thm)],[c_91892,c_181]) ).
cnf(c_91907,plain,
( sdtasdt0(sK26,sK9(xn,sK26)) = xn
| szAzrzSzezqlpdtcmdtrp0(sz00,sK25(sK28)) = sK28 ),
inference(superposition,[status(thm)],[c_89654,c_91893]) ).
cnf(c_93240,plain,
( ~ aInteger0(sK9(xn,sK26))
| ~ aInteger0(sK26)
| ~ isPrime0(sK26)
| szAzrzSzezqlpdtcmdtrp0(sz00,sK25(sK28)) = sK28
| sz00 = sK26 ),
inference(superposition,[status(thm)],[c_91907,c_88121]) ).
cnf(c_93246,plain,
szAzrzSzezqlpdtcmdtrp0(sz00,sK25(sK28)) = sK28,
inference(global_subsumption_just,[status(thm)],[c_93240,c_181,c_189,c_184,c_188,c_6341,c_18177,c_93240]) ).
cnf(c_94999,plain,
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ~ sP7(X1)
| aDivisorOf0(X1,sdtpldt0(X0,sz00)) ),
inference(light_normalisation,[status(thm)],[c_159,c_88849]) ).
cnf(c_95018,plain,
( ~ aElementOf0(X0,sK28)
| ~ sP7(sK25(sK28))
| aDivisorOf0(sK25(sK28),sdtpldt0(X0,sz00)) ),
inference(superposition,[status(thm)],[c_93246,c_94999]) ).
cnf(c_96805,plain,
( ~ isPrime0(sK10(xn))
| ~ aInteger0(xn)
| smndt0(sz10) = xn
| sz10 = xn
| sP8 ),
inference(superposition,[status(thm)],[c_84,c_13773]) ).
cnf(c_96810,plain,
( ~ isPrime0(sK10(xn))
| smndt0(sz10) = xn
| sz10 = xn
| sP8 ),
inference(forward_subsumption_resolution,[status(thm)],[c_96805,c_181]) ).
cnf(c_101137,plain,
( smndt0(sz10) = xn
| sz10 = xn
| sP8 ),
inference(global_subsumption_just,[status(thm)],[c_96810,c_24440]) ).
cnf(c_101151,plain,
( sdtasdt0(sK26,sK27) = xn
| smndt0(sz10) = xn
| sz10 = xn ),
inference(superposition,[status(thm)],[c_101137,c_186]) ).
cnf(c_111537,plain,
( ~ aInteger0(sK16(xn,xn))
| ~ sP4(sK28,X0)
| ~ sP4(xn,sK28)
| ~ sP4(sP3_iProver_def,xn)
| aElementOf0(sK16(xn,xn),X0)
| sP8 ),
inference(superposition,[status(thm)],[c_13770,c_32840]) ).
cnf(c_112350,plain,
( ~ aInteger0(sK26)
| ~ aInteger0(sK27)
| ~ isPrime0(sK26)
| smndt0(sz10) = xn
| sz00 = sK26
| sz10 = xn ),
inference(superposition,[status(thm)],[c_101151,c_88121]) ).
cnf(c_112363,plain,
( aElementOf0(sK16(xn,xn),X0)
| ~ aInteger0(sK16(xn,xn))
| ~ sP4(sK28,X0)
| ~ sP4(xn,sK28) ),
inference(global_subsumption_just,[status(thm)],[c_111537,c_50,c_189,c_187,c_184,c_188,c_6781,c_6827,c_17130,c_30860,c_112350]) ).
cnf(c_112364,plain,
( ~ aInteger0(sK16(xn,xn))
| ~ sP4(sK28,X0)
| ~ sP4(xn,sK28)
| aElementOf0(sK16(xn,xn),X0) ),
inference(renaming,[status(thm)],[c_112363]) ).
cnf(c_112397,plain,
( ~ aElementOf0(xn,sK16(xn,xn))
| ~ aInteger0(sK16(xn,xn))
| ~ sP4(xn,sK28)
| ~ sP4(sK28,cS2043)
| ~ sP8 ),
inference(superposition,[status(thm)],[c_112364,c_183]) ).
cnf(c_113651,plain,
~ sP8,
inference(global_subsumption_just,[status(thm)],[c_112397,c_50,c_189,c_187,c_184,c_188,c_6781,c_6827,c_17130,c_112350]) ).
cnf(c_113771,plain,
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| sdtasdt0(sdtasdt0(sK25(sK28),X0),X1) = sdtasdt0(sK25(sK28),sdtasdt0(X0,X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_31878,c_113651]) ).
cnf(c_113895,plain,
szAzrzSzezqlpdtcmdtrp0(sz00,sK25(sK28)) = sK28,
inference(backward_subsumption_resolution,[status(thm)],[c_18177,c_113651]) ).
cnf(c_113907,plain,
aInteger0(sK25(sK28)),
inference(backward_subsumption_resolution,[status(thm)],[c_16241,c_113651]) ).
cnf(c_113911,plain,
aElementOf0(xn,sK28),
inference(backward_subsumption_resolution,[status(thm)],[c_13770,c_113651]) ).
cnf(c_113912,plain,
( sdtasdt0(X0,X1) != xn
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ isPrime0(X0)
| X0 = sz00 ),
inference(backward_subsumption_resolution,[status(thm)],[c_13772,c_113651]) ).
cnf(c_115036,plain,
( ~ aElementOf0(X0,sK28)
| ~ aInteger0(sK25(sK28))
| ~ aInteger0(sz00)
| sK25(sK28) = sz00
| sdteqdtlpzmzozddtrp0(X0,sz00,sK25(sK28)) ),
inference(superposition,[status(thm)],[c_113895,c_139]) ).
cnf(c_115046,plain,
( ~ aElementOf0(X0,sK28)
| ~ sP7(sK25(sK28))
| sdteqdtlpzmzozddtrp0(X0,sz00,sK25(sK28)) ),
inference(superposition,[status(thm)],[c_113895,c_158]) ).
cnf(c_115085,plain,
( ~ aElementOf0(X0,sK28)
| sK25(sK28) = sz00
| sdteqdtlpzmzozddtrp0(X0,sz00,sK25(sK28)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_115036,c_49,c_113907]) ).
cnf(c_129278,plain,
~ sP8,
inference(global_subsumption_just,[status(thm)],[c_91121,c_50,c_189,c_187,c_184,c_188,c_6781,c_6827,c_17130,c_112350]) ).
cnf(c_129365,plain,
isPrime0(sK25(sK28)),
inference(backward_subsumption_resolution,[status(thm)],[c_88219,c_129278]) ).
cnf(c_129368,plain,
aElementOf0(xn,sK28),
inference(backward_subsumption_resolution,[status(thm)],[c_13770,c_129278]) ).
cnf(c_129369,plain,
( ~ aDivisorOf0(X0,xn)
| ~ isPrime0(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_13773,c_129278]) ).
cnf(c_181587,plain,
( ~ aElementOf0(X0,sK28)
| sdteqdtlpzmzozddtrp0(X0,sz00,sK25(sK28)) ),
inference(global_subsumption_just,[status(thm)],[c_115046,c_50,c_194,c_189,c_187,c_184,c_188,c_6781,c_6827,c_17130,c_23393,c_112350,c_115085]) ).
cnf(c_181595,plain,
( ~ aElementOf0(X0,sK28)
| ~ aInteger0(sK25(sK28))
| ~ aInteger0(X0)
| ~ aInteger0(sz00)
| sK25(sK28) = sz00
| sdteqdtlpzmzozddtrp0(sz00,X0,sK25(sK28)) ),
inference(superposition,[status(thm)],[c_181587,c_79]) ).
cnf(c_181597,plain,
( ~ aElementOf0(X0,sK28)
| ~ aInteger0(X0)
| sK25(sK28) = sz00
| sdteqdtlpzmzozddtrp0(sz00,X0,sK25(sK28)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_181595,c_49,c_113907]) ).
cnf(c_190387,plain,
( ~ aElementOf0(xn,sK28)
| ~ sP7(sK25(sK28))
| aDivisorOf0(sK25(sK28),xn) ),
inference(superposition,[status(thm)],[c_88322,c_95018]) ).
cnf(c_190390,plain,
( ~ sP7(sK25(sK28))
| aDivisorOf0(sK25(sK28),xn) ),
inference(forward_subsumption_resolution,[status(thm)],[c_190387,c_129368]) ).
cnf(c_193941,plain,
( ~ isPrime0(sK25(sK28))
| ~ sP7(sK25(sK28)) ),
inference(superposition,[status(thm)],[c_190390,c_129369]) ).
cnf(c_193942,plain,
~ sP7(sK25(sK28)),
inference(forward_subsumption_resolution,[status(thm)],[c_193941,c_129365]) ).
cnf(c_206416,plain,
~ sP2_iProver_def,
inference(global_subsumption_just,[status(thm)],[c_13766,c_194,c_16230,c_16241,c_23393,c_26310,c_113651,c_193942]) ).
cnf(c_206418,plain,
sP0_iProver_def,
inference(backward_subsumption_resolution,[status(thm)],[c_13767,c_206416]) ).
cnf(c_206443,plain,
szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X0)) = X0,
inference(backward_subsumption_resolution,[status(thm)],[c_18176,c_206418]) ).
cnf(c_206456,plain,
isPrime0(sK25(X0)),
inference(backward_subsumption_resolution,[status(thm)],[c_16229,c_206418]) ).
cnf(c_206457,plain,
aElementOf0(X0,cS2043),
inference(backward_subsumption_resolution,[status(thm)],[c_13763,c_206418]) ).
cnf(c_206496,plain,
( ~ aElementOf0(X0,X1)
| ~ aElementOf0(X1,cS2043)
| aInteger0(X0) ),
inference(demodulation,[status(thm)],[c_2882,c_206443]) ).
cnf(c_206504,plain,
( ~ aElementOf0(X0,X1)
| aInteger0(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_206496,c_206457]) ).
cnf(c_206687,plain,
sK25(X0) != sz00,
inference(backward_subsumption_resolution,[status(thm)],[c_178,c_206457]) ).
cnf(c_207343,plain,
aInteger0(X0),
inference(superposition,[status(thm)],[c_206457,c_206504]) ).
cnf(c_207505,plain,
( sdtasdt0(X0,X1) != xn
| ~ isPrime0(X0)
| X0 = sz00 ),
inference(backward_subsumption_resolution,[status(thm)],[c_113912,c_207343]) ).
cnf(c_207558,plain,
( ~ aDivisorOf0(X0,X1)
| sdtasdt0(X0,sK9(X1,X0)) = X1 ),
inference(backward_subsumption_resolution,[status(thm)],[c_72,c_207343]) ).
cnf(c_207560,plain,
sdtasdt0(smndt0(sz10),X0) = smndt0(X0),
inference(backward_subsumption_resolution,[status(thm)],[c_69,c_207343]) ).
cnf(c_207568,plain,
sdtasdt0(X0,X1) = sdtasdt0(X1,X0),
inference(backward_subsumption_resolution,[status(thm)],[c_61,c_207343]) ).
cnf(c_207569,plain,
sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)),
inference(backward_subsumption_resolution,[status(thm)],[c_60,c_207343]) ).
cnf(c_207570,plain,
sdtpldt0(X0,smndt0(X0)) = sz00,
inference(backward_subsumption_resolution,[status(thm)],[c_59,c_207343]) ).
cnf(c_207572,plain,
sdtpldt0(X0,sz00) = X0,
inference(backward_subsumption_resolution,[status(thm)],[c_57,c_207343]) ).
cnf(c_207573,plain,
sdtpldt0(sz00,X0) = X0,
inference(backward_subsumption_resolution,[status(thm)],[c_56,c_207343]) ).
cnf(c_207575,plain,
sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)),
inference(backward_subsumption_resolution,[status(thm)],[c_54,c_207343]) ).
cnf(c_212548,plain,
sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X1,sdtasdt0(X0,X2)),
inference(superposition,[status(thm)],[c_207568,c_207569]) ).
cnf(c_216975,plain,
( ~ aElementOf0(X0,sK28)
| sdteqdtlpzmzozddtrp0(sz00,X0,sK25(sK28)) ),
inference(global_subsumption_just,[status(thm)],[c_181597,c_50,c_194,c_189,c_187,c_184,c_188,c_6781,c_6827,c_17130,c_23393,c_112350,c_181597,c_207343]) ).
cnf(c_225077,plain,
( ~ sdteqdtlpzmzozddtrp0(sz00,xn,X0)
| X0 = sz00
| aDivisorOf0(X0,smndt0(xn)) ),
inference(global_subsumption_just,[status(thm)],[c_37718,c_37718,c_207343]) ).
cnf(c_225085,plain,
( ~ aElementOf0(xn,sK28)
| sK25(sK28) = sz00
| aDivisorOf0(sK25(sK28),smndt0(xn)) ),
inference(superposition,[status(thm)],[c_216975,c_225077]) ).
cnf(c_225088,plain,
aDivisorOf0(sK25(sK28),smndt0(xn)),
inference(forward_subsumption_resolution,[status(thm)],[c_225085,c_206687,c_113911]) ).
cnf(c_225104,plain,
sdtasdt0(sK25(sK28),sK9(smndt0(xn),sK25(sK28))) = smndt0(xn),
inference(superposition,[status(thm)],[c_225088,c_207558]) ).
cnf(c_229437,plain,
( ~ aInteger0(X1)
| sdtasdt0(sdtasdt0(sK25(sK28),X0),X1) = sdtasdt0(sK25(sK28),sdtasdt0(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_113771,c_50,c_189,c_187,c_184,c_188,c_6781,c_6827,c_17130,c_31878,c_112350,c_207343]) ).
cnf(c_229438,plain,
( ~ aInteger0(X0)
| sdtasdt0(sdtasdt0(sK25(sK28),X1),X0) = sdtasdt0(sK25(sK28),sdtasdt0(X1,X0)) ),
inference(renaming,[status(thm)],[c_229437]) ).
cnf(c_229439,plain,
sdtasdt0(sdtasdt0(sK25(sK28),X1),X0) = sdtasdt0(sK25(sK28),sdtasdt0(X1,X0)),
inference(global_subsumption_just,[status(thm)],[c_229438,c_207343,c_229438]) ).
cnf(c_229440,plain,
sdtasdt0(sdtasdt0(sK25(sK28),X0),X1) = sdtasdt0(sK25(sK28),sdtasdt0(X0,X1)),
inference(renaming,[status(thm)],[c_229439]) ).
cnf(c_229441,plain,
sdtasdt0(sK25(sK28),sdtasdt0(X0,X1)) = sdtasdt0(X0,sdtasdt0(sK25(sK28),X1)),
inference(demodulation,[status(thm)],[c_229440,c_212548]) ).
cnf(c_229480,plain,
( sdtasdt0(X0,sdtasdt0(sK25(sK28),X1)) != xn
| ~ isPrime0(sK25(sK28))
| sK25(sK28) = sz00 ),
inference(superposition,[status(thm)],[c_229441,c_207505]) ).
cnf(c_229768,plain,
sdtasdt0(X0,sdtasdt0(sK25(sK28),X1)) != xn,
inference(forward_subsumption_resolution,[status(thm)],[c_229480,c_206687,c_206456]) ).
cnf(c_233706,plain,
sdtasdt0(X0,smndt0(xn)) != xn,
inference(superposition,[status(thm)],[c_225104,c_229768]) ).
cnf(c_233909,plain,
smndt0(smndt0(xn)) != xn,
inference(superposition,[status(thm)],[c_207560,c_233706]) ).
cnf(c_256578,plain,
sdtpldt0(X0,sdtpldt0(smndt0(X0),X1)) = sdtpldt0(sz00,X1),
inference(superposition,[status(thm)],[c_207570,c_207575]) ).
cnf(c_256654,plain,
sdtpldt0(X0,sdtpldt0(smndt0(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_256578,c_207573]) ).
cnf(c_256662,plain,
smndt0(smndt0(X0)) = sdtpldt0(X0,sz00),
inference(superposition,[status(thm)],[c_207570,c_256654]) ).
cnf(c_256690,plain,
smndt0(smndt0(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_256662,c_207572]) ).
cnf(c_256698,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_233909,c_256690]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM447+5 : TPTP v8.2.0. Released v4.0.0.
% 0.10/0.12 % Command : run_iprover %s %d THM
% 0.11/0.36 % Computer : n019.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8042.1875MB
% 0.11/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Jun 23 01:58:09 EDT 2024
% 0.11/0.36 % CPUTime :
% 0.23/0.48 Running first-order theorem proving
% 0.23/0.48 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 61.41/9.23 % SZS status Started for theBenchmark.p
% 61.41/9.23 % SZS status Theorem for theBenchmark.p
% 61.41/9.23
% 61.41/9.23 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 61.41/9.23
% 61.41/9.23 ------ iProver source info
% 61.41/9.23
% 61.41/9.23 git: date: 2024-06-12 09:56:46 +0000
% 61.41/9.23 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 61.41/9.23 git: non_committed_changes: false
% 61.41/9.23
% 61.41/9.23 ------ Parsing...
% 61.41/9.23 ------ Clausification by vclausify_rel & Parsing by iProver...
% 61.41/9.23
% 61.41/9.23 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 61.41/9.23
% 61.41/9.23 ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e
% 61.41/9.23
% 61.41/9.23 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 61.41/9.23 ------ Proving...
% 61.41/9.23 ------ Problem Properties
% 61.41/9.23
% 61.41/9.23
% 61.41/9.23 clauses 147
% 61.41/9.23 conjectures 5
% 61.41/9.23 EPR 39
% 61.41/9.23 Horn 100
% 61.41/9.23 unary 5
% 61.41/9.23 binary 36
% 61.41/9.23 lits 517
% 61.41/9.23 lits eq 68
% 61.41/9.23 fd_pure 0
% 61.41/9.23 fd_pseudo 0
% 61.41/9.23 fd_cond 22
% 61.41/9.23 fd_pseudo_cond 9
% 61.41/9.23 AC symbols 0
% 61.41/9.23
% 61.41/9.23 ------ Schedule dynamic 5 is on
% 61.41/9.23
% 61.41/9.23 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 61.41/9.23
% 61.41/9.23
% 61.41/9.23 ------
% 61.41/9.23 Current options:
% 61.41/9.23 ------
% 61.41/9.23
% 61.41/9.23
% 61.41/9.23
% 61.41/9.23
% 61.41/9.23 ------ Proving...
% 61.41/9.23
% 61.41/9.23
% 61.41/9.23 % SZS status Theorem for theBenchmark.p
% 61.41/9.23
% 61.41/9.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 61.41/9.24
% 61.41/9.24
%------------------------------------------------------------------------------