TSTP Solution File: NUM448+5 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : NUM448+5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n004.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 : Fri May 3 02:49:20 EDT 2024
% Result : Theorem 11.98s 2.67s
% Output : CNFRefutation 11.98s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% Comments :
%------------------------------------------------------------------------------
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(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(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,conjecture,
( ! [X0] :
( aInteger0(X0)
=> ( ( ? [X1] :
( isPrime0(X1)
& ( aDivisorOf0(X1,X0)
| ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& sz00 != X1
& aInteger0(X1) ) ) )
=> ( aElementOf0(X0,sbsmnsldt0(xS))
& ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) ) ) )
& ( ( aElementOf0(X0,sbsmnsldt0(xS))
| ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) ) )
=> ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,X0)
& ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& sz00 != X1
& aInteger0(X1) ) ) ) )
=> ( ( ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) ) )
& aSet0(sbsmnsldt0(xS)) )
=> ( ( ! [X0] :
( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X0,sbsmnsldt0(xS))
& aInteger0(X0) ) )
& aSet0(stldt0(sbsmnsldt0(xS))) )
=> ( stldt0(sbsmnsldt0(xS)) = cS2076
| ! [X0] :
( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
<=> ( smndt0(sz10) = X0
| sz10 = X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f44,negated_conjecture,
~ ( ! [X0] :
( aInteger0(X0)
=> ( ( ? [X1] :
( isPrime0(X1)
& ( aDivisorOf0(X1,X0)
| ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& sz00 != X1
& aInteger0(X1) ) ) )
=> ( aElementOf0(X0,sbsmnsldt0(xS))
& ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) ) ) )
& ( ( aElementOf0(X0,sbsmnsldt0(xS))
| ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) ) )
=> ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,X0)
& ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& sz00 != X1
& aInteger0(X1) ) ) ) )
=> ( ( ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) ) )
& aSet0(sbsmnsldt0(xS)) )
=> ( ( ! [X0] :
( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X0,sbsmnsldt0(xS))
& aInteger0(X0) ) )
& aSet0(stldt0(sbsmnsldt0(xS))) )
=> ( stldt0(sbsmnsldt0(xS)) = cS2076
| ! [X0] :
( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
<=> ( smndt0(sz10) = X0
| sz10 = X0 ) ) ) ) ) ),
inference(negated_conjecture,[],[f43]) ).
fof(f51,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(f52,plain,
~ ( ! [X0] :
( aInteger0(X0)
=> ( ( ? [X1] :
( isPrime0(X1)
& ( aDivisorOf0(X1,X0)
| ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& sz00 != X1
& aInteger0(X1) ) ) )
=> ( aElementOf0(X0,sbsmnsldt0(xS))
& ? [X3] :
( aElementOf0(X0,X3)
& aElementOf0(X3,xS) ) ) )
& ( ( aElementOf0(X0,sbsmnsldt0(xS))
| ? [X4] :
( aElementOf0(X0,X4)
& aElementOf0(X4,xS) ) )
=> ? [X5] :
( isPrime0(X5)
& aDivisorOf0(X5,X0)
& ? [X6] :
( sdtasdt0(X5,X6) = X0
& aInteger0(X6) )
& sz00 != X5
& aInteger0(X5) ) ) ) )
=> ( ( ! [X7] :
( aElementOf0(X7,sbsmnsldt0(xS))
<=> ( ? [X8] :
( aElementOf0(X7,X8)
& aElementOf0(X8,xS) )
& aInteger0(X7) ) )
& aSet0(sbsmnsldt0(xS)) )
=> ( ( ! [X9] :
( aElementOf0(X9,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X9,sbsmnsldt0(xS))
& aInteger0(X9) ) )
& aSet0(stldt0(sbsmnsldt0(xS))) )
=> ( stldt0(sbsmnsldt0(xS)) = cS2076
| ! [X10] :
( aElementOf0(X10,stldt0(sbsmnsldt0(xS)))
<=> ( smndt0(sz10) = X10
| sz10 = X10 ) ) ) ) ) ),
inference(rectify,[],[f44]) ).
fof(f54,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f87,plain,
! [X0] :
( ( ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,X0) )
<=> ( smndt0(sz10) != X0
& sz10 != X0 ) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f108,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,[],[f51]) ).
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(flattening,[],[f108]) ).
fof(f110,plain,
( stldt0(sbsmnsldt0(xS)) != cS2076
& ? [X10] :
( aElementOf0(X10,stldt0(sbsmnsldt0(xS)))
<~> ( smndt0(sz10) = X10
| sz10 = X10 ) )
& ! [X9] :
( aElementOf0(X9,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X9,sbsmnsldt0(xS))
& aInteger0(X9) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X7] :
( aElementOf0(X7,sbsmnsldt0(xS))
<=> ( ? [X8] :
( aElementOf0(X7,X8)
& aElementOf0(X8,xS) )
& aInteger0(X7) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( ( ( aElementOf0(X0,sbsmnsldt0(xS))
& ? [X3] :
( aElementOf0(X0,X3)
& aElementOf0(X3,xS) ) )
| ! [X1] :
( ~ isPrime0(X1)
| ( ~ aDivisorOf0(X1,X0)
& ( ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1) ) ) ) )
& ( ? [X5] :
( isPrime0(X5)
& aDivisorOf0(X5,X0)
& ? [X6] :
( sdtasdt0(X5,X6) = X0
& aInteger0(X6) )
& sz00 != X5
& aInteger0(X5) )
| ( ~ aElementOf0(X0,sbsmnsldt0(xS))
& ! [X4] :
( ~ aElementOf0(X0,X4)
| ~ aElementOf0(X4,xS) ) ) ) )
| ~ aInteger0(X0) ) ),
inference(ennf_transformation,[],[f52]) ).
fof(f111,plain,
( stldt0(sbsmnsldt0(xS)) != cS2076
& ? [X10] :
( aElementOf0(X10,stldt0(sbsmnsldt0(xS)))
<~> ( smndt0(sz10) = X10
| sz10 = X10 ) )
& ! [X9] :
( aElementOf0(X9,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X9,sbsmnsldt0(xS))
& aInteger0(X9) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X7] :
( aElementOf0(X7,sbsmnsldt0(xS))
<=> ( ? [X8] :
( aElementOf0(X7,X8)
& aElementOf0(X8,xS) )
& aInteger0(X7) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( ( ( aElementOf0(X0,sbsmnsldt0(xS))
& ? [X3] :
( aElementOf0(X0,X3)
& aElementOf0(X3,xS) ) )
| ! [X1] :
( ~ isPrime0(X1)
| ( ~ aDivisorOf0(X1,X0)
& ( ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1) ) ) ) )
& ( ? [X5] :
( isPrime0(X5)
& aDivisorOf0(X5,X0)
& ? [X6] :
( sdtasdt0(X5,X6) = X0
& aInteger0(X6) )
& sz00 != X5
& aInteger0(X5) )
| ( ~ aElementOf0(X0,sbsmnsldt0(xS))
& ! [X4] :
( ~ aElementOf0(X0,X4)
| ~ aElementOf0(X4,xS) ) ) ) )
| ~ aInteger0(X0) ) ),
inference(flattening,[],[f110]) ).
fof(f121,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(f122,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(f123,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,[],[f109,f122,f121]) ).
fof(f124,plain,
! [X0] :
( ? [X5] :
( isPrime0(X5)
& aDivisorOf0(X5,X0)
& ? [X6] :
( sdtasdt0(X5,X6) = X0
& aInteger0(X6) )
& sz00 != X5
& aInteger0(X5) )
| ~ sP8(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f125,plain,
( stldt0(sbsmnsldt0(xS)) != cS2076
& ? [X10] :
( aElementOf0(X10,stldt0(sbsmnsldt0(xS)))
<~> ( smndt0(sz10) = X10
| sz10 = X10 ) )
& ! [X9] :
( aElementOf0(X9,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X9,sbsmnsldt0(xS))
& aInteger0(X9) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X7] :
( aElementOf0(X7,sbsmnsldt0(xS))
<=> ( ? [X8] :
( aElementOf0(X7,X8)
& aElementOf0(X8,xS) )
& aInteger0(X7) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( ( ( aElementOf0(X0,sbsmnsldt0(xS))
& ? [X3] :
( aElementOf0(X0,X3)
& aElementOf0(X3,xS) ) )
| ! [X1] :
( ~ isPrime0(X1)
| ( ~ aDivisorOf0(X1,X0)
& ( ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1) ) ) ) )
& ( sP8(X0)
| ( ~ aElementOf0(X0,sbsmnsldt0(xS))
& ! [X4] :
( ~ aElementOf0(X0,X4)
| ~ aElementOf0(X4,xS) ) ) ) )
| ~ aInteger0(X0) ) ),
inference(definition_folding,[],[f111,f124]) ).
fof(f132,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,[],[f87]) ).
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(flattening,[],[f132]) ).
fof(f134,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,[],[f133]) ).
fof(f135,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,X0) )
=> ( isPrime0(sK10(X0))
& aDivisorOf0(sK10(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f136,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])],[f134,f135]) ).
fof(f191,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,[],[f123]) ).
fof(f192,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(f193,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])],[f191,f192]) ).
fof(f194,plain,
! [X0] :
( ? [X5] :
( isPrime0(X5)
& aDivisorOf0(X5,X0)
& ? [X6] :
( sdtasdt0(X5,X6) = X0
& aInteger0(X6) )
& sz00 != X5
& aInteger0(X5) )
| ~ sP8(X0) ),
inference(nnf_transformation,[],[f124]) ).
fof(f195,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,X0)
& ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& sz00 != X1
& aInteger0(X1) )
| ~ sP8(X0) ),
inference(rectify,[],[f194]) ).
fof(f196,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,X0)
& ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& sz00 != X1
& aInteger0(X1) )
=> ( isPrime0(sK26(X0))
& aDivisorOf0(sK26(X0),X0)
& ? [X2] :
( sdtasdt0(sK26(X0),X2) = X0
& aInteger0(X2) )
& sz00 != sK26(X0)
& aInteger0(sK26(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f197,plain,
! [X0] :
( ? [X2] :
( sdtasdt0(sK26(X0),X2) = X0
& aInteger0(X2) )
=> ( sdtasdt0(sK26(X0),sK27(X0)) = X0
& aInteger0(sK27(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f198,plain,
! [X0] :
( ( isPrime0(sK26(X0))
& aDivisorOf0(sK26(X0),X0)
& sdtasdt0(sK26(X0),sK27(X0)) = X0
& aInteger0(sK27(X0))
& sz00 != sK26(X0)
& aInteger0(sK26(X0)) )
| ~ sP8(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26,sK27])],[f195,f197,f196]) ).
fof(f199,plain,
( stldt0(sbsmnsldt0(xS)) != cS2076
& ? [X10] :
( ( ( smndt0(sz10) != X10
& sz10 != X10 )
| ~ aElementOf0(X10,stldt0(sbsmnsldt0(xS))) )
& ( smndt0(sz10) = X10
| sz10 = X10
| aElementOf0(X10,stldt0(sbsmnsldt0(xS))) ) )
& ! [X9] :
( ( aElementOf0(X9,stldt0(sbsmnsldt0(xS)))
| aElementOf0(X9,sbsmnsldt0(xS))
| ~ aInteger0(X9) )
& ( ( ~ aElementOf0(X9,sbsmnsldt0(xS))
& aInteger0(X9) )
| ~ aElementOf0(X9,stldt0(sbsmnsldt0(xS))) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X7] :
( ( aElementOf0(X7,sbsmnsldt0(xS))
| ! [X8] :
( ~ aElementOf0(X7,X8)
| ~ aElementOf0(X8,xS) )
| ~ aInteger0(X7) )
& ( ( ? [X8] :
( aElementOf0(X7,X8)
& aElementOf0(X8,xS) )
& aInteger0(X7) )
| ~ aElementOf0(X7,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( ( ( aElementOf0(X0,sbsmnsldt0(xS))
& ? [X3] :
( aElementOf0(X0,X3)
& aElementOf0(X3,xS) ) )
| ! [X1] :
( ~ isPrime0(X1)
| ( ~ aDivisorOf0(X1,X0)
& ( ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1) ) ) ) )
& ( sP8(X0)
| ( ~ aElementOf0(X0,sbsmnsldt0(xS))
& ! [X4] :
( ~ aElementOf0(X0,X4)
| ~ aElementOf0(X4,xS) ) ) ) )
| ~ aInteger0(X0) ) ),
inference(nnf_transformation,[],[f125]) ).
fof(f200,plain,
( stldt0(sbsmnsldt0(xS)) != cS2076
& ? [X10] :
( ( ( smndt0(sz10) != X10
& sz10 != X10 )
| ~ aElementOf0(X10,stldt0(sbsmnsldt0(xS))) )
& ( smndt0(sz10) = X10
| sz10 = X10
| aElementOf0(X10,stldt0(sbsmnsldt0(xS))) ) )
& ! [X9] :
( ( aElementOf0(X9,stldt0(sbsmnsldt0(xS)))
| aElementOf0(X9,sbsmnsldt0(xS))
| ~ aInteger0(X9) )
& ( ( ~ aElementOf0(X9,sbsmnsldt0(xS))
& aInteger0(X9) )
| ~ aElementOf0(X9,stldt0(sbsmnsldt0(xS))) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X7] :
( ( aElementOf0(X7,sbsmnsldt0(xS))
| ! [X8] :
( ~ aElementOf0(X7,X8)
| ~ aElementOf0(X8,xS) )
| ~ aInteger0(X7) )
& ( ( ? [X8] :
( aElementOf0(X7,X8)
& aElementOf0(X8,xS) )
& aInteger0(X7) )
| ~ aElementOf0(X7,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( ( ( aElementOf0(X0,sbsmnsldt0(xS))
& ? [X3] :
( aElementOf0(X0,X3)
& aElementOf0(X3,xS) ) )
| ! [X1] :
( ~ isPrime0(X1)
| ( ~ aDivisorOf0(X1,X0)
& ( ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1) ) ) ) )
& ( sP8(X0)
| ( ~ aElementOf0(X0,sbsmnsldt0(xS))
& ! [X4] :
( ~ aElementOf0(X0,X4)
| ~ aElementOf0(X4,xS) ) ) ) )
| ~ aInteger0(X0) ) ),
inference(flattening,[],[f199]) ).
fof(f201,plain,
( stldt0(sbsmnsldt0(xS)) != cS2076
& ? [X0] :
( ( ( smndt0(sz10) != X0
& sz10 != X0 )
| ~ aElementOf0(X0,stldt0(sbsmnsldt0(xS))) )
& ( smndt0(sz10) = X0
| sz10 = X0
| aElementOf0(X0,stldt0(sbsmnsldt0(xS))) ) )
& ! [X1] :
( ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
| aElementOf0(X1,sbsmnsldt0(xS))
| ~ aInteger0(X1) )
& ( ( ~ aElementOf0(X1,sbsmnsldt0(xS))
& aInteger0(X1) )
| ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X2] :
( ( aElementOf0(X2,sbsmnsldt0(xS))
| ! [X3] :
( ~ aElementOf0(X2,X3)
| ~ aElementOf0(X3,xS) )
| ~ aInteger0(X2) )
& ( ( ? [X4] :
( aElementOf0(X2,X4)
& aElementOf0(X4,xS) )
& aInteger0(X2) )
| ~ aElementOf0(X2,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X5] :
( ( ( ( aElementOf0(X5,sbsmnsldt0(xS))
& ? [X6] :
( aElementOf0(X5,X6)
& aElementOf0(X6,xS) ) )
| ! [X7] :
( ~ isPrime0(X7)
| ( ~ aDivisorOf0(X7,X5)
& ( ! [X8] :
( sdtasdt0(X7,X8) != X5
| ~ aInteger0(X8) )
| sz00 = X7
| ~ aInteger0(X7) ) ) ) )
& ( sP8(X5)
| ( ~ aElementOf0(X5,sbsmnsldt0(xS))
& ! [X9] :
( ~ aElementOf0(X5,X9)
| ~ aElementOf0(X9,xS) ) ) ) )
| ~ aInteger0(X5) ) ),
inference(rectify,[],[f200]) ).
fof(f202,plain,
( ? [X0] :
( ( ( smndt0(sz10) != X0
& sz10 != X0 )
| ~ aElementOf0(X0,stldt0(sbsmnsldt0(xS))) )
& ( smndt0(sz10) = X0
| sz10 = X0
| aElementOf0(X0,stldt0(sbsmnsldt0(xS))) ) )
=> ( ( ( smndt0(sz10) != sK28
& sz10 != sK28 )
| ~ aElementOf0(sK28,stldt0(sbsmnsldt0(xS))) )
& ( smndt0(sz10) = sK28
| sz10 = sK28
| aElementOf0(sK28,stldt0(sbsmnsldt0(xS))) ) ) ),
introduced(choice_axiom,[]) ).
fof(f203,plain,
! [X2] :
( ? [X4] :
( aElementOf0(X2,X4)
& aElementOf0(X4,xS) )
=> ( aElementOf0(X2,sK29(X2))
& aElementOf0(sK29(X2),xS) ) ),
introduced(choice_axiom,[]) ).
fof(f204,plain,
! [X5] :
( ? [X6] :
( aElementOf0(X5,X6)
& aElementOf0(X6,xS) )
=> ( aElementOf0(X5,sK30(X5))
& aElementOf0(sK30(X5),xS) ) ),
introduced(choice_axiom,[]) ).
fof(f205,plain,
( stldt0(sbsmnsldt0(xS)) != cS2076
& ( ( smndt0(sz10) != sK28
& sz10 != sK28 )
| ~ aElementOf0(sK28,stldt0(sbsmnsldt0(xS))) )
& ( smndt0(sz10) = sK28
| sz10 = sK28
| aElementOf0(sK28,stldt0(sbsmnsldt0(xS))) )
& ! [X1] :
( ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
| aElementOf0(X1,sbsmnsldt0(xS))
| ~ aInteger0(X1) )
& ( ( ~ aElementOf0(X1,sbsmnsldt0(xS))
& aInteger0(X1) )
| ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X2] :
( ( aElementOf0(X2,sbsmnsldt0(xS))
| ! [X3] :
( ~ aElementOf0(X2,X3)
| ~ aElementOf0(X3,xS) )
| ~ aInteger0(X2) )
& ( ( aElementOf0(X2,sK29(X2))
& aElementOf0(sK29(X2),xS)
& aInteger0(X2) )
| ~ aElementOf0(X2,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X5] :
( ( ( ( aElementOf0(X5,sbsmnsldt0(xS))
& aElementOf0(X5,sK30(X5))
& aElementOf0(sK30(X5),xS) )
| ! [X7] :
( ~ isPrime0(X7)
| ( ~ aDivisorOf0(X7,X5)
& ( ! [X8] :
( sdtasdt0(X7,X8) != X5
| ~ aInteger0(X8) )
| sz00 = X7
| ~ aInteger0(X7) ) ) ) )
& ( sP8(X5)
| ( ~ aElementOf0(X5,sbsmnsldt0(xS))
& ! [X9] :
( ~ aElementOf0(X5,X9)
| ~ aElementOf0(X9,xS) ) ) ) )
| ~ aInteger0(X5) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28,sK29,sK30])],[f201,f204,f203,f202]) ).
fof(f207,plain,
aInteger0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f208,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f240,plain,
! [X2,X0] :
( sz10 != X0
| ~ isPrime0(X2)
| ~ aDivisorOf0(X2,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f241,plain,
! [X2,X0] :
( smndt0(sz10) != X0
| ~ isPrime0(X2)
| ~ aDivisorOf0(X2,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f242,plain,
! [X0] :
( aDivisorOf0(sK10(X0),X0)
| smndt0(sz10) = X0
| sz10 = X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f243,plain,
! [X0] :
( isPrime0(sK10(X0))
| smndt0(sz10) = X0
| sz10 = X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f338,plain,
xS = cS2043,
inference(cnf_transformation,[],[f193]) ).
fof(f343,plain,
! [X0] :
( aDivisorOf0(sK26(X0),X0)
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f344,plain,
! [X0] :
( isPrime0(sK26(X0))
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f346,plain,
! [X5] :
( sP8(X5)
| ~ aElementOf0(X5,sbsmnsldt0(xS))
| ~ aInteger0(X5) ),
inference(cnf_transformation,[],[f205]) ).
fof(f352,plain,
! [X7,X5] :
( aElementOf0(X5,sbsmnsldt0(xS))
| ~ isPrime0(X7)
| ~ aDivisorOf0(X7,X5)
| ~ aInteger0(X5) ),
inference(cnf_transformation,[],[f205]) ).
fof(f354,plain,
! [X2] :
( aInteger0(X2)
| ~ aElementOf0(X2,sbsmnsldt0(xS)) ),
inference(cnf_transformation,[],[f205]) ).
fof(f359,plain,
! [X1] :
( aInteger0(X1)
| ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ),
inference(cnf_transformation,[],[f205]) ).
fof(f360,plain,
! [X1] :
( ~ aElementOf0(X1,sbsmnsldt0(xS))
| ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ),
inference(cnf_transformation,[],[f205]) ).
fof(f361,plain,
! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
| aElementOf0(X1,sbsmnsldt0(xS))
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f205]) ).
fof(f362,plain,
( smndt0(sz10) = sK28
| sz10 = sK28
| aElementOf0(sK28,stldt0(sbsmnsldt0(xS))) ),
inference(cnf_transformation,[],[f205]) ).
fof(f363,plain,
( sz10 != sK28
| ~ aElementOf0(sK28,stldt0(sbsmnsldt0(xS))) ),
inference(cnf_transformation,[],[f205]) ).
fof(f364,plain,
( smndt0(sz10) != sK28
| ~ aElementOf0(sK28,stldt0(sbsmnsldt0(xS))) ),
inference(cnf_transformation,[],[f205]) ).
fof(f377,plain,
( smndt0(sz10) != sK28
| ~ aElementOf0(sK28,stldt0(sbsmnsldt0(cS2043))) ),
inference(definition_unfolding,[],[f364,f338]) ).
fof(f378,plain,
( sz10 != sK28
| ~ aElementOf0(sK28,stldt0(sbsmnsldt0(cS2043))) ),
inference(definition_unfolding,[],[f363,f338]) ).
fof(f379,plain,
( smndt0(sz10) = sK28
| sz10 = sK28
| aElementOf0(sK28,stldt0(sbsmnsldt0(cS2043))) ),
inference(definition_unfolding,[],[f362,f338]) ).
fof(f380,plain,
! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(cS2043)))
| aElementOf0(X1,sbsmnsldt0(cS2043))
| ~ aInteger0(X1) ),
inference(definition_unfolding,[],[f361,f338,f338]) ).
fof(f381,plain,
! [X1] :
( ~ aElementOf0(X1,sbsmnsldt0(cS2043))
| ~ aElementOf0(X1,stldt0(sbsmnsldt0(cS2043))) ),
inference(definition_unfolding,[],[f360,f338,f338]) ).
fof(f382,plain,
! [X1] :
( aInteger0(X1)
| ~ aElementOf0(X1,stldt0(sbsmnsldt0(cS2043))) ),
inference(definition_unfolding,[],[f359,f338]) ).
fof(f387,plain,
! [X2] :
( aInteger0(X2)
| ~ aElementOf0(X2,sbsmnsldt0(cS2043)) ),
inference(definition_unfolding,[],[f354,f338]) ).
fof(f389,plain,
! [X7,X5] :
( aElementOf0(X5,sbsmnsldt0(cS2043))
| ~ isPrime0(X7)
| ~ aDivisorOf0(X7,X5)
| ~ aInteger0(X5) ),
inference(definition_unfolding,[],[f352,f338]) ).
fof(f393,plain,
! [X5] :
( sP8(X5)
| ~ aElementOf0(X5,sbsmnsldt0(cS2043))
| ~ aInteger0(X5) ),
inference(definition_unfolding,[],[f346,f338]) ).
fof(f397,plain,
! [X2] :
( ~ isPrime0(X2)
| ~ aDivisorOf0(X2,smndt0(sz10))
| ~ aInteger0(smndt0(sz10)) ),
inference(equality_resolution,[],[f241]) ).
fof(f398,plain,
! [X2] :
( ~ isPrime0(X2)
| ~ aDivisorOf0(X2,sz10)
| ~ aInteger0(sz10) ),
inference(equality_resolution,[],[f240]) ).
cnf(c_50,plain,
aInteger0(sz10),
inference(cnf_transformation,[],[f207]) ).
cnf(c_51,plain,
( ~ aInteger0(X0)
| aInteger0(smndt0(X0)) ),
inference(cnf_transformation,[],[f208]) ).
cnf(c_83,plain,
( ~ aInteger0(X0)
| smndt0(sz10) = X0
| X0 = sz10
| isPrime0(sK10(X0)) ),
inference(cnf_transformation,[],[f243]) ).
cnf(c_84,plain,
( ~ aInteger0(X0)
| smndt0(sz10) = X0
| X0 = sz10
| aDivisorOf0(sK10(X0),X0) ),
inference(cnf_transformation,[],[f242]) ).
cnf(c_85,plain,
( ~ aDivisorOf0(X0,smndt0(sz10))
| ~ aInteger0(smndt0(sz10))
| ~ isPrime0(X0) ),
inference(cnf_transformation,[],[f397]) ).
cnf(c_86,plain,
( ~ aDivisorOf0(X0,sz10)
| ~ isPrime0(X0)
| ~ aInteger0(sz10) ),
inference(cnf_transformation,[],[f398]) ).
cnf(c_181,plain,
( ~ sP8(X0)
| isPrime0(sK26(X0)) ),
inference(cnf_transformation,[],[f344]) ).
cnf(c_182,plain,
( ~ sP8(X0)
| aDivisorOf0(sK26(X0),X0) ),
inference(cnf_transformation,[],[f343]) ).
cnf(c_188,negated_conjecture,
( smndt0(sz10) != sK28
| ~ aElementOf0(sK28,stldt0(sbsmnsldt0(cS2043))) ),
inference(cnf_transformation,[],[f377]) ).
cnf(c_189,negated_conjecture,
( sz10 != sK28
| ~ aElementOf0(sK28,stldt0(sbsmnsldt0(cS2043))) ),
inference(cnf_transformation,[],[f378]) ).
cnf(c_190,negated_conjecture,
( smndt0(sz10) = sK28
| sz10 = sK28
| aElementOf0(sK28,stldt0(sbsmnsldt0(cS2043))) ),
inference(cnf_transformation,[],[f379]) ).
cnf(c_191,negated_conjecture,
( ~ aInteger0(X0)
| aElementOf0(X0,stldt0(sbsmnsldt0(cS2043)))
| aElementOf0(X0,sbsmnsldt0(cS2043)) ),
inference(cnf_transformation,[],[f380]) ).
cnf(c_192,negated_conjecture,
( ~ aElementOf0(X0,stldt0(sbsmnsldt0(cS2043)))
| ~ aElementOf0(X0,sbsmnsldt0(cS2043)) ),
inference(cnf_transformation,[],[f381]) ).
cnf(c_193,negated_conjecture,
( ~ aElementOf0(X0,stldt0(sbsmnsldt0(cS2043)))
| aInteger0(X0) ),
inference(cnf_transformation,[],[f382]) ).
cnf(c_198,negated_conjecture,
( ~ aElementOf0(X0,sbsmnsldt0(cS2043))
| aInteger0(X0) ),
inference(cnf_transformation,[],[f387]) ).
cnf(c_200,negated_conjecture,
( ~ aDivisorOf0(X0,X1)
| ~ aInteger0(X1)
| ~ isPrime0(X0)
| aElementOf0(X1,sbsmnsldt0(cS2043)) ),
inference(cnf_transformation,[],[f389]) ).
cnf(c_206,negated_conjecture,
( ~ aElementOf0(X0,sbsmnsldt0(cS2043))
| ~ aInteger0(X0)
| sP8(X0) ),
inference(cnf_transformation,[],[f393]) ).
cnf(c_324,negated_conjecture,
( ~ aElementOf0(X0,sbsmnsldt0(cS2043))
| sP8(X0) ),
inference(global_subsumption_just,[status(thm)],[c_206,c_198,c_206]) ).
cnf(c_327,plain,
( ~ isPrime0(X0)
| ~ aDivisorOf0(X0,sz10) ),
inference(global_subsumption_just,[status(thm)],[c_86,c_50,c_86]) ).
cnf(c_328,plain,
( ~ aDivisorOf0(X0,sz10)
| ~ isPrime0(X0) ),
inference(renaming,[status(thm)],[c_327]) ).
cnf(c_6827,plain,
( sK26(X0) != X1
| X0 != sz10
| ~ isPrime0(X1)
| ~ sP8(X0) ),
inference(resolution_lifted,[status(thm)],[c_328,c_182]) ).
cnf(c_6828,plain,
( ~ isPrime0(sK26(sz10))
| ~ sP8(sz10) ),
inference(unflattening,[status(thm)],[c_6827]) ).
cnf(c_6833,plain,
~ sP8(sz10),
inference(forward_subsumption_resolution,[status(thm)],[c_6828,c_181]) ).
cnf(c_13694,plain,
smndt0(sz10) = sP5_iProver_def,
definition ).
cnf(c_13698,negated_conjecture,
( ~ aElementOf0(X0,sP3_iProver_def)
| sP8(X0) ),
inference(demodulation,[status(thm)],[c_324]) ).
cnf(c_13702,negated_conjecture,
( ~ aDivisorOf0(X0,X1)
| ~ aInteger0(X1)
| ~ isPrime0(X0)
| aElementOf0(X1,sP3_iProver_def) ),
inference(demodulation,[status(thm)],[c_200]) ).
cnf(c_13709,negated_conjecture,
( ~ aElementOf0(X0,sP4_iProver_def)
| aInteger0(X0) ),
inference(demodulation,[status(thm)],[c_193]) ).
cnf(c_13710,negated_conjecture,
( ~ aElementOf0(X0,sP3_iProver_def)
| ~ aElementOf0(X0,sP4_iProver_def) ),
inference(demodulation,[status(thm)],[c_192]) ).
cnf(c_13711,negated_conjecture,
( ~ aInteger0(X0)
| aElementOf0(X0,sP3_iProver_def)
| aElementOf0(X0,sP4_iProver_def) ),
inference(demodulation,[status(thm)],[c_191]) ).
cnf(c_13712,negated_conjecture,
( sz10 = sK28
| sP5_iProver_def = sK28
| aElementOf0(sK28,sP4_iProver_def) ),
inference(demodulation,[status(thm)],[c_190,c_13694]) ).
cnf(c_13713,negated_conjecture,
( sz10 != sK28
| ~ aElementOf0(sK28,sP4_iProver_def) ),
inference(demodulation,[status(thm)],[c_189]) ).
cnf(c_13714,negated_conjecture,
( sP5_iProver_def != sK28
| ~ aElementOf0(sK28,sP4_iProver_def) ),
inference(demodulation,[status(thm)],[c_188]) ).
cnf(c_16373,plain,
( ~ aInteger0(sz10)
| aInteger0(sP5_iProver_def) ),
inference(superposition,[status(thm)],[c_13694,c_51]) ).
cnf(c_16374,plain,
aInteger0(sP5_iProver_def),
inference(forward_subsumption_resolution,[status(thm)],[c_16373,c_50]) ).
cnf(c_17598,plain,
( ~ aInteger0(sz10)
| aInteger0(smndt0(sz10)) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_19081,plain,
( ~ isPrime0(sK26(sz10))
| ~ sP8(sz10) ),
inference(superposition,[status(thm)],[c_182,c_328]) ).
cnf(c_19714,plain,
( ~ aDivisorOf0(X0,smndt0(sz10))
| ~ isPrime0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_85,c_50,c_85,c_17598]) ).
cnf(c_19717,plain,
( ~ aDivisorOf0(X0,sP5_iProver_def)
| ~ isPrime0(X0) ),
inference(light_normalisation,[status(thm)],[c_19714,c_13694]) ).
cnf(c_19722,plain,
( ~ isPrime0(sK26(sP5_iProver_def))
| ~ sP8(sP5_iProver_def) ),
inference(superposition,[status(thm)],[c_182,c_19717]) ).
cnf(c_20585,plain,
~ sP8(sz10),
inference(global_subsumption_just,[status(thm)],[c_19081,c_6833]) ).
cnf(c_21948,plain,
~ sP8(sP5_iProver_def),
inference(forward_subsumption_resolution,[status(thm)],[c_19722,c_181]) ).
cnf(c_23956,plain,
( ~ aInteger0(X0)
| X0 = sz10
| X0 = sP5_iProver_def
| isPrime0(sK10(X0)) ),
inference(light_normalisation,[status(thm)],[c_83,c_13694]) ).
cnf(c_26464,plain,
( ~ aInteger0(X0)
| X0 = sz10
| X0 = sP5_iProver_def
| aDivisorOf0(sK10(X0),X0) ),
inference(light_normalisation,[status(thm)],[c_84,c_13694]) ).
cnf(c_26477,plain,
( ~ isPrime0(sK10(X0))
| ~ aInteger0(X0)
| X0 = sz10
| X0 = sP5_iProver_def
| aElementOf0(X0,sP3_iProver_def) ),
inference(superposition,[status(thm)],[c_26464,c_13702]) ).
cnf(c_40375,plain,
( ~ aInteger0(X0)
| X0 = sz10
| X0 = sP5_iProver_def
| aElementOf0(X0,sP3_iProver_def) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26477,c_23956]) ).
cnf(c_40393,plain,
( ~ aElementOf0(X0,sP4_iProver_def)
| ~ aInteger0(X0)
| X0 = sz10
| X0 = sP5_iProver_def ),
inference(superposition,[status(thm)],[c_40375,c_13710]) ).
cnf(c_41052,plain,
( ~ aElementOf0(X0,sP4_iProver_def)
| X0 = sz10
| X0 = sP5_iProver_def ),
inference(global_subsumption_just,[status(thm)],[c_40393,c_13709,c_40393]) ).
cnf(c_41079,plain,
( sz10 = sK28
| sK28 = sP5_iProver_def ),
inference(superposition,[status(thm)],[c_13712,c_41052]) ).
cnf(c_41402,plain,
( ~ aElementOf0(sK28,sP4_iProver_def)
| sK28 = sP5_iProver_def ),
inference(superposition,[status(thm)],[c_41079,c_13713]) ).
cnf(c_41411,plain,
( ~ aElementOf0(sz10,sP4_iProver_def)
| sK28 = sP5_iProver_def ),
inference(superposition,[status(thm)],[c_41079,c_41402]) ).
cnf(c_41985,plain,
( ~ aInteger0(sz10)
| sK28 = sP5_iProver_def
| aElementOf0(sz10,sP3_iProver_def) ),
inference(superposition,[status(thm)],[c_13711,c_41411]) ).
cnf(c_41986,plain,
( sK28 = sP5_iProver_def
| aElementOf0(sz10,sP3_iProver_def) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41985,c_50]) ).
cnf(c_42026,plain,
( sK28 = sP5_iProver_def
| sP8(sz10) ),
inference(superposition,[status(thm)],[c_41986,c_13698]) ).
cnf(c_42027,plain,
sK28 = sP5_iProver_def,
inference(forward_subsumption_resolution,[status(thm)],[c_42026,c_20585]) ).
cnf(c_42029,plain,
( sP5_iProver_def != sP5_iProver_def
| ~ aElementOf0(sP5_iProver_def,sP4_iProver_def) ),
inference(demodulation,[status(thm)],[c_13714,c_42027]) ).
cnf(c_42033,plain,
~ aElementOf0(sP5_iProver_def,sP4_iProver_def),
inference(equality_resolution_simp,[status(thm)],[c_42029]) ).
cnf(c_42034,plain,
( ~ aInteger0(sP5_iProver_def)
| aElementOf0(sP5_iProver_def,sP3_iProver_def) ),
inference(superposition,[status(thm)],[c_13711,c_42033]) ).
cnf(c_42035,plain,
aElementOf0(sP5_iProver_def,sP3_iProver_def),
inference(forward_subsumption_resolution,[status(thm)],[c_42034,c_16374]) ).
cnf(c_43462,plain,
sP8(sP5_iProver_def),
inference(superposition,[status(thm)],[c_42035,c_13698]) ).
cnf(c_43463,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_43462,c_21948]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM448+5 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.13 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu May 2 19:19:33 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.18/0.46 Running first-order theorem proving
% 0.18/0.46 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
% 11.98/2.67 % SZS status Started for theBenchmark.p
% 11.98/2.67 % SZS status Theorem for theBenchmark.p
% 11.98/2.67
% 11.98/2.67 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 11.98/2.67
% 11.98/2.67 ------ iProver source info
% 11.98/2.67
% 11.98/2.67 git: date: 2024-05-02 19:28:25 +0000
% 11.98/2.67 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 11.98/2.67 git: non_committed_changes: false
% 11.98/2.67
% 11.98/2.67 ------ Parsing...
% 11.98/2.67 ------ Clausification by vclausify_rel & Parsing by iProver...
% 11.98/2.67
% 11.98/2.67 ------ 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
% 11.98/2.67
% 11.98/2.67 ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e
% 11.98/2.67
% 11.98/2.67 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 11.98/2.67 ------ Proving...
% 11.98/2.67 ------ Problem Properties
% 11.98/2.67
% 11.98/2.67
% 11.98/2.67 clauses 162
% 11.98/2.67 conjectures 21
% 11.98/2.67 EPR 42
% 11.98/2.67 Horn 114
% 11.98/2.67 unary 9
% 11.98/2.67 binary 40
% 11.98/2.67 lits 558
% 11.98/2.67 lits eq 76
% 11.98/2.67 fd_pure 0
% 11.98/2.67 fd_pseudo 0
% 11.98/2.67 fd_cond 24
% 11.98/2.67 fd_pseudo_cond 9
% 11.98/2.67 AC symbols 0
% 11.98/2.67
% 11.98/2.67 ------ Schedule dynamic 5 is on
% 11.98/2.67
% 11.98/2.67 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 11.98/2.67
% 11.98/2.67
% 11.98/2.67 ------
% 11.98/2.67 Current options:
% 11.98/2.67 ------
% 11.98/2.67
% 11.98/2.67
% 11.98/2.67
% 11.98/2.67
% 11.98/2.67 ------ Proving...
% 11.98/2.67
% 11.98/2.67
% 11.98/2.67 % SZS status Theorem for theBenchmark.p
% 11.98/2.67
% 11.98/2.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 11.98/2.67
% 11.98/2.68
%------------------------------------------------------------------------------