%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM456+6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:24:31 PM UTC 2026
% Result : Theorem 3.59s 1.10s
% Output : CNFRefutation 3.59s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f136ERROR: Could not build tree for root c_9506ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f43,axiom,
( stldt0(sbsmnsldt0(xS)) = cS2076
& ! [X0] :
( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
<=> ( X0 = smndt0(sz10)
| X0 = sz10 ) )
& ! [X0] :
( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X0,sbsmnsldt0(xS))
& aInteger0(X0) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) ) )
& aSet0(sbsmnsldt0(xS)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2079) ).
fof(f46,axiom,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [X0] :
( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> aElementOf0(X0,stldt0(sbsmnsldt0(xS))) )
& ! [X0] :
( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X0,sbsmnsldt0(xS))
& aInteger0(X0) ) )
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( ( ( sdteqdtlpzmzozddtrp0(X0,sz10,xp)
| aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
| ? [X1] :
( sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10))
& aInteger0(X1) ) )
& aInteger0(X0) )
=> aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> ( sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ? [X1] :
( sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10))
& aInteger0(X1) )
& aInteger0(X0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2171) ).
fof(f47,axiom,
? [X0] :
( ~ ( aElementOf0(X0,cS2200)
| X0 = smndt0(sz10)
| X0 = sz10 )
& aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ? [X1] :
( sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10))
& aInteger0(X1) )
& aInteger0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2203) ).
fof(f57,plain,
( stldt0(sbsmnsldt0(xS)) = cS2076
& ! [X3] :
( aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
<=> ( smndt0(sz10) = X3
| sz10 = X3 ) )
& ! [X2] :
( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X2,sbsmnsldt0(xS))
& aInteger0(X2) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(rectify,[],[f43]) ).
fof(f59,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [X6] :
( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> aElementOf0(X6,stldt0(sbsmnsldt0(xS))) )
& ! [X5] :
( aElementOf0(X5,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X5,sbsmnsldt0(xS))
& aInteger0(X5) ) )
& ! [X3] :
( aElementOf0(X3,sbsmnsldt0(xS))
<=> ( ? [X4] :
( aElementOf0(X3,X4)
& aElementOf0(X4,xS) )
& aInteger0(X3) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( ( ( sdteqdtlpzmzozddtrp0(X0,sz10,xp)
| aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
| ? [X2] :
( sdtpldt0(X0,smndt0(sz10)) = sdtasdt0(xp,X2)
& aInteger0(X2) ) )
& aInteger0(X0) )
=> aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> ( sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ? [X1] :
( sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10))
& aInteger0(X1) )
& aInteger0(X0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
inference(rectify,[],[f46]) ).
fof(f121,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [X6] :
( ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aElementOf0(X6,stldt0(sbsmnsldt0(xS))) )
& ! [X5] :
( aElementOf0(X5,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X5,sbsmnsldt0(xS))
& aInteger0(X5) ) )
& ! [X3] :
( aElementOf0(X3,sbsmnsldt0(xS))
<=> ( ? [X4] :
( aElementOf0(X3,X4)
& aElementOf0(X4,xS) )
& aInteger0(X3) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& ~ aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ! [X2] :
( sdtpldt0(X0,smndt0(sz10)) != sdtasdt0(xp,X2)
| ~ aInteger0(X2) ) )
| ~ aInteger0(X0)
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ( sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ? [X1] :
( sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10))
& aInteger0(X1) )
& aInteger0(X0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
inference(ennf_transformation,[],[f59]) ).
fof(f122,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [X6] :
( ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aElementOf0(X6,stldt0(sbsmnsldt0(xS))) )
& ! [X5] :
( aElementOf0(X5,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X5,sbsmnsldt0(xS))
& aInteger0(X5) ) )
& ! [X3] :
( aElementOf0(X3,sbsmnsldt0(xS))
<=> ( ? [X4] :
( aElementOf0(X3,X4)
& aElementOf0(X4,xS) )
& aInteger0(X3) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& ~ aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ! [X2] :
( sdtpldt0(X0,smndt0(sz10)) != sdtasdt0(xp,X2)
| ~ aInteger0(X2) ) )
| ~ aInteger0(X0)
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ( sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ? [X1] :
( sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10))
& aInteger0(X1) )
& aInteger0(X0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
inference(flattening,[],[f121]) ).
fof(f123,plain,
? [X0] :
( ~ aElementOf0(X0,cS2200)
& smndt0(sz10) != X0
& sz10 != X0
& aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ? [X1] :
( sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10))
& aInteger0(X1) )
& aInteger0(X0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f124,plain,
? [X0] :
( ~ aElementOf0(X0,cS2200)
& smndt0(sz10) != X0
& sz10 != X0
& aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ? [X1] :
( sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10))
& aInteger0(X1) )
& aInteger0(X0) ),
inference(flattening,[],[f123]) ).
fof(f192,plain,
( xS = cS2043
& ! [X0] :
( ( ! [X2] :
( ( sP6(X2)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
& szAzrzSzezqlpdtcmdtrp0(sz00,X2) != X0 )
| ~ isPrime0(X2)
| sz00 = X2
| ~ aInteger0(X2) )
| aElementOf0(X0,xS) )
& ( ~ aElementOf0(X0,xS)
| ? [X1] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0
& sP7(X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
& isPrime0(X1)
& X1 != sz00
& aInteger0(X1) ) ) )
& aSet0(xS) ),
inference(rectify,[],[f136]) ).
fof(f193,plain,
( xS = cS2043
& ! [X0] :
( ( ! [X2] :
( ( sP6(X2)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
& szAzrzSzezqlpdtcmdtrp0(sz00,X2) != X0 )
| ~ isPrime0(X2)
| sz00 = X2
| ~ aInteger0(X2) )
| aElementOf0(X0,xS) )
& ( ~ aElementOf0(X0,xS)
| ( szAzrzSzezqlpdtcmdtrp0(sz00,sK27(X0)) = X0
& sP7(sK27(X0))
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,sK27(X0)))
& isPrime0(sK27(X0))
& sz00 != sK27(X0)
& aInteger0(sK27(X0)) ) ) )
& aSet0(xS) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(X1,sK27(X0))],[f192]) ).
fof(f194,plain,
( stldt0(sbsmnsldt0(xS)) = cS2076
& ! [X3] :
( ( ~ aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
| smndt0(sz10) = X3
| sz10 = X3 )
& ( ( smndt0(sz10) != X3
& sz10 != X3 )
| aElementOf0(X3,stldt0(sbsmnsldt0(xS))) ) )
& ! [X2] :
( ( ~ aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
| ( ~ aElementOf0(X2,sbsmnsldt0(xS))
& aInteger0(X2) ) )
& ( aElementOf0(X2,sbsmnsldt0(xS))
| ~ aInteger0(X2)
| aElementOf0(X2,stldt0(sbsmnsldt0(xS))) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X0] :
( ( ~ aElementOf0(X0,sbsmnsldt0(xS))
| ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) ) )
& ( ! [X1] :
( ~ aElementOf0(X0,X1)
| ~ aElementOf0(X1,xS) )
| ~ aInteger0(X0)
| aElementOf0(X0,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(nnf_transformation,[],[f57]) ).
fof(f195,plain,
( stldt0(sbsmnsldt0(xS)) = cS2076
& ! [X3] :
( ( ~ aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
| smndt0(sz10) = X3
| sz10 = X3 )
& ( ( smndt0(sz10) != X3
& sz10 != X3 )
| aElementOf0(X3,stldt0(sbsmnsldt0(xS))) ) )
& ! [X2] :
( ( ~ aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
| ( ~ aElementOf0(X2,sbsmnsldt0(xS))
& aInteger0(X2) ) )
& ( aElementOf0(X2,sbsmnsldt0(xS))
| ~ aInteger0(X2)
| aElementOf0(X2,stldt0(sbsmnsldt0(xS))) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X0] :
( ( ~ aElementOf0(X0,sbsmnsldt0(xS))
| ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) ) )
& ( ! [X1] :
( ~ aElementOf0(X0,X1)
| ~ aElementOf0(X1,xS) )
| ~ aInteger0(X0)
| aElementOf0(X0,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(flattening,[],[f194]) ).
fof(f196,plain,
( stldt0(sbsmnsldt0(xS)) = cS2076
& ! [X4] :
( ( ~ aElementOf0(X4,stldt0(sbsmnsldt0(xS)))
| smndt0(sz10) = X4
| sz10 = X4 )
& ( ( smndt0(sz10) != X4
& sz10 != X4 )
| aElementOf0(X4,stldt0(sbsmnsldt0(xS))) ) )
& ! [X3] :
( ( ~ aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
| ( ~ aElementOf0(X3,sbsmnsldt0(xS))
& aInteger0(X3) ) )
& ( aElementOf0(X3,sbsmnsldt0(xS))
| ~ aInteger0(X3)
| aElementOf0(X3,stldt0(sbsmnsldt0(xS))) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X0] :
( ( ~ aElementOf0(X0,sbsmnsldt0(xS))
| ( ? [X2] :
( aElementOf0(X0,X2)
& aElementOf0(X2,xS) )
& aInteger0(X0) ) )
& ( ! [X1] :
( ~ aElementOf0(X0,X1)
| ~ aElementOf0(X1,xS) )
| ~ aInteger0(X0)
| aElementOf0(X0,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(rectify,[],[f195]) ).
fof(f197,plain,
( stldt0(sbsmnsldt0(xS)) = cS2076
& ! [X4] :
( ( ~ aElementOf0(X4,stldt0(sbsmnsldt0(xS)))
| smndt0(sz10) = X4
| sz10 = X4 )
& ( ( smndt0(sz10) != X4
& sz10 != X4 )
| aElementOf0(X4,stldt0(sbsmnsldt0(xS))) ) )
& ! [X3] :
( ( ~ aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
| ( ~ aElementOf0(X3,sbsmnsldt0(xS))
& aInteger0(X3) ) )
& ( aElementOf0(X3,sbsmnsldt0(xS))
| ~ aInteger0(X3)
| aElementOf0(X3,stldt0(sbsmnsldt0(xS))) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X0] :
( ( ~ aElementOf0(X0,sbsmnsldt0(xS))
| ( aElementOf0(X0,sK28(X0))
& aElementOf0(sK28(X0),xS)
& aInteger0(X0) ) )
& ( ! [X1] :
( ~ aElementOf0(X0,X1)
| ~ aElementOf0(X1,xS) )
| ~ aInteger0(X0)
| aElementOf0(X0,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(X2,sK28(X0))],[f196]) ).
fof(f208,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [X6] :
( ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aElementOf0(X6,stldt0(sbsmnsldt0(xS))) )
& ! [X5] :
( ( ~ aElementOf0(X5,stldt0(sbsmnsldt0(xS)))
| ( ~ aElementOf0(X5,sbsmnsldt0(xS))
& aInteger0(X5) ) )
& ( aElementOf0(X5,sbsmnsldt0(xS))
| ~ aInteger0(X5)
| aElementOf0(X5,stldt0(sbsmnsldt0(xS))) ) )
& ! [X3] :
( ( ~ aElementOf0(X3,sbsmnsldt0(xS))
| ( ? [X4] :
( aElementOf0(X3,X4)
& aElementOf0(X4,xS) )
& aInteger0(X3) ) )
& ( ! [X4] :
( ~ aElementOf0(X3,X4)
| ~ aElementOf0(X4,xS) )
| ~ aInteger0(X3)
| aElementOf0(X3,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& ~ aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ! [X2] :
( sdtpldt0(X0,smndt0(sz10)) != sdtasdt0(xp,X2)
| ~ aInteger0(X2) ) )
| ~ aInteger0(X0)
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ( sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ? [X1] :
( sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10))
& aInteger0(X1) )
& aInteger0(X0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
inference(nnf_transformation,[],[f122]) ).
fof(f209,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [X6] :
( ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aElementOf0(X6,stldt0(sbsmnsldt0(xS))) )
& ! [X5] :
( ( ~ aElementOf0(X5,stldt0(sbsmnsldt0(xS)))
| ( ~ aElementOf0(X5,sbsmnsldt0(xS))
& aInteger0(X5) ) )
& ( aElementOf0(X5,sbsmnsldt0(xS))
| ~ aInteger0(X5)
| aElementOf0(X5,stldt0(sbsmnsldt0(xS))) ) )
& ! [X3] :
( ( ~ aElementOf0(X3,sbsmnsldt0(xS))
| ( ? [X4] :
( aElementOf0(X3,X4)
& aElementOf0(X4,xS) )
& aInteger0(X3) ) )
& ( ! [X4] :
( ~ aElementOf0(X3,X4)
| ~ aElementOf0(X4,xS) )
| ~ aInteger0(X3)
| aElementOf0(X3,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& ~ aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ! [X2] :
( sdtpldt0(X0,smndt0(sz10)) != sdtasdt0(xp,X2)
| ~ aInteger0(X2) ) )
| ~ aInteger0(X0)
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ( sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ? [X1] :
( sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10))
& aInteger0(X1) )
& aInteger0(X0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
inference(flattening,[],[f208]) ).
fof(f210,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [X7] :
( ~ aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aElementOf0(X7,stldt0(sbsmnsldt0(xS))) )
& ! [X6] :
( ( ~ aElementOf0(X6,stldt0(sbsmnsldt0(xS)))
| ( ~ aElementOf0(X6,sbsmnsldt0(xS))
& aInteger0(X6) ) )
& ( aElementOf0(X6,sbsmnsldt0(xS))
| ~ aInteger0(X6)
| aElementOf0(X6,stldt0(sbsmnsldt0(xS))) ) )
& ! [X3] :
( ( ~ aElementOf0(X3,sbsmnsldt0(xS))
| ( ? [X5] :
( aElementOf0(X3,X5)
& aElementOf0(X5,xS) )
& aInteger0(X3) ) )
& ( ! [X4] :
( ~ aElementOf0(X3,X4)
| ~ aElementOf0(X4,xS) )
| ~ aInteger0(X3)
| aElementOf0(X3,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& ~ aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ! [X2] :
( sdtpldt0(X0,smndt0(sz10)) != sdtasdt0(xp,X2)
| ~ aInteger0(X2) ) )
| ~ aInteger0(X0)
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ( sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ? [X1] :
( sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10))
& aInteger0(X1) )
& aInteger0(X0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
inference(rectify,[],[f209]) ).
fof(f211,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [X7] :
( ~ aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aElementOf0(X7,stldt0(sbsmnsldt0(xS))) )
& ! [X6] :
( ( ~ aElementOf0(X6,stldt0(sbsmnsldt0(xS)))
| ( ~ aElementOf0(X6,sbsmnsldt0(xS))
& aInteger0(X6) ) )
& ( aElementOf0(X6,sbsmnsldt0(xS))
| ~ aInteger0(X6)
| aElementOf0(X6,stldt0(sbsmnsldt0(xS))) ) )
& ! [X3] :
( ( ~ aElementOf0(X3,sbsmnsldt0(xS))
| ( aElementOf0(X3,sK36(X3))
& aElementOf0(sK36(X3),xS)
& aInteger0(X3) ) )
& ( ! [X4] :
( ~ aElementOf0(X3,X4)
| ~ aElementOf0(X4,xS) )
| ~ aInteger0(X3)
| aElementOf0(X3,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& ~ aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ! [X2] :
( sdtpldt0(X0,smndt0(sz10)) != sdtasdt0(xp,X2)
| ~ aInteger0(X2) ) )
| ~ aInteger0(X0)
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ( sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& sdtpldt0(X0,smndt0(sz10)) = sdtasdt0(xp,sK35(X0))
& aInteger0(sK35(X0))
& aInteger0(X0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35,sK36]),skolemize(X1,sK35(X0)),skolemize(X5,sK36(X3))],[f210]) ).
fof(f212,plain,
( ~ aElementOf0(sK37,cS2200)
& smndt0(sz10) != sK37
& sz10 != sK37
& aElementOf0(sK37,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sdteqdtlpzmzozddtrp0(sK37,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(sK37,smndt0(sz10)))
& sdtasdt0(xp,sK38) = sdtpldt0(sK37,smndt0(sz10))
& aInteger0(sK38)
& aInteger0(sK37) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37,sK38]),skolemize(X0,sK37),skolemize(X1,sK38)],[f124]) ).
fof(f337,plain,
xS = cS2043,
inference(cnf_transformation,[],[f193]) ).
fof(f348,plain,
stldt0(sbsmnsldt0(xS)) = cS2076,
inference(cnf_transformation,[],[f197]) ).
fof(f349,plain,
! [X4] :
( ~ aElementOf0(X4,stldt0(sbsmnsldt0(xS)))
| smndt0(sz10) = X4
| sz10 = X4 ),
inference(cnf_transformation,[],[f197]) ).
fof(f409,plain,
! [X7] :
( ~ aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aElementOf0(X7,stldt0(sbsmnsldt0(xS))) ),
inference(cnf_transformation,[],[f211]) ).
fof(f430,plain,
smndt0(sz10) != sK37,
inference(cnf_transformation,[],[f212]) ).
fof(f431,plain,
sz10 != sK37,
inference(cnf_transformation,[],[f212]) ).
fof(f432,plain,
aElementOf0(sK37,szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(cnf_transformation,[],[f212]) ).
fof(f459,plain,
! [X4] :
( ~ aElementOf0(X4,stldt0(sbsmnsldt0(cS2043)))
| smndt0(sz10) = X4
| sz10 = X4 ),
inference(definition_unfolding,[],[f349,f337]) ).
fof(f460,plain,
cS2076 = stldt0(sbsmnsldt0(cS2043)),
inference(definition_unfolding,[],[f348,f337]) ).
fof(f500,plain,
! [X7] :
( ~ aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aElementOf0(X7,stldt0(sbsmnsldt0(cS2043))) ),
inference(definition_unfolding,[],[f409,f337]) ).
tcf(c_194,plain,
! [X0: $i] :
( ( X0 = sz10 )
| ( smndt0(sz10) = X0 )
| ~ aElementOf0(X0,stldt0(sbsmnsldt0(cS2043))) ),
inference(cnf_transformation,[],[f459]) ).
tcf(c_195,plain,
stldt0(sbsmnsldt0(cS2043)) = cS2076,
inference(cnf_transformation,[],[f460]) ).
tcf(c_262,plain,
! [X0: $i] :
( aElementOf0(X0,stldt0(sbsmnsldt0(cS2043)))
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(cnf_transformation,[],[f500]) ).
tcf(c_269,plain,
aElementOf0(sK37,szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(cnf_transformation,[],[f432]) ).
tcf(c_270,plain,
sz10 != sK37,
inference(cnf_transformation,[],[f431]) ).
tcf(c_271,plain,
smndt0(sz10) != sK37,
inference(cnf_transformation,[],[f430]) ).
tcf(c_915,plain,
! [X0: $i] :
( aElementOf0(X0,cS2076)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(light_normalisation,[status(thm)],[c_262,c_195]) ).
tcf(c_923,plain,
aElementOf0(sK37,cS2076),
inference(superposition,[status(thm)],[c_269,c_915]) ).
tcf(c_1897,plain,
! [X0: $i] :
( ( X0 = sz10 )
| ( smndt0(sz10) = X0 )
| ~ aElementOf0(X0,cS2076) ),
inference(light_normalisation,[status(thm)],[c_194,c_195]) ).
tcf(c_9502,plain,
( ( sz10 = sK37 )
| ( smndt0(sz10) = sK37 ) ),
inference(superposition,[status(thm)],[c_923,c_1897]) ).
tcf(c_9506,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_9502,c_271,c_270]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM456+6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 04:04:06 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.43
% 0.14/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.43
% 0.14/0.43 % Detected problem language: tptp
% 0.14/0.44 % Proving...
% 3.59/1.10 % SZS status Started for theBenchmark.p
% 3.59/1.10 % SZS status Theorem for theBenchmark.p
% 3.59/1.10
% 3.59/1.10 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.59/1.10
% 3.59/1.10 % ------ iProver source info
% 3.59/1.10
% 3.59/1.10 % git: date: 2026-07-19 20:42:38 +0200
% 3.59/1.10 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.59/1.10 % git: non_committed_changes: false
% 3.59/1.10
% 3.59/1.10 % ------ Parsing...
% 3.59/1.10 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.59/1.10 % ------ Proving...
% 3.59/1.10 % ------ Problem Properties
% 3.59/1.10
% 3.59/1.10 %
% 3.59/1.10 % clauses 225
% 3.59/1.10 % conjectures 1
% 3.59/1.10 % EPR 36
% 3.59/1.10 % Horn 178
% 3.59/1.10 % unary 27
% 3.59/1.10 % binary 62
% 3.59/1.10 % lits 693
% 3.59/1.10 % lits eq 78
% 3.59/1.10 % fd_pure 0
% 3.59/1.10 % fd_pseudo 0
% 3.59/1.10 % fd_cond 22
% 3.59/1.10 % fd_pseudo_cond 9
% 3.59/1.10 % AC symbols 0
% 3.59/1.10
% 3.59/1.10 % ------ Input Options Time Limit: Unbounded
% 3.59/1.10
% 3.59/1.10
% 3.59/1.10 % ------
% 3.59/1.10 % Current options:
% 3.59/1.10 % ------
% 3.59/1.10
% 3.59/1.10
% 3.59/1.10 %
% 3.59/1.10
% 3.59/1.10 % ------ Proving...
% 3.59/1.10 %
% 3.59/1.10
% 3.59/1.10 % ------ Proving...
% 3.59/1.10 %
% 3.59/1.10
% 3.59/1.10 % ------ Proving...
% 3.59/1.10 %
% 3.59/1.10
% 3.59/1.10 % SZS status Theorem for theBenchmark.p
% 3.59/1.10
% 3.59/1.10 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.59/1.10
% 3.59/1.10
%------------------------------------------------------------------------------