%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM437+5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n015.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 02:24:27 PM UTC 2026
% Result : Theorem 35.52s 18.26s
% Output : CNFRefutation 35.52s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f89ERROR: Could not build tree for root c_123426ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f38,conjecture,
( ( ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) ) )
& aSet0(sbsmnsldt0(xS)) )
=> ( isOpen0(sbsmnsldt0(xS))
| ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
=> ? [X1] :
( ( ( ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
| ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),sbsmnsldt0(xS))
| ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> aElementOf0(X2,sbsmnsldt0(xS)) ) ) )
& X1 != sz00
& aInteger0(X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f39,negated_conjecture,
~ ( ( ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) ) )
& aSet0(sbsmnsldt0(xS)) )
=> ( isOpen0(sbsmnsldt0(xS))
| ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
=> ? [X1] :
( ( ( ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
| ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),sbsmnsldt0(xS))
| ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> aElementOf0(X2,sbsmnsldt0(xS)) ) ) )
& X1 != sz00
& aInteger0(X1) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
fof(f41,plain,
~ ( ( ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) ) )
& aSet0(sbsmnsldt0(xS)) )
=> ( isOpen0(sbsmnsldt0(xS))
| ! [X2] :
( aElementOf0(X2,sbsmnsldt0(xS))
=> ? [X3] :
( ( ( ! [X4] :
( ( ( ( sdteqdtlpzmzozddtrp0(X4,X2,X3)
| aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
| ? [X6] :
( sdtpldt0(X4,smndt0(X2)) = sdtasdt0(X3,X6)
& aInteger0(X6) ) )
& aInteger0(X4) )
=> aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
& ( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3))
=> ( sdteqdtlpzmzozddtrp0(X4,X2,X3)
& aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& ? [X5] :
( sdtasdt0(X3,X5) = sdtpldt0(X4,smndt0(X2))
& aInteger0(X5) )
& aInteger0(X4) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X2,X3),sbsmnsldt0(xS))
| ! [X7] :
( aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X2,X3))
=> aElementOf0(X7,sbsmnsldt0(xS)) ) ) )
& sz00 != X3
& aInteger0(X3) ) ) ) ),
inference(rectify,[],[f39]) ).
fof(f48,plain,
( ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) ) )
& aSet0(sbsmnsldt0(xS))
& ~ isOpen0(sbsmnsldt0(xS))
& ? [X2] :
( aElementOf0(X2,sbsmnsldt0(xS))
& ! [X3] :
( ( ! [X4] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X4,X2,X3)
& ~ aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& ! [X6] :
( sdtpldt0(X4,smndt0(X2)) != sdtasdt0(X3,X6)
| ~ aInteger0(X6) ) )
| ~ aInteger0(X4)
| aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
& ( ~ aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3))
| ( sdteqdtlpzmzozddtrp0(X4,X2,X3)
& aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& ? [X5] :
( sdtasdt0(X3,X5) = sdtpldt0(X4,smndt0(X2))
& aInteger0(X5) )
& aInteger0(X4) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X2,X3))
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X2,X3),sbsmnsldt0(xS))
& ? [X7] :
( aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X2,X3))
& ~ aElementOf0(X7,sbsmnsldt0(xS)) ) )
| sz00 = X3
| ~ aInteger0(X3) ) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f49,plain,
( ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) ) )
& aSet0(sbsmnsldt0(xS))
& ~ isOpen0(sbsmnsldt0(xS))
& ? [X2] :
( aElementOf0(X2,sbsmnsldt0(xS))
& ! [X3] :
( ( ! [X4] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X4,X2,X3)
& ~ aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& ! [X6] :
( sdtpldt0(X4,smndt0(X2)) != sdtasdt0(X3,X6)
| ~ aInteger0(X6) ) )
| ~ aInteger0(X4)
| aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
& ( ~ aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3))
| ( sdteqdtlpzmzozddtrp0(X4,X2,X3)
& aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& ? [X5] :
( sdtasdt0(X3,X5) = sdtpldt0(X4,smndt0(X2))
& aInteger0(X5) )
& aInteger0(X4) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X2,X3))
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X2,X3),sbsmnsldt0(xS))
& ? [X7] :
( aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X2,X3))
& ~ aElementOf0(X7,sbsmnsldt0(xS)) ) )
| sz00 = X3
| ~ aInteger0(X3) ) ) ),
inference(flattening,[],[f48]) ).
fof(f95,plain,
! [X0] :
( ~ sP1(X0)
| ! [X3] :
( ~ aElementOf0(X3,X0)
| ? [X4] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),X0)
& ! [X8] :
( ~ aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(X3,X4))
| aElementOf0(X8,X0) )
& sP0(X3,X4)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X3,X4))
& sz00 != X4
& aInteger0(X4) ) ) ),
inference(nnf_transformation,[],[f88]) ).
fof(f96,plain,
! [X0] :
( ~ sP1(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| ? [X2] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),X0)
& ! [X3] :
( ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
| aElementOf0(X3,X0) )
& sP0(X1,X2)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
& sz00 != X2
& aInteger0(X2) ) ) ),
inference(rectify,[],[f95]) ).
fof(f97,plain,
! [X0] :
( ~ sP1(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,sK5(X0,X1)),X0)
& ! [X3] :
( ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,sK5(X0,X1)))
| aElementOf0(X3,X0) )
& sP0(X1,sK5(X0,X1))
& aSet0(szAzrzSzezqlpdtcmdtrp0(X1,sK5(X0,X1)))
& sz00 != sK5(X0,X1)
& aInteger0(sK5(X0,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f96]) ).
fof(f101,plain,
( ! [X0] :
( ~ aElementOf0(X0,xS)
| ( isOpen0(X0)
& sP1(X0)
& aSubsetOf0(X0,cS1395)
& ! [X2] :
( ~ aElementOf0(X2,X0)
| aElementOf0(X2,cS1395) )
& aSet0(X0)
& ! [X1] :
( ( ~ aElementOf0(X1,cS1395)
| aInteger0(X1) )
& ( ~ aInteger0(X1)
| aElementOf0(X1,cS1395) ) )
& aSet0(cS1395) ) )
& aSet0(xS) ),
inference(nnf_transformation,[],[f89]) ).
fof(f105,plain,
( ! [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))
& ~ isOpen0(sbsmnsldt0(xS))
& ? [X2] :
( aElementOf0(X2,sbsmnsldt0(xS))
& ! [X3] :
( ( sP2(X2,X3)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X2,X3))
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X2,X3),sbsmnsldt0(xS))
& ? [X7] :
( aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X2,X3))
& ~ aElementOf0(X7,sbsmnsldt0(xS)) ) )
| sz00 = X3
| ~ aInteger0(X3) ) ) ),
inference(nnf_transformation,[],[f91]) ).
fof(f106,plain,
( ! [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))
& ~ isOpen0(sbsmnsldt0(xS))
& ? [X2] :
( aElementOf0(X2,sbsmnsldt0(xS))
& ! [X3] :
( ( sP2(X2,X3)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X2,X3))
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X2,X3),sbsmnsldt0(xS))
& ? [X7] :
( aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X2,X3))
& ~ aElementOf0(X7,sbsmnsldt0(xS)) ) )
| sz00 = X3
| ~ aInteger0(X3) ) ) ),
inference(flattening,[],[f105]) ).
fof(f107,plain,
( ! [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))
& ~ isOpen0(sbsmnsldt0(xS))
& ? [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
& ! [X1] :
( ( sP2(X0,X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),sbsmnsldt0(xS))
& ? [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
& ~ aElementOf0(X2,sbsmnsldt0(xS)) ) )
| sz00 = X1
| ~ aInteger0(X1) ) ) ),
inference(rectify,[],[f106]) ).
fof(f108,plain,
( ! [X3] :
( ( ~ aElementOf0(X3,sbsmnsldt0(xS))
| ( aElementOf0(X3,sK10(X3))
& aElementOf0(sK10(X3),xS)
& aInteger0(X3) ) )
& ( ! [X4] :
( ~ aElementOf0(X3,X4)
| ~ aElementOf0(X4,xS) )
| ~ aInteger0(X3)
| aElementOf0(X3,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS))
& ~ isOpen0(sbsmnsldt0(xS))
& aElementOf0(sK8,sbsmnsldt0(xS))
& ! [X1] :
( ( sP2(sK8,X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sK8,X1))
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sK8,X1),sbsmnsldt0(xS))
& aElementOf0(sK9(X1),szAzrzSzezqlpdtcmdtrp0(sK8,X1))
& ~ aElementOf0(sK9(X1),sbsmnsldt0(xS)) )
| sz00 = X1
| ~ aInteger0(X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10]),skolemize(X0,sK8),skolemize(X2,sK9(X1)),skolemize(X5,sK10(X3))],[f107]) ).
fof(f133,plain,
! [X3,X0,X1] :
( ~ sP1(X0)
| ~ aElementOf0(X1,X0)
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,sK5(X0,X1)))
| aElementOf0(X3,X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f136,plain,
! [X0,X1] :
( ~ sP1(X0)
| ~ aElementOf0(X1,X0)
| sz00 != sK5(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f137,plain,
! [X0,X1] :
( ~ sP1(X0)
| ~ aElementOf0(X1,X0)
| aInteger0(sK5(X0,X1)) ),
inference(cnf_transformation,[],[f97]) ).
fof(f147,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| sP1(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f163,plain,
! [X3] :
( ~ aElementOf0(X3,sbsmnsldt0(xS))
| aElementOf0(X3,sK10(X3)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f164,plain,
! [X3] :
( ~ aElementOf0(X3,sbsmnsldt0(xS))
| aElementOf0(sK10(X3),xS) ),
inference(cnf_transformation,[],[f108]) ).
fof(f166,plain,
! [X3,X4] :
( ~ aElementOf0(X3,X4)
| ~ aElementOf0(X4,xS)
| ~ aInteger0(X3)
| aElementOf0(X3,sbsmnsldt0(xS)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f169,plain,
aElementOf0(sK8,sbsmnsldt0(xS)),
inference(cnf_transformation,[],[f108]) ).
fof(f170,plain,
! [X1] :
( sP2(sK8,X1)
| sz00 = X1
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f108]) ).
fof(f173,plain,
! [X1] :
( aElementOf0(sK9(X1),szAzrzSzezqlpdtcmdtrp0(sK8,X1))
| sz00 = X1
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f108]) ).
fof(f174,plain,
! [X1] :
( ~ aElementOf0(sK9(X1),sbsmnsldt0(xS))
| sz00 = X1
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f108]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( aInteger0(sK5(X1,X0))
| ~ sP1(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( ~ sP1(X0)
| ~ aElementOf0(X1,X0)
| ( sK5(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,X2)
| ~ sP1(X2)
| ~ aElementOf0(X1,X2)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(X1,sK5(X2,X1))) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_70,plain,
! [X0: $i] :
( sP1(X0)
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_80,negated_conjecture,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aInteger0(X0)
| ~ aElementOf0(sK9(X0),sbsmnsldt0(xS)) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_81,negated_conjecture,
! [X0: $i] :
( aElementOf0(sK9(X0),szAzrzSzezqlpdtcmdtrp0(sK8,X0))
| ( X0 = sz00 )
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_84,negated_conjecture,
! [X0: $i] :
( sP2(sK8,X0)
| ( X0 = sz00 )
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_85,negated_conjecture,
aElementOf0(sK8,sbsmnsldt0(xS)),
inference(cnf_transformation,[],[f169]) ).
tcf(c_88,negated_conjecture,
! [X0: $i,X1: $i] :
( aElementOf0(X0,sbsmnsldt0(xS))
| ~ aInteger0(X0)
| ~ aElementOf0(X1,xS)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_90,negated_conjecture,
! [X0: $i] :
( aElementOf0(sK10(X0),xS)
| ~ aElementOf0(X0,sbsmnsldt0(xS)) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_91,negated_conjecture,
! [X0: $i] :
( aElementOf0(X0,sK10(X0))
| ~ aElementOf0(X0,sbsmnsldt0(xS)) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_1718,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ aElementOf0(X2,xS)
| ~ aElementOf0(X1,X0)
| ( X0 != X2 )
| ( sK5(X0,X1) != sz00 ) ),
inference(resolution_lifted,[status(thm)],[c_70,c_50]) ).
tcf(c_1719,plain,
! [X0: $i,X1: $i] :
( ~ aElementOf0(X0,xS)
| ~ aElementOf0(X1,X0)
| ( sK5(X0,X1) != sz00 ) ),
inference(unflattening,[status(thm)],[c_1718]) ).
tcf(c_1766,plain,
! [X0: $i,X1: $i,X2: $i] :
( aInteger0(sK5(X1,X2))
| ~ aElementOf0(X0,xS)
| ~ aElementOf0(X2,X1)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_70,c_49]) ).
tcf(c_1767,plain,
! [X0: $i,X1: $i] :
( aInteger0(sK5(X1,X0))
| ~ aElementOf0(X1,xS)
| ~ aElementOf0(X0,X1) ),
inference(unflattening,[status(thm)],[c_1766]) ).
tcf(c_1778,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X2,X1)
| ~ aElementOf0(X0,xS)
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X3,sK5(X1,X3)))
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_70,c_53]) ).
tcf(c_1779,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,X2)
| ~ aElementOf0(X2,xS)
| ~ aElementOf0(X1,X2)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(X1,sK5(X2,X1))) ),
inference(unflattening,[status(thm)],[c_1778]) ).
tcf(c_8260,plain,
aElementOf0(sK10(sK8),xS),
inference(superposition,[status(thm)],[c_85,c_90]) ).
tcf(c_8265,plain,
aElementOf0(sK8,sK10(sK8)),
inference(superposition,[status(thm)],[c_85,c_91]) ).
tcf(c_9695,plain,
! [X0: $i] :
( ~ aElementOf0(sK10(sK8),xS)
| ~ aElementOf0(X0,sK10(sK8))
| ( sK5(sK10(sK8),X0) != sz00 ) ),
inference(instantiation,[status(thm)],[c_1719]) ).
tcf(c_9703,plain,
! [X0: $i] :
( aInteger0(sK5(sK10(sK8),X0))
| ~ aElementOf0(sK10(sK8),xS)
| ~ aElementOf0(X0,sK10(sK8)) ),
inference(instantiation,[status(thm)],[c_1767]) ).
tcf(c_9704,plain,
! [X0: $i] :
( aElementOf0(X0,sbsmnsldt0(xS))
| ~ aInteger0(X0)
| ~ aElementOf0(sK10(sK8),xS)
| ~ aElementOf0(X0,sK10(sK8)) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_9712,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,sK10(sK8))
| ~ aElementOf0(sK10(sK8),xS)
| ~ aElementOf0(X1,sK10(sK8))
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(X1,sK5(sK10(sK8),X1))) ),
inference(instantiation,[status(thm)],[c_1779]) ).
tcf(c_13869,plain,
( ~ aElementOf0(sK8,sK10(sK8))
| ~ aElementOf0(sK10(sK8),xS)
| ( sK5(sK10(sK8),sK8) != sz00 ) ),
inference(instantiation,[status(thm)],[c_9695]) ).
tcf(c_13910,plain,
( aInteger0(sK5(sK10(sK8),sK8))
| ~ aElementOf0(sK8,sK10(sK8))
| ~ aElementOf0(sK10(sK8),xS) ),
inference(instantiation,[status(thm)],[c_9703]) ).
tcf(c_15046,plain,
! [X0: $i] :
( aElementOf0(X0,sK10(sK8))
| ~ aElementOf0(sK8,sK10(sK8))
| ~ aElementOf0(sK10(sK8),xS)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sK8,sK5(sK10(sK8),sK8))) ),
inference(instantiation,[status(thm)],[c_9712]) ).
tcf(c_21718,plain,
( aElementOf0(sK9(sK5(sK10(sK8),sK8)),szAzrzSzezqlpdtcmdtrp0(sK8,sK5(sK10(sK8),sK8)))
| ( sK5(sK10(sK8),sK8) = sz00 )
| ~ aInteger0(sK5(sK10(sK8),sK8)) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_21721,plain,
( ( sK5(sK10(sK8),sK8) = sz00 )
| ~ aInteger0(sK5(sK10(sK8),sK8))
| ~ aElementOf0(sK9(sK5(sK10(sK8),sK8)),sbsmnsldt0(xS)) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_35297,plain,
( aElementOf0(sK9(sK5(sK10(sK8),sK8)),sbsmnsldt0(xS))
| ~ aElementOf0(sK10(sK8),xS)
| ~ aInteger0(sK9(sK5(sK10(sK8),sK8)))
| ~ aElementOf0(sK9(sK5(sK10(sK8),sK8)),sK10(sK8)) ),
inference(instantiation,[status(thm)],[c_9704]) ).
tcf(c_41874,plain,
( aElementOf0(sK9(sK5(sK10(sK8),sK8)),sK10(sK8))
| ~ aElementOf0(sK8,sK10(sK8))
| ~ aElementOf0(sK10(sK8),xS)
| ~ aElementOf0(sK9(sK5(sK10(sK8),sK8)),szAzrzSzezqlpdtcmdtrp0(sK8,sK5(sK10(sK8),sK8))) ),
inference(instantiation,[status(thm)],[c_15046]) ).
fof(f90,definition,
! [X2,X3] :
( ~ sP2(X2,X3)
| ! [X4] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X4,X2,X3)
& ~ aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& ! [X6] :
( sdtpldt0(X4,smndt0(X2)) != sdtasdt0(X3,X6)
| ~ aInteger0(X6) ) )
| ~ aInteger0(X4)
| aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
& ( ~ aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3))
| ( sdteqdtlpzmzozddtrp0(X4,X2,X3)
& aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& ? [X5] :
( sdtasdt0(X3,X5) = sdtpldt0(X4,smndt0(X2))
& aInteger0(X5) )
& aInteger0(X4) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f91,plain,
( ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) ) )
& aSet0(sbsmnsldt0(xS))
& ~ isOpen0(sbsmnsldt0(xS))
& ? [X2] :
( aElementOf0(X2,sbsmnsldt0(xS))
& ! [X3] :
( ( sP2(X2,X3)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X2,X3))
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X2,X3),sbsmnsldt0(xS))
& ? [X7] :
( aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X2,X3))
& ~ aElementOf0(X7,sbsmnsldt0(xS)) ) )
| sz00 = X3
| ~ aInteger0(X3) ) ) ),
inference(definition_folding,[],[f49,f90]) ).
fof(f102,plain,
! [X2,X3] :
( ~ sP2(X2,X3)
| ! [X4] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X4,X2,X3)
& ~ aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& ! [X6] :
( sdtpldt0(X4,smndt0(X2)) != sdtasdt0(X3,X6)
| ~ aInteger0(X6) ) )
| ~ aInteger0(X4)
| aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
& ( ~ aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3))
| ( sdteqdtlpzmzozddtrp0(X4,X2,X3)
& aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& ? [X5] :
( sdtasdt0(X3,X5) = sdtpldt0(X4,smndt0(X2))
& aInteger0(X5) )
& aInteger0(X4) ) ) ) ),
inference(nnf_transformation,[],[f90]) ).
fof(f103,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| ! [X2] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X2,X0,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& ! [X4] :
( sdtpldt0(X2,smndt0(X0)) != sdtasdt0(X1,X4)
| ~ aInteger0(X4) ) )
| ~ aInteger0(X2)
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ( ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) )
& aInteger0(X2) ) ) ) ),
inference(rectify,[],[f102]) ).
fof(f104,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| ! [X2] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X2,X0,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& ! [X4] :
( sdtpldt0(X2,smndt0(X0)) != sdtasdt0(X1,X4)
| ~ aInteger0(X4) ) )
| ~ aInteger0(X2)
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ( ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& sdtpldt0(X2,smndt0(X0)) = sdtasdt0(X1,sK7(X0,X1,X2))
& aInteger0(sK7(X0,X1,X2))
& aInteger0(X2) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X3,sK7(X0,X1,X2))],[f103]) ).
fof(f162,plain,
! [X2,X0,X1] :
( ~ sP2(X0,X1)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| aInteger0(X2) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( aInteger0(X0)
| ~ sP2(X1,X2)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_2077,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aInteger0(X3)
| ( X2 = sz00 )
| ~ aInteger0(X2)
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| ( X1 != X2 )
| ( X0 != sK8 ) ),
inference(resolution_lifted,[status(thm)],[c_72,c_84]) ).
tcf(c_2078,plain,
! [X0: $i,X1: $i] :
( aInteger0(X0)
| ( X1 = sz00 )
| ~ aInteger0(X1)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sK8,X1)) ),
inference(unflattening,[status(thm)],[c_2077]) ).
tcf(c_54432,plain,
! [X0: $i] :
( aInteger0(sK9(sK5(sK10(sK8),sK8)))
| ( X0 = sz00 )
| ~ aInteger0(X0)
| ~ aElementOf0(sK9(sK5(sK10(sK8),sK8)),szAzrzSzezqlpdtcmdtrp0(sK8,X0)) ),
inference(instantiation,[status(thm)],[c_2078]) ).
tcf(c_123425,plain,
( aInteger0(sK9(sK5(sK10(sK8),sK8)))
| ( sK5(sK10(sK8),sK8) = sz00 )
| ~ aInteger0(sK5(sK10(sK8),sK8))
| ~ aElementOf0(sK9(sK5(sK10(sK8),sK8)),szAzrzSzezqlpdtcmdtrp0(sK8,sK5(sK10(sK8),sK8))) ),
inference(instantiation,[status(thm)],[c_54432]) ).
tcf(c_123426,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_123425,c_41874,c_35297,c_21718,c_21721,c_13910,c_13869,c_8265,c_8260]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM437+5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/10.39 % Computer : n015.cluster.edu
% 0.12/10.39 % Model : x86_64 x86_64
% 0.12/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.39 % Memory : 8046.5625MB
% 0.12/10.39 % OS : Linux 6.8.0-71-generic
% 0.12/10.39 % CPULimit : 300
% 0.12/10.39 % WCLimit : 300
% 0.12/10.39 % DateTime : Thu Sep 24 04:01:53 UTC 2026
% 0.12/10.40 % CPUTime :
% 0.12/10.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/10.43 Running first-order theorem proving
% 0.16/10.43 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/10.45
% 0.16/10.45 % ======== iProver multi-core TPTP/SMT =========
% 0.16/10.45
% 0.16/10.45 % Detected problem language: tptp
% 0.16/10.46 % Proving...
% 35.52/18.26 % SZS status Started for theBenchmark.p
% 35.52/18.26 % SZS status Theorem for theBenchmark.p
% 35.52/18.26
% 35.52/18.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 35.52/18.26
% 35.52/18.26 % ------ iProver source info
% 35.52/18.26
% 35.52/18.26 % git: date: 2026-07-19 20:42:38 +0200
% 35.52/18.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 35.52/18.26 % git: non_committed_changes: false
% 35.52/18.26
% 35.52/18.26 % ------ Parsing...
% 35.52/18.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 35.52/18.26
% 35.52/18.26 % ------ 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 %
% 35.52/18.26
% 35.52/18.26 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 35.52/18.26
% 35.52/18.26 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 35.52/18.26 % ------ Proving...
% 35.52/18.26 % ------ Problem Properties
% 35.52/18.26
% 35.52/18.26 %
% 35.52/18.26 % clauses 102
% 35.52/18.26 % conjectures 11
% 35.52/18.26 % EPR 22
% 35.52/18.26 % Horn 67
% 35.52/18.26 % unary 5
% 35.52/18.26 % binary 20
% 35.52/18.26 % lits 363
% 35.52/18.26 % lits eq 56
% 35.52/18.26 % fd_pure 0
% 35.52/18.26 % fd_pseudo 0
% 35.52/18.26 % fd_cond 26
% 35.52/18.26 % fd_pseudo_cond 4
% 35.52/18.26 % AC symbols 0
% 35.52/18.26
% 35.52/18.26 % ------ Schedule dynamic 5 is on
% 35.52/18.26
% 35.52/18.26 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 35.52/18.26
% 35.52/18.26
% 35.52/18.26 % ------
% 35.52/18.26 % Current options:
% 35.52/18.26 % ------
% 35.52/18.26
% 35.52/18.26
% 35.52/18.26 %
% 35.52/18.26
% 35.52/18.26 % ------ Proving...
% 35.52/18.26 %
% 35.52/18.26
% 35.52/18.26 % SZS status Theorem for theBenchmark.p
% 35.52/18.26
% 35.52/18.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 35.52/18.26
% 35.52/18.26
%------------------------------------------------------------------------------