%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM441+6 : 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 : n001.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 02:24:28 PM UTC 2026
% Result : Theorem 5.01s 2.40s
% Output : CNFRefutation 5.01s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f101ERROR: Could not build tree for root c_23756ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f38,axiom,
! [X0,X1] :
( ( isOpen0(X1)
& isOpen0(X0)
& aSubsetOf0(X1,cS1395)
& aSubsetOf0(X0,cS1395) )
=> isOpen0(sdtslmnbsdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mInterOpen) ).
fof(f40,axiom,
( stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB))
& ! [X0] :
( aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aElementOf0(X0,stldt0(xB))
& aElementOf0(X0,stldt0(xA))
& aInteger0(X0) ) )
& ! [X0] :
( aElementOf0(X0,stldt0(xB))
<=> ( ~ aElementOf0(X0,xB)
& aInteger0(X0) ) )
& ! [X0] :
( aElementOf0(X0,stldt0(xA))
<=> ( ~ aElementOf0(X0,xA)
& aInteger0(X0) ) )
& ! [X0] :
( aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB))
& aInteger0(X0) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X0] :
( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
<=> ( ( aElementOf0(X0,xB)
| aElementOf0(X0,xA) )
& aInteger0(X0) ) )
& aSet0(sdtbsmnsldt0(xA,xB))
& aSubsetOf0(stldt0(xB),cS1395)
& ! [X0] :
( aElementOf0(X0,stldt0(xB))
=> aElementOf0(X0,cS1395) )
& ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) )
& aSet0(cS1395)
& ! [X0] :
( aElementOf0(X0,stldt0(xB))
<=> ( ~ aElementOf0(X0,xB)
& aInteger0(X0) ) )
& aSet0(stldt0(xB))
& aSubsetOf0(stldt0(xA),cS1395)
& ! [X0] :
( aElementOf0(X0,stldt0(xA))
=> aElementOf0(X0,cS1395) )
& ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) )
& aSet0(cS1395)
& ! [X0] :
( aElementOf0(X0,stldt0(xA))
<=> ( ~ aElementOf0(X0,xA)
& aInteger0(X0) ) )
& aSet0(stldt0(xA)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1883) ).
fof(f44,plain,
( stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB))
& ! [X10] :
( aElementOf0(X10,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aElementOf0(X10,stldt0(xB))
& aElementOf0(X10,stldt0(xA))
& aInteger0(X10) ) )
& ! [X9] :
( aElementOf0(X9,stldt0(xB))
<=> ( ~ aElementOf0(X9,xB)
& aInteger0(X9) ) )
& ! [X8] :
( aElementOf0(X8,stldt0(xA))
<=> ( ~ aElementOf0(X8,xA)
& aInteger0(X8) ) )
& ! [X7] :
( aElementOf0(X7,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( ~ aElementOf0(X7,sdtbsmnsldt0(xA,xB))
& aInteger0(X7) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X6] :
( aElementOf0(X6,sdtbsmnsldt0(xA,xB))
<=> ( ( aElementOf0(X6,xB)
| aElementOf0(X6,xA) )
& aInteger0(X6) ) )
& aSet0(sdtbsmnsldt0(xA,xB))
& aSubsetOf0(stldt0(xB),cS1395)
& ! [X5] :
( aElementOf0(X5,stldt0(xB))
=> aElementOf0(X5,cS1395) )
& ! [X4] :
( aElementOf0(X4,cS1395)
<=> aInteger0(X4) )
& aSet0(cS1395)
& ! [X3] :
( aElementOf0(X3,stldt0(xB))
<=> ( ~ aElementOf0(X3,xB)
& aInteger0(X3) ) )
& aSet0(stldt0(xB))
& aSubsetOf0(stldt0(xA),cS1395)
& ! [X2] :
( aElementOf0(X2,stldt0(xA))
=> aElementOf0(X2,cS1395) )
& ! [X1] :
( aElementOf0(X1,cS1395)
<=> aInteger0(X1) )
& aSet0(cS1395)
& ! [X0] :
( aElementOf0(X0,stldt0(xA))
<=> ( ~ aElementOf0(X0,xA)
& aInteger0(X0) ) )
& aSet0(stldt0(xA)) ),
inference(rectify,[],[f40]) ).
fof(f51,plain,
( stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB))
& ! [X10] :
( aElementOf0(X10,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aElementOf0(X10,stldt0(xB))
& aElementOf0(X10,stldt0(xA))
& aInteger0(X10) ) )
& ! [X9] :
( aElementOf0(X9,stldt0(xB))
<=> ( ~ aElementOf0(X9,xB)
& aInteger0(X9) ) )
& ! [X8] :
( aElementOf0(X8,stldt0(xA))
<=> ( ~ aElementOf0(X8,xA)
& aInteger0(X8) ) )
& ! [X7] :
( aElementOf0(X7,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( ~ aElementOf0(X7,sdtbsmnsldt0(xA,xB))
& aInteger0(X7) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X6] :
( aElementOf0(X6,sdtbsmnsldt0(xA,xB))
<=> ( ( aElementOf0(X6,xB)
| aElementOf0(X6,xA) )
& aInteger0(X6) ) )
& aSet0(sdtbsmnsldt0(xA,xB))
& aSubsetOf0(stldt0(xB),cS1395)
& ! [X5] :
( ~ aElementOf0(X5,stldt0(xB))
| aElementOf0(X5,cS1395) )
& ! [X4] :
( aElementOf0(X4,cS1395)
<=> aInteger0(X4) )
& aSet0(cS1395)
& ! [X3] :
( aElementOf0(X3,stldt0(xB))
<=> ( ~ aElementOf0(X3,xB)
& aInteger0(X3) ) )
& aSet0(stldt0(xB))
& aSubsetOf0(stldt0(xA),cS1395)
& ! [X2] :
( ~ aElementOf0(X2,stldt0(xA))
| aElementOf0(X2,cS1395) )
& ! [X1] :
( aElementOf0(X1,cS1395)
<=> aInteger0(X1) )
& aSet0(cS1395)
& ! [X0] :
( aElementOf0(X0,stldt0(xA))
<=> ( ~ aElementOf0(X0,xA)
& aInteger0(X0) ) )
& aSet0(stldt0(xA)) ),
inference(ennf_transformation,[],[f44]) ).
fof(f93,plain,
! [X0,X1] :
( ~ isOpen0(X1)
| ~ isOpen0(X0)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395)
| isOpen0(sdtslmnbsdt0(X0,X1)) ),
inference(ennf_transformation,[],[f38]) ).
fof(f94,plain,
! [X0,X1] :
( ~ isOpen0(X1)
| ~ isOpen0(X0)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395)
| isOpen0(sdtslmnbsdt0(X0,X1)) ),
inference(flattening,[],[f93]) ).
fof(f114,plain,
( isClosed0(xB)
& isOpen0(stldt0(xB))
& ! [X12] :
( ~ aElementOf0(X12,stldt0(xB))
| ? [X13] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X12,X13),stldt0(xB))
& ! [X17] :
( ~ aElementOf0(X17,szAzrzSzezqlpdtcmdtrp0(X12,X13))
| aElementOf0(X17,stldt0(xB)) )
& sP0(X12,X13)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X12,X13))
& sz00 != X13
& aInteger0(X13) ) )
& ! [X11] :
( ( ~ aElementOf0(X11,stldt0(xB))
| ( ~ aElementOf0(X11,xB)
& aInteger0(X11) ) )
& ( aElementOf0(X11,xB)
| ~ aInteger0(X11)
| aElementOf0(X11,stldt0(xB)) ) )
& aSet0(stldt0(xB))
& isClosed0(xA)
& isOpen0(stldt0(xA))
& ! [X5] :
( ~ aElementOf0(X5,stldt0(xA))
| ? [X6] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X5,X6),stldt0(xA))
& ! [X10] :
( ~ aElementOf0(X10,szAzrzSzezqlpdtcmdtrp0(X5,X6))
| aElementOf0(X10,stldt0(xA)) )
& sP1(X5,X6)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X5,X6))
& sz00 != X6
& aInteger0(X6) ) )
& ! [X4] :
( ( ~ aElementOf0(X4,stldt0(xA))
| ( ~ aElementOf0(X4,xA)
& aInteger0(X4) ) )
& ( aElementOf0(X4,xA)
| ~ aInteger0(X4)
| aElementOf0(X4,stldt0(xA)) ) )
& aSet0(stldt0(xA))
& aSubsetOf0(xB,cS1395)
& ! [X3] :
( ~ aElementOf0(X3,xB)
| aElementOf0(X3,cS1395) )
& aSet0(xB)
& ! [X2] :
( ( ~ aElementOf0(X2,cS1395)
| aInteger0(X2) )
& ( ~ aInteger0(X2)
| aElementOf0(X2,cS1395) ) )
& aSet0(cS1395)
& aSubsetOf0(xA,cS1395)
& ! [X1] :
( ~ aElementOf0(X1,xA)
| aElementOf0(X1,cS1395) )
& aSet0(xA)
& ! [X0] :
( ( ~ aElementOf0(X0,cS1395)
| aInteger0(X0) )
& ( ~ aInteger0(X0)
| aElementOf0(X0,cS1395) ) )
& aSet0(cS1395) ),
inference(nnf_transformation,[],[f99]) ).
fof(f115,plain,
( isClosed0(xB)
& isOpen0(stldt0(xB))
& ! [X12] :
( ~ aElementOf0(X12,stldt0(xB))
| ? [X13] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X12,X13),stldt0(xB))
& ! [X17] :
( ~ aElementOf0(X17,szAzrzSzezqlpdtcmdtrp0(X12,X13))
| aElementOf0(X17,stldt0(xB)) )
& sP0(X12,X13)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X12,X13))
& sz00 != X13
& aInteger0(X13) ) )
& ! [X11] :
( ( ~ aElementOf0(X11,stldt0(xB))
| ( ~ aElementOf0(X11,xB)
& aInteger0(X11) ) )
& ( aElementOf0(X11,xB)
| ~ aInteger0(X11)
| aElementOf0(X11,stldt0(xB)) ) )
& aSet0(stldt0(xB))
& isClosed0(xA)
& isOpen0(stldt0(xA))
& ! [X5] :
( ~ aElementOf0(X5,stldt0(xA))
| ? [X6] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X5,X6),stldt0(xA))
& ! [X10] :
( ~ aElementOf0(X10,szAzrzSzezqlpdtcmdtrp0(X5,X6))
| aElementOf0(X10,stldt0(xA)) )
& sP1(X5,X6)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X5,X6))
& sz00 != X6
& aInteger0(X6) ) )
& ! [X4] :
( ( ~ aElementOf0(X4,stldt0(xA))
| ( ~ aElementOf0(X4,xA)
& aInteger0(X4) ) )
& ( aElementOf0(X4,xA)
| ~ aInteger0(X4)
| aElementOf0(X4,stldt0(xA)) ) )
& aSet0(stldt0(xA))
& aSubsetOf0(xB,cS1395)
& ! [X3] :
( ~ aElementOf0(X3,xB)
| aElementOf0(X3,cS1395) )
& aSet0(xB)
& ! [X2] :
( ( ~ aElementOf0(X2,cS1395)
| aInteger0(X2) )
& ( ~ aInteger0(X2)
| aElementOf0(X2,cS1395) ) )
& aSet0(cS1395)
& aSubsetOf0(xA,cS1395)
& ! [X1] :
( ~ aElementOf0(X1,xA)
| aElementOf0(X1,cS1395) )
& aSet0(xA)
& ! [X0] :
( ( ~ aElementOf0(X0,cS1395)
| aInteger0(X0) )
& ( ~ aInteger0(X0)
| aElementOf0(X0,cS1395) ) )
& aSet0(cS1395) ),
inference(flattening,[],[f114]) ).
fof(f116,plain,
( isClosed0(xB)
& isOpen0(stldt0(xB))
& ! [X9] :
( ~ aElementOf0(X9,stldt0(xB))
| ? [X10] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X9,X10),stldt0(xB))
& ! [X11] :
( ~ aElementOf0(X11,szAzrzSzezqlpdtcmdtrp0(X9,X10))
| aElementOf0(X11,stldt0(xB)) )
& sP0(X9,X10)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X9,X10))
& sz00 != X10
& aInteger0(X10) ) )
& ! [X8] :
( ( ~ aElementOf0(X8,stldt0(xB))
| ( ~ aElementOf0(X8,xB)
& aInteger0(X8) ) )
& ( aElementOf0(X8,xB)
| ~ aInteger0(X8)
| aElementOf0(X8,stldt0(xB)) ) )
& aSet0(stldt0(xB))
& isClosed0(xA)
& isOpen0(stldt0(xA))
& ! [X5] :
( ~ aElementOf0(X5,stldt0(xA))
| ? [X6] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X5,X6),stldt0(xA))
& ! [X7] :
( ~ aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X5,X6))
| aElementOf0(X7,stldt0(xA)) )
& sP1(X5,X6)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X5,X6))
& sz00 != X6
& aInteger0(X6) ) )
& ! [X4] :
( ( ~ aElementOf0(X4,stldt0(xA))
| ( ~ aElementOf0(X4,xA)
& aInteger0(X4) ) )
& ( aElementOf0(X4,xA)
| ~ aInteger0(X4)
| aElementOf0(X4,stldt0(xA)) ) )
& aSet0(stldt0(xA))
& aSubsetOf0(xB,cS1395)
& ! [X3] :
( ~ aElementOf0(X3,xB)
| aElementOf0(X3,cS1395) )
& aSet0(xB)
& ! [X2] :
( ( ~ aElementOf0(X2,cS1395)
| aInteger0(X2) )
& ( ~ aInteger0(X2)
| aElementOf0(X2,cS1395) ) )
& aSet0(cS1395)
& aSubsetOf0(xA,cS1395)
& ! [X1] :
( ~ aElementOf0(X1,xA)
| aElementOf0(X1,cS1395) )
& aSet0(xA)
& ! [X0] :
( ( ~ aElementOf0(X0,cS1395)
| aInteger0(X0) )
& ( ~ aInteger0(X0)
| aElementOf0(X0,cS1395) ) )
& aSet0(cS1395) ),
inference(rectify,[],[f115]) ).
fof(f117,plain,
( isClosed0(xB)
& isOpen0(stldt0(xB))
& ! [X9] :
( ~ aElementOf0(X9,stldt0(xB))
| ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X9,sK10(X9)),stldt0(xB))
& ! [X11] :
( ~ aElementOf0(X11,szAzrzSzezqlpdtcmdtrp0(X9,sK10(X9)))
| aElementOf0(X11,stldt0(xB)) )
& sP0(X9,sK10(X9))
& aSet0(szAzrzSzezqlpdtcmdtrp0(X9,sK10(X9)))
& sz00 != sK10(X9)
& aInteger0(sK10(X9)) ) )
& ! [X8] :
( ( ~ aElementOf0(X8,stldt0(xB))
| ( ~ aElementOf0(X8,xB)
& aInteger0(X8) ) )
& ( aElementOf0(X8,xB)
| ~ aInteger0(X8)
| aElementOf0(X8,stldt0(xB)) ) )
& aSet0(stldt0(xB))
& isClosed0(xA)
& isOpen0(stldt0(xA))
& ! [X5] :
( ~ aElementOf0(X5,stldt0(xA))
| ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X5,sK9(X5)),stldt0(xA))
& ! [X7] :
( ~ aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X5,sK9(X5)))
| aElementOf0(X7,stldt0(xA)) )
& sP1(X5,sK9(X5))
& aSet0(szAzrzSzezqlpdtcmdtrp0(X5,sK9(X5)))
& sz00 != sK9(X5)
& aInteger0(sK9(X5)) ) )
& ! [X4] :
( ( ~ aElementOf0(X4,stldt0(xA))
| ( ~ aElementOf0(X4,xA)
& aInteger0(X4) ) )
& ( aElementOf0(X4,xA)
| ~ aInteger0(X4)
| aElementOf0(X4,stldt0(xA)) ) )
& aSet0(stldt0(xA))
& aSubsetOf0(xB,cS1395)
& ! [X3] :
( ~ aElementOf0(X3,xB)
| aElementOf0(X3,cS1395) )
& aSet0(xB)
& ! [X2] :
( ( ~ aElementOf0(X2,cS1395)
| aInteger0(X2) )
& ( ~ aInteger0(X2)
| aElementOf0(X2,cS1395) ) )
& aSet0(cS1395)
& aSubsetOf0(xA,cS1395)
& ! [X1] :
( ~ aElementOf0(X1,xA)
| aElementOf0(X1,cS1395) )
& aSet0(xA)
& ! [X0] :
( ( ~ aElementOf0(X0,cS1395)
| aInteger0(X0) )
& ( ~ aInteger0(X0)
| aElementOf0(X0,cS1395) ) )
& aSet0(cS1395) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X6,sK9(X5)),skolemize(X10,sK10(X9))],[f116]) ).
fof(f118,plain,
( stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB))
& ! [X10] :
( ( ~ aElementOf0(X10,stldt0(sdtbsmnsldt0(xA,xB)))
| ( aElementOf0(X10,stldt0(xB))
& aElementOf0(X10,stldt0(xA))
& aInteger0(X10) ) )
& ( ~ aElementOf0(X10,stldt0(xB))
| ~ aElementOf0(X10,stldt0(xA))
| ~ aInteger0(X10)
| aElementOf0(X10,stldt0(sdtbsmnsldt0(xA,xB))) ) )
& ! [X9] :
( ( ~ aElementOf0(X9,stldt0(xB))
| ( ~ aElementOf0(X9,xB)
& aInteger0(X9) ) )
& ( aElementOf0(X9,xB)
| ~ aInteger0(X9)
| aElementOf0(X9,stldt0(xB)) ) )
& ! [X8] :
( ( ~ aElementOf0(X8,stldt0(xA))
| ( ~ aElementOf0(X8,xA)
& aInteger0(X8) ) )
& ( aElementOf0(X8,xA)
| ~ aInteger0(X8)
| aElementOf0(X8,stldt0(xA)) ) )
& ! [X7] :
( ( ~ aElementOf0(X7,stldt0(sdtbsmnsldt0(xA,xB)))
| ( ~ aElementOf0(X7,sdtbsmnsldt0(xA,xB))
& aInteger0(X7) ) )
& ( aElementOf0(X7,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(X7)
| aElementOf0(X7,stldt0(sdtbsmnsldt0(xA,xB))) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X6] :
( ( ~ aElementOf0(X6,sdtbsmnsldt0(xA,xB))
| ( ( aElementOf0(X6,xB)
| aElementOf0(X6,xA) )
& aInteger0(X6) ) )
& ( ( ~ aElementOf0(X6,xB)
& ~ aElementOf0(X6,xA) )
| ~ aInteger0(X6)
| aElementOf0(X6,sdtbsmnsldt0(xA,xB)) ) )
& aSet0(sdtbsmnsldt0(xA,xB))
& aSubsetOf0(stldt0(xB),cS1395)
& ! [X5] :
( ~ aElementOf0(X5,stldt0(xB))
| aElementOf0(X5,cS1395) )
& ! [X4] :
( ( ~ aElementOf0(X4,cS1395)
| aInteger0(X4) )
& ( ~ aInteger0(X4)
| aElementOf0(X4,cS1395) ) )
& aSet0(cS1395)
& ! [X3] :
( ( ~ aElementOf0(X3,stldt0(xB))
| ( ~ aElementOf0(X3,xB)
& aInteger0(X3) ) )
& ( aElementOf0(X3,xB)
| ~ aInteger0(X3)
| aElementOf0(X3,stldt0(xB)) ) )
& aSet0(stldt0(xB))
& aSubsetOf0(stldt0(xA),cS1395)
& ! [X2] :
( ~ aElementOf0(X2,stldt0(xA))
| aElementOf0(X2,cS1395) )
& ! [X1] :
( ( ~ aElementOf0(X1,cS1395)
| aInteger0(X1) )
& ( ~ aInteger0(X1)
| aElementOf0(X1,cS1395) ) )
& aSet0(cS1395)
& ! [X0] :
( ( ~ aElementOf0(X0,stldt0(xA))
| ( ~ aElementOf0(X0,xA)
& aInteger0(X0) ) )
& ( aElementOf0(X0,xA)
| ~ aInteger0(X0)
| aElementOf0(X0,stldt0(xA)) ) )
& aSet0(stldt0(xA)) ),
inference(nnf_transformation,[],[f51]) ).
fof(f119,plain,
( stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB))
& ! [X10] :
( ( ~ aElementOf0(X10,stldt0(sdtbsmnsldt0(xA,xB)))
| ( aElementOf0(X10,stldt0(xB))
& aElementOf0(X10,stldt0(xA))
& aInteger0(X10) ) )
& ( ~ aElementOf0(X10,stldt0(xB))
| ~ aElementOf0(X10,stldt0(xA))
| ~ aInteger0(X10)
| aElementOf0(X10,stldt0(sdtbsmnsldt0(xA,xB))) ) )
& ! [X9] :
( ( ~ aElementOf0(X9,stldt0(xB))
| ( ~ aElementOf0(X9,xB)
& aInteger0(X9) ) )
& ( aElementOf0(X9,xB)
| ~ aInteger0(X9)
| aElementOf0(X9,stldt0(xB)) ) )
& ! [X8] :
( ( ~ aElementOf0(X8,stldt0(xA))
| ( ~ aElementOf0(X8,xA)
& aInteger0(X8) ) )
& ( aElementOf0(X8,xA)
| ~ aInteger0(X8)
| aElementOf0(X8,stldt0(xA)) ) )
& ! [X7] :
( ( ~ aElementOf0(X7,stldt0(sdtbsmnsldt0(xA,xB)))
| ( ~ aElementOf0(X7,sdtbsmnsldt0(xA,xB))
& aInteger0(X7) ) )
& ( aElementOf0(X7,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(X7)
| aElementOf0(X7,stldt0(sdtbsmnsldt0(xA,xB))) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X6] :
( ( ~ aElementOf0(X6,sdtbsmnsldt0(xA,xB))
| ( ( aElementOf0(X6,xB)
| aElementOf0(X6,xA) )
& aInteger0(X6) ) )
& ( ( ~ aElementOf0(X6,xB)
& ~ aElementOf0(X6,xA) )
| ~ aInteger0(X6)
| aElementOf0(X6,sdtbsmnsldt0(xA,xB)) ) )
& aSet0(sdtbsmnsldt0(xA,xB))
& aSubsetOf0(stldt0(xB),cS1395)
& ! [X5] :
( ~ aElementOf0(X5,stldt0(xB))
| aElementOf0(X5,cS1395) )
& ! [X4] :
( ( ~ aElementOf0(X4,cS1395)
| aInteger0(X4) )
& ( ~ aInteger0(X4)
| aElementOf0(X4,cS1395) ) )
& aSet0(cS1395)
& ! [X3] :
( ( ~ aElementOf0(X3,stldt0(xB))
| ( ~ aElementOf0(X3,xB)
& aInteger0(X3) ) )
& ( aElementOf0(X3,xB)
| ~ aInteger0(X3)
| aElementOf0(X3,stldt0(xB)) ) )
& aSet0(stldt0(xB))
& aSubsetOf0(stldt0(xA),cS1395)
& ! [X2] :
( ~ aElementOf0(X2,stldt0(xA))
| aElementOf0(X2,cS1395) )
& ! [X1] :
( ( ~ aElementOf0(X1,cS1395)
| aInteger0(X1) )
& ( ~ aInteger0(X1)
| aElementOf0(X1,cS1395) ) )
& aSet0(cS1395)
& ! [X0] :
( ( ~ aElementOf0(X0,stldt0(xA))
| ( ~ aElementOf0(X0,xA)
& aInteger0(X0) ) )
& ( aElementOf0(X0,xA)
| ~ aInteger0(X0)
| aElementOf0(X0,stldt0(xA)) ) )
& aSet0(stldt0(xA)) ),
inference(flattening,[],[f118]) ).
fof(f123,plain,
( ! [X0] :
( ( ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| ( ( aElementOf0(X0,xB)
| aElementOf0(X0,xA) )
& aInteger0(X0) ) )
& ( ( ~ aElementOf0(X0,xB)
& ~ aElementOf0(X0,xA) )
| ~ aInteger0(X0)
| aElementOf0(X0,sdtbsmnsldt0(xA,xB)) ) )
& aSet0(sdtbsmnsldt0(xA,xB))
& ~ isClosed0(sdtbsmnsldt0(xA,xB))
& ! [X1] :
( ( ~ aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB)))
| ( ~ aElementOf0(X1,sdtbsmnsldt0(xA,xB))
& aInteger0(X1) ) )
& ( aElementOf0(X1,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(X1)
| aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB))) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
& ? [X2] :
( aElementOf0(X2,stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X3] :
( ( sP2(X2,X3)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X2,X3))
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X2,X3),stldt0(sdtbsmnsldt0(xA,xB)))
& ? [X7] :
( aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X2,X3))
& ~ aElementOf0(X7,stldt0(sdtbsmnsldt0(xA,xB))) ) )
| sz00 = X3
| ~ aInteger0(X3) ) ) ),
inference(nnf_transformation,[],[f101]) ).
fof(f124,plain,
( ! [X0] :
( ( ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| ( ( aElementOf0(X0,xB)
| aElementOf0(X0,xA) )
& aInteger0(X0) ) )
& ( ( ~ aElementOf0(X0,xB)
& ~ aElementOf0(X0,xA) )
| ~ aInteger0(X0)
| aElementOf0(X0,sdtbsmnsldt0(xA,xB)) ) )
& aSet0(sdtbsmnsldt0(xA,xB))
& ~ isClosed0(sdtbsmnsldt0(xA,xB))
& ! [X1] :
( ( ~ aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB)))
| ( ~ aElementOf0(X1,sdtbsmnsldt0(xA,xB))
& aInteger0(X1) ) )
& ( aElementOf0(X1,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(X1)
| aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB))) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
& ? [X2] :
( aElementOf0(X2,stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X3] :
( ( sP2(X2,X3)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X2,X3))
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X2,X3),stldt0(sdtbsmnsldt0(xA,xB)))
& ? [X7] :
( aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X2,X3))
& ~ aElementOf0(X7,stldt0(sdtbsmnsldt0(xA,xB))) ) )
| sz00 = X3
| ~ aInteger0(X3) ) ) ),
inference(flattening,[],[f123]) ).
fof(f125,plain,
( ! [X4] :
( ( ~ aElementOf0(X4,sdtbsmnsldt0(xA,xB))
| ( ( aElementOf0(X4,xB)
| aElementOf0(X4,xA) )
& aInteger0(X4) ) )
& ( ( ~ aElementOf0(X4,xB)
& ~ aElementOf0(X4,xA) )
| ~ aInteger0(X4)
| aElementOf0(X4,sdtbsmnsldt0(xA,xB)) ) )
& aSet0(sdtbsmnsldt0(xA,xB))
& ~ isClosed0(sdtbsmnsldt0(xA,xB))
& ! [X3] :
( ( ~ aElementOf0(X3,stldt0(sdtbsmnsldt0(xA,xB)))
| ( ~ aElementOf0(X3,sdtbsmnsldt0(xA,xB))
& aInteger0(X3) ) )
& ( aElementOf0(X3,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(X3)
| aElementOf0(X3,stldt0(sdtbsmnsldt0(xA,xB))) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
& ? [X0] :
( aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X1] :
( ( sP2(X0,X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(sdtbsmnsldt0(xA,xB)))
& ? [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
& ~ aElementOf0(X2,stldt0(sdtbsmnsldt0(xA,xB))) ) )
| sz00 = X1
| ~ aInteger0(X1) ) ) ),
inference(rectify,[],[f124]) ).
fof(f126,plain,
( ! [X4] :
( ( ~ aElementOf0(X4,sdtbsmnsldt0(xA,xB))
| ( ( aElementOf0(X4,xB)
| aElementOf0(X4,xA) )
& aInteger0(X4) ) )
& ( ( ~ aElementOf0(X4,xB)
& ~ aElementOf0(X4,xA) )
| ~ aInteger0(X4)
| aElementOf0(X4,sdtbsmnsldt0(xA,xB)) ) )
& aSet0(sdtbsmnsldt0(xA,xB))
& ~ isClosed0(sdtbsmnsldt0(xA,xB))
& ! [X3] :
( ( ~ aElementOf0(X3,stldt0(sdtbsmnsldt0(xA,xB)))
| ( ~ aElementOf0(X3,sdtbsmnsldt0(xA,xB))
& aInteger0(X3) ) )
& ( aElementOf0(X3,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(X3)
| aElementOf0(X3,stldt0(sdtbsmnsldt0(xA,xB))) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
& aElementOf0(sK12,stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X1] :
( ( sP2(sK12,X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sK12,X1))
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sK12,X1),stldt0(sdtbsmnsldt0(xA,xB)))
& aElementOf0(sK13(X1),szAzrzSzezqlpdtcmdtrp0(sK12,X1))
& ~ aElementOf0(sK13(X1),stldt0(sdtbsmnsldt0(xA,xB))) )
| sz00 = X1
| ~ aInteger0(X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X0,sK12),skolemize(X2,sK13(X1))],[f125]) ).
fof(f177,plain,
isOpen0(stldt0(xB)),
inference(cnf_transformation,[],[f117]) ).
fof(f189,plain,
isOpen0(stldt0(xA)),
inference(cnf_transformation,[],[f117]) ).
fof(f212,plain,
stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB)),
inference(cnf_transformation,[],[f119]) ).
fof(f232,plain,
aSubsetOf0(stldt0(xB),cS1395),
inference(cnf_transformation,[],[f119]) ).
fof(f241,plain,
aSubsetOf0(stldt0(xA),cS1395),
inference(cnf_transformation,[],[f119]) ).
fof(f268,plain,
~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB))),
inference(cnf_transformation,[],[f126]) ).
fof(f341,plain,
! [X0,X1] :
( ~ isOpen0(X1)
| ~ isOpen0(X0)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395)
| isOpen0(sdtslmnbsdt0(X0,X1)) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_87,plain,
isOpen0(stldt0(xA)),
inference(cnf_transformation,[],[f189]) ).
tcf(c_99,plain,
isOpen0(stldt0(xB)),
inference(cnf_transformation,[],[f177]) ).
tcf(c_109,plain,
aSubsetOf0(stldt0(xA),cS1395),
inference(cnf_transformation,[],[f241]) ).
tcf(c_118,plain,
aSubsetOf0(stldt0(xB),cS1395),
inference(cnf_transformation,[],[f232]) ).
tcf(c_138,plain,
sdtslmnbsdt0(stldt0(xA),stldt0(xB)) = stldt0(sdtbsmnsldt0(xA,xB)),
inference(cnf_transformation,[],[f212]) ).
tcf(c_153,negated_conjecture,
~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB))),
inference(cnf_transformation,[],[f268]) ).
tcf(c_230,plain,
! [X0: $i,X1: $i] :
( isOpen0(sdtslmnbsdt0(X0,X1))
| ~ isOpen0(X1)
| ~ isOpen0(X0)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[],[f341]) ).
tcf(c_23755,plain,
( isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
| ~ isOpen0(stldt0(xB))
| ~ isOpen0(stldt0(xA))
| ~ aSubsetOf0(stldt0(xB),cS1395)
| ~ aSubsetOf0(stldt0(xA),cS1395) ),
inference(superposition,[status(thm)],[c_138,c_230]) ).
tcf(c_23756,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_23755,c_153,c_99,c_87,c_118,c_109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM441+6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.41 % Computer : n001.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Thu Sep 24 04:05:22 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.45 Running first-order theorem proving
% 0.13/0.45 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
% 0.13/0.47
% 0.13/0.47 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.47
% 0.13/0.47 % Detected problem language: tptp
% 0.20/0.49 % Proving...
% 5.01/2.40 % SZS status Started for theBenchmark.p
% 5.01/2.40 % SZS status Theorem for theBenchmark.p
% 5.01/2.40
% 5.01/2.40 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 5.01/2.40
% 5.01/2.40 % ------ iProver source info
% 5.01/2.40
% 5.01/2.40 % git: date: 2026-07-19 20:42:38 +0200
% 5.01/2.40 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 5.01/2.40 % git: non_committed_changes: false
% 5.01/2.40
% 5.01/2.40 % ------ Parsing...
% 5.01/2.40 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 5.01/2.40
% 5.01/2.40 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e %
% 5.01/2.40
% 5.01/2.40 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 5.01/2.40
% 5.01/2.40 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 5.01/2.40 % ------ Proving...
% 5.01/2.40 % ------ Problem Properties
% 5.01/2.40
% 5.01/2.40 %
% 5.01/2.40 % clauses 151
% 5.01/2.40 % conjectures 13
% 5.01/2.40 % EPR 27
% 5.01/2.40 % Horn 108
% 5.01/2.40 % unary 19
% 5.01/2.40 % binary 34
% 5.01/2.40 % lits 492
% 5.01/2.40 % lits eq 66
% 5.01/2.40 % fd_pure 0
% 5.01/2.40 % fd_pseudo 0
% 5.01/2.40 % fd_cond 26
% 5.01/2.40 % fd_pseudo_cond 8
% 5.01/2.40 % AC symbols 0
% 5.01/2.40
% 5.01/2.40 % ------ Schedule dynamic 5 is on
% 5.01/2.40
% 5.01/2.40 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 5.01/2.40
% 5.01/2.40
% 5.01/2.40 % ------
% 5.01/2.40 % Current options:
% 5.01/2.40 % ------
% 5.01/2.40
% 5.01/2.40
% 5.01/2.40 %
% 5.01/2.40
% 5.01/2.40 % ------ Proving...
% 5.01/2.40 %
% 5.01/2.40
% 5.01/2.40 % SZS status Theorem for theBenchmark.p
% 5.01/2.40
% 5.01/2.40 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 5.01/2.40
% 5.01/2.40
%------------------------------------------------------------------------------