%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM441+6 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n031.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 : Tue May 5 04:57:21 PM UTC 2026
% Result : Theorem 1.35s 1.75s
% Output : CNFRefutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 7 unt; 0 def)
% Number of atoms : 554 ( 42 equ)
% Maximal formula atoms : 116 ( 29 avg)
% Number of connectives : 711 ( 176 ~; 182 |; 284 &)
% ( 30 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 67 ( 18 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-2 aty)
% Number of variables : 112 ( 0 sgn 92 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__1883,hypothesis,
( aSet0(stldt0(xA))
& ! [X1] :
( aElementOf0(X1,stldt0(xA))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,xA) ) )
& aSet0(cS1395)
& ! [X1] :
( aElementOf0(X1,cS1395)
<=> aInteger0(X1) )
& ! [X1] :
( aElementOf0(X1,stldt0(xA))
=> aElementOf0(X1,cS1395) )
& aSubsetOf0(stldt0(xA),cS1395)
& aSet0(stldt0(xB))
& ! [X1] :
( aElementOf0(X1,stldt0(xB))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,xB) ) )
& aSet0(cS1395)
& ! [X1] :
( aElementOf0(X1,cS1395)
<=> aInteger0(X1) )
& ! [X1] :
( aElementOf0(X1,stldt0(xB))
=> aElementOf0(X1,cS1395) )
& aSubsetOf0(stldt0(xB),cS1395)
& aSet0(sdtbsmnsldt0(xA,xB))
& ! [X1] :
( aElementOf0(X1,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(X1)
& ( aElementOf0(X1,xA)
| aElementOf0(X1,xB) ) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X1] :
( aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sdtbsmnsldt0(xA,xB)) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(xA))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,xA) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(xB))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,xB) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(X1)
& aElementOf0(X1,stldt0(xA))
& aElementOf0(X1,stldt0(xB)) ) )
& stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1883) ).
fof(m__1826,hypothesis,
( aSet0(cS1395)
& ! [X1] :
( aElementOf0(X1,cS1395)
<=> aInteger0(X1) )
& aSet0(xA)
& ! [X1] :
( aElementOf0(X1,xA)
=> aElementOf0(X1,cS1395) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ! [X1] :
( aElementOf0(X1,cS1395)
<=> aInteger0(X1) )
& aSet0(xB)
& ! [X1] :
( aElementOf0(X1,xB)
=> aElementOf0(X1,cS1395) )
& aSubsetOf0(xB,cS1395)
& aSet0(stldt0(xA))
& ! [X1] :
( aElementOf0(X1,stldt0(xA))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,xA) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(xA))
=> ? [X2] :
( aInteger0(X2)
& X2 != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
& ( ( aInteger0(X3)
& ( ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
| sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ) )
& ! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X3,stldt0(xA)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(xA)) ) )
& isOpen0(stldt0(xA))
& isClosed0(xA)
& aSet0(stldt0(xB))
& ! [X1] :
( aElementOf0(X1,stldt0(xB))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,xB) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(xB))
=> ? [X2] :
( aInteger0(X2)
& X2 != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
& ( ( aInteger0(X3)
& ( ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
| sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ) )
& ! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X3,stldt0(xB)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(xB)) ) )
& isOpen0(stldt0(xB))
& isClosed0(xB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1826) ).
fof(m__,conjecture,
( ( aSet0(sdtbsmnsldt0(xA,xB))
& ! [X1] :
( aElementOf0(X1,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(X1)
& ( aElementOf0(X1,xA)
| aElementOf0(X1,xB) ) ) ) )
=> ( ( ( aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X1] :
( aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sdtbsmnsldt0(xA,xB)) ) ) )
=> ( ! [X1] :
( aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB)))
=> ? [X2] :
( aInteger0(X2)
& X2 != sz00
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
& ( ( aInteger0(X3)
& ( ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
| sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ) ) )
=> ( ! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X3,stldt0(sdtbsmnsldt0(xA,xB))) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(sdtbsmnsldt0(xA,xB))) ) ) ) )
| isOpen0(stldt0(sdtbsmnsldt0(xA,xB))) ) )
| isClosed0(sdtbsmnsldt0(xA,xB)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mInterOpen,axiom,
! [X1,X2] :
( ( aSubsetOf0(X1,cS1395)
& aSubsetOf0(X2,cS1395)
& isOpen0(X1)
& isOpen0(X2) )
=> isOpen0(sdtslmnbsdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mInterOpen) ).
fof(c_0_4,hypothesis,
( aSet0(stldt0(xA))
& ! [X1] :
( aElementOf0(X1,stldt0(xA))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,xA) ) )
& aSet0(cS1395)
& ! [X1] :
( aElementOf0(X1,cS1395)
<=> aInteger0(X1) )
& ! [X1] :
( aElementOf0(X1,stldt0(xA))
=> aElementOf0(X1,cS1395) )
& aSubsetOf0(stldt0(xA),cS1395)
& aSet0(stldt0(xB))
& ! [X1] :
( aElementOf0(X1,stldt0(xB))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,xB) ) )
& aSet0(cS1395)
& ! [X1] :
( aElementOf0(X1,cS1395)
<=> aInteger0(X1) )
& ! [X1] :
( aElementOf0(X1,stldt0(xB))
=> aElementOf0(X1,cS1395) )
& aSubsetOf0(stldt0(xB),cS1395)
& aSet0(sdtbsmnsldt0(xA,xB))
& ! [X1] :
( aElementOf0(X1,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(X1)
& ( aElementOf0(X1,xA)
| aElementOf0(X1,xB) ) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X1] :
( aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sdtbsmnsldt0(xA,xB)) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(xA))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,xA) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(xB))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,xB) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(X1)
& aElementOf0(X1,stldt0(xA))
& aElementOf0(X1,stldt0(xB)) ) )
& stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB)) ),
inference(fof_simplification,[status(thm)],[m__1883]) ).
fof(c_0_5,hypothesis,
( aSet0(cS1395)
& ! [X1] :
( aElementOf0(X1,cS1395)
<=> aInteger0(X1) )
& aSet0(xA)
& ! [X1] :
( aElementOf0(X1,xA)
=> aElementOf0(X1,cS1395) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ! [X1] :
( aElementOf0(X1,cS1395)
<=> aInteger0(X1) )
& aSet0(xB)
& ! [X1] :
( aElementOf0(X1,xB)
=> aElementOf0(X1,cS1395) )
& aSubsetOf0(xB,cS1395)
& aSet0(stldt0(xA))
& ! [X1] :
( aElementOf0(X1,stldt0(xA))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,xA) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(xA))
=> ? [X2] :
( aInteger0(X2)
& X2 != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
& ( ( aInteger0(X3)
& ( ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
| sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ) )
& ! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X3,stldt0(xA)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(xA)) ) )
& isOpen0(stldt0(xA))
& isClosed0(xA)
& aSet0(stldt0(xB))
& ! [X1] :
( aElementOf0(X1,stldt0(xB))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,xB) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(xB))
=> ? [X2] :
( aInteger0(X2)
& X2 != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
& ( ( aInteger0(X3)
& ( ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
| sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ) )
& ! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X3,stldt0(xB)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(xB)) ) )
& isOpen0(stldt0(xB))
& isClosed0(xB) ),
inference(fof_simplification,[status(thm)],[m__1826]) ).
fof(c_0_6,negated_conjecture,
~ ( ( aSet0(sdtbsmnsldt0(xA,xB))
& ! [X1] :
( aElementOf0(X1,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(X1)
& ( aElementOf0(X1,xA)
| aElementOf0(X1,xB) ) ) ) )
=> ( ( ( aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X1] :
( aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sdtbsmnsldt0(xA,xB)) ) ) )
=> ( ! [X1] :
( aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB)))
=> ? [X2] :
( aInteger0(X2)
& X2 != sz00
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
& ( ( aInteger0(X3)
& ( ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
| sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ) ) )
=> ( ! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X3,stldt0(sdtbsmnsldt0(xA,xB))) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(sdtbsmnsldt0(xA,xB))) ) ) ) )
| isOpen0(stldt0(sdtbsmnsldt0(xA,xB))) ) )
| isClosed0(sdtbsmnsldt0(xA,xB)) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
fof(c_0_7,plain,
! [X225,X226] :
( ~ aSubsetOf0(X225,cS1395)
| ~ aSubsetOf0(X226,cS1395)
| ~ isOpen0(X225)
| ~ isOpen0(X226)
| isOpen0(sdtslmnbsdt0(X225,X226)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mInterOpen])]) ).
fof(c_0_8,hypothesis,
! [X247,X248,X249,X250,X251,X252,X253,X254,X255,X256,X257] :
( aSet0(stldt0(xA))
& ( aInteger0(X247)
| ~ aElementOf0(X247,stldt0(xA)) )
& ( ~ aElementOf0(X247,xA)
| ~ aElementOf0(X247,stldt0(xA)) )
& ( ~ aInteger0(X247)
| aElementOf0(X247,xA)
| aElementOf0(X247,stldt0(xA)) )
& aSet0(cS1395)
& ( ~ aElementOf0(X248,cS1395)
| aInteger0(X248) )
& ( ~ aInteger0(X248)
| aElementOf0(X248,cS1395) )
& ( ~ aElementOf0(X249,stldt0(xA))
| aElementOf0(X249,cS1395) )
& aSubsetOf0(stldt0(xA),cS1395)
& aSet0(stldt0(xB))
& ( aInteger0(X250)
| ~ aElementOf0(X250,stldt0(xB)) )
& ( ~ aElementOf0(X250,xB)
| ~ aElementOf0(X250,stldt0(xB)) )
& ( ~ aInteger0(X250)
| aElementOf0(X250,xB)
| aElementOf0(X250,stldt0(xB)) )
& aSet0(cS1395)
& ( ~ aElementOf0(X251,cS1395)
| aInteger0(X251) )
& ( ~ aInteger0(X251)
| aElementOf0(X251,cS1395) )
& ( ~ aElementOf0(X252,stldt0(xB))
| aElementOf0(X252,cS1395) )
& aSubsetOf0(stldt0(xB),cS1395)
& aSet0(sdtbsmnsldt0(xA,xB))
& ( aInteger0(X253)
| ~ aElementOf0(X253,sdtbsmnsldt0(xA,xB)) )
& ( aElementOf0(X253,xA)
| aElementOf0(X253,xB)
| ~ aElementOf0(X253,sdtbsmnsldt0(xA,xB)) )
& ( ~ aElementOf0(X253,xA)
| ~ aInteger0(X253)
| aElementOf0(X253,sdtbsmnsldt0(xA,xB)) )
& ( ~ aElementOf0(X253,xB)
| ~ aInteger0(X253)
| aElementOf0(X253,sdtbsmnsldt0(xA,xB)) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ( aInteger0(X254)
| ~ aElementOf0(X254,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( ~ aElementOf0(X254,sdtbsmnsldt0(xA,xB))
| ~ aElementOf0(X254,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( ~ aInteger0(X254)
| aElementOf0(X254,sdtbsmnsldt0(xA,xB))
| aElementOf0(X254,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( aInteger0(X255)
| ~ aElementOf0(X255,stldt0(xA)) )
& ( ~ aElementOf0(X255,xA)
| ~ aElementOf0(X255,stldt0(xA)) )
& ( ~ aInteger0(X255)
| aElementOf0(X255,xA)
| aElementOf0(X255,stldt0(xA)) )
& ( aInteger0(X256)
| ~ aElementOf0(X256,stldt0(xB)) )
& ( ~ aElementOf0(X256,xB)
| ~ aElementOf0(X256,stldt0(xB)) )
& ( ~ aInteger0(X256)
| aElementOf0(X256,xB)
| aElementOf0(X256,stldt0(xB)) )
& ( aInteger0(X257)
| ~ aElementOf0(X257,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( aElementOf0(X257,stldt0(xA))
| ~ aElementOf0(X257,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( aElementOf0(X257,stldt0(xB))
| ~ aElementOf0(X257,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( ~ aInteger0(X257)
| ~ aElementOf0(X257,stldt0(xA))
| ~ aElementOf0(X257,stldt0(xB))
| aElementOf0(X257,stldt0(sdtbsmnsldt0(xA,xB))) )
& stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB)) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_9,hypothesis,
! [X227,X228,X229,X230,X231,X232,X234,X236,X237,X238,X239,X240,X242,X244,X245,X246] :
( aSet0(cS1395)
& ( ~ aElementOf0(X227,cS1395)
| aInteger0(X227) )
& ( ~ aInteger0(X227)
| aElementOf0(X227,cS1395) )
& aSet0(xA)
& ( ~ aElementOf0(X228,xA)
| aElementOf0(X228,cS1395) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ( ~ aElementOf0(X229,cS1395)
| aInteger0(X229) )
& ( ~ aInteger0(X229)
| aElementOf0(X229,cS1395) )
& aSet0(xB)
& ( ~ aElementOf0(X230,xB)
| aElementOf0(X230,cS1395) )
& aSubsetOf0(xB,cS1395)
& aSet0(stldt0(xA))
& ( aInteger0(X231)
| ~ aElementOf0(X231,stldt0(xA)) )
& ( ~ aElementOf0(X231,xA)
| ~ aElementOf0(X231,stldt0(xA)) )
& ( ~ aInteger0(X231)
| aElementOf0(X231,xA)
| aElementOf0(X231,stldt0(xA)) )
& ( aInteger0(esk15_1(X232))
| ~ aElementOf0(X232,stldt0(xA)) )
& ( esk15_1(X232) != sz00
| ~ aElementOf0(X232,stldt0(xA)) )
& ( aSet0(szAzrzSzezqlpdtcmdtrp0(X232,esk15_1(X232)))
| ~ aElementOf0(X232,stldt0(xA)) )
& ( aInteger0(X234)
| ~ aElementOf0(X234,szAzrzSzezqlpdtcmdtrp0(X232,esk15_1(X232)))
| ~ aElementOf0(X232,stldt0(xA)) )
& ( aInteger0(esk16_2(X232,X234))
| ~ aElementOf0(X234,szAzrzSzezqlpdtcmdtrp0(X232,esk15_1(X232)))
| ~ aElementOf0(X232,stldt0(xA)) )
& ( sdtasdt0(esk15_1(X232),esk16_2(X232,X234)) = sdtpldt0(X234,smndt0(X232))
| ~ aElementOf0(X234,szAzrzSzezqlpdtcmdtrp0(X232,esk15_1(X232)))
| ~ aElementOf0(X232,stldt0(xA)) )
& ( aDivisorOf0(esk15_1(X232),sdtpldt0(X234,smndt0(X232)))
| ~ aElementOf0(X234,szAzrzSzezqlpdtcmdtrp0(X232,esk15_1(X232)))
| ~ aElementOf0(X232,stldt0(xA)) )
& ( sdteqdtlpzmzozddtrp0(X234,X232,esk15_1(X232))
| ~ aElementOf0(X234,szAzrzSzezqlpdtcmdtrp0(X232,esk15_1(X232)))
| ~ aElementOf0(X232,stldt0(xA)) )
& ( ~ aInteger0(X237)
| sdtasdt0(esk15_1(X232),X237) != sdtpldt0(X236,smndt0(X232))
| ~ aInteger0(X236)
| aElementOf0(X236,szAzrzSzezqlpdtcmdtrp0(X232,esk15_1(X232)))
| ~ aElementOf0(X232,stldt0(xA)) )
& ( ~ aDivisorOf0(esk15_1(X232),sdtpldt0(X236,smndt0(X232)))
| ~ aInteger0(X236)
| aElementOf0(X236,szAzrzSzezqlpdtcmdtrp0(X232,esk15_1(X232)))
| ~ aElementOf0(X232,stldt0(xA)) )
& ( ~ sdteqdtlpzmzozddtrp0(X236,X232,esk15_1(X232))
| ~ aInteger0(X236)
| aElementOf0(X236,szAzrzSzezqlpdtcmdtrp0(X232,esk15_1(X232)))
| ~ aElementOf0(X232,stldt0(xA)) )
& ( ~ aElementOf0(X238,szAzrzSzezqlpdtcmdtrp0(X232,esk15_1(X232)))
| aElementOf0(X238,stldt0(xA))
| ~ aElementOf0(X232,stldt0(xA)) )
& ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X232,esk15_1(X232)),stldt0(xA))
| ~ aElementOf0(X232,stldt0(xA)) )
& isOpen0(stldt0(xA))
& isClosed0(xA)
& aSet0(stldt0(xB))
& ( aInteger0(X239)
| ~ aElementOf0(X239,stldt0(xB)) )
& ( ~ aElementOf0(X239,xB)
| ~ aElementOf0(X239,stldt0(xB)) )
& ( ~ aInteger0(X239)
| aElementOf0(X239,xB)
| aElementOf0(X239,stldt0(xB)) )
& ( aInteger0(esk17_1(X240))
| ~ aElementOf0(X240,stldt0(xB)) )
& ( esk17_1(X240) != sz00
| ~ aElementOf0(X240,stldt0(xB)) )
& ( aSet0(szAzrzSzezqlpdtcmdtrp0(X240,esk17_1(X240)))
| ~ aElementOf0(X240,stldt0(xB)) )
& ( aInteger0(X242)
| ~ aElementOf0(X242,szAzrzSzezqlpdtcmdtrp0(X240,esk17_1(X240)))
| ~ aElementOf0(X240,stldt0(xB)) )
& ( aInteger0(esk18_2(X240,X242))
| ~ aElementOf0(X242,szAzrzSzezqlpdtcmdtrp0(X240,esk17_1(X240)))
| ~ aElementOf0(X240,stldt0(xB)) )
& ( sdtasdt0(esk17_1(X240),esk18_2(X240,X242)) = sdtpldt0(X242,smndt0(X240))
| ~ aElementOf0(X242,szAzrzSzezqlpdtcmdtrp0(X240,esk17_1(X240)))
| ~ aElementOf0(X240,stldt0(xB)) )
& ( aDivisorOf0(esk17_1(X240),sdtpldt0(X242,smndt0(X240)))
| ~ aElementOf0(X242,szAzrzSzezqlpdtcmdtrp0(X240,esk17_1(X240)))
| ~ aElementOf0(X240,stldt0(xB)) )
& ( sdteqdtlpzmzozddtrp0(X242,X240,esk17_1(X240))
| ~ aElementOf0(X242,szAzrzSzezqlpdtcmdtrp0(X240,esk17_1(X240)))
| ~ aElementOf0(X240,stldt0(xB)) )
& ( ~ aInteger0(X245)
| sdtasdt0(esk17_1(X240),X245) != sdtpldt0(X244,smndt0(X240))
| ~ aInteger0(X244)
| aElementOf0(X244,szAzrzSzezqlpdtcmdtrp0(X240,esk17_1(X240)))
| ~ aElementOf0(X240,stldt0(xB)) )
& ( ~ aDivisorOf0(esk17_1(X240),sdtpldt0(X244,smndt0(X240)))
| ~ aInteger0(X244)
| aElementOf0(X244,szAzrzSzezqlpdtcmdtrp0(X240,esk17_1(X240)))
| ~ aElementOf0(X240,stldt0(xB)) )
& ( ~ sdteqdtlpzmzozddtrp0(X244,X240,esk17_1(X240))
| ~ aInteger0(X244)
| aElementOf0(X244,szAzrzSzezqlpdtcmdtrp0(X240,esk17_1(X240)))
| ~ aElementOf0(X240,stldt0(xB)) )
& ( ~ aElementOf0(X246,szAzrzSzezqlpdtcmdtrp0(X240,esk17_1(X240)))
| aElementOf0(X246,stldt0(xB))
| ~ aElementOf0(X240,stldt0(xB)) )
& ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X240,esk17_1(X240)),stldt0(xB))
| ~ aElementOf0(X240,stldt0(xB)) )
& isOpen0(stldt0(xB))
& isClosed0(xB) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])])]) ).
fof(c_0_10,negated_conjecture,
! [X258,X259,X261,X262,X264] :
( aSet0(sdtbsmnsldt0(xA,xB))
& ( aInteger0(X258)
| ~ aElementOf0(X258,sdtbsmnsldt0(xA,xB)) )
& ( aElementOf0(X258,xA)
| aElementOf0(X258,xB)
| ~ aElementOf0(X258,sdtbsmnsldt0(xA,xB)) )
& ( ~ aElementOf0(X258,xA)
| ~ aInteger0(X258)
| aElementOf0(X258,sdtbsmnsldt0(xA,xB)) )
& ( ~ aElementOf0(X258,xB)
| ~ aInteger0(X258)
| aElementOf0(X258,sdtbsmnsldt0(xA,xB)) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ( aInteger0(X259)
| ~ aElementOf0(X259,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( ~ aElementOf0(X259,sdtbsmnsldt0(xA,xB))
| ~ aElementOf0(X259,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( ~ aInteger0(X259)
| aElementOf0(X259,sdtbsmnsldt0(xA,xB))
| aElementOf0(X259,stldt0(sdtbsmnsldt0(xA,xB))) )
& aElementOf0(esk19_0,stldt0(sdtbsmnsldt0(xA,xB)))
& ( aSet0(szAzrzSzezqlpdtcmdtrp0(esk19_0,X261))
| ~ aInteger0(X261)
| X261 = sz00 )
& ( aInteger0(X262)
| ~ aElementOf0(X262,szAzrzSzezqlpdtcmdtrp0(esk19_0,X261))
| ~ aInteger0(X261)
| X261 = sz00 )
& ( aInteger0(esk20_2(X261,X262))
| ~ aElementOf0(X262,szAzrzSzezqlpdtcmdtrp0(esk19_0,X261))
| ~ aInteger0(X261)
| X261 = sz00 )
& ( sdtasdt0(X261,esk20_2(X261,X262)) = sdtpldt0(X262,smndt0(esk19_0))
| ~ aElementOf0(X262,szAzrzSzezqlpdtcmdtrp0(esk19_0,X261))
| ~ aInteger0(X261)
| X261 = sz00 )
& ( aDivisorOf0(X261,sdtpldt0(X262,smndt0(esk19_0)))
| ~ aElementOf0(X262,szAzrzSzezqlpdtcmdtrp0(esk19_0,X261))
| ~ aInteger0(X261)
| X261 = sz00 )
& ( sdteqdtlpzmzozddtrp0(X262,esk19_0,X261)
| ~ aElementOf0(X262,szAzrzSzezqlpdtcmdtrp0(esk19_0,X261))
| ~ aInteger0(X261)
| X261 = sz00 )
& ( ~ aInteger0(X264)
| sdtasdt0(X261,X264) != sdtpldt0(X262,smndt0(esk19_0))
| ~ aInteger0(X262)
| aElementOf0(X262,szAzrzSzezqlpdtcmdtrp0(esk19_0,X261))
| ~ aInteger0(X261)
| X261 = sz00 )
& ( ~ aDivisorOf0(X261,sdtpldt0(X262,smndt0(esk19_0)))
| ~ aInteger0(X262)
| aElementOf0(X262,szAzrzSzezqlpdtcmdtrp0(esk19_0,X261))
| ~ aInteger0(X261)
| X261 = sz00 )
& ( ~ sdteqdtlpzmzozddtrp0(X262,esk19_0,X261)
| ~ aInteger0(X262)
| aElementOf0(X262,szAzrzSzezqlpdtcmdtrp0(esk19_0,X261))
| ~ aInteger0(X261)
| X261 = sz00 )
& ( aElementOf0(esk21_1(X261),szAzrzSzezqlpdtcmdtrp0(esk19_0,X261))
| ~ aInteger0(X261)
| X261 = sz00 )
& ( ~ aElementOf0(esk21_1(X261),stldt0(sdtbsmnsldt0(xA,xB)))
| ~ aInteger0(X261)
| X261 = sz00 )
& ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(esk19_0,X261),stldt0(sdtbsmnsldt0(xA,xB)))
| ~ aInteger0(X261)
| X261 = sz00 )
& ~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
& ~ isClosed0(sdtbsmnsldt0(xA,xB)) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])]) ).
cnf(c_0_11,plain,
( isOpen0(sdtslmnbsdt0(X1,X2))
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X2,cS1395)
| ~ isOpen0(X1)
| ~ isOpen0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,hypothesis,
stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,hypothesis,
isOpen0(stldt0(xB)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,hypothesis,
isOpen0(stldt0(xA)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,hypothesis,
aSubsetOf0(stldt0(xB),cS1395),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,hypothesis,
aSubsetOf0(stldt0(xA),cS1395),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB))),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14]),c_0_15]),c_0_16])]),c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM441+6 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.34 % Computer : n031.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 00:36:53 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.35/1.75 % Version : CSE_E---1.7
% 1.35/1.75 % Problem : theBenchmark.p
% 1.35/1.75 % SZS status Theorem for theBenchmark.p
% 1.35/1.75 % SZS output start CNFRefutation
% See solution above
% 1.35/1.75 % Total time : 1.372s
%------------------------------------------------------------------------------