%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM449+6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 : Thu Sep 24 01:49:07 PM UTC 2026
% Result : Theorem 0.15s 0.52s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 11 unt; 0 def)
% Number of atoms : 405 ( 71 equ)
% Maximal formula atoms : 102 ( 12 avg)
% Number of connectives : 510 ( 137 ~; 177 |; 151 &)
% ( 6 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 40 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-3 aty)
% Number of variables : 79 ( 0 sgn 46 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( ? [X2] :
( aElementOf0(X1,X2)
& aElementOf0(X2,xS) )
& aInteger0(X1) ) )
& aSet0(sbsmnsldt0(xS)) )
=> ( isClosed0(sbsmnsldt0(xS))
| ( ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X1,sbsmnsldt0(xS))
& aInteger0(X1) ) )
=> ( isOpen0(stldt0(sbsmnsldt0(xS)))
| ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
=> ? [X2] :
( ( ( ! [X3] :
( ( ( ( sdteqdtlpzmzozddtrp0(X3,X1,X2)
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
| ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1))
& aInteger0(X4) ) )
& aInteger0(X3) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) )
& ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> ( sdteqdtlpzmzozddtrp0(X3,X1,X2)
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1))
& aInteger0(X4) )
& aInteger0(X3) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2)) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(sbsmnsldt0(xS)))
| ! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X3,stldt0(sbsmnsldt0(xS))) ) ) )
& X2 != sz00
& aInteger0(X2) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__2046,hypothesis,
( xS = cS2043
& ! [X1] :
( ( ? [X2] :
( ( ( ! [X3] :
( ( ( ( sdteqdtlpzmzozddtrp0(X3,sz00,X2)
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
| ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00))
& aInteger0(X4) ) )
& aInteger0(X3) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2)) )
& ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2))
=> ( sdteqdtlpzmzozddtrp0(X3,sz00,X2)
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
& ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00))
& aInteger0(X4) )
& aInteger0(X3) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2)) )
=> szAzrzSzezqlpdtcmdtrp0(sz00,X2) = X1 )
& isPrime0(X2)
& X2 != sz00
& aInteger0(X2) )
=> aElementOf0(X1,xS) )
& ( aElementOf0(X1,xS)
=> ? [X2] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X2) = X1
& ! [X3] :
( ( ( ( sdteqdtlpzmzozddtrp0(X3,sz00,X2)
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
| ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00))
& aInteger0(X4) ) )
& aInteger0(X3) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2)) )
& ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2))
=> ( sdteqdtlpzmzozddtrp0(X3,sz00,X2)
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
& ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00))
& aInteger0(X4) )
& aInteger0(X3) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
& isPrime0(X2)
& X2 != sz00
& aInteger0(X2) ) ) )
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2046) ).
fof(mUnionSClosed,axiom,
! [X1] :
( ( ! [X2] :
( aElementOf0(X2,X1)
=> ( isClosed0(X2)
& aSubsetOf0(X2,cS1395) ) )
& isFinite0(X1)
& aSet0(X1) )
=> isClosed0(sbsmnsldt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mUnionSClosed) ).
fof(mArSeqClosed,axiom,
! [X1,X2] :
( ( X2 != sz00
& aInteger0(X2)
& aInteger0(X1) )
=> ( isClosed0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),cS1395) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mArSeqClosed) ).
fof(m__2117,hypothesis,
isFinite0(xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2117) ).
fof(mIntZero,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).
fof(c_0_6,negated_conjecture,
~ ( ( ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( ? [X2] :
( aElementOf0(X1,X2)
& aElementOf0(X2,xS) )
& aInteger0(X1) ) )
& aSet0(sbsmnsldt0(xS)) )
=> ( isClosed0(sbsmnsldt0(xS))
| ( ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X1,sbsmnsldt0(xS))
& aInteger0(X1) ) )
=> ( isOpen0(stldt0(sbsmnsldt0(xS)))
| ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
=> ? [X2] :
( ( ( ! [X3] :
( ( ( ( sdteqdtlpzmzozddtrp0(X3,X1,X2)
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
| ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1))
& aInteger0(X4) ) )
& aInteger0(X3) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) )
& ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> ( sdteqdtlpzmzozddtrp0(X3,X1,X2)
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1))
& aInteger0(X4) )
& aInteger0(X3) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2)) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(sbsmnsldt0(xS)))
| ! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X3,stldt0(sbsmnsldt0(xS))) ) ) )
& X2 != sz00
& aInteger0(X2) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_7,negated_conjecture,
~ ( ( ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( ? [X2] :
( aElementOf0(X1,X2)
& aElementOf0(X2,xS) )
& aInteger0(X1) ) )
& aSet0(sbsmnsldt0(xS)) )
=> ( isClosed0(sbsmnsldt0(xS))
| ( ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X1,sbsmnsldt0(xS))
& aInteger0(X1) ) )
=> ( isOpen0(stldt0(sbsmnsldt0(xS)))
| ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
=> ? [X2] :
( ( ( ! [X3] :
( ( ( ( sdteqdtlpzmzozddtrp0(X3,X1,X2)
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
| ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1))
& aInteger0(X4) ) )
& aInteger0(X3) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) )
& ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> ( sdteqdtlpzmzozddtrp0(X3,X1,X2)
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1))
& aInteger0(X4) )
& aInteger0(X3) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2)) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(sbsmnsldt0(xS)))
| ! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X3,stldt0(sbsmnsldt0(xS))) ) ) )
& X2 != sz00
& aInteger0(X2) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_8,hypothesis,
( xS = cS2043
& ! [X1] :
( ( ? [X2] :
( ( ( ! [X3] :
( ( ( ( sdteqdtlpzmzozddtrp0(X3,sz00,X2)
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
| ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00))
& aInteger0(X4) ) )
& aInteger0(X3) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2)) )
& ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2))
=> ( sdteqdtlpzmzozddtrp0(X3,sz00,X2)
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
& ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00))
& aInteger0(X4) )
& aInteger0(X3) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2)) )
=> szAzrzSzezqlpdtcmdtrp0(sz00,X2) = X1 )
& isPrime0(X2)
& X2 != sz00
& aInteger0(X2) )
=> aElementOf0(X1,xS) )
& ( aElementOf0(X1,xS)
=> ? [X2] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X2) = X1
& ! [X3] :
( ( ( ( sdteqdtlpzmzozddtrp0(X3,sz00,X2)
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
| ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00))
& aInteger0(X4) ) )
& aInteger0(X3) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2)) )
& ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2))
=> ( sdteqdtlpzmzozddtrp0(X3,sz00,X2)
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
& ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00))
& aInteger0(X4) )
& aInteger0(X3) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
& isPrime0(X2)
& X2 != sz00
& aInteger0(X2) ) ) )
& aSet0(xS) ),
inference(fof_simplification,[status(thm)],[m__2046]) ).
fof(c_0_9,negated_conjecture,
! [X137,X139,X140,X141,X143,X144,X146] :
( ~ isClosed0(sbsmnsldt0(xS))
& ~ isOpen0(stldt0(sbsmnsldt0(xS)))
& ( X143 = sz00
| ~ aInteger0(X143)
| ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(esk21_0,X143),stldt0(sbsmnsldt0(xS))) )
& ( X143 = sz00
| ~ aInteger0(X143)
| ~ aElementOf0(esk23_1(X143),stldt0(sbsmnsldt0(xS))) )
& ( X143 = sz00
| ~ aInteger0(X143)
| aElementOf0(esk23_1(X143),szAzrzSzezqlpdtcmdtrp0(esk21_0,X143)) )
& ( X143 = sz00
| ~ aInteger0(X143)
| aElementOf0(X144,szAzrzSzezqlpdtcmdtrp0(esk21_0,X143))
| ~ aInteger0(X144)
| ~ sdteqdtlpzmzozddtrp0(X144,esk21_0,X143) )
& ( X143 = sz00
| ~ aInteger0(X143)
| aElementOf0(X144,szAzrzSzezqlpdtcmdtrp0(esk21_0,X143))
| ~ aInteger0(X144)
| ~ aDivisorOf0(X143,sdtpldt0(X144,smndt0(esk21_0))) )
& ( X143 = sz00
| ~ aInteger0(X143)
| aElementOf0(X144,szAzrzSzezqlpdtcmdtrp0(esk21_0,X143))
| ~ aInteger0(X144)
| sdtasdt0(X143,X146) != sdtpldt0(X144,smndt0(esk21_0))
| ~ aInteger0(X146) )
& ( X143 = sz00
| ~ aInteger0(X143)
| ~ aElementOf0(X144,szAzrzSzezqlpdtcmdtrp0(esk21_0,X143))
| sdteqdtlpzmzozddtrp0(X144,esk21_0,X143) )
& ( X143 = sz00
| ~ aInteger0(X143)
| ~ aElementOf0(X144,szAzrzSzezqlpdtcmdtrp0(esk21_0,X143))
| aDivisorOf0(X143,sdtpldt0(X144,smndt0(esk21_0))) )
& ( X143 = sz00
| ~ aInteger0(X143)
| ~ aElementOf0(X144,szAzrzSzezqlpdtcmdtrp0(esk21_0,X143))
| sdtasdt0(X143,esk22_2(X143,X144)) = sdtpldt0(X144,smndt0(esk21_0)) )
& ( X143 = sz00
| ~ aInteger0(X143)
| ~ aElementOf0(X144,szAzrzSzezqlpdtcmdtrp0(esk21_0,X143))
| aInteger0(esk22_2(X143,X144)) )
& ( X143 = sz00
| ~ aInteger0(X143)
| ~ aElementOf0(X144,szAzrzSzezqlpdtcmdtrp0(esk21_0,X143))
| aInteger0(X144) )
& ( X143 = sz00
| ~ aInteger0(X143)
| aSet0(szAzrzSzezqlpdtcmdtrp0(esk21_0,X143)) )
& aElementOf0(esk21_0,stldt0(sbsmnsldt0(xS)))
& ( aElementOf0(X141,stldt0(sbsmnsldt0(xS)))
| aElementOf0(X141,sbsmnsldt0(xS))
| ~ aInteger0(X141) )
& ( ~ aElementOf0(X141,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X141,sbsmnsldt0(xS)) )
& ( ~ aElementOf0(X141,stldt0(sbsmnsldt0(xS)))
| aInteger0(X141) )
& ( aElementOf0(X139,sbsmnsldt0(xS))
| ~ aElementOf0(X139,X140)
| ~ aElementOf0(X140,xS)
| ~ aInteger0(X139) )
& ( ~ aElementOf0(X137,sbsmnsldt0(xS))
| aElementOf0(X137,esk20_1(X137)) )
& ( ~ aElementOf0(X137,sbsmnsldt0(xS))
| aElementOf0(esk20_1(X137),xS) )
& ( ~ aElementOf0(X137,sbsmnsldt0(xS))
| aInteger0(X137) )
& aSet0(sbsmnsldt0(xS)) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_7])])])])])])]) ).
fof(c_0_10,plain,
! [X115] :
( ( isClosed0(sbsmnsldt0(X115))
| ~ isFinite0(X115)
| ~ aSet0(X115)
| ~ isClosed0(esk15_1(X115))
| ~ aSubsetOf0(esk15_1(X115),cS1395) )
& ( isClosed0(sbsmnsldt0(X115))
| ~ isFinite0(X115)
| ~ aSet0(X115)
| aElementOf0(esk15_1(X115),X115) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mUnionSClosed])])])])]) ).
fof(c_0_11,hypothesis,
! [X119,X121,X123,X124,X125,X126,X127,X129,X130] :
( xS = cS2043
& ( aElementOf0(X125,xS)
| ~ isPrime0(X126)
| X126 = sz00
| ~ aInteger0(X126)
| szAzrzSzezqlpdtcmdtrp0(sz00,X126) != X125 )
& ( aElementOf0(X125,xS)
| ~ isPrime0(X126)
| X126 = sz00
| ~ aInteger0(X126)
| aElementOf0(X129,szAzrzSzezqlpdtcmdtrp0(sz00,X126))
| ~ aInteger0(X129)
| ~ sdteqdtlpzmzozddtrp0(X129,sz00,X126) )
& ( aElementOf0(X125,xS)
| ~ isPrime0(X126)
| X126 = sz00
| ~ aInteger0(X126)
| aElementOf0(X129,szAzrzSzezqlpdtcmdtrp0(sz00,X126))
| ~ aInteger0(X129)
| ~ aDivisorOf0(X126,sdtpldt0(X129,smndt0(sz00))) )
& ( aElementOf0(X125,xS)
| ~ isPrime0(X126)
| X126 = sz00
| ~ aInteger0(X126)
| aElementOf0(X129,szAzrzSzezqlpdtcmdtrp0(sz00,X126))
| ~ aInteger0(X129)
| sdtasdt0(X126,X130) != sdtpldt0(X129,smndt0(sz00))
| ~ aInteger0(X130) )
& ( aElementOf0(X125,xS)
| ~ isPrime0(X126)
| X126 = sz00
| ~ aInteger0(X126)
| ~ aElementOf0(X127,szAzrzSzezqlpdtcmdtrp0(sz00,X126))
| sdteqdtlpzmzozddtrp0(X127,sz00,X126) )
& ( aElementOf0(X125,xS)
| ~ isPrime0(X126)
| X126 = sz00
| ~ aInteger0(X126)
| ~ aElementOf0(X127,szAzrzSzezqlpdtcmdtrp0(sz00,X126))
| aDivisorOf0(X126,sdtpldt0(X127,smndt0(sz00))) )
& ( aElementOf0(X125,xS)
| ~ isPrime0(X126)
| X126 = sz00
| ~ aInteger0(X126)
| ~ aElementOf0(X127,szAzrzSzezqlpdtcmdtrp0(sz00,X126))
| sdtasdt0(X126,esk18_3(X125,X126,X127)) = sdtpldt0(X127,smndt0(sz00)) )
& ( aElementOf0(X125,xS)
| ~ isPrime0(X126)
| X126 = sz00
| ~ aInteger0(X126)
| ~ aElementOf0(X127,szAzrzSzezqlpdtcmdtrp0(sz00,X126))
| aInteger0(esk18_3(X125,X126,X127)) )
& ( aElementOf0(X125,xS)
| ~ isPrime0(X126)
| X126 = sz00
| ~ aInteger0(X126)
| ~ aElementOf0(X127,szAzrzSzezqlpdtcmdtrp0(sz00,X126))
| aInteger0(X127) )
& ( aElementOf0(X125,xS)
| ~ isPrime0(X126)
| X126 = sz00
| ~ aInteger0(X126)
| aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X126)) )
& ( ~ aElementOf0(X119,xS)
| szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X119)) = X119 )
& ( ~ aElementOf0(X119,xS)
| aElementOf0(X123,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X119)))
| ~ aInteger0(X123)
| ~ sdteqdtlpzmzozddtrp0(X123,sz00,esk16_1(X119)) )
& ( ~ aElementOf0(X119,xS)
| aElementOf0(X123,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X119)))
| ~ aInteger0(X123)
| ~ aDivisorOf0(esk16_1(X119),sdtpldt0(X123,smndt0(sz00))) )
& ( ~ aElementOf0(X119,xS)
| aElementOf0(X123,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X119)))
| ~ aInteger0(X123)
| sdtasdt0(esk16_1(X119),X124) != sdtpldt0(X123,smndt0(sz00))
| ~ aInteger0(X124) )
& ( ~ aElementOf0(X119,xS)
| ~ aElementOf0(X121,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X119)))
| sdteqdtlpzmzozddtrp0(X121,sz00,esk16_1(X119)) )
& ( ~ aElementOf0(X119,xS)
| ~ aElementOf0(X121,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X119)))
| aDivisorOf0(esk16_1(X119),sdtpldt0(X121,smndt0(sz00))) )
& ( ~ aElementOf0(X119,xS)
| ~ aElementOf0(X121,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X119)))
| sdtasdt0(esk16_1(X119),esk17_2(X119,X121)) = sdtpldt0(X121,smndt0(sz00)) )
& ( ~ aElementOf0(X119,xS)
| ~ aElementOf0(X121,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X119)))
| aInteger0(esk17_2(X119,X121)) )
& ( ~ aElementOf0(X119,xS)
| ~ aElementOf0(X121,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X119)))
| aInteger0(X121) )
& ( ~ aElementOf0(X119,xS)
| aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X119))) )
& ( ~ aElementOf0(X119,xS)
| isPrime0(esk16_1(X119)) )
& ( ~ aElementOf0(X119,xS)
| esk16_1(X119) != sz00 )
& ( ~ aElementOf0(X119,xS)
| aInteger0(esk16_1(X119)) )
& aSet0(xS) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_8])])])])])])]) ).
fof(c_0_12,plain,
! [X1,X2] :
( ( X2 != sz00
& aInteger0(X2)
& aInteger0(X1) )
=> ( isClosed0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),cS1395) ) ),
inference(fof_simplification,[status(thm)],[mArSeqClosed]) ).
cnf(c_0_13,negated_conjecture,
~ isClosed0(sbsmnsldt0(xS)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( ~ isFinite0(X1)
| ~ aSet0(X1)
| isClosed0(sbsmnsldt0(X1))
| aElementOf0(esk15_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,hypothesis,
isFinite0(xS),
inference(split_conjunct,[status(thm)],[m__2117]) ).
cnf(c_0_16,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,plain,
! [X117,X118] :
( ( X118 = sz00
| ~ aInteger0(X118)
| ~ aInteger0(X117)
| isClosed0(szAzrzSzezqlpdtcmdtrp0(X117,X118)) )
& ( X118 = sz00
| ~ aInteger0(X118)
| ~ aInteger0(X117)
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X117,X118),cS1395) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).
cnf(c_0_18,hypothesis,
( ~ aElementOf0(X1,xS)
| szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,negated_conjecture,
aElementOf0(esk15_1(xS),xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16])]) ).
cnf(c_0_20,hypothesis,
( ~ aElementOf0(X1,xS)
| aInteger0(esk16_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| X2 = sz00
| isClosed0(szAzrzSzezqlpdtcmdtrp0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,hypothesis,
szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(esk15_1(xS))) = esk15_1(xS),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,hypothesis,
aInteger0(esk16_1(esk15_1(xS))),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_24,plain,
aInteger0(sz00),
inference(split_conjunct,[status(thm)],[mIntZero]) ).
cnf(c_0_25,plain,
( ~ isFinite0(X1)
| ~ aSet0(X1)
| ~ isClosed0(esk15_1(X1))
| ~ aSubsetOf0(esk15_1(X1),cS1395)
| isClosed0(sbsmnsldt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_26,hypothesis,
( isClosed0(esk15_1(xS))
| esk16_1(esk15_1(xS)) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_24])]) ).
cnf(c_0_27,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| X2 = sz00
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),cS1395) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_28,hypothesis,
( ~ aSubsetOf0(esk15_1(xS),cS1395)
| esk16_1(esk15_1(xS)) = sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_15]),c_0_16])]),c_0_13]) ).
cnf(c_0_29,hypothesis,
( ~ aElementOf0(X1,xS)
| esk16_1(X1) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_30,hypothesis,
esk16_1(esk15_1(xS)) = sz00,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_22]),c_0_23]),c_0_24])]),c_0_28]) ).
cnf(c_0_31,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM449+6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n003.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 02:32:01 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.43 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.52 % Version: 3.5.1
% 0.15/0.52 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.52 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.52 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.52 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.52 % Starting sh5l with 300s (1) cores
% 0.15/0.52 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 3212254 completed with status 0
% 0.15/0.52 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.15/0.52 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.52 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.52 % No SInE strategy applied
% 0.15/0.52 % Search class: FGHSF-FSLM31-SFFFFFNN
% 0.15/0.52 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.52 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.52 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.15/0.52 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 198s (1) cores
% 0.15/0.52 % Starting new_bool_3 with 194s (1) cores
% 0.15/0.52 % Starting new_bool_1 with 188s (1) cores
% 0.15/0.52 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 3212271 completed with status 0
% 0.15/0.52 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.15/0.52 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.52 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.52 % No SInE strategy applied
% 0.15/0.52 % Search class: FGHSF-FSLM31-SFFFFFNN
% 0.15/0.52 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.52 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.52 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.15/0.52 % Preprocessing time : 0.004 s
% 0.15/0.52 % Presaturation interreduction done
% 0.15/0.52
% 0.15/0.52 % Proof found!
% 0.15/0.52 % SZS status Theorem
% 0.15/0.52 % SZS output start CNFRefutation
% See solution above
% 0.15/0.52 % Parsed axioms : 45
% 0.15/0.52 % Removed by relevancy pruning/SinE : 0
% 0.15/0.52 % Initial clauses : 174
% 0.15/0.52 % Removed in clause preprocessing : 5
% 0.15/0.52 % Initial clauses in saturation : 169
% 0.15/0.52 % Processed clauses : 417
% 0.15/0.52 % ...of these trivial : 6
% 0.15/0.52 % ...subsumed : 13
% 0.15/0.52 % ...remaining for further processing : 398
% 0.15/0.52 % Other redundant clauses eliminated : 42
% 0.15/0.52 % Clauses deleted for lack of memory : 0
% 0.15/0.52 % Backward-subsumed : 1
% 0.15/0.52 % Backward-rewritten : 13
% 0.15/0.52 % Generated clauses : 742
% 0.15/0.52 % ...of the previous two non-redundant : 695
% 0.15/0.52 % ...aggressively subsumed : 0
% 0.15/0.52 % Contextual simplify-reflections : 2
% 0.15/0.52 % Paramodulations : 700
% 0.15/0.52 % Factorizations : 0
% 0.15/0.52 % NegExts : 0
% 0.15/0.52 % Equation resolutions : 42
% 0.15/0.52 % Disequality decompositions : 0
% 0.15/0.52 % Total rewrite steps : 341
% 0.15/0.52 % ...of those cached : 321
% 0.15/0.52 % Propositional unsat checks : 0
% 0.15/0.52 % Propositional check models : 0
% 0.15/0.52 % Propositional check unsatisfiable : 0
% 0.15/0.52 % Propositional clauses : 0
% 0.15/0.52 % Propositional clauses after purity: 0
% 0.15/0.52 % Propositional unsat core size : 0
% 0.15/0.52 % Propositional preprocessing time : 0.000
% 0.15/0.52 % Propositional encoding time : 0.000
% 0.15/0.52 % Propositional solver time : 0.000
% 0.15/0.52 % Success case prop preproc time : 0.000
% 0.15/0.52 % Success case prop encoding time : 0.000
% 0.15/0.52 % Success case prop solver time : 0.000
% 0.15/0.52 % Current number of processed clauses : 186
% 0.15/0.52 % Positive orientable unit clauses : 18
% 0.15/0.52 % Positive unorientable unit clauses: 0
% 0.15/0.52 % Negative unit clauses : 5
% 0.15/0.52 % Non-unit-clauses : 163
% 0.15/0.52 % Current number of unprocessed clauses: 608
% 0.15/0.52 % ...number of literals in the above : 3581
% 0.15/0.52 % Current number of archived formulas : 0
% 0.15/0.52 % Current number of archived clauses : 177
% 0.15/0.52 % Clause-clause subsumption calls (NU) : 9516
% 0.15/0.52 % Rec. Clause-clause subsumption calls : 1606
% 0.15/0.52 % Non-unit clause-clause subsumptions : 14
% 0.15/0.52 % Unit Clause-clause subsumption calls : 352
% 0.15/0.52 % Rewrite failures with RHS unbound : 0
% 0.15/0.52 % BW rewrite match attempts : 5
% 0.15/0.52 % BW rewrite match successes : 4
% 0.15/0.52 % Condensation attempts : 0
% 0.15/0.52 % Condensation successes : 0
% 0.15/0.52 % Termbank termtop insertions : 31157
% 0.15/0.52 % Search garbage collected termcells : 3437
% 0.15/0.52
% 0.15/0.52 % -------------------------------------------------
% 0.15/0.52 % User time : 0.061 s
% 0.15/0.52 % System time : 0.003 s
% 0.15/0.52 % Total time : 0.064 s
% 0.15/0.52 % Maximum resident set size: 3908 pages
% 0.15/0.52
% 0.15/0.52 % -------------------------------------------------
% 0.15/0.52 % User time : 0.230 s
% 0.15/0.52 % System time : 0.022 s
% 0.15/0.52 % Total time : 0.252 s
% 0.15/0.52 % Maximum resident set size: 4864 pages
% 0.15/0.52 % E exiting
%------------------------------------------------------------------------------