TSTP Solution File: NUM449+6 by E-SAT---3.1.00
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%------------------------------------------------------------------------------
% File : E-SAT---3.1.00
% Problem : NUM449+6 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n023.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 : Sat May 4 09:06:05 EDT 2024
% Result : Theorem 0.22s 0.62s
% Output : CNFRefutation 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 11 unt; 0 def)
% Number of atoms : 376 ( 68 equ)
% Maximal formula atoms : 102 ( 12 avg)
% Number of connectives : 479 ( 134 ~; 172 |; 137 &)
% ( 4 <=>; 32 =>; 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 : 70 ( 0 sgn 41 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( aSet0(sbsmnsldt0(xS))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( aInteger0(X1)
& ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X1,X2) ) ) ) )
=> ( ( ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sbsmnsldt0(xS)) ) )
=> ( ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
=> ? [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(sbsmnsldt0(xS))) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(sbsmnsldt0(xS))) ) ) ) )
| isOpen0(stldt0(sbsmnsldt0(xS))) ) )
| isClosed0(sbsmnsldt0(xS)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ksFBCc62lG/E---3.1_20433.p',m__) ).
fof(m__2046,hypothesis,
( aSet0(xS)
& ! [X1] :
( ( aElementOf0(X1,xS)
=> ? [X2] :
( aInteger0(X2)
& X2 != sz00
& isPrime0(X2)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2))
=> ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
& sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
& ( ( aInteger0(X3)
& ( ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
| sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2)) ) )
& szAzrzSzezqlpdtcmdtrp0(sz00,X2) = X1 ) )
& ( ? [X2] :
( aInteger0(X2)
& X2 != sz00
& isPrime0(X2)
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2))
=> ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
& sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
& ( ( aInteger0(X3)
& ( ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
| sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2)) ) ) )
=> szAzrzSzezqlpdtcmdtrp0(sz00,X2) = X1 ) )
=> aElementOf0(X1,xS) ) )
& xS = cS2043 ),
file('/export/starexec/sandbox2/tmp/tmp.ksFBCc62lG/E---3.1_20433.p',m__2046) ).
fof(mUnionSClosed,axiom,
! [X1] :
( ( aSet0(X1)
& isFinite0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> ( aSubsetOf0(X2,cS1395)
& isClosed0(X2) ) ) )
=> isClosed0(sbsmnsldt0(X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.ksFBCc62lG/E---3.1_20433.p',mUnionSClosed) ).
fof(mArSeqClosed,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2)
& X2 != sz00 )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),cS1395)
& isClosed0(szAzrzSzezqlpdtcmdtrp0(X1,X2)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ksFBCc62lG/E---3.1_20433.p',mArSeqClosed) ).
fof(m__2117,hypothesis,
isFinite0(xS),
file('/export/starexec/sandbox2/tmp/tmp.ksFBCc62lG/E---3.1_20433.p',m__2117) ).
fof(mIntZero,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox2/tmp/tmp.ksFBCc62lG/E---3.1_20433.p',mIntZero) ).
fof(c_0_6,negated_conjecture,
~ ( ( aSet0(sbsmnsldt0(xS))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( aInteger0(X1)
& ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X1,X2) ) ) ) )
=> ( ( ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sbsmnsldt0(xS)) ) )
=> ( ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
=> ? [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(sbsmnsldt0(xS))) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(sbsmnsldt0(xS))) ) ) ) )
| isOpen0(stldt0(sbsmnsldt0(xS))) ) )
| isClosed0(sbsmnsldt0(xS)) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
fof(c_0_7,hypothesis,
( aSet0(xS)
& ! [X1] :
( ( aElementOf0(X1,xS)
=> ? [X2] :
( aInteger0(X2)
& X2 != sz00
& isPrime0(X2)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2))
=> ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
& sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
& ( ( aInteger0(X3)
& ( ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
| sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2)) ) )
& szAzrzSzezqlpdtcmdtrp0(sz00,X2) = X1 ) )
& ( ? [X2] :
( aInteger0(X2)
& X2 != sz00
& isPrime0(X2)
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2))
=> ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
& sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
& ( ( aInteger0(X3)
& ( ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
| sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2)) ) ) )
=> szAzrzSzezqlpdtcmdtrp0(sz00,X2) = X1 ) )
=> aElementOf0(X1,xS) ) )
& xS = cS2043 ),
inference(fof_simplification,[status(thm)],[m__2046]) ).
fof(c_0_8,negated_conjecture,
! [X137,X139,X140,X141,X143,X144,X146] :
( aSet0(sbsmnsldt0(xS))
& ( aInteger0(X137)
| ~ aElementOf0(X137,sbsmnsldt0(xS)) )
& ( aElementOf0(esk20_1(X137),xS)
| ~ aElementOf0(X137,sbsmnsldt0(xS)) )
& ( aElementOf0(X137,esk20_1(X137))
| ~ aElementOf0(X137,sbsmnsldt0(xS)) )
& ( ~ aInteger0(X139)
| ~ aElementOf0(X140,xS)
| ~ aElementOf0(X139,X140)
| aElementOf0(X139,sbsmnsldt0(xS)) )
& ( aInteger0(X141)
| ~ aElementOf0(X141,stldt0(sbsmnsldt0(xS))) )
& ( ~ aElementOf0(X141,sbsmnsldt0(xS))
| ~ aElementOf0(X141,stldt0(sbsmnsldt0(xS))) )
& ( ~ aInteger0(X141)
| aElementOf0(X141,sbsmnsldt0(xS))
| aElementOf0(X141,stldt0(sbsmnsldt0(xS))) )
& aElementOf0(esk21_0,stldt0(sbsmnsldt0(xS)))
& ( aSet0(szAzrzSzezqlpdtcmdtrp0(esk21_0,X143))
| ~ aInteger0(X143)
| X143 = sz00 )
& ( aInteger0(X144)
| ~ aElementOf0(X144,szAzrzSzezqlpdtcmdtrp0(esk21_0,X143))
| ~ aInteger0(X143)
| X143 = sz00 )
& ( aInteger0(esk22_2(X143,X144))
| ~ aElementOf0(X144,szAzrzSzezqlpdtcmdtrp0(esk21_0,X143))
| ~ aInteger0(X143)
| X143 = sz00 )
& ( sdtasdt0(X143,esk22_2(X143,X144)) = sdtpldt0(X144,smndt0(esk21_0))
| ~ aElementOf0(X144,szAzrzSzezqlpdtcmdtrp0(esk21_0,X143))
| ~ aInteger0(X143)
| X143 = sz00 )
& ( aDivisorOf0(X143,sdtpldt0(X144,smndt0(esk21_0)))
| ~ aElementOf0(X144,szAzrzSzezqlpdtcmdtrp0(esk21_0,X143))
| ~ aInteger0(X143)
| X143 = sz00 )
& ( sdteqdtlpzmzozddtrp0(X144,esk21_0,X143)
| ~ aElementOf0(X144,szAzrzSzezqlpdtcmdtrp0(esk21_0,X143))
| ~ aInteger0(X143)
| X143 = sz00 )
& ( ~ aInteger0(X146)
| sdtasdt0(X143,X146) != sdtpldt0(X144,smndt0(esk21_0))
| ~ aInteger0(X144)
| aElementOf0(X144,szAzrzSzezqlpdtcmdtrp0(esk21_0,X143))
| ~ aInteger0(X143)
| X143 = sz00 )
& ( ~ aDivisorOf0(X143,sdtpldt0(X144,smndt0(esk21_0)))
| ~ aInteger0(X144)
| aElementOf0(X144,szAzrzSzezqlpdtcmdtrp0(esk21_0,X143))
| ~ aInteger0(X143)
| X143 = sz00 )
& ( ~ sdteqdtlpzmzozddtrp0(X144,esk21_0,X143)
| ~ aInteger0(X144)
| aElementOf0(X144,szAzrzSzezqlpdtcmdtrp0(esk21_0,X143))
| ~ aInteger0(X143)
| X143 = sz00 )
& ( aElementOf0(esk23_1(X143),szAzrzSzezqlpdtcmdtrp0(esk21_0,X143))
| ~ aInteger0(X143)
| X143 = sz00 )
& ( ~ aElementOf0(esk23_1(X143),stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X143)
| X143 = sz00 )
& ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(esk21_0,X143),stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X143)
| X143 = sz00 )
& ~ isOpen0(stldt0(sbsmnsldt0(xS)))
& ~ isClosed0(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_6])])])])])])]) ).
fof(c_0_9,plain,
! [X115] :
( ( aElementOf0(esk15_1(X115),X115)
| ~ aSet0(X115)
| ~ isFinite0(X115)
| isClosed0(sbsmnsldt0(X115)) )
& ( ~ aSubsetOf0(esk15_1(X115),cS1395)
| ~ isClosed0(esk15_1(X115))
| ~ aSet0(X115)
| ~ isFinite0(X115)
| isClosed0(sbsmnsldt0(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_10,hypothesis,
! [X119,X121,X123,X124,X125,X126,X127,X129,X130] :
( aSet0(xS)
& ( aInteger0(esk16_1(X119))
| ~ aElementOf0(X119,xS) )
& ( esk16_1(X119) != sz00
| ~ aElementOf0(X119,xS) )
& ( isPrime0(esk16_1(X119))
| ~ aElementOf0(X119,xS) )
& ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X119)))
| ~ aElementOf0(X119,xS) )
& ( aInteger0(X121)
| ~ aElementOf0(X121,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X119)))
| ~ aElementOf0(X119,xS) )
& ( aInteger0(esk17_2(X119,X121))
| ~ aElementOf0(X121,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X119)))
| ~ aElementOf0(X119,xS) )
& ( sdtasdt0(esk16_1(X119),esk17_2(X119,X121)) = sdtpldt0(X121,smndt0(sz00))
| ~ aElementOf0(X121,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X119)))
| ~ aElementOf0(X119,xS) )
& ( aDivisorOf0(esk16_1(X119),sdtpldt0(X121,smndt0(sz00)))
| ~ aElementOf0(X121,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X119)))
| ~ aElementOf0(X119,xS) )
& ( sdteqdtlpzmzozddtrp0(X121,sz00,esk16_1(X119))
| ~ aElementOf0(X121,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X119)))
| ~ aElementOf0(X119,xS) )
& ( ~ aInteger0(X124)
| sdtasdt0(esk16_1(X119),X124) != sdtpldt0(X123,smndt0(sz00))
| ~ aInteger0(X123)
| aElementOf0(X123,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X119)))
| ~ aElementOf0(X119,xS) )
& ( ~ aDivisorOf0(esk16_1(X119),sdtpldt0(X123,smndt0(sz00)))
| ~ aInteger0(X123)
| aElementOf0(X123,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X119)))
| ~ aElementOf0(X119,xS) )
& ( ~ sdteqdtlpzmzozddtrp0(X123,sz00,esk16_1(X119))
| ~ aInteger0(X123)
| aElementOf0(X123,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X119)))
| ~ aElementOf0(X119,xS) )
& ( szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X119)) = X119
| ~ aElementOf0(X119,xS) )
& ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X126))
| ~ aInteger0(X126)
| X126 = sz00
| ~ isPrime0(X126)
| aElementOf0(X125,xS) )
& ( aInteger0(X127)
| ~ aElementOf0(X127,szAzrzSzezqlpdtcmdtrp0(sz00,X126))
| ~ aInteger0(X126)
| X126 = sz00
| ~ isPrime0(X126)
| aElementOf0(X125,xS) )
& ( aInteger0(esk18_3(X125,X126,X127))
| ~ aElementOf0(X127,szAzrzSzezqlpdtcmdtrp0(sz00,X126))
| ~ aInteger0(X126)
| X126 = sz00
| ~ isPrime0(X126)
| aElementOf0(X125,xS) )
& ( sdtasdt0(X126,esk18_3(X125,X126,X127)) = sdtpldt0(X127,smndt0(sz00))
| ~ aElementOf0(X127,szAzrzSzezqlpdtcmdtrp0(sz00,X126))
| ~ aInteger0(X126)
| X126 = sz00
| ~ isPrime0(X126)
| aElementOf0(X125,xS) )
& ( aDivisorOf0(X126,sdtpldt0(X127,smndt0(sz00)))
| ~ aElementOf0(X127,szAzrzSzezqlpdtcmdtrp0(sz00,X126))
| ~ aInteger0(X126)
| X126 = sz00
| ~ isPrime0(X126)
| aElementOf0(X125,xS) )
& ( sdteqdtlpzmzozddtrp0(X127,sz00,X126)
| ~ aElementOf0(X127,szAzrzSzezqlpdtcmdtrp0(sz00,X126))
| ~ aInteger0(X126)
| X126 = sz00
| ~ isPrime0(X126)
| aElementOf0(X125,xS) )
& ( ~ aInteger0(X130)
| sdtasdt0(X126,X130) != sdtpldt0(X129,smndt0(sz00))
| ~ aInteger0(X129)
| aElementOf0(X129,szAzrzSzezqlpdtcmdtrp0(sz00,X126))
| ~ aInteger0(X126)
| X126 = sz00
| ~ isPrime0(X126)
| aElementOf0(X125,xS) )
& ( ~ aDivisorOf0(X126,sdtpldt0(X129,smndt0(sz00)))
| ~ aInteger0(X129)
| aElementOf0(X129,szAzrzSzezqlpdtcmdtrp0(sz00,X126))
| ~ aInteger0(X126)
| X126 = sz00
| ~ isPrime0(X126)
| aElementOf0(X125,xS) )
& ( ~ sdteqdtlpzmzozddtrp0(X129,sz00,X126)
| ~ aInteger0(X129)
| aElementOf0(X129,szAzrzSzezqlpdtcmdtrp0(sz00,X126))
| ~ aInteger0(X126)
| X126 = sz00
| ~ isPrime0(X126)
| aElementOf0(X125,xS) )
& ( szAzrzSzezqlpdtcmdtrp0(sz00,X126) != X125
| ~ aInteger0(X126)
| X126 = sz00
| ~ isPrime0(X126)
| aElementOf0(X125,xS) )
& xS = cS2043 ),
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_11,plain,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2)
& X2 != sz00 )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),cS1395)
& isClosed0(szAzrzSzezqlpdtcmdtrp0(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[mArSeqClosed]) ).
cnf(c_0_12,negated_conjecture,
~ isClosed0(sbsmnsldt0(xS)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( aElementOf0(esk15_1(X1),X1)
| isClosed0(sbsmnsldt0(X1))
| ~ aSet0(X1)
| ~ isFinite0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,hypothesis,
isFinite0(xS),
inference(split_conjunct,[status(thm)],[m__2117]) ).
cnf(c_0_15,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,plain,
! [X117,X118] :
( ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X117,X118),cS1395)
| ~ aInteger0(X117)
| ~ aInteger0(X118)
| X118 = sz00 )
& ( isClosed0(szAzrzSzezqlpdtcmdtrp0(X117,X118))
| ~ aInteger0(X117)
| ~ aInteger0(X118)
| X118 = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
cnf(c_0_17,hypothesis,
( szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X1)) = X1
| ~ aElementOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,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_12,c_0_13]),c_0_14]),c_0_15])]) ).
cnf(c_0_19,hypothesis,
( aInteger0(esk16_1(X1))
| ~ aElementOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_20,plain,
( isClosed0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
| X2 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,hypothesis,
szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(esk15_1(xS))) = esk15_1(xS),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,hypothesis,
aInteger0(esk16_1(esk15_1(xS))),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_23,plain,
aInteger0(sz00),
inference(split_conjunct,[status(thm)],[mIntZero]) ).
cnf(c_0_24,plain,
( isClosed0(sbsmnsldt0(X1))
| ~ aSubsetOf0(esk15_1(X1),cS1395)
| ~ isClosed0(esk15_1(X1))
| ~ aSet0(X1)
| ~ isFinite0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_25,hypothesis,
( esk16_1(esk15_1(xS)) = sz00
| isClosed0(esk15_1(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23])]) ).
cnf(c_0_26,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),cS1395)
| X2 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_27,hypothesis,
( esk16_1(esk15_1(xS)) = sz00
| ~ aSubsetOf0(esk15_1(xS),cS1395) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_14]),c_0_15])]),c_0_12]) ).
cnf(c_0_28,hypothesis,
( esk16_1(X1) != sz00
| ~ aElementOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_29,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_26,c_0_21]),c_0_22]),c_0_23])]),c_0_27]) ).
cnf(c_0_30,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : NUM449+6 : TPTP v8.1.2. Released v4.0.0.
% 0.09/0.16 % Command : run_E %s %d THM
% 0.15/0.37 % Computer : n023.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.38 % WCLimit : 300
% 0.15/0.38 % DateTime : Fri May 3 09:51:08 EDT 2024
% 0.15/0.38 % CPUTime :
% 0.22/0.54 Running first-order model finding
% 0.22/0.54 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.ksFBCc62lG/E---3.1_20433.p
% 0.22/0.62 # Version: 3.1.0
% 0.22/0.62 # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.22/0.62 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.62 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.22/0.62 # Starting new_bool_3 with 300s (1) cores
% 0.22/0.62 # Starting new_bool_1 with 300s (1) cores
% 0.22/0.62 # Starting sh5l with 300s (1) cores
% 0.22/0.62 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 20510 completed with status 0
% 0.22/0.62 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.22/0.62 # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.22/0.62 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.62 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.22/0.62 # No SInE strategy applied
% 0.22/0.62 # Search class: FGHSF-FSLM31-SFFFFFNN
% 0.22/0.62 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.62 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 666s (1) cores
% 0.22/0.62 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.22/0.62 # Starting new_bool_3 with 194s (1) cores
% 0.22/0.62 # Starting new_bool_1 with 188s (1) cores
% 0.22/0.62 # Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.22/0.62 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 20517 completed with status 0
% 0.22/0.62 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.22/0.62 # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.22/0.62 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.62 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.22/0.62 # No SInE strategy applied
% 0.22/0.62 # Search class: FGHSF-FSLM31-SFFFFFNN
% 0.22/0.62 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.62 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 666s (1) cores
% 0.22/0.62 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.22/0.62 # Preprocessing time : 0.004 s
% 0.22/0.62 # Presaturation interreduction done
% 0.22/0.62
% 0.22/0.62 # Proof found!
% 0.22/0.62 # SZS status Theorem
% 0.22/0.62 # SZS output start CNFRefutation
% See solution above
% 0.85/0.62 # Parsed axioms : 45
% 0.85/0.62 # Removed by relevancy pruning/SinE : 0
% 0.85/0.62 # Initial clauses : 174
% 0.85/0.62 # Removed in clause preprocessing : 5
% 0.85/0.62 # Initial clauses in saturation : 169
% 0.85/0.62 # Processed clauses : 417
% 0.85/0.62 # ...of these trivial : 6
% 0.85/0.62 # ...subsumed : 13
% 0.85/0.62 # ...remaining for further processing : 398
% 0.85/0.62 # Other redundant clauses eliminated : 42
% 0.85/0.62 # Clauses deleted for lack of memory : 0
% 0.85/0.62 # Backward-subsumed : 1
% 0.85/0.62 # Backward-rewritten : 13
% 0.85/0.62 # Generated clauses : 742
% 0.85/0.62 # ...of the previous two non-redundant : 695
% 0.85/0.62 # ...aggressively subsumed : 0
% 0.85/0.62 # Contextual simplify-reflections : 2
% 0.85/0.62 # Paramodulations : 700
% 0.85/0.62 # Factorizations : 0
% 0.85/0.62 # NegExts : 0
% 0.85/0.62 # Equation resolutions : 42
% 0.85/0.62 # Disequality decompositions : 0
% 0.85/0.62 # Total rewrite steps : 341
% 0.85/0.62 # ...of those cached : 321
% 0.85/0.62 # Propositional unsat checks : 0
% 0.85/0.62 # Propositional check models : 0
% 0.85/0.62 # Propositional check unsatisfiable : 0
% 0.85/0.62 # Propositional clauses : 0
% 0.85/0.62 # Propositional clauses after purity: 0
% 0.85/0.62 # Propositional unsat core size : 0
% 0.85/0.62 # Propositional preprocessing time : 0.000
% 0.85/0.62 # Propositional encoding time : 0.000
% 0.85/0.62 # Propositional solver time : 0.000
% 0.85/0.62 # Success case prop preproc time : 0.000
% 0.85/0.62 # Success case prop encoding time : 0.000
% 0.85/0.62 # Success case prop solver time : 0.000
% 0.85/0.62 # Current number of processed clauses : 186
% 0.85/0.62 # Positive orientable unit clauses : 18
% 0.85/0.62 # Positive unorientable unit clauses: 0
% 0.85/0.62 # Negative unit clauses : 5
% 0.85/0.62 # Non-unit-clauses : 163
% 0.85/0.62 # Current number of unprocessed clauses: 608
% 0.85/0.62 # ...number of literals in the above : 3581
% 0.85/0.62 # Current number of archived formulas : 0
% 0.85/0.62 # Current number of archived clauses : 177
% 0.85/0.62 # Clause-clause subsumption calls (NU) : 9234
% 0.85/0.62 # Rec. Clause-clause subsumption calls : 1538
% 0.85/0.62 # Non-unit clause-clause subsumptions : 14
% 0.85/0.62 # Unit Clause-clause subsumption calls : 314
% 0.85/0.62 # Rewrite failures with RHS unbound : 0
% 0.85/0.62 # BW rewrite match attempts : 5
% 0.85/0.62 # BW rewrite match successes : 4
% 0.85/0.62 # Condensation attempts : 0
% 0.85/0.62 # Condensation successes : 0
% 0.85/0.62 # Termbank termtop insertions : 30553
% 0.85/0.62 # Search garbage collected termcells : 3438
% 0.85/0.62
% 0.85/0.62 # -------------------------------------------------
% 0.85/0.62 # User time : 0.057 s
% 0.85/0.62 # System time : 0.012 s
% 0.85/0.62 # Total time : 0.069 s
% 0.85/0.62 # Maximum resident set size: 2324 pages
% 0.85/0.62
% 0.85/0.62 # -------------------------------------------------
% 0.85/0.62 # User time : 0.259 s
% 0.85/0.62 # System time : 0.021 s
% 0.85/0.62 # Total time : 0.280 s
% 0.85/0.62 # Maximum resident set size: 1764 pages
% 0.85/0.62 % E---3.1 exiting
%------------------------------------------------------------------------------