TSTP Solution File: NUM441+6 by E-SAT---3.1
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%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : NUM441+6 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n014.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 19:07:09 EDT 2023
% Result : Theorem 0.17s 0.48s
% Output : CNFRefutation 0.17s
% 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/sandbox/tmp/tmp.PP909vJXjD/E---3.1_5565.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/sandbox/tmp/tmp.PP909vJXjD/E---3.1_5565.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/sandbox/tmp/tmp.PP909vJXjD/E---3.1_5565.p',m__) ).
fof(mInterOpen,axiom,
! [X1,X2] :
( ( aSubsetOf0(X1,cS1395)
& aSubsetOf0(X2,cS1395)
& isOpen0(X1)
& isOpen0(X2) )
=> isOpen0(sdtslmnbsdt0(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.PP909vJXjD/E---3.1_5565.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,
! [X119,X120] :
( ~ aSubsetOf0(X119,cS1395)
| ~ aSubsetOf0(X120,cS1395)
| ~ isOpen0(X119)
| ~ isOpen0(X120)
| isOpen0(sdtslmnbsdt0(X119,X120)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mInterOpen])]) ).
fof(c_0_8,hypothesis,
! [X25,X26,X27,X28,X29,X30,X31,X32,X33,X34,X35] :
( aSet0(stldt0(xA))
& ( aInteger0(X25)
| ~ aElementOf0(X25,stldt0(xA)) )
& ( ~ aElementOf0(X25,xA)
| ~ aElementOf0(X25,stldt0(xA)) )
& ( ~ aInteger0(X25)
| aElementOf0(X25,xA)
| aElementOf0(X25,stldt0(xA)) )
& aSet0(cS1395)
& ( ~ aElementOf0(X26,cS1395)
| aInteger0(X26) )
& ( ~ aInteger0(X26)
| aElementOf0(X26,cS1395) )
& ( ~ aElementOf0(X27,stldt0(xA))
| aElementOf0(X27,cS1395) )
& aSubsetOf0(stldt0(xA),cS1395)
& aSet0(stldt0(xB))
& ( aInteger0(X28)
| ~ aElementOf0(X28,stldt0(xB)) )
& ( ~ aElementOf0(X28,xB)
| ~ aElementOf0(X28,stldt0(xB)) )
& ( ~ aInteger0(X28)
| aElementOf0(X28,xB)
| aElementOf0(X28,stldt0(xB)) )
& aSet0(cS1395)
& ( ~ aElementOf0(X29,cS1395)
| aInteger0(X29) )
& ( ~ aInteger0(X29)
| aElementOf0(X29,cS1395) )
& ( ~ aElementOf0(X30,stldt0(xB))
| aElementOf0(X30,cS1395) )
& aSubsetOf0(stldt0(xB),cS1395)
& aSet0(sdtbsmnsldt0(xA,xB))
& ( aInteger0(X31)
| ~ aElementOf0(X31,sdtbsmnsldt0(xA,xB)) )
& ( aElementOf0(X31,xA)
| aElementOf0(X31,xB)
| ~ aElementOf0(X31,sdtbsmnsldt0(xA,xB)) )
& ( ~ aElementOf0(X31,xA)
| ~ aInteger0(X31)
| aElementOf0(X31,sdtbsmnsldt0(xA,xB)) )
& ( ~ aElementOf0(X31,xB)
| ~ aInteger0(X31)
| aElementOf0(X31,sdtbsmnsldt0(xA,xB)) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ( aInteger0(X32)
| ~ aElementOf0(X32,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( ~ aElementOf0(X32,sdtbsmnsldt0(xA,xB))
| ~ aElementOf0(X32,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( ~ aInteger0(X32)
| aElementOf0(X32,sdtbsmnsldt0(xA,xB))
| aElementOf0(X32,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( aInteger0(X33)
| ~ aElementOf0(X33,stldt0(xA)) )
& ( ~ aElementOf0(X33,xA)
| ~ aElementOf0(X33,stldt0(xA)) )
& ( ~ aInteger0(X33)
| aElementOf0(X33,xA)
| aElementOf0(X33,stldt0(xA)) )
& ( aInteger0(X34)
| ~ aElementOf0(X34,stldt0(xB)) )
& ( ~ aElementOf0(X34,xB)
| ~ aElementOf0(X34,stldt0(xB)) )
& ( ~ aInteger0(X34)
| aElementOf0(X34,xB)
| aElementOf0(X34,stldt0(xB)) )
& ( aInteger0(X35)
| ~ aElementOf0(X35,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( aElementOf0(X35,stldt0(xA))
| ~ aElementOf0(X35,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( aElementOf0(X35,stldt0(xB))
| ~ aElementOf0(X35,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( ~ aInteger0(X35)
| ~ aElementOf0(X35,stldt0(xA))
| ~ aElementOf0(X35,stldt0(xB))
| aElementOf0(X35,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,
! [X5,X6,X7,X8,X9,X10,X12,X14,X15,X16,X17,X18,X20,X22,X23,X24] :
( aSet0(cS1395)
& ( ~ aElementOf0(X5,cS1395)
| aInteger0(X5) )
& ( ~ aInteger0(X5)
| aElementOf0(X5,cS1395) )
& aSet0(xA)
& ( ~ aElementOf0(X6,xA)
| aElementOf0(X6,cS1395) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ( ~ aElementOf0(X7,cS1395)
| aInteger0(X7) )
& ( ~ aInteger0(X7)
| aElementOf0(X7,cS1395) )
& aSet0(xB)
& ( ~ aElementOf0(X8,xB)
| aElementOf0(X8,cS1395) )
& aSubsetOf0(xB,cS1395)
& aSet0(stldt0(xA))
& ( aInteger0(X9)
| ~ aElementOf0(X9,stldt0(xA)) )
& ( ~ aElementOf0(X9,xA)
| ~ aElementOf0(X9,stldt0(xA)) )
& ( ~ aInteger0(X9)
| aElementOf0(X9,xA)
| aElementOf0(X9,stldt0(xA)) )
& ( aInteger0(esk1_1(X10))
| ~ aElementOf0(X10,stldt0(xA)) )
& ( esk1_1(X10) != sz00
| ~ aElementOf0(X10,stldt0(xA)) )
& ( aSet0(szAzrzSzezqlpdtcmdtrp0(X10,esk1_1(X10)))
| ~ aElementOf0(X10,stldt0(xA)) )
& ( aInteger0(X12)
| ~ aElementOf0(X12,szAzrzSzezqlpdtcmdtrp0(X10,esk1_1(X10)))
| ~ aElementOf0(X10,stldt0(xA)) )
& ( aInteger0(esk2_2(X10,X12))
| ~ aElementOf0(X12,szAzrzSzezqlpdtcmdtrp0(X10,esk1_1(X10)))
| ~ aElementOf0(X10,stldt0(xA)) )
& ( sdtasdt0(esk1_1(X10),esk2_2(X10,X12)) = sdtpldt0(X12,smndt0(X10))
| ~ aElementOf0(X12,szAzrzSzezqlpdtcmdtrp0(X10,esk1_1(X10)))
| ~ aElementOf0(X10,stldt0(xA)) )
& ( aDivisorOf0(esk1_1(X10),sdtpldt0(X12,smndt0(X10)))
| ~ aElementOf0(X12,szAzrzSzezqlpdtcmdtrp0(X10,esk1_1(X10)))
| ~ aElementOf0(X10,stldt0(xA)) )
& ( sdteqdtlpzmzozddtrp0(X12,X10,esk1_1(X10))
| ~ aElementOf0(X12,szAzrzSzezqlpdtcmdtrp0(X10,esk1_1(X10)))
| ~ aElementOf0(X10,stldt0(xA)) )
& ( ~ aInteger0(X15)
| sdtasdt0(esk1_1(X10),X15) != sdtpldt0(X14,smndt0(X10))
| ~ aInteger0(X14)
| aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(X10,esk1_1(X10)))
| ~ aElementOf0(X10,stldt0(xA)) )
& ( ~ aDivisorOf0(esk1_1(X10),sdtpldt0(X14,smndt0(X10)))
| ~ aInteger0(X14)
| aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(X10,esk1_1(X10)))
| ~ aElementOf0(X10,stldt0(xA)) )
& ( ~ sdteqdtlpzmzozddtrp0(X14,X10,esk1_1(X10))
| ~ aInteger0(X14)
| aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(X10,esk1_1(X10)))
| ~ aElementOf0(X10,stldt0(xA)) )
& ( ~ aElementOf0(X16,szAzrzSzezqlpdtcmdtrp0(X10,esk1_1(X10)))
| aElementOf0(X16,stldt0(xA))
| ~ aElementOf0(X10,stldt0(xA)) )
& ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X10,esk1_1(X10)),stldt0(xA))
| ~ aElementOf0(X10,stldt0(xA)) )
& isOpen0(stldt0(xA))
& isClosed0(xA)
& aSet0(stldt0(xB))
& ( aInteger0(X17)
| ~ aElementOf0(X17,stldt0(xB)) )
& ( ~ aElementOf0(X17,xB)
| ~ aElementOf0(X17,stldt0(xB)) )
& ( ~ aInteger0(X17)
| aElementOf0(X17,xB)
| aElementOf0(X17,stldt0(xB)) )
& ( aInteger0(esk3_1(X18))
| ~ aElementOf0(X18,stldt0(xB)) )
& ( esk3_1(X18) != sz00
| ~ aElementOf0(X18,stldt0(xB)) )
& ( aSet0(szAzrzSzezqlpdtcmdtrp0(X18,esk3_1(X18)))
| ~ aElementOf0(X18,stldt0(xB)) )
& ( aInteger0(X20)
| ~ aElementOf0(X20,szAzrzSzezqlpdtcmdtrp0(X18,esk3_1(X18)))
| ~ aElementOf0(X18,stldt0(xB)) )
& ( aInteger0(esk4_2(X18,X20))
| ~ aElementOf0(X20,szAzrzSzezqlpdtcmdtrp0(X18,esk3_1(X18)))
| ~ aElementOf0(X18,stldt0(xB)) )
& ( sdtasdt0(esk3_1(X18),esk4_2(X18,X20)) = sdtpldt0(X20,smndt0(X18))
| ~ aElementOf0(X20,szAzrzSzezqlpdtcmdtrp0(X18,esk3_1(X18)))
| ~ aElementOf0(X18,stldt0(xB)) )
& ( aDivisorOf0(esk3_1(X18),sdtpldt0(X20,smndt0(X18)))
| ~ aElementOf0(X20,szAzrzSzezqlpdtcmdtrp0(X18,esk3_1(X18)))
| ~ aElementOf0(X18,stldt0(xB)) )
& ( sdteqdtlpzmzozddtrp0(X20,X18,esk3_1(X18))
| ~ aElementOf0(X20,szAzrzSzezqlpdtcmdtrp0(X18,esk3_1(X18)))
| ~ aElementOf0(X18,stldt0(xB)) )
& ( ~ aInteger0(X23)
| sdtasdt0(esk3_1(X18),X23) != sdtpldt0(X22,smndt0(X18))
| ~ aInteger0(X22)
| aElementOf0(X22,szAzrzSzezqlpdtcmdtrp0(X18,esk3_1(X18)))
| ~ aElementOf0(X18,stldt0(xB)) )
& ( ~ aDivisorOf0(esk3_1(X18),sdtpldt0(X22,smndt0(X18)))
| ~ aInteger0(X22)
| aElementOf0(X22,szAzrzSzezqlpdtcmdtrp0(X18,esk3_1(X18)))
| ~ aElementOf0(X18,stldt0(xB)) )
& ( ~ sdteqdtlpzmzozddtrp0(X22,X18,esk3_1(X18))
| ~ aInteger0(X22)
| aElementOf0(X22,szAzrzSzezqlpdtcmdtrp0(X18,esk3_1(X18)))
| ~ aElementOf0(X18,stldt0(xB)) )
& ( ~ aElementOf0(X24,szAzrzSzezqlpdtcmdtrp0(X18,esk3_1(X18)))
| aElementOf0(X24,stldt0(xB))
| ~ aElementOf0(X18,stldt0(xB)) )
& ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X18,esk3_1(X18)),stldt0(xB))
| ~ aElementOf0(X18,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,
! [X36,X37,X39,X40,X42] :
( aSet0(sdtbsmnsldt0(xA,xB))
& ( aInteger0(X36)
| ~ aElementOf0(X36,sdtbsmnsldt0(xA,xB)) )
& ( aElementOf0(X36,xA)
| aElementOf0(X36,xB)
| ~ aElementOf0(X36,sdtbsmnsldt0(xA,xB)) )
& ( ~ aElementOf0(X36,xA)
| ~ aInteger0(X36)
| aElementOf0(X36,sdtbsmnsldt0(xA,xB)) )
& ( ~ aElementOf0(X36,xB)
| ~ aInteger0(X36)
| aElementOf0(X36,sdtbsmnsldt0(xA,xB)) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ( aInteger0(X37)
| ~ aElementOf0(X37,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( ~ aElementOf0(X37,sdtbsmnsldt0(xA,xB))
| ~ aElementOf0(X37,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( ~ aInteger0(X37)
| aElementOf0(X37,sdtbsmnsldt0(xA,xB))
| aElementOf0(X37,stldt0(sdtbsmnsldt0(xA,xB))) )
& aElementOf0(esk5_0,stldt0(sdtbsmnsldt0(xA,xB)))
& ( aSet0(szAzrzSzezqlpdtcmdtrp0(esk5_0,X39))
| ~ aInteger0(X39)
| X39 = sz00 )
& ( aInteger0(X40)
| ~ aElementOf0(X40,szAzrzSzezqlpdtcmdtrp0(esk5_0,X39))
| ~ aInteger0(X39)
| X39 = sz00 )
& ( aInteger0(esk6_2(X39,X40))
| ~ aElementOf0(X40,szAzrzSzezqlpdtcmdtrp0(esk5_0,X39))
| ~ aInteger0(X39)
| X39 = sz00 )
& ( sdtasdt0(X39,esk6_2(X39,X40)) = sdtpldt0(X40,smndt0(esk5_0))
| ~ aElementOf0(X40,szAzrzSzezqlpdtcmdtrp0(esk5_0,X39))
| ~ aInteger0(X39)
| X39 = sz00 )
& ( aDivisorOf0(X39,sdtpldt0(X40,smndt0(esk5_0)))
| ~ aElementOf0(X40,szAzrzSzezqlpdtcmdtrp0(esk5_0,X39))
| ~ aInteger0(X39)
| X39 = sz00 )
& ( sdteqdtlpzmzozddtrp0(X40,esk5_0,X39)
| ~ aElementOf0(X40,szAzrzSzezqlpdtcmdtrp0(esk5_0,X39))
| ~ aInteger0(X39)
| X39 = sz00 )
& ( ~ aInteger0(X42)
| sdtasdt0(X39,X42) != sdtpldt0(X40,smndt0(esk5_0))
| ~ aInteger0(X40)
| aElementOf0(X40,szAzrzSzezqlpdtcmdtrp0(esk5_0,X39))
| ~ aInteger0(X39)
| X39 = sz00 )
& ( ~ aDivisorOf0(X39,sdtpldt0(X40,smndt0(esk5_0)))
| ~ aInteger0(X40)
| aElementOf0(X40,szAzrzSzezqlpdtcmdtrp0(esk5_0,X39))
| ~ aInteger0(X39)
| X39 = sz00 )
& ( ~ sdteqdtlpzmzozddtrp0(X40,esk5_0,X39)
| ~ aInteger0(X40)
| aElementOf0(X40,szAzrzSzezqlpdtcmdtrp0(esk5_0,X39))
| ~ aInteger0(X39)
| X39 = sz00 )
& ( aElementOf0(esk7_1(X39),szAzrzSzezqlpdtcmdtrp0(esk5_0,X39))
| ~ aInteger0(X39)
| X39 = sz00 )
& ( ~ aElementOf0(esk7_1(X39),stldt0(sdtbsmnsldt0(xA,xB)))
| ~ aInteger0(X39)
| X39 = sz00 )
& ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(esk5_0,X39),stldt0(sdtbsmnsldt0(xA,xB)))
| ~ aInteger0(X39)
| X39 = 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
% 0.00/0.10 % Problem : NUM441+6 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 2400
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Oct 2 14:28:49 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.17/0.44 Running first-order model finding
% 0.17/0.44 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.PP909vJXjD/E---3.1_5565.p
% 0.17/0.48 # Version: 3.1pre001
% 0.17/0.48 # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.48 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.48 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.48 # Starting new_bool_3 with 300s (1) cores
% 0.17/0.48 # Starting new_bool_1 with 300s (1) cores
% 0.17/0.48 # Starting sh5l with 300s (1) cores
% 0.17/0.48 # new_bool_3 with pid 5643 completed with status 0
% 0.17/0.48 # Result found by new_bool_3
% 0.17/0.48 # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.48 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.48 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.48 # Starting new_bool_3 with 300s (1) cores
% 0.17/0.48 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.48 # Search class: FGHSF-FSLM31-SFFFFFNN
% 0.17/0.48 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.48 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 148s (1) cores
% 0.17/0.48 # G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 5646 completed with status 0
% 0.17/0.48 # Result found by G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 0.17/0.48 # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.48 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.48 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.48 # Starting new_bool_3 with 300s (1) cores
% 0.17/0.48 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.48 # Search class: FGHSF-FSLM31-SFFFFFNN
% 0.17/0.48 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.48 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 148s (1) cores
% 0.17/0.48 # Preprocessing time : 0.003 s
% 0.17/0.48 # Presaturation interreduction done
% 0.17/0.48
% 0.17/0.48 # Proof found!
% 0.17/0.48 # SZS status Theorem
% 0.17/0.48 # SZS output start CNFRefutation
% See solution above
% 0.17/0.48 # Parsed axioms : 41
% 0.17/0.48 # Removed by relevancy pruning/SinE : 8
% 0.17/0.48 # Initial clauses : 188
% 0.17/0.48 # Removed in clause preprocessing : 3
% 0.17/0.48 # Initial clauses in saturation : 185
% 0.17/0.48 # Processed clauses : 351
% 0.17/0.48 # ...of these trivial : 9
% 0.17/0.48 # ...subsumed : 42
% 0.17/0.48 # ...remaining for further processing : 300
% 0.17/0.48 # Other redundant clauses eliminated : 21
% 0.17/0.48 # Clauses deleted for lack of memory : 0
% 0.17/0.48 # Backward-subsumed : 0
% 0.17/0.48 # Backward-rewritten : 1
% 0.17/0.48 # Generated clauses : 256
% 0.17/0.48 # ...of the previous two non-redundant : 187
% 0.17/0.48 # ...aggressively subsumed : 0
% 0.17/0.48 # Contextual simplify-reflections : 2
% 0.17/0.48 # Paramodulations : 235
% 0.17/0.48 # Factorizations : 0
% 0.17/0.48 # NegExts : 0
% 0.17/0.48 # Equation resolutions : 21
% 0.17/0.48 # Total rewrite steps : 135
% 0.17/0.48 # Propositional unsat checks : 0
% 0.17/0.48 # Propositional check models : 0
% 0.17/0.48 # Propositional check unsatisfiable : 0
% 0.17/0.48 # Propositional clauses : 0
% 0.17/0.48 # Propositional clauses after purity: 0
% 0.17/0.48 # Propositional unsat core size : 0
% 0.17/0.48 # Propositional preprocessing time : 0.000
% 0.17/0.48 # Propositional encoding time : 0.000
% 0.17/0.48 # Propositional solver time : 0.000
% 0.17/0.48 # Success case prop preproc time : 0.000
% 0.17/0.48 # Success case prop encoding time : 0.000
% 0.17/0.48 # Success case prop solver time : 0.000
% 0.17/0.48 # Current number of processed clauses : 127
% 0.17/0.48 # Positive orientable unit clauses : 25
% 0.17/0.48 # Positive unorientable unit clauses: 0
% 0.17/0.48 # Negative unit clauses : 5
% 0.17/0.48 # Non-unit-clauses : 97
% 0.17/0.48 # Current number of unprocessed clauses: 172
% 0.17/0.48 # ...number of literals in the above : 693
% 0.17/0.48 # Current number of archived formulas : 0
% 0.17/0.48 # Current number of archived clauses : 153
% 0.17/0.48 # Clause-clause subsumption calls (NU) : 3623
% 0.17/0.48 # Rec. Clause-clause subsumption calls : 1205
% 0.17/0.48 # Non-unit clause-clause subsumptions : 38
% 0.17/0.48 # Unit Clause-clause subsumption calls : 7
% 0.17/0.48 # Rewrite failures with RHS unbound : 0
% 0.17/0.48 # BW rewrite match attempts : 1
% 0.17/0.48 # BW rewrite match successes : 1
% 0.17/0.48 # Condensation attempts : 0
% 0.17/0.48 # Condensation successes : 0
% 0.17/0.48 # Termbank termtop insertions : 16897
% 0.17/0.48
% 0.17/0.48 # -------------------------------------------------
% 0.17/0.48 # User time : 0.025 s
% 0.17/0.48 # System time : 0.006 s
% 0.17/0.48 # Total time : 0.032 s
% 0.17/0.48 # Maximum resident set size: 2252 pages
% 0.17/0.48
% 0.17/0.48 # -------------------------------------------------
% 0.17/0.48 # User time : 0.027 s
% 0.17/0.48 # System time : 0.008 s
% 0.17/0.48 # Total time : 0.036 s
% 0.17/0.48 # Maximum resident set size: 1748 pages
% 0.17/0.48 % E---3.1 exiting
%------------------------------------------------------------------------------