TSTP Solution File: NUM442+6 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : NUM442+6 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n008.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 : 600s
% DateTime : Mon Jul 18 09:32:28 EDT 2022
% Result : Theorem 0.30s 14.47s
% Output : CNFRefutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 56 ( 10 unt; 0 def)
% Number of atoms : 483 ( 59 equ)
% Maximal formula atoms : 106 ( 8 avg)
% Number of connectives : 602 ( 175 ~; 246 |; 131 &)
% ( 7 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 2 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 116 ( 5 sgn 55 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X1] :
( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(X1)
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X1,xa,xq) ) )
& ( ( aInteger0(X1)
& ( ? [X2] :
( aInteger0(X2)
& sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(X1,xa,xq) ) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
=> ( ( aSet0(cS1395)
& ! [X1] :
( aElementOf0(X1,cS1395)
<=> aInteger0(X1) ) )
=> ( ! [X1] :
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> aElementOf0(X1,cS1395) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395) ) ) )
& ( ! [X1] :
( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(X1)
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X1,xa,xq) ) )
& ( ( aInteger0(X1)
& ( ? [X2] :
( aInteger0(X2)
& sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(X1,xa,xq) ) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
=> ( ( ( aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ! [X1] :
( aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
=> ( ! [X1] :
( aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
=> ? [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(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) ) ) )
| isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) )
| isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m__) ).
fof(mEquModTrn,axiom,
! [X1,X2,X3,X4] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3)
& X3 != sz00
& aInteger0(X4) )
=> ( ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
& sdteqdtlpzmzozddtrp0(X2,X4,X3) )
=> sdteqdtlpzmzozddtrp0(X1,X4,X3) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mEquModTrn) ).
fof(mEquModSym,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3)
& X3 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
=> sdteqdtlpzmzozddtrp0(X2,X1,X3) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mEquModSym) ).
fof(m__1962,hypothesis,
( aInteger0(xa)
& aInteger0(xq)
& xq != sz00 ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m__1962) ).
fof(mEquMod,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3)
& X3 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
<=> aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mEquMod) ).
fof(c_0_5,plain,
( epred1_0
<=> ( ! [X1] :
( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(X1)
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X1,xa,xq) ) )
& ( ( aInteger0(X1)
& ( ? [X2] :
( aInteger0(X2)
& sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(X1,xa,xq) ) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
=> ( ( ( aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ! [X1] :
( aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
=> ( ! [X1] :
( aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
=> ? [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(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) ) ) )
| isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) )
| isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) ),
introduced(definition) ).
fof(c_0_6,plain,
( ( ! [X1] :
( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(X1)
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X1,xa,xq) ) )
& ( ( aInteger0(X1)
& ( ? [X2] :
( aInteger0(X2)
& sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(X1,xa,xq) ) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
=> ( ( ( aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ! [X1] :
( aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
=> ( ! [X1] :
( aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
=> ? [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(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) ) ) )
| isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) )
| isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
=> epred1_0 ),
inference(split_equiv,[status(thm)],[c_0_5]) ).
fof(c_0_7,negated_conjecture,
~ ( ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X1] :
( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(X1)
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X1,xa,xq) ) )
& ( ( aInteger0(X1)
& ( ? [X2] :
( aInteger0(X2)
& sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(X1,xa,xq) ) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
=> ( ( aSet0(cS1395)
& ! [X1] :
( aElementOf0(X1,cS1395)
<=> aInteger0(X1) ) )
=> ( ! [X1] :
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> aElementOf0(X1,cS1395) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395) ) ) )
& epred1_0 ),
inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[m__]),c_0_5]) ).
fof(c_0_8,plain,
! [X5,X5,X7,X8,X8,X10,X11,X11,X13] :
( ( aInteger0(X5)
| ~ aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| epred1_0 )
& ( aInteger0(esk18_1(X5))
| ~ aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| epred1_0 )
& ( sdtasdt0(xq,esk18_1(X5)) = sdtpldt0(X5,smndt0(xa))
| ~ aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| epred1_0 )
& ( aDivisorOf0(xq,sdtpldt0(X5,smndt0(xa)))
| ~ aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| epred1_0 )
& ( sdteqdtlpzmzozddtrp0(X5,xa,xq)
| ~ aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| epred1_0 )
& ( ~ aInteger0(X7)
| sdtasdt0(xq,X7) != sdtpldt0(X5,smndt0(xa))
| ~ aInteger0(X5)
| aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| epred1_0 )
& ( ~ aDivisorOf0(xq,sdtpldt0(X5,smndt0(xa)))
| ~ aInteger0(X5)
| aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| epred1_0 )
& ( ~ sdteqdtlpzmzozddtrp0(X5,xa,xq)
| ~ aInteger0(X5)
| aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| epred1_0 )
& ( aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| epred1_0 )
& ( aInteger0(X8)
| ~ aElementOf0(X8,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| epred1_0 )
& ( ~ aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aElementOf0(X8,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| epred1_0 )
& ( ~ aInteger0(X8)
| aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aElementOf0(X8,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| epred1_0 )
& ( aElementOf0(esk19_0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| epred1_0 )
& ( aSet0(szAzrzSzezqlpdtcmdtrp0(esk19_0,X10))
| ~ aInteger0(X10)
| X10 = sz00
| epred1_0 )
& ( aInteger0(X11)
| ~ aElementOf0(X11,szAzrzSzezqlpdtcmdtrp0(esk19_0,X10))
| ~ aInteger0(X10)
| X10 = sz00
| epred1_0 )
& ( aInteger0(esk20_2(X10,X11))
| ~ aElementOf0(X11,szAzrzSzezqlpdtcmdtrp0(esk19_0,X10))
| ~ aInteger0(X10)
| X10 = sz00
| epred1_0 )
& ( sdtasdt0(X10,esk20_2(X10,X11)) = sdtpldt0(X11,smndt0(esk19_0))
| ~ aElementOf0(X11,szAzrzSzezqlpdtcmdtrp0(esk19_0,X10))
| ~ aInteger0(X10)
| X10 = sz00
| epred1_0 )
& ( aDivisorOf0(X10,sdtpldt0(X11,smndt0(esk19_0)))
| ~ aElementOf0(X11,szAzrzSzezqlpdtcmdtrp0(esk19_0,X10))
| ~ aInteger0(X10)
| X10 = sz00
| epred1_0 )
& ( sdteqdtlpzmzozddtrp0(X11,esk19_0,X10)
| ~ aElementOf0(X11,szAzrzSzezqlpdtcmdtrp0(esk19_0,X10))
| ~ aInteger0(X10)
| X10 = sz00
| epred1_0 )
& ( ~ aInteger0(X13)
| sdtasdt0(X10,X13) != sdtpldt0(X11,smndt0(esk19_0))
| ~ aInteger0(X11)
| aElementOf0(X11,szAzrzSzezqlpdtcmdtrp0(esk19_0,X10))
| ~ aInteger0(X10)
| X10 = sz00
| epred1_0 )
& ( ~ aDivisorOf0(X10,sdtpldt0(X11,smndt0(esk19_0)))
| ~ aInteger0(X11)
| aElementOf0(X11,szAzrzSzezqlpdtcmdtrp0(esk19_0,X10))
| ~ aInteger0(X10)
| X10 = sz00
| epred1_0 )
& ( ~ sdteqdtlpzmzozddtrp0(X11,esk19_0,X10)
| ~ aInteger0(X11)
| aElementOf0(X11,szAzrzSzezqlpdtcmdtrp0(esk19_0,X10))
| ~ aInteger0(X10)
| X10 = sz00
| epred1_0 )
& ( aElementOf0(esk21_1(X10),szAzrzSzezqlpdtcmdtrp0(esk19_0,X10))
| ~ aInteger0(X10)
| X10 = sz00
| epred1_0 )
& ( ~ aElementOf0(esk21_1(X10),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ aInteger0(X10)
| X10 = sz00
| epred1_0 )
& ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(esk19_0,X10),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ aInteger0(X10)
| X10 = sz00
| epred1_0 )
& ( ~ isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| epred1_0 )
& ( ~ isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
| epred1_0 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_6])])])])])])])]) ).
fof(c_0_9,negated_conjecture,
! [X3,X3,X5,X6,X6] :
( ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ epred1_0 )
& ( aInteger0(X3)
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ epred1_0 )
& ( aInteger0(esk16_1(X3))
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ epred1_0 )
& ( sdtasdt0(xq,esk16_1(X3)) = sdtpldt0(X3,smndt0(xa))
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ epred1_0 )
& ( aDivisorOf0(xq,sdtpldt0(X3,smndt0(xa)))
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ epred1_0 )
& ( sdteqdtlpzmzozddtrp0(X3,xa,xq)
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ epred1_0 )
& ( ~ aInteger0(X5)
| sdtasdt0(xq,X5) != sdtpldt0(X3,smndt0(xa))
| ~ aInteger0(X3)
| aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ epred1_0 )
& ( ~ aDivisorOf0(xq,sdtpldt0(X3,smndt0(xa)))
| ~ aInteger0(X3)
| aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ epred1_0 )
& ( ~ sdteqdtlpzmzozddtrp0(X3,xa,xq)
| ~ aInteger0(X3)
| aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ epred1_0 )
& ( aSet0(cS1395)
| ~ epred1_0 )
& ( ~ aElementOf0(X6,cS1395)
| aInteger0(X6)
| ~ epred1_0 )
& ( ~ aInteger0(X6)
| aElementOf0(X6,cS1395)
| ~ epred1_0 )
& ( aElementOf0(esk17_0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ epred1_0 )
& ( ~ aElementOf0(esk17_0,cS1395)
| ~ epred1_0 )
& ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395)
| ~ epred1_0 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])])])]) ).
cnf(c_0_10,plain,
( epred1_0
| aInteger0(X1)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,negated_conjecture,
( aInteger0(X1)
| ~ epred1_0
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,negated_conjecture,
( ~ epred1_0
| ~ aElementOf0(esk17_0,cS1395) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,negated_conjecture,
( aElementOf0(X1,cS1395)
| ~ epred1_0
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( aInteger0(X1)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(csr,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,negated_conjecture,
( aElementOf0(esk17_0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,negated_conjecture,
( ~ epred1_0
| ~ aInteger0(esk17_0) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( epred1_0
| aElementOf0(esk19_0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_18,negated_conjecture,
~ epred1_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
fof(c_0_19,plain,
! [X5,X6,X7,X8] :
( ~ aInteger0(X5)
| ~ aInteger0(X6)
| ~ aInteger0(X7)
| X7 = sz00
| ~ aInteger0(X8)
| ~ sdteqdtlpzmzozddtrp0(X5,X6,X7)
| ~ sdteqdtlpzmzozddtrp0(X6,X8,X7)
| sdteqdtlpzmzozddtrp0(X5,X8,X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquModTrn])]) ).
cnf(c_0_20,plain,
( epred1_0
| aInteger0(X1)
| ~ aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,plain,
aElementOf0(esk19_0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))),
inference(sr,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_22,plain,
! [X4,X5,X6] :
( ~ aInteger0(X4)
| ~ aInteger0(X5)
| ~ aInteger0(X6)
| X6 = sz00
| ~ sdteqdtlpzmzozddtrp0(X4,X5,X6)
| sdteqdtlpzmzozddtrp0(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquModSym])]) ).
cnf(c_0_23,negated_conjecture,
( sdteqdtlpzmzozddtrp0(X1,xa,xq)
| ~ epred1_0
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_24,plain,
( epred1_0
| sdteqdtlpzmzozddtrp0(X1,xa,xq)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_25,plain,
( sdteqdtlpzmzozddtrp0(X1,X2,X3)
| X3 = sz00
| ~ sdteqdtlpzmzozddtrp0(X4,X2,X3)
| ~ sdteqdtlpzmzozddtrp0(X1,X4,X3)
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| ~ aInteger0(X4)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( epred1_0
| X1 = sz00
| sdteqdtlpzmzozddtrp0(X2,esk19_0,X1)
| ~ aInteger0(X1)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(esk19_0,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_27,plain,
aInteger0(esk19_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_18]) ).
cnf(c_0_28,plain,
( sdteqdtlpzmzozddtrp0(X1,X2,X3)
| X3 = sz00
| ~ sdteqdtlpzmzozddtrp0(X2,X1,X3)
| ~ aInteger0(X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,negated_conjecture,
( sdteqdtlpzmzozddtrp0(X1,xa,xq)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(csr,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,hypothesis,
aInteger0(xq),
inference(split_conjunct,[status(thm)],[m__1962]) ).
cnf(c_0_31,hypothesis,
aInteger0(xa),
inference(split_conjunct,[status(thm)],[m__1962]) ).
cnf(c_0_32,hypothesis,
xq != sz00,
inference(split_conjunct,[status(thm)],[m__1962]) ).
cnf(c_0_33,plain,
( X1 = sz00
| sdteqdtlpzmzozddtrp0(X2,esk19_0,X1)
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(esk19_0,X1))
| ~ sdteqdtlpzmzozddtrp0(X2,X3,X1)
| ~ aInteger0(X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]),c_0_18]) ).
cnf(c_0_34,negated_conjecture,
( sdteqdtlpzmzozddtrp0(xa,X1,xq)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31])]),c_0_32]),c_0_14]) ).
cnf(c_0_35,plain,
( epred1_0
| X1 = sz00
| aInteger0(X2)
| ~ aInteger0(X1)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(esk19_0,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_36,plain,
( epred1_0
| X1 = sz00
| aElementOf0(esk21_1(X1),szAzrzSzezqlpdtcmdtrp0(esk19_0,X1))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_37,plain,
! [X4,X5,X6] :
( ( ~ sdteqdtlpzmzozddtrp0(X4,X5,X6)
| aDivisorOf0(X6,sdtpldt0(X4,smndt0(X5)))
| ~ aInteger0(X4)
| ~ aInteger0(X5)
| ~ aInteger0(X6)
| X6 = sz00 )
& ( ~ aDivisorOf0(X6,sdtpldt0(X4,smndt0(X5)))
| sdteqdtlpzmzozddtrp0(X4,X5,X6)
| ~ aInteger0(X4)
| ~ aInteger0(X5)
| ~ aInteger0(X6)
| X6 = sz00 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquMod])])]) ).
cnf(c_0_38,negated_conjecture,
( sdteqdtlpzmzozddtrp0(xa,esk19_0,xq)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(esk19_0,xq))
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_30]),c_0_31])]),c_0_32]),c_0_14]) ).
cnf(c_0_39,plain,
( epred1_0
| X1 = sz00
| ~ aInteger0(X1)
| ~ aElementOf0(esk21_1(X1),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_40,plain,
( epred1_0
| aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_41,plain,
( X1 = sz00
| aInteger0(esk21_1(X1))
| ~ aInteger0(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_18]) ).
cnf(c_0_42,plain,
( epred1_0
| aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X1)
| ~ sdteqdtlpzmzozddtrp0(X1,xa,xq) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_43,negated_conjecture,
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ epred1_0
| ~ aInteger0(X1)
| ~ sdteqdtlpzmzozddtrp0(X1,xa,xq) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_44,plain,
( epred1_0
| ~ aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_45,plain,
( epred1_0
| X1 = sz00
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(esk19_0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(esk19_0))) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_46,plain,
( X1 = sz00
| aDivisorOf0(X1,sdtpldt0(X3,smndt0(X2)))
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| ~ sdteqdtlpzmzozddtrp0(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_47,plain,
( sdteqdtlpzmzozddtrp0(xa,esk19_0,xq)
| ~ aElementOf0(esk21_1(xq),szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_36]),c_0_30])]),c_0_32]),c_0_18]) ).
cnf(c_0_48,plain,
( X1 = sz00
| aElementOf0(esk21_1(X1),szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_18]),c_0_41]) ).
cnf(c_0_49,plain,
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ sdteqdtlpzmzozddtrp0(X1,xa,xq)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_50,plain,
( X1 = sz00
| sdteqdtlpzmzozddtrp0(esk19_0,X2,X1)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(esk19_0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_26]),c_0_27])]),c_0_18]) ).
cnf(c_0_51,plain,
~ aElementOf0(esk19_0,szAzrzSzezqlpdtcmdtrp0(xa,xq)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_21]),c_0_18]) ).
cnf(c_0_52,plain,
( X1 = sz00
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(esk19_0,X1))
| ~ sdteqdtlpzmzozddtrp0(X2,esk19_0,X1)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_27])]),c_0_18]) ).
cnf(c_0_53,plain,
sdteqdtlpzmzozddtrp0(xa,esk19_0,xq),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_30])]),c_0_32]) ).
cnf(c_0_54,plain,
~ aElementOf0(xa,szAzrzSzezqlpdtcmdtrp0(esk19_0,xq)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_27]),c_0_30]),c_0_31])]),c_0_51]),c_0_32]) ).
cnf(c_0_55,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_31]),c_0_30])]),c_0_32]),c_0_54]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM442+6 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : run_ET %s %d
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jul 7 10:46:38 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.30/14.47 # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.30/14.47 # Preprocessing time : 0.024 s
% 0.30/14.47
% 0.30/14.47 # Proof found!
% 0.30/14.47 # SZS status Theorem
% 0.30/14.47 # SZS output start CNFRefutation
% See solution above
% 0.30/14.47 # Proof object total steps : 56
% 0.30/14.47 # Proof object clause steps : 43
% 0.30/14.47 # Proof object formula steps : 13
% 0.30/14.47 # Proof object conjectures : 14
% 0.30/14.47 # Proof object clause conjectures : 11
% 0.30/14.47 # Proof object formula conjectures : 3
% 0.30/14.47 # Proof object initial clauses used : 24
% 0.30/14.47 # Proof object initial formulas used : 5
% 0.30/14.47 # Proof object generating inferences : 15
% 0.30/14.47 # Proof object simplifying inferences : 47
% 0.30/14.47 # Training examples: 0 positive, 0 negative
% 0.30/14.47 # Parsed axioms : 42
% 0.30/14.47 # Removed by relevancy pruning/SinE : 0
% 0.30/14.47 # Initial clauses : 155
% 0.30/14.47 # Removed in clause preprocessing : 5
% 0.30/14.47 # Initial clauses in saturation : 150
% 0.30/14.47 # Processed clauses : 11769
% 0.30/14.47 # ...of these trivial : 470
% 0.30/14.47 # ...subsumed : 7960
% 0.30/14.47 # ...remaining for further processing : 3339
% 0.30/14.47 # Other redundant clauses eliminated : 1212
% 0.30/14.47 # Clauses deleted for lack of memory : 680503
% 0.30/14.47 # Backward-subsumed : 257
% 0.30/14.47 # Backward-rewritten : 254
% 0.30/14.47 # Generated clauses : 863626
% 0.30/14.47 # ...of the previous two non-trivial : 838773
% 0.30/14.47 # Contextual simplify-reflections : 3715
% 0.30/14.47 # Paramodulations : 862186
% 0.30/14.47 # Factorizations : 0
% 0.30/14.47 # Equation resolutions : 1393
% 0.30/14.47 # Current number of processed clauses : 2781
% 0.30/14.47 # Positive orientable unit clauses : 324
% 0.30/14.47 # Positive unorientable unit clauses: 0
% 0.30/14.47 # Negative unit clauses : 7
% 0.30/14.47 # Non-unit-clauses : 2450
% 0.30/14.47 # Current number of unprocessed clauses: 123827
% 0.30/14.47 # ...number of literals in the above : 742879
% 0.30/14.47 # Current number of archived formulas : 0
% 0.30/14.47 # Current number of archived clauses : 558
% 0.30/14.47 # Clause-clause subsumption calls (NU) : 1841197
% 0.30/14.47 # Rec. Clause-clause subsumption calls : 554573
% 0.30/14.47 # Non-unit clause-clause subsumptions : 11410
% 0.30/14.47 # Unit Clause-clause subsumption calls : 37559
% 0.30/14.47 # Rewrite failures with RHS unbound : 0
% 0.30/14.47 # BW rewrite match attempts : 266
% 0.30/14.47 # BW rewrite match successes : 65
% 0.30/14.47 # Condensation attempts : 0
% 0.30/14.47 # Condensation successes : 0
% 0.30/14.47 # Termbank termtop insertions : 22922290
% 0.30/14.47
% 0.30/14.47 # -------------------------------------------------
% 0.30/14.47 # User time : 13.906 s
% 0.30/14.47 # System time : 0.123 s
% 0.30/14.47 # Total time : 14.029 s
% 0.30/14.47 # Maximum resident set size: 143008 pages
%------------------------------------------------------------------------------