%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM442+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 : n004.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 01:49:06 PM UTC 2026
% Result : Theorem 9.35s 1.79s
% Output : CNFRefutation 9.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 77 ( 14 unt; 0 def)
% Number of atoms : 637 ( 89 equ)
% Maximal formula atoms : 106 ( 8 avg)
% Number of connectives : 782 ( 222 ~; 304 |; 182 &)
% ( 12 <=>; 62 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 2 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 158 ( 0 sgn 75 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( ! [X1] :
( ( ( ( sdteqdtlpzmzozddtrp0(X1,xa,xq)
| aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
| ? [X2] :
( sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa))
& aInteger0(X2) ) )
& aInteger0(X1) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(X1,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
& ? [X2] :
( sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa))
& aInteger0(X2) )
& aInteger0(X1) ) ) )
=> ( isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( ( ! [X1] :
( aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
<=> ( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aInteger0(X1) ) )
& aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
=> ( isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ! [X1] :
( aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
=> ? [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(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X3,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) ) )
& X2 != sz00
& aInteger0(X2) ) ) ) ) ) )
& ( ( ! [X1] :
( ( ( ( sdteqdtlpzmzozddtrp0(X1,xa,xq)
| aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
| ? [X2] :
( sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa))
& aInteger0(X2) ) )
& aInteger0(X1) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(X1,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
& ? [X2] :
( sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa))
& aInteger0(X2) )
& aInteger0(X1) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
=> ( ( ! [X1] :
( aElementOf0(X1,cS1395)
<=> aInteger0(X1) )
& aSet0(cS1395) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395)
| ! [X1] :
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> aElementOf0(X1,cS1395) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__1962,hypothesis,
( xq != sz00
& aInteger0(xq)
& aInteger0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1962) ).
fof(mArSeq,axiom,
! [X1,X2] :
( ( X2 != sz00
& aInteger0(X2)
& aInteger0(X1) )
=> ! [X3] :
( X3 = szAzrzSzezqlpdtcmdtrp0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( sdteqdtlpzmzozddtrp0(X4,X1,X2)
& aInteger0(X4) ) )
& aSet0(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mArSeq) ).
fof(mEquModSym,axiom,
! [X1,X2,X3] :
( ( X3 != sz00
& aInteger0(X3)
& aInteger0(X2)
& aInteger0(X1) )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
=> sdteqdtlpzmzozddtrp0(X2,X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquModSym) ).
fof(mEquModTrn,axiom,
! [X1,X2,X3,X4] :
( ( aInteger0(X4)
& X3 != sz00
& aInteger0(X3)
& aInteger0(X2)
& aInteger0(X1) )
=> ( ( sdteqdtlpzmzozddtrp0(X2,X4,X3)
& sdteqdtlpzmzozddtrp0(X1,X2,X3) )
=> sdteqdtlpzmzozddtrp0(X1,X4,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquModTrn) ).
fof(c_0_5,plain,
( epred1_0
<=> ( ! [X1] :
( ( ( ( sdteqdtlpzmzozddtrp0(X1,xa,xq)
| aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
| ? [X2] :
( sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa))
& aInteger0(X2) ) )
& aInteger0(X1) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(X1,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
& ? [X2] :
( sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa))
& aInteger0(X2) )
& aInteger0(X1) ) ) )
=> ( isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( ( ! [X1] :
( aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
<=> ( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aInteger0(X1) ) )
& aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
=> ( isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ! [X1] :
( aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
=> ? [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(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X3,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) ) )
& X2 != sz00
& aInteger0(X2) ) ) ) ) ) ) ),
introduced(definition) ).
fof(c_0_6,negated_conjecture,
~ ( ( ! [X1] :
( ( ( ( sdteqdtlpzmzozddtrp0(X1,xa,xq)
| aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
| ? [X2] :
( sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa))
& aInteger0(X2) ) )
& aInteger0(X1) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(X1,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
& ? [X2] :
( sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa))
& aInteger0(X2) )
& aInteger0(X1) ) ) )
=> ( isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( ( ! [X1] :
( aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
<=> ( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aInteger0(X1) ) )
& aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
=> ( isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ! [X1] :
( aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
=> ? [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(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X3,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) ) )
& X2 != sz00
& aInteger0(X2) ) ) ) ) ) )
& ( ( ! [X1] :
( ( ( ( sdteqdtlpzmzozddtrp0(X1,xa,xq)
| aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
| ? [X2] :
( sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa))
& aInteger0(X2) ) )
& aInteger0(X1) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(X1,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
& ? [X2] :
( sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa))
& aInteger0(X2) )
& aInteger0(X1) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
=> ( ( ! [X1] :
( aElementOf0(X1,cS1395)
<=> aInteger0(X1) )
& aSet0(cS1395) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395)
| ! [X1] :
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> aElementOf0(X1,cS1395) ) ) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_7,plain,
( ( ! [X1] :
( ( ( ( sdteqdtlpzmzozddtrp0(X1,xa,xq)
| aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
| ? [X2] :
( sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa))
& aInteger0(X2) ) )
& aInteger0(X1) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(X1,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
& ? [X2] :
( sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa))
& aInteger0(X2) )
& aInteger0(X1) ) ) )
=> ( isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( ( ! [X1] :
( aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
<=> ( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aInteger0(X1) ) )
& aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
=> ( isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ! [X1] :
( aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
=> ? [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(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X3,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) ) )
& X2 != sz00
& aInteger0(X2) ) ) ) ) ) )
=> epred1_0 ),
inference(split_equiv,[status(thm)],[c_0_5]) ).
fof(c_0_8,negated_conjecture,
~ ( epred1_0
& ( ( ! [X1] :
( ( ( ( sdteqdtlpzmzozddtrp0(X1,xa,xq)
| aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
| ? [X2] :
( sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa))
& aInteger0(X2) ) )
& aInteger0(X1) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(X1,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
& ? [X2] :
( sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa))
& aInteger0(X2) )
& aInteger0(X1) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
=> ( ( ! [X1] :
( aElementOf0(X1,cS1395)
<=> aInteger0(X1) )
& aSet0(cS1395) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395)
| ! [X1] :
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> aElementOf0(X1,cS1395) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_6]),c_0_5]) ).
fof(c_0_9,plain,
! [X123,X125,X126,X127,X129,X130,X132] :
( ( epred1_0
| ~ isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( epred1_0
| ~ isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
& ( epred1_0
| X129 = sz00
| ~ aInteger0(X129)
| ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(esk19_0,X129),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
& ( epred1_0
| X129 = sz00
| ~ aInteger0(X129)
| ~ aElementOf0(esk21_1(X129),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
& ( epred1_0
| X129 = sz00
| ~ aInteger0(X129)
| aElementOf0(esk21_1(X129),szAzrzSzezqlpdtcmdtrp0(esk19_0,X129)) )
& ( epred1_0
| X129 = sz00
| ~ aInteger0(X129)
| aElementOf0(X130,szAzrzSzezqlpdtcmdtrp0(esk19_0,X129))
| ~ aInteger0(X130)
| ~ sdteqdtlpzmzozddtrp0(X130,esk19_0,X129) )
& ( epred1_0
| X129 = sz00
| ~ aInteger0(X129)
| aElementOf0(X130,szAzrzSzezqlpdtcmdtrp0(esk19_0,X129))
| ~ aInteger0(X130)
| ~ aDivisorOf0(X129,sdtpldt0(X130,smndt0(esk19_0))) )
& ( epred1_0
| X129 = sz00
| ~ aInteger0(X129)
| aElementOf0(X130,szAzrzSzezqlpdtcmdtrp0(esk19_0,X129))
| ~ aInteger0(X130)
| sdtasdt0(X129,X132) != sdtpldt0(X130,smndt0(esk19_0))
| ~ aInteger0(X132) )
& ( epred1_0
| X129 = sz00
| ~ aInteger0(X129)
| ~ aElementOf0(X130,szAzrzSzezqlpdtcmdtrp0(esk19_0,X129))
| sdteqdtlpzmzozddtrp0(X130,esk19_0,X129) )
& ( epred1_0
| X129 = sz00
| ~ aInteger0(X129)
| ~ aElementOf0(X130,szAzrzSzezqlpdtcmdtrp0(esk19_0,X129))
| aDivisorOf0(X129,sdtpldt0(X130,smndt0(esk19_0))) )
& ( epred1_0
| X129 = sz00
| ~ aInteger0(X129)
| ~ aElementOf0(X130,szAzrzSzezqlpdtcmdtrp0(esk19_0,X129))
| sdtasdt0(X129,esk20_2(X129,X130)) = sdtpldt0(X130,smndt0(esk19_0)) )
& ( epred1_0
| X129 = sz00
| ~ aInteger0(X129)
| ~ aElementOf0(X130,szAzrzSzezqlpdtcmdtrp0(esk19_0,X129))
| aInteger0(esk20_2(X129,X130)) )
& ( epred1_0
| X129 = sz00
| ~ aInteger0(X129)
| ~ aElementOf0(X130,szAzrzSzezqlpdtcmdtrp0(esk19_0,X129))
| aInteger0(X130) )
& ( epred1_0
| X129 = sz00
| ~ aInteger0(X129)
| aSet0(szAzrzSzezqlpdtcmdtrp0(esk19_0,X129)) )
& ( epred1_0
| aElementOf0(esk19_0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
& ( epred1_0
| aElementOf0(X127,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| aElementOf0(X127,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X127) )
& ( epred1_0
| ~ aElementOf0(X127,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ aElementOf0(X127,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( epred1_0
| ~ aElementOf0(X127,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| aInteger0(X127) )
& ( epred1_0
| aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
& ( epred1_0
| aElementOf0(X125,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X125)
| ~ sdteqdtlpzmzozddtrp0(X125,xa,xq) )
& ( epred1_0
| aElementOf0(X125,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X125)
| ~ aDivisorOf0(xq,sdtpldt0(X125,smndt0(xa))) )
& ( epred1_0
| aElementOf0(X125,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X125)
| sdtasdt0(xq,X126) != sdtpldt0(X125,smndt0(xa))
| ~ aInteger0(X126) )
& ( epred1_0
| ~ aElementOf0(X123,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| sdteqdtlpzmzozddtrp0(X123,xa,xq) )
& ( epred1_0
| ~ aElementOf0(X123,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aDivisorOf0(xq,sdtpldt0(X123,smndt0(xa))) )
& ( epred1_0
| ~ aElementOf0(X123,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| sdtasdt0(xq,esk18_1(X123)) = sdtpldt0(X123,smndt0(xa)) )
& ( epred1_0
| ~ aElementOf0(X123,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aInteger0(esk18_1(X123)) )
& ( epred1_0
| ~ aElementOf0(X123,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aInteger0(X123) ) ),
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,negated_conjecture,
! [X117,X119,X120,X121] :
( ( ~ epred1_0
| ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395) )
& ( ~ epred1_0
| ~ aElementOf0(esk17_0,cS1395) )
& ( ~ epred1_0
| aElementOf0(esk17_0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ epred1_0
| aElementOf0(X121,cS1395)
| ~ aInteger0(X121) )
& ( ~ epred1_0
| aInteger0(X121)
| ~ aElementOf0(X121,cS1395) )
& ( ~ epred1_0
| aSet0(cS1395) )
& ( ~ epred1_0
| aElementOf0(X119,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X119)
| ~ sdteqdtlpzmzozddtrp0(X119,xa,xq) )
& ( ~ epred1_0
| aElementOf0(X119,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X119)
| ~ aDivisorOf0(xq,sdtpldt0(X119,smndt0(xa))) )
& ( ~ epred1_0
| aElementOf0(X119,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X119)
| sdtasdt0(xq,X120) != sdtpldt0(X119,smndt0(xa))
| ~ aInteger0(X120) )
& ( ~ epred1_0
| ~ aElementOf0(X117,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| sdteqdtlpzmzozddtrp0(X117,xa,xq) )
& ( ~ epred1_0
| ~ aElementOf0(X117,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aDivisorOf0(xq,sdtpldt0(X117,smndt0(xa))) )
& ( ~ epred1_0
| ~ aElementOf0(X117,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| sdtasdt0(xq,esk16_1(X117)) = sdtpldt0(X117,smndt0(xa)) )
& ( ~ epred1_0
| ~ aElementOf0(X117,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aInteger0(esk16_1(X117)) )
& ( ~ epred1_0
| ~ aElementOf0(X117,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aInteger0(X117) )
& ( ~ epred1_0
| aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ),
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])])])])])])]) ).
cnf(c_0_11,plain,
( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| epred1_0
| aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,negated_conjecture,
( ~ epred1_0
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,plain,
( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aInteger0(X1) ),
inference(csr,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,negated_conjecture,
( ~ epred1_0
| aElementOf0(esk17_0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
( ~ epred1_0
| ~ aElementOf0(esk17_0,cS1395) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
( ~ epred1_0
| ~ aInteger0(X1)
| aElementOf0(X1,cS1395) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
( ~ epred1_0
| aInteger0(esk17_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_18,hypothesis,
( xq != sz00
& aInteger0(xq)
& aInteger0(xa) ),
inference(fof_simplification,[status(thm)],[m__1962]) ).
fof(c_0_19,plain,
! [X1,X2] :
( ( X2 != sz00
& aInteger0(X2)
& aInteger0(X1) )
=> ! [X3] :
( X3 = szAzrzSzezqlpdtcmdtrp0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( sdteqdtlpzmzozddtrp0(X4,X1,X2)
& aInteger0(X4) ) )
& aSet0(X3) ) ) ),
inference(fof_simplification,[status(thm)],[mArSeq]) ).
cnf(c_0_20,plain,
( ~ aInteger0(X1)
| epred1_0
| X1 = sz00
| aElementOf0(esk21_1(X1),szAzrzSzezqlpdtcmdtrp0(esk19_0,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_21,negated_conjecture,
~ epred1_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
fof(c_0_22,hypothesis,
( xq != sz00
& aInteger0(xq)
& aInteger0(xa) ),
inference(fof_nnf,[status(thm)],[c_0_18]) ).
fof(c_0_23,plain,
! [X96,X97,X98,X99,X100,X101] :
( ( X97 = sz00
| ~ aInteger0(X97)
| ~ aInteger0(X96)
| X101 = szAzrzSzezqlpdtcmdtrp0(X96,X97)
| ~ aSet0(X101)
| aElementOf0(esk11_3(X96,X97,X101),X101)
| sdteqdtlpzmzozddtrp0(esk11_3(X96,X97,X101),X96,X97) )
& ( X97 = sz00
| ~ aInteger0(X97)
| ~ aInteger0(X96)
| X101 = szAzrzSzezqlpdtcmdtrp0(X96,X97)
| ~ aSet0(X101)
| aElementOf0(esk11_3(X96,X97,X101),X101)
| aInteger0(esk11_3(X96,X97,X101)) )
& ( X97 = sz00
| ~ aInteger0(X97)
| ~ aInteger0(X96)
| X101 = szAzrzSzezqlpdtcmdtrp0(X96,X97)
| ~ aSet0(X101)
| ~ sdteqdtlpzmzozddtrp0(esk11_3(X96,X97,X101),X96,X97)
| ~ aInteger0(esk11_3(X96,X97,X101))
| ~ aElementOf0(esk11_3(X96,X97,X101),X101) )
& ( X97 = sz00
| ~ aInteger0(X97)
| ~ aInteger0(X96)
| X98 != szAzrzSzezqlpdtcmdtrp0(X96,X97)
| aElementOf0(X100,X98)
| ~ sdteqdtlpzmzozddtrp0(X100,X96,X97)
| ~ aInteger0(X100) )
& ( X97 = sz00
| ~ aInteger0(X97)
| ~ aInteger0(X96)
| X98 != szAzrzSzezqlpdtcmdtrp0(X96,X97)
| ~ aElementOf0(X99,X98)
| sdteqdtlpzmzozddtrp0(X99,X96,X97) )
& ( X97 = sz00
| ~ aInteger0(X97)
| ~ aInteger0(X96)
| X98 != szAzrzSzezqlpdtcmdtrp0(X96,X97)
| ~ aElementOf0(X99,X98)
| aInteger0(X99) )
& ( X97 = sz00
| ~ aInteger0(X97)
| ~ aInteger0(X96)
| X98 != szAzrzSzezqlpdtcmdtrp0(X96,X97)
| aSet0(X98) ) ),
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_19])])])])])])]) ).
cnf(c_0_24,plain,
( ~ aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| epred1_0
| aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_25,plain,
( epred1_0
| aElementOf0(esk19_0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_26,plain,
! [X1,X2,X3] :
( ( X3 != sz00
& aInteger0(X3)
& aInteger0(X2)
& aInteger0(X1) )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
=> sdteqdtlpzmzozddtrp0(X2,X1,X3) ) ),
inference(fof_simplification,[status(thm)],[mEquModSym]) ).
cnf(c_0_27,plain,
( ~ aInteger0(X2)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(esk19_0,X2))
| epred1_0
| X2 = sz00
| sdteqdtlpzmzozddtrp0(X1,esk19_0,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_28,plain,
( ~ aInteger0(X1)
| aElementOf0(esk21_1(X1),szAzrzSzezqlpdtcmdtrp0(esk19_0,X1))
| X1 = sz00 ),
inference(sr,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_29,hypothesis,
aInteger0(xq),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,hypothesis,
xq != sz00,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,plain,
( ~ aInteger0(X4)
| ~ aInteger0(X3)
| X2 != szAzrzSzezqlpdtcmdtrp0(X3,X4)
| ~ aElementOf0(X1,X2)
| X4 = sz00
| aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,plain,
( ~ aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| aInteger0(X1) ),
inference(sr,[status(thm)],[c_0_24,c_0_21]) ).
cnf(c_0_33,plain,
aElementOf0(esk19_0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))),
inference(sr,[status(thm)],[c_0_25,c_0_21]) ).
fof(c_0_34,plain,
! [X1,X2,X3,X4] :
( ( aInteger0(X4)
& X3 != sz00
& aInteger0(X3)
& aInteger0(X2)
& aInteger0(X1) )
=> ( ( sdteqdtlpzmzozddtrp0(X2,X4,X3)
& sdteqdtlpzmzozddtrp0(X1,X2,X3) )
=> sdteqdtlpzmzozddtrp0(X1,X4,X3) ) ),
inference(fof_simplification,[status(thm)],[mEquModTrn]) ).
fof(c_0_35,plain,
! [X41,X42,X43] :
( sdteqdtlpzmzozddtrp0(X42,X41,X43)
| ~ sdteqdtlpzmzozddtrp0(X41,X42,X43)
| X43 = sz00
| ~ aInteger0(X43)
| ~ aInteger0(X42)
| ~ aInteger0(X41) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])]) ).
cnf(c_0_36,plain,
( ~ aInteger0(X1)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(esk19_0,X1))
| sdteqdtlpzmzozddtrp0(X2,esk19_0,X1)
| X1 = sz00 ),
inference(sr,[status(thm)],[c_0_27,c_0_21]) ).
cnf(c_0_37,hypothesis,
aElementOf0(esk21_1(xq),szAzrzSzezqlpdtcmdtrp0(esk19_0,xq)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_38,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X1)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X3,X1))
| aInteger0(X2)
| X1 = sz00 ),
inference(er,[status(thm)],[c_0_31]) ).
cnf(c_0_39,plain,
aInteger0(esk19_0),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
fof(c_0_40,plain,
! [X44,X45,X46,X47] :
( sdteqdtlpzmzozddtrp0(X44,X47,X46)
| ~ sdteqdtlpzmzozddtrp0(X45,X47,X46)
| ~ sdteqdtlpzmzozddtrp0(X44,X45,X46)
| ~ aInteger0(X47)
| X46 = sz00
| ~ aInteger0(X46)
| ~ aInteger0(X45)
| ~ aInteger0(X44) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])]) ).
cnf(c_0_41,plain,
( ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdteqdtlpzmzozddtrp0(X2,X1,X3)
| X3 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_42,hypothesis,
sdteqdtlpzmzozddtrp0(esk21_1(xq),esk19_0,xq),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_29])]),c_0_30]) ).
cnf(c_0_43,hypothesis,
aInteger0(esk21_1(xq)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_37]),c_0_29]),c_0_39])]),c_0_30]) ).
cnf(c_0_44,plain,
( ~ sdteqdtlpzmzozddtrp0(X2,X4,X3)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ aInteger0(X4)
| ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdteqdtlpzmzozddtrp0(X1,X4,X3)
| X3 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_45,hypothesis,
sdteqdtlpzmzozddtrp0(esk19_0,esk21_1(xq),xq),
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_41,c_0_42]),c_0_29]),c_0_39]),c_0_43])]),c_0_30]) ).
cnf(c_0_46,plain,
( ~ aInteger0(X1)
| ~ sdteqdtlpzmzozddtrp0(X1,xa,xq)
| epred1_0
| aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_47,negated_conjecture,
( ~ epred1_0
| ~ aInteger0(X1)
| ~ sdteqdtlpzmzozddtrp0(X1,xa,xq)
| aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_48,hypothesis,
( ~ aInteger0(X1)
| ~ sdteqdtlpzmzozddtrp0(X1,esk19_0,xq)
| sdteqdtlpzmzozddtrp0(X1,esk21_1(xq),xq) ),
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_44,c_0_45]),c_0_43]),c_0_29]),c_0_39])]),c_0_30]) ).
cnf(c_0_49,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| X4 != szAzrzSzezqlpdtcmdtrp0(X2,X3)
| ~ aElementOf0(X1,X4)
| X3 = sz00
| sdteqdtlpzmzozddtrp0(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_50,plain,
( ~ aInteger0(X1)
| ~ sdteqdtlpzmzozddtrp0(X1,xa,xq)
| aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(csr,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_51,hypothesis,
( ~ aInteger0(X1)
| ~ sdteqdtlpzmzozddtrp0(X1,esk19_0,xq)
| sdteqdtlpzmzozddtrp0(esk21_1(xq),X1,xq) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_48]),c_0_29]),c_0_43])]),c_0_30]) ).
cnf(c_0_52,hypothesis,
aInteger0(xa),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_53,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X1)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X3,X1))
| sdteqdtlpzmzozddtrp0(X2,X3,X1)
| X1 = sz00 ),
inference(er,[status(thm)],[c_0_49]) ).
cnf(c_0_54,plain,
( ~ sdteqdtlpzmzozddtrp0(xa,esk19_0,xq)
| aElementOf0(esk21_1(xq),szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_43]),c_0_52])]) ).
cnf(c_0_55,plain,
( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| epred1_0
| sdteqdtlpzmzozddtrp0(X1,xa,xq) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_56,negated_conjecture,
( ~ epred1_0
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| sdteqdtlpzmzozddtrp0(X1,xa,xq) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_57,plain,
( ~ aInteger0(X1)
| epred1_0
| aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_58,plain,
( ~ sdteqdtlpzmzozddtrp0(xa,esk19_0,xq)
| sdteqdtlpzmzozddtrp0(esk21_1(xq),xa,xq) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_29]),c_0_52])]),c_0_30]) ).
cnf(c_0_59,plain,
( ~ aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_60,plain,
( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| sdteqdtlpzmzozddtrp0(X1,xa,xq) ),
inference(csr,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_61,plain,
( ~ aInteger0(X1)
| ~ aElementOf0(esk21_1(X1),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| epred1_0
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_62,plain,
( ~ aInteger0(X1)
| aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ),
inference(sr,[status(thm)],[c_0_57,c_0_21]) ).
cnf(c_0_63,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| X4 != szAzrzSzezqlpdtcmdtrp0(X2,X3)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ aInteger0(X1)
| X3 = sz00
| aElementOf0(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_64,plain,
( ~ aInteger0(X1)
| ~ sdteqdtlpzmzozddtrp0(xa,esk19_0,xq)
| ~ sdteqdtlpzmzozddtrp0(X1,esk21_1(xq),xq)
| sdteqdtlpzmzozddtrp0(X1,xa,xq) ),
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_44,c_0_58]),c_0_52]),c_0_29]),c_0_43])]),c_0_30]) ).
cnf(c_0_65,plain,
( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ),
inference(sr,[status(thm)],[c_0_59,c_0_21]) ).
cnf(c_0_66,hypothesis,
( ~ aInteger0(X1)
| ~ sdteqdtlpzmzozddtrp0(X1,esk21_1(xq),xq)
| sdteqdtlpzmzozddtrp0(X1,esk19_0,xq) ),
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_44,c_0_42]),c_0_39]),c_0_29]),c_0_43])]),c_0_30]) ).
cnf(c_0_67,plain,
( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| sdteqdtlpzmzozddtrp0(xa,X1,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_41,c_0_60]),c_0_29]),c_0_52])]),c_0_30]),c_0_13]) ).
cnf(c_0_68,plain,
( ~ aInteger0(X1)
| ~ aElementOf0(esk21_1(X1),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| X1 = sz00 ),
inference(sr,[status(thm)],[c_0_61,c_0_21]) ).
cnf(c_0_69,plain,
( aElementOf0(esk21_1(xq),szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aElementOf0(esk21_1(xq),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ),
inference(spm,[status(thm)],[c_0_62,c_0_43]) ).
cnf(c_0_70,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X3)
| ~ aInteger0(X1)
| ~ sdteqdtlpzmzozddtrp0(X2,X3,X1)
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X3,X1))
| X1 = sz00 ),
inference(er,[status(thm)],[c_0_63]) ).
cnf(c_0_71,hypothesis,
( ~ sdteqdtlpzmzozddtrp0(xa,esk19_0,xq)
| sdteqdtlpzmzozddtrp0(esk19_0,xa,xq) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_45]),c_0_39])]) ).
cnf(c_0_72,plain,
~ aElementOf0(esk19_0,szAzrzSzezqlpdtcmdtrp0(xa,xq)),
inference(spm,[status(thm)],[c_0_65,c_0_33]) ).
cnf(c_0_73,plain,
( ~ aElementOf0(esk21_1(xq),szAzrzSzezqlpdtcmdtrp0(xa,xq))
| sdteqdtlpzmzozddtrp0(xa,esk19_0,xq) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_52])]) ).
cnf(c_0_74,plain,
aElementOf0(esk21_1(xq),szAzrzSzezqlpdtcmdtrp0(xa,xq)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_29])]),c_0_30]) ).
cnf(c_0_75,hypothesis,
~ sdteqdtlpzmzozddtrp0(xa,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_70,c_0_71]),c_0_29]),c_0_52]),c_0_39])]),c_0_30]),c_0_72]) ).
cnf(c_0_76,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_74])]),c_0_75]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM442+6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.44 % Computer : n004.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 02:29:53 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.51 Running first-order theorem proving
% 0.24/0.51 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
% 9.35/1.79 % Version: 3.5.1
% 9.35/1.79 % Preprocessing class: FSLSSMSSSSSNFFN.
% 9.35/1.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.35/1.79 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 9.35/1.79 % Starting new_bool_3 with 300s (1) cores
% 9.35/1.79 % Starting new_bool_1 with 300s (1) cores
% 9.35/1.79 % Starting sh5l with 300s (1) cores
% 9.35/1.79 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2057053 completed with status 0
% 9.35/1.79 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 9.35/1.79 % Preprocessing class: FSLSSMSSSSSNFFN.
% 9.35/1.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.35/1.79 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 9.35/1.79 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 9.35/1.79 % No SInE strategy applied
% 9.35/1.79 % Search class: FGHSF-FSLM31-SFFFFFNN
% 9.35/1.79 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 9.35/1.79 % Starting SubtermCWHack with 136s (1) cores
% 9.35/1.79 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 9.35/1.79 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 198s (1) cores
% 9.35/1.79 % Starting new_bool_3 with 194s (1) cores
% 9.35/1.79 % Starting new_bool_1 with 188s (1) cores
% 9.35/1.79 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 2057061 completed with status 0
% 9.35/1.79 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 9.35/1.79 % Preprocessing class: FSLSSMSSSSSNFFN.
% 9.35/1.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.35/1.79 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 9.35/1.79 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 9.35/1.79 % No SInE strategy applied
% 9.35/1.79 % Search class: FGHSF-FSLM31-SFFFFFNN
% 9.35/1.79 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 9.35/1.79 % Starting SubtermCWHack with 136s (1) cores
% 9.35/1.79 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 9.35/1.79 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 198s (1) cores
% 9.35/1.79 % Preprocessing time : 0.006 s
% 9.35/1.79 % Presaturation interreduction done
% 9.35/1.79
% 9.35/1.79 % Proof found!
% 9.35/1.79 % SZS status Theorem
% 9.35/1.79 % SZS output start CNFRefutation
% See solution above
% 9.35/1.79 % Parsed axioms : 42
% 9.35/1.79 % Removed by relevancy pruning/SinE : 0
% 9.35/1.79 % Initial clauses : 155
% 9.35/1.79 % Removed in clause preprocessing : 5
% 9.35/1.79 % Initial clauses in saturation : 150
% 9.35/1.79 % Processed clauses : 3417
% 9.35/1.79 % ...of these trivial : 17
% 9.35/1.79 % ...subsumed : 1397
% 9.35/1.79 % ...remaining for further processing : 2003
% 9.35/1.79 % Other redundant clauses eliminated : 42
% 9.35/1.79 % Clauses deleted for lack of memory : 0
% 9.35/1.79 % Backward-subsumed : 108
% 9.35/1.79 % Backward-rewritten : 50
% 9.35/1.79 % Generated clauses : 30207
% 9.35/1.79 % ...of the previous two non-redundant : 29539
% 9.35/1.79 % ...aggressively subsumed : 0
% 9.35/1.79 % Contextual simplify-reflections : 100
% 9.35/1.79 % Paramodulations : 30163
% 9.35/1.79 % Factorizations : 0
% 9.35/1.79 % NegExts : 0
% 9.35/1.79 % Equation resolutions : 43
% 9.35/1.79 % Disequality decompositions : 0
% 9.35/1.79 % Total rewrite steps : 5230
% 9.35/1.79 % ...of those cached : 5184
% 9.35/1.79 % Propositional unsat checks : 0
% 9.35/1.79 % Propositional check models : 0
% 9.35/1.79 % Propositional check unsatisfiable : 0
% 9.35/1.79 % Propositional clauses : 0
% 9.35/1.79 % Propositional clauses after purity: 0
% 9.35/1.79 % Propositional unsat core size : 0
% 9.35/1.79 % Propositional preprocessing time : 0.000
% 9.35/1.79 % Propositional encoding time : 0.000
% 9.35/1.79 % Propositional solver time : 0.000
% 9.35/1.79 % Success case prop preproc time : 0.000
% 9.35/1.79 % Success case prop encoding time : 0.000
% 9.35/1.79 % Success case prop solver time : 0.000
% 9.35/1.79 % Current number of processed clauses : 1668
% 9.35/1.79 % Positive orientable unit clauses : 54
% 9.35/1.79 % Positive unorientable unit clauses: 0
% 9.35/1.79 % Negative unit clauses : 4
% 9.35/1.79 % Non-unit-clauses : 1610
% 9.35/1.79 % Current number of unprocessed clauses: 26376
% 9.35/1.79 % ...number of literals in the above : 93493
% 9.35/1.79 % Current number of archived formulas : 0
% 9.35/1.79 % Current number of archived clauses : 303
% 9.35/1.79 % Clause-clause subsumption calls (NU) : 441255
% 9.35/1.79 % Rec. Clause-clause subsumption calls : 277035
% 9.35/1.79 % Non-unit clause-clause subsumptions : 1582
% 9.35/1.79 % Unit Clause-clause subsumption calls : 2476
% 9.35/1.79 % Rewrite failures with RHS unbound : 0
% 9.35/1.79 % BW rewrite match attempts : 30
% 9.35/1.79 % BW rewrite match successes : 10
% 9.35/1.79 % Condensation attempts : 0
% 9.35/1.79 % Condensation successes : 0
% 9.35/1.79 % Termbank termtop insertions : 606051
% 9.35/1.79 % Search garbage collected termcells : 3175
% 9.35/1.79
% 9.35/1.79 % -------------------------------------------------
% 9.35/1.79 % User time : 1.165 s
% 9.35/1.79 % System time : 0.056 s
% 9.35/1.79 % Total time : 1.221 s
% 9.35/1.79 % Maximum resident set size: 3912 pages
% 9.35/1.79
% 9.35/1.79 % -------------------------------------------------
% 9.35/1.79 % User time : 5.873 s
% 9.35/1.79 % System time : 0.219 s
% 9.35/1.79 % Total time : 6.092 s
% 9.35/1.79 % Maximum resident set size: 4608 pages
% 9.35/1.79 % E exiting
%------------------------------------------------------------------------------