%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM437+5 : 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 : n013.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 01:49:05 PM UTC 2026
% Result : Theorem 0.13s 5.49s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 7 unt; 0 def)
% Number of atoms : 343 ( 42 equ)
% Maximal formula atoms : 69 ( 10 avg)
% Number of connectives : 425 ( 114 ~; 135 |; 133 &)
% ( 7 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-3 aty)
% Number of variables : 87 ( 0 sgn 47 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( ? [X2] :
( aElementOf0(X1,X2)
& aElementOf0(X2,xS) )
& aInteger0(X1) ) )
& aSet0(sbsmnsldt0(xS)) )
=> ( isOpen0(sbsmnsldt0(xS))
| ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
=> ? [X2] :
( ( ( ! [X3] :
( ( ( ( sdteqdtlpzmzozddtrp0(X3,X1,X2)
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
| ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1))
& aInteger0(X4) ) )
& aInteger0(X3) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) )
& ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> ( sdteqdtlpzmzozddtrp0(X3,X1,X2)
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1))
& aInteger0(X4) )
& aInteger0(X3) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2)) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),sbsmnsldt0(xS))
| ! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X3,sbsmnsldt0(xS)) ) ) )
& X2 != sz00
& aInteger0(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__1750,hypothesis,
( ! [X1] :
( aElementOf0(X1,xS)
=> ( isOpen0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> ? [X3] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X2,X3),X1)
& ! [X4] :
( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3))
=> aElementOf0(X4,X1) )
& ! [X4] :
( ( ( ( sdteqdtlpzmzozddtrp0(X4,X2,X3)
| aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
| ? [X5] :
( sdtasdt0(X3,X5) = sdtpldt0(X4,smndt0(X2))
& aInteger0(X5) ) )
& aInteger0(X4) )
=> aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
& ( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3))
=> ( sdteqdtlpzmzozddtrp0(X4,X2,X3)
& aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& ? [X5] :
( sdtasdt0(X3,X5) = sdtpldt0(X4,smndt0(X2))
& aInteger0(X5) )
& aInteger0(X4) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X2,X3))
& X3 != sz00
& aInteger0(X3) ) )
& aSubsetOf0(X1,cS1395)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,cS1395) )
& aSet0(X1)
& ! [X2] :
( aElementOf0(X2,cS1395)
<=> aInteger0(X2) )
& aSet0(cS1395) ) )
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1750) ).
fof(c_0_2,negated_conjecture,
~ ( ( ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( ? [X2] :
( aElementOf0(X1,X2)
& aElementOf0(X2,xS) )
& aInteger0(X1) ) )
& aSet0(sbsmnsldt0(xS)) )
=> ( isOpen0(sbsmnsldt0(xS))
| ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
=> ? [X2] :
( ( ( ! [X3] :
( ( ( ( sdteqdtlpzmzozddtrp0(X3,X1,X2)
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
| ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1))
& aInteger0(X4) ) )
& aInteger0(X3) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) )
& ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> ( sdteqdtlpzmzozddtrp0(X3,X1,X2)
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1))
& aInteger0(X4) )
& aInteger0(X3) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2)) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),sbsmnsldt0(xS))
| ! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X3,sbsmnsldt0(xS)) ) ) )
& X2 != sz00
& aInteger0(X2) ) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_3,plain,
! [X1] :
( epred1_1(X1)
<=> ( isOpen0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> ? [X3] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X2,X3),X1)
& ! [X4] :
( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3))
=> aElementOf0(X4,X1) )
& ! [X4] :
( ( ( ( sdteqdtlpzmzozddtrp0(X4,X2,X3)
| aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
| ? [X5] :
( sdtasdt0(X3,X5) = sdtpldt0(X4,smndt0(X2))
& aInteger0(X5) ) )
& aInteger0(X4) )
=> aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
& ( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3))
=> ( sdteqdtlpzmzozddtrp0(X4,X2,X3)
& aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& ? [X5] :
( sdtasdt0(X3,X5) = sdtpldt0(X4,smndt0(X2))
& aInteger0(X5) )
& aInteger0(X4) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X2,X3))
& X3 != sz00
& aInteger0(X3) ) )
& aSubsetOf0(X1,cS1395)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,cS1395) )
& aSet0(X1)
& ! [X2] :
( aElementOf0(X2,cS1395)
<=> aInteger0(X2) )
& aSet0(cS1395) ) ),
introduced(definition) ).
fof(c_0_4,negated_conjecture,
~ ( ( ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( ? [X2] :
( aElementOf0(X1,X2)
& aElementOf0(X2,xS) )
& aInteger0(X1) ) )
& aSet0(sbsmnsldt0(xS)) )
=> ( isOpen0(sbsmnsldt0(xS))
| ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
=> ? [X2] :
( ( ( ! [X3] :
( ( ( ( sdteqdtlpzmzozddtrp0(X3,X1,X2)
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
| ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1))
& aInteger0(X4) ) )
& aInteger0(X3) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) )
& ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> ( sdteqdtlpzmzozddtrp0(X3,X1,X2)
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1))
& aInteger0(X4) )
& aInteger0(X3) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2)) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),sbsmnsldt0(xS))
| ! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X3,sbsmnsldt0(xS)) ) ) )
& X2 != sz00
& aInteger0(X2) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_5,hypothesis,
( ! [X1] :
( aElementOf0(X1,xS)
=> epred1_1(X1) )
& aSet0(xS) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[m__1750]),c_0_3]) ).
fof(c_0_6,negated_conjecture,
! [X111,X113,X114,X116,X117,X119] :
( ~ isOpen0(sbsmnsldt0(xS))
& ( X116 = sz00
| ~ aInteger0(X116)
| ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(esk15_0,X116),sbsmnsldt0(xS)) )
& ( X116 = sz00
| ~ aInteger0(X116)
| ~ aElementOf0(esk17_1(X116),sbsmnsldt0(xS)) )
& ( X116 = sz00
| ~ aInteger0(X116)
| aElementOf0(esk17_1(X116),szAzrzSzezqlpdtcmdtrp0(esk15_0,X116)) )
& ( X116 = sz00
| ~ aInteger0(X116)
| aElementOf0(X117,szAzrzSzezqlpdtcmdtrp0(esk15_0,X116))
| ~ aInteger0(X117)
| ~ sdteqdtlpzmzozddtrp0(X117,esk15_0,X116) )
& ( X116 = sz00
| ~ aInteger0(X116)
| aElementOf0(X117,szAzrzSzezqlpdtcmdtrp0(esk15_0,X116))
| ~ aInteger0(X117)
| ~ aDivisorOf0(X116,sdtpldt0(X117,smndt0(esk15_0))) )
& ( X116 = sz00
| ~ aInteger0(X116)
| aElementOf0(X117,szAzrzSzezqlpdtcmdtrp0(esk15_0,X116))
| ~ aInteger0(X117)
| sdtasdt0(X116,X119) != sdtpldt0(X117,smndt0(esk15_0))
| ~ aInteger0(X119) )
& ( X116 = sz00
| ~ aInteger0(X116)
| ~ aElementOf0(X117,szAzrzSzezqlpdtcmdtrp0(esk15_0,X116))
| sdteqdtlpzmzozddtrp0(X117,esk15_0,X116) )
& ( X116 = sz00
| ~ aInteger0(X116)
| ~ aElementOf0(X117,szAzrzSzezqlpdtcmdtrp0(esk15_0,X116))
| aDivisorOf0(X116,sdtpldt0(X117,smndt0(esk15_0))) )
& ( X116 = sz00
| ~ aInteger0(X116)
| ~ aElementOf0(X117,szAzrzSzezqlpdtcmdtrp0(esk15_0,X116))
| sdtasdt0(X116,esk16_2(X116,X117)) = sdtpldt0(X117,smndt0(esk15_0)) )
& ( X116 = sz00
| ~ aInteger0(X116)
| ~ aElementOf0(X117,szAzrzSzezqlpdtcmdtrp0(esk15_0,X116))
| aInteger0(esk16_2(X116,X117)) )
& ( X116 = sz00
| ~ aInteger0(X116)
| ~ aElementOf0(X117,szAzrzSzezqlpdtcmdtrp0(esk15_0,X116))
| aInteger0(X117) )
& ( X116 = sz00
| ~ aInteger0(X116)
| aSet0(szAzrzSzezqlpdtcmdtrp0(esk15_0,X116)) )
& aElementOf0(esk15_0,sbsmnsldt0(xS))
& ( aElementOf0(X113,sbsmnsldt0(xS))
| ~ aElementOf0(X113,X114)
| ~ aElementOf0(X114,xS)
| ~ aInteger0(X113) )
& ( ~ aElementOf0(X111,sbsmnsldt0(xS))
| aElementOf0(X111,esk14_1(X111)) )
& ( ~ aElementOf0(X111,sbsmnsldt0(xS))
| aElementOf0(esk14_1(X111),xS) )
& ( ~ aElementOf0(X111,sbsmnsldt0(xS))
| aInteger0(X111) )
& aSet0(sbsmnsldt0(xS)) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])])])]) ).
fof(c_0_7,plain,
! [X1] :
( epred1_1(X1)
=> ( isOpen0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> ? [X3] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X2,X3),X1)
& ! [X4] :
( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3))
=> aElementOf0(X4,X1) )
& ! [X4] :
( ( ( ( sdteqdtlpzmzozddtrp0(X4,X2,X3)
| aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
| ? [X5] :
( sdtasdt0(X3,X5) = sdtpldt0(X4,smndt0(X2))
& aInteger0(X5) ) )
& aInteger0(X4) )
=> aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
& ( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3))
=> ( sdteqdtlpzmzozddtrp0(X4,X2,X3)
& aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& ? [X5] :
( sdtasdt0(X3,X5) = sdtpldt0(X4,smndt0(X2))
& aInteger0(X5) )
& aInteger0(X4) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X2,X3))
& X3 != sz00
& aInteger0(X3) ) )
& aSubsetOf0(X1,cS1395)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,cS1395) )
& aSet0(X1)
& ! [X2] :
( aElementOf0(X2,cS1395)
<=> aInteger0(X2) )
& aSet0(cS1395) ) ),
inference(split_equiv,[status(thm)],[c_0_3]) ).
fof(c_0_8,hypothesis,
! [X110] :
( ( epred1_1(X110)
| ~ aElementOf0(X110,xS) )
& aSet0(xS) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
cnf(c_0_9,negated_conjecture,
( ~ aElementOf0(X1,sbsmnsldt0(xS))
| aElementOf0(esk14_1(X1),xS) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
aElementOf0(esk15_0,sbsmnsldt0(xS)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,plain,
! [X121,X122,X123,X124,X125,X127,X129,X130,X131] :
( ( ~ epred1_1(X121)
| isOpen0(X121) )
& ( ~ epred1_1(X121)
| ~ aElementOf0(X125,X121)
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X125,esk18_2(X121,X125)),X121) )
& ( ~ epred1_1(X121)
| ~ aElementOf0(X125,X121)
| aElementOf0(X131,X121)
| ~ aElementOf0(X131,szAzrzSzezqlpdtcmdtrp0(X125,esk18_2(X121,X125))) )
& ( ~ epred1_1(X121)
| ~ aElementOf0(X125,X121)
| aElementOf0(X129,szAzrzSzezqlpdtcmdtrp0(X125,esk18_2(X121,X125)))
| ~ aInteger0(X129)
| ~ sdteqdtlpzmzozddtrp0(X129,X125,esk18_2(X121,X125)) )
& ( ~ epred1_1(X121)
| ~ aElementOf0(X125,X121)
| aElementOf0(X129,szAzrzSzezqlpdtcmdtrp0(X125,esk18_2(X121,X125)))
| ~ aInteger0(X129)
| ~ aDivisorOf0(esk18_2(X121,X125),sdtpldt0(X129,smndt0(X125))) )
& ( ~ epred1_1(X121)
| ~ aElementOf0(X125,X121)
| aElementOf0(X129,szAzrzSzezqlpdtcmdtrp0(X125,esk18_2(X121,X125)))
| ~ aInteger0(X129)
| sdtasdt0(esk18_2(X121,X125),X130) != sdtpldt0(X129,smndt0(X125))
| ~ aInteger0(X130) )
& ( ~ epred1_1(X121)
| ~ aElementOf0(X125,X121)
| ~ aElementOf0(X127,szAzrzSzezqlpdtcmdtrp0(X125,esk18_2(X121,X125)))
| sdteqdtlpzmzozddtrp0(X127,X125,esk18_2(X121,X125)) )
& ( ~ epred1_1(X121)
| ~ aElementOf0(X125,X121)
| ~ aElementOf0(X127,szAzrzSzezqlpdtcmdtrp0(X125,esk18_2(X121,X125)))
| aDivisorOf0(esk18_2(X121,X125),sdtpldt0(X127,smndt0(X125))) )
& ( ~ epred1_1(X121)
| ~ aElementOf0(X125,X121)
| ~ aElementOf0(X127,szAzrzSzezqlpdtcmdtrp0(X125,esk18_2(X121,X125)))
| sdtasdt0(esk18_2(X121,X125),esk19_3(X121,X125,X127)) = sdtpldt0(X127,smndt0(X125)) )
& ( ~ epred1_1(X121)
| ~ aElementOf0(X125,X121)
| ~ aElementOf0(X127,szAzrzSzezqlpdtcmdtrp0(X125,esk18_2(X121,X125)))
| aInteger0(esk19_3(X121,X125,X127)) )
& ( ~ epred1_1(X121)
| ~ aElementOf0(X125,X121)
| ~ aElementOf0(X127,szAzrzSzezqlpdtcmdtrp0(X125,esk18_2(X121,X125)))
| aInteger0(X127) )
& ( ~ epred1_1(X121)
| ~ aElementOf0(X125,X121)
| aSet0(szAzrzSzezqlpdtcmdtrp0(X125,esk18_2(X121,X125))) )
& ( ~ epred1_1(X121)
| ~ aElementOf0(X125,X121)
| esk18_2(X121,X125) != sz00 )
& ( ~ epred1_1(X121)
| ~ aElementOf0(X125,X121)
| aInteger0(esk18_2(X121,X125)) )
& ( ~ epred1_1(X121)
| aSubsetOf0(X121,cS1395) )
& ( ~ epred1_1(X121)
| aElementOf0(X124,cS1395)
| ~ aElementOf0(X124,X121) )
& ( ~ epred1_1(X121)
| aSet0(X121) )
& ( ~ epred1_1(X121)
| aElementOf0(X123,cS1395)
| ~ aInteger0(X123) )
& ( ~ epred1_1(X121)
| aInteger0(X122)
| ~ aElementOf0(X122,cS1395) )
& ( ~ epred1_1(X121)
| aSet0(cS1395) ) ),
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])])])])])])]) ).
cnf(c_0_12,negated_conjecture,
( ~ aElementOf0(X1,sbsmnsldt0(xS))
| aElementOf0(X1,esk14_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,hypothesis,
( ~ aElementOf0(X1,xS)
| epred1_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
aElementOf0(esk14_1(esk15_0),xS),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,plain,
( ~ epred1_1(X3)
| ~ aElementOf0(X2,X3)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(X2,esk18_2(X3,X2)))
| aElementOf0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
aElementOf0(esk15_0,esk14_1(esk15_0)),
inference(spm,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_17,hypothesis,
epred1_1(esk14_1(esk15_0)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
( ~ epred1_1(X1)
| ~ aElementOf0(X2,X1)
| aInteger0(esk18_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
( ~ epred1_1(X3)
| ~ aElementOf0(X2,X3)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(X2,esk18_2(X3,X2)))
| aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,negated_conjecture,
( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(esk15_0,esk18_2(esk14_1(esk15_0),esk15_0)))
| aElementOf0(X1,esk14_1(esk15_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
cnf(c_0_21,negated_conjecture,
( ~ aInteger0(X1)
| X1 = sz00
| aElementOf0(esk17_1(X1),szAzrzSzezqlpdtcmdtrp0(esk15_0,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_22,negated_conjecture,
aInteger0(esk18_2(esk14_1(esk15_0),esk15_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_16]),c_0_17])]) ).
cnf(c_0_23,negated_conjecture,
( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(esk15_0,esk18_2(esk14_1(esk15_0),esk15_0)))
| aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_16]),c_0_17])]) ).
cnf(c_0_24,negated_conjecture,
( ~ aElementOf0(X1,X2)
| ~ aElementOf0(X2,xS)
| ~ aInteger0(X1)
| aElementOf0(X1,sbsmnsldt0(xS)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_25,negated_conjecture,
( aElementOf0(esk17_1(esk18_2(esk14_1(esk15_0),esk15_0)),esk14_1(esk15_0))
| esk18_2(esk14_1(esk15_0),esk15_0) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_26,negated_conjecture,
( aInteger0(esk17_1(esk18_2(esk14_1(esk15_0),esk15_0)))
| esk18_2(esk14_1(esk15_0),esk15_0) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_21]),c_0_22])]) ).
cnf(c_0_27,negated_conjecture,
( ~ aInteger0(X1)
| ~ aElementOf0(esk17_1(X1),sbsmnsldt0(xS))
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_28,negated_conjecture,
( aElementOf0(esk17_1(esk18_2(esk14_1(esk15_0),esk15_0)),sbsmnsldt0(xS))
| esk18_2(esk14_1(esk15_0),esk15_0) = sz00 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_14])]),c_0_26]) ).
cnf(c_0_29,plain,
( ~ epred1_1(X1)
| ~ aElementOf0(X2,X1)
| esk18_2(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_30,negated_conjecture,
esk18_2(esk14_1(esk15_0),esk15_0) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_22])]) ).
cnf(c_0_31,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_17]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM437+5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/5.37 % Computer : n013.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Mon Sep 21 02:29:14 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/5.42 Running first-order theorem proving
% 0.13/5.42 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/5.49 % Version: 3.5.1
% 0.13/5.49 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.13/5.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/5.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.13/5.49 % Starting new_bool_3 with 300s (1) cores
% 0.13/5.49 % Starting new_bool_1 with 300s (1) cores
% 0.13/5.49 % Starting sh5l with 300s (1) cores
% 0.13/5.49 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 3951607 completed with status 0
% 0.13/5.49 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.13/5.49 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.13/5.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/5.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.13/5.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/5.49 % No SInE strategy applied
% 0.13/5.49 % Search class: FGHSF-FSLS31-SFFFFFNN
% 0.13/5.49 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/5.49 % Starting SubtermCWHack with 136s (1) cores
% 0.13/5.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.13/5.49 % Starting new_bool_3 with 307s (1) cores
% 0.13/5.49 % Starting new_bool_1 with 306s (1) cores
% 0.13/5.49 % Starting sh5l with 304s (1) cores
% 0.13/5.49 % new_bool_1 with pid 3951617 completed with status 0
% 0.13/5.49 % Result found by new_bool_1
% 0.13/5.49 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.13/5.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/5.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.13/5.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/5.49 % No SInE strategy applied
% 0.13/5.49 % Search class: FGHSF-FSLS31-SFFFFFNN
% 0.13/5.49 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/5.49 % Starting SubtermCWHack with 136s (1) cores
% 0.13/5.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.13/5.49 % Starting new_bool_3 with 307s (1) cores
% 0.13/5.49 % Starting new_bool_1 with 306s (1) cores
% 0.13/5.49 % Preprocessing time : 0.002 s
% 0.13/5.49 % Presaturation interreduction done
% 0.13/5.49
% 0.13/5.49 % Proof found!
% 0.13/5.49 % SZS status Theorem
% 0.13/5.49 % SZS output start CNFRefutation
% See solution above
% 0.13/5.49 % Parsed axioms : 38
% 0.13/5.49 % Removed by relevancy pruning/SinE : 0
% 0.13/5.49 % Initial clauses : 145
% 0.13/5.49 % Removed in clause preprocessing : 5
% 0.13/5.49 % Initial clauses in saturation : 140
% 0.13/5.49 % Processed clauses : 586
% 0.13/5.49 % ...of these trivial : 3
% 0.13/5.49 % ...subsumed : 75
% 0.13/5.49 % ...remaining for further processing : 508
% 0.13/5.49 % Other redundant clauses eliminated : 34
% 0.13/5.49 % Clauses deleted for lack of memory : 0
% 0.13/5.49 % Backward-subsumed : 15
% 0.13/5.49 % Backward-rewritten : 9
% 0.13/5.49 % Generated clauses : 1395
% 0.13/5.49 % ...of the previous two non-redundant : 1311
% 0.13/5.49 % ...aggressively subsumed : 0
% 0.13/5.49 % Contextual simplify-reflections : 8
% 0.13/5.49 % Paramodulations : 1361
% 0.13/5.49 % Factorizations : 0
% 0.13/5.49 % NegExts : 0
% 0.13/5.49 % Equation resolutions : 34
% 0.13/5.49 % Disequality decompositions : 0
% 0.13/5.49 % Total rewrite steps : 542
% 0.13/5.49 % ...of those cached : 509
% 0.13/5.49 % Propositional unsat checks : 0
% 0.13/5.49 % Propositional check models : 0
% 0.13/5.49 % Propositional check unsatisfiable : 0
% 0.13/5.49 % Propositional clauses : 0
% 0.13/5.49 % Propositional clauses after purity: 0
% 0.13/5.49 % Propositional unsat core size : 0
% 0.13/5.49 % Propositional preprocessing time : 0.000
% 0.13/5.49 % Propositional encoding time : 0.000
% 0.13/5.49 % Propositional solver time : 0.000
% 0.13/5.49 % Success case prop preproc time : 0.000
% 0.13/5.49 % Success case prop encoding time : 0.000
% 0.13/5.49 % Success case prop solver time : 0.000
% 0.13/5.49 % Current number of processed clauses : 312
% 0.13/5.49 % Positive orientable unit clauses : 49
% 0.13/5.49 % Positive unorientable unit clauses: 0
% 0.13/5.49 % Negative unit clauses : 6
% 0.13/5.49 % Non-unit-clauses : 257
% 0.13/5.49 % Current number of unprocessed clauses: 1002
% 0.13/5.49 % ...number of literals in the above : 5189
% 0.13/5.49 % Current number of archived formulas : 0
% 0.13/5.49 % Current number of archived clauses : 164
% 0.13/5.49 % Clause-clause subsumption calls (NU) : 11540
% 0.13/5.49 % Rec. Clause-clause subsumption calls : 3427
% 0.13/5.49 % Non-unit clause-clause subsumptions : 71
% 0.13/5.49 % Unit Clause-clause subsumption calls : 810
% 0.13/5.49 % Rewrite failures with RHS unbound : 0
% 0.13/5.49 % BW rewrite match attempts : 5
% 0.13/5.49 % BW rewrite match successes : 5
% 0.13/5.49 % Condensation attempts : 0
% 0.13/5.49 % Condensation successes : 0
% 0.13/5.49 % Termbank termtop insertions : 40307
% 0.13/5.49 % Search garbage collected termcells : 2955
% 0.13/5.49
% 0.13/5.49 % -------------------------------------------------
% 0.13/5.49 % User time : 0.045 s
% 0.13/5.49 % System time : 0.009 s
% 0.13/5.49 % Total time : 0.054 s
% 0.13/5.49 % Maximum resident set size: 3952 pages
% 0.13/5.49
% 0.13/5.49 % -------------------------------------------------
% 0.13/5.49 % User time : 0.205 s
% 0.13/5.49 % System time : 0.029 s
% 0.13/5.49 % Total time : 0.234 s
% 0.13/5.49 % Maximum resident set size: 4864 pages
% 0.13/5.49 % E exiting
%------------------------------------------------------------------------------