%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM443+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 01:55:02 PM UTC 2026
% Result : Theorem 0.31s 0.46s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 13 unt; 0 def)
% Number of atoms : 321 ( 56 equ)
% Maximal formula atoms : 50 ( 8 avg)
% Number of connectives : 395 ( 111 ~; 124 |; 128 &)
% ( 4 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 84 ( 0 sgn 47 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p',mArSeq) ).
fof(m__,conjecture,
( ( sdteqdtlpzmzozddtrp0(xc,xb,xq)
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& ? [X1] :
( sdtasdt0(xq,X1) = sdtpldt0(xc,smndt0(xb))
& aInteger0(X1) )
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [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] :
( ( ( ( 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)) )
=> ( aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__1962,hypothesis,
( xq != sz00
& aInteger0(xq)
& aInteger0(xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1962) ).
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/sandbox/benchmark/theBenchmark.p',mEquModTrn) ).
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/sandbox/benchmark/theBenchmark.p',mEquModSym) ).
fof(m__2010,hypothesis,
( aInteger0(xc)
& aInteger0(xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2010) ).
fof(c_0_6,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]) ).
fof(c_0_7,negated_conjecture,
~ ( ( sdteqdtlpzmzozddtrp0(xc,xb,xq)
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& ? [X1] :
( sdtasdt0(xq,X1) = sdtpldt0(xc,smndt0(xb))
& aInteger0(X1) )
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [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] :
( ( ( ( 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)) )
=> ( aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_8,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_6])])])])])])]) ).
fof(c_0_9,negated_conjecture,
~ ( ( sdteqdtlpzmzozddtrp0(xc,xb,xq)
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& ? [X1] :
( sdtasdt0(xq,X1) = sdtpldt0(xc,smndt0(xb))
& aInteger0(X1) )
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [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] :
( ( ( ( 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)) )
=> ( aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_10,hypothesis,
( xq != sz00
& aInteger0(xq)
& aInteger0(xa) ),
inference(fof_simplification,[status(thm)],[m__1962]) ).
fof(c_0_11,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_12,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_13,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_8]) ).
fof(c_0_14,negated_conjecture,
! [X117,X119,X120,X122,X124,X125] :
( ~ aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ( aElementOf0(X124,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X124)
| ~ sdteqdtlpzmzozddtrp0(X124,xa,xq) )
& ( aElementOf0(X124,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X124)
| ~ aDivisorOf0(xq,sdtpldt0(X124,smndt0(xa))) )
& ( aElementOf0(X124,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X124)
| sdtasdt0(xq,X125) != sdtpldt0(X124,smndt0(xa))
| ~ aInteger0(X125) )
& ( ~ aElementOf0(X122,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| sdteqdtlpzmzozddtrp0(X122,xa,xq) )
& ( ~ aElementOf0(X122,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aDivisorOf0(xq,sdtpldt0(X122,smndt0(xa))) )
& ( ~ aElementOf0(X122,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| sdtasdt0(xq,esk18_1(X122)) = sdtpldt0(X122,smndt0(xa)) )
& ( ~ aElementOf0(X122,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aInteger0(esk18_1(X122)) )
& ( ~ aElementOf0(X122,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aInteger0(X122) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& sdteqdtlpzmzozddtrp0(xc,xb,xq)
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& sdtasdt0(xq,esk17_0) = sdtpldt0(xc,smndt0(xb))
& aInteger0(esk17_0)
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ( aElementOf0(X119,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X119)
| ~ sdteqdtlpzmzozddtrp0(X119,xa,xq) )
& ( aElementOf0(X119,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X119)
| ~ aDivisorOf0(xq,sdtpldt0(X119,smndt0(xa))) )
& ( aElementOf0(X119,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X119)
| sdtasdt0(xq,X120) != sdtpldt0(X119,smndt0(xa))
| ~ aInteger0(X120) )
& ( ~ aElementOf0(X117,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| sdteqdtlpzmzozddtrp0(X117,xa,xq) )
& ( ~ aElementOf0(X117,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aDivisorOf0(xq,sdtpldt0(X117,smndt0(xa))) )
& ( ~ aElementOf0(X117,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| sdtasdt0(xq,esk16_1(X117)) = sdtpldt0(X117,smndt0(xa)) )
& ( ~ aElementOf0(X117,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aInteger0(esk16_1(X117)) )
& ( ~ aElementOf0(X117,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aInteger0(X117) )
& 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_9])])])])])])]) ).
fof(c_0_15,hypothesis,
( xq != sz00
& aInteger0(xq)
& aInteger0(xa) ),
inference(fof_nnf,[status(thm)],[c_0_10]) ).
fof(c_0_16,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_11])])]) ).
fof(c_0_17,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_12])])]) ).
cnf(c_0_18,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X1)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X3,X1))
| sdteqdtlpzmzozddtrp0(X2,X3,X1)
| X1 = sz00 ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,hypothesis,
aInteger0(xq),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,hypothesis,
aInteger0(xa),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,hypothesis,
xq != sz00,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,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_16]) ).
cnf(c_0_24,negated_conjecture,
sdteqdtlpzmzozddtrp0(xc,xb,xq),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_25,hypothesis,
aInteger0(xb),
inference(split_conjunct,[status(thm)],[m__2010]) ).
cnf(c_0_26,hypothesis,
aInteger0(xc),
inference(split_conjunct,[status(thm)],[m__2010]) ).
cnf(c_0_27,plain,
( ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdteqdtlpzmzozddtrp0(X2,X1,X3)
| X3 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_28,negated_conjecture,
sdteqdtlpzmzozddtrp0(xc,xa,xq),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]),c_0_22]) ).
cnf(c_0_29,negated_conjecture,
( ~ aInteger0(X1)
| ~ sdteqdtlpzmzozddtrp0(X1,xc,xq)
| sdteqdtlpzmzozddtrp0(X1,xb,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_23,c_0_24]),c_0_25]),c_0_20]),c_0_26])]),c_0_22]) ).
cnf(c_0_30,negated_conjecture,
sdteqdtlpzmzozddtrp0(xa,xc,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_27,c_0_28]),c_0_20]),c_0_21]),c_0_26])]),c_0_22]) ).
cnf(c_0_31,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_8]) ).
cnf(c_0_32,negated_conjecture,
sdteqdtlpzmzozddtrp0(xa,xb,xq),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_21])]) ).
cnf(c_0_33,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X3)
| ~ aInteger0(X1)
| ~ sdteqdtlpzmzozddtrp0(X2,X3,X1)
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X3,X1))
| X1 = sz00 ),
inference(er,[status(thm)],[c_0_31]) ).
cnf(c_0_34,negated_conjecture,
sdteqdtlpzmzozddtrp0(xb,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_27,c_0_32]),c_0_20]),c_0_25]),c_0_21])]),c_0_22]) ).
cnf(c_0_35,negated_conjecture,
~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_36,negated_conjecture,
$false,
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_33,c_0_34]),c_0_20]),c_0_21]),c_0_25])]),c_0_22]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM443+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 02:34:53 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.31/0.46 % Version: 3.5.1
% 0.31/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.31/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.31/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.31/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.31/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.31/0.46 % Starting sh5l with 300s (1) cores
% 0.31/0.46 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1368489 completed with status 0
% 0.31/0.46 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.31/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.31/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.31/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.31/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.31/0.46 % No SInE strategy applied
% 0.31/0.46 % Search class: FGHSF-FSLM31-SFFFFFNN
% 0.31/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.31/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.31/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.31/0.46 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 198s (1) cores
% 0.31/0.46 % Starting new_bool_3 with 194s (1) cores
% 0.31/0.46 % Starting new_bool_1 with 188s (1) cores
% 0.31/0.46 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1368496 completed with status 0
% 0.31/0.46 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.31/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.31/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.31/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.31/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.31/0.46 % No SInE strategy applied
% 0.31/0.46 % Search class: FGHSF-FSLM31-SFFFFFNN
% 0.31/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.31/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.31/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.31/0.46 % Preprocessing time : 0.002 s
% 0.31/0.46 % Presaturation interreduction done
% 0.31/0.46
% 0.31/0.46 % Proof found!
% 0.31/0.46 % SZS status Theorem
% 0.31/0.46 % SZS output start CNFRefutation
% See solution above
% 0.31/0.46 % Parsed axioms : 43
% 0.31/0.46 % Removed by relevancy pruning/SinE : 0
% 0.31/0.46 % Initial clauses : 141
% 0.31/0.46 % Removed in clause preprocessing : 5
% 0.31/0.46 % Initial clauses in saturation : 136
% 0.31/0.46 % Processed clauses : 319
% 0.31/0.46 % ...of these trivial : 3
% 0.31/0.46 % ...subsumed : 6
% 0.31/0.46 % ...remaining for further processing : 310
% 0.31/0.46 % Other redundant clauses eliminated : 32
% 0.31/0.46 % Clauses deleted for lack of memory : 0
% 0.31/0.46 % Backward-subsumed : 1
% 0.31/0.46 % Backward-rewritten : 1
% 0.31/0.46 % Generated clauses : 417
% 0.31/0.46 % ...of the previous two non-redundant : 373
% 0.31/0.46 % ...aggressively subsumed : 0
% 0.31/0.46 % Contextual simplify-reflections : 1
% 0.31/0.46 % Paramodulations : 385
% 0.31/0.46 % Factorizations : 0
% 0.31/0.46 % NegExts : 0
% 0.31/0.46 % Equation resolutions : 32
% 0.31/0.46 % Disequality decompositions : 0
% 0.31/0.46 % Total rewrite steps : 287
% 0.31/0.46 % ...of those cached : 269
% 0.31/0.46 % Propositional unsat checks : 0
% 0.31/0.46 % Propositional check models : 0
% 0.31/0.46 % Propositional check unsatisfiable : 0
% 0.31/0.46 % Propositional clauses : 0
% 0.31/0.46 % Propositional clauses after purity: 0
% 0.31/0.46 % Propositional unsat core size : 0
% 0.31/0.46 % Propositional preprocessing time : 0.000
% 0.31/0.46 % Propositional encoding time : 0.000
% 0.31/0.46 % Propositional solver time : 0.000
% 0.31/0.46 % Success case prop preproc time : 0.000
% 0.31/0.46 % Success case prop encoding time : 0.000
% 0.31/0.46 % Success case prop solver time : 0.000
% 0.31/0.46 % Current number of processed clauses : 147
% 0.31/0.46 % Positive orientable unit clauses : 30
% 0.31/0.46 % Positive unorientable unit clauses: 0
% 0.31/0.46 % Negative unit clauses : 3
% 0.31/0.46 % Non-unit-clauses : 114
% 0.31/0.46 % Current number of unprocessed clauses: 318
% 0.31/0.46 % ...number of literals in the above : 1541
% 0.31/0.46 % Current number of archived formulas : 0
% 0.31/0.46 % Current number of archived clauses : 131
% 0.31/0.46 % Clause-clause subsumption calls (NU) : 5187
% 0.31/0.46 % Rec. Clause-clause subsumption calls : 1029
% 0.31/0.46 % Non-unit clause-clause subsumptions : 8
% 0.31/0.46 % Unit Clause-clause subsumption calls : 102
% 0.31/0.46 % Rewrite failures with RHS unbound : 0
% 0.31/0.46 % BW rewrite match attempts : 1
% 0.31/0.46 % BW rewrite match successes : 1
% 0.31/0.46 % Condensation attempts : 0
% 0.31/0.46 % Condensation successes : 0
% 0.31/0.46 % Termbank termtop insertions : 21077
% 0.31/0.46 % Search garbage collected termcells : 2657
% 0.31/0.46
% 0.31/0.46 % -------------------------------------------------
% 0.31/0.46 % User time : 0.024 s
% 0.31/0.46 % System time : 0.007 s
% 0.31/0.46 % Total time : 0.031 s
% 0.31/0.46 % Maximum resident set size: 3696 pages
% 0.31/0.46
% 0.31/0.46 % -------------------------------------------------
% 0.31/0.46 % User time : 0.081 s
% 0.31/0.46 % System time : 0.021 s
% 0.31/0.46 % Total time : 0.103 s
% 0.31/0.46 % Maximum resident set size: 4608 pages
% 0.31/0.46 % E exiting
%------------------------------------------------------------------------------