%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM498+1 : 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 : n014.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 01:49:19 PM UTC 2026
% Result : Theorem 0.14s 0.45s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 15
% Syntax : Number of formulae : 74 ( 18 unt; 0 def)
% Number of atoms : 297 ( 128 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 346 ( 123 ~; 147 |; 51 &)
% ( 6 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 69 ( 0 sgn 41 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefQuot,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X2)
& X1 != sz00 )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(m__1860,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(m__2306,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(m__2287,hypothesis,
( sdtlseqdt0(xm,xp)
& xm != xp
& sdtlseqdt0(xn,xp)
& xn != xp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2287) ).
fof(m__,conjecture,
( ( xk = sz10
| xk = sz00 )
=> ( doDivides0(xp,xm)
| doDivides0(xp,xn) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( sdtpldt0(X1,X3) = X2
& aNaturalNumber0(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
fof(mZeroAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtpldt0(X1,X2) = sz00
=> ( X2 = sz00
& X1 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroAdd) ).
fof(mDefPrime,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( isPrime0(X1)
<=> ( ! [X2] :
( ( doDivides0(X2,X1)
& aNaturalNumber0(X2) )
=> ( X2 = X1
| X2 = sz10 ) )
& X1 != sz10
& X1 != sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtasdt0(sz10,X1)
& sdtasdt0(X1,sz10) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(mZeroMul,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X2 = sz00
| X1 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroMul) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sz00 = sdtasdt0(sz00,X1)
& sdtasdt0(X1,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(c_0_15,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X2)
& X1 != sz00 )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[mDefQuot]) ).
fof(c_0_16,plain,
! [X67,X68,X69] :
( ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 = sdtsldt0(X68,X67)
| X68 != sdtasdt0(X67,X69)
| ~ aNaturalNumber0(X69) )
& ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 != sdtsldt0(X68,X67)
| X68 = sdtasdt0(X67,X69) )
& ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 != sdtsldt0(X68,X67)
| aNaturalNumber0(X69) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])])]) ).
cnf(c_0_17,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X3 != sdtsldt0(X1,X2)
| X2 = sz00
| X1 = sdtasdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_18,plain,
! [X63,X64,X66] :
( ( ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63)
| doDivides0(X63,X64)
| X64 != sdtasdt0(X63,X66)
| ~ aNaturalNumber0(X66) )
& ( ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63)
| ~ doDivides0(X63,X64)
| X64 = sdtasdt0(X63,esk2_2(X63,X64)) )
& ( ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63)
| ~ doDivides0(X63,X64)
| aNaturalNumber0(esk2_2(X63,X64)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiv])])])])])]) ).
fof(c_0_19,plain,
! [X7,X8] :
( aNaturalNumber0(sdtasdt0(X7,X8))
| ~ aNaturalNumber0(X8)
| ~ aNaturalNumber0(X7) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).
cnf(c_0_20,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| X1 = sz00
| sdtasdt0(X1,sdtsldt0(X2,X1)) = X2 ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_21,hypothesis,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_22,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_23,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_24,hypothesis,
( sdtlseqdt0(xm,xp)
& xm != xp
& sdtlseqdt0(xn,xp)
& xn != xp ),
inference(fof_simplification,[status(thm)],[m__2287]) ).
cnf(c_0_25,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| doDivides0(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| xp = sz00
| sdtasdt0(xn,xm) = sdtasdt0(xp,xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23])]) ).
cnf(c_0_28,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_29,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_30,negated_conjecture,
~ ( ( xk = sz10
| xk = sz00 )
=> ( doDivides0(xp,xm)
| doDivides0(xp,xn) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_31,plain,
! [X35,X36,X38] :
( ( ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X35)
| sdtlseqdt0(X35,X36)
| sdtpldt0(X35,X38) != X36
| ~ aNaturalNumber0(X38) )
& ( ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X35)
| ~ sdtlseqdt0(X35,X36)
| sdtpldt0(X35,esk1_2(X35,X36)) = X36 )
& ( ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X35)
| ~ sdtlseqdt0(X35,X36)
| aNaturalNumber0(esk1_2(X35,X36)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefLE])])])])])]) ).
fof(c_0_32,hypothesis,
( sdtlseqdt0(xm,xp)
& xm != xp
& sdtlseqdt0(xn,xp)
& xn != xp ),
inference(fof_nnf,[status(thm)],[c_0_24]) ).
cnf(c_0_33,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,sdtasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_25]),c_0_26]) ).
cnf(c_0_34,hypothesis,
( xp = sz00
| sdtasdt0(xn,xm) = sdtasdt0(xp,xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_26]),c_0_28]),c_0_29])]) ).
fof(c_0_35,negated_conjecture,
( ~ doDivides0(xp,xm)
& ~ doDivides0(xp,xn)
& ( xk = sz10
| xk = sz00 ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])]) ).
fof(c_0_36,plain,
! [X31,X32] :
( ( ~ aNaturalNumber0(X32)
| ~ aNaturalNumber0(X31)
| sdtpldt0(X31,X32) != sz00
| X32 = sz00 )
& ( ~ aNaturalNumber0(X32)
| ~ aNaturalNumber0(X31)
| sdtpldt0(X31,X32) != sz00
| X31 = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroAdd])])])]) ).
cnf(c_0_37,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X2)
| sdtpldt0(X1,esk1_2(X1,X2)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,hypothesis,
sdtlseqdt0(xn,xp),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_39,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X2)
| aNaturalNumber0(esk1_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_40,plain,
! [X1] :
( aNaturalNumber0(X1)
=> ( isPrime0(X1)
<=> ( ! [X2] :
( ( doDivides0(X2,X1)
& aNaturalNumber0(X2) )
=> ( X2 = X1
| X2 = sz10 ) )
& X1 != sz10
& X1 != sz00 ) ) ),
inference(fof_simplification,[status(thm)],[mDefPrime]) ).
cnf(c_0_41,hypothesis,
( doDivides0(xn,sdtasdt0(xp,xk))
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_29]),c_0_28])]) ).
cnf(c_0_42,negated_conjecture,
( xk = sz10
| xk = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_43,plain,
! [X20] :
( ( ~ aNaturalNumber0(X20)
| X20 = sdtasdt0(sz10,X20) )
& ( ~ aNaturalNumber0(X20)
| sdtasdt0(X20,sz10) = X20 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])])]) ).
fof(c_0_44,plain,
! [X33,X34] :
( X34 = sz00
| X33 = sz00
| sdtasdt0(X33,X34) != sz00
| ~ aNaturalNumber0(X34)
| ~ aNaturalNumber0(X33) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroMul])])]) ).
cnf(c_0_45,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X2) != sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_46,hypothesis,
sdtpldt0(xn,esk1_2(xn,xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_23]),c_0_29])]) ).
cnf(c_0_47,hypothesis,
aNaturalNumber0(esk1_2(xn,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_38]),c_0_23]),c_0_29])]) ).
fof(c_0_48,plain,
! [X84,X85] :
( ( ~ aNaturalNumber0(X84)
| isPrime0(X84)
| X84 = sz10
| X84 = sz00
| esk3_1(X84) != X84 )
& ( ~ aNaturalNumber0(X84)
| isPrime0(X84)
| X84 = sz10
| X84 = sz00
| esk3_1(X84) != sz10 )
& ( ~ aNaturalNumber0(X84)
| isPrime0(X84)
| X84 = sz10
| X84 = sz00
| doDivides0(esk3_1(X84),X84) )
& ( ~ aNaturalNumber0(X84)
| isPrime0(X84)
| X84 = sz10
| X84 = sz00
| aNaturalNumber0(esk3_1(X84)) )
& ( ~ aNaturalNumber0(X84)
| ~ isPrime0(X84)
| X85 = X84
| X85 = sz10
| ~ doDivides0(X85,X84)
| ~ aNaturalNumber0(X85) )
& ( ~ aNaturalNumber0(X84)
| ~ isPrime0(X84)
| X84 != sz10 )
& ( ~ aNaturalNumber0(X84)
| ~ isPrime0(X84)
| X84 != sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])])])])]) ).
cnf(c_0_49,negated_conjecture,
( doDivides0(xn,sdtasdt0(xp,sz10))
| xp = sz00
| xk = sz00 ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_50,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz10) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_51,plain,
( sdtasdt0(X1,X2) != sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X2 = sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_52,hypothesis,
( xp != sz00
| xn = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_29])]) ).
cnf(c_0_53,plain,
( ~ aNaturalNumber0(X2)
| ~ isPrime0(X2)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| X1 = X2
| X1 = sz10 ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_54,negated_conjecture,
( doDivides0(xn,xp)
| xk = sz00
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_23])]) ).
cnf(c_0_55,hypothesis,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_56,hypothesis,
xn != xp,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_57,hypothesis,
( sdtasdt0(xp,xk) != sz00
| xm = sz00
| xn = sz00 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_34]),c_0_28]),c_0_29])]),c_0_52]) ).
cnf(c_0_58,negated_conjecture,
( xn = sz10
| xp = sz00
| xk = sz00 ),
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_53,c_0_54]),c_0_55]),c_0_23]),c_0_29])]),c_0_56]) ).
fof(c_0_59,plain,
! [X21] :
( ( ~ aNaturalNumber0(X21)
| sz00 = sdtasdt0(sz00,X21) )
& ( ~ aNaturalNumber0(X21)
| sdtasdt0(X21,sz00) = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])])]) ).
cnf(c_0_60,hypothesis,
( sdtasdt0(xp,sz00) != sz00
| xn = sz00
| xm = sz00
| xn = sz10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_52]) ).
cnf(c_0_61,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz00) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_62,negated_conjecture,
~ doDivides0(xp,xm),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_63,hypothesis,
( xn = sz10
| xm = sz00
| xn = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_23])]) ).
cnf(c_0_64,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_65,negated_conjecture,
( ~ doDivides0(xp,sz00)
| xn = sz00
| xn = sz10 ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_66,plain,
( ~ aNaturalNumber0(X1)
| doDivides0(X1,sz00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_61]),c_0_64])]) ).
cnf(c_0_67,negated_conjecture,
( xn = sz10
| xn = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_23])]) ).
cnf(c_0_68,hypothesis,
( doDivides0(xp,sdtasdt0(sz10,xm))
| xn = sz00 ),
inference(spm,[status(thm)],[c_0_21,c_0_67]) ).
cnf(c_0_69,plain,
( ~ aNaturalNumber0(X1)
| X1 = sdtasdt0(sz10,X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_70,negated_conjecture,
~ doDivides0(xp,xn),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_71,hypothesis,
xn = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_28])]),c_0_62]) ).
cnf(c_0_72,negated_conjecture,
~ doDivides0(xp,sz00),
inference(rw,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_73,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_66]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM498+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n014.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 02:34:49 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.14/0.45 % Version: 3.5.1
% 0.14/0.45 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.45 % Starting sh5l with 300s (1) cores
% 0.14/0.45 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2958126 completed with status 0
% 0.14/0.45 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.14/0.45 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.45 % No SInE strategy applied
% 0.14/0.45 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.14/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.14/0.45 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 0.14/0.45 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 0.14/0.45 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 0.14/0.45 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with pid 2958136 completed with status 0
% 0.14/0.45 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m
% 0.14/0.45 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.45 % No SInE strategy applied
% 0.14/0.45 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.14/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.14/0.45 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 0.14/0.45 % Preprocessing time : 0.001 s
% 0.14/0.45 % Presaturation interreduction done
% 0.14/0.45
% 0.14/0.45 % Proof found!
% 0.14/0.45 % SZS status Theorem
% 0.14/0.45 % SZS output start CNFRefutation
% See solution above
% 0.14/0.45 % Parsed axioms : 46
% 0.14/0.45 % Removed by relevancy pruning/SinE : 0
% 0.14/0.45 % Initial clauses : 86
% 0.14/0.45 % Removed in clause preprocessing : 3
% 0.14/0.45 % Initial clauses in saturation : 83
% 0.14/0.45 % Processed clauses : 323
% 0.14/0.45 % ...of these trivial : 2
% 0.14/0.45 % ...subsumed : 64
% 0.14/0.45 % ...remaining for further processing : 257
% 0.14/0.45 % Other redundant clauses eliminated : 23
% 0.14/0.45 % Clauses deleted for lack of memory : 0
% 0.14/0.45 % Backward-subsumed : 10
% 0.14/0.45 % Backward-rewritten : 46
% 0.14/0.45 % Generated clauses : 771
% 0.14/0.45 % ...of the previous two non-redundant : 699
% 0.14/0.45 % ...aggressively subsumed : 0
% 0.14/0.45 % Contextual simplify-reflections : 13
% 0.14/0.45 % Paramodulations : 737
% 0.14/0.45 % Factorizations : 4
% 0.14/0.45 % NegExts : 0
% 0.14/0.45 % Equation resolutions : 27
% 0.14/0.45 % Disequality decompositions : 0
% 0.14/0.45 % Total rewrite steps : 785
% 0.14/0.45 % ...of those cached : 753
% 0.14/0.45 % Propositional unsat checks : 0
% 0.14/0.45 % Propositional check models : 0
% 0.14/0.45 % Propositional check unsatisfiable : 0
% 0.14/0.45 % Propositional clauses : 0
% 0.14/0.45 % Propositional clauses after purity: 0
% 0.14/0.45 % Propositional unsat core size : 0
% 0.14/0.45 % Propositional preprocessing time : 0.000
% 0.14/0.45 % Propositional encoding time : 0.000
% 0.14/0.45 % Propositional solver time : 0.000
% 0.14/0.45 % Success case prop preproc time : 0.000
% 0.14/0.45 % Success case prop encoding time : 0.000
% 0.14/0.45 % Success case prop solver time : 0.000
% 0.14/0.45 % Current number of processed clauses : 109
% 0.14/0.45 % Positive orientable unit clauses : 27
% 0.14/0.45 % Positive unorientable unit clauses: 0
% 0.14/0.45 % Negative unit clauses : 8
% 0.14/0.45 % Non-unit-clauses : 74
% 0.14/0.45 % Current number of unprocessed clauses: 514
% 0.14/0.45 % ...number of literals in the above : 2097
% 0.14/0.45 % Current number of archived formulas : 0
% 0.14/0.45 % Current number of archived clauses : 137
% 0.14/0.45 % Clause-clause subsumption calls (NU) : 2111
% 0.14/0.45 % Rec. Clause-clause subsumption calls : 876
% 0.14/0.45 % Non-unit clause-clause subsumptions : 80
% 0.14/0.45 % Unit Clause-clause subsumption calls : 274
% 0.14/0.45 % Rewrite failures with RHS unbound : 0
% 0.14/0.45 % BW rewrite match attempts : 9
% 0.14/0.45 % BW rewrite match successes : 9
% 0.14/0.45 % Condensation attempts : 0
% 0.14/0.45 % Condensation successes : 0
% 0.14/0.45 % Termbank termtop insertions : 19216
% 0.14/0.45 % Search garbage collected termcells : 1370
% 0.14/0.45
% 0.14/0.45 % -------------------------------------------------
% 0.14/0.45 % User time : 0.019 s
% 0.14/0.45 % System time : 0.006 s
% 0.14/0.45 % Total time : 0.025 s
% 0.14/0.45 % Maximum resident set size: 3940 pages
% 0.14/0.45
% 0.14/0.45 % -------------------------------------------------
% 0.14/0.45 % User time : 0.077 s
% 0.14/0.45 % System time : 0.018 s
% 0.14/0.45 % Total time : 0.096 s
% 0.14/0.45 % Maximum resident set size: 4864 pages
% 0.14/0.45 % E exiting
%------------------------------------------------------------------------------