%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM494+3 : 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 : n009.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 01:49:18 PM UTC 2026
% Result : Theorem 1.22s 0.85s
% Output : CNFRefutation 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 70 ( 18 unt; 0 def)
% Number of atoms : 289 ( 116 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 341 ( 122 ~; 129 |; 72 &)
% ( 3 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 41 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ? [X1] :
( sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),X1) = sdtpldt0(sdtpldt0(xn,xm),xp)
& aNaturalNumber0(X1) ) )
& sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mPrimDiv,axiom,
! [X1] :
( ( X1 != sz10
& X1 != sz00
& aNaturalNumber0(X1) )
=> ? [X2] :
( isPrime0(X2)
& doDivides0(X2,X1)
& aNaturalNumber0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPrimDiv) ).
fof(m__1860,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X1] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) )
& isPrime0(xp)
& ! [X1] :
( ( ( doDivides0(X1,xp)
| ? [X2] :
( xp = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( X1 = xp
| X1 = sz10 ) )
& xp != sz10
& xp != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
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(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(m__1883,hypothesis,
( xr = sdtmndt0(xn,xp)
& sdtpldt0(xp,xr) = xn
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1883) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(mAddCanc,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtpldt0(X2,X1) = sdtpldt0(X3,X1)
| sdtpldt0(X1,X2) = sdtpldt0(X1,X3) )
=> X2 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddCanc) ).
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(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(c_0_14,negated_conjecture,
~ ( ( sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ? [X1] :
( sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),X1) = sdtpldt0(sdtpldt0(xn,xm),xp)
& aNaturalNumber0(X1) ) )
& sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_15,plain,
! [X1] :
( ( X1 != sz10
& X1 != sz00
& aNaturalNumber0(X1) )
=> ? [X2] :
( isPrime0(X2)
& doDivides0(X2,X1)
& aNaturalNumber0(X2) ) ),
inference(fof_simplification,[status(thm)],[mPrimDiv]) ).
fof(c_0_16,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X1] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) )
& isPrime0(xp)
& ! [X1] :
( ( ( doDivides0(X1,xp)
| ? [X2] :
( xp = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( X1 = xp
| X1 = sz10 ) )
& xp != sz10
& xp != sz00 ),
inference(fof_simplification,[status(thm)],[m__1860]) ).
fof(c_0_17,negated_conjecture,
~ ( ( sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ? [X1] :
( sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),X1) = sdtpldt0(sdtpldt0(xn,xm),xp)
& aNaturalNumber0(X1) ) )
& sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_18,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]) ).
fof(c_0_19,plain,
! [X89] :
( ( X89 = sz10
| X89 = sz00
| ~ aNaturalNumber0(X89)
| isPrime0(esk4_1(X89)) )
& ( X89 = sz10
| X89 = sz00
| ~ aNaturalNumber0(X89)
| doDivides0(esk4_1(X89),X89) )
& ( X89 = sz10
| X89 = sz00
| ~ aNaturalNumber0(X89)
| aNaturalNumber0(esk4_1(X89)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])])]) ).
fof(c_0_20,hypothesis,
! [X99,X100] :
( doDivides0(xp,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xp,esk9_0)
& aNaturalNumber0(esk9_0)
& isPrime0(xp)
& ( X99 = xp
| X99 = sz10
| ~ aNaturalNumber0(X99)
| ~ doDivides0(X99,xp) )
& ( X99 = xp
| X99 = sz10
| ~ aNaturalNumber0(X99)
| xp != sdtasdt0(X99,X100)
| ~ aNaturalNumber0(X100) )
& xp != sz10
& xp != 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_16])])])])])]) ).
fof(c_0_21,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_simplification,[status(thm)],[mSortsC_01]) ).
fof(c_0_22,negated_conjecture,
! [X105] :
( ( sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) )
& ( sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),X105) != sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ aNaturalNumber0(X105) ) ),
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_17])])])])]) ).
fof(c_0_23,plain,
! [X11,X12] :
( sdtpldt0(X11,X12) = sdtpldt0(X12,X11)
| ~ aNaturalNumber0(X12)
| ~ aNaturalNumber0(X11) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])])]) ).
fof(c_0_24,plain,
! [X86,X87] :
( ( ~ aNaturalNumber0(X86)
| isPrime0(X86)
| X86 = sz10
| X86 = sz00
| esk3_1(X86) != X86 )
& ( ~ aNaturalNumber0(X86)
| isPrime0(X86)
| X86 = sz10
| X86 = sz00
| esk3_1(X86) != sz10 )
& ( ~ aNaturalNumber0(X86)
| isPrime0(X86)
| X86 = sz10
| X86 = sz00
| doDivides0(esk3_1(X86),X86) )
& ( ~ aNaturalNumber0(X86)
| isPrime0(X86)
| X86 = sz10
| X86 = sz00
| aNaturalNumber0(esk3_1(X86)) )
& ( ~ aNaturalNumber0(X86)
| ~ isPrime0(X86)
| X87 = X86
| X87 = sz10
| ~ doDivides0(X87,X86)
| ~ aNaturalNumber0(X87) )
& ( ~ aNaturalNumber0(X86)
| ~ isPrime0(X86)
| X86 != sz10 )
& ( ~ aNaturalNumber0(X86)
| ~ isPrime0(X86)
| X86 != 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_18])])])])])]) ).
cnf(c_0_25,plain,
( ~ aNaturalNumber0(X1)
| X1 = sz10
| X1 = sz00
| doDivides0(esk4_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_27,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,hypothesis,
xp != sz10,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,plain,
( ~ aNaturalNumber0(X1)
| X1 = sz10
| X1 = sz00
| aNaturalNumber0(esk4_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_30,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_21]) ).
cnf(c_0_31,negated_conjecture,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[m__1883]) ).
cnf(c_0_34,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_35,plain,
! [X13,X14,X15] :
( sdtpldt0(sdtpldt0(X13,X14),X15) = sdtpldt0(X13,sdtpldt0(X14,X15))
| ~ aNaturalNumber0(X15)
| ~ aNaturalNumber0(X14)
| ~ aNaturalNumber0(X13) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])])]) ).
fof(c_0_36,plain,
! [X27,X28,X29] :
( ( ~ aNaturalNumber0(X29)
| ~ aNaturalNumber0(X28)
| ~ aNaturalNumber0(X27)
| X28 = X29
| sdtpldt0(X28,X27) != sdtpldt0(X29,X27) )
& ( ~ aNaturalNumber0(X29)
| ~ aNaturalNumber0(X28)
| ~ aNaturalNumber0(X27)
| X28 = X29
| sdtpldt0(X27,X28) != sdtpldt0(X27,X29) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddCanc])])])]) ).
cnf(c_0_37,plain,
( ~ aNaturalNumber0(X1)
| X1 = sz10
| X1 = sz00
| isPrime0(esk4_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_38,plain,
( ~ aNaturalNumber0(X2)
| ~ isPrime0(X2)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| X1 = X2
| X1 = sz10 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_39,hypothesis,
doDivides0(esk4_1(xp),xp),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28]) ).
cnf(c_0_40,hypothesis,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_41,hypothesis,
aNaturalNumber0(esk4_1(xp)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_26]),c_0_27]),c_0_28]) ).
cnf(c_0_42,plain,
( ~ aNaturalNumber0(X1)
| ~ isPrime0(X1)
| X1 != sz10 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_43,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_44,negated_conjecture,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xm,xr),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xm,xr),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_34])]) ).
cnf(c_0_45,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_46,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X2) != sdtpldt0(X1,X3)
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_47,hypothesis,
isPrime0(esk4_1(xp)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_26]),c_0_27]),c_0_28]) ).
cnf(c_0_48,hypothesis,
( esk4_1(xp) = sz10
| esk4_1(xp) = xp ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_26]),c_0_41])]) ).
cnf(c_0_49,plain,
~ isPrime0(sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_42]),c_0_43])]) ).
cnf(c_0_50,negated_conjecture,
( ~ sdtlseqdt0(sdtpldt0(xm,sdtpldt0(xr,xp)),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xm,sdtpldt0(xr,xp)) ),
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_26]),c_0_33]),c_0_34])]) ).
cnf(c_0_51,hypothesis,
sdtpldt0(xp,xr) = xn,
inference(split_conjunct,[status(thm)],[m__1883]) ).
fof(c_0_52,plain,
! [X37,X38,X40] :
( ( ~ aNaturalNumber0(X38)
| ~ aNaturalNumber0(X37)
| sdtlseqdt0(X37,X38)
| sdtpldt0(X37,X40) != X38
| ~ aNaturalNumber0(X40) )
& ( ~ aNaturalNumber0(X38)
| ~ aNaturalNumber0(X37)
| ~ sdtlseqdt0(X37,X38)
| sdtpldt0(X37,esk1_2(X37,X38)) = X38 )
& ( ~ aNaturalNumber0(X38)
| ~ aNaturalNumber0(X37)
| ~ sdtlseqdt0(X37,X38)
| aNaturalNumber0(esk1_2(X37,X38)) ) ),
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_53,plain,
! [X7,X8] :
( aNaturalNumber0(sdtpldt0(X7,X8))
| ~ aNaturalNumber0(X8)
| ~ aNaturalNumber0(X7) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])])]) ).
cnf(c_0_54,hypothesis,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != sdtpldt0(X2,esk4_1(xp))
| X1 = esk4_1(xp) ),
inference(spm,[status(thm)],[c_0_46,c_0_41]) ).
cnf(c_0_55,hypothesis,
esk4_1(xp) = xp,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
fof(c_0_56,plain,
! [X16] :
( ( ~ aNaturalNumber0(X16)
| X16 = sdtpldt0(sz00,X16) )
& ( ~ aNaturalNumber0(X16)
| sdtpldt0(X16,sz00) = X16 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])])]) ).
cnf(c_0_57,negated_conjecture,
( ~ sdtlseqdt0(sdtpldt0(xm,xn),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xm,xn) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_32]),c_0_51]),c_0_51]),c_0_26]),c_0_33])]) ).
cnf(c_0_58,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_59,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_60,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_61,hypothesis,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != sdtpldt0(X2,xp)
| X1 = xp ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55]),c_0_55]) ).
cnf(c_0_62,plain,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X1,sz00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_63,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_64,negated_conjecture,
( ~ sdtlseqdt0(sdtpldt0(xn,xm),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xn,xm) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_32]),c_0_58]),c_0_34])]) ).
cnf(c_0_65,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,sdtpldt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_59]),c_0_60]) ).
cnf(c_0_66,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X1,xp) != X1 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63])]),c_0_27]) ).
cnf(c_0_67,negated_conjecture,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xn,xm) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_26])]) ).
cnf(c_0_68,negated_conjecture,
~ aNaturalNumber0(sdtpldt0(xn,xm)),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_69,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_60]),c_0_34]),c_0_58])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM494+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.49 % Computer : n009.cluster.edu
% 0.17/0.49 % Model : x86_64 x86_64
% 0.17/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.49 % Memory : 8046.5625MB
% 0.17/0.49 % OS : Linux 6.8.0-71-generic
% 0.17/0.49 % CPULimit : 300
% 0.17/0.49 % WCLimit : 300
% 0.17/0.49 % DateTime : Mon Sep 21 02:35:13 UTC 2026
% 0.17/0.49 % CPUTime :
% 0.17/0.49 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.58 Running first-order theorem proving
% 0.21/0.58 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
% 1.22/0.85 % Version: 3.5.1
% 1.22/0.85 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.22/0.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.22/0.85 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.22/0.85 % Starting new_bool_3 with 300s (1) cores
% 1.22/0.85 % Starting new_bool_1 with 300s (1) cores
% 1.22/0.85 % Starting sh5l with 300s (1) cores
% 1.22/0.85 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 659058 completed with status 0
% 1.22/0.85 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.22/0.85 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.22/0.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.22/0.85 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.22/0.85 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.22/0.85 % No SInE strategy applied
% 1.22/0.85 % Search class: FGHSF-FSLM32-MFFFFFNN
% 1.22/0.85 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.22/0.85 % Starting SubtermCWHack with 136s (1) cores
% 1.22/0.85 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.22/0.85 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 1.22/0.85 % Starting G-E--_302_C18_F1_URBAN_S0Y with 136s (1) cores
% 1.22/0.85 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0U with 136s (1) cores
% 1.22/0.85 % G-E--_208_C18_F1_SE_CS_SP_PS_S0U with pid 659066 completed with status 0
% 1.22/0.85 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S0U
% 1.22/0.85 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.22/0.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.22/0.85 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.22/0.85 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.22/0.85 % No SInE strategy applied
% 1.22/0.85 % Search class: FGHSF-FSLM32-MFFFFFNN
% 1.22/0.85 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.22/0.85 % Starting SubtermCWHack with 136s (1) cores
% 1.22/0.85 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.22/0.85 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 1.22/0.85 % Starting G-E--_302_C18_F1_URBAN_S0Y with 136s (1) cores
% 1.22/0.85 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0U with 136s (1) cores
% 1.22/0.85 % Preprocessing time : 0.009 s
% 1.22/0.85 % Presaturation interreduction done
% 1.22/0.85
% 1.22/0.85 % Proof found!
% 1.22/0.85 % SZS status Theorem
% 1.22/0.85 % SZS output start CNFRefutation
% See solution above
% 1.22/0.85 % Parsed axioms : 46
% 1.22/0.85 % Removed by relevancy pruning/SinE : 0
% 1.22/0.85 % Initial clauses : 222
% 1.22/0.85 % Removed in clause preprocessing : 3
% 1.22/0.85 % Initial clauses in saturation : 219
% 1.22/0.85 % Processed clauses : 518
% 1.22/0.85 % ...of these trivial : 5
% 1.22/0.85 % ...subsumed : 78
% 1.22/0.85 % ...remaining for further processing : 435
% 1.22/0.85 % Other redundant clauses eliminated : 31
% 1.22/0.85 % Clauses deleted for lack of memory : 0
% 1.22/0.85 % Backward-subsumed : 15
% 1.22/0.85 % Backward-rewritten : 26
% 1.22/0.85 % Generated clauses : 1033
% 1.22/0.85 % ...of the previous two non-redundant : 869
% 1.22/0.85 % ...aggressively subsumed : 0
% 1.22/0.85 % Contextual simplify-reflections : 6
% 1.22/0.85 % Paramodulations : 998
% 1.22/0.85 % Factorizations : 1
% 1.22/0.85 % NegExts : 0
% 1.22/0.85 % Equation resolutions : 34
% 1.22/0.85 % Disequality decompositions : 0
% 1.22/0.85 % Total rewrite steps : 970
% 1.22/0.85 % ...of those cached : 934
% 1.22/0.85 % Propositional unsat checks : 0
% 1.22/0.85 % Propositional check models : 0
% 1.22/0.85 % Propositional check unsatisfiable : 0
% 1.22/0.85 % Propositional clauses : 0
% 1.22/0.85 % Propositional clauses after purity: 0
% 1.22/0.85 % Propositional unsat core size : 0
% 1.22/0.85 % Propositional preprocessing time : 0.000
% 1.22/0.85 % Propositional encoding time : 0.000
% 1.22/0.85 % Propositional solver time : 0.000
% 1.22/0.85 % Success case prop preproc time : 0.000
% 1.22/0.85 % Success case prop encoding time : 0.000
% 1.22/0.85 % Success case prop solver time : 0.000
% 1.22/0.85 % Current number of processed clauses : 169
% 1.22/0.85 % Positive orientable unit clauses : 38
% 1.22/0.85 % Positive unorientable unit clauses: 0
% 1.22/0.85 % Negative unit clauses : 13
% 1.22/0.85 % Non-unit-clauses : 118
% 1.22/0.85 % Current number of unprocessed clauses: 759
% 1.22/0.85 % ...number of literals in the above : 3917
% 1.22/0.85 % Current number of archived formulas : 0
% 1.22/0.85 % Current number of archived clauses : 255
% 1.22/0.85 % Clause-clause subsumption calls (NU) : 30350
% 1.22/0.85 % Rec. Clause-clause subsumption calls : 989
% 1.22/0.85 % Non-unit clause-clause subsumptions : 61
% 1.22/0.85 % Unit Clause-clause subsumption calls : 357
% 1.22/0.85 % Rewrite failures with RHS unbound : 0
% 1.22/0.85 % BW rewrite match attempts : 9
% 1.22/0.85 % BW rewrite match successes : 9
% 1.22/0.85 % Condensation attempts : 0
% 1.22/0.85 % Condensation successes : 0
% 1.22/0.85 % Termbank termtop insertions : 36781
% 1.22/0.85 % Search garbage collected termcells : 2275
% 1.22/0.85
% 1.22/0.85 % -------------------------------------------------
% 1.22/0.85 % User time : 0.137 s
% 1.22/0.85 % System time : 0.011 s
% 1.22/0.85 % Total time : 0.148 s
% 1.22/0.85 % Maximum resident set size: 4208 pages
% 1.22/0.85
% 1.22/0.85 % -------------------------------------------------
% 1.22/0.85 % User time : 0.619 s
% 1.22/0.85 % System time : 0.047 s
% 1.22/0.85 % Total time : 0.667 s
% 1.22/0.85 % Maximum resident set size: 4864 pages
% 1.22/0.85 % E exiting
%------------------------------------------------------------------------------