%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM493+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 01:49:18 PM UTC 2026
% Result : Theorem 0.14s 0.87s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 19
% Syntax : Number of formulae : 83 ( 29 unt; 0 def)
% Number of atoms : 299 ( 87 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 362 ( 146 ~; 147 |; 44 &)
% ( 4 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 99 ( 0 sgn 55 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefDiff,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X1,X2)
=> ! [X3] :
( X3 = sdtmndt0(X2,X1)
<=> ( sdtpldt0(X1,X3) = X2
& aNaturalNumber0(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
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(m__1870,hypothesis,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).
fof(m__1883,hypothesis,
xr = sdtmndt0(xn,xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1883) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(m__1894,hypothesis,
( sdtlseqdt0(xr,xn)
& xr != xn ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1894) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(m__,conjecture,
( doDivides0(xp,xm)
| doDivides0(xp,xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__1799,hypothesis,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X3,sdtasdt0(X1,X2))
& isPrime0(X3) )
=> ( iLess0(sdtpldt0(sdtpldt0(X1,X2),X3),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(X3,X2)
| doDivides0(X3,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1799) ).
fof(m__1913,hypothesis,
doDivides0(xp,sdtasdt0(xr,xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1913) ).
fof(m__1860,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
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(mIH_03,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X1,X2)
& X1 != X2 )
=> iLess0(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH_03) ).
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(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(c_0_19,plain,
! [X39,X40,X41] :
( ( ~ aNaturalNumber0(X40)
| ~ aNaturalNumber0(X39)
| ~ sdtlseqdt0(X39,X40)
| X41 = sdtmndt0(X40,X39)
| sdtpldt0(X39,X41) != X40
| ~ aNaturalNumber0(X41) )
& ( ~ aNaturalNumber0(X40)
| ~ aNaturalNumber0(X39)
| ~ sdtlseqdt0(X39,X40)
| X41 != sdtmndt0(X40,X39)
| sdtpldt0(X39,X41) = X40 )
& ( ~ aNaturalNumber0(X40)
| ~ aNaturalNumber0(X39)
| ~ sdtlseqdt0(X39,X40)
| X41 != sdtmndt0(X40,X39)
| aNaturalNumber0(X41) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])])]) ).
cnf(c_0_20,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X3)
| X2 != sdtmndt0(X3,X1)
| sdtpldt0(X1,X2) = X3 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_21,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X3,X2)
| X1 != sdtmndt0(X2,X3)
| aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_22,plain,
! [X25,X26,X27] :
( ( ~ aNaturalNumber0(X27)
| ~ aNaturalNumber0(X26)
| ~ aNaturalNumber0(X25)
| X26 = X27
| sdtpldt0(X26,X25) != sdtpldt0(X27,X25) )
& ( ~ aNaturalNumber0(X27)
| ~ aNaturalNumber0(X26)
| ~ aNaturalNumber0(X25)
| X26 = X27
| sdtpldt0(X25,X26) != sdtpldt0(X25,X27) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddCanc])])])]) ).
cnf(c_0_23,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| sdtpldt0(X1,sdtmndt0(X2,X1)) = X2 ),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_24,hypothesis,
sdtlseqdt0(xp,xn),
inference(split_conjunct,[status(thm)],[m__1870]) ).
cnf(c_0_25,hypothesis,
xr = sdtmndt0(xn,xp),
inference(split_conjunct,[status(thm)],[m__1883]) ).
cnf(c_0_26,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_27,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_28,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1)
| aNaturalNumber0(sdtmndt0(X1,X2)) ),
inference(er,[status(thm)],[c_0_21]) ).
fof(c_0_29,hypothesis,
( sdtlseqdt0(xr,xn)
& xr != xn ),
inference(fof_simplification,[status(thm)],[m__1894]) ).
cnf(c_0_30,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X1,X2) != sdtpldt0(X3,X2)
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,hypothesis,
sdtpldt0(xp,xr) = xn,
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_26]),c_0_27])]) ).
cnf(c_0_32,hypothesis,
aNaturalNumber0(xr),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_24]),c_0_25]),c_0_27]),c_0_26])]) ).
fof(c_0_33,plain,
! [X9,X10] :
( sdtpldt0(X9,X10) = sdtpldt0(X10,X9)
| ~ aNaturalNumber0(X10)
| ~ aNaturalNumber0(X9) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])])]) ).
fof(c_0_34,hypothesis,
( sdtlseqdt0(xr,xn)
& xr != xn ),
inference(fof_nnf,[status(thm)],[c_0_29]) ).
fof(c_0_35,plain,
! [X15,X16] :
( sdtasdt0(X15,X16) = sdtasdt0(X16,X15)
| ~ aNaturalNumber0(X16)
| ~ aNaturalNumber0(X15) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
fof(c_0_36,negated_conjecture,
~ ( doDivides0(xp,xm)
| doDivides0(xp,xr) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_37,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X1,xr) != xn
| X1 = xp ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_27]),c_0_32])]) ).
cnf(c_0_38,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_39,hypothesis,
sdtlseqdt0(xr,xn),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_40,hypothesis,
! [X89,X90,X91] :
( doDivides0(X91,X90)
| doDivides0(X91,X89)
| ~ iLess0(sdtpldt0(sdtpldt0(X89,X90),X91),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X91,sdtasdt0(X89,X90))
| ~ isPrime0(X91)
| ~ aNaturalNumber0(X91)
| ~ aNaturalNumber0(X90)
| ~ aNaturalNumber0(X89) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1799])])]) ).
cnf(c_0_41,hypothesis,
doDivides0(xp,sdtasdt0(xr,xm)),
inference(split_conjunct,[status(thm)],[m__1913]) ).
cnf(c_0_42,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_44,negated_conjecture,
( ~ doDivides0(xp,xm)
& ~ doDivides0(xp,xr) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])]) ).
cnf(c_0_45,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtpldt0(xr,X1) != xn
| X1 = xp ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_32])]) ).
cnf(c_0_46,hypothesis,
sdtpldt0(xr,sdtmndt0(xn,xr)) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_39]),c_0_26])]),c_0_32])]) ).
cnf(c_0_47,hypothesis,
aNaturalNumber0(sdtmndt0(xn,xr)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_39]),c_0_26])]),c_0_32])]) ).
cnf(c_0_48,hypothesis,
( ~ iLess0(sdtpldt0(sdtpldt0(X1,X2),X3),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X3,sdtasdt0(X1,X2))
| ~ isPrime0(X3)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X3,X2)
| doDivides0(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_49,hypothesis,
doDivides0(xp,sdtasdt0(xm,xr)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]),c_0_32])]) ).
cnf(c_0_50,hypothesis,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_51,negated_conjecture,
~ doDivides0(xp,xr),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_52,negated_conjecture,
~ doDivides0(xp,xm),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_53,plain,
! [X11,X12,X13] :
( sdtpldt0(sdtpldt0(X11,X12),X13) = sdtpldt0(X11,sdtpldt0(X12,X13))
| ~ aNaturalNumber0(X13)
| ~ aNaturalNumber0(X12)
| ~ aNaturalNumber0(X11) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])])]) ).
cnf(c_0_54,hypothesis,
sdtmndt0(xn,xr) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47])]) ).
fof(c_0_55,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X1,X2)
& X1 != X2 )
=> iLess0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mIH_03]) ).
fof(c_0_56,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_57,plain,
! [X5,X6] :
( aNaturalNumber0(sdtpldt0(X5,X6))
| ~ aNaturalNumber0(X6)
| ~ aNaturalNumber0(X5) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])])]) ).
cnf(c_0_58,hypothesis,
~ iLess0(sdtpldt0(sdtpldt0(xm,xr),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_27]),c_0_32]),c_0_43])]),c_0_51]),c_0_52]) ).
cnf(c_0_59,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_60,hypothesis,
sdtpldt0(xr,xp) = xn,
inference(rw,[status(thm)],[c_0_46,c_0_54]) ).
fof(c_0_61,plain,
! [X61,X62] :
( iLess0(X61,X62)
| ~ sdtlseqdt0(X61,X62)
| X61 = X62
| ~ aNaturalNumber0(X62)
| ~ aNaturalNumber0(X61) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])]) ).
cnf(c_0_62,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_63,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_64,hypothesis,
~ iLess0(sdtpldt0(xm,xn),sdtpldt0(sdtpldt0(xn,xm),xp)),
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_58,c_0_59]),c_0_60]),c_0_27]),c_0_32]),c_0_43])]) ).
cnf(c_0_65,plain,
( ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| iLess0(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_66,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,sdtpldt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_62]),c_0_63]) ).
fof(c_0_67,plain,
! [X14] :
( ( ~ aNaturalNumber0(X14)
| X14 = sdtpldt0(sz00,X14) )
& ( ~ aNaturalNumber0(X14)
| sdtpldt0(X14,sz00) = X14 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])])]) ).
cnf(c_0_68,hypothesis,
~ iLess0(sdtpldt0(xn,xm),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_38]),c_0_26]),c_0_43])]) ).
cnf(c_0_69,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| iLess0(X1,sdtpldt0(X1,X2))
| sdtpldt0(X1,X2) = X1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_63]) ).
cnf(c_0_70,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X2) != sdtpldt0(X1,X3)
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_71,plain,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X1,sz00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_72,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_73,hypothesis,
( ~ 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_68,c_0_69]),c_0_27])]) ).
fof(c_0_74,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_75,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X2
| X1 = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72])]) ).
cnf(c_0_76,hypothesis,
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_73,c_0_63]),c_0_43]),c_0_26])]) ).
fof(c_0_77,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_74])])])])])]) ).
cnf(c_0_78,hypothesis,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_27])]) ).
cnf(c_0_79,plain,
( ~ aNaturalNumber0(X1)
| ~ isPrime0(X1)
| X1 != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_80,hypothesis,
xp = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_63]),c_0_43]),c_0_26])]) ).
cnf(c_0_81,plain,
~ isPrime0(sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_79]),c_0_72])]) ).
cnf(c_0_82,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_80]),c_0_81]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM493+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.58 % Computer : n014.cluster.edu
% 0.09/0.58 % Model : x86_64 x86_64
% 0.09/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.58 % Memory : 8046.5625MB
% 0.09/0.58 % OS : Linux 6.8.0-71-generic
% 0.09/0.58 % CPULimit : 300
% 0.09/0.58 % WCLimit : 300
% 0.09/0.58 % DateTime : Mon Sep 21 02:35:05 UTC 2026
% 0.09/0.58 % CPUTime :
% 0.09/0.58 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.67 Running first-order theorem proving
% 0.14/0.67 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
% 0.14/0.87 % Version: 3.5.1
% 0.14/0.87 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.87 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.87 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.87 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.87 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.87 % Starting sh5l with 300s (1) cores
% 0.14/0.87 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2958893 completed with status 0
% 0.14/0.87 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.14/0.87 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.87 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.87 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.87 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.87 % No SInE strategy applied
% 0.14/0.87 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.14/0.87 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.87 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.87 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.14/0.87 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 0.14/0.87 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 0.14/0.87 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 0.14/0.87 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2958900 completed with status 0
% 0.14/0.87 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.14/0.87 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.87 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.87 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.87 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.87 % No SInE strategy applied
% 0.14/0.87 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.14/0.87 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.87 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.87 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.14/0.87 % Preprocessing time : 0.004 s
% 0.14/0.87 % Presaturation interreduction done
% 0.14/0.87
% 0.14/0.87 % Proof found!
% 0.14/0.87 % SZS status Theorem
% 0.14/0.87 % SZS output start CNFRefutation
% See solution above
% 0.14/0.87 % Parsed axioms : 46
% 0.14/0.87 % Removed by relevancy pruning/SinE : 0
% 0.14/0.87 % Initial clauses : 83
% 0.14/0.87 % Removed in clause preprocessing : 3
% 0.14/0.87 % Initial clauses in saturation : 80
% 0.14/0.87 % Processed clauses : 487
% 0.14/0.87 % ...of these trivial : 10
% 0.14/0.87 % ...subsumed : 134
% 0.14/0.87 % ...remaining for further processing : 343
% 0.14/0.87 % Other redundant clauses eliminated : 25
% 0.14/0.87 % Clauses deleted for lack of memory : 0
% 0.14/0.87 % Backward-subsumed : 4
% 0.14/0.87 % Backward-rewritten : 99
% 0.14/0.87 % Generated clauses : 1241
% 0.14/0.87 % ...of the previous two non-redundant : 1093
% 0.14/0.87 % ...aggressively subsumed : 0
% 0.14/0.87 % Contextual simplify-reflections : 18
% 0.14/0.87 % Paramodulations : 1208
% 0.14/0.87 % Factorizations : 4
% 0.14/0.87 % NegExts : 0
% 0.14/0.87 % Equation resolutions : 29
% 0.14/0.87 % Disequality decompositions : 0
% 0.14/0.87 % Total rewrite steps : 1619
% 0.14/0.87 % ...of those cached : 1563
% 0.14/0.87 % Propositional unsat checks : 0
% 0.14/0.87 % Propositional check models : 0
% 0.14/0.87 % Propositional check unsatisfiable : 0
% 0.14/0.87 % Propositional clauses : 0
% 0.14/0.87 % Propositional clauses after purity: 0
% 0.14/0.87 % Propositional unsat core size : 0
% 0.14/0.87 % Propositional preprocessing time : 0.000
% 0.14/0.87 % Propositional encoding time : 0.000
% 0.14/0.87 % Propositional solver time : 0.000
% 0.14/0.87 % Success case prop preproc time : 0.000
% 0.14/0.87 % Success case prop encoding time : 0.000
% 0.14/0.87 % Success case prop solver time : 0.000
% 0.14/0.87 % Current number of processed clauses : 154
% 0.14/0.87 % Positive orientable unit clauses : 32
% 0.14/0.87 % Positive unorientable unit clauses: 0
% 0.14/0.87 % Negative unit clauses : 19
% 0.14/0.87 % Non-unit-clauses : 103
% 0.14/0.87 % Current number of unprocessed clauses: 679
% 0.14/0.87 % ...number of literals in the above : 2800
% 0.14/0.87 % Current number of archived formulas : 0
% 0.14/0.87 % Current number of archived clauses : 178
% 0.14/0.87 % Clause-clause subsumption calls (NU) : 3081
% 0.14/0.87 % Rec. Clause-clause subsumption calls : 1465
% 0.14/0.87 % Non-unit clause-clause subsumptions : 122
% 0.14/0.87 % Unit Clause-clause subsumption calls : 907
% 0.14/0.87 % Rewrite failures with RHS unbound : 0
% 0.14/0.87 % BW rewrite match attempts : 25
% 0.14/0.87 % BW rewrite match successes : 21
% 0.14/0.87 % Condensation attempts : 0
% 0.14/0.87 % Condensation successes : 0
% 0.14/0.87 % Termbank termtop insertions : 27492
% 0.14/0.87 % Search garbage collected termcells : 1342
% 0.14/0.87
% 0.14/0.87 % -------------------------------------------------
% 0.14/0.87 % User time : 0.080 s
% 0.14/0.87 % System time : 0.007 s
% 0.14/0.87 % Total time : 0.087 s
% 0.14/0.87 % Maximum resident set size: 3940 pages
% 0.14/0.87
% 0.14/0.87 % -------------------------------------------------
% 0.14/0.87 % User time : 0.509 s
% 0.14/0.87 % System time : 0.042 s
% 0.14/0.87 % Total time : 0.551 s
% 0.14/0.87 % Maximum resident set size: 4608 pages
% 0.14/0.87 % E exiting
%------------------------------------------------------------------------------