%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM481+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 : n011.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 01:49:15 PM UTC 2026
% Result : Theorem 0.17s 6.06s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 71 ( 20 unt; 0 def)
% Number of atoms : 320 ( 104 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 387 ( 138 ~; 151 |; 65 &)
% ( 3 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 84 ( 0 sgn 45 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
! [X1] :
( ( X1 != sz10
& X1 != sz00
& aNaturalNumber0(X1) )
=> ( ! [X2] :
( ( X2 != sz10
& X2 != sz00
& aNaturalNumber0(X2) )
=> ( iLess0(X2,X1)
=> ? [X3] :
( isPrime0(X3)
& doDivides0(X3,X2)
& aNaturalNumber0(X3) ) ) )
=> ? [X2] :
( isPrime0(X2)
& doDivides0(X2,X1)
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
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_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtasdt0(sz10,X1)
& sdtasdt0(X1,sz10) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
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(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(mDivLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( X2 != sz00
& doDivides0(X1,X2) )
=> sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivLE) ).
fof(mDivTrans,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X2,X3)
& doDivides0(X1,X2) )
=> doDivides0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivTrans) ).
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_11,negated_conjecture,
~ ! [X1] :
( ( X1 != sz10
& X1 != sz00
& aNaturalNumber0(X1) )
=> ( ! [X2] :
( ( X2 != sz10
& X2 != sz00
& aNaturalNumber0(X2) )
=> ( iLess0(X2,X1)
=> ? [X3] :
( isPrime0(X3)
& doDivides0(X3,X2)
& aNaturalNumber0(X3) ) ) )
=> ? [X2] :
( isPrime0(X2)
& doDivides0(X2,X1)
& aNaturalNumber0(X2) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1] :
( ( X1 != sz10
& X1 != sz00
& aNaturalNumber0(X1) )
=> ( ! [X2] :
( ( X2 != sz10
& X2 != sz00
& aNaturalNumber0(X2) )
=> ( iLess0(X2,X1)
=> ? [X3] :
( isPrime0(X3)
& doDivides0(X3,X2)
& aNaturalNumber0(X3) ) ) )
=> ? [X2] :
( isPrime0(X2)
& doDivides0(X2,X1)
& aNaturalNumber0(X2) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_13,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_14,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])])]) ).
fof(c_0_15,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_16,negated_conjecture,
! [X88,X90] :
( ( ~ isPrime0(X90)
| ~ doDivides0(X90,esk4_0)
| ~ aNaturalNumber0(X90) )
& ( X88 = sz10
| X88 = sz00
| ~ aNaturalNumber0(X88)
| ~ iLess0(X88,esk4_0)
| isPrime0(esk5_1(X88)) )
& ( X88 = sz10
| X88 = sz00
| ~ aNaturalNumber0(X88)
| ~ iLess0(X88,esk4_0)
| doDivides0(esk5_1(X88),X88) )
& ( X88 = sz10
| X88 = sz00
| ~ aNaturalNumber0(X88)
| ~ iLess0(X88,esk4_0)
| aNaturalNumber0(esk5_1(X88)) )
& esk4_0 != sz10
& esk4_0 != sz00
& aNaturalNumber0(esk4_0) ),
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_12])])])])])]) ).
fof(c_0_17,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_simplification,[status(thm)],[mSortsC_01]) ).
cnf(c_0_18,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| doDivides0(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz10) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
aNaturalNumber0(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_22,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,sdtasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_18]),c_0_19]) ).
cnf(c_0_24,negated_conjecture,
sdtasdt0(esk4_0,sz10) = esk4_0,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_26,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_27,negated_conjecture,
( ~ isPrime0(X1)
| ~ doDivides0(X1,esk4_0)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_28,negated_conjecture,
doDivides0(esk4_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_21]),c_0_25])]) ).
fof(c_0_29,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_26])])])])])]) ).
fof(c_0_30,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_31,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( X2 != sz00
& doDivides0(X1,X2) )
=> sdtlseqdt0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mDivLE]) ).
fof(c_0_32,plain,
! [X70,X71,X72] :
( doDivides0(X70,X72)
| ~ doDivides0(X71,X72)
| ~ doDivides0(X70,X71)
| ~ aNaturalNumber0(X72)
| ~ aNaturalNumber0(X71)
| ~ aNaturalNumber0(X70) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivTrans])])]) ).
cnf(c_0_33,negated_conjecture,
~ isPrime0(esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_21])]) ).
cnf(c_0_34,plain,
( ~ aNaturalNumber0(X1)
| isPrime0(X1)
| X1 = sz10
| X1 = sz00
| doDivides0(esk3_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,negated_conjecture,
esk4_0 != sz00,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_36,negated_conjecture,
esk4_0 != sz10,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_37,plain,
( ~ aNaturalNumber0(X1)
| isPrime0(X1)
| X1 = sz10
| X1 = sz00
| aNaturalNumber0(esk3_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_38,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_30])])]) ).
fof(c_0_39,plain,
! [X79,X80] :
( sdtlseqdt0(X79,X80)
| X80 = sz00
| ~ doDivides0(X79,X80)
| ~ aNaturalNumber0(X80)
| ~ aNaturalNumber0(X79) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])]) ).
cnf(c_0_40,plain,
( ~ doDivides0(X2,X3)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_41,negated_conjecture,
doDivides0(esk3_1(esk4_0),esk4_0),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_21])]),c_0_35]),c_0_36]) ).
cnf(c_0_42,negated_conjecture,
aNaturalNumber0(esk3_1(esk4_0)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_37]),c_0_21])]),c_0_35]),c_0_36]) ).
cnf(c_0_43,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ iLess0(X1,esk4_0)
| X1 = sz10
| X1 = sz00
| doDivides0(esk5_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_44,plain,
( ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| iLess0(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_45,plain,
( ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X2)
| X2 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_46,plain,
( ~ aNaturalNumber0(X1)
| esk3_1(X1) != X1
| isPrime0(X1)
| X1 = sz10
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_47,plain,
( ~ aNaturalNumber0(X1)
| esk3_1(X1) != sz10
| isPrime0(X1)
| X1 = sz10
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_48,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,esk3_1(esk4_0))
| doDivides0(X1,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_21]),c_0_42])]) ).
cnf(c_0_49,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,esk4_0)
| doDivides0(esk5_1(X1),X1)
| X1 = sz00
| X1 = sz10
| X1 = esk4_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_21])]) ).
cnf(c_0_50,negated_conjecture,
sdtlseqdt0(esk3_1(esk4_0),esk4_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_41]),c_0_21]),c_0_42])]),c_0_35]) ).
cnf(c_0_51,negated_conjecture,
esk3_1(esk4_0) != esk4_0,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_46]),c_0_21])]),c_0_35]),c_0_36]) ).
cnf(c_0_52,negated_conjecture,
esk3_1(esk4_0) != sz10,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_47]),c_0_21])]),c_0_35]),c_0_36]) ).
cnf(c_0_53,negated_conjecture,
( ~ aNaturalNumber0(esk5_1(esk3_1(esk4_0)))
| doDivides0(esk5_1(esk3_1(esk4_0)),esk4_0)
| esk3_1(esk4_0) = sz00 ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[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_42])]),c_0_51]),c_0_52]) ).
cnf(c_0_54,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ iLess0(X1,esk4_0)
| X1 = sz10
| X1 = sz00
| isPrime0(esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_55,negated_conjecture,
( ~ aNaturalNumber0(esk5_1(esk3_1(esk4_0)))
| ~ isPrime0(esk5_1(esk3_1(esk4_0)))
| esk3_1(esk4_0) = sz00 ),
inference(spm,[status(thm)],[c_0_27,c_0_53]) ).
cnf(c_0_56,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,esk4_0)
| isPrime0(esk5_1(X1))
| X1 = sz00
| X1 = sz10
| X1 = esk4_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_44]),c_0_21])]) ).
cnf(c_0_57,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ iLess0(X1,esk4_0)
| X1 = sz10
| X1 = sz00
| aNaturalNumber0(esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_58,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_59,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| aNaturalNumber0(esk2_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_60,negated_conjecture,
( ~ aNaturalNumber0(esk5_1(esk3_1(esk4_0)))
| esk3_1(esk4_0) = sz00 ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_50]),c_0_42])]),c_0_51]),c_0_52]) ).
cnf(c_0_61,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,esk4_0)
| aNaturalNumber0(esk5_1(X1))
| X1 = sz00
| X1 = sz10
| X1 = esk4_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_44]),c_0_21])]) ).
cnf(c_0_62,plain,
( ~ aNaturalNumber0(X1)
| sz00 = sdtasdt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_63,negated_conjecture,
aNaturalNumber0(esk2_2(esk3_1(esk4_0),esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_41]),c_0_21]),c_0_42])]) ).
cnf(c_0_64,negated_conjecture,
esk3_1(esk4_0) = sz00,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_50]),c_0_42])]),c_0_51]),c_0_52]) ).
cnf(c_0_65,negated_conjecture,
sdtasdt0(sz00,esk2_2(esk3_1(esk4_0),esk4_0)) = sz00,
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_66,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X1 = sdtasdt0(X2,esk2_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_67,negated_conjecture,
doDivides0(sz00,esk4_0),
inference(rw,[status(thm)],[c_0_41,c_0_64]) ).
cnf(c_0_68,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_69,negated_conjecture,
sdtasdt0(sz00,esk2_2(sz00,esk4_0)) = sz00,
inference(spm,[status(thm)],[c_0_65,c_0_64]) ).
cnf(c_0_70,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]),c_0_21])]),c_0_69]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM481+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/5.40 % Computer : n011.cluster.edu
% 0.03/5.40 % Model : x86_64 x86_64
% 0.03/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/5.40 % Memory : 8046.5625MB
% 0.03/5.40 % OS : Linux 6.8.0-71-generic
% 0.03/5.40 % CPULimit : 300
% 0.03/5.40 % WCLimit : 300
% 0.03/5.40 % DateTime : Mon Sep 21 02:33:46 UTC 2026
% 0.03/5.40 % CPUTime :
% 0.03/5.40 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/5.47 Running first-order theorem proving
% 0.03/5.47 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
% 0.17/6.06 % Version: 3.5.1
% 0.17/6.06 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/6.06 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/6.06 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/6.06 % Starting new_bool_3 with 300s (1) cores
% 0.17/6.06 % Starting new_bool_1 with 300s (1) cores
% 0.17/6.06 % Starting sh5l with 300s (1) cores
% 0.17/6.06 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 779729 completed with status 0
% 0.17/6.06 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.17/6.06 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/6.06 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/6.06 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/6.06 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.17/6.06 % No SInE strategy applied
% 0.17/6.06 % Search class: FGHSF-FFMS21-SFFFFFNN
% 0.17/6.06 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/6.06 % Starting SubtermCWHack with 136s (1) cores
% 0.17/6.06 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.17/6.06 % Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 0.17/6.06 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 0.17/6.06 % Starting new_bool_3 with 136s (1) cores
% 0.17/6.06 % 208_C09_12_F1_SE_CS_SP_PS_S070I with pid 779738 completed with status 0
% 0.17/6.06 % Result found by 208_C09_12_F1_SE_CS_SP_PS_S070I
% 0.17/6.06 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/6.06 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/6.06 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/6.06 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.17/6.06 % No SInE strategy applied
% 0.17/6.06 % Search class: FGHSF-FFMS21-SFFFFFNN
% 0.17/6.06 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/6.06 % Starting SubtermCWHack with 136s (1) cores
% 0.17/6.06 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.17/6.06 % Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 0.17/6.06 % Preprocessing time : 0.003 s
% 0.17/6.06 % Presaturation interreduction done
% 0.17/6.06
% 0.17/6.06 % Proof found!
% 0.17/6.06 % SZS status Theorem
% 0.17/6.06 % SZS output start CNFRefutation
% See solution above
% 0.17/6.06 % Parsed axioms : 38
% 0.17/6.06 % Removed by relevancy pruning/SinE : 0
% 0.17/6.06 % Initial clauses : 74
% 0.17/6.06 % Removed in clause preprocessing : 3
% 0.17/6.06 % Initial clauses in saturation : 71
% 0.17/6.06 % Processed clauses : 1470
% 0.17/6.06 % ...of these trivial : 106
% 0.17/6.06 % ...subsumed : 278
% 0.17/6.06 % ...remaining for further processing : 1085
% 0.17/6.06 % Other redundant clauses eliminated : 11
% 0.17/6.06 % Clauses deleted for lack of memory : 0
% 0.17/6.06 % Backward-subsumed : 22
% 0.17/6.06 % Backward-rewritten : 263
% 0.17/6.06 % Generated clauses : 21556
% 0.17/6.06 % ...of the previous two non-redundant : 20147
% 0.17/6.06 % ...aggressively subsumed : 0
% 0.17/6.06 % Contextual simplify-reflections : 6
% 0.17/6.06 % Paramodulations : 21541
% 0.17/6.06 % Factorizations : 0
% 0.17/6.06 % NegExts : 0
% 0.17/6.06 % Equation resolutions : 15
% 0.17/6.06 % Disequality decompositions : 0
% 0.17/6.06 % Total rewrite steps : 9056
% 0.17/6.06 % ...of those cached : 8814
% 0.17/6.06 % Propositional unsat checks : 0
% 0.17/6.06 % Propositional check models : 0
% 0.17/6.06 % Propositional check unsatisfiable : 0
% 0.17/6.06 % Propositional clauses : 0
% 0.17/6.06 % Propositional clauses after purity: 0
% 0.17/6.06 % Propositional unsat core size : 0
% 0.17/6.06 % Propositional preprocessing time : 0.000
% 0.17/6.06 % Propositional encoding time : 0.000
% 0.17/6.06 % Propositional solver time : 0.000
% 0.17/6.06 % Success case prop preproc time : 0.000
% 0.17/6.06 % Success case prop encoding time : 0.000
% 0.17/6.06 % Success case prop solver time : 0.000
% 0.17/6.06 % Current number of processed clauses : 723
% 0.17/6.06 % Positive orientable unit clauses : 267
% 0.17/6.06 % Positive unorientable unit clauses: 0
% 0.17/6.06 % Negative unit clauses : 19
% 0.17/6.06 % Non-unit-clauses : 437
% 0.17/6.06 % Current number of unprocessed clauses: 18613
% 0.17/6.06 % ...number of literals in the above : 40303
% 0.17/6.06 % Current number of archived formulas : 0
% 0.17/6.06 % Current number of archived clauses : 351
% 0.17/6.06 % Clause-clause subsumption calls (NU) : 16795
% 0.17/6.06 % Rec. Clause-clause subsumption calls : 11616
% 0.17/6.06 % Non-unit clause-clause subsumptions : 210
% 0.17/6.06 % Unit Clause-clause subsumption calls : 5460
% 0.17/6.06 % Rewrite failures with RHS unbound : 0
% 0.17/6.06 % BW rewrite match attempts : 94
% 0.17/6.06 % BW rewrite match successes : 57
% 0.17/6.06 % Condensation attempts : 0
% 0.17/6.06 % Condensation successes : 0
% 0.17/6.06 % Termbank termtop insertions : 391759
% 0.17/6.06 % Search garbage collected termcells : 1453
% 0.17/6.06
% 0.17/6.06 % -------------------------------------------------
% 0.17/6.06 % User time : 0.488 s
% 0.17/6.06 % System time : 0.029 s
% 0.17/6.06 % Total time : 0.517 s
% 0.17/6.06 % Maximum resident set size: 3932 pages
% 0.17/6.06
% 0.17/6.06 % -------------------------------------------------
% 0.17/6.06 % User time : 2.400 s
% 0.17/6.06 % System time : 0.110 s
% 0.17/6.06 % Total time : 2.511 s
% 0.17/6.06 % Maximum resident set size: 4608 pages
% 0.17/6.06 % E exiting
%------------------------------------------------------------------------------