%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM483+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : 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 01:49:15 PM UTC 2026
% Result : Theorem 2.35s 0.75s
% Output : CNFRefutation 2.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 20
% Syntax : Number of formulae : 100 ( 28 unt; 0 def)
% Number of atoms : 379 ( 114 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 458 ( 179 ~; 183 |; 63 &)
% ( 4 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 114 ( 0 sgn 64 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__1725,hypothesis,
~ isPrime0(xk),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1725) ).
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/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
fof(m__1716_04,hypothesis,
( xk != sz10
& xk != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1716_04) ).
fof(mDivLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( X2 != sz00
& doDivides0(X1,X2) )
=> sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivLE) ).
fof(mIH_03,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X1,X2)
& X1 != X2 )
=> iLess0(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH_03) ).
fof(m__1716,hypothesis,
aNaturalNumber0(xk),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1716) ).
fof(mDivTrans,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X2,X3)
& doDivides0(X1,X2) )
=> doDivides0(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivTrans) ).
fof(m__1700,hypothesis,
! [X1] :
( ( X1 != sz10
& X1 != sz00
& aNaturalNumber0(X1) )
=> ( iLess0(X1,xk)
=> ? [X2] :
( isPrime0(X2)
& doDivides0(X2,X1)
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1700) ).
fof(m__,conjecture,
? [X1] :
( isPrime0(X1)
& doDivides0(X1,xk)
& aNaturalNumber0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( sdtpldt0(X1,X3) = X2
& aNaturalNumber0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
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/sandbox/benchmark/theBenchmark.p',mAddCanc) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sz00 = sdtasdt0(sz00,X1)
& sdtasdt0(X1,sz00) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& sdtlseqdt0(X1,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).
fof(c_0_20,hypothesis,
~ isPrime0(xk),
inference(fof_simplification,[status(thm)],[m__1725]) ).
fof(c_0_21,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_22,hypothesis,
( xk != sz10
& xk != sz00 ),
inference(fof_simplification,[status(thm)],[m__1716_04]) ).
fof(c_0_23,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( X2 != sz00
& doDivides0(X1,X2) )
=> sdtlseqdt0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mDivLE]) ).
fof(c_0_24,hypothesis,
~ isPrime0(xk),
inference(fof_nnf,[status(thm)],[c_0_20]) ).
fof(c_0_25,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_21])])])])])]) ).
fof(c_0_26,hypothesis,
( xk != sz10
& xk != sz00 ),
inference(fof_nnf,[status(thm)],[c_0_22]) ).
fof(c_0_27,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_28,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_23])])]) ).
cnf(c_0_29,hypothesis,
~ isPrime0(xk),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
( ~ aNaturalNumber0(X1)
| isPrime0(X1)
| X1 = sz10
| X1 = sz00
| doDivides0(esk3_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,hypothesis,
aNaturalNumber0(xk),
inference(split_conjunct,[status(thm)],[m__1716]) ).
cnf(c_0_32,hypothesis,
xk != sz00,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,hypothesis,
xk != sz10,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_34,plain,
( ~ aNaturalNumber0(X1)
| isPrime0(X1)
| X1 = sz10
| X1 = sz00
| aNaturalNumber0(esk3_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_35,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])])]) ).
fof(c_0_36,hypothesis,
! [X1] :
( ( X1 != sz10
& X1 != sz00
& aNaturalNumber0(X1) )
=> ( iLess0(X1,xk)
=> ? [X2] :
( isPrime0(X2)
& doDivides0(X2,X1)
& aNaturalNumber0(X2) ) ) ),
inference(fof_simplification,[status(thm)],[m__1700]) ).
fof(c_0_37,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_27])])]) ).
cnf(c_0_38,plain,
( ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X2)
| X2 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_39,hypothesis,
doDivides0(esk3_1(xk),xk),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]),c_0_32]),c_0_33]) ).
cnf(c_0_40,hypothesis,
aNaturalNumber0(esk3_1(xk)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_34]),c_0_31])]),c_0_32]),c_0_33]) ).
cnf(c_0_41,plain,
( ~ aNaturalNumber0(X1)
| esk3_1(X1) != X1
| isPrime0(X1)
| X1 = sz10
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_42,negated_conjecture,
~ ? [X1] :
( isPrime0(X1)
& doDivides0(X1,xk)
& aNaturalNumber0(X1) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_43,plain,
( ~ doDivides0(X2,X3)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_44,hypothesis,
! [X87] :
( ( X87 = sz10
| X87 = sz00
| ~ aNaturalNumber0(X87)
| ~ iLess0(X87,xk)
| isPrime0(esk4_1(X87)) )
& ( X87 = sz10
| X87 = sz00
| ~ aNaturalNumber0(X87)
| ~ iLess0(X87,xk)
| doDivides0(esk4_1(X87),X87) )
& ( X87 = sz10
| X87 = sz00
| ~ aNaturalNumber0(X87)
| ~ iLess0(X87,xk)
| aNaturalNumber0(esk4_1(X87)) ) ),
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_36])])])])]) ).
cnf(c_0_45,plain,
( ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| iLess0(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_46,hypothesis,
sdtlseqdt0(esk3_1(xk),xk),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_31]),c_0_40])]),c_0_32]) ).
cnf(c_0_47,hypothesis,
esk3_1(xk) != xk,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_41]),c_0_31])]),c_0_32]),c_0_33]) ).
cnf(c_0_48,plain,
( ~ aNaturalNumber0(X1)
| esk3_1(X1) != sz10
| isPrime0(X1)
| X1 = sz10
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_49,negated_conjecture,
! [X89] :
( ~ isPrime0(X89)
| ~ doDivides0(X89,xk)
| ~ aNaturalNumber0(X89) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])]) ).
cnf(c_0_50,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,esk3_1(xk))
| doDivides0(X1,xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_39]),c_0_31]),c_0_40])]) ).
cnf(c_0_51,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ iLess0(X1,xk)
| X1 = sz10
| X1 = sz00
| doDivides0(esk4_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_52,hypothesis,
iLess0(esk3_1(xk),xk),
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_46]),c_0_31]),c_0_40])]),c_0_47]) ).
cnf(c_0_53,hypothesis,
esk3_1(xk) != sz10,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_48]),c_0_31])]),c_0_32]),c_0_33]) ).
fof(c_0_54,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_55,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_simplification,[status(thm)],[mSortsC_01]) ).
cnf(c_0_56,negated_conjecture,
( ~ isPrime0(X1)
| ~ doDivides0(X1,xk)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_57,hypothesis,
( ~ aNaturalNumber0(esk4_1(esk3_1(xk)))
| doDivides0(esk4_1(esk3_1(xk)),xk)
| esk3_1(xk) = sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_40])]),c_0_53]) ).
cnf(c_0_58,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
fof(c_0_59,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_55]) ).
fof(c_0_60,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_61,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])])]) ).
fof(c_0_62,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_63,negated_conjecture,
( ~ aNaturalNumber0(esk4_1(esk3_1(xk)))
| ~ isPrime0(esk4_1(esk3_1(xk)))
| esk3_1(xk) = sz00 ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_64,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ iLess0(X1,xk)
| X1 = sz10
| X1 = sz00
| isPrime0(esk4_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_65,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtpldt0(xk,X1) = sdtpldt0(X1,xk) ),
inference(spm,[status(thm)],[c_0_58,c_0_31]) ).
cnf(c_0_66,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_67,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_68,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
fof(c_0_69,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_70,plain,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X1,sz00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_71,hypothesis,
( ~ aNaturalNumber0(esk4_1(esk3_1(xk)))
| esk3_1(xk) = sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_52]),c_0_40])]),c_0_53]) ).
cnf(c_0_72,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ iLess0(X1,xk)
| X1 = sz10
| X1 = sz00
| aNaturalNumber0(esk4_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_73,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_74,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_75,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_76,hypothesis,
sdtpldt0(xk,sz10) = sdtpldt0(sz10,xk),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_77,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,sdtpldt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_67]),c_0_68]) ).
cnf(c_0_78,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X2) != sdtpldt0(X1,X3)
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_79,hypothesis,
sdtpldt0(xk,sz00) = xk,
inference(spm,[status(thm)],[c_0_70,c_0_31]) ).
cnf(c_0_80,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_81,hypothesis,
esk3_1(xk) = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_52]),c_0_40])]),c_0_53]) ).
cnf(c_0_82,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| doDivides0(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_83,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_84,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz00) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_85,hypothesis,
aNaturalNumber0(sdtpldt0(sz10,xk)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_76]),c_0_66]),c_0_31])]) ).
fof(c_0_86,plain,
! [X43,X44] :
( X43 = X44
| ~ sdtlseqdt0(X44,X43)
| ~ sdtlseqdt0(X43,X44)
| ~ aNaturalNumber0(X44)
| ~ aNaturalNumber0(X43) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])])]) ).
cnf(c_0_87,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(xk,sdtpldt0(xk,X1)) ),
inference(spm,[status(thm)],[c_0_77,c_0_31]) ).
cnf(c_0_88,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtpldt0(xk,X1) != xk
| X1 = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80]),c_0_31])]) ).
cnf(c_0_89,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_90,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,sz00)
| doDivides0(X1,xk) ),
inference(rw,[status(thm)],[c_0_50,c_0_81]) ).
cnf(c_0_91,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,sdtasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_82]),c_0_83]) ).
cnf(c_0_92,hypothesis,
sdtasdt0(sdtpldt0(sz10,xk),sz00) = sz00,
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_93,plain,
( ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_94,hypothesis,
sdtlseqdt0(xk,sdtpldt0(sz10,xk)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_66]),c_0_76]) ).
cnf(c_0_95,hypothesis,
sdtpldt0(sz10,xk) != xk,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_76]),c_0_66])]),c_0_89]) ).
cnf(c_0_96,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,sz00)
| sdtlseqdt0(X1,xk) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_90]),c_0_31])]),c_0_32]) ).
cnf(c_0_97,hypothesis,
doDivides0(sdtpldt0(sz10,xk),sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_85]),c_0_80])]) ).
cnf(c_0_98,hypothesis,
~ sdtlseqdt0(sdtpldt0(sz10,xk),xk),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_31]),c_0_85])]),c_0_95]) ).
cnf(c_0_99,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_85])]),c_0_98]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM483+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.36 % Computer : n014.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Mon Sep 21 02:33:49 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.35/0.75 % Version: 3.5.1
% 2.35/0.75 % Preprocessing class: FSLSSMSSSSSNFFN.
% 2.35/0.75 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.35/0.75 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.35/0.75 % Starting new_bool_3 with 300s (1) cores
% 2.35/0.75 % Starting new_bool_1 with 300s (1) cores
% 2.35/0.75 % Starting sh5l with 300s (1) cores
% 2.35/0.75 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2955623 completed with status 0
% 2.35/0.75 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 2.35/0.75 % Preprocessing class: FSLSSMSSSSSNFFN.
% 2.35/0.75 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.35/0.75 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.35/0.75 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.35/0.75 % No SInE strategy applied
% 2.35/0.75 % Search class: FGHSF-FFMS21-SFFFFFNN
% 2.35/0.75 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.35/0.75 % Starting SubtermCWHack with 136s (1) cores
% 2.35/0.75 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 2.35/0.75 % Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 2.35/0.75 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 2.35/0.75 % Starting new_bool_3 with 136s (1) cores
% 2.35/0.75 % 208_C09_12_F1_SE_CS_SP_PS_S070I with pid 2955632 completed with status 0
% 2.35/0.75 % Result found by 208_C09_12_F1_SE_CS_SP_PS_S070I
% 2.35/0.75 % Preprocessing class: FSLSSMSSSSSNFFN.
% 2.35/0.75 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.35/0.75 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.35/0.75 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.35/0.75 % No SInE strategy applied
% 2.35/0.75 % Search class: FGHSF-FFMS21-SFFFFFNN
% 2.35/0.75 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.35/0.75 % Starting SubtermCWHack with 136s (1) cores
% 2.35/0.75 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 2.35/0.75 % Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 2.35/0.75 % Preprocessing time : 0.002 s
% 2.35/0.75 % Presaturation interreduction done
% 2.35/0.75
% 2.35/0.75 % Proof found!
% 2.35/0.75 % SZS status Theorem
% 2.35/0.75 % SZS output start CNFRefutation
% See solution above
% 2.35/0.75 % Parsed axioms : 42
% 2.35/0.75 % Removed by relevancy pruning/SinE : 0
% 2.35/0.75 % Initial clauses : 75
% 2.35/0.75 % Removed in clause preprocessing : 3
% 2.35/0.75 % Initial clauses in saturation : 72
% 2.35/0.75 % Processed clauses : 1242
% 2.35/0.75 % ...of these trivial : 70
% 2.35/0.75 % ...subsumed : 253
% 2.35/0.75 % ...remaining for further processing : 919
% 2.35/0.75 % Other redundant clauses eliminated : 11
% 2.35/0.75 % Clauses deleted for lack of memory : 0
% 2.35/0.75 % Backward-subsumed : 52
% 2.35/0.75 % Backward-rewritten : 170
% 2.35/0.75 % Generated clauses : 18039
% 2.35/0.75 % ...of the previous two non-redundant : 17032
% 2.35/0.75 % ...aggressively subsumed : 0
% 2.35/0.75 % Contextual simplify-reflections : 13
% 2.35/0.75 % Paramodulations : 18024
% 2.35/0.75 % Factorizations : 0
% 2.35/0.75 % NegExts : 0
% 2.35/0.75 % Equation resolutions : 15
% 2.35/0.75 % Disequality decompositions : 0
% 2.35/0.75 % Total rewrite steps : 7331
% 2.35/0.75 % ...of those cached : 7155
% 2.35/0.75 % Propositional unsat checks : 0
% 2.35/0.75 % Propositional check models : 0
% 2.35/0.75 % Propositional check unsatisfiable : 0
% 2.35/0.75 % Propositional clauses : 0
% 2.35/0.75 % Propositional clauses after purity: 0
% 2.35/0.75 % Propositional unsat core size : 0
% 2.35/0.75 % Propositional preprocessing time : 0.000
% 2.35/0.75 % Propositional encoding time : 0.000
% 2.35/0.75 % Propositional solver time : 0.000
% 2.35/0.75 % Success case prop preproc time : 0.000
% 2.35/0.75 % Success case prop encoding time : 0.000
% 2.35/0.75 % Success case prop solver time : 0.000
% 2.35/0.75 % Current number of processed clauses : 619
% 2.35/0.75 % Positive orientable unit clauses : 181
% 2.35/0.75 % Positive unorientable unit clauses: 0
% 2.35/0.75 % Negative unit clauses : 34
% 2.35/0.75 % Non-unit-clauses : 404
% 2.35/0.75 % Current number of unprocessed clauses: 15801
% 2.35/0.75 % ...number of literals in the above : 35872
% 2.35/0.75 % Current number of archived formulas : 0
% 2.35/0.75 % Current number of archived clauses : 289
% 2.35/0.75 % Clause-clause subsumption calls (NU) : 13536
% 2.35/0.75 % Rec. Clause-clause subsumption calls : 9744
% 2.35/0.75 % Non-unit clause-clause subsumptions : 204
% 2.35/0.75 % Unit Clause-clause subsumption calls : 3338
% 2.35/0.75 % Rewrite failures with RHS unbound : 0
% 2.35/0.75 % BW rewrite match attempts : 54
% 2.35/0.75 % BW rewrite match successes : 30
% 2.35/0.75 % Condensation attempts : 0
% 2.35/0.75 % Condensation successes : 0
% 2.35/0.75 % Termbank termtop insertions : 323163
% 2.35/0.75 % Search garbage collected termcells : 1344
% 2.35/0.75
% 2.35/0.75 % -------------------------------------------------
% 2.35/0.75 % User time : 0.300 s
% 2.35/0.75 % System time : 0.022 s
% 2.35/0.75 % Total time : 0.322 s
% 2.35/0.75 % Maximum resident set size: 3624 pages
% 2.35/0.75
% 2.35/0.75 % -------------------------------------------------
% 2.35/0.75 % User time : 1.513 s
% 2.35/0.75 % System time : 0.091 s
% 2.35/0.75 % Total time : 1.604 s
% 2.35/0.75 % Maximum resident set size: 4608 pages
% 2.35/0.75 % E exiting
%------------------------------------------------------------------------------