%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM502+3 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:57:35 PM UTC 2026
% Result : Theorem 8.70s 5.94s
% Output : CNFRefutation 8.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 21
% Syntax : Number of formulae : 108 ( 36 unt; 0 def)
% Number of atoms : 442 ( 157 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 528 ( 194 ~; 210 |; 100 &)
% ( 2 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 13 con; 0-2 aty)
% Number of variables : 123 ( 0 sgn 60 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
| ( X2 != X1
& sdtlseqdt0(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETotal) ).
fof(m__2362,hypothesis,
( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xr,X1) = xk )
& ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xn,xm) = sdtasdt0(xr,X1) )
& doDivides0(xr,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2362) ).
fof(m__2342,hypothesis,
( aNaturalNumber0(xr)
& ? [X1] :
( aNaturalNumber0(X1)
& xk = sdtasdt0(xr,X1) )
& doDivides0(xr,xk)
& xr != sz00
& xr != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& xr = sdtasdt0(X1,X2) )
| doDivides0(X1,xr) ) )
=> ( X1 = sz10
| X1 = xr ) )
& isPrime0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
fof(m__1860,hypothesis,
( xp != sz00
& xp != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& xp = sdtasdt0(X1,X2) )
| doDivides0(X1,xp) ) )
=> ( X1 = sz10
| X1 = xp ) )
& isPrime0(xp)
& ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X1) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(m__,conjecture,
( xk != xp
& ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xk,X1) = xp )
| sdtlseqdt0(xk,xp) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__2306,hypothesis,
( aNaturalNumber0(xk)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(mLETran,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X3) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETran) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
fof(mMonMul,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( X1 != sz00
& X2 != X3
& sdtlseqdt0(X2,X3) )
=> ( sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
& sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(X2,X1) != sdtasdt0(X3,X1)
& sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mMulCanc,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtasdt0(X1,X2) = sdtasdt0(X1,X3)
| sdtasdt0(X2,X1) = sdtasdt0(X3,X1) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
fof(m__2287,hypothesis,
( xn != xp
& ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xn,X1) = xp )
& sdtlseqdt0(xn,xp)
& xm != xp
& ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xm,X1) = xp )
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2287) ).
fof(m__2315,hypothesis,
~ ( xk = sz00
| xk = sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2315) ).
fof(mDefQuot,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != sz00
& doDivides0(X1,X2) )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(c_0_21,plain,
! [X139,X140,X142] :
( ( aNaturalNumber0(esk1_2(X139,X140))
| ~ sdtlseqdt0(X139,X140)
| ~ aNaturalNumber0(X139)
| ~ aNaturalNumber0(X140) )
& ( sdtpldt0(X139,esk1_2(X139,X140)) = X140
| ~ sdtlseqdt0(X139,X140)
| ~ aNaturalNumber0(X139)
| ~ aNaturalNumber0(X140) )
& ( ~ aNaturalNumber0(X142)
| sdtpldt0(X139,X142) != X140
| sdtlseqdt0(X139,X140)
| ~ aNaturalNumber0(X139)
| ~ aNaturalNumber0(X140) ) ),
inference(distribute,[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_22,plain,
! [X109,X110] :
( ~ aNaturalNumber0(X109)
| ~ aNaturalNumber0(X110)
| aNaturalNumber0(sdtpldt0(X109,X110)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
fof(c_0_23,plain,
! [X152,X153] :
( ( X153 != X152
| sdtlseqdt0(X152,X153)
| ~ aNaturalNumber0(X152)
| ~ aNaturalNumber0(X153) )
& ( sdtlseqdt0(X153,X152)
| sdtlseqdt0(X152,X153)
| ~ aNaturalNumber0(X152)
| ~ aNaturalNumber0(X153) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).
cnf(c_0_24,plain,
( sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_26,hypothesis,
( aNaturalNumber0(esk13_0)
& sdtpldt0(xr,esk13_0) = xk
& aNaturalNumber0(esk14_0)
& sdtasdt0(xn,xm) = sdtasdt0(xr,esk14_0)
& doDivides0(xr,sdtasdt0(xn,xm)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2362])]) ).
fof(c_0_27,hypothesis,
! [X207,X208] :
( aNaturalNumber0(xr)
& aNaturalNumber0(esk12_0)
& xk = sdtasdt0(xr,esk12_0)
& doDivides0(xr,xk)
& xr != sz00
& xr != sz10
& ( ~ aNaturalNumber0(X208)
| xr != sdtasdt0(X207,X208)
| ~ aNaturalNumber0(X207)
| X207 = sz10
| X207 = xr )
& ( ~ doDivides0(X207,xr)
| ~ aNaturalNumber0(X207)
| X207 = sz10
| X207 = xr )
& isPrime0(xr) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2342])])])])]) ).
fof(c_0_28,hypothesis,
! [X199,X200] :
( xp != sz00
& xp != sz10
& ( ~ aNaturalNumber0(X200)
| xp != sdtasdt0(X199,X200)
| ~ aNaturalNumber0(X199)
| X199 = sz10
| X199 = xp )
& ( ~ doDivides0(X199,xp)
| ~ aNaturalNumber0(X199)
| X199 = sz10
| X199 = xp )
& isPrime0(xp)
& aNaturalNumber0(esk9_0)
& sdtasdt0(xn,xm) = sdtasdt0(xp,esk9_0)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1860])])])])]) ).
fof(c_0_29,negated_conjecture,
~ ( xk != xp
& ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xk,X1) = xp )
| sdtlseqdt0(xk,xp) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_30,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,hypothesis,
aNaturalNumber0(xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_32,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_24]),c_0_25]) ).
cnf(c_0_33,hypothesis,
sdtpldt0(xr,esk13_0) = xk,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_34,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,hypothesis,
aNaturalNumber0(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,hypothesis,
( X2 = sz10
| X2 = xp
| ~ aNaturalNumber0(X1)
| xp != sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_37,hypothesis,
xk = sdtasdt0(xr,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_38,hypothesis,
aNaturalNumber0(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_39,hypothesis,
xr != sz10,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_40,negated_conjecture,
! [X211] :
( ( ~ aNaturalNumber0(X211)
| sdtpldt0(xk,X211) != xp
| xk = xp )
& ( ~ sdtlseqdt0(xk,xp)
| xk = xp ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])])]) ).
cnf(c_0_41,hypothesis,
( sdtlseqdt0(X1,xk)
| sdtlseqdt0(xk,X1)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_42,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_43,hypothesis,
sdtlseqdt0(xr,xk),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_35])]) ).
cnf(c_0_44,hypothesis,
( xr = xp
| xk != xp ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_34]),c_0_38])]),c_0_39]) ).
fof(c_0_45,plain,
! [X149,X150,X151] :
( ~ aNaturalNumber0(X149)
| ~ aNaturalNumber0(X150)
| ~ aNaturalNumber0(X151)
| ~ sdtlseqdt0(X149,X150)
| ~ sdtlseqdt0(X150,X151)
| sdtlseqdt0(X149,X151) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])]) ).
cnf(c_0_46,negated_conjecture,
( xk = xp
| ~ sdtlseqdt0(xk,xp) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_47,hypothesis,
( sdtlseqdt0(xk,xp)
| sdtlseqdt0(xp,xk) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,hypothesis,
( sdtlseqdt0(xp,xk)
| xk != xp ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
fof(c_0_49,plain,
! [X147,X148] :
( ~ aNaturalNumber0(X147)
| ~ aNaturalNumber0(X148)
| ~ sdtlseqdt0(X147,X148)
| ~ sdtlseqdt0(X148,X147)
| X147 = X148 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])]) ).
cnf(c_0_50,plain,
( sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_51,negated_conjecture,
sdtlseqdt0(xp,xk),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
fof(c_0_52,plain,
! [X157,X158,X159] :
( ( sdtasdt0(X157,X158) != sdtasdt0(X157,X159)
| X157 = sz00
| X158 = X159
| ~ sdtlseqdt0(X158,X159)
| ~ aNaturalNumber0(X157)
| ~ aNaturalNumber0(X158)
| ~ aNaturalNumber0(X159) )
& ( sdtlseqdt0(sdtasdt0(X157,X158),sdtasdt0(X157,X159))
| X157 = sz00
| X158 = X159
| ~ sdtlseqdt0(X158,X159)
| ~ aNaturalNumber0(X157)
| ~ aNaturalNumber0(X158)
| ~ aNaturalNumber0(X159) )
& ( sdtasdt0(X158,X157) != sdtasdt0(X159,X157)
| X157 = sz00
| X158 = X159
| ~ sdtlseqdt0(X158,X159)
| ~ aNaturalNumber0(X157)
| ~ aNaturalNumber0(X158)
| ~ aNaturalNumber0(X159) )
& ( sdtlseqdt0(sdtasdt0(X158,X157),sdtasdt0(X159,X157))
| X157 = sz00
| X158 = X159
| ~ sdtlseqdt0(X158,X159)
| ~ aNaturalNumber0(X157)
| ~ aNaturalNumber0(X158)
| ~ aNaturalNumber0(X159) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul])])]) ).
fof(c_0_53,plain,
! [X111,X112] :
( ~ aNaturalNumber0(X111)
| ~ aNaturalNumber0(X112)
| aNaturalNumber0(sdtasdt0(X111,X112)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(c_0_54,plain,
! [X132,X133,X134] :
( ( sdtasdt0(X132,X133) != sdtasdt0(X132,X134)
| X133 = X134
| ~ aNaturalNumber0(X133)
| ~ aNaturalNumber0(X134)
| X132 = sz00
| ~ aNaturalNumber0(X132) )
& ( sdtasdt0(X133,X132) != sdtasdt0(X134,X132)
| X133 = X134
| ~ aNaturalNumber0(X133)
| ~ aNaturalNumber0(X134)
| X132 = sz00
| ~ aNaturalNumber0(X132) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulCanc])])])]) ).
cnf(c_0_55,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_56,negated_conjecture,
( sdtlseqdt0(X1,xk)
| ~ sdtlseqdt0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_31]),c_0_42])]) ).
cnf(c_0_57,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_58,hypothesis,
( xn != xp
& aNaturalNumber0(esk10_0)
& sdtpldt0(xn,esk10_0) = xp
& sdtlseqdt0(xn,xp)
& xm != xp
& aNaturalNumber0(esk11_0)
& sdtpldt0(xm,esk11_0) = xp
& sdtlseqdt0(xm,xp) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2287])]) ).
cnf(c_0_59,plain,
( sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X3,X2))
| X2 = sz00
| X1 = X3
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_60,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_61,plain,
( X1 = X3
| X2 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X3,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_62,plain,
( sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| X1 = sz00
| X2 = X3
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_63,hypothesis,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_64,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_65,hypothesis,
( xk != sz00
& xk != sz10 ),
inference(fof_nnf,[status(thm)],[m__2315]) ).
cnf(c_0_66,negated_conjecture,
( xk = X1
| ~ sdtlseqdt0(xk,X1)
| ~ sdtlseqdt0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_31])]) ).
cnf(c_0_67,hypothesis,
( sdtlseqdt0(xk,xm)
| sdtlseqdt0(xm,xk) ),
inference(spm,[status(thm)],[c_0_41,c_0_57]) ).
cnf(c_0_68,hypothesis,
sdtlseqdt0(xm,xp),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
fof(c_0_69,plain,
! [X169,X170,X171] :
( ( aNaturalNumber0(X171)
| X171 != sdtsldt0(X170,X169)
| X169 = sz00
| ~ doDivides0(X169,X170)
| ~ aNaturalNumber0(X169)
| ~ aNaturalNumber0(X170) )
& ( X170 = sdtasdt0(X169,X171)
| X171 != sdtsldt0(X170,X169)
| X169 = sz00
| ~ doDivides0(X169,X170)
| ~ aNaturalNumber0(X169)
| ~ aNaturalNumber0(X170) )
& ( ~ aNaturalNumber0(X171)
| X170 != sdtasdt0(X169,X171)
| X171 = sdtsldt0(X170,X169)
| X169 = sz00
| ~ doDivides0(X169,X170)
| ~ aNaturalNumber0(X169)
| ~ aNaturalNumber0(X170) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).
cnf(c_0_70,plain,
( X1 = sz00
| X2 = X3
| ~ sdtlseqdt0(sdtasdt0(X3,X1),sdtasdt0(X2,X1))
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_59]),c_0_60]),c_0_60]),c_0_61]) ).
cnf(c_0_71,hypothesis,
( xn = sz00
| xm = X1
| sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xn,X1))
| ~ sdtlseqdt0(xm,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_57]),c_0_64])]) ).
cnf(c_0_72,hypothesis,
sdtlseqdt0(xn,xp),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_73,hypothesis,
xk != sz00,
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_74,hypothesis,
xn != xp,
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_75,negated_conjecture,
( xk = xm
| sdtlseqdt0(xm,xk) ),
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_57])]) ).
fof(c_0_76,plain,
! [X118] :
( ( sdtpldt0(X118,sz00) = X118
| ~ aNaturalNumber0(X118) )
& ( X118 = sdtpldt0(sz00,X118)
| ~ aNaturalNumber0(X118) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).
fof(c_0_77,plain,
! [X161,X162] :
( ~ aNaturalNumber0(X161)
| ~ aNaturalNumber0(X162)
| X161 = sz00
| sdtlseqdt0(X162,sdtasdt0(X162,X161)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul2])]) ).
cnf(c_0_78,plain,
( X1 = sdtasdt0(X2,X3)
| X2 = sz00
| X3 != sdtsldt0(X1,X2)
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_79,plain,
( aNaturalNumber0(X1)
| X3 = sz00
| X1 != sdtsldt0(X2,X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_80,hypothesis,
sdtasdt0(xn,xm) = sdtasdt0(xr,esk14_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_81,hypothesis,
( xk = xm
| xn = sz00 ),
inference(csr,[status(thm)],[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_70,c_0_71]),c_0_72]),c_0_42]),c_0_31]),c_0_64])]),c_0_73]),c_0_74]),c_0_75]) ).
cnf(c_0_82,hypothesis,
xm != xp,
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_83,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_84,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_85,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_86,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_87,plain,
( sdtasdt0(X1,sdtsldt0(X2,X1)) = X2
| X1 = sz00
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_78]) ).
cnf(c_0_88,plain,
( X1 = sz00
| aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_79]) ).
cnf(c_0_89,hypothesis,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_90,hypothesis,
sdtasdt0(xr,esk14_0) = sdtasdt0(xp,xk),
inference(rw,[status(thm)],[c_0_80,c_0_63]) ).
cnf(c_0_91,hypothesis,
aNaturalNumber0(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_92,plain,
! [X125] :
( ( sdtasdt0(X125,sz00) = sz00
| ~ aNaturalNumber0(X125) )
& ( sz00 = sdtasdt0(sz00,X125)
| ~ aNaturalNumber0(X125) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).
cnf(c_0_93,negated_conjecture,
xn = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_81]),c_0_68])]),c_0_82]) ).
cnf(c_0_94,hypothesis,
( sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,xm)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_68]),c_0_42]),c_0_57])]) ).
cnf(c_0_95,plain,
( sdtlseqdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_83]),c_0_84])]) ).
cnf(c_0_96,hypothesis,
sdtsldt0(sdtasdt0(xp,xk),xp) = xk,
inference(rw,[status(thm)],[c_0_85,c_0_63]) ).
cnf(c_0_97,plain,
( sdtsldt0(X1,X2) = sz00
| X2 = sz00
| sdtlseqdt0(X2,X1)
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88]) ).
cnf(c_0_98,hypothesis,
doDivides0(xp,sdtasdt0(xp,xk)),
inference(rw,[status(thm)],[c_0_89,c_0_63]) ).
cnf(c_0_99,hypothesis,
aNaturalNumber0(sdtasdt0(xp,xk)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_90]),c_0_91]),c_0_34])]) ).
cnf(c_0_100,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_101,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_102,hypothesis,
sdtasdt0(sz00,xm) = sdtasdt0(xp,xk),
inference(rw,[status(thm)],[c_0_63,c_0_93]) ).
cnf(c_0_103,hypothesis,
sdtlseqdt0(sz00,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_84]),c_0_57])]) ).
cnf(c_0_104,hypothesis,
sdtlseqdt0(xp,sdtasdt0(xp,xk)),
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(spm,[status(thm)],[c_0_96,c_0_97]),c_0_98]),c_0_42]),c_0_99])]),c_0_73]),c_0_100]) ).
cnf(c_0_105,hypothesis,
sdtasdt0(xp,xk) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_57])]) ).
cnf(c_0_106,hypothesis,
~ sdtlseqdt0(xp,sz00),
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_103]),c_0_84]),c_0_42])]),c_0_100]) ).
cnf(c_0_107,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_104,c_0_105]),c_0_106]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM502+3 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n019.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 00:39:44 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 8.70/5.94 % Version : CSE_E---1.7
% 8.70/5.94 % Problem : theBenchmark.p
% 8.70/5.94 % SZS status Theorem for theBenchmark.p
% 8.70/5.94 % SZS output start CNFRefutation
% See solution above
% 8.70/5.98 % Total time : 4.374s
%------------------------------------------------------------------------------