%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM510+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 : n008.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 04:57:37 PM UTC 2026
% Result : Theorem 2.14s 1.97s
% Output : CNFRefutation 2.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 17
% Syntax : Number of formulae : 78 ( 23 unt; 0 def)
% Number of atoms : 285 ( 117 equ)
% Maximal formula atoms : 27 ( 3 avg)
% Number of connectives : 318 ( 111 ~; 120 |; 70 &)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 42 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
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__,conjecture,
( ~ ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& sdtsldt0(xn,xr) = xn )
& ( ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
=> ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtsldt0(xn,xr),X1) = xn )
| sdtlseqdt0(sdtsldt0(xn,xr),xn) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__2487,hypothesis,
( ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xr,X1) )
& doDivides0(xr,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2487) ).
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(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(mDivLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( doDivides0(X1,X2)
& X2 != sz00 )
=> sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivLE) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(m__2315,hypothesis,
~ ( xk = sz00
| xk = sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2315) ).
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(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__1870,hypothesis,
~ ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xp,X1) = xn )
| sdtlseqdt0(xp,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).
fof(c_0_17,plain,
! [X169,X170,X172] :
( ( aNaturalNumber0(esk2_2(X169,X170))
| ~ doDivides0(X169,X170)
| ~ aNaturalNumber0(X169)
| ~ aNaturalNumber0(X170) )
& ( X170 = sdtasdt0(X169,esk2_2(X169,X170))
| ~ doDivides0(X169,X170)
| ~ aNaturalNumber0(X169)
| ~ aNaturalNumber0(X170) )
& ( ~ aNaturalNumber0(X172)
| X170 != sdtasdt0(X169,X172)
| doDivides0(X169,X170)
| ~ aNaturalNumber0(X169)
| ~ aNaturalNumber0(X170) ) ),
inference(distribute,[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_18,plain,
! [X115,X116] :
( ~ aNaturalNumber0(X115)
| ~ aNaturalNumber0(X116)
| aNaturalNumber0(sdtasdt0(X115,X116)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(c_0_19,plain,
! [X173,X174,X175] :
( ( aNaturalNumber0(X175)
| X175 != sdtsldt0(X174,X173)
| X173 = sz00
| ~ doDivides0(X173,X174)
| ~ aNaturalNumber0(X173)
| ~ aNaturalNumber0(X174) )
& ( X174 = sdtasdt0(X173,X175)
| X175 != sdtsldt0(X174,X173)
| X173 = sz00
| ~ doDivides0(X173,X174)
| ~ aNaturalNumber0(X173)
| ~ aNaturalNumber0(X174) )
& ( ~ aNaturalNumber0(X175)
| X174 != sdtasdt0(X173,X175)
| X175 = sdtsldt0(X174,X173)
| X173 = sz00
| ~ doDivides0(X173,X174)
| ~ aNaturalNumber0(X173)
| ~ aNaturalNumber0(X174) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).
cnf(c_0_20,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_22,negated_conjecture,
~ ( ~ ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& sdtsldt0(xn,xr) = xn )
& ( ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
=> ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtsldt0(xn,xr),X1) = xn )
| sdtlseqdt0(sdtsldt0(xn,xr),xn) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_23,plain,
( X1 = sdtsldt0(X2,X3)
| X3 = sz00
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_20]),c_0_21]) ).
fof(c_0_25,hypothesis,
( aNaturalNumber0(esk18_0)
& xn = sdtasdt0(xr,esk18_0)
& doDivides0(xr,xn) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2487])]) ).
fof(c_0_26,hypothesis,
! [X211,X212] :
( aNaturalNumber0(xr)
& aNaturalNumber0(esk12_0)
& xk = sdtasdt0(xr,esk12_0)
& doDivides0(xr,xk)
& xr != sz00
& xr != sz10
& ( ~ aNaturalNumber0(X212)
| xr != sdtasdt0(X211,X212)
| ~ aNaturalNumber0(X211)
| X211 = sz10
| X211 = xr )
& ( ~ doDivides0(X211,xr)
| ~ aNaturalNumber0(X211)
| X211 = sz10
| X211 = 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_27,plain,
! [X165,X166] :
( ~ aNaturalNumber0(X165)
| ~ aNaturalNumber0(X166)
| X165 = sz00
| sdtlseqdt0(X166,sdtasdt0(X166,X165)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul2])]) ).
fof(c_0_28,plain,
! [X123,X124] :
( ~ aNaturalNumber0(X123)
| ~ aNaturalNumber0(X124)
| sdtasdt0(X123,X124) = sdtasdt0(X124,X123) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
fof(c_0_29,negated_conjecture,
! [X219] :
( ( aNaturalNumber0(sdtsldt0(xn,xr))
| aNaturalNumber0(sdtsldt0(xn,xr)) )
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
| aNaturalNumber0(sdtsldt0(xn,xr)) )
& ( ~ aNaturalNumber0(X219)
| sdtpldt0(sdtsldt0(xn,xr),X219) != xn
| aNaturalNumber0(sdtsldt0(xn,xr)) )
& ( ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
| aNaturalNumber0(sdtsldt0(xn,xr)) )
& ( aNaturalNumber0(sdtsldt0(xn,xr))
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
& ( ~ aNaturalNumber0(X219)
| sdtpldt0(sdtsldt0(xn,xr),X219) != xn
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
& ( ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
& ( aNaturalNumber0(sdtsldt0(xn,xr))
| sdtsldt0(xn,xr) = xn )
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
| sdtsldt0(xn,xr) = xn )
& ( ~ aNaturalNumber0(X219)
| sdtpldt0(sdtsldt0(xn,xr),X219) != xn
| sdtsldt0(xn,xr) = xn )
& ( ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])])]) ).
cnf(c_0_30,plain,
( sdtsldt0(sdtasdt0(X1,X2),X1) = X2
| X1 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_23]),c_0_21]),c_0_24]) ).
cnf(c_0_31,hypothesis,
xn = sdtasdt0(xr,esk18_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,hypothesis,
aNaturalNumber0(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,hypothesis,
xr != sz00,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_36,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_37,negated_conjecture,
( sdtsldt0(xn,xr) = xn
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,hypothesis,
sdtsldt0(xn,xr) = esk18_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_39,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
fof(c_0_40,plain,
! [X185,X186] :
( ~ aNaturalNumber0(X185)
| ~ aNaturalNumber0(X186)
| ~ doDivides0(X185,X186)
| X186 = sz00
| sdtlseqdt0(X185,X186) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivLE])]) ).
cnf(c_0_41,negated_conjecture,
( esk18_0 = xn
| ~ sdtlseqdt0(esk18_0,xn) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38]),c_0_38]) ).
cnf(c_0_42,hypothesis,
sdtlseqdt0(esk18_0,xn),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_31]),c_0_33]),c_0_32])]),c_0_34]) ).
cnf(c_0_43,plain,
( X2 = sz00
| sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_44,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_45,plain,
( doDivides0(X1,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_36]) ).
cnf(c_0_46,negated_conjecture,
esk18_0 = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]) ).
cnf(c_0_47,negated_conjecture,
( sz00 = xn
| esk18_0 = xn
| ~ doDivides0(esk18_0,xn) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_43]),c_0_44]),c_0_33])]) ).
cnf(c_0_48,hypothesis,
doDivides0(esk18_0,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_31]),c_0_33]),c_0_32])]) ).
fof(c_0_49,plain,
! [X125,X126,X127] :
( ~ aNaturalNumber0(X125)
| ~ aNaturalNumber0(X126)
| ~ aNaturalNumber0(X127)
| sdtasdt0(sdtasdt0(X125,X126),X127) = sdtasdt0(X125,sdtasdt0(X126,X127)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
cnf(c_0_50,hypothesis,
sdtasdt0(xr,xn) = xn,
inference(rw,[status(thm)],[c_0_31,c_0_46]) ).
cnf(c_0_51,negated_conjecture,
( esk18_0 = xn
| sz00 = xn ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]) ).
cnf(c_0_52,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_53,hypothesis,
sdtasdt0(xn,xr) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_50]),c_0_44]),c_0_32])]) ).
fof(c_0_54,plain,
! [X128] :
( ( sdtasdt0(X128,sz10) = X128
| ~ aNaturalNumber0(X128) )
& ( X128 = sdtasdt0(sz10,X128)
| ~ aNaturalNumber0(X128) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).
cnf(c_0_55,hypothesis,
( sdtasdt0(xr,xn) = xn
| sz00 = xn ),
inference(spm,[status(thm)],[c_0_31,c_0_51]) ).
cnf(c_0_56,hypothesis,
( sdtasdt0(xn,sdtasdt0(xr,X1)) = sdtasdt0(xn,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_32]),c_0_44])]) ).
cnf(c_0_57,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_58,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_59,hypothesis,
( sdtasdt0(xn,xr) = xn
| sz00 = xn ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_55]),c_0_44]),c_0_32])]) ).
cnf(c_0_60,hypothesis,
sdtasdt0(xn,sz10) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_53]),c_0_58]),c_0_32])]) ).
fof(c_0_61,hypothesis,
( xk != sz00
& xk != sz10 ),
inference(fof_nnf,[status(thm)],[m__2315]) ).
fof(c_0_62,plain,
! [X129] :
( ( sdtasdt0(X129,sz00) = sz00
| ~ aNaturalNumber0(X129) )
& ( sz00 = sdtasdt0(sz00,X129)
| ~ aNaturalNumber0(X129) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).
cnf(c_0_63,hypothesis,
( sdtsldt0(xn,xn) = xr
| sz00 = xn ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_59]),c_0_44]),c_0_32])]) ).
cnf(c_0_64,hypothesis,
( sdtsldt0(xn,xn) = sz10
| sz00 = xn ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_60]),c_0_44]),c_0_58])]) ).
cnf(c_0_65,hypothesis,
xr != sz10,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_66,hypothesis,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_67,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_68,hypothesis,
aNaturalNumber0(xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_69,hypothesis,
xk != sz00,
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_70,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_71,hypothesis,
sz00 = xn,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]) ).
fof(c_0_72,hypothesis,
! [X206] :
( ( ~ aNaturalNumber0(X206)
| sdtpldt0(xp,X206) != xn )
& ~ sdtlseqdt0(xp,xn) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1870])])]) ).
cnf(c_0_73,hypothesis,
sdtlseqdt0(xp,sdtasdt0(xn,xm)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_66]),c_0_67]),c_0_68])]),c_0_69]) ).
cnf(c_0_74,plain,
( sdtasdt0(xn,X1) = xn
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_71]),c_0_71]) ).
cnf(c_0_75,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_76,hypothesis,
~ sdtlseqdt0(xp,xn),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_77,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75])]),c_0_76]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM510+3 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.12 % 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
% 0.16/0.33 % Computer : n008.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 00:40:58 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 2.14/1.97 % Version : CSE_E---1.7
% 2.14/1.97 % Problem : theBenchmark.p
% 2.14/1.97 % SZS status Theorem for theBenchmark.p
% 2.14/1.97 % SZS output start CNFRefutation
% See solution above
% 2.14/1.98 % Total time : 1.374s
%------------------------------------------------------------------------------