%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM510+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n022.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 1.76s 1.87s
% Output : CNFRefutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 32
% Syntax : Number of formulae : 162 ( 47 unt; 0 def)
% Number of atoms : 586 ( 192 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 706 ( 282 ~; 307 |; 75 &)
% ( 4 <=>; 38 =>; 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 : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 189 ( 0 sgn 98 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(mMonAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != X2
& sdtlseqdt0(X1,X2) )
=> ! [X3] :
( aNaturalNumber0(X3)
=> ( sdtpldt0(X3,X1) != sdtpldt0(X3,X2)
& sdtlseqdt0(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
& sdtpldt0(X1,X3) != sdtpldt0(X2,X3)
& sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X3)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonAdd) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(m__2287,hypothesis,
( xn != xp
& sdtlseqdt0(xn,xp)
& xm != xp
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2287) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(mDivTrans,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X2,X3) )
=> doDivides0(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivTrans) ).
fof(mZeroMul,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroMul) ).
fof(mLETran,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X3) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETran) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(m__2487,hypothesis,
doDivides0(xr,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2487) ).
fof(m__2342,hypothesis,
( aNaturalNumber0(xr)
& doDivides0(xr,xk)
& isPrime0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).
fof(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul2) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(m__,conjecture,
( sdtsldt0(xn,xr) != xn
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mDivSum,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X1,X3) )
=> doDivides0(X1,sdtpldt0(X2,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivSum) ).
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/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(mDefPrime,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( isPrime0(X1)
<=> ( X1 != sz00
& X1 != sz10
& ! [X2] :
( ( aNaturalNumber0(X2)
& doDivides0(X2,X1) )
=> ( X2 = sz10
| X2 = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
fof(mAddCanc,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtpldt0(X1,X2) = sdtpldt0(X1,X3)
| sdtpldt0(X2,X1) = sdtpldt0(X3,X1) )
=> X2 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddCanc) ).
fof(mDivLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( doDivides0(X1,X2)
& X2 != sz00 )
=> sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivLE) ).
fof(m__1860,hypothesis,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(mZeroAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtpldt0(X1,X2) = sz00
=> ( X1 = sz00
& X2 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroAdd) ).
fof(m__2306,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).
fof(m__2315,hypothesis,
~ ( xk = sz00
| xk = sz10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2315) ).
fof(c_0_32,plain,
! [X145,X146,X148] :
( ( aNaturalNumber0(esk2_2(X145,X146))
| ~ doDivides0(X145,X146)
| ~ aNaturalNumber0(X145)
| ~ aNaturalNumber0(X146) )
& ( X146 = sdtasdt0(X145,esk2_2(X145,X146))
| ~ doDivides0(X145,X146)
| ~ aNaturalNumber0(X145)
| ~ aNaturalNumber0(X146) )
& ( ~ aNaturalNumber0(X148)
| X146 != sdtasdt0(X145,X148)
| doDivides0(X145,X146)
| ~ aNaturalNumber0(X145)
| ~ aNaturalNumber0(X146) ) ),
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_33,plain,
! [X91,X92] :
( ~ aNaturalNumber0(X91)
| ~ aNaturalNumber0(X92)
| aNaturalNumber0(sdtasdt0(X91,X92)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(c_0_34,plain,
! [X149,X150,X151] :
( ( aNaturalNumber0(X151)
| X151 != sdtsldt0(X150,X149)
| X149 = sz00
| ~ doDivides0(X149,X150)
| ~ aNaturalNumber0(X149)
| ~ aNaturalNumber0(X150) )
& ( X150 = sdtasdt0(X149,X151)
| X151 != sdtsldt0(X150,X149)
| X149 = sz00
| ~ doDivides0(X149,X150)
| ~ aNaturalNumber0(X149)
| ~ aNaturalNumber0(X150) )
& ( ~ aNaturalNumber0(X151)
| X150 != sdtasdt0(X149,X151)
| X151 = sdtsldt0(X150,X149)
| X149 = sz00
| ~ doDivides0(X149,X150)
| ~ aNaturalNumber0(X149)
| ~ aNaturalNumber0(X150) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).
cnf(c_0_35,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_37,plain,
! [X104] :
( ( sdtasdt0(X104,sz10) = X104
| ~ aNaturalNumber0(X104) )
& ( X104 = sdtasdt0(sz10,X104)
| ~ aNaturalNumber0(X104) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).
fof(c_0_38,plain,
! [X134,X135,X136] :
( ( sdtpldt0(X136,X134) != sdtpldt0(X136,X135)
| ~ aNaturalNumber0(X136)
| X134 = X135
| ~ sdtlseqdt0(X134,X135)
| ~ aNaturalNumber0(X134)
| ~ aNaturalNumber0(X135) )
& ( sdtlseqdt0(sdtpldt0(X136,X134),sdtpldt0(X136,X135))
| ~ aNaturalNumber0(X136)
| X134 = X135
| ~ sdtlseqdt0(X134,X135)
| ~ aNaturalNumber0(X134)
| ~ aNaturalNumber0(X135) )
& ( sdtpldt0(X134,X136) != sdtpldt0(X135,X136)
| ~ aNaturalNumber0(X136)
| X134 = X135
| ~ sdtlseqdt0(X134,X135)
| ~ aNaturalNumber0(X134)
| ~ aNaturalNumber0(X135) )
& ( sdtlseqdt0(sdtpldt0(X134,X136),sdtpldt0(X135,X136))
| ~ aNaturalNumber0(X136)
| X134 = X135
| ~ sdtlseqdt0(X134,X135)
| ~ aNaturalNumber0(X134)
| ~ aNaturalNumber0(X135) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonAdd])])])]) ).
cnf(c_0_39,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_34]) ).
cnf(c_0_40,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_35]),c_0_36]) ).
cnf(c_0_41,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_42,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_43,plain,
( sdtlseqdt0(sdtpldt0(X1,X2),sdtpldt0(X1,X3))
| X2 = X3
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_44,hypothesis,
sdtlseqdt0(xn,xp),
inference(split_conjunct,[status(thm)],[m__2287]) ).
cnf(c_0_45,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_46,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_47,hypothesis,
xn != xp,
inference(split_conjunct,[status(thm)],[m__2287]) ).
fof(c_0_48,plain,
! [X98] :
( ( sdtpldt0(X98,sz00) = X98
| ~ aNaturalNumber0(X98) )
& ( X98 = sdtpldt0(sz00,X98)
| ~ aNaturalNumber0(X98) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).
fof(c_0_49,plain,
! [X152,X153,X154] :
( ~ aNaturalNumber0(X152)
| ~ aNaturalNumber0(X153)
| ~ aNaturalNumber0(X154)
| ~ doDivides0(X152,X153)
| ~ doDivides0(X153,X154)
| doDivides0(X152,X154) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivTrans])]) ).
fof(c_0_50,plain,
! [X117,X118] :
( ~ aNaturalNumber0(X117)
| ~ aNaturalNumber0(X118)
| sdtasdt0(X117,X118) != sz00
| X117 = sz00
| X118 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroMul])]) ).
cnf(c_0_51,plain,
( sdtasdt0(X1,sdtsldt0(X2,X1)) = X2
| X1 = sz00
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_39]) ).
cnf(c_0_52,plain,
( doDivides0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]) ).
cnf(c_0_53,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_54,plain,
( aNaturalNumber0(X1)
| X3 = sz00
| X1 != sdtsldt0(X2,X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_55,plain,
! [X129,X130,X131] :
( ~ aNaturalNumber0(X129)
| ~ aNaturalNumber0(X130)
| ~ aNaturalNumber0(X131)
| ~ sdtlseqdt0(X129,X130)
| ~ sdtlseqdt0(X130,X131)
| sdtlseqdt0(X129,X131) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])]) ).
cnf(c_0_56,hypothesis,
( sdtlseqdt0(sdtpldt0(X1,xn),sdtpldt0(X1,xp))
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_46])]),c_0_47]) ).
cnf(c_0_57,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_58,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_59,plain,
! [X119,X120,X122] :
( ( aNaturalNumber0(esk1_2(X119,X120))
| ~ sdtlseqdt0(X119,X120)
| ~ aNaturalNumber0(X119)
| ~ aNaturalNumber0(X120) )
& ( sdtpldt0(X119,esk1_2(X119,X120)) = X120
| ~ sdtlseqdt0(X119,X120)
| ~ aNaturalNumber0(X119)
| ~ aNaturalNumber0(X120) )
& ( ~ aNaturalNumber0(X122)
| sdtpldt0(X119,X122) != X120
| sdtlseqdt0(X119,X120)
| ~ aNaturalNumber0(X119)
| ~ aNaturalNumber0(X120) ) ),
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_60,plain,
! [X89,X90] :
( ~ aNaturalNumber0(X89)
| ~ aNaturalNumber0(X90)
| aNaturalNumber0(sdtpldt0(X89,X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
cnf(c_0_61,plain,
( doDivides0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_62,hypothesis,
doDivides0(xr,xn),
inference(split_conjunct,[status(thm)],[m__2487]) ).
cnf(c_0_63,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[m__2342]) ).
cnf(c_0_64,plain,
( X1 = sz00
| X2 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_65,plain,
( sdtasdt0(sz10,sdtsldt0(X1,sz10)) = X1
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_42])]),c_0_53]) ).
cnf(c_0_66,plain,
( X1 = sz00
| aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_54]) ).
cnf(c_0_67,plain,
( sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_68,hypothesis,
sdtlseqdt0(sdtpldt0(sz00,xn),xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]),c_0_45])]) ).
cnf(c_0_69,plain,
( sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_70,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_71,hypothesis,
( doDivides0(X1,xn)
| ~ doDivides0(X1,xr)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_46]),c_0_63])]) ).
fof(c_0_72,plain,
! [X141,X142] :
( ~ aNaturalNumber0(X141)
| ~ aNaturalNumber0(X142)
| X141 = sz00
| sdtlseqdt0(X142,sdtasdt0(X142,X141)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul2])]) ).
fof(c_0_73,plain,
! [X99,X100] :
( ~ aNaturalNumber0(X99)
| ~ aNaturalNumber0(X100)
| sdtasdt0(X99,X100) = sdtasdt0(X100,X99) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_74,plain,
( sdtsldt0(sz00,sz10) = sz00
| ~ aNaturalNumber0(sdtsldt0(sz00,sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_42])]),c_0_53])]),c_0_58])]) ).
cnf(c_0_75,plain,
( aNaturalNumber0(sdtsldt0(X1,sz10))
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_52]),c_0_42])]),c_0_53]) ).
cnf(c_0_76,hypothesis,
( sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,sdtpldt0(sz00,xn))
| ~ aNaturalNumber0(sdtpldt0(sz00,xn))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_45])]) ).
cnf(c_0_77,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_69]),c_0_70]) ).
cnf(c_0_78,hypothesis,
doDivides0(sz10,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_52]),c_0_42]),c_0_63])]) ).
fof(c_0_79,negated_conjecture,
~ ( sdtsldt0(xn,xr) != xn
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_80,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_81,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_82,plain,
sdtsldt0(sz00,sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_58])]) ).
cnf(c_0_83,hypothesis,
( sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,xn)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_57]),c_0_46])]) ).
cnf(c_0_84,plain,
( sdtlseqdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_57]),c_0_58])]) ).
cnf(c_0_85,hypothesis,
sdtasdt0(sz10,sdtsldt0(xn,sz10)) = xn,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_78]),c_0_42]),c_0_46])]),c_0_53]) ).
cnf(c_0_86,hypothesis,
aNaturalNumber0(sdtsldt0(xn,sz10)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_78]),c_0_42]),c_0_46])]),c_0_53]) ).
fof(c_0_87,negated_conjecture,
( sdtsldt0(xn,xr) = xn
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(fof_nnf,[status(thm)],[c_0_79]) ).
cnf(c_0_88,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_89,hypothesis,
( sdtasdt0(xr,sdtsldt0(xn,xr)) = xn
| xr = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_62]),c_0_63]),c_0_46])]) ).
cnf(c_0_90,hypothesis,
( xr = sz00
| aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_62]),c_0_63]),c_0_46])]) ).
cnf(c_0_91,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_34]) ).
fof(c_0_92,plain,
! [X155,X156,X157] :
( ~ aNaturalNumber0(X155)
| ~ aNaturalNumber0(X156)
| ~ aNaturalNumber0(X157)
| ~ doDivides0(X155,X156)
| ~ doDivides0(X155,X157)
| doDivides0(X155,sdtpldt0(X156,X157)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivSum])]) ).
cnf(c_0_93,plain,
sdtasdt0(sz10,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_82]),c_0_58])]) ).
cnf(c_0_94,plain,
( sdtpldt0(X1,esk1_2(X1,X2)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_95,hypothesis,
sdtlseqdt0(sz00,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_58]),c_0_46])]) ).
cnf(c_0_96,plain,
( aNaturalNumber0(esk1_2(X1,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
fof(c_0_97,plain,
! [X112,X113,X114] :
( ( sdtasdt0(X112,X113) != sdtasdt0(X112,X114)
| X113 = X114
| ~ aNaturalNumber0(X113)
| ~ aNaturalNumber0(X114)
| X112 = sz00
| ~ aNaturalNumber0(X112) )
& ( sdtasdt0(X113,X112) != sdtasdt0(X114,X112)
| X113 = X114
| ~ aNaturalNumber0(X113)
| ~ aNaturalNumber0(X114)
| X112 = sz00
| ~ aNaturalNumber0(X112) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulCanc])])])]) ).
cnf(c_0_98,hypothesis,
sdtsldt0(xn,sz10) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_85]),c_0_86])]) ).
cnf(c_0_99,negated_conjecture,
( sdtsldt0(xn,xr) = xn
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_100,hypothesis,
( xr = sz00
| sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_63])]),c_0_90]) ).
cnf(c_0_101,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_91]),c_0_36]),c_0_40]) ).
cnf(c_0_102,plain,
( doDivides0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_103,plain,
doDivides0(sz10,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_93]),c_0_42]),c_0_58])]) ).
fof(c_0_104,plain,
! [X93,X94] :
( ~ aNaturalNumber0(X93)
| ~ aNaturalNumber0(X94)
| sdtpldt0(X93,X94) = sdtpldt0(X94,X93) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_105,hypothesis,
sdtpldt0(sz00,esk1_2(sz00,xp)) = 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_45]),c_0_58])]) ).
cnf(c_0_106,hypothesis,
aNaturalNumber0(esk1_2(sz00,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_95]),c_0_45]),c_0_58])]) ).
cnf(c_0_107,plain,
( X1 = X3
| X2 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X3,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_108,hypothesis,
sdtasdt0(sz10,xn) = xn,
inference(rw,[status(thm)],[c_0_85,c_0_98]) ).
cnf(c_0_109,negated_conjecture,
( sdtsldt0(xn,xr) = xn
| xr = sz00 ),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
fof(c_0_110,plain,
! [X166,X167] :
( ( X166 != sz00
| ~ isPrime0(X166)
| ~ aNaturalNumber0(X166) )
& ( X166 != sz10
| ~ isPrime0(X166)
| ~ aNaturalNumber0(X166) )
& ( ~ aNaturalNumber0(X167)
| ~ doDivides0(X167,X166)
| X167 = sz10
| X167 = X166
| ~ isPrime0(X166)
| ~ aNaturalNumber0(X166) )
& ( aNaturalNumber0(esk3_1(X166))
| X166 = sz00
| X166 = sz10
| isPrime0(X166)
| ~ aNaturalNumber0(X166) )
& ( doDivides0(esk3_1(X166),X166)
| X166 = sz00
| X166 = sz10
| isPrime0(X166)
| ~ aNaturalNumber0(X166) )
& ( esk3_1(X166) != sz10
| X166 = sz00
| X166 = sz10
| isPrime0(X166)
| ~ aNaturalNumber0(X166) )
& ( esk3_1(X166) != X166
| X166 = sz00
| X166 = sz10
| isPrime0(X166)
| ~ aNaturalNumber0(X166) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefPrime])])])])]) ).
cnf(c_0_111,plain,
( sdtsldt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_41]),c_0_42])]),c_0_53]) ).
cnf(c_0_112,plain,
( sdtsldt0(X1,sz10) = sz00
| sdtlseqdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_65]),c_0_42])]),c_0_75]) ).
cnf(c_0_113,plain,
( doDivides0(sz10,sdtpldt0(X1,sz00))
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_58]),c_0_42])]),c_0_52]) ).
cnf(c_0_114,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_115,hypothesis,
esk1_2(sz00,xp) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_105]),c_0_106])]) ).
cnf(c_0_116,hypothesis,
( xn = sz00
| sz10 = X1
| sdtasdt0(X1,xn) != xn
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_46]),c_0_42])]) ).
cnf(c_0_117,hypothesis,
( sdtasdt0(xr,xn) = xn
| xr = sz00 ),
inference(spm,[status(thm)],[c_0_89,c_0_109]) ).
cnf(c_0_118,plain,
( X1 != sz10
| ~ isPrime0(X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
fof(c_0_119,plain,
! [X109,X110,X111] :
( ( sdtpldt0(X109,X110) != sdtpldt0(X109,X111)
| X110 = X111
| ~ aNaturalNumber0(X109)
| ~ aNaturalNumber0(X110)
| ~ aNaturalNumber0(X111) )
& ( sdtpldt0(X110,X109) != sdtpldt0(X111,X109)
| X110 = X111
| ~ aNaturalNumber0(X109)
| ~ aNaturalNumber0(X110)
| ~ aNaturalNumber0(X111) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddCanc])])]) ).
cnf(c_0_120,plain,
( sz00 = X1
| sdtlseqdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
fof(c_0_121,plain,
! [X161,X162] :
( ~ aNaturalNumber0(X161)
| ~ aNaturalNumber0(X162)
| ~ doDivides0(X161,X162)
| X162 = sz00
| sdtlseqdt0(X161,X162) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivLE])]) ).
cnf(c_0_122,plain,
( doDivides0(sz10,sdtpldt0(sz00,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_58])]) ).
cnf(c_0_123,hypothesis,
sdtpldt0(sz00,xp) = xp,
inference(rw,[status(thm)],[c_0_105,c_0_115]) ).
cnf(c_0_124,hypothesis,
isPrime0(xr),
inference(split_conjunct,[status(thm)],[m__2342]) ).
cnf(c_0_125,hypothesis,
( xr = sz00
| xr = sz10
| xn = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_63])]) ).
cnf(c_0_126,plain,
~ isPrime0(sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_118]),c_0_42])]) ).
cnf(c_0_127,plain,
( X1 != sz00
| ~ isPrime0(X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_128,plain,
( X2 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_129,hypothesis,
( sdtpldt0(sz00,xn) = sz00
| sdtlseqdt0(sz10,xp)
| ~ aNaturalNumber0(sdtpldt0(sz00,xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_120]),c_0_42])]) ).
cnf(c_0_130,plain,
( X2 = sz00
| sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_131,hypothesis,
doDivides0(sz10,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_45])]) ).
cnf(c_0_132,hypothesis,
( xn = sz00
| xr = sz00 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_126]) ).
cnf(c_0_133,plain,
~ isPrime0(sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_127]),c_0_58])]) ).
cnf(c_0_134,hypothesis,
( xp = X1
| sdtpldt0(sz00,X1) != xp
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_123]),c_0_45]),c_0_58])]) ).
cnf(c_0_135,hypothesis,
( sdtpldt0(sz00,xn) = sz00
| sdtlseqdt0(sz10,xp) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_70]),c_0_46]),c_0_58])]) ).
cnf(c_0_136,hypothesis,
( xp = sz00
| sdtlseqdt0(sz10,xp) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_45]),c_0_42])]) ).
cnf(c_0_137,hypothesis,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_138,hypothesis,
xn = sz00,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_132]),c_0_133]) ).
fof(c_0_139,plain,
! [X105] :
( ( sdtasdt0(X105,sz00) = sz00
| ~ aNaturalNumber0(X105) )
& ( sz00 = sdtasdt0(sz00,X105)
| ~ aNaturalNumber0(X105) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).
fof(c_0_140,plain,
! [X115,X116] :
( ( X115 = sz00
| sdtpldt0(X115,X116) != sz00
| ~ aNaturalNumber0(X115)
| ~ aNaturalNumber0(X116) )
& ( X116 = sz00
| sdtpldt0(X115,X116) != sz00
| ~ aNaturalNumber0(X115)
| ~ aNaturalNumber0(X116) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroAdd])])]) ).
cnf(c_0_141,hypothesis,
sdtlseqdt0(sz10,xp),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_46])]),c_0_47]),c_0_136]) ).
cnf(c_0_142,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_143,hypothesis,
doDivides0(xp,sdtasdt0(sz00,xm)),
inference(rw,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_144,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_139]) ).
cnf(c_0_145,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_146,plain,
( X1 = sz00
| sdtpldt0(X1,X2) != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_140]) ).
cnf(c_0_147,hypothesis,
sdtpldt0(sz10,esk1_2(sz10,xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_141]),c_0_45]),c_0_42])]) ).
cnf(c_0_148,hypothesis,
aNaturalNumber0(esk1_2(sz10,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_141]),c_0_45]),c_0_42])]) ).
fof(c_0_149,plain,
! [X127,X128] :
( ~ aNaturalNumber0(X127)
| ~ aNaturalNumber0(X128)
| ~ sdtlseqdt0(X127,X128)
| ~ sdtlseqdt0(X128,X127)
| X127 = X128 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])]) ).
cnf(c_0_150,hypothesis,
sdtsldt0(sdtasdt0(sz00,xm),xp) = xk,
inference(rw,[status(thm)],[c_0_142,c_0_138]) ).
cnf(c_0_151,hypothesis,
doDivides0(xp,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_145])]) ).
cnf(c_0_152,hypothesis,
xp != sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_148]),c_0_42])]),c_0_53]) ).
cnf(c_0_153,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_149]) ).
cnf(c_0_154,hypothesis,
sdtsldt0(sz00,xp) = xk,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_144]),c_0_145])]) ).
cnf(c_0_155,hypothesis,
aNaturalNumber0(sdtsldt0(sz00,xp)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_151]),c_0_45]),c_0_58])]),c_0_152]) ).
fof(c_0_156,hypothesis,
( xk != sz00
& xk != sz10 ),
inference(fof_nnf,[status(thm)],[m__2315]) ).
cnf(c_0_157,plain,
( sdtasdt0(X1,X2) = X1
| X2 = sz00
| ~ sdtlseqdt0(sdtasdt0(X1,X2),X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_80]),c_0_36]) ).
cnf(c_0_158,hypothesis,
sdtasdt0(xp,xk) = sz00,
inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_151]),c_0_45]),c_0_58])]),c_0_152]),c_0_154]) ).
cnf(c_0_159,hypothesis,
aNaturalNumber0(xk),
inference(rw,[status(thm)],[c_0_155,c_0_154]) ).
cnf(c_0_160,hypothesis,
xk != sz00,
inference(split_conjunct,[status(thm)],[c_0_156]) ).
cnf(c_0_161,hypothesis,
$false,
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_157,c_0_158]),c_0_95]),c_0_45]),c_0_159])]),c_0_152]),c_0_160]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM510+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n022.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 00:40:51 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.76/1.87 % Version : CSE_E---1.7
% 1.76/1.87 % Problem : theBenchmark.p
% 1.76/1.87 % SZS status Theorem for theBenchmark.p
% 1.76/1.87 % SZS output start CNFRefutation
% See solution above
% 1.76/1.87 % Total time : 1.371s
%------------------------------------------------------------------------------