%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM484+3 : 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 : n011.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 04:57:30 PM UTC 2026
% Result : Theorem 39.51s 37.72s
% Output : CNFRefutation 44.71s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named i_0_212)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
? [X1] :
( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& xk = sdtasdt0(X1,X2) )
| doDivides0(X1,xk) )
& ( ( X1 != sz00
& X1 != sz10
& ! [X2] :
( ( aNaturalNumber0(X2)
& ? [X3] :
( aNaturalNumber0(X3)
& X1 = sdtasdt0(X2,X3) )
& doDivides0(X2,X1) )
=> ( X2 = sz10
| X2 = X1 ) ) )
| isPrime0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__1737,hypothesis,
~ ~ ~ $true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1737) ).
fof(mAMDistr,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(sdtpldt0(X2,X3),X1) = sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
fof(mDivAsso,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != sz00
& doDivides0(X1,X2) )
=> ! [X3] :
( aNaturalNumber0(X3)
=> sdtasdt0(X3,sdtsldt0(X2,X1)) = sdtsldt0(sdtasdt0(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivAsso) ).
fof(mDivMin,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X1,sdtpldt0(X2,X3)) )
=> doDivides0(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivMin) ).
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/sandbox/benchmark/theBenchmark.p',mMonMul) ).
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(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(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
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(mDefDiff,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
=> ! [X3] :
( X3 = sdtmndt0(X2,X1)
<=> ( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
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(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(m__1700,hypothesis,
! [X1] :
( ( aNaturalNumber0(X1)
& X1 != sz00
& X1 != sz10 )
=> ( iLess0(X1,xk)
=> ? [X2] :
( aNaturalNumber0(X2)
& ? [X3] :
( aNaturalNumber0(X3)
& X1 = sdtasdt0(X2,X3) )
& doDivides0(X2,X1)
& X2 != sz00
& X2 != sz10
& ! [X3] :
( ( aNaturalNumber0(X3)
& ( ? [X4] :
( aNaturalNumber0(X4)
& X2 = sdtasdt0(X3,X4) )
| doDivides0(X3,X2) ) )
=> ( X3 = sz10
| X3 = X2 ) )
& isPrime0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1700) ).
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(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(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(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(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(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul2) ).
fof(mIH_03,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != X2
& sdtlseqdt0(X1,X2) )
=> iLess0(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH_03) ).
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(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(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
| ( X2 != X1
& sdtlseqdt0(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
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(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(mLENTr,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sz00
| X1 = sz10
| ( sz10 != X1
& sdtlseqdt0(sz10,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLENTr) ).
fof(mLERefl,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> sdtlseqdt0(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERefl) ).
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(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
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(m__1725,hypothesis,
~ ( ! [X1] :
( ( aNaturalNumber0(X1)
& ? [X2] :
( aNaturalNumber0(X2)
& xk = sdtasdt0(X1,X2) )
& doDivides0(X1,xk) )
=> ( X1 = sz10
| X1 = xk ) )
| isPrime0(xk) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1725) ).
fof(m__1716,hypothesis,
aNaturalNumber0(xk),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1716) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(m__1716_04,hypothesis,
( xk != sz00
& xk != sz10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1716_04) ).
fof(i_0_41,negated_conjecture,
~ ? [X1] :
( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& xk = sdtasdt0(X1,X2) )
| doDivides0(X1,xk) )
& ( ( X1 != sz00
& X1 != sz10
& ! [X2] :
( ( aNaturalNumber0(X2)
& ? [X3] :
( aNaturalNumber0(X3)
& X1 = sdtasdt0(X2,X3) )
& doDivides0(X2,X1) )
=> ( X2 = sz10
| X2 = X1 ) ) )
| isPrime0(X1) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(i_0_42,hypothesis,
~ $true,
inference(fof_simplification,[status(thm)],[m__1737]) ).
fof(i_0_43,plain,
! [X113,X114,X115] :
( ( sdtasdt0(X113,sdtpldt0(X114,X115)) = sdtpldt0(sdtasdt0(X113,X114),sdtasdt0(X113,X115))
| ~ aNaturalNumber0(X113)
| ~ aNaturalNumber0(X114)
| ~ aNaturalNumber0(X115) )
& ( sdtasdt0(sdtpldt0(X114,X115),X113) = sdtpldt0(sdtasdt0(X114,X113),sdtasdt0(X115,X113))
| ~ aNaturalNumber0(X113)
| ~ aNaturalNumber0(X114)
| ~ aNaturalNumber0(X115) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])]) ).
fof(i_0_44,plain,
! [X170,X171,X172] :
( ~ aNaturalNumber0(X170)
| ~ aNaturalNumber0(X171)
| X170 = sz00
| ~ doDivides0(X170,X171)
| ~ aNaturalNumber0(X172)
| sdtasdt0(X172,sdtsldt0(X171,X170)) = sdtsldt0(sdtasdt0(X172,X171),X170) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivAsso])])]) ).
fof(i_0_45,plain,
! [X165,X166,X167] :
( ~ aNaturalNumber0(X165)
| ~ aNaturalNumber0(X166)
| ~ aNaturalNumber0(X167)
| ~ doDivides0(X165,X166)
| ~ doDivides0(X165,sdtpldt0(X166,X167))
| doDivides0(X165,X167) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivMin])]) ).
fof(i_0_46,plain,
! [X144,X145,X146] :
( ( sdtasdt0(X144,X145) != sdtasdt0(X144,X146)
| X144 = sz00
| X145 = X146
| ~ sdtlseqdt0(X145,X146)
| ~ aNaturalNumber0(X144)
| ~ aNaturalNumber0(X145)
| ~ aNaturalNumber0(X146) )
& ( sdtlseqdt0(sdtasdt0(X144,X145),sdtasdt0(X144,X146))
| X144 = sz00
| X145 = X146
| ~ sdtlseqdt0(X145,X146)
| ~ aNaturalNumber0(X144)
| ~ aNaturalNumber0(X145)
| ~ aNaturalNumber0(X146) )
& ( sdtasdt0(X145,X144) != sdtasdt0(X146,X144)
| X144 = sz00
| X145 = X146
| ~ sdtlseqdt0(X145,X146)
| ~ aNaturalNumber0(X144)
| ~ aNaturalNumber0(X145)
| ~ aNaturalNumber0(X146) )
& ( sdtlseqdt0(sdtasdt0(X145,X144),sdtasdt0(X146,X144))
| X144 = sz00
| X145 = X146
| ~ sdtlseqdt0(X145,X146)
| ~ aNaturalNumber0(X144)
| ~ aNaturalNumber0(X145)
| ~ aNaturalNumber0(X146) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul])])]) ).
fof(i_0_47,plain,
! [X141,X142,X143] :
( ( sdtpldt0(X143,X141) != sdtpldt0(X143,X142)
| ~ aNaturalNumber0(X143)
| X141 = X142
| ~ sdtlseqdt0(X141,X142)
| ~ aNaturalNumber0(X141)
| ~ aNaturalNumber0(X142) )
& ( sdtlseqdt0(sdtpldt0(X143,X141),sdtpldt0(X143,X142))
| ~ aNaturalNumber0(X143)
| X141 = X142
| ~ sdtlseqdt0(X141,X142)
| ~ aNaturalNumber0(X141)
| ~ aNaturalNumber0(X142) )
& ( sdtpldt0(X141,X143) != sdtpldt0(X142,X143)
| ~ aNaturalNumber0(X143)
| X141 = X142
| ~ sdtlseqdt0(X141,X142)
| ~ aNaturalNumber0(X141)
| ~ aNaturalNumber0(X142) )
& ( sdtlseqdt0(sdtpldt0(X141,X143),sdtpldt0(X142,X143))
| ~ aNaturalNumber0(X143)
| X141 = X142
| ~ sdtlseqdt0(X141,X142)
| ~ aNaturalNumber0(X141)
| ~ aNaturalNumber0(X142) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonAdd])])])]) ).
fof(i_0_48,plain,
! [X162,X163,X164] :
( ~ aNaturalNumber0(X162)
| ~ aNaturalNumber0(X163)
| ~ aNaturalNumber0(X164)
| ~ doDivides0(X162,X163)
| ~ doDivides0(X162,X164)
| doDivides0(X162,sdtpldt0(X163,X164)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivSum])]) ).
fof(i_0_49,plain,
! [X108,X109,X110] :
( ~ aNaturalNumber0(X108)
| ~ aNaturalNumber0(X109)
| ~ aNaturalNumber0(X110)
| sdtasdt0(sdtasdt0(X108,X109),X110) = sdtasdt0(X108,sdtasdt0(X109,X110)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
fof(i_0_50,plain,
! [X102,X103,X104] :
( ~ aNaturalNumber0(X102)
| ~ aNaturalNumber0(X103)
| ~ aNaturalNumber0(X104)
| sdtpldt0(sdtpldt0(X102,X103),X104) = sdtpldt0(X102,sdtpldt0(X103,X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
fof(i_0_51,plain,
! [X156,X157,X158] :
( ( aNaturalNumber0(X158)
| X158 != sdtsldt0(X157,X156)
| X156 = sz00
| ~ doDivides0(X156,X157)
| ~ aNaturalNumber0(X156)
| ~ aNaturalNumber0(X157) )
& ( X157 = sdtasdt0(X156,X158)
| X158 != sdtsldt0(X157,X156)
| X156 = sz00
| ~ doDivides0(X156,X157)
| ~ aNaturalNumber0(X156)
| ~ aNaturalNumber0(X157) )
& ( ~ aNaturalNumber0(X158)
| X157 != sdtasdt0(X156,X158)
| X158 = sdtsldt0(X157,X156)
| X156 = sz00
| ~ doDivides0(X156,X157)
| ~ aNaturalNumber0(X156)
| ~ aNaturalNumber0(X157) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).
fof(i_0_52,plain,
! [X130,X131,X132] :
( ( aNaturalNumber0(X132)
| X132 != sdtmndt0(X131,X130)
| ~ sdtlseqdt0(X130,X131)
| ~ aNaturalNumber0(X130)
| ~ aNaturalNumber0(X131) )
& ( sdtpldt0(X130,X132) = X131
| X132 != sdtmndt0(X131,X130)
| ~ sdtlseqdt0(X130,X131)
| ~ aNaturalNumber0(X130)
| ~ aNaturalNumber0(X131) )
& ( ~ aNaturalNumber0(X132)
| sdtpldt0(X130,X132) != X131
| X132 = sdtmndt0(X131,X130)
| ~ sdtlseqdt0(X130,X131)
| ~ aNaturalNumber0(X130)
| ~ aNaturalNumber0(X131) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])]) ).
fof(i_0_53,plain,
! [X159,X160,X161] :
( ~ aNaturalNumber0(X159)
| ~ aNaturalNumber0(X160)
| ~ aNaturalNumber0(X161)
| ~ doDivides0(X159,X160)
| ~ doDivides0(X160,X161)
| doDivides0(X159,X161) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivTrans])]) ).
fof(i_0_54,plain,
! [X136,X137,X138] :
( ~ aNaturalNumber0(X136)
| ~ aNaturalNumber0(X137)
| ~ aNaturalNumber0(X138)
| ~ sdtlseqdt0(X136,X137)
| ~ sdtlseqdt0(X137,X138)
| sdtlseqdt0(X136,X138) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])]) ).
fof(i_0_55,hypothesis,
! [X176,X179,X180] :
( ( aNaturalNumber0(esk4_1(X176))
| ~ iLess0(X176,xk)
| ~ aNaturalNumber0(X176)
| X176 = sz00
| X176 = sz10 )
& ( aNaturalNumber0(esk5_1(X176))
| ~ iLess0(X176,xk)
| ~ aNaturalNumber0(X176)
| X176 = sz00
| X176 = sz10 )
& ( X176 = sdtasdt0(esk4_1(X176),esk5_1(X176))
| ~ iLess0(X176,xk)
| ~ aNaturalNumber0(X176)
| X176 = sz00
| X176 = sz10 )
& ( doDivides0(esk4_1(X176),X176)
| ~ iLess0(X176,xk)
| ~ aNaturalNumber0(X176)
| X176 = sz00
| X176 = sz10 )
& ( esk4_1(X176) != sz00
| ~ iLess0(X176,xk)
| ~ aNaturalNumber0(X176)
| X176 = sz00
| X176 = sz10 )
& ( esk4_1(X176) != sz10
| ~ iLess0(X176,xk)
| ~ aNaturalNumber0(X176)
| X176 = sz00
| X176 = sz10 )
& ( ~ aNaturalNumber0(X180)
| esk4_1(X176) != sdtasdt0(X179,X180)
| ~ aNaturalNumber0(X179)
| X179 = sz10
| X179 = esk4_1(X176)
| ~ iLess0(X176,xk)
| ~ aNaturalNumber0(X176)
| X176 = sz00
| X176 = sz10 )
& ( ~ doDivides0(X179,esk4_1(X176))
| ~ aNaturalNumber0(X179)
| X179 = sz10
| X179 = esk4_1(X176)
| ~ iLess0(X176,xk)
| ~ aNaturalNumber0(X176)
| X176 = sz00
| X176 = sz10 )
& ( isPrime0(esk4_1(X176))
| ~ iLess0(X176,xk)
| ~ aNaturalNumber0(X176)
| X176 = sz00
| X176 = sz10 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1700])])])])]) ).
fof(i_0_56,plain,
! [X126,X127,X129] :
( ( aNaturalNumber0(esk1_2(X126,X127))
| ~ sdtlseqdt0(X126,X127)
| ~ aNaturalNumber0(X126)
| ~ aNaturalNumber0(X127) )
& ( sdtpldt0(X126,esk1_2(X126,X127)) = X127
| ~ sdtlseqdt0(X126,X127)
| ~ aNaturalNumber0(X126)
| ~ aNaturalNumber0(X127) )
& ( ~ aNaturalNumber0(X129)
| sdtpldt0(X126,X129) != X127
| sdtlseqdt0(X126,X127)
| ~ aNaturalNumber0(X126)
| ~ aNaturalNumber0(X127) ) ),
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(i_0_57,plain,
! [X152,X153,X155] :
( ( aNaturalNumber0(esk2_2(X152,X153))
| ~ doDivides0(X152,X153)
| ~ aNaturalNumber0(X152)
| ~ aNaturalNumber0(X153) )
& ( X153 = sdtasdt0(X152,esk2_2(X152,X153))
| ~ doDivides0(X152,X153)
| ~ aNaturalNumber0(X152)
| ~ aNaturalNumber0(X153) )
& ( ~ aNaturalNumber0(X155)
| X153 != sdtasdt0(X152,X155)
| doDivides0(X152,X153)
| ~ aNaturalNumber0(X152)
| ~ aNaturalNumber0(X153) ) ),
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(i_0_58,plain,
! [X119,X120,X121] :
( ( sdtasdt0(X119,X120) != sdtasdt0(X119,X121)
| X120 = X121
| ~ aNaturalNumber0(X120)
| ~ aNaturalNumber0(X121)
| X119 = sz00
| ~ aNaturalNumber0(X119) )
& ( sdtasdt0(X120,X119) != sdtasdt0(X121,X119)
| X120 = X121
| ~ aNaturalNumber0(X120)
| ~ aNaturalNumber0(X121)
| X119 = sz00
| ~ aNaturalNumber0(X119) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulCanc])])])]) ).
fof(i_0_59,plain,
! [X116,X117,X118] :
( ( sdtpldt0(X116,X117) != sdtpldt0(X116,X118)
| X117 = X118
| ~ aNaturalNumber0(X116)
| ~ aNaturalNumber0(X117)
| ~ aNaturalNumber0(X118) )
& ( sdtpldt0(X117,X116) != sdtpldt0(X118,X116)
| X117 = X118
| ~ aNaturalNumber0(X116)
| ~ aNaturalNumber0(X117)
| ~ aNaturalNumber0(X118) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddCanc])])]) ).
fof(i_0_60,negated_conjecture,
! [X183,X184] :
( ( aNaturalNumber0(esk8_1(X183))
| X183 = sz00
| X183 = sz10
| ~ aNaturalNumber0(X184)
| xk != sdtasdt0(X183,X184)
| ~ aNaturalNumber0(X183) )
& ( aNaturalNumber0(esk9_1(X183))
| X183 = sz00
| X183 = sz10
| ~ aNaturalNumber0(X184)
| xk != sdtasdt0(X183,X184)
| ~ aNaturalNumber0(X183) )
& ( X183 = sdtasdt0(esk8_1(X183),esk9_1(X183))
| X183 = sz00
| X183 = sz10
| ~ aNaturalNumber0(X184)
| xk != sdtasdt0(X183,X184)
| ~ aNaturalNumber0(X183) )
& ( doDivides0(esk8_1(X183),X183)
| X183 = sz00
| X183 = sz10
| ~ aNaturalNumber0(X184)
| xk != sdtasdt0(X183,X184)
| ~ aNaturalNumber0(X183) )
& ( esk8_1(X183) != sz10
| X183 = sz00
| X183 = sz10
| ~ aNaturalNumber0(X184)
| xk != sdtasdt0(X183,X184)
| ~ aNaturalNumber0(X183) )
& ( esk8_1(X183) != X183
| X183 = sz00
| X183 = sz10
| ~ aNaturalNumber0(X184)
| xk != sdtasdt0(X183,X184)
| ~ aNaturalNumber0(X183) )
& ( ~ isPrime0(X183)
| ~ aNaturalNumber0(X184)
| xk != sdtasdt0(X183,X184)
| ~ aNaturalNumber0(X183) )
& ( aNaturalNumber0(esk8_1(X183))
| X183 = sz00
| X183 = sz10
| ~ doDivides0(X183,xk)
| ~ aNaturalNumber0(X183) )
& ( aNaturalNumber0(esk9_1(X183))
| X183 = sz00
| X183 = sz10
| ~ doDivides0(X183,xk)
| ~ aNaturalNumber0(X183) )
& ( X183 = sdtasdt0(esk8_1(X183),esk9_1(X183))
| X183 = sz00
| X183 = sz10
| ~ doDivides0(X183,xk)
| ~ aNaturalNumber0(X183) )
& ( doDivides0(esk8_1(X183),X183)
| X183 = sz00
| X183 = sz10
| ~ doDivides0(X183,xk)
| ~ aNaturalNumber0(X183) )
& ( esk8_1(X183) != sz10
| X183 = sz00
| X183 = sz10
| ~ doDivides0(X183,xk)
| ~ aNaturalNumber0(X183) )
& ( esk8_1(X183) != X183
| X183 = sz00
| X183 = sz10
| ~ doDivides0(X183,xk)
| ~ aNaturalNumber0(X183) )
& ( ~ isPrime0(X183)
| ~ doDivides0(X183,xk)
| ~ aNaturalNumber0(X183) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_41])])])])]) ).
fof(i_0_61,plain,
! [X134,X135] :
( ~ aNaturalNumber0(X134)
| ~ aNaturalNumber0(X135)
| ~ sdtlseqdt0(X134,X135)
| ~ sdtlseqdt0(X135,X134)
| X134 = X135 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])]) ).
fof(i_0_62,plain,
! [X148,X149] :
( ~ aNaturalNumber0(X148)
| ~ aNaturalNumber0(X149)
| X148 = sz00
| sdtlseqdt0(X149,sdtasdt0(X149,X148)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul2])]) ).
fof(i_0_63,plain,
! [X150,X151] :
( ~ aNaturalNumber0(X150)
| ~ aNaturalNumber0(X151)
| X150 = X151
| ~ sdtlseqdt0(X150,X151)
| iLess0(X150,X151) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIH_03])]) ).
fof(i_0_64,plain,
! [X168,X169] :
( ~ aNaturalNumber0(X168)
| ~ aNaturalNumber0(X169)
| ~ doDivides0(X168,X169)
| X169 = sz00
| sdtlseqdt0(X168,X169) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivLE])]) ).
fof(i_0_65,plain,
! [X173,X174] :
( ( X173 != sz00
| ~ isPrime0(X173)
| ~ aNaturalNumber0(X173) )
& ( X173 != sz10
| ~ isPrime0(X173)
| ~ aNaturalNumber0(X173) )
& ( ~ aNaturalNumber0(X174)
| ~ doDivides0(X174,X173)
| X174 = sz10
| X174 = X173
| ~ isPrime0(X173)
| ~ aNaturalNumber0(X173) )
& ( aNaturalNumber0(esk3_1(X173))
| X173 = sz00
| X173 = sz10
| isPrime0(X173)
| ~ aNaturalNumber0(X173) )
& ( doDivides0(esk3_1(X173),X173)
| X173 = sz00
| X173 = sz10
| isPrime0(X173)
| ~ aNaturalNumber0(X173) )
& ( esk3_1(X173) != sz10
| X173 = sz00
| X173 = sz10
| isPrime0(X173)
| ~ aNaturalNumber0(X173) )
& ( esk3_1(X173) != X173
| X173 = sz00
| X173 = sz10
| isPrime0(X173)
| ~ aNaturalNumber0(X173) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefPrime])])])])]) ).
fof(i_0_66,plain,
! [X98,X99] :
( ~ aNaturalNumber0(X98)
| ~ aNaturalNumber0(X99)
| aNaturalNumber0(sdtasdt0(X98,X99)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(i_0_67,plain,
! [X96,X97] :
( ~ aNaturalNumber0(X96)
| ~ aNaturalNumber0(X97)
| aNaturalNumber0(sdtpldt0(X96,X97)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
fof(i_0_68,plain,
! [X139,X140] :
( ( X140 != X139
| sdtlseqdt0(X139,X140)
| ~ aNaturalNumber0(X139)
| ~ aNaturalNumber0(X140) )
& ( sdtlseqdt0(X140,X139)
| sdtlseqdt0(X139,X140)
| ~ aNaturalNumber0(X139)
| ~ aNaturalNumber0(X140) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).
fof(i_0_69,plain,
! [X106,X107] :
( ~ aNaturalNumber0(X106)
| ~ aNaturalNumber0(X107)
| sdtasdt0(X106,X107) = sdtasdt0(X107,X106) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
fof(i_0_70,plain,
! [X100,X101] :
( ~ aNaturalNumber0(X100)
| ~ aNaturalNumber0(X101)
| sdtpldt0(X100,X101) = sdtpldt0(X101,X100) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
fof(i_0_71,plain,
! [X124,X125] :
( ~ aNaturalNumber0(X124)
| ~ aNaturalNumber0(X125)
| sdtasdt0(X124,X125) != sz00
| X124 = sz00
| X125 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroMul])]) ).
fof(i_0_72,plain,
! [X122,X123] :
( ( X122 = sz00
| sdtpldt0(X122,X123) != sz00
| ~ aNaturalNumber0(X122)
| ~ aNaturalNumber0(X123) )
& ( X123 = sz00
| sdtpldt0(X122,X123) != sz00
| ~ aNaturalNumber0(X122)
| ~ aNaturalNumber0(X123) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroAdd])])]) ).
fof(i_0_73,plain,
! [X147] :
( ( sz10 != X147
| X147 = sz00
| X147 = sz10
| ~ aNaturalNumber0(X147) )
& ( sdtlseqdt0(sz10,X147)
| X147 = sz00
| X147 = sz10
| ~ aNaturalNumber0(X147) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLENTr])])]) ).
fof(i_0_74,plain,
! [X133] :
( ~ aNaturalNumber0(X133)
| sdtlseqdt0(X133,X133) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLERefl])]) ).
fof(i_0_75,plain,
! [X111] :
( ( sdtasdt0(X111,sz10) = X111
| ~ aNaturalNumber0(X111) )
& ( X111 = sdtasdt0(sz10,X111)
| ~ aNaturalNumber0(X111) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).
fof(i_0_76,plain,
! [X105] :
( ( sdtpldt0(X105,sz00) = X105
| ~ aNaturalNumber0(X105) )
& ( X105 = sdtpldt0(sz00,X105)
| ~ aNaturalNumber0(X105) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).
fof(i_0_77,plain,
! [X112] :
( ( sdtasdt0(X112,sz00) = sz00
| ~ aNaturalNumber0(X112) )
& ( sz00 = sdtasdt0(sz00,X112)
| ~ aNaturalNumber0(X112) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).
fof(i_0_78,hypothesis,
( aNaturalNumber0(esk6_0)
& aNaturalNumber0(esk7_0)
& xk = sdtasdt0(esk6_0,esk7_0)
& doDivides0(esk6_0,xk)
& esk6_0 != sz10
& esk6_0 != xk
& ~ isPrime0(xk) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1725])])]) ).
cnf(i_0_79,hypothesis,
$false,
inference(split_conjunct,[status(thm)],[i_0_42]) ).
cnf(i_0_80,plain,
( sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_81,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_82,plain,
( X1 = sz00
| sdtasdt0(X3,sdtsldt0(X2,X1)) = sdtsldt0(sdtasdt0(X3,X2),X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_83,plain,
( doDivides0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X1,sdtpldt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_84,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)],[i_0_46]),
[final] ).
cnf(i_0_85,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)],[i_0_46]),
[final] ).
cnf(i_0_86,plain,
( sdtlseqdt0(sdtpldt0(X1,X2),sdtpldt0(X3,X2))
| X1 = X3
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_87,plain,
( sdtlseqdt0(sdtpldt0(X1,X2),sdtpldt0(X1,X3))
| X2 = X3
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_88,plain,
( doDivides0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_89,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_90,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_91,plain,
( X2 = sz00
| X1 = X3
| sdtasdt0(X1,X2) != sdtasdt0(X3,X2)
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_92,plain,
( X1 = sz00
| X2 = X3
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_93,plain,
( X1 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X3,X2)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_94,plain,
( X2 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_95,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)],[i_0_51]),
[final] ).
cnf(i_0_96,plain,
( X1 = sdtmndt0(X3,X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_97,plain,
( doDivides0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_98,plain,
( sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_99,hypothesis,
( X3 = sz10
| X3 = esk4_1(X2)
| X2 = sz00
| X2 = sz10
| ~ aNaturalNumber0(X1)
| esk4_1(X2) != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ iLess0(X2,xk)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_100,plain,
( sdtpldt0(X1,esk1_2(X1,X2)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_101,plain,
( X1 = sdtasdt0(X2,esk2_2(X2,X1))
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_102,plain,
( X1 = sdtasdt0(X2,X3)
| X2 = sz00
| X3 != sdtsldt0(X1,X2)
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_103,hypothesis,
( X1 = sz10
| X1 = esk4_1(X2)
| X2 = sz00
| X2 = sz10
| ~ doDivides0(X1,esk4_1(X2))
| ~ aNaturalNumber0(X1)
| ~ iLess0(X2,xk)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_104,plain,
( sdtpldt0(X1,X2) = X3
| X2 != sdtmndt0(X3,X1)
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_105,plain,
( X1 = X3
| X2 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X3,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_106,plain,
( X2 = X3
| X1 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_107,plain,
( X1 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X3,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_108,plain,
( X2 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_109,negated_conjecture,
( X1 = sdtasdt0(esk8_1(X1),esk9_1(X1))
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X2)
| xk != sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_110,plain,
( aNaturalNumber0(esk2_2(X1,X2))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_111,plain,
( aNaturalNumber0(esk1_2(X1,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_112,plain,
( aNaturalNumber0(X1)
| X3 = sz00
| X1 != sdtsldt0(X2,X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_113,plain,
( aNaturalNumber0(X1)
| X1 != sdtmndt0(X2,X3)
| ~ sdtlseqdt0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_114,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_115,negated_conjecture,
( doDivides0(esk8_1(X1),X1)
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X2)
| xk != sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_116,plain,
( sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_117,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_118,negated_conjecture,
( X1 = sdtasdt0(esk8_1(X1),esk9_1(X1))
| X1 = sz00
| X1 = sz10
| ~ doDivides0(X1,xk)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_119,hypothesis,
( X1 = sdtasdt0(esk4_1(X1),esk5_1(X1))
| X1 = sz00
| X1 = sz10
| ~ iLess0(X1,xk)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_120,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_121,plain,
( X1 = X2
| iLess0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_122,plain,
( X2 = sz00
| sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_123,negated_conjecture,
( doDivides0(esk8_1(X1),X1)
| X1 = sz00
| X1 = sz10
| ~ doDivides0(X1,xk)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_124,hypothesis,
( doDivides0(esk4_1(X1),X1)
| X1 = sz00
| X1 = sz10
| ~ iLess0(X1,xk)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_125,negated_conjecture,
( aNaturalNumber0(esk9_1(X1))
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X2)
| xk != sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_126,negated_conjecture,
( aNaturalNumber0(esk8_1(X1))
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X2)
| xk != sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_127,negated_conjecture,
( X1 = sz00
| X1 = sz10
| esk8_1(X1) != X1
| ~ aNaturalNumber0(X2)
| xk != sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_128,plain,
( X1 = sz10
| X1 = X2
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| ~ isPrime0(X2)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_129,negated_conjecture,
( X1 = sz00
| X1 = sz10
| esk8_1(X1) != sz10
| ~ aNaturalNumber0(X2)
| xk != sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_130,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_131,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_132,negated_conjecture,
( ~ isPrime0(X1)
| ~ aNaturalNumber0(X2)
| xk != sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_133,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_134,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_135,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_136,hypothesis,
( isPrime0(esk4_1(X1))
| X1 = sz00
| X1 = sz10
| ~ iLess0(X1,xk)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_137,negated_conjecture,
( aNaturalNumber0(esk9_1(X1))
| X1 = sz00
| X1 = sz10
| ~ doDivides0(X1,xk)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_138,negated_conjecture,
( aNaturalNumber0(esk8_1(X1))
| X1 = sz00
| X1 = sz10
| ~ doDivides0(X1,xk)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_139,hypothesis,
( aNaturalNumber0(esk5_1(X1))
| X1 = sz00
| X1 = sz10
| ~ iLess0(X1,xk)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_140,hypothesis,
( aNaturalNumber0(esk4_1(X1))
| X1 = sz00
| X1 = sz10
| ~ iLess0(X1,xk)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_141,plain,
( X1 = sz00
| X2 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_142,negated_conjecture,
( X1 = sz00
| X1 = sz10
| esk8_1(X1) != X1
| ~ doDivides0(X1,xk)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_143,plain,
( X1 = sz00
| sdtpldt0(X1,X2) != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_144,plain,
( X1 = sz00
| sdtpldt0(X2,X1) != sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_145,negated_conjecture,
( X1 = sz00
| X1 = sz10
| esk8_1(X1) != sz10
| ~ doDivides0(X1,xk)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_146,hypothesis,
( X1 = sz00
| X1 = sz10
| esk4_1(X1) != sz10
| ~ iLess0(X1,xk)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_147,hypothesis,
( X1 = sz00
| X1 = sz10
| esk4_1(X1) != sz00
| ~ iLess0(X1,xk)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_148,plain,
( doDivides0(esk3_1(X1),X1)
| X1 = sz00
| X1 = sz10
| isPrime0(X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_149,negated_conjecture,
( ~ isPrime0(X1)
| ~ doDivides0(X1,xk)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_150,plain,
( sdtlseqdt0(X2,X1)
| X1 != X2
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_151,plain,
( aNaturalNumber0(esk3_1(X1))
| X1 = sz00
| X1 = sz10
| isPrime0(X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_152,plain,
( X1 = sz00
| X1 = sz10
| isPrime0(X1)
| esk3_1(X1) != X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_153,plain,
( sdtlseqdt0(sz10,X1)
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_73]),
[final] ).
cnf(i_0_154,plain,
( X1 = sz00
| X1 = sz10
| isPrime0(X1)
| esk3_1(X1) != sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_155,plain,
( sdtlseqdt0(X1,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_74]),
[final] ).
cnf(i_0_156,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_75]),
[final] ).
cnf(i_0_157,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_76]),
[final] ).
cnf(i_0_158,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_75]),
[final] ).
cnf(i_0_159,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_76]),
[final] ).
cnf(i_0_160,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_77]),
[final] ).
cnf(i_0_161,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_77]),
[final] ).
cnf(i_0_162,plain,
( X1 != sz10
| ~ isPrime0(X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_163,plain,
( X1 != sz00
| ~ isPrime0(X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_164,hypothesis,
doDivides0(esk6_0,xk),
inference(split_conjunct,[status(thm)],[i_0_78]),
[final] ).
cnf(i_0_165,hypothesis,
xk = sdtasdt0(esk6_0,esk7_0),
inference(split_conjunct,[status(thm)],[i_0_78]),
[final] ).
cnf(i_0_166,hypothesis,
~ isPrime0(xk),
inference(split_conjunct,[status(thm)],[i_0_78]),
[final] ).
cnf(i_0_167,hypothesis,
aNaturalNumber0(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_78]),
[final] ).
cnf(i_0_168,hypothesis,
aNaturalNumber0(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_78]),
[final] ).
cnf(i_0_169,hypothesis,
aNaturalNumber0(xk),
inference(split_conjunct,[status(thm)],[m__1716]),
[final] ).
cnf(i_0_170,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]),
[final] ).
cnf(i_0_171,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]),
[final] ).
cnf(i_0_172,hypothesis,
esk6_0 != xk,
inference(split_conjunct,[status(thm)],[i_0_78]),
[final] ).
cnf(i_0_173,hypothesis,
esk6_0 != sz10,
inference(split_conjunct,[status(thm)],[i_0_78]),
[final] ).
cnf(i_0_174,hypothesis,
xk != sz10,
inference(split_conjunct,[status(thm)],[m__1716_04]),
[final] ).
cnf(i_0_175,hypothesis,
xk != sz00,
inference(split_conjunct,[status(thm)],[m__1716_04]),
[final] ).
cnf(i_0_176,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mSortsC_01]),
[final] ).
cnf(i_0_177,hypothesis,
$false,
inference(cn,[status(thm)],[i_0_79]),
[proof] ).
cnf(i_0_177_001,axiom,
X1 = X1 ).
cnf(i_0_178,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_179,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_180,axiom,
( X1 != X2
| sdtasdt0(X1,X3) = sdtasdt0(X2,X3) ) ).
cnf(i_0_181,axiom,
( X1 != X2
| sdtasdt0(X3,X1) = sdtasdt0(X3,X2) ) ).
cnf(i_0_182,axiom,
( X1 != X2
| esk3_1(X1) = esk3_1(X2) ) ).
cnf(i_0_183,axiom,
( X1 != X2
| sdtpldt0(X1,X3) = sdtpldt0(X2,X3) ) ).
cnf(i_0_184,axiom,
( X1 != X2
| sdtpldt0(X3,X1) = sdtpldt0(X3,X2) ) ).
cnf(i_0_185,axiom,
( X1 != X2
| sdtsldt0(X1,X3) = sdtsldt0(X2,X3) ) ).
cnf(i_0_186,axiom,
( X1 != X2
| sdtsldt0(X3,X1) = sdtsldt0(X3,X2) ) ).
cnf(i_0_187,axiom,
( X1 != X2
| sdtmndt0(X1,X3) = sdtmndt0(X2,X3) ) ).
cnf(i_0_188,axiom,
( X1 != X2
| sdtmndt0(X3,X1) = sdtmndt0(X3,X2) ) ).
cnf(i_0_189,axiom,
( X1 != X2
| esk4_1(X1) = esk4_1(X2) ) ).
cnf(i_0_190,axiom,
( X1 != X2
| esk8_1(X1) = esk8_1(X2) ) ).
cnf(i_0_191,axiom,
( X1 != X2
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(X2) ) ).
cnf(i_0_192,axiom,
( X1 != X2
| ~ doDivides0(X1,X3)
| doDivides0(X2,X3) ) ).
cnf(i_0_193,axiom,
( X1 != X2
| ~ doDivides0(X3,X1)
| doDivides0(X3,X2) ) ).
cnf(i_0_194,axiom,
( X1 != X2
| ~ sdtlseqdt0(X1,X3)
| sdtlseqdt0(X2,X3) ) ).
cnf(i_0_195,axiom,
( X1 != X2
| ~ sdtlseqdt0(X3,X1)
| sdtlseqdt0(X3,X2) ) ).
cnf(i_0_196,axiom,
( X1 != X2
| ~ iLess0(X1,X3)
| iLess0(X2,X3) ) ).
cnf(i_0_197,axiom,
( X1 != X2
| ~ iLess0(X3,X1)
| iLess0(X3,X2) ) ).
cnf(i_0_198,axiom,
( X1 != X2
| ~ isPrime0(X1)
| isPrime0(X2) ) ).
cnf(i_0_216,plain,
sdtasdt0(esk6_0,esk7_0) = xk,
inference(scs_inference,[],[i_0_165,i_0_178]) ).
cnf(i_0_217,plain,
sdtlseqdt0(esk7_0,esk7_0),
inference(scs_inference,[],[i_0_167,i_0_165,i_0_178,i_0_155]) ).
cnf(i_0_219,plain,
~ isPrime0(esk6_0),
inference(scs_inference,[],[i_0_164,i_0_167,i_0_168,i_0_165,i_0_178,i_0_155,i_0_149]) ).
cnf(i_0_221,plain,
esk6_0 != sdtasdt0(esk6_0,esk7_0),
inference(scs_inference,[],[i_0_164,i_0_167,i_0_168,i_0_172,i_0_165,i_0_178,i_0_155,i_0_149,i_0_179]) ).
cnf(i_0_222,plain,
aNaturalNumber0(sdtasdt0(esk6_0,esk7_0)),
inference(scs_inference,[],[i_0_164,i_0_167,i_0_168,i_0_169,i_0_172,i_0_165,i_0_178,i_0_155,i_0_149,i_0_179,i_0_191]) ).
cnf(i_0_223,plain,
sdtlseqdt0(sdtasdt0(esk6_0,esk7_0),xk),
inference(scs_inference,[],[i_0_164,i_0_167,i_0_168,i_0_169,i_0_172,i_0_165,i_0_178,i_0_155,i_0_149,i_0_179,i_0_191,i_0_150]) ).
cnf(i_0_361,plain,
sdtlseqdt0(sz00,sz00),
inference(scs_inference,[],[i_0_171,i_0_155]) ).
cnf(i_0_441,plain,
sdtlseqdt0(esk6_0,esk6_0),
inference(scs_inference,[],[i_0_168,i_0_155]) ).
cnf(i_0_501,plain,
sdtlseqdt0(sz10,sz10),
inference(scs_inference,[],[i_0_170,i_0_155]) ).
cnf(i_0_214,plain,
~ isPrime0(sz10),
inference(scs_inference,[],[i_0_170,i_0_212]) ).
cnf(i_0_215,plain,
~ isPrime0(sz00),
inference(scs_inference,[],[i_0_171,i_0_213]) ).
cnf(i_0_225,plain,
sdtpldt0(esk7_0,sdtmndt0(esk7_0,esk7_0)) = esk7_0,
inference(scs_inference,[],[i_0_164,i_0_167,i_0_168,i_0_169,i_0_172,i_0_165,i_0_178,i_0_155,i_0_149,i_0_179,i_0_191,i_0_150,i_0_202]) ).
cnf(i_0_227,plain,
aNaturalNumber0(sdtmndt0(esk7_0,esk7_0)),
inference(scs_inference,[],[i_0_164,i_0_167,i_0_168,i_0_169,i_0_172,i_0_165,i_0_178,i_0_155,i_0_149,i_0_179,i_0_191,i_0_150,i_0_202,i_0_208]) ).
cnf(i_0_229,plain,
sdtlseqdt0(sz10,xk),
inference(scs_inference,[],[i_0_164,i_0_167,i_0_168,i_0_169,i_0_172,i_0_174,i_0_175,i_0_165,i_0_178,i_0_155,i_0_149,i_0_179,i_0_191,i_0_150,i_0_202,i_0_208,i_0_153]) ).
cnf(i_0_231,plain,
doDivides0(esk3_1(xk),xk),
inference(scs_inference,[],[i_0_164,i_0_166,i_0_167,i_0_168,i_0_169,i_0_172,i_0_174,i_0_175,i_0_165,i_0_178,i_0_155,i_0_149,i_0_179,i_0_191,i_0_150,i_0_202,i_0_208,i_0_153,i_0_148]) ).
cnf(i_0_233,plain,
esk3_1(xk) != xk,
inference(scs_inference,[],[i_0_164,i_0_166,i_0_167,i_0_168,i_0_169,i_0_172,i_0_174,i_0_175,i_0_165,i_0_178,i_0_155,i_0_149,i_0_179,i_0_191,i_0_150,i_0_202,i_0_208,i_0_153,i_0_148,i_0_152]) ).
cnf(i_0_503,plain,
aNaturalNumber0(sdtmndt0(sz10,sz10)),
inference(scs_inference,[],[i_0_170,i_0_155,i_0_208]) ).
cnf(i_0_505,plain,
sdtpldt0(sz10,sdtmndt0(sz10,sz10)) = sz10,
inference(scs_inference,[],[i_0_170,i_0_155,i_0_208,i_0_202]) ).
cnf(i_0_246,plain,
sdtlseqdt0(sdtmndt0(esk7_0,esk7_0),sdtmndt0(esk7_0,esk7_0)),
inference(scs_inference,[],[i_0_227,i_0_155]) ).
cnf(i_0_248,plain,
esk7_0 = sdtpldt0(esk7_0,sdtmndt0(esk7_0,esk7_0)),
inference(scs_inference,[],[i_0_227,i_0_225,i_0_155,i_0_178]) ).
cnf(i_0_249,plain,
esk3_1(xk) != sdtasdt0(esk6_0,esk7_0),
inference(scs_inference,[],[i_0_227,i_0_216,i_0_225,i_0_233,i_0_155,i_0_178,i_0_179]) ).
cnf(i_0_250,plain,
aNaturalNumber0(sdtpldt0(esk7_0,sdtmndt0(esk7_0,esk7_0))),
inference(scs_inference,[],[i_0_227,i_0_216,i_0_167,i_0_225,i_0_233,i_0_155,i_0_178,i_0_179,i_0_191]) ).
cnf(i_0_251,plain,
sdtlseqdt0(xk,sdtasdt0(esk6_0,esk7_0)),
inference(scs_inference,[],[i_0_227,i_0_222,i_0_216,i_0_167,i_0_225,i_0_233,i_0_169,i_0_155,i_0_178,i_0_179,i_0_191,i_0_150]) ).
cnf(i_0_253,plain,
aNaturalNumber0(sdtmndt0(sdtmndt0(esk7_0,esk7_0),sdtmndt0(esk7_0,esk7_0))),
inference(scs_inference,[],[i_0_227,i_0_222,i_0_216,i_0_167,i_0_225,i_0_233,i_0_169,i_0_155,i_0_178,i_0_179,i_0_191,i_0_150,i_0_208]) ).
cnf(i_0_259,plain,
sdtlseqdt0(sdtasdt0(esk6_0,esk7_0),sdtasdt0(esk6_0,esk7_0)),
inference(scs_inference,[],[i_0_227,i_0_222,i_0_216,i_0_223,i_0_167,i_0_217,i_0_225,i_0_233,i_0_169,i_0_155,i_0_178,i_0_179,i_0_191,i_0_150,i_0_208,i_0_202,i_0_113,i_0_98]) ).
cnf(i_0_535,plain,
sdtlseqdt0(sdtmndt0(sz10,sz10),sdtmndt0(sz10,sz10)),
inference(scs_inference,[],[i_0_503,i_0_155]) ).
cnf(i_0_537,plain,
aNaturalNumber0(sdtmndt0(sdtmndt0(sz10,sz10),sdtmndt0(sz10,sz10))),
inference(scs_inference,[],[i_0_503,i_0_155,i_0_208]) ).
cnf(i_0_539,plain,
sdtpldt0(sdtmndt0(sz10,sz10),sdtmndt0(sdtmndt0(sz10,sz10),sdtmndt0(sz10,sz10))) = sdtmndt0(sz10,sz10),
inference(scs_inference,[],[i_0_503,i_0_155,i_0_208,i_0_202]) ).
cnf(i_0_267,plain,
sdtlseqdt0(sdtpldt0(esk7_0,sdtmndt0(esk7_0,esk7_0)),esk7_0),
inference(scs_inference,[],[i_0_253,i_0_250,i_0_248,i_0_167,i_0_255,i_0_155,i_0_178,i_0_150]) ).
cnf(i_0_269,plain,
aNaturalNumber0(sdtmndt0(sdtasdt0(esk6_0,esk7_0),sdtasdt0(esk6_0,esk7_0))),
inference(scs_inference,[],[i_0_253,i_0_250,i_0_248,i_0_222,i_0_167,i_0_255,i_0_259,i_0_155,i_0_178,i_0_150,i_0_208]) ).
cnf(i_0_273,plain,
sdtlseqdt0(xk,xk),
inference(scs_inference,[],[i_0_253,i_0_250,i_0_248,i_0_251,i_0_223,i_0_222,i_0_167,i_0_255,i_0_259,i_0_169,i_0_155,i_0_178,i_0_150,i_0_208,i_0_202,i_0_98]) ).
cnf(i_0_352,plain,
sdtlseqdt0(sdtpldt0(esk7_0,sdtmndt0(esk7_0,esk7_0)),sdtpldt0(esk7_0,sdtmndt0(esk7_0,esk7_0))),
inference(scs_inference,[],[i_0_250,i_0_155]) ).
cnf(i_0_1181,plain,
sdtasdt0(esk7_0,X1) = sdtasdt0(sdtpldt0(esk7_0,sdtmndt0(esk7_0,esk7_0)),X1),
inference(scs_inference,[],[i_0_248,i_0_180]) ).
cnf(i_0_1182,plain,
sdtasdt0(X1,esk7_0) = sdtasdt0(X1,sdtpldt0(esk7_0,sdtmndt0(esk7_0,esk7_0))),
inference(scs_inference,[],[i_0_248,i_0_180,i_0_181]) ).
cnf(i_0_1183,plain,
esk3_1(esk7_0) = esk3_1(sdtpldt0(esk7_0,sdtmndt0(esk7_0,esk7_0))),
inference(scs_inference,[],[i_0_248,i_0_180,i_0_181,i_0_182]) ).
cnf(i_0_1184,plain,
sdtpldt0(esk7_0,X1) = sdtpldt0(sdtpldt0(esk7_0,sdtmndt0(esk7_0,esk7_0)),X1),
inference(scs_inference,[],[i_0_248,i_0_180,i_0_181,i_0_182,i_0_183]) ).
cnf(i_0_1185,plain,
sdtpldt0(X1,esk7_0) = sdtpldt0(X1,sdtpldt0(esk7_0,sdtmndt0(esk7_0,esk7_0))),
inference(scs_inference,[],[i_0_248,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184]) ).
cnf(i_0_1186,plain,
sdtsldt0(esk7_0,X1) = sdtsldt0(sdtpldt0(esk7_0,sdtmndt0(esk7_0,esk7_0)),X1),
inference(scs_inference,[],[i_0_248,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185]) ).
cnf(i_0_1187,plain,
sdtsldt0(X1,esk7_0) = sdtsldt0(X1,sdtpldt0(esk7_0,sdtmndt0(esk7_0,esk7_0))),
inference(scs_inference,[],[i_0_248,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186]) ).
cnf(i_0_1188,plain,
sdtmndt0(esk7_0,X1) = sdtmndt0(sdtpldt0(esk7_0,sdtmndt0(esk7_0,esk7_0)),X1),
inference(scs_inference,[],[i_0_248,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187]) ).
cnf(i_0_1189,plain,
sdtmndt0(X1,esk7_0) = sdtmndt0(X1,sdtpldt0(esk7_0,sdtmndt0(esk7_0,esk7_0))),
inference(scs_inference,[],[i_0_248,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188]) ).
cnf(i_0_1190,plain,
esk4_1(esk7_0) = esk4_1(sdtpldt0(esk7_0,sdtmndt0(esk7_0,esk7_0))),
inference(scs_inference,[],[i_0_248,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189]) ).
cnf(i_0_1191,plain,
esk8_1(esk7_0) = esk8_1(sdtpldt0(esk7_0,sdtmndt0(esk7_0,esk7_0))),
inference(scs_inference,[],[i_0_248,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190]) ).
cnf(i_0_282,plain,
aNaturalNumber0(sdtmndt0(sdtmndt0(esk7_0,esk7_0),sdtmndt0(esk7_0,esk7_0))),
inference(equality_inference,[],[276]) ).
cnf(i_0_286,plain,
esk6_0 != sdtpldt0(sdtasdt0(esk6_0,esk7_0),sdtmndt0(sdtasdt0(esk6_0,esk7_0),sdtasdt0(esk6_0,esk7_0))),
inference(scs_inference,[],[i_0_269,i_0_271,i_0_221,i_0_155,i_0_178,i_0_179]) ).
cnf(i_0_289,plain,
aNaturalNumber0(sdtmndt0(xk,xk)),
inference(scs_inference,[],[i_0_257,i_0_266,i_0_269,i_0_227,i_0_271,i_0_221,i_0_273,i_0_169,i_0_155,i_0_178,i_0_179,i_0_150,i_0_208]) ).
cnf(i_0_291,plain,
sdtpldt0(xk,sdtmndt0(xk,xk)) = xk,
inference(scs_inference,[],[i_0_257,i_0_266,i_0_269,i_0_227,i_0_271,i_0_221,i_0_273,i_0_169,i_0_155,i_0_178,i_0_179,i_0_150,i_0_208,i_0_202]) ).
cnf(i_0_360,plain,
aNaturalNumber0(sz10),
inference(equality_inference,[],[356]) ).
cnf(i_0_1335,plain,
sdtmndt0(esk7_0,X1) = sdtmndt0(sdtpldt0(esk7_0,sdtmndt0(esk7_0,esk7_0)),X1),
inference(rename_variables,[],[i_0_1188]) ).
cnf(i_0_1407,plain,
sdtasdt0(X1,esk7_0) = sdtasdt0(X1,sdtpldt0(esk7_0,sdtmndt0(esk7_0,esk7_0))),
inference(rename_variables,[],[i_0_1182]) ).
cnf(i_0_1487,plain,
sdtasdt0(X1,esk7_0) = sdtasdt0(X1,sdtpldt0(esk7_0,sdtmndt0(esk7_0,esk7_0))),
inference(rename_variables,[],[i_0_1182]) ).
cnf(i_0_1556,plain,
sdtasdt0(X1,esk7_0) = sdtasdt0(X1,sdtpldt0(esk7_0,sdtmndt0(esk7_0,esk7_0))),
inference(rename_variables,[],[i_0_1182]) ).
cnf(i_0_1628,plain,
sdtasdt0(X1,esk7_0) = sdtasdt0(X1,sdtpldt0(esk7_0,sdtmndt0(esk7_0,esk7_0))),
inference(rename_variables,[],[i_0_1182]) ).
cnf(i_0_2058,plain,
sdtpldt0(esk7_0,X1) = sdtpldt0(sdtpldt0(esk7_0,sdtmndt0(esk7_0,esk7_0)),X1),
inference(rename_variables,[],[i_0_1184]) ).
cnf(i_0_297,plain,
aNaturalNumber0(sdtmndt0(sdtasdt0(esk6_0,esk7_0),sdtasdt0(esk6_0,esk7_0))),
inference(equality_inference,[],[293]) ).
cnf(i_0_298,plain,
sdtlseqdt0(sdtmndt0(xk,xk),sdtmndt0(xk,xk)),
inference(scs_inference,[],[i_0_289,i_0_155]) ).
cnf(i_0_300,plain,
xk = sdtpldt0(xk,sdtmndt0(xk,xk)),
inference(scs_inference,[],[i_0_289,i_0_291,i_0_155,i_0_178]) ).
cnf(i_0_301,plain,
esk3_1(xk) != sdtpldt0(xk,sdtmndt0(xk,xk)),
inference(scs_inference,[],[i_0_289,i_0_291,i_0_233,i_0_155,i_0_178,i_0_179]) ).
cnf(i_0_305,plain,
aNaturalNumber0(sdtmndt0(sdtmndt0(xk,xk),sdtmndt0(xk,xk))),
inference(scs_inference,[],[i_0_222,i_0_285,i_0_289,i_0_291,i_0_233,i_0_155,i_0_178,i_0_179,i_0_191,i_0_150,i_0_208]) ).
cnf(i_0_307,plain,
sdtpldt0(sdtmndt0(xk,xk),sdtmndt0(sdtmndt0(xk,xk),sdtmndt0(xk,xk))) = sdtmndt0(xk,xk),
inference(scs_inference,[],[i_0_222,i_0_285,i_0_289,i_0_291,i_0_233,i_0_155,i_0_178,i_0_179,i_0_191,i_0_150,i_0_208,i_0_202]) ).
cnf(i_0_309,plain,
aNaturalNumber0(sdtpldt0(sdtmndt0(xk,xk),sdtmndt0(sdtmndt0(xk,xk),sdtmndt0(xk,xk)))),
inference(scs_inference,[],[i_0_222,i_0_285,i_0_289,i_0_169,i_0_291,i_0_233,i_0_273,i_0_155,i_0_178,i_0_179,i_0_191,i_0_150,i_0_208,i_0_202,i_0_113]) ).
cnf(i_0_325,plain,
sdtlseqdt0(sdtmndt0(sdtmndt0(xk,xk),sdtmndt0(xk,xk)),sdtmndt0(sdtmndt0(xk,xk),sdtmndt0(xk,xk))),
inference(scs_inference,[],[i_0_305,i_0_155]) ).
cnf(i_0_327,plain,
sdtmndt0(xk,xk) = sdtpldt0(sdtmndt0(xk,xk),sdtmndt0(sdtmndt0(xk,xk),sdtmndt0(xk,xk))),
inference(scs_inference,[],[i_0_305,i_0_307,i_0_155,i_0_178]) ).
cnf(i_0_328,plain,
esk6_0 != sdtpldt0(xk,sdtmndt0(xk,xk)),
inference(scs_inference,[],[i_0_305,i_0_291,i_0_307,i_0_172,i_0_155,i_0_178,i_0_179]) ).
cnf(i_0_329,plain,
aNaturalNumber0(sdtpldt0(xk,sdtmndt0(xk,xk))),
inference(scs_inference,[],[i_0_305,i_0_300,i_0_291,i_0_169,i_0_307,i_0_172,i_0_155,i_0_178,i_0_179,i_0_191]) ).
cnf(i_0_330,plain,
sdtlseqdt0(sdtpldt0(xk,sdtmndt0(xk,xk)),xk),
inference(scs_inference,[],[i_0_305,i_0_300,i_0_291,i_0_169,i_0_307,i_0_172,i_0_155,i_0_178,i_0_179,i_0_191,i_0_150]) ).
cnf(i_0_365,plain,
aNaturalNumber0(sdtmndt0(sz00,sz00)),
inference(scs_inference,[],[i_0_222,i_0_302,i_0_271,i_0_171,i_0_155,i_0_150,i_0_208]) ).
cnf(i_0_367,plain,
sdtpldt0(sz00,sdtmndt0(sz00,sz00)) = sz00,
inference(scs_inference,[],[i_0_222,i_0_302,i_0_271,i_0_171,i_0_155,i_0_150,i_0_208,i_0_202]) ).
cnf(i_0_369,plain,
sz00 = sdtpldt0(sz00,sdtmndt0(sz00,sz00)),
inference(scs_inference,[],[i_0_222,i_0_302,i_0_271,i_0_171,i_0_155,i_0_150,i_0_208,i_0_202,i_0_178]) ).
cnf(i_0_372,plain,
xk != sdtpldt0(sz00,sdtmndt0(sz00,sz00)),
inference(scs_inference,[],[i_0_222,i_0_302,i_0_175,i_0_271,i_0_171,i_0_155,i_0_150,i_0_208,i_0_202,i_0_178,i_0_163,i_0_179]) ).
cnf(i_0_373,plain,
aNaturalNumber0(sdtpldt0(sz00,sdtmndt0(sz00,sz00))),
inference(scs_inference,[],[i_0_222,i_0_302,i_0_175,i_0_271,i_0_171,i_0_155,i_0_150,i_0_208,i_0_202,i_0_178,i_0_163,i_0_179,i_0_191]) ).
cnf(i_0_374,plain,
sdtmndt0(sz00,sz00) = sz00,
inference(scs_inference,[],[i_0_222,i_0_302,i_0_175,i_0_271,i_0_171,i_0_155,i_0_150,i_0_208,i_0_202,i_0_178,i_0_163,i_0_179,i_0_191,i_0_144]) ).
cnf(i_0_689,plain,
sdtlseqdt0(sdtmndt0(xk,xk),sdtpldt0(sdtmndt0(xk,xk),sdtmndt0(sdtmndt0(xk,xk),sdtmndt0(xk,xk)))),
inference(scs_inference,[],[i_0_289,i_0_309,i_0_307,i_0_150]) ).
cnf(i_0_343,plain,
sdtlseqdt0(sdtpldt0(xk,sdtmndt0(xk,xk)),sdtpldt0(xk,sdtmndt0(xk,xk))),
inference(scs_inference,[],[i_0_329,i_0_155]) ).
cnf(i_0_345,plain,
sdtlseqdt0(sdtpldt0(sdtmndt0(xk,xk),sdtmndt0(sdtmndt0(xk,xk),sdtmndt0(xk,xk))),sdtmndt0(xk,xk)),
inference(scs_inference,[],[i_0_289,i_0_309,i_0_327,i_0_329,i_0_155,i_0_150]) ).
cnf(i_0_386,plain,
sdtlseqdt0(sdtpldt0(sz00,sdtmndt0(sz00,sz00)),sdtpldt0(sz00,sdtmndt0(sz00,sz00))),
inference(scs_inference,[],[i_0_373,i_0_155]) ).
cnf(i_0_388,plain,
sz00 = sdtmndt0(sz00,sz00),
inference(scs_inference,[],[i_0_373,i_0_374,i_0_155,i_0_178]) ).
cnf(i_0_389,plain,
~ isPrime0(sdtpldt0(sz00,sdtmndt0(sz00,sz00))),
inference(scs_inference,[],[i_0_373,i_0_367,i_0_374,i_0_155,i_0_178,i_0_163]) ).
cnf(i_0_391,plain,
xk != sdtmndt0(sz00,sz00),
inference(scs_inference,[],[i_0_373,i_0_175,i_0_367,i_0_374,i_0_155,i_0_178,i_0_163,i_0_179]) ).
cnf(i_0_392,plain,
sdtlseqdt0(sdtpldt0(sz00,sdtmndt0(sz00,sz00)),sz00),
inference(scs_inference,[],[i_0_373,i_0_369,i_0_175,i_0_171,i_0_367,i_0_374,i_0_155,i_0_178,i_0_163,i_0_179,i_0_150]) ).
cnf(i_0_394,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(scs_inference,[],[i_0_373,i_0_369,i_0_175,i_0_171,i_0_361,i_0_367,i_0_374,i_0_155,i_0_178,i_0_163,i_0_179,i_0_150,i_0_104]) ).
cnf(i_0_401,plain,
sdtlseqdt0(sdtmndt0(sz00,sz00),sdtmndt0(sz00,sz00)),
inference(scs_inference,[],[i_0_365,i_0_155]) ).
cnf(i_0_541,plain,
sdtlseqdt0(sz00,sdtpldt0(sz00,sdtmndt0(sz00,sz00))),
inference(scs_inference,[],[i_0_373,i_0_503,i_0_367,i_0_171,i_0_155,i_0_208,i_0_202,i_0_150]) ).
cnf(i_0_543,plain,
sdtmndt0(sz00,sz00) = sdtmndt0(sdtpldt0(sz00,sdtmndt0(sz00,sz00)),sz00),
inference(scs_inference,[],[i_0_365,i_0_373,i_0_503,i_0_367,i_0_171,i_0_155,i_0_208,i_0_202,i_0_150,i_0_200]) ).
cnf(i_0_545,plain,
aNaturalNumber0(sdtpldt0(sdtmndt0(sz10,sz10),sdtmndt0(sdtmndt0(sz10,sz10),sdtmndt0(sz10,sz10)))),
inference(scs_inference,[],[i_0_365,i_0_373,i_0_503,i_0_367,i_0_171,i_0_170,i_0_501,i_0_155,i_0_208,i_0_202,i_0_150,i_0_200,i_0_113]) ).
cnf(i_0_547,plain,
sdtmndt0(sz10,sz10) = sdtpldt0(sdtmndt0(sz10,sz10),sdtmndt0(sdtmndt0(sz10,sz10),sdtmndt0(sz10,sz10))),
inference(scs_inference,[],[i_0_365,i_0_373,i_0_503,i_0_367,i_0_171,i_0_170,i_0_501,i_0_155,i_0_208,i_0_202,i_0_150,i_0_200,i_0_113,i_0_178]) ).
cnf(i_0_694,plain,
sdtlseqdt0(xk,sdtpldt0(xk,sdtmndt0(xk,xk))),
inference(scs_inference,[],[i_0_329,i_0_169,i_0_291,i_0_150]) ).
cnf(i_0_696,plain,
sdtmndt0(xk,xk) = sdtmndt0(sdtpldt0(xk,sdtmndt0(xk,xk)),xk),
inference(scs_inference,[],[i_0_289,i_0_329,i_0_169,i_0_291,i_0_150,i_0_200]) ).
cnf(i_0_698,plain,
sdtmndt0(sdtpldt0(xk,sdtmndt0(xk,xk)),xk) = sdtmndt0(xk,xk),
inference(scs_inference,[],[i_0_289,i_0_329,i_0_169,i_0_291,i_0_150,i_0_200,i_0_178]) ).
cnf(i_0_699,plain,
aNaturalNumber0(sdtmndt0(sdtpldt0(xk,sdtmndt0(xk,xk)),xk)),
inference(scs_inference,[],[i_0_289,i_0_329,i_0_169,i_0_291,i_0_273,i_0_150,i_0_200,i_0_178,i_0_113]) ).
cnf(i_0_756,plain,
sdtlseqdt0(sz00,sdtmndt0(sz00,sz00)),
inference(scs_inference,[],[i_0_365,i_0_171,i_0_374,i_0_150]) ).
cnf(i_0_901,plain,
sz10 != sdtpldt0(sz00,sdtmndt0(sz00,sz00)),
inference(scs_inference,[],[i_0_176,i_0_367,i_0_179]) ).
cnf(i_0_914,plain,
sz10 != sdtmndt0(sz00,sz00),
inference(scs_inference,[],[i_0_176,i_0_374,i_0_179]) ).
cnf(i_0_351,plain,
aNaturalNumber0(sdtmndt0(sdtmndt0(xk,xk),sdtmndt0(xk,xk))),
inference(equality_inference,[],[347]) ).
cnf(c_0_199,negated_conjecture,
( ~ isPrime0(X1)
| ~ aNaturalNumber0(X2)
| xk != sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X1) ),
i_0_132 ).
cnf(c_0_200,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
i_0_134 ).
cnf(c_0_201,negated_conjecture,
( sdtasdt0(X1,X2) != xk
| ~ isPrime0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_199,c_0_200]) ).
cnf(c_0_202,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
i_0_89 ).
cnf(c_0_203,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
i_0_130 ).
cnf(c_0_204,negated_conjecture,
( sdtasdt0(X1,sdtasdt0(X2,X3)) != xk
| ~ isPrime0(X3)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_202]),c_0_203]) ).
cnf(c_0_205,plain,
( sdtasdt0(X1,sdtasdt0(X2,X3)) != xk
| ~ isPrime0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_204,c_0_200]) ).
cnf(c_0_206,plain,
( X1 = sdtasdt0(X2,esk2_2(X2,X1))
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
i_0_101 ).
cnf(c_0_207,plain,
( aNaturalNumber0(esk2_2(X1,X2))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
i_0_110 ).
cnf(c_0_208,plain,
( sdtasdt0(X1,X2) != xk
| ~ isPrime0(X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_205,c_0_206]),c_0_207]) ).
cnf(c_0_209,negated_conjecture,
( X1 = sdtasdt0(esk8_1(X1),esk9_1(X1))
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X2)
| xk != sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X1) ),
i_0_109 ).
cnf(c_0_210,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
i_0_156 ).
cnf(c_0_211,plain,
aNaturalNumber0(sz10),
i_0_170 ).
cnf(c_0_212,hypothesis,
aNaturalNumber0(xk),
i_0_169 ).
cnf(c_0_213,hypothesis,
xk != sz00,
i_0_175 ).
cnf(c_0_214,hypothesis,
xk != sz10,
i_0_174 ).
cnf(c_0_215,negated_conjecture,
( aNaturalNumber0(esk9_1(X1))
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X2)
| xk != sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X1) ),
i_0_125 ).
cnf(c_0_216,negated_conjecture,
( aNaturalNumber0(esk8_1(X1))
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X2)
| xk != sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X1) ),
i_0_126 ).
cnf(c_0_217,plain,
( sdtasdt0(X1,X2) != xk
| ~ isPrime0(X3)
| ~ doDivides0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_208,c_0_200]) ).
cnf(c_0_218,plain,
sdtasdt0(esk8_1(xk),esk9_1(xk)) = xk,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_210]),c_0_211])])]),c_0_212])]),c_0_213]),c_0_214]) ).
cnf(c_0_219,plain,
aNaturalNumber0(esk9_1(xk)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_210]),c_0_211])])]),c_0_212])]),c_0_213]),c_0_214]) ).
cnf(c_0_220,plain,
aNaturalNumber0(esk8_1(xk)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_216,c_0_210]),c_0_211])])]),c_0_212])]),c_0_213]),c_0_214]) ).
cnf(c_0_221,negated_conjecture,
( X1 = sz00
| X1 = sz10
| esk8_1(X1) != sz10
| ~ aNaturalNumber0(X2)
| xk != sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X1) ),
i_0_129 ).
cnf(c_0_222,plain,
( ~ isPrime0(X1)
| ~ doDivides0(X1,esk8_1(xk))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_218]),c_0_219]),c_0_220])]) ).
cnf(c_0_223,hypothesis,
( doDivides0(esk4_1(X1),X1)
| X1 = sz00
| X1 = sz10
| ~ iLess0(X1,xk)
| ~ aNaturalNumber0(X1) ),
i_0_124 ).
cnf(c_0_224,plain,
esk8_1(xk) != sz10,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_210]),c_0_211])])]),c_0_212])]),c_0_213]),c_0_214]) ).
cnf(c_0_225,negated_conjecture,
( doDivides0(esk8_1(X1),X1)
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X2)
| xk != sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X1) ),
i_0_115 ).
cnf(c_0_226,hypothesis,
( esk8_1(xk) = sz00
| ~ isPrime0(esk4_1(esk8_1(xk)))
| ~ iLess0(esk8_1(xk),xk)
| ~ aNaturalNumber0(esk4_1(esk8_1(xk))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_222,c_0_223]),c_0_220])]),c_0_224]) ).
cnf(c_0_227,hypothesis,
( isPrime0(esk4_1(X1))
| X1 = sz00
| X1 = sz10
| ~ iLess0(X1,xk)
| ~ aNaturalNumber0(X1) ),
i_0_136 ).
cnf(c_0_228,plain,
( X1 = sz00
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X2,X1) ),
i_0_122 ).
cnf(c_0_229,plain,
doDivides0(esk8_1(xk),xk),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_225,c_0_210]),c_0_211])])]),c_0_212])]),c_0_213]),c_0_214]) ).
cnf(c_0_230,negated_conjecture,
( X1 = sz00
| X1 = sz10
| esk8_1(X1) != X1
| ~ aNaturalNumber0(X2)
| xk != sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X1) ),
i_0_127 ).
cnf(c_0_231,hypothesis,
( esk8_1(xk) = sz00
| ~ iLess0(esk8_1(xk),xk)
| ~ aNaturalNumber0(esk4_1(esk8_1(xk))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_226,c_0_227]),c_0_220])]),c_0_224]) ).
cnf(c_0_232,plain,
( X1 = X2
| iLess0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2) ),
i_0_121 ).
cnf(c_0_233,plain,
sdtlseqdt0(esk8_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_228,c_0_229]),c_0_220]),c_0_212])]),c_0_213]) ).
cnf(c_0_234,plain,
esk8_1(xk) != xk,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_230,c_0_210]),c_0_211])])]),c_0_212])]),c_0_213]),c_0_214]) ).
cnf(c_0_235,hypothesis,
( aNaturalNumber0(esk4_1(X1))
| X1 = sz00
| X1 = sz10
| ~ iLess0(X1,xk)
| ~ aNaturalNumber0(X1) ),
i_0_140 ).
cnf(c_0_236,plain,
( esk8_1(xk) = sz00
| ~ aNaturalNumber0(esk4_1(esk8_1(xk))) ),
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_231,c_0_232]),c_0_233]),c_0_212]),c_0_220])]),c_0_234]) ).
cnf(c_0_237,plain,
( X1 = xk
| X1 = sz10
| X1 = sz00
| aNaturalNumber0(esk4_1(X1))
| ~ sdtlseqdt0(X1,xk)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_232]),c_0_212])]) ).
cnf(c_0_238,plain,
esk8_1(xk) = sz00,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_236,c_0_237]),c_0_233]),c_0_220])]),c_0_234]),c_0_224]) ).
cnf(c_0_239,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
i_0_161 ).
cnf(c_0_240,plain,
sdtasdt0(sz00,esk9_1(xk)) = xk,
inference(rw,[status(thm)],[c_0_218,c_0_238]) ).
cnf(c_0_241,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_239,c_0_240]),c_0_219])]),c_0_213]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM484+3 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n011.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 00:37:32 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 39.51/37.72 % Version : CSE_E---1.7
% 39.51/37.72 % Problem : theBenchmark.p
% 39.51/37.72 % SZS status Theorem for theBenchmark.p
% 39.51/37.72 % SZS output start CNFRefutation
% See solution above
% 44.71/42.95 % Total time : 37.301s
%------------------------------------------------------------------------------