%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM489+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:57:31 PM UTC 2026
% Result : Theorem 0.35s 1.61s
% Output : CNFRefutation 0.44s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 95)
% Comments :
%------------------------------------------------------------------------------
fof(m__1799,hypothesis,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( isPrime0(X3)
& doDivides0(X3,sdtasdt0(X1,X2)) )
=> ( iLess0(sdtpldt0(sdtpldt0(X1,X2),X3),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(X3,X1)
| doDivides0(X3,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1799) ).
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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mLETran) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(mMulCanc,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtasdt0(X1,X2) = sdtasdt0(X1,X3)
| sdtasdt0(X2,X1) = sdtasdt0(X3,X1) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
fof(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/sandbox2/benchmark/theBenchmark.p',mAddCanc) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
fof(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
| ( X2 != X1
& sdtlseqdt0(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETotal) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(mZeroMul,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroMul) ).
fof(mZeroAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtpldt0(X1,X2) = sz00
=> ( X1 = sz00
& X2 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroAdd) ).
fof(mPrimDiv,axiom,
! [X1] :
( ( aNaturalNumber0(X1)
& X1 != sz00
& X1 != sz10 )
=> ? [X2] :
( aNaturalNumber0(X2)
& doDivides0(X2,X1)
& isPrime0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPrimDiv) ).
fof(mLENTr,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sz00
| X1 = sz10
| ( sz10 != X1
& sdtlseqdt0(sz10,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLENTr) ).
fof(mLERefl,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> sdtlseqdt0(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERefl) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(m__,conjecture,
xn = sdtpldt0(xp,xr),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__1860,hypothesis,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(m__1894,hypothesis,
( xr != xn
& sdtlseqdt0(xr,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1894) ).
fof(m__1870,hypothesis,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).
fof(m__1883,hypothesis,
xr = sdtmndt0(xn,xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1883) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(i_0_43,hypothesis,
! [X171,X172,X173] :
( ~ aNaturalNumber0(X171)
| ~ aNaturalNumber0(X172)
| ~ aNaturalNumber0(X173)
| ~ isPrime0(X173)
| ~ doDivides0(X173,sdtasdt0(X171,X172))
| ~ iLess0(sdtpldt0(sdtpldt0(X171,X172),X173),sdtpldt0(sdtpldt0(xn,xm),xp))
| doDivides0(X173,X171)
| doDivides0(X173,X172) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1799])]) ).
fof(i_0_44,plain,
! [X106,X107,X108] :
( ( sdtasdt0(X106,sdtpldt0(X107,X108)) = sdtpldt0(sdtasdt0(X106,X107),sdtasdt0(X106,X108))
| ~ aNaturalNumber0(X106)
| ~ aNaturalNumber0(X107)
| ~ aNaturalNumber0(X108) )
& ( sdtasdt0(sdtpldt0(X107,X108),X106) = sdtpldt0(sdtasdt0(X107,X106),sdtasdt0(X108,X106))
| ~ aNaturalNumber0(X106)
| ~ aNaturalNumber0(X107)
| ~ aNaturalNumber0(X108) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])]) ).
fof(i_0_45,plain,
! [X163,X164,X165] :
( ~ aNaturalNumber0(X163)
| ~ aNaturalNumber0(X164)
| X163 = sz00
| ~ doDivides0(X163,X164)
| ~ aNaturalNumber0(X165)
| sdtasdt0(X165,sdtsldt0(X164,X163)) = sdtsldt0(sdtasdt0(X165,X164),X163) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivAsso])])]) ).
fof(i_0_46,plain,
! [X158,X159,X160] :
( ~ aNaturalNumber0(X158)
| ~ aNaturalNumber0(X159)
| ~ aNaturalNumber0(X160)
| ~ doDivides0(X158,X159)
| ~ doDivides0(X158,sdtpldt0(X159,X160))
| doDivides0(X158,X160) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivMin])]) ).
fof(i_0_47,plain,
! [X137,X138,X139] :
( ( sdtasdt0(X137,X138) != sdtasdt0(X137,X139)
| X137 = sz00
| X138 = X139
| ~ sdtlseqdt0(X138,X139)
| ~ aNaturalNumber0(X137)
| ~ aNaturalNumber0(X138)
| ~ aNaturalNumber0(X139) )
& ( sdtlseqdt0(sdtasdt0(X137,X138),sdtasdt0(X137,X139))
| X137 = sz00
| X138 = X139
| ~ sdtlseqdt0(X138,X139)
| ~ aNaturalNumber0(X137)
| ~ aNaturalNumber0(X138)
| ~ aNaturalNumber0(X139) )
& ( sdtasdt0(X138,X137) != sdtasdt0(X139,X137)
| X137 = sz00
| X138 = X139
| ~ sdtlseqdt0(X138,X139)
| ~ aNaturalNumber0(X137)
| ~ aNaturalNumber0(X138)
| ~ aNaturalNumber0(X139) )
& ( sdtlseqdt0(sdtasdt0(X138,X137),sdtasdt0(X139,X137))
| X137 = sz00
| X138 = X139
| ~ sdtlseqdt0(X138,X139)
| ~ aNaturalNumber0(X137)
| ~ aNaturalNumber0(X138)
| ~ aNaturalNumber0(X139) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul])])]) ).
fof(i_0_48,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])])])]) ).
fof(i_0_49,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])]) ).
fof(i_0_50,plain,
! [X101,X102,X103] :
( ~ aNaturalNumber0(X101)
| ~ aNaturalNumber0(X102)
| ~ aNaturalNumber0(X103)
| sdtasdt0(sdtasdt0(X101,X102),X103) = sdtasdt0(X101,sdtasdt0(X102,X103)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
fof(i_0_51,plain,
! [X95,X96,X97] :
( ~ aNaturalNumber0(X95)
| ~ aNaturalNumber0(X96)
| ~ aNaturalNumber0(X97)
| sdtpldt0(sdtpldt0(X95,X96),X97) = sdtpldt0(X95,sdtpldt0(X96,X97)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
fof(i_0_52,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])])])]) ).
fof(i_0_53,plain,
! [X123,X124,X125] :
( ( aNaturalNumber0(X125)
| X125 != sdtmndt0(X124,X123)
| ~ sdtlseqdt0(X123,X124)
| ~ aNaturalNumber0(X123)
| ~ aNaturalNumber0(X124) )
& ( sdtpldt0(X123,X125) = X124
| X125 != sdtmndt0(X124,X123)
| ~ sdtlseqdt0(X123,X124)
| ~ aNaturalNumber0(X123)
| ~ aNaturalNumber0(X124) )
& ( ~ aNaturalNumber0(X125)
| sdtpldt0(X123,X125) != X124
| X125 = sdtmndt0(X124,X123)
| ~ sdtlseqdt0(X123,X124)
| ~ aNaturalNumber0(X123)
| ~ aNaturalNumber0(X124) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])]) ).
fof(i_0_54,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(i_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])]) ).
fof(i_0_56,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(i_0_57,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(i_0_58,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])])])]) ).
fof(i_0_59,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])])]) ).
fof(i_0_60,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])]) ).
fof(i_0_61,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(i_0_62,plain,
! [X143,X144] :
( ~ aNaturalNumber0(X143)
| ~ aNaturalNumber0(X144)
| X143 = X144
| ~ sdtlseqdt0(X143,X144)
| iLess0(X143,X144) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIH_03])]) ).
fof(i_0_63,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])]) ).
fof(i_0_64,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])])])])]) ).
fof(i_0_65,plain,
! [X91,X92] :
( ~ aNaturalNumber0(X91)
| ~ aNaturalNumber0(X92)
| aNaturalNumber0(sdtasdt0(X91,X92)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(i_0_66,plain,
! [X89,X90] :
( ~ aNaturalNumber0(X89)
| ~ aNaturalNumber0(X90)
| aNaturalNumber0(sdtpldt0(X89,X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
fof(i_0_67,plain,
! [X132,X133] :
( ( X133 != X132
| sdtlseqdt0(X132,X133)
| ~ aNaturalNumber0(X132)
| ~ aNaturalNumber0(X133) )
& ( sdtlseqdt0(X133,X132)
| sdtlseqdt0(X132,X133)
| ~ aNaturalNumber0(X132)
| ~ aNaturalNumber0(X133) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).
fof(i_0_68,plain,
! [X99,X100] :
( ~ aNaturalNumber0(X99)
| ~ aNaturalNumber0(X100)
| sdtasdt0(X99,X100) = sdtasdt0(X100,X99) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
fof(i_0_69,plain,
! [X93,X94] :
( ~ aNaturalNumber0(X93)
| ~ aNaturalNumber0(X94)
| sdtpldt0(X93,X94) = sdtpldt0(X94,X93) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
fof(i_0_70,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])]) ).
fof(i_0_71,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])])]) ).
fof(i_0_72,plain,
! [X169] :
( ( aNaturalNumber0(esk4_1(X169))
| ~ aNaturalNumber0(X169)
| X169 = sz00
| X169 = sz10 )
& ( doDivides0(esk4_1(X169),X169)
| ~ aNaturalNumber0(X169)
| X169 = sz00
| X169 = sz10 )
& ( isPrime0(esk4_1(X169))
| ~ aNaturalNumber0(X169)
| X169 = sz00
| X169 = sz10 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPrimDiv])])])]) ).
fof(i_0_73,plain,
! [X140] :
( ( sz10 != X140
| X140 = sz00
| X140 = sz10
| ~ aNaturalNumber0(X140) )
& ( sdtlseqdt0(sz10,X140)
| X140 = sz00
| X140 = sz10
| ~ aNaturalNumber0(X140) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLENTr])])]) ).
fof(i_0_74,plain,
! [X126] :
( ~ aNaturalNumber0(X126)
| sdtlseqdt0(X126,X126) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLERefl])]) ).
fof(i_0_75,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(i_0_76,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(i_0_77,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(i_0_78,negated_conjecture,
xn != sdtpldt0(xp,xr),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(i_0_79,hypothesis,
( doDivides0(X3,X1)
| doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ isPrime0(X3)
| ~ doDivides0(X3,sdtasdt0(X1,X2))
| ~ iLess0(sdtpldt0(sdtpldt0(X1,X2),X3),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
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_44]),
[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_44]),
[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_45]),
[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_46]),
[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_47]),
[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_47]),
[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_48]),
[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_48]),
[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_49]),
[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_50]),
[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_51]),
[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_47]),
[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_47]),
[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_48]),
[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_48]),
[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_52]),
[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_53]),
[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_54]),
[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_55]),
[final] ).
cnf(i_0_99,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_100,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_101,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_52]),
[final] ).
cnf(i_0_102,plain,
( sdtpldt0(X1,X2) = X3
| X2 != sdtmndt0(X3,X1)
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_103,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_104,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_105,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_106,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_107,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_108,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_109,plain,
( aNaturalNumber0(X1)
| X3 = sz00
| X1 != sdtsldt0(X2,X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_110,plain,
( aNaturalNumber0(X1)
| X1 != sdtmndt0(X2,X3)
| ~ sdtlseqdt0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_111,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_112,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_113,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_114,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_115,plain,
( X1 = X2
| iLess0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_116,plain,
( X2 = sz00
| sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_117,plain,
( X1 = sz10
| X1 = X2
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| ~ isPrime0(X2)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_118,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_119,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_120,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_121,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_122,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_123,plain,
( X1 = sz00
| X2 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_124,plain,
( X1 = sz00
| sdtpldt0(X1,X2) != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_125,plain,
( X1 = sz00
| sdtpldt0(X2,X1) != sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_126,plain,
( doDivides0(esk3_1(X1),X1)
| X1 = sz00
| X1 = sz10
| isPrime0(X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_127,hypothesis,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__1860]),
[final] ).
cnf(i_0_128,plain,
( sdtlseqdt0(X2,X1)
| X1 != X2
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_129,plain,
( doDivides0(esk4_1(X1),X1)
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_130,plain,
( aNaturalNumber0(esk3_1(X1))
| X1 = sz00
| X1 = sz10
| isPrime0(X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_131,plain,
( X1 = sz00
| X1 = sz10
| isPrime0(X1)
| esk3_1(X1) != X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_132,plain,
( sdtlseqdt0(sz10,X1)
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_73]),
[final] ).
cnf(i_0_133,plain,
( X1 = sz00
| X1 = sz10
| isPrime0(X1)
| esk3_1(X1) != sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_134,plain,
( sdtlseqdt0(X1,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_74]),
[final] ).
cnf(i_0_135,plain,
( isPrime0(esk4_1(X1))
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_136,plain,
( aNaturalNumber0(esk4_1(X1))
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_137,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_75]),
[final] ).
cnf(i_0_138,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_76]),
[final] ).
cnf(i_0_139,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_75]),
[final] ).
cnf(i_0_140,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_76]),
[final] ).
cnf(i_0_141,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_77]),
[final] ).
cnf(i_0_142,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_77]),
[final] ).
cnf(i_0_143,negated_conjecture,
xn != sdtpldt0(xp,xr),
inference(split_conjunct,[status(thm)],[i_0_78]),
[final] ).
cnf(i_0_144,plain,
( X1 != sz10
| ~ isPrime0(X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_145,plain,
( X1 != sz00
| ~ isPrime0(X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_146,hypothesis,
sdtlseqdt0(xr,xn),
inference(split_conjunct,[status(thm)],[m__1894]),
[final] ).
cnf(i_0_147,hypothesis,
sdtlseqdt0(xp,xn),
inference(split_conjunct,[status(thm)],[m__1870]),
[final] ).
cnf(i_0_148,hypothesis,
xr = sdtmndt0(xn,xp),
inference(split_conjunct,[status(thm)],[m__1883]),
[final] ).
cnf(i_0_149,hypothesis,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[m__1860]),
[final] ).
cnf(i_0_150,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]),
[final] ).
cnf(i_0_151,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]),
[final] ).
cnf(i_0_152,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]),
[final] ).
cnf(i_0_153,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]),
[final] ).
cnf(i_0_154,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]),
[final] ).
cnf(i_0_155,hypothesis,
xr != xn,
inference(split_conjunct,[status(thm)],[m__1894]),
[final] ).
cnf(i_0_156,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mSortsC_01]),
[final] ).
cnf(i_0_157,axiom,
X1 = X1 ).
cnf(i_0_158,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_159,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_160,axiom,
( X1 != X2
| sdtasdt0(X1,X3) = sdtasdt0(X2,X3) ) ).
cnf(i_0_161,axiom,
( X1 != X2
| sdtasdt0(X3,X1) = sdtasdt0(X3,X2) ) ).
cnf(i_0_162,axiom,
( X1 != X2
| sdtpldt0(X1,X3) = sdtpldt0(X2,X3) ) ).
cnf(i_0_163,axiom,
( X1 != X2
| sdtpldt0(X3,X1) = sdtpldt0(X3,X2) ) ).
cnf(i_0_164,axiom,
( X1 != X2
| sdtsldt0(X1,X3) = sdtsldt0(X2,X3) ) ).
cnf(i_0_165,axiom,
( X1 != X2
| sdtsldt0(X3,X1) = sdtsldt0(X3,X2) ) ).
cnf(i_0_166,axiom,
( X1 != X2
| sdtmndt0(X1,X3) = sdtmndt0(X2,X3) ) ).
cnf(i_0_167,axiom,
( X1 != X2
| sdtmndt0(X3,X1) = sdtmndt0(X3,X2) ) ).
cnf(i_0_168,axiom,
( X1 != X2
| esk3_1(X1) = esk3_1(X2) ) ).
cnf(i_0_169,axiom,
( X1 != X2
| ~ doDivides0(X1,X3)
| doDivides0(X2,X3) ) ).
cnf(i_0_170,axiom,
( X1 != X2
| ~ doDivides0(X3,X1)
| doDivides0(X3,X2) ) ).
cnf(i_0_171,axiom,
( X1 != X2
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(X2) ) ).
cnf(i_0_172,axiom,
( X1 != X2
| ~ isPrime0(X1)
| isPrime0(X2) ) ).
cnf(i_0_173,axiom,
( X1 != X2
| ~ iLess0(X1,X3)
| iLess0(X2,X3) ) ).
cnf(i_0_174,axiom,
( X1 != X2
| ~ iLess0(X3,X1)
| iLess0(X3,X2) ) ).
cnf(i_0_175,axiom,
( X1 != X2
| ~ sdtlseqdt0(X1,X3)
| sdtlseqdt0(X2,X3) ) ).
cnf(i_0_176,axiom,
( X1 != X2
| ~ sdtlseqdt0(X3,X1)
| sdtlseqdt0(X3,X2) ) ).
cnf(i_0_157_001,axiom,
X1 = X1 ).
cnf(i_0_158_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_159_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_160_004,axiom,
( X1 != X2
| sdtasdt0(X1,X3) = sdtasdt0(X2,X3) ) ).
cnf(i_0_161_005,axiom,
( X1 != X2
| sdtasdt0(X3,X1) = sdtasdt0(X3,X2) ) ).
cnf(i_0_162_006,axiom,
( X1 != X2
| sdtpldt0(X1,X3) = sdtpldt0(X2,X3) ) ).
cnf(i_0_163_007,axiom,
( X1 != X2
| sdtpldt0(X3,X1) = sdtpldt0(X3,X2) ) ).
cnf(i_0_164_008,axiom,
( X1 != X2
| sdtsldt0(X1,X3) = sdtsldt0(X2,X3) ) ).
cnf(i_0_165_009,axiom,
( X1 != X2
| sdtsldt0(X3,X1) = sdtsldt0(X3,X2) ) ).
cnf(i_0_166_010,axiom,
( X1 != X2
| sdtmndt0(X1,X3) = sdtmndt0(X2,X3) ) ).
cnf(i_0_167_011,axiom,
( X1 != X2
| sdtmndt0(X3,X1) = sdtmndt0(X3,X2) ) ).
cnf(i_0_168_012,axiom,
( X1 != X2
| esk3_1(X1) = esk3_1(X2) ) ).
cnf(i_0_169_013,axiom,
( X1 != X2
| ~ doDivides0(X1,X3)
| doDivides0(X2,X3) ) ).
cnf(i_0_170_014,axiom,
( X1 != X2
| ~ doDivides0(X3,X1)
| doDivides0(X3,X2) ) ).
cnf(i_0_171_015,axiom,
( X1 != X2
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(X2) ) ).
cnf(i_0_172_016,axiom,
( X1 != X2
| ~ isPrime0(X1)
| isPrime0(X2) ) ).
cnf(i_0_173_017,axiom,
( X1 != X2
| ~ iLess0(X1,X3)
| iLess0(X2,X3) ) ).
cnf(i_0_174_018,axiom,
( X1 != X2
| ~ iLess0(X3,X1)
| iLess0(X3,X2) ) ).
cnf(i_0_175_019,axiom,
( X1 != X2
| ~ sdtlseqdt0(X1,X3)
| sdtlseqdt0(X2,X3) ) ).
cnf(i_0_176_020,axiom,
( X1 != X2
| ~ sdtlseqdt0(X3,X1)
| sdtlseqdt0(X3,X2) ) ).
cnf(i_0_177,plain,
( ~ aNaturalNumber0(X1)
| ~ doDivides0(X2,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtasdt0(X2,X1))
| X2 = sz00
| X1 = sdtsldt0(sdtasdt0(X2,X1),X2) ),
inference(equality_inference,[],[95]) ).
cnf(i_0_178,plain,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X2,sdtpldt0(X2,X1))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtpldt0(X2,X1))
| X1 = sdtmndt0(sdtpldt0(X2,X1),X2) ),
inference(equality_inference,[],[96]) ).
cnf(i_0_179,plain,
( ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X1 = sz00
| X2 = sdtasdt0(X1,sdtsldt0(X2,X1)) ),
inference(equality_inference,[],[101]) ).
cnf(i_0_180,plain,
( ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X1,sdtmndt0(X2,X1)) = X2 ),
inference(equality_inference,[],[102]) ).
cnf(i_0_181,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X1 = X1
| X2 = sz00 ),
inference(equality_inference,[],[103]) ).
cnf(i_0_182,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X1 = X1
| X2 = sz00 ),
inference(equality_inference,[],[104]) ).
cnf(i_0_183,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X2)
| X2 = X2 ),
inference(equality_inference,[],[105]) ).
cnf(i_0_184,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X2)
| X2 = X2 ),
inference(equality_inference,[],[106]) ).
cnf(i_0_185,plain,
( ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| aNaturalNumber0(sdtsldt0(X2,X1))
| X1 = sz00 ),
inference(equality_inference,[],[109]) ).
cnf(i_0_186,plain,
( ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| aNaturalNumber0(sdtmndt0(X2,X1)) ),
inference(equality_inference,[],[110]) ).
cnf(i_0_187,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtpldt0(X1,X2))
| sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2) ),
inference(equality_inference,[],[112]) ).
cnf(i_0_188,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtasdt0(X1,X2))
| doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2) ),
inference(equality_inference,[],[113]) ).
cnf(i_0_189,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X1) ),
inference(equality_inference,[],[128]) ).
cnf(i_0_190,plain,
( ~ isPrime0(sz10)
| ~ aNaturalNumber0(sz10) ),
inference(equality_inference,[],[144]) ).
cnf(i_0_191,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(equality_inference,[],[145]) ).
cnf(i_0_192,plain,
~ isPrime0(sz10),
inference(scs_inference,[],[i_0_153,i_0_190]) ).
cnf(i_0_193,plain,
~ isPrime0(sz00),
inference(scs_inference,[],[i_0_154,i_0_191]) ).
cnf(i_0_194,plain,
sdtmndt0(xn,xp) = xr,
inference(scs_inference,[],[i_0_148,i_0_158]) ).
cnf(i_0_195,plain,
sdtlseqdt0(xp,xp),
inference(scs_inference,[],[i_0_150,i_0_148,i_0_158,i_0_134]) ).
cnf(i_0_196,plain,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X1) ),
inference(rename_variables,[],[i_0_134]) ).
cnf(i_0_197,plain,
sdtpldt0(xp,sdtmndt0(xp,xp)) = xp,
inference(scs_inference,[],[i_0_150,i_0_148,i_0_158,i_0_134,i_0_180]) ).
cnf(i_0_198,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X1,sdtmndt0(X2,X1)) = X2
| ~ sdtlseqdt0(X1,X2) ),
inference(rename_variables,[],[i_0_180]) ).
cnf(i_0_199,plain,
aNaturalNumber0(sdtmndt0(xp,xp)),
inference(scs_inference,[],[i_0_150,i_0_148,i_0_158,i_0_134,i_0_180,i_0_186]) ).
cnf(i_0_200,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| aNaturalNumber0(sdtmndt0(X2,X1))
| ~ sdtlseqdt0(X1,X2) ),
inference(rename_variables,[],[i_0_186]) ).
cnf(i_0_201,plain,
sdtpldt0(xp,xr) = xn,
inference(scs_inference,[],[i_0_147,i_0_150,i_0_152,i_0_148,i_0_158,i_0_134,i_0_180,i_0_186,i_0_102]) ).
cnf(i_0_202,plain,
( X1 != sdtmndt0(X2,X3)
| sdtpldt0(X3,X1) = X2
| ~ sdtlseqdt0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(rename_variables,[],[i_0_102]) ).
cnf(i_0_203,plain,
aNaturalNumber0(xr),
inference(scs_inference,[],[i_0_147,i_0_150,i_0_152,i_0_148,i_0_158,i_0_134,i_0_180,i_0_186,i_0_102,i_0_110]) ).
cnf(i_0_204,plain,
( X1 != sdtmndt0(X2,X3)
| ~ sdtlseqdt0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| aNaturalNumber0(X1) ),
inference(rename_variables,[],[i_0_110]) ).
cnf(i_0_205,plain,
( X1 = xp
| X1 != sdtpldt0(xp,sdtmndt0(xp,xp)) ),
inference(scs_inference,[],[i_0_147,i_0_150,i_0_152,i_0_148,i_0_158,i_0_134,i_0_180,i_0_186,i_0_102,i_0_110,i_0_159]) ).
cnf(i_0_206,plain,
aNaturalNumber0(sdtmndt0(xn,xp)),
inference(scs_inference,[],[i_0_147,i_0_150,i_0_152,i_0_148,i_0_158,i_0_134,i_0_180,i_0_186,i_0_102,i_0_110,i_0_159,i_0_171]) ).
cnf(i_0_207,plain,
sdtlseqdt0(sdtmndt0(xn,xp),xr),
inference(scs_inference,[],[i_0_147,i_0_150,i_0_152,i_0_148,i_0_158,i_0_134,i_0_180,i_0_186,i_0_102,i_0_110,i_0_159,i_0_171,i_0_128]) ).
cnf(i_0_208,plain,
( X1 != X2
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,X1) ),
inference(rename_variables,[],[i_0_128]) ).
cnf(i_0_209,plain,
( sdtpldt0(xp,xp) != sdtpldt0(xp,sdtmndt0(xp,xp))
| xp = sdtmndt0(xp,xp) ),
inference(scs_inference,[],[i_0_147,i_0_150,i_0_152,i_0_148,i_0_158,i_0_134,i_0_180,i_0_186,i_0_102,i_0_110,i_0_159,i_0_171,i_0_128,i_0_96]) ).
cnf(i_0_210,plain,
( sdtpldt0(X1,X2) != X3
| X2 = sdtmndt0(X3,X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(rename_variables,[],[i_0_96]) ).
cnf(i_0_211,plain,
( isPrime0(sdtmndt0(xp,xp))
| sdtpldt0(xp,xp) != sdtpldt0(xp,sdtmndt0(xp,xp)) ),
inference(scs_inference,[],[i_0_147,i_0_149,i_0_150,i_0_152,i_0_148,i_0_158,i_0_134,i_0_180,i_0_186,i_0_102,i_0_110,i_0_159,i_0_171,i_0_128,i_0_96,i_0_172]) ).
cnf(i_0_212,plain,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,sdtpldt0(X2,X1))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtpldt0(X2,X1)) ),
inference(rename_variables,[],[i_0_187]) ).
cnf(i_0_213,plain,
( xp = sdtasdt0(sz10,sdtsldt0(xp,sz10))
| ~ aNaturalNumber0(sdtpldt0(xp,xp))
| ~ doDivides0(sz10,xp)
| sdtpldt0(xp,xp) != sdtpldt0(xp,sdtmndt0(xp,xp)) ),
inference(scs_inference,[],[i_0_147,i_0_149,i_0_150,i_0_152,i_0_153,i_0_156,i_0_148,i_0_158,i_0_134,i_0_180,i_0_186,i_0_102,i_0_110,i_0_159,i_0_171,i_0_128,i_0_96,i_0_172,i_0_187,i_0_179]) ).
cnf(i_0_214,plain,
sdtpldt0(xp,sdtmndt0(xp,xp)) = xp,
inference(equality_inference,[],[205]) ).
cnf(i_0_215,plain,
sdtlseqdt0(xm,xm),
inference(scs_inference,[],[i_0_151,i_0_134]) ).
cnf(i_0_216,plain,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X1) ),
inference(rename_variables,[],[i_0_134]) ).
cnf(i_0_217,plain,
xp = sdtpldt0(xp,sdtmndt0(xp,xp)),
inference(scs_inference,[],[i_0_151,i_0_197,i_0_134,i_0_158]) ).
cnf(i_0_218,plain,
aNaturalNumber0(sdtpldt0(xp,sdtmndt0(xp,xp))),
inference(scs_inference,[],[i_0_151,i_0_150,i_0_197,i_0_134,i_0_158,i_0_171]) ).
cnf(i_0_219,plain,
xp != sz10,
inference(scs_inference,[],[i_0_151,i_0_149,i_0_150,i_0_197,i_0_192,i_0_134,i_0_158,i_0_171,i_0_172]) ).
cnf(i_0_220,plain,
xr != sdtpldt0(xp,xr),
inference(scs_inference,[],[i_0_151,i_0_149,i_0_150,i_0_197,i_0_201,i_0_155,i_0_192,i_0_134,i_0_158,i_0_171,i_0_172,i_0_159]) ).
cnf(i_0_221,plain,
sdtlseqdt0(xr,sdtmndt0(xn,xp)),
inference(scs_inference,[],[i_0_194,i_0_151,i_0_149,i_0_150,i_0_206,i_0_197,i_0_201,i_0_155,i_0_192,i_0_203,i_0_134,i_0_158,i_0_171,i_0_172,i_0_159,i_0_128]) ).
cnf(i_0_222,plain,
( X1 != X2
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,X1) ),
inference(rename_variables,[],[i_0_128]) ).
cnf(i_0_223,plain,
aNaturalNumber0(sdtmndt0(xm,xm)),
inference(scs_inference,[],[i_0_194,i_0_151,i_0_149,i_0_150,i_0_206,i_0_197,i_0_201,i_0_155,i_0_192,i_0_203,i_0_134,i_0_158,i_0_171,i_0_172,i_0_159,i_0_128,i_0_186]) ).
cnf(i_0_224,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| aNaturalNumber0(sdtmndt0(X2,X1))
| ~ sdtlseqdt0(X1,X2) ),
inference(rename_variables,[],[i_0_186]) ).
cnf(i_0_225,plain,
sdtpldt0(xm,sdtmndt0(xm,xm)) = xm,
inference(scs_inference,[],[i_0_194,i_0_151,i_0_149,i_0_150,i_0_206,i_0_197,i_0_201,i_0_155,i_0_192,i_0_203,i_0_134,i_0_158,i_0_171,i_0_172,i_0_159,i_0_128,i_0_186,i_0_180]) ).
cnf(i_0_226,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X1,sdtmndt0(X2,X1)) = X2
| ~ sdtlseqdt0(X1,X2) ),
inference(rename_variables,[],[i_0_180]) ).
cnf(i_0_227,plain,
sdtlseqdt0(sdtmndt0(xn,xp),sdtmndt0(xn,xp)),
inference(scs_inference,[],[i_0_194,i_0_151,i_0_149,i_0_150,i_0_206,i_0_197,i_0_201,i_0_207,i_0_155,i_0_192,i_0_203,i_0_134,i_0_158,i_0_171,i_0_172,i_0_159,i_0_128,i_0_186,i_0_180,i_0_98]) ).
cnf(i_0_228,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X3)
| ~ sdtlseqdt0(X3,X2)
| sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X3) ),
inference(rename_variables,[],[i_0_98]) ).
cnf(i_0_229,plain,
( sdtlseqdt0(xm,sdtpldt0(xm,xm))
| ~ aNaturalNumber0(sdtpldt0(xm,xm)) ),
inference(scs_inference,[],[i_0_194,i_0_151,i_0_149,i_0_150,i_0_206,i_0_197,i_0_201,i_0_207,i_0_155,i_0_192,i_0_203,i_0_134,i_0_158,i_0_171,i_0_172,i_0_159,i_0_128,i_0_186,i_0_180,i_0_98,i_0_187]) ).
cnf(i_0_230,plain,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,sdtpldt0(X2,X1))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtpldt0(X2,X1)) ),
inference(rename_variables,[],[i_0_187]) ).
cnf(i_0_231,plain,
( doDivides0(xm,sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(scs_inference,[],[i_0_194,i_0_151,i_0_149,i_0_150,i_0_206,i_0_197,i_0_201,i_0_207,i_0_155,i_0_192,i_0_203,i_0_134,i_0_158,i_0_171,i_0_172,i_0_159,i_0_128,i_0_186,i_0_180,i_0_98,i_0_187,i_0_188]) ).
cnf(i_0_232,plain,
( ~ aNaturalNumber0(X1)
| doDivides0(X2,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtasdt0(X2,X1)) ),
inference(rename_variables,[],[i_0_188]) ).
cnf(i_0_233,plain,
( ~ doDivides0(xm,sz10)
| sdtlseqdt0(xm,sz10)
| esk3_1(xp) != xp
| xp = sz00 ),
inference(scs_inference,[],[i_0_194,i_0_151,i_0_149,i_0_152,i_0_153,i_0_150,i_0_199,i_0_206,i_0_197,i_0_201,i_0_207,i_0_155,i_0_192,i_0_203,i_0_147,i_0_156,i_0_148,i_0_134,i_0_158,i_0_171,i_0_172,i_0_159,i_0_128,i_0_186,i_0_180,i_0_98,i_0_131,i_0_112,i_0_110,i_0_116]) ).
cnf(i_0_234,plain,
sdtlseqdt0(sz00,sz00),
inference(scs_inference,[],[i_0_154,i_0_134]) ).
cnf(i_0_235,plain,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X1) ),
inference(rename_variables,[],[i_0_134]) ).
cnf(i_0_236,plain,
$false,
inference(scs_inference,[],[i_0_143,i_0_201,i_0_154,i_0_134,i_0_158]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM489+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n019.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 00:39:14 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.35/1.61 % Version : CSE_E---1.7
% 0.35/1.61 % Problem : theBenchmark.p
% 0.35/1.61 % SZS status Theorem for theBenchmark.p
% 0.35/1.61 % SZS output start CNFRefutation
% See solution above
% 0.44/1.78 % Total time : 1.271s
%------------------------------------------------------------------------------