%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM504+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:57:35 PM UTC 2026
% Result : Theorem 41.91s 40.25s
% Output : CNFRefutation 49.84s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 228)
% 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/sandbox/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/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(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(mPrimDiv,axiom,
! [X1] :
( ( aNaturalNumber0(X1)
& X1 != sz00
& X1 != sz10 )
=> ? [X2] :
( aNaturalNumber0(X2)
& doDivides0(X2,X1)
& isPrime0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPrimDiv) ).
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__2075,hypothesis,
~ sdtlseqdt0(xp,xm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2075) ).
fof(m__1870,hypothesis,
~ sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1870) ).
fof(m__2315,hypothesis,
~ ( xk = sz00
| xk = sz10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2315) ).
fof(m__2414,hypothesis,
( sdtasdt0(xn,xm) != sdtasdt0(xp,xm)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2414) ).
fof(m__2362,hypothesis,
( sdtlseqdt0(xr,xk)
& doDivides0(xr,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2362) ).
fof(m__1860,hypothesis,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
fof(m__2306,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(m__2342,hypothesis,
( aNaturalNumber0(xr)
& doDivides0(xr,xk)
& isPrime0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).
fof(m__2389,hypothesis,
sdtlseqdt0(xp,xk),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2389) ).
fof(m__2287,hypothesis,
( xn != xp
& sdtlseqdt0(xn,xp)
& xm != xp
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2287) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(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__2327,hypothesis,
( xk != sz00
& xk != sz10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2327) ).
fof(i_0_49,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_50,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_51,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_52,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_53,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_54,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_55,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_56,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_57,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_58,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_59,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_60,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_61,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_62,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_63,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_64,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_65,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_66,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_67,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_68,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_69,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_70,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_71,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_72,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_73,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_74,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_75,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_76,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_77,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_78,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_79,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_80,plain,
! [X126] :
( ~ aNaturalNumber0(X126)
| sdtlseqdt0(X126,X126) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLERefl])]) ).
fof(i_0_81,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_82,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_83,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_84,hypothesis,
~ sdtlseqdt0(xp,xm),
inference(fof_simplification,[status(thm)],[m__2075]) ).
fof(i_0_85,hypothesis,
~ sdtlseqdt0(xp,xn),
inference(fof_simplification,[status(thm)],[m__1870]) ).
fof(i_0_86,hypothesis,
( xk != sz00
& xk != sz10 ),
inference(fof_nnf,[status(thm)],[m__2315]) ).
cnf(i_0_87,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_49]),
[final] ).
cnf(i_0_88,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_50]),
[final] ).
cnf(i_0_89,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_50]),
[final] ).
cnf(i_0_90,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_51]),
[final] ).
cnf(i_0_91,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_52]),
[final] ).
cnf(i_0_92,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_53]),
[final] ).
cnf(i_0_93,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_53]),
[final] ).
cnf(i_0_94,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_54]),
[final] ).
cnf(i_0_95,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_54]),
[final] ).
cnf(i_0_96,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_55]),
[final] ).
cnf(i_0_97,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_98,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_99,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_53]),
[final] ).
cnf(i_0_100,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_53]),
[final] ).
cnf(i_0_101,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_54]),
[final] ).
cnf(i_0_102,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_54]),
[final] ).
cnf(i_0_103,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_58]),
[final] ).
cnf(i_0_104,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_59]),
[final] ).
cnf(i_0_105,plain,
( doDivides0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_106,plain,
( sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_107,plain,
( sdtpldt0(X1,esk1_2(X1,X2)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_108,plain,
( X1 = sdtasdt0(X2,esk2_2(X2,X1))
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_109,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_58]),
[final] ).
cnf(i_0_110,plain,
( sdtpldt0(X1,X2) = X3
| X2 != sdtmndt0(X3,X1)
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_111,plain,
( X1 = X3
| X2 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X3,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_112,plain,
( X2 = X3
| X1 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_113,plain,
( X1 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X3,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_114,plain,
( X2 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_115,plain,
( aNaturalNumber0(esk2_2(X1,X2))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_116,plain,
( aNaturalNumber0(esk1_2(X1,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_117,plain,
( aNaturalNumber0(X1)
| X3 = sz00
| X1 != sdtsldt0(X2,X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_118,plain,
( aNaturalNumber0(X1)
| X1 != sdtmndt0(X2,X3)
| ~ sdtlseqdt0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_119,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_120,plain,
( sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_121,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_122,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_123,hypothesis,
sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)),
inference(split_conjunct,[status(thm)],[m__2414]),
[final] ).
cnf(i_0_124,hypothesis,
sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(split_conjunct,[status(thm)],[m__2414]),
[final] ).
cnf(i_0_125,plain,
( X1 = X2
| iLess0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_126,plain,
( X2 = sz00
| sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_127,plain,
( X1 = sz10
| X1 = X2
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| ~ isPrime0(X2)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_128,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_129,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_130,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_73]),
[final] ).
cnf(i_0_131,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_74]),
[final] ).
cnf(i_0_132,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_75]),
[final] ).
cnf(i_0_133,plain,
( X1 = sz00
| X2 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[i_0_76]),
[final] ).
cnf(i_0_134,plain,
( X1 = sz00
| sdtpldt0(X1,X2) != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_77]),
[final] ).
cnf(i_0_135,plain,
( X1 = sz00
| sdtpldt0(X2,X1) != sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_77]),
[final] ).
cnf(i_0_136,plain,
( doDivides0(esk3_1(X1),X1)
| X1 = sz00
| X1 = sz10
| isPrime0(X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_137,hypothesis,
sdtasdt0(xp,xm) != sdtasdt0(xp,xk),
inference(split_conjunct,[status(thm)],[m__2414]),
[final] ).
cnf(i_0_138,hypothesis,
sdtasdt0(xn,xm) != sdtasdt0(xp,xm),
inference(split_conjunct,[status(thm)],[m__2414]),
[final] ).
cnf(i_0_139,hypothesis,
doDivides0(xr,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__2362]),
[final] ).
cnf(i_0_140,hypothesis,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__1860]),
[final] ).
cnf(i_0_141,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[m__2306]),
[final] ).
cnf(i_0_142,plain,
( sdtlseqdt0(X2,X1)
| X1 != X2
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_73]),
[final] ).
cnf(i_0_143,plain,
( doDivides0(esk4_1(X1),X1)
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_78]),
[final] ).
cnf(i_0_144,plain,
( aNaturalNumber0(esk3_1(X1))
| X1 = sz00
| X1 = sz10
| isPrime0(X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_145,plain,
( X1 = sz00
| X1 = sz10
| isPrime0(X1)
| esk3_1(X1) != X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_146,plain,
( sdtlseqdt0(sz10,X1)
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_79]),
[final] ).
cnf(i_0_147,plain,
( X1 = sz00
| X1 = sz10
| isPrime0(X1)
| esk3_1(X1) != sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_148,plain,
( sdtlseqdt0(X1,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_80]),
[final] ).
cnf(i_0_149,plain,
( isPrime0(esk4_1(X1))
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_78]),
[final] ).
cnf(i_0_150,plain,
( aNaturalNumber0(esk4_1(X1))
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_78]),
[final] ).
cnf(i_0_151,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_81]),
[final] ).
cnf(i_0_152,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_82]),
[final] ).
cnf(i_0_153,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_81]),
[final] ).
cnf(i_0_154,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_82]),
[final] ).
cnf(i_0_155,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_156,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_157,hypothesis,
~ sdtlseqdt0(xp,xm),
inference(split_conjunct,[status(thm)],[i_0_84]),
[final] ).
cnf(i_0_158,hypothesis,
~ sdtlseqdt0(xp,xn),
inference(split_conjunct,[status(thm)],[i_0_85]),
[final] ).
cnf(i_0_159,plain,
( X1 != sz10
| ~ isPrime0(X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_160,plain,
( X1 != sz00
| ~ isPrime0(X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_161,hypothesis,
doDivides0(xr,xk),
inference(split_conjunct,[status(thm)],[m__2342]),
[final] ).
cnf(i_0_162,hypothesis,
sdtlseqdt0(xr,xk),
inference(split_conjunct,[status(thm)],[m__2362]),
[final] ).
cnf(i_0_163,hypothesis,
sdtlseqdt0(xp,xk),
inference(split_conjunct,[status(thm)],[m__2389]),
[final] ).
cnf(i_0_164,hypothesis,
sdtlseqdt0(xm,xp),
inference(split_conjunct,[status(thm)],[m__2287]),
[final] ).
cnf(i_0_165,hypothesis,
sdtlseqdt0(xn,xp),
inference(split_conjunct,[status(thm)],[m__2287]),
[final] ).
cnf(i_0_166,hypothesis,
isPrime0(xr),
inference(split_conjunct,[status(thm)],[m__2342]),
[final] ).
cnf(i_0_167,hypothesis,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[m__1860]),
[final] ).
cnf(i_0_168,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[m__2342]),
[final] ).
cnf(i_0_169,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]),
[final] ).
cnf(i_0_170,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]),
[final] ).
cnf(i_0_171,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]),
[final] ).
cnf(i_0_172,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]),
[final] ).
cnf(i_0_173,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]),
[final] ).
cnf(i_0_174,hypothesis,
xk != sz10,
inference(split_conjunct,[status(thm)],[m__2327]),
[final] ).
cnf(i_0_175,hypothesis,
xk != sz10,
inference(split_conjunct,[status(thm)],[i_0_86]),
[final] ).
cnf(i_0_176,hypothesis,
xk != sz00,
inference(split_conjunct,[status(thm)],[m__2327]),
[final] ).
cnf(i_0_177,hypothesis,
xk != sz00,
inference(split_conjunct,[status(thm)],[i_0_86]),
[final] ).
cnf(i_0_178,hypothesis,
xm != xp,
inference(split_conjunct,[status(thm)],[m__2287]),
[final] ).
cnf(i_0_179,hypothesis,
xn != xp,
inference(split_conjunct,[status(thm)],[m__2287]),
[final] ).
cnf(i_0_180,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mSortsC_01]),
[final] ).
cnf(i_0_181,axiom,
X1 = X1 ).
cnf(i_0_182,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_183,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_184,axiom,
( X1 != X2
| sdtasdt0(X1,X3) = sdtasdt0(X2,X3) ) ).
cnf(i_0_185,axiom,
( X1 != X2
| sdtasdt0(X3,X1) = sdtasdt0(X3,X2) ) ).
cnf(i_0_186,axiom,
( X1 != X2
| sdtpldt0(X1,X3) = sdtpldt0(X2,X3) ) ).
cnf(i_0_187,axiom,
( X1 != X2
| sdtpldt0(X3,X1) = sdtpldt0(X3,X2) ) ).
cnf(i_0_188,axiom,
( X1 != X2
| sdtsldt0(X1,X3) = sdtsldt0(X2,X3) ) ).
cnf(i_0_189,axiom,
( X1 != X2
| sdtsldt0(X3,X1) = sdtsldt0(X3,X2) ) ).
cnf(i_0_190,axiom,
( X1 != X2
| sdtmndt0(X1,X3) = sdtmndt0(X2,X3) ) ).
cnf(i_0_191,axiom,
( X1 != X2
| sdtmndt0(X3,X1) = sdtmndt0(X3,X2) ) ).
cnf(i_0_192,axiom,
( X1 != X2
| esk3_1(X1) = esk3_1(X2) ) ).
cnf(i_0_193,axiom,
( X1 != X2
| ~ doDivides0(X1,X3)
| doDivides0(X2,X3) ) ).
cnf(i_0_194,axiom,
( X1 != X2
| ~ doDivides0(X3,X1)
| doDivides0(X3,X2) ) ).
cnf(i_0_195,axiom,
( X1 != X2
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(X2) ) ).
cnf(i_0_196,axiom,
( X1 != X2
| ~ isPrime0(X1)
| isPrime0(X2) ) ).
cnf(i_0_197,axiom,
( X1 != X2
| ~ iLess0(X1,X3)
| iLess0(X2,X3) ) ).
cnf(i_0_198,axiom,
( X1 != X2
| ~ iLess0(X3,X1)
| iLess0(X3,X2) ) ).
cnf(i_0_199,axiom,
( X1 != X2
| ~ sdtlseqdt0(X1,X3)
| sdtlseqdt0(X2,X3) ) ).
cnf(i_0_200,axiom,
( X1 != X2
| ~ sdtlseqdt0(X3,X1)
| sdtlseqdt0(X3,X2) ) ).
cnf(i_0_218,plain,
sdtlseqdt0(xr,xr),
inference(scs_inference,[],[i_0_168,i_0_148]) ).
cnf(i_0_220,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) = xk,
inference(scs_inference,[],[i_0_168,i_0_141,i_0_148,i_0_182]) ).
cnf(i_0_221,plain,
xm != xk,
inference(scs_inference,[],[i_0_137,i_0_168,i_0_141,i_0_148,i_0_182,i_0_185]) ).
cnf(i_0_222,plain,
xm != sdtsldt0(sdtasdt0(xn,xm),xp),
inference(scs_inference,[],[i_0_137,i_0_168,i_0_141,i_0_148,i_0_182,i_0_185,i_0_183]) ).
cnf(i_0_223,plain,
xk != xm,
inference(scs_inference,[],[i_0_137,i_0_157,i_0_163,i_0_168,i_0_141,i_0_148,i_0_182,i_0_185,i_0_183,i_0_200]) ).
cnf(i_0_273,plain,
sdtlseqdt0(sz10,sz10),
inference(scs_inference,[],[i_0_172,i_0_148]) ).
cnf(i_0_345,plain,
sdtlseqdt0(sz00,sz00),
inference(scs_inference,[],[i_0_173,i_0_148]) ).
cnf(i_0_491,plain,
sdtlseqdt0(xn,xn),
inference(scs_inference,[],[i_0_171,i_0_148]) ).
cnf(i_0_521,plain,
sdtlseqdt0(xm,xm),
inference(scs_inference,[],[i_0_170,i_0_148]) ).
cnf(i_0_592,plain,
sdtlseqdt0(xp,xp),
inference(scs_inference,[],[i_0_169,i_0_148]) ).
cnf(i_0_216,plain,
~ isPrime0(sz10),
inference(scs_inference,[],[i_0_172,i_0_214]) ).
cnf(i_0_217,plain,
~ isPrime0(sz00),
inference(scs_inference,[],[i_0_173,i_0_215]) ).
cnf(i_0_224,plain,
sdtpldt0(xr,sdtmndt0(xr,xr)) = xr,
inference(scs_inference,[],[i_0_137,i_0_157,i_0_163,i_0_168,i_0_141,i_0_148,i_0_182,i_0_185,i_0_183,i_0_200,i_0_204]) ).
cnf(i_0_226,plain,
aNaturalNumber0(sdtmndt0(xr,xr)),
inference(scs_inference,[],[i_0_137,i_0_157,i_0_163,i_0_168,i_0_141,i_0_148,i_0_182,i_0_185,i_0_183,i_0_200,i_0_204,i_0_210]) ).
cnf(i_0_1319,plain,
sdtpldt0(X1,sdtsldt0(sdtasdt0(xn,xm),xp)) = sdtpldt0(X1,xk),
inference(scs_inference,[],[i_0_220,i_0_187]) ).
cnf(i_0_1320,plain,
sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),X1) = sdtsldt0(xk,X1),
inference(scs_inference,[],[i_0_220,i_0_187,i_0_188]) ).
cnf(i_0_1321,plain,
sdtsldt0(X1,sdtsldt0(sdtasdt0(xn,xm),xp)) = sdtsldt0(X1,xk),
inference(scs_inference,[],[i_0_220,i_0_187,i_0_188,i_0_189]) ).
cnf(i_0_1322,plain,
sdtmndt0(sdtsldt0(sdtasdt0(xn,xm),xp),X1) = sdtmndt0(xk,X1),
inference(scs_inference,[],[i_0_220,i_0_187,i_0_188,i_0_189,i_0_190]) ).
cnf(i_0_1323,plain,
sdtmndt0(X1,sdtsldt0(sdtasdt0(xn,xm),xp)) = sdtmndt0(X1,xk),
inference(scs_inference,[],[i_0_220,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191]) ).
cnf(i_0_1324,plain,
esk3_1(sdtsldt0(sdtasdt0(xn,xm),xp)) = esk3_1(xk),
inference(scs_inference,[],[i_0_220,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191,i_0_192]) ).
cnf(i_0_232,plain,
aNaturalNumber0(xr),
inference(equality_inference,[],[228]) ).
cnf(i_0_233,plain,
sdtlseqdt0(sdtmndt0(xr,xr),sdtmndt0(xr,xr)),
inference(scs_inference,[],[i_0_226,i_0_148]) ).
cnf(i_0_235,plain,
xr = sdtpldt0(xr,sdtmndt0(xr,xr)),
inference(scs_inference,[],[i_0_226,i_0_224,i_0_148,i_0_182]) ).
cnf(i_0_236,plain,
aNaturalNumber0(sdtpldt0(xr,sdtmndt0(xr,xr))),
inference(scs_inference,[],[i_0_168,i_0_226,i_0_224,i_0_148,i_0_182,i_0_195]) ).
cnf(i_0_237,plain,
xp != sz10,
inference(scs_inference,[],[i_0_168,i_0_226,i_0_224,i_0_167,i_0_216,i_0_148,i_0_182,i_0_195,i_0_196]) ).
cnf(i_0_238,plain,
xk != xn,
inference(scs_inference,[],[i_0_158,i_0_168,i_0_226,i_0_224,i_0_167,i_0_216,i_0_163,i_0_148,i_0_182,i_0_195,i_0_196,i_0_200]) ).
cnf(i_0_239,plain,
sdtlseqdt0(xr,sdtpldt0(xr,sdtmndt0(xr,xr))),
inference(scs_inference,[],[i_0_158,i_0_168,i_0_226,i_0_224,i_0_167,i_0_216,i_0_163,i_0_148,i_0_182,i_0_195,i_0_196,i_0_200,i_0_142]) ).
cnf(i_0_241,plain,
aNaturalNumber0(sdtmndt0(sdtmndt0(xr,xr),sdtmndt0(xr,xr))),
inference(scs_inference,[],[i_0_158,i_0_168,i_0_226,i_0_224,i_0_167,i_0_216,i_0_163,i_0_148,i_0_182,i_0_195,i_0_196,i_0_200,i_0_142,i_0_210]) ).
cnf(i_0_243,plain,
sdtpldt0(sdtmndt0(xr,xr),sdtmndt0(sdtmndt0(xr,xr),sdtmndt0(xr,xr))) = sdtmndt0(xr,xr),
inference(scs_inference,[],[i_0_158,i_0_168,i_0_226,i_0_224,i_0_167,i_0_216,i_0_163,i_0_148,i_0_182,i_0_195,i_0_196,i_0_200,i_0_142,i_0_210,i_0_204]) ).
cnf(i_0_245,plain,
aNaturalNumber0(sdtpldt0(sdtmndt0(xr,xr),sdtmndt0(sdtmndt0(xr,xr),sdtmndt0(xr,xr)))),
inference(scs_inference,[],[i_0_158,i_0_168,i_0_218,i_0_226,i_0_224,i_0_167,i_0_216,i_0_163,i_0_148,i_0_182,i_0_195,i_0_196,i_0_200,i_0_142,i_0_210,i_0_204,i_0_118]) ).
cnf(i_0_247,plain,
sdtmndt0(xr,xr) = sdtmndt0(sdtpldt0(xr,sdtmndt0(xr,xr)),xr),
inference(scs_inference,[],[i_0_158,i_0_168,i_0_218,i_0_226,i_0_224,i_0_167,i_0_216,i_0_163,i_0_148,i_0_182,i_0_195,i_0_196,i_0_200,i_0_142,i_0_210,i_0_204,i_0_118,i_0_202]) ).
cnf(i_0_259,plain,
sdtpldt0(sdtmndt0(xr,xr),sdtmndt0(sdtmndt0(xr,xr),sdtmndt0(xr,xr))) = sdtmndt0(xr,xr),
inference(equality_inference,[],[249]) ).
cnf(i_0_260,plain,
sdtpldt0(xr,sdtpldt0(sdtmndt0(xr,xr),sdtmndt0(sdtmndt0(xr,xr),sdtmndt0(xr,xr)))) = xr,
inference(equality_inference,[],[250]) ).
cnf(i_0_262,plain,
sdtlseqdt0(sdtmndt0(sdtmndt0(xr,xr),sdtmndt0(xr,xr)),sdtmndt0(sdtmndt0(xr,xr),sdtmndt0(xr,xr))),
inference(scs_inference,[],[i_0_241,i_0_148]) ).
cnf(i_0_264,plain,
sdtmndt0(xr,xr) = sdtpldt0(sdtmndt0(xr,xr),sdtmndt0(sdtmndt0(xr,xr),sdtmndt0(xr,xr))),
inference(scs_inference,[],[i_0_243,i_0_241,i_0_148,i_0_182]) ).
cnf(i_0_265,plain,
aNaturalNumber0(sdtmndt0(sdtpldt0(xr,sdtmndt0(xr,xr)),xr)),
inference(scs_inference,[],[i_0_226,i_0_243,i_0_241,i_0_247,i_0_148,i_0_182,i_0_195]) ).
cnf(i_0_266,plain,
xr != sz00,
inference(scs_inference,[],[i_0_226,i_0_243,i_0_241,i_0_247,i_0_217,i_0_166,i_0_148,i_0_182,i_0_195,i_0_196]) ).
cnf(i_0_267,plain,
sdtlseqdt0(sdtmndt0(xr,xr),sdtpldt0(sdtmndt0(xr,xr),sdtmndt0(sdtmndt0(xr,xr),sdtmndt0(xr,xr)))),
inference(scs_inference,[],[i_0_226,i_0_245,i_0_243,i_0_241,i_0_247,i_0_217,i_0_166,i_0_148,i_0_182,i_0_195,i_0_196,i_0_142]) ).
cnf(i_0_275,plain,
sdtmndt0(sdtpldt0(xr,sdtmndt0(xr,xr)),xr) = sdtmndt0(xr,xr),
inference(scs_inference,[],[i_0_247,i_0_172,i_0_148,i_0_182]) ).
cnf(i_0_276,plain,
xr != sz10,
inference(scs_inference,[],[i_0_247,i_0_172,i_0_216,i_0_166,i_0_148,i_0_182,i_0_196]) ).
cnf(i_0_277,plain,
sdtpldt0(sz10,sdtmndt0(sz10,sz10)) = sz10,
inference(scs_inference,[],[i_0_247,i_0_172,i_0_216,i_0_166,i_0_148,i_0_182,i_0_196,i_0_204]) ).
cnf(i_0_272,plain,
~ sdtlseqdt0(xp,xn),
inference(equality_inference,[],[269]) ).
cnf(i_0_279,plain,
doDivides0(esk4_1(xr),xr),
inference(scs_inference,[],[i_0_168,i_0_247,i_0_172,i_0_266,i_0_216,i_0_166,i_0_148,i_0_182,i_0_196,i_0_204,i_0_143]) ).
cnf(i_0_281,plain,
sdtlseqdt0(sz10,xr),
inference(scs_inference,[],[i_0_168,i_0_247,i_0_172,i_0_266,i_0_216,i_0_166,i_0_148,i_0_182,i_0_196,i_0_204,i_0_143,i_0_146]) ).
cnf(i_0_283,plain,
sdtlseqdt0(sdtpldt0(xr,sdtmndt0(xr,xr)),xr),
inference(scs_inference,[],[i_0_168,i_0_235,i_0_247,i_0_172,i_0_266,i_0_236,i_0_216,i_0_166,i_0_148,i_0_182,i_0_196,i_0_204,i_0_143,i_0_146,i_0_142]) ).
cnf(i_0_285,plain,
aNaturalNumber0(sdtmndt0(sz10,sz10)),
inference(scs_inference,[],[i_0_168,i_0_235,i_0_247,i_0_172,i_0_266,i_0_236,i_0_216,i_0_166,i_0_148,i_0_182,i_0_196,i_0_204,i_0_143,i_0_146,i_0_142,i_0_210]) ).
cnf(i_0_287,plain,
sdtlseqdt0(sdtpldt0(xr,sdtmndt0(xr,xr)),sdtpldt0(xr,sdtmndt0(xr,xr))),
inference(scs_inference,[],[i_0_168,i_0_235,i_0_247,i_0_239,i_0_172,i_0_266,i_0_236,i_0_216,i_0_166,i_0_148,i_0_182,i_0_196,i_0_204,i_0_143,i_0_146,i_0_142,i_0_210,i_0_106]) ).
cnf(i_0_291,plain,
xp != sdtpldt0(sz10,sdtmndt0(sz10,sz10)),
inference(scs_inference,[],[i_0_168,i_0_235,i_0_247,i_0_239,i_0_172,i_0_237,i_0_266,i_0_236,i_0_216,i_0_166,i_0_148,i_0_182,i_0_196,i_0_204,i_0_143,i_0_146,i_0_142,i_0_210,i_0_106,i_0_159,i_0_183]) ).
cnf(i_0_927,plain,
sdtlseqdt0(sdtpldt0(sdtmndt0(xr,xr),sdtmndt0(sdtmndt0(xr,xr),sdtmndt0(xr,xr))),sdtmndt0(xr,xr)),
inference(scs_inference,[],[i_0_226,i_0_245,i_0_264,i_0_142]) ).
cnf(i_0_297,plain,
~ sdtlseqdt0(xp,xm),
inference(equality_inference,[],[292]) ).
cnf(i_0_298,plain,
aNaturalNumber0(sdtmndt0(sdtmndt0(xr,xr),sdtmndt0(xr,xr))),
inference(equality_inference,[],[293]) ).
cnf(i_0_300,plain,
sdtlseqdt0(sdtmndt0(sz10,sz10),sdtmndt0(sz10,sz10)),
inference(scs_inference,[],[i_0_285,i_0_148]) ).
cnf(i_0_302,plain,
sz10 = sdtpldt0(sz10,sdtmndt0(sz10,sz10)),
inference(scs_inference,[],[i_0_285,i_0_277,i_0_148,i_0_182]) ).
cnf(i_0_303,plain,
xr != sdtpldt0(sz10,sdtmndt0(sz10,sz10)),
inference(scs_inference,[],[i_0_285,i_0_277,i_0_276,i_0_148,i_0_182,i_0_183]) ).
cnf(i_0_304,plain,
xp != sz00,
inference(scs_inference,[],[i_0_285,i_0_277,i_0_276,i_0_167,i_0_217,i_0_148,i_0_182,i_0_183,i_0_196]) ).
cnf(i_0_305,plain,
aNaturalNumber0(sdtpldt0(sz10,sdtmndt0(sz10,sz10))),
inference(scs_inference,[],[i_0_285,i_0_277,i_0_276,i_0_167,i_0_217,i_0_172,i_0_148,i_0_182,i_0_183,i_0_196,i_0_195]) ).
cnf(i_0_306,plain,
sdtpldt0(sdtmndt0(sz10,sz10),sdtmndt0(sdtmndt0(sz10,sz10),sdtmndt0(sz10,sz10))) = sdtmndt0(sz10,sz10),
inference(scs_inference,[],[i_0_285,i_0_277,i_0_276,i_0_167,i_0_217,i_0_172,i_0_148,i_0_182,i_0_183,i_0_196,i_0_195,i_0_204]) ).
cnf(i_0_308,plain,
doDivides0(esk4_1(xp),xp),
inference(scs_inference,[],[i_0_285,i_0_277,i_0_276,i_0_237,i_0_167,i_0_217,i_0_172,i_0_169,i_0_148,i_0_182,i_0_183,i_0_196,i_0_195,i_0_204,i_0_143]) ).
cnf(i_0_310,plain,
sdtlseqdt0(sz10,xp),
inference(scs_inference,[],[i_0_285,i_0_277,i_0_276,i_0_237,i_0_167,i_0_217,i_0_172,i_0_169,i_0_148,i_0_182,i_0_183,i_0_196,i_0_195,i_0_204,i_0_143,i_0_146]) ).
cnf(i_0_312,plain,
sdtlseqdt0(sdtmndt0(sdtpldt0(xr,sdtmndt0(xr,xr)),xr),sdtmndt0(xr,xr)),
inference(scs_inference,[],[i_0_226,i_0_247,i_0_265,i_0_285,i_0_277,i_0_276,i_0_237,i_0_167,i_0_217,i_0_172,i_0_169,i_0_148,i_0_182,i_0_183,i_0_196,i_0_195,i_0_204,i_0_143,i_0_146,i_0_142]) ).
cnf(i_0_314,plain,
aNaturalNumber0(sdtmndt0(sdtmndt0(sz10,sz10),sdtmndt0(sz10,sz10))),
inference(scs_inference,[],[i_0_226,i_0_247,i_0_265,i_0_285,i_0_277,i_0_276,i_0_237,i_0_167,i_0_217,i_0_172,i_0_169,i_0_148,i_0_182,i_0_183,i_0_196,i_0_195,i_0_204,i_0_143,i_0_146,i_0_142,i_0_210]) ).
cnf(i_0_316,plain,
aNaturalNumber0(sdtpldt0(sdtmndt0(sz10,sz10),sdtmndt0(sdtmndt0(sz10,sz10),sdtmndt0(sz10,sz10)))),
inference(scs_inference,[],[i_0_226,i_0_247,i_0_265,i_0_273,i_0_285,i_0_277,i_0_276,i_0_237,i_0_167,i_0_217,i_0_172,i_0_169,i_0_148,i_0_182,i_0_183,i_0_196,i_0_195,i_0_204,i_0_143,i_0_146,i_0_142,i_0_210,i_0_118]) ).
cnf(i_0_318,plain,
~ isPrime0(sdtpldt0(sz10,sdtmndt0(sz10,sz10))),
inference(scs_inference,[],[i_0_226,i_0_247,i_0_265,i_0_273,i_0_285,i_0_277,i_0_276,i_0_237,i_0_167,i_0_217,i_0_172,i_0_169,i_0_148,i_0_182,i_0_183,i_0_196,i_0_195,i_0_204,i_0_143,i_0_146,i_0_142,i_0_210,i_0_118,i_0_159]) ).
cnf(i_0_330,plain,
sdtmndt0(sz10,sz10) = sdtpldt0(sdtmndt0(sz10,sz10),sdtmndt0(sdtmndt0(sz10,sz10),sdtmndt0(sz10,sz10))),
inference(scs_inference,[],[i_0_314,i_0_306,i_0_148,i_0_182]) ).
cnf(i_0_331,plain,
sdtlseqdt0(sz10,sdtpldt0(sz10,sdtmndt0(sz10,sz10))),
inference(scs_inference,[],[i_0_277,i_0_172,i_0_314,i_0_306,i_0_305,i_0_148,i_0_182,i_0_142]) ).
cnf(i_0_333,plain,
sdtmndt0(sz10,sz10) = sdtmndt0(sdtpldt0(sz10,sdtmndt0(sz10,sz10)),sz10),
inference(scs_inference,[],[i_0_285,i_0_277,i_0_172,i_0_314,i_0_306,i_0_305,i_0_148,i_0_182,i_0_142,i_0_202]) ).
cnf(i_0_366,plain,
sdtlseqdt0(sdtpldt0(sz10,sdtmndt0(sz10,sz10)),sdtpldt0(sz10,sdtmndt0(sz10,sz10))),
inference(scs_inference,[],[i_0_305,i_0_148]) ).
cnf(i_0_344,plain,
aNaturalNumber0(sdtmndt0(sdtmndt0(sz10,sz10),sdtmndt0(sz10,sz10))),
inference(equality_inference,[],[335]) ).
cnf(i_0_347,plain,
sdtmndt0(sdtpldt0(sz10,sdtmndt0(sz10,sz10)),sz10) = sdtmndt0(sz10,sz10),
inference(scs_inference,[],[i_0_333,i_0_173,i_0_148,i_0_182]) ).
cnf(i_0_348,plain,
sdtpldt0(sz00,sdtmndt0(sz00,sz00)) = sz00,
inference(scs_inference,[],[i_0_333,i_0_173,i_0_148,i_0_182,i_0_204]) ).
cnf(i_0_352,plain,
aNaturalNumber0(sdtmndt0(sz00,sz00)),
inference(scs_inference,[],[i_0_285,i_0_306,i_0_316,i_0_333,i_0_173,i_0_148,i_0_182,i_0_204,i_0_142,i_0_210]) ).
cnf(i_0_354,plain,
aNaturalNumber0(sdtmndt0(sdtpldt0(sz10,sdtmndt0(sz10,sz10)),sz10)),
inference(scs_inference,[],[i_0_285,i_0_172,i_0_306,i_0_316,i_0_333,i_0_173,i_0_273,i_0_148,i_0_182,i_0_204,i_0_142,i_0_210,i_0_118]) ).
cnf(i_0_358,plain,
xp != sdtpldt0(sz00,sdtmndt0(sz00,sz00)),
inference(scs_inference,[],[i_0_285,i_0_172,i_0_306,i_0_304,i_0_316,i_0_333,i_0_173,i_0_273,i_0_148,i_0_182,i_0_204,i_0_142,i_0_210,i_0_118,i_0_160,i_0_183]) ).
cnf(i_0_359,plain,
sdtmndt0(sz00,sz00) = sz00,
inference(scs_inference,[],[i_0_285,i_0_172,i_0_306,i_0_304,i_0_316,i_0_333,i_0_173,i_0_273,i_0_148,i_0_182,i_0_204,i_0_142,i_0_210,i_0_118,i_0_160,i_0_183,i_0_135]) ).
cnf(i_0_365,plain,
aNaturalNumber0(sz00),
inference(equality_inference,[],[361]) ).
cnf(i_0_368,plain,
sz00 = sdtmndt0(sz00,sz00),
inference(scs_inference,[],[i_0_305,i_0_359,i_0_148,i_0_182]) ).
cnf(i_0_369,plain,
~ isPrime0(sdtmndt0(sz00,sz00)),
inference(scs_inference,[],[i_0_305,i_0_352,i_0_359,i_0_148,i_0_182,i_0_160]) ).
cnf(i_0_371,plain,
xr != sdtmndt0(sz00,sz00),
inference(scs_inference,[],[i_0_266,i_0_305,i_0_352,i_0_359,i_0_148,i_0_182,i_0_160,i_0_183]) ).
cnf(i_0_372,plain,
sdtlseqdt0(sdtpldt0(sz10,sdtmndt0(sz10,sz10)),sz10),
inference(scs_inference,[],[i_0_266,i_0_172,i_0_302,i_0_305,i_0_352,i_0_359,i_0_148,i_0_182,i_0_160,i_0_183,i_0_142]) ).
cnf(i_0_374,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(scs_inference,[],[i_0_266,i_0_172,i_0_302,i_0_305,i_0_173,i_0_345,i_0_352,i_0_359,i_0_148,i_0_182,i_0_160,i_0_183,i_0_142,i_0_110]) ).
cnf(i_0_385,plain,
sdtlseqdt0(sdtmndt0(sz00,sz00),sdtmndt0(sz00,sz00)),
inference(scs_inference,[],[i_0_352,i_0_148]) ).
cnf(i_0_387,plain,
sz00 = sdtpldt0(sz00,sdtmndt0(sz00,sz00)),
inference(scs_inference,[],[i_0_348,i_0_352,i_0_148,i_0_182]) ).
cnf(i_0_845,plain,
sdtlseqdt0(sz00,sdtmndt0(sz00,sz00)),
inference(scs_inference,[],[i_0_173,i_0_352,i_0_359,i_0_142]) ).
cnf(i_0_1082,plain,
xk != sdtpldt0(sz00,sdtmndt0(sz00,sz00)),
inference(scs_inference,[],[i_0_177,i_0_348,i_0_183]) ).
cnf(i_0_1120,plain,
xk != sdtmndt0(sz00,sz00),
inference(scs_inference,[],[i_0_177,i_0_359,i_0_183]) ).
cnf(i_0_1141,plain,
sz10 != sdtpldt0(sz00,sdtmndt0(sz00,sz00)),
inference(scs_inference,[],[i_0_180,i_0_348,i_0_183]) ).
cnf(i_0_1159,plain,
sz10 != sdtmndt0(sz00,sz00),
inference(scs_inference,[],[i_0_180,i_0_359,i_0_183]) ).
cnf(i_0_384,plain,
aNaturalNumber0(xn),
inference(equality_inference,[],[376]) ).
cnf(i_0_388,plain,
xp != sdtmndt0(sz00,sz00),
inference(scs_inference,[],[i_0_167,i_0_348,i_0_369,i_0_352,i_0_148,i_0_182,i_0_196]) ).
cnf(i_0_389,plain,
xp != sdtpldt0(sz00,sz00),
inference(scs_inference,[],[i_0_304,i_0_167,i_0_348,i_0_369,i_0_374,i_0_352,i_0_148,i_0_182,i_0_196,i_0_183]) ).
cnf(i_0_390,plain,
sdtpldt0(sdtmndt0(sz00,sz00),sdtmndt0(sdtmndt0(sz00,sz00),sdtmndt0(sz00,sz00))) = sdtmndt0(sz00,sz00),
inference(scs_inference,[],[i_0_304,i_0_167,i_0_348,i_0_369,i_0_374,i_0_352,i_0_148,i_0_182,i_0_196,i_0_183,i_0_204]) ).
cnf(i_0_392,plain,
aNaturalNumber0(sdtmndt0(sdtmndt0(sz00,sz00),sdtmndt0(sz00,sz00))),
inference(scs_inference,[],[i_0_304,i_0_167,i_0_348,i_0_369,i_0_374,i_0_352,i_0_148,i_0_182,i_0_196,i_0_183,i_0_204,i_0_210]) ).
cnf(i_0_394,plain,
sdtlseqdt0(sdtmndt0(xr,xr),sdtmndt0(sdtpldt0(xr,sdtmndt0(xr,xr)),xr)),
inference(scs_inference,[],[i_0_226,i_0_304,i_0_167,i_0_348,i_0_265,i_0_275,i_0_369,i_0_374,i_0_352,i_0_148,i_0_182,i_0_196,i_0_183,i_0_204,i_0_210,i_0_142]) ).
cnf(i_0_396,plain,
aNaturalNumber0(sdtpldt0(sdtmndt0(sz00,sz00),sdtmndt0(sdtmndt0(sz00,sz00),sdtmndt0(sz00,sz00)))),
inference(scs_inference,[],[i_0_226,i_0_304,i_0_167,i_0_173,i_0_348,i_0_265,i_0_275,i_0_369,i_0_374,i_0_345,i_0_352,i_0_148,i_0_182,i_0_196,i_0_183,i_0_204,i_0_210,i_0_142,i_0_118]) ).
cnf(i_0_398,plain,
aNaturalNumber0(sdtpldt0(sz00,sdtmndt0(sz00,sz00))),
inference(scs_inference,[],[i_0_226,i_0_304,i_0_167,i_0_173,i_0_348,i_0_265,i_0_275,i_0_369,i_0_374,i_0_345,i_0_352,i_0_148,i_0_182,i_0_196,i_0_183,i_0_204,i_0_210,i_0_142,i_0_118,i_0_361]) ).
cnf(i_0_399,plain,
~ isPrime0(sdtpldt0(sz00,sdtmndt0(sz00,sz00))),
inference(scs_inference,[],[i_0_226,i_0_304,i_0_167,i_0_173,i_0_348,i_0_265,i_0_275,i_0_369,i_0_374,i_0_345,i_0_352,i_0_148,i_0_182,i_0_196,i_0_183,i_0_204,i_0_210,i_0_142,i_0_118,i_0_361,i_0_160]) ).
cnf(i_0_1088,plain,
xk != sdtpldt0(sz00,sz00),
inference(scs_inference,[],[i_0_177,i_0_374,i_0_183]) ).
cnf(i_0_1147,plain,
sz10 != sdtpldt0(sz00,sz00),
inference(scs_inference,[],[i_0_180,i_0_374,i_0_183]) ).
cnf(i_0_409,plain,
aNaturalNumber0(xm),
inference(equality_inference,[],[401]) ).
cnf(i_0_412,plain,
sz00 = sdtpldt0(sz00,sz00),
inference(scs_inference,[],[i_0_374,i_0_392,i_0_148,i_0_182]) ).
cnf(i_0_413,plain,
xp != sdtpldt0(sdtmndt0(sz00,sz00),sdtmndt0(sdtmndt0(sz00,sz00),sdtmndt0(sz00,sz00))),
inference(scs_inference,[],[i_0_374,i_0_392,i_0_390,i_0_388,i_0_148,i_0_182,i_0_183]) ).
cnf(i_0_414,plain,
sdtlseqdt0(sz00,sdtpldt0(sz00,sdtmndt0(sz00,sz00))),
inference(scs_inference,[],[i_0_348,i_0_173,i_0_374,i_0_392,i_0_390,i_0_398,i_0_388,i_0_148,i_0_182,i_0_183,i_0_142]) ).
cnf(i_0_416,plain,
sdtmndt0(sz00,sz00) = sdtmndt0(sdtpldt0(sz00,sdtmndt0(sz00,sz00)),sz00),
inference(scs_inference,[],[i_0_348,i_0_173,i_0_374,i_0_352,i_0_392,i_0_390,i_0_398,i_0_388,i_0_148,i_0_182,i_0_183,i_0_142,i_0_202]) ).
cnf(i_0_418,plain,
aNaturalNumber0(sdtpldt0(sz00,sz00)),
inference(scs_inference,[],[i_0_348,i_0_173,i_0_374,i_0_352,i_0_392,i_0_390,i_0_398,i_0_388,i_0_148,i_0_182,i_0_183,i_0_142,i_0_202,i_0_361]) ).
cnf(i_0_419,plain,
~ isPrime0(sdtpldt0(sz00,sz00)),
inference(scs_inference,[],[i_0_348,i_0_173,i_0_374,i_0_352,i_0_392,i_0_390,i_0_398,i_0_388,i_0_148,i_0_182,i_0_183,i_0_142,i_0_202,i_0_361,i_0_160]) ).
cnf(i_0_509,plain,
sdtlseqdt0(sdtpldt0(sz00,sdtmndt0(sz00,sz00)),sdtpldt0(sz00,sdtmndt0(sz00,sz00))),
inference(scs_inference,[],[i_0_398,i_0_148]) ).
cnf(i_0_1123,plain,
xk != sdtpldt0(sdtmndt0(sz00,sz00),sdtmndt0(sdtmndt0(sz00,sz00),sdtmndt0(sz00,sz00))),
inference(scs_inference,[],[i_0_390,i_0_1120,i_0_183]) ).
cnf(i_0_1162,plain,
sz10 != sdtpldt0(sdtmndt0(sz00,sz00),sdtmndt0(sdtmndt0(sz00,sz00),sdtmndt0(sz00,sz00))),
inference(scs_inference,[],[i_0_390,i_0_1159,i_0_183]) ).
cnf(i_0_431,plain,
aNaturalNumber0(sdtmndt0(sdtmndt0(sz00,sz00),sdtmndt0(sz00,sz00))),
inference(equality_inference,[],[421]) ).
cnf(i_0_432,plain,
sdtlseqdt0(sdtpldt0(sz00,sz00),sdtpldt0(sz00,sz00)),
inference(scs_inference,[],[i_0_418,i_0_148]) ).
cnf(i_0_434,plain,
sdtmndt0(sz00,sz00) = sdtpldt0(sdtmndt0(sz00,sz00),sdtmndt0(sdtmndt0(sz00,sz00),sdtmndt0(sz00,sz00))),
inference(scs_inference,[],[i_0_390,i_0_418,i_0_148,i_0_182]) ).
cnf(i_0_435,plain,
xr != sdtpldt0(sz00,sz00),
inference(scs_inference,[],[i_0_166,i_0_390,i_0_418,i_0_419,i_0_148,i_0_182,i_0_196]) ).
cnf(i_0_436,plain,
xr != sdtpldt0(sz00,sdtmndt0(sz00,sz00)),
inference(scs_inference,[],[i_0_266,i_0_348,i_0_166,i_0_390,i_0_418,i_0_419,i_0_148,i_0_182,i_0_196,i_0_183]) ).
cnf(i_0_437,plain,
aNaturalNumber0(sdtmndt0(sdtpldt0(sz00,sdtmndt0(sz00,sz00)),sz00)),
inference(scs_inference,[],[i_0_266,i_0_348,i_0_166,i_0_352,i_0_390,i_0_418,i_0_419,i_0_416,i_0_148,i_0_182,i_0_196,i_0_183,i_0_195]) ).
cnf(i_0_438,plain,
sdtpldt0(sdtpldt0(sz00,sz00),sdtmndt0(sdtpldt0(sz00,sz00),sdtpldt0(sz00,sz00))) = sdtpldt0(sz00,sz00),
inference(scs_inference,[],[i_0_266,i_0_348,i_0_166,i_0_352,i_0_390,i_0_418,i_0_419,i_0_416,i_0_148,i_0_182,i_0_196,i_0_183,i_0_195,i_0_204]) ).
cnf(i_0_440,plain,
sdtlseqdt0(sz00,sdtpldt0(sz00,sz00)),
inference(scs_inference,[],[i_0_266,i_0_348,i_0_173,i_0_166,i_0_352,i_0_390,i_0_418,i_0_419,i_0_416,i_0_148,i_0_182,i_0_196,i_0_183,i_0_195,i_0_204,i_0_211]) ).
cnf(i_0_442,plain,
aNaturalNumber0(sdtmndt0(sdtpldt0(sz00,sz00),sdtpldt0(sz00,sz00))),
inference(scs_inference,[],[i_0_266,i_0_348,i_0_173,i_0_166,i_0_352,i_0_390,i_0_418,i_0_419,i_0_416,i_0_148,i_0_182,i_0_196,i_0_183,i_0_195,i_0_204,i_0_211,i_0_210]) ).
cnf(i_0_444,plain,
sdtlseqdt0(sdtmndt0(sz00,sz00),sz00),
inference(scs_inference,[],[i_0_266,i_0_348,i_0_173,i_0_166,i_0_352,i_0_368,i_0_390,i_0_418,i_0_419,i_0_416,i_0_148,i_0_182,i_0_196,i_0_183,i_0_195,i_0_204,i_0_211,i_0_210,i_0_142]) ).
cnf(i_0_446,plain,
sz00 = sdtmndt0(sdtpldt0(sz00,sz00),sz00),
inference(scs_inference,[],[i_0_266,i_0_348,i_0_173,i_0_166,i_0_352,i_0_368,i_0_390,i_0_418,i_0_419,i_0_416,i_0_148,i_0_182,i_0_196,i_0_183,i_0_195,i_0_204,i_0_211,i_0_210,i_0_142,i_0_202]) ).
cnf(i_0_448,plain,
aNaturalNumber0(sdtmndt0(sdtpldt0(sz00,sz00),sz00)),
inference(scs_inference,[],[i_0_266,i_0_348,i_0_173,i_0_166,i_0_352,i_0_368,i_0_390,i_0_418,i_0_419,i_0_416,i_0_148,i_0_182,i_0_196,i_0_183,i_0_195,i_0_204,i_0_211,i_0_210,i_0_142,i_0_202,i_0_361]) ).
cnf(i_0_463,plain,
sdtmndt0(sdtpldt0(sz00,sdtmndt0(sz00,sz00)),sz00) = sdtmndt0(sz00,sz00),
inference(scs_inference,[],[i_0_416,i_0_442,i_0_148,i_0_182]) ).
cnf(c_0_318,plain,
( X1 = sdtasdt0(X2,X3)
| X2 = sz00
| X3 != sdtsldt0(X1,X2)
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
i_0_109 ).
cnf(c_0_319,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
i_0_141 ).
cnf(c_0_320,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
i_0_131 ).
cnf(c_0_321,hypothesis,
aNaturalNumber0(xn),
i_0_171 ).
cnf(c_0_322,hypothesis,
aNaturalNumber0(xm),
i_0_170 ).
cnf(c_0_323,hypothesis,
doDivides0(xp,sdtasdt0(xn,xm)),
i_0_140 ).
cnf(c_0_324,plain,
( sdtasdt0(X1,sdtsldt0(X2,X1)) = X2
| X1 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X1,X2) ),
inference(er,[status(thm)],[c_0_318]) ).
cnf(c_0_325,hypothesis,
sdtsldt0(sdtasdt0(xm,xn),xp) = xk,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_319,c_0_320]),c_0_321]),c_0_322])]) ).
cnf(c_0_326,hypothesis,
aNaturalNumber0(xp),
i_0_169 ).
cnf(c_0_327,hypothesis,
doDivides0(xp,sdtasdt0(xm,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_323,c_0_320]),c_0_321]),c_0_322])]) ).
cnf(c_0_328,plain,
xp != sz00,
i_0_304 ).
cnf(c_0_329,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
i_0_119 ).
cnf(c_0_330,hypothesis,
sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
i_0_124 ).
cnf(c_0_331,hypothesis,
sdtasdt0(xn,xm) != sdtasdt0(xp,xm),
i_0_138 ).
cnf(c_0_332,hypothesis,
( sdtasdt0(xm,xn) = sdtasdt0(xp,xk)
| ~ aNaturalNumber0(sdtasdt0(xm,xn)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_324,c_0_325]),c_0_326]),c_0_327])]),c_0_328]) ).
cnf(c_0_333,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
i_0_128 ).
cnf(c_0_334,hypothesis,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_329,c_0_330]),c_0_331]) ).
cnf(c_0_335,plain,
sdtasdt0(xm,xn) = sdtasdt0(xp,xk),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_332,c_0_333]),c_0_321]),c_0_322])]) ).
cnf(c_0_336,hypothesis,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xm,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_334,c_0_320]),c_0_321]),c_0_322])]) ).
cnf(c_0_337,hypothesis,
sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)),
i_0_123 ).
cnf(c_0_338,plain,
aNaturalNumber0(sdtasdt0(xp,xk)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_333,c_0_335]),c_0_321]),c_0_322])]) ).
cnf(c_0_339,hypothesis,
~ aNaturalNumber0(sdtasdt0(xp,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_336,c_0_335]),c_0_337]),c_0_335])]),c_0_338])]) ).
cnf(c_0_340,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_339,c_0_333]),c_0_322]),c_0_326])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM504+1 : 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
% 0.17/0.33 % Computer : n018.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue May 5 00:39:47 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 % start to proof: theBenchmark
% 41.91/40.25 % Version : CSE_E---1.7
% 41.91/40.25 % Problem : theBenchmark.p
% 41.91/40.25 % SZS status Theorem for theBenchmark.p
% 41.91/40.25 % SZS output start CNFRefutation
% See solution above
% 49.84/48.20 % Total time : 39.885s
%------------------------------------------------------------------------------