%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG125+4 : 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 : n004.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 05:05:26 PM UTC 2026
% Result : Theorem 0.34s 5.61s
% Output : CNFRefutation 0.34s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 86)
% Comments :
%------------------------------------------------------------------------------
fof(m__2273,hypothesis,
( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = xu )
& aElementOf0(xu,xI)
& xu != sz00
& ! [X1] :
( ( ( ? [X2,X3] :
( aElementOf0(X2,slsdtgt0(xa))
& aElementOf0(X3,slsdtgt0(xb))
& sdtpldt0(X2,X3) = X1 )
| aElementOf0(X1,xI) )
& X1 != sz00 )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2273) ).
fof(mDefSSum,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aSet0(X2) )
=> ! [X3] :
( X3 = sdtpldt1(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ? [X5,X6] :
( aElementOf0(X5,X1)
& aElementOf0(X6,X2)
& sdtpldt0(X5,X6) = X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSSum) ).
fof(mChineseRemainder,axiom,
! [X1,X2] :
( ( aIdeal0(X1)
& aIdeal0(X2) )
=> ( ! [X3] :
( aElement0(X3)
=> aElementOf0(X3,sdtpldt1(X1,X2)) )
=> ! [X3,X4] :
( ( aElement0(X3)
& aElement0(X4) )
=> ? [X5] :
( aElement0(X5)
& sdteqdtlpzmzozddtrp0(X5,X3,X1)
& sdteqdtlpzmzozddtrp0(X5,X4,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mChineseRemainder) ).
fof(mDefSInt,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aSet0(X2) )
=> ! [X3] :
( X3 = sdtasasdt0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aElementOf0(X4,X1)
& aElementOf0(X4,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSInt) ).
fof(mDefGCD,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> ! [X3] :
( aGcdOfAnd0(X3,X1,X2)
<=> ( aDivisorOf0(X3,X1)
& aDivisorOf0(X3,X2)
& ! [X4] :
( ( aDivisorOf0(X4,X1)
& aDivisorOf0(X4,X2) )
=> doDivides0(X4,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefGCD) ).
fof(mDefIdeal,axiom,
! [X1] :
( aIdeal0(X1)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> ( ! [X3] :
( aElementOf0(X3,X1)
=> aElementOf0(sdtpldt0(X2,X3),X1) )
& ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X2),X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).
fof(mDefMod,axiom,
! [X1,X2,X3] :
( ( aElement0(X1)
& aElement0(X2)
& aIdeal0(X3) )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
<=> aElementOf0(sdtpldt0(X1,smndt0(X2)),X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefMod) ).
fof(mDefPrIdeal,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( X2 = slsdtgt0(X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4] :
( aElement0(X4)
& sdtasdt0(X1,X4) = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrIdeal) ).
fof(mSetEq,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aSet0(X2) )
=> ( ( ! [X3] :
( aElementOf0(X3,X1)
=> aElementOf0(X3,X2) )
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) ) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSetEq) ).
fof(mDivision,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2)
& X2 != sz00 )
=> ? [X3,X4] :
( aElement0(X3)
& aElement0(X4)
& X1 = sdtpldt0(sdtasdt0(X3,X2),X4)
& ( X4 != sz00
=> iLess0(sbrdtbr0(X4),sbrdtbr0(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivision) ).
fof(mAMDistr,axiom,
! [X1,X2,X3] :
( ( aElement0(X1)
& aElement0(X2)
& aElement0(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(mDefRel,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> ( misRelativelyPrime0(X1,X2)
<=> aGcdOfAnd0(sz10,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefRel) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aElement0(X1)
& aElement0(X2)
& aElement0(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] :
( ( aElement0(X1)
& aElement0(X2)
& aElement0(X3) )
=> sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(m__2174,hypothesis,
( aSet0(xI)
& ! [X1] :
( aElementOf0(X1,xI)
=> ( ! [X2] :
( aElementOf0(X2,xI)
=> aElementOf0(sdtpldt0(X1,X2),xI) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),xI) ) ) )
& aIdeal0(xI)
& ! [X1] :
( aElementOf0(X1,slsdtgt0(xa))
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(xa,X2) = X1 ) )
& ! [X1] :
( aElementOf0(X1,slsdtgt0(xb))
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(xb,X2) = X1 ) )
& ! [X1] :
( aElementOf0(X1,xI)
<=> ? [X2,X3] :
( aElementOf0(X2,slsdtgt0(xa))
& aElementOf0(X3,slsdtgt0(xb))
& sdtpldt0(X2,X3) = X1 ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).
fof(m__2129,hypothesis,
( aElement0(xc)
& ? [X1] :
( aElement0(X1)
& sdtasdt0(xc,X1) = xa )
& doDivides0(xc,xa)
& aDivisorOf0(xc,xa)
& aElement0(xc)
& ? [X1] :
( aElement0(X1)
& sdtasdt0(xc,X1) = xb )
& doDivides0(xc,xb)
& aDivisorOf0(xc,xb)
& ! [X1] :
( ( ( ( aElement0(X1)
& ( ? [X2] :
( aElement0(X2)
& sdtasdt0(X1,X2) = xa )
| doDivides0(X1,xa) ) )
| aDivisorOf0(X1,xa) )
& ( ? [X2] :
( aElement0(X2)
& sdtasdt0(X1,X2) = xb )
| doDivides0(X1,xb)
| aDivisorOf0(X1,xb) ) )
=> ( ? [X2] :
( aElement0(X2)
& sdtasdt0(X1,X2) = xc )
& doDivides0(X1,xc) ) )
& aGcdOfAnd0(xc,xa,xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2129) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(X1,X3) = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(m__2383,hypothesis,
~ ( ( ? [X1] :
( aElement0(X1)
& sdtasdt0(xu,X1) = xa )
| doDivides0(xu,xa)
| aDivisorOf0(xu,xa) )
& ( ? [X1] :
( aElement0(X1)
& sdtasdt0(xu,X1) = xb )
| doDivides0(xu,xb)
| aDivisorOf0(xu,xb) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2383) ).
fof(m__2416,hypothesis,
? [X1,X2] :
( aElement0(X1)
& aElement0(X2)
& xu = sdtpldt0(sdtasdt0(xa,X1),sdtasdt0(xb,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2416) ).
fof(mDefDvs,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( aDivisorOf0(X2,X1)
<=> ( aElement0(X2)
& doDivides0(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDvs) ).
fof(m__2228,hypothesis,
? [X1] :
( ! [X2] :
( aElementOf0(X2,slsdtgt0(xa))
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(xa,X3) = X2 ) )
& ! [X2] :
( aElementOf0(X2,slsdtgt0(xb))
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(xb,X3) = X2 ) )
& ? [X2,X3] :
( aElementOf0(X2,slsdtgt0(xa))
& aElementOf0(X3,slsdtgt0(xb))
& sdtpldt0(X2,X3) = X1 )
& aElementOf0(X1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& X1 != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2228) ).
fof(mIdeInt,axiom,
! [X1,X2] :
( ( aIdeal0(X1)
& aIdeal0(X2) )
=> aIdeal0(sdtasasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIdeInt) ).
fof(mIdeSum,axiom,
! [X1,X2] :
( ( aIdeal0(X1)
& aIdeal0(X2) )
=> aIdeal0(sdtpldt1(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIdeSum) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(mCancel,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCancel) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(mMulMnOne,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
& smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulMnOne) ).
fof(mAddInvr,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddInvr) ).
fof(mMulUnit,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulUnit) ).
fof(mAddZero,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(mMulZero,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
fof(mEucSort,axiom,
! [X1] :
( ( aElement0(X1)
& X1 != sz00 )
=> aNaturalNumber0(sbrdtbr0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEucSort) ).
fof(mPrIdeal,axiom,
! [X1] :
( aElement0(X1)
=> aIdeal0(slsdtgt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPrIdeal) ).
fof(mSortsU,axiom,
! [X1] :
( aElement0(X1)
=> aElement0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsU) ).
fof(m__2203,hypothesis,
( ? [X1] :
( aElement0(X1)
& sdtasdt0(xa,X1) = sz00 )
& aElementOf0(sz00,slsdtgt0(xa))
& ? [X1] :
( aElement0(X1)
& sdtasdt0(xa,X1) = xa )
& aElementOf0(xa,slsdtgt0(xa))
& ? [X1] :
( aElement0(X1)
& sdtasdt0(xb,X1) = sz00 )
& aElementOf0(sz00,slsdtgt0(xb))
& ? [X1] :
( aElement0(X1)
& sdtasdt0(xb,X1) = xb )
& aElementOf0(xb,slsdtgt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2203) ).
fof(m__2612,hypothesis,
~ ~ ( ? [X1] :
( aElement0(X1)
& sdtasdt0(xu,X1) = xb )
& doDivides0(xu,xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2612) ).
fof(m__2479,hypothesis,
~ ~ ( ? [X1] :
( aElement0(X1)
& sdtasdt0(xu,X1) = xa )
& doDivides0(xu,xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2479) ).
fof(m__2091,hypothesis,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).
fof(mSortsC_01,axiom,
aElement0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(mSortsC,axiom,
aElement0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(m__2110,hypothesis,
( xa != sz00
| xb != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2110) ).
fof(mUnNeZr,axiom,
sz10 != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mUnNeZr) ).
fof(i_0_45,hypothesis,
( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = xu )
& aElementOf0(xu,xI)
& xu != sz00
& ! [X1] :
( ( ( ? [X2,X3] :
( aElementOf0(X2,slsdtgt0(xa))
& aElementOf0(X3,slsdtgt0(xb))
& sdtpldt0(X2,X3) = X1 )
| aElementOf0(X1,xI) )
& X1 != sz00 )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
inference(fof_simplification,[status(thm)],[m__2273]) ).
fof(i_0_46,plain,
! [X160,X161,X162,X163,X166,X167,X168,X169,X171,X172] :
( ( aSet0(X162)
| X162 != sdtpldt1(X160,X161)
| ~ aSet0(X160)
| ~ aSet0(X161) )
& ( aElementOf0(esk3_4(X160,X161,X162,X163),X160)
| ~ aElementOf0(X163,X162)
| X162 != sdtpldt1(X160,X161)
| ~ aSet0(X160)
| ~ aSet0(X161) )
& ( aElementOf0(esk4_4(X160,X161,X162,X163),X161)
| ~ aElementOf0(X163,X162)
| X162 != sdtpldt1(X160,X161)
| ~ aSet0(X160)
| ~ aSet0(X161) )
& ( sdtpldt0(esk3_4(X160,X161,X162,X163),esk4_4(X160,X161,X162,X163)) = X163
| ~ aElementOf0(X163,X162)
| X162 != sdtpldt1(X160,X161)
| ~ aSet0(X160)
| ~ aSet0(X161) )
& ( ~ aElementOf0(X167,X160)
| ~ aElementOf0(X168,X161)
| sdtpldt0(X167,X168) != X166
| aElementOf0(X166,X162)
| X162 != sdtpldt1(X160,X161)
| ~ aSet0(X160)
| ~ aSet0(X161) )
& ( ~ aElementOf0(esk5_3(X160,X161,X169),X169)
| ~ aElementOf0(X171,X160)
| ~ aElementOf0(X172,X161)
| sdtpldt0(X171,X172) != esk5_3(X160,X161,X169)
| ~ aSet0(X169)
| X169 = sdtpldt1(X160,X161)
| ~ aSet0(X160)
| ~ aSet0(X161) )
& ( aElementOf0(esk6_3(X160,X161,X169),X160)
| aElementOf0(esk5_3(X160,X161,X169),X169)
| ~ aSet0(X169)
| X169 = sdtpldt1(X160,X161)
| ~ aSet0(X160)
| ~ aSet0(X161) )
& ( aElementOf0(esk7_3(X160,X161,X169),X161)
| aElementOf0(esk5_3(X160,X161,X169),X169)
| ~ aSet0(X169)
| X169 = sdtpldt1(X160,X161)
| ~ aSet0(X160)
| ~ aSet0(X161) )
& ( sdtpldt0(esk6_3(X160,X161,X169),esk7_3(X160,X161,X169)) = esk5_3(X160,X161,X169)
| aElementOf0(esk5_3(X160,X161,X169),X169)
| ~ aSet0(X169)
| X169 = sdtpldt1(X160,X161)
| ~ aSet0(X160)
| ~ aSet0(X161) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefSSum])])])])])]) ).
fof(i_0_47,plain,
! [X197,X198,X200,X201] :
( ( aElement0(esk13_4(X197,X198,X200,X201))
| ~ aElement0(X200)
| ~ aElement0(X201)
| aElement0(esk12_2(X197,X198))
| ~ aIdeal0(X197)
| ~ aIdeal0(X198) )
& ( sdteqdtlpzmzozddtrp0(esk13_4(X197,X198,X200,X201),X200,X197)
| ~ aElement0(X200)
| ~ aElement0(X201)
| aElement0(esk12_2(X197,X198))
| ~ aIdeal0(X197)
| ~ aIdeal0(X198) )
& ( sdteqdtlpzmzozddtrp0(esk13_4(X197,X198,X200,X201),X201,X198)
| ~ aElement0(X200)
| ~ aElement0(X201)
| aElement0(esk12_2(X197,X198))
| ~ aIdeal0(X197)
| ~ aIdeal0(X198) )
& ( aElement0(esk13_4(X197,X198,X200,X201))
| ~ aElement0(X200)
| ~ aElement0(X201)
| ~ aElementOf0(esk12_2(X197,X198),sdtpldt1(X197,X198))
| ~ aIdeal0(X197)
| ~ aIdeal0(X198) )
& ( sdteqdtlpzmzozddtrp0(esk13_4(X197,X198,X200,X201),X200,X197)
| ~ aElement0(X200)
| ~ aElement0(X201)
| ~ aElementOf0(esk12_2(X197,X198),sdtpldt1(X197,X198))
| ~ aIdeal0(X197)
| ~ aIdeal0(X198) )
& ( sdteqdtlpzmzozddtrp0(esk13_4(X197,X198,X200,X201),X201,X198)
| ~ aElement0(X200)
| ~ aElement0(X201)
| ~ aElementOf0(esk12_2(X197,X198),sdtpldt1(X197,X198))
| ~ aIdeal0(X197)
| ~ aIdeal0(X198) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mChineseRemainder])])])])]) ).
fof(i_0_48,plain,
! [X175,X176,X177,X178,X179,X180] :
( ( aSet0(X177)
| X177 != sdtasasdt0(X175,X176)
| ~ aSet0(X175)
| ~ aSet0(X176) )
& ( aElementOf0(X178,X175)
| ~ aElementOf0(X178,X177)
| X177 != sdtasasdt0(X175,X176)
| ~ aSet0(X175)
| ~ aSet0(X176) )
& ( aElementOf0(X178,X176)
| ~ aElementOf0(X178,X177)
| X177 != sdtasasdt0(X175,X176)
| ~ aSet0(X175)
| ~ aSet0(X176) )
& ( ~ aElementOf0(X179,X175)
| ~ aElementOf0(X179,X176)
| aElementOf0(X179,X177)
| X177 != sdtasasdt0(X175,X176)
| ~ aSet0(X175)
| ~ aSet0(X176) )
& ( ~ aElementOf0(esk8_3(X175,X176,X180),X180)
| ~ aElementOf0(esk8_3(X175,X176,X180),X175)
| ~ aElementOf0(esk8_3(X175,X176,X180),X176)
| ~ aSet0(X180)
| X180 = sdtasasdt0(X175,X176)
| ~ aSet0(X175)
| ~ aSet0(X176) )
& ( aElementOf0(esk8_3(X175,X176,X180),X175)
| aElementOf0(esk8_3(X175,X176,X180),X180)
| ~ aSet0(X180)
| X180 = sdtasasdt0(X175,X176)
| ~ aSet0(X175)
| ~ aSet0(X176) )
& ( aElementOf0(esk8_3(X175,X176,X180),X176)
| aElementOf0(esk8_3(X175,X176,X180),X180)
| ~ aSet0(X180)
| X180 = sdtasasdt0(X175,X176)
| ~ aSet0(X175)
| ~ aSet0(X176) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefSInt])])])])])]) ).
fof(i_0_49,plain,
! [X214,X215,X216,X217,X218] :
( ( aDivisorOf0(X216,X214)
| ~ aGcdOfAnd0(X216,X214,X215)
| ~ aElement0(X214)
| ~ aElement0(X215) )
& ( aDivisorOf0(X216,X215)
| ~ aGcdOfAnd0(X216,X214,X215)
| ~ aElement0(X214)
| ~ aElement0(X215) )
& ( ~ aDivisorOf0(X217,X214)
| ~ aDivisorOf0(X217,X215)
| doDivides0(X217,X216)
| ~ aGcdOfAnd0(X216,X214,X215)
| ~ aElement0(X214)
| ~ aElement0(X215) )
& ( aDivisorOf0(esk17_3(X214,X215,X218),X214)
| ~ aDivisorOf0(X218,X214)
| ~ aDivisorOf0(X218,X215)
| aGcdOfAnd0(X218,X214,X215)
| ~ aElement0(X214)
| ~ aElement0(X215) )
& ( aDivisorOf0(esk17_3(X214,X215,X218),X215)
| ~ aDivisorOf0(X218,X214)
| ~ aDivisorOf0(X218,X215)
| aGcdOfAnd0(X218,X214,X215)
| ~ aElement0(X214)
| ~ aElement0(X215) )
& ( ~ doDivides0(esk17_3(X214,X215,X218),X218)
| ~ aDivisorOf0(X218,X214)
| ~ aDivisorOf0(X218,X215)
| aGcdOfAnd0(X218,X214,X215)
| ~ aElement0(X214)
| ~ aElement0(X215) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefGCD])])])])])]) ).
fof(i_0_50,plain,
! [X182,X183,X184,X185,X186] :
( ( aSet0(X182)
| ~ aIdeal0(X182) )
& ( ~ aElementOf0(X184,X182)
| aElementOf0(sdtpldt0(X183,X184),X182)
| ~ aElementOf0(X183,X182)
| ~ aIdeal0(X182) )
& ( ~ aElement0(X185)
| aElementOf0(sdtasdt0(X185,X183),X182)
| ~ aElementOf0(X183,X182)
| ~ aIdeal0(X182) )
& ( aElementOf0(esk9_1(X186),X186)
| ~ aSet0(X186)
| aIdeal0(X186) )
& ( aElement0(esk11_1(X186))
| aElementOf0(esk10_1(X186),X186)
| ~ aSet0(X186)
| aIdeal0(X186) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X186),esk9_1(X186)),X186)
| aElementOf0(esk10_1(X186),X186)
| ~ aSet0(X186)
| aIdeal0(X186) )
& ( aElement0(esk11_1(X186))
| ~ aElementOf0(sdtpldt0(esk9_1(X186),esk10_1(X186)),X186)
| ~ aSet0(X186)
| aIdeal0(X186) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X186),esk9_1(X186)),X186)
| ~ aElementOf0(sdtpldt0(esk9_1(X186),esk10_1(X186)),X186)
| ~ aSet0(X186)
| aIdeal0(X186) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefIdeal])])])])])]) ).
fof(i_0_51,plain,
! [X194,X195,X196] :
( ( ~ sdteqdtlpzmzozddtrp0(X194,X195,X196)
| aElementOf0(sdtpldt0(X194,smndt0(X195)),X196)
| ~ aElement0(X194)
| ~ aElement0(X195)
| ~ aIdeal0(X196) )
& ( ~ aElementOf0(sdtpldt0(X194,smndt0(X195)),X196)
| sdteqdtlpzmzozddtrp0(X194,X195,X196)
| ~ aElement0(X194)
| ~ aElement0(X195)
| ~ aIdeal0(X196) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefMod])])]) ).
fof(i_0_52,plain,
! [X222,X223,X224,X226,X227,X228,X230] :
( ( aSet0(X223)
| X223 != slsdtgt0(X222)
| ~ aElement0(X222) )
& ( aElement0(esk18_3(X222,X223,X224))
| ~ aElementOf0(X224,X223)
| X223 != slsdtgt0(X222)
| ~ aElement0(X222) )
& ( sdtasdt0(X222,esk18_3(X222,X223,X224)) = X224
| ~ aElementOf0(X224,X223)
| X223 != slsdtgt0(X222)
| ~ aElement0(X222) )
& ( ~ aElement0(X227)
| sdtasdt0(X222,X227) != X226
| aElementOf0(X226,X223)
| X223 != slsdtgt0(X222)
| ~ aElement0(X222) )
& ( ~ aElementOf0(esk19_2(X222,X228),X228)
| ~ aElement0(X230)
| sdtasdt0(X222,X230) != esk19_2(X222,X228)
| ~ aSet0(X228)
| X228 = slsdtgt0(X222)
| ~ aElement0(X222) )
& ( aElement0(esk20_2(X222,X228))
| aElementOf0(esk19_2(X222,X228),X228)
| ~ aSet0(X228)
| X228 = slsdtgt0(X222)
| ~ aElement0(X222) )
& ( sdtasdt0(X222,esk20_2(X222,X228)) = esk19_2(X222,X228)
| aElementOf0(esk19_2(X222,X228),X228)
| ~ aSet0(X228)
| X228 = slsdtgt0(X222)
| ~ aElement0(X222) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefPrIdeal])])])])])]) ).
fof(i_0_53,plain,
! [X156,X157] :
( ( aElementOf0(esk2_2(X156,X157),X157)
| aElementOf0(esk1_2(X156,X157),X156)
| X156 = X157
| ~ aSet0(X156)
| ~ aSet0(X157) )
& ( ~ aElementOf0(esk2_2(X156,X157),X156)
| aElementOf0(esk1_2(X156,X157),X156)
| X156 = X157
| ~ aSet0(X156)
| ~ aSet0(X157) )
& ( aElementOf0(esk2_2(X156,X157),X157)
| ~ aElementOf0(esk1_2(X156,X157),X157)
| X156 = X157
| ~ aSet0(X156)
| ~ aSet0(X157) )
& ( ~ aElementOf0(esk2_2(X156,X157),X156)
| ~ aElementOf0(esk1_2(X156,X157),X157)
| X156 = X157
| ~ aSet0(X156)
| ~ aSet0(X157) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSetEq])])])]) ).
fof(i_0_54,plain,
! [X204,X205] :
( ( aElement0(esk14_2(X204,X205))
| ~ aElement0(X204)
| ~ aElement0(X205)
| X205 = sz00 )
& ( aElement0(esk15_2(X204,X205))
| ~ aElement0(X204)
| ~ aElement0(X205)
| X205 = sz00 )
& ( X204 = sdtpldt0(sdtasdt0(esk14_2(X204,X205),X205),esk15_2(X204,X205))
| ~ aElement0(X204)
| ~ aElement0(X205)
| X205 = sz00 )
& ( esk15_2(X204,X205) = sz00
| iLess0(sbrdtbr0(esk15_2(X204,X205)),sbrdtbr0(X205))
| ~ aElement0(X204)
| ~ aElement0(X205)
| X205 = sz00 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivision])])])]) ).
fof(i_0_55,plain,
! [X147,X148,X149] :
( ( sdtasdt0(X147,sdtpldt0(X148,X149)) = sdtpldt0(sdtasdt0(X147,X148),sdtasdt0(X147,X149))
| ~ aElement0(X147)
| ~ aElement0(X148)
| ~ aElement0(X149) )
& ( sdtasdt0(sdtpldt0(X148,X149),X147) = sdtpldt0(sdtasdt0(X148,X147),sdtasdt0(X149,X147))
| ~ aElement0(X147)
| ~ aElement0(X148)
| ~ aElement0(X149) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])]) ).
fof(i_0_56,hypothesis,
! [X271,X272,X273] :
( aElementOf0(esk37_0,slsdtgt0(xa))
& aElementOf0(esk38_0,slsdtgt0(xb))
& sdtpldt0(esk37_0,esk38_0) = xu
& aElementOf0(xu,xI)
& xu != sz00
& ( ~ aElementOf0(X272,slsdtgt0(xa))
| ~ aElementOf0(X273,slsdtgt0(xb))
| sdtpldt0(X272,X273) != X271
| X271 = sz00
| ~ iLess0(sbrdtbr0(X271),sbrdtbr0(xu)) )
& ( ~ aElementOf0(X271,xI)
| X271 = sz00
| ~ iLess0(sbrdtbr0(X271),sbrdtbr0(xu)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_45])])])])]) ).
fof(i_0_57,plain,
! [X220,X221] :
( ( ~ misRelativelyPrime0(X220,X221)
| aGcdOfAnd0(sz10,X220,X221)
| ~ aElement0(X220)
| ~ aElement0(X221) )
& ( ~ aGcdOfAnd0(sz10,X220,X221)
| misRelativelyPrime0(X220,X221)
| ~ aElement0(X220)
| ~ aElement0(X221) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefRel])])]) ).
fof(i_0_58,plain,
! [X143,X144,X145] :
( ~ aElement0(X143)
| ~ aElement0(X144)
| ~ aElement0(X145)
| sdtasdt0(sdtasdt0(X143,X144),X145) = sdtasdt0(X143,sdtasdt0(X144,X145)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
fof(i_0_59,plain,
! [X136,X137,X138] :
( ~ aElement0(X136)
| ~ aElement0(X137)
| ~ aElement0(X138)
| sdtpldt0(sdtpldt0(X136,X137),X138) = sdtpldt0(X136,sdtpldt0(X137,X138)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
fof(i_0_60,hypothesis,
! [X239,X240,X241,X242,X244,X245,X246,X248,X249,X250,X253,X254,X255] :
( aSet0(xI)
& ( ~ aElementOf0(X240,xI)
| aElementOf0(sdtpldt0(X239,X240),xI)
| ~ aElementOf0(X239,xI) )
& ( ~ aElement0(X241)
| aElementOf0(sdtasdt0(X241,X239),xI)
| ~ aElementOf0(X239,xI) )
& aIdeal0(xI)
& ( aElement0(esk24_1(X242))
| ~ aElementOf0(X242,slsdtgt0(xa)) )
& ( sdtasdt0(xa,esk24_1(X242)) = X242
| ~ aElementOf0(X242,slsdtgt0(xa)) )
& ( ~ aElement0(X245)
| sdtasdt0(xa,X245) != X244
| aElementOf0(X244,slsdtgt0(xa)) )
& ( aElement0(esk25_1(X246))
| ~ aElementOf0(X246,slsdtgt0(xb)) )
& ( sdtasdt0(xb,esk25_1(X246)) = X246
| ~ aElementOf0(X246,slsdtgt0(xb)) )
& ( ~ aElement0(X249)
| sdtasdt0(xb,X249) != X248
| aElementOf0(X248,slsdtgt0(xb)) )
& ( aElementOf0(esk26_1(X250),slsdtgt0(xa))
| ~ aElementOf0(X250,xI) )
& ( aElementOf0(esk27_1(X250),slsdtgt0(xb))
| ~ aElementOf0(X250,xI) )
& ( sdtpldt0(esk26_1(X250),esk27_1(X250)) = X250
| ~ aElementOf0(X250,xI) )
& ( ~ aElementOf0(X254,slsdtgt0(xa))
| ~ aElementOf0(X255,slsdtgt0(xb))
| sdtpldt0(X254,X255) != X253
| aElementOf0(X253,xI) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2174])])])])])]) ).
fof(i_0_61,hypothesis,
! [X235,X236,X237] :
( aElement0(xc)
& aElement0(esk21_0)
& sdtasdt0(xc,esk21_0) = xa
& doDivides0(xc,xa)
& aDivisorOf0(xc,xa)
& aElement0(xc)
& aElement0(esk22_0)
& sdtasdt0(xc,esk22_0) = xb
& doDivides0(xc,xb)
& aDivisorOf0(xc,xb)
& ( aElement0(esk23_1(X235))
| ~ aElement0(X237)
| sdtasdt0(X235,X237) != xb
| ~ aElement0(X236)
| sdtasdt0(X235,X236) != xa
| ~ aElement0(X235) )
& ( sdtasdt0(X235,esk23_1(X235)) = xc
| ~ aElement0(X237)
| sdtasdt0(X235,X237) != xb
| ~ aElement0(X236)
| sdtasdt0(X235,X236) != xa
| ~ aElement0(X235) )
& ( doDivides0(X235,xc)
| ~ aElement0(X237)
| sdtasdt0(X235,X237) != xb
| ~ aElement0(X236)
| sdtasdt0(X235,X236) != xa
| ~ aElement0(X235) )
& ( aElement0(esk23_1(X235))
| ~ doDivides0(X235,xb)
| ~ aElement0(X236)
| sdtasdt0(X235,X236) != xa
| ~ aElement0(X235) )
& ( sdtasdt0(X235,esk23_1(X235)) = xc
| ~ doDivides0(X235,xb)
| ~ aElement0(X236)
| sdtasdt0(X235,X236) != xa
| ~ aElement0(X235) )
& ( doDivides0(X235,xc)
| ~ doDivides0(X235,xb)
| ~ aElement0(X236)
| sdtasdt0(X235,X236) != xa
| ~ aElement0(X235) )
& ( aElement0(esk23_1(X235))
| ~ aDivisorOf0(X235,xb)
| ~ aElement0(X236)
| sdtasdt0(X235,X236) != xa
| ~ aElement0(X235) )
& ( sdtasdt0(X235,esk23_1(X235)) = xc
| ~ aDivisorOf0(X235,xb)
| ~ aElement0(X236)
| sdtasdt0(X235,X236) != xa
| ~ aElement0(X235) )
& ( doDivides0(X235,xc)
| ~ aDivisorOf0(X235,xb)
| ~ aElement0(X236)
| sdtasdt0(X235,X236) != xa
| ~ aElement0(X235) )
& ( aElement0(esk23_1(X235))
| ~ aElement0(X237)
| sdtasdt0(X235,X237) != xb
| ~ doDivides0(X235,xa)
| ~ aElement0(X235) )
& ( sdtasdt0(X235,esk23_1(X235)) = xc
| ~ aElement0(X237)
| sdtasdt0(X235,X237) != xb
| ~ doDivides0(X235,xa)
| ~ aElement0(X235) )
& ( doDivides0(X235,xc)
| ~ aElement0(X237)
| sdtasdt0(X235,X237) != xb
| ~ doDivides0(X235,xa)
| ~ aElement0(X235) )
& ( aElement0(esk23_1(X235))
| ~ doDivides0(X235,xb)
| ~ doDivides0(X235,xa)
| ~ aElement0(X235) )
& ( sdtasdt0(X235,esk23_1(X235)) = xc
| ~ doDivides0(X235,xb)
| ~ doDivides0(X235,xa)
| ~ aElement0(X235) )
& ( doDivides0(X235,xc)
| ~ doDivides0(X235,xb)
| ~ doDivides0(X235,xa)
| ~ aElement0(X235) )
& ( aElement0(esk23_1(X235))
| ~ aDivisorOf0(X235,xb)
| ~ doDivides0(X235,xa)
| ~ aElement0(X235) )
& ( sdtasdt0(X235,esk23_1(X235)) = xc
| ~ aDivisorOf0(X235,xb)
| ~ doDivides0(X235,xa)
| ~ aElement0(X235) )
& ( doDivides0(X235,xc)
| ~ aDivisorOf0(X235,xb)
| ~ doDivides0(X235,xa)
| ~ aElement0(X235) )
& ( aElement0(esk23_1(X235))
| ~ aElement0(X237)
| sdtasdt0(X235,X237) != xb
| ~ aDivisorOf0(X235,xa) )
& ( sdtasdt0(X235,esk23_1(X235)) = xc
| ~ aElement0(X237)
| sdtasdt0(X235,X237) != xb
| ~ aDivisorOf0(X235,xa) )
& ( doDivides0(X235,xc)
| ~ aElement0(X237)
| sdtasdt0(X235,X237) != xb
| ~ aDivisorOf0(X235,xa) )
& ( aElement0(esk23_1(X235))
| ~ doDivides0(X235,xb)
| ~ aDivisorOf0(X235,xa) )
& ( sdtasdt0(X235,esk23_1(X235)) = xc
| ~ doDivides0(X235,xb)
| ~ aDivisorOf0(X235,xa) )
& ( doDivides0(X235,xc)
| ~ doDivides0(X235,xb)
| ~ aDivisorOf0(X235,xa) )
& ( aElement0(esk23_1(X235))
| ~ aDivisorOf0(X235,xb)
| ~ aDivisorOf0(X235,xa) )
& ( sdtasdt0(X235,esk23_1(X235)) = xc
| ~ aDivisorOf0(X235,xb)
| ~ aDivisorOf0(X235,xa) )
& ( doDivides0(X235,xc)
| ~ aDivisorOf0(X235,xb)
| ~ aDivisorOf0(X235,xa) )
& aGcdOfAnd0(xc,xa,xb) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2129])])])])]) ).
fof(i_0_62,plain,
! [X208,X209,X211] :
( ( aElement0(esk16_2(X208,X209))
| ~ doDivides0(X208,X209)
| ~ aElement0(X208)
| ~ aElement0(X209) )
& ( sdtasdt0(X208,esk16_2(X208,X209)) = X209
| ~ doDivides0(X208,X209)
| ~ aElement0(X208)
| ~ aElement0(X209) )
& ( ~ aElement0(X211)
| sdtasdt0(X208,X211) != X209
| doDivides0(X208,X209)
| ~ aElement0(X208)
| ~ aElement0(X209) ) ),
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_63,hypothesis,
! [X274,X275] :
( ( ~ aElement0(X275)
| sdtasdt0(xu,X275) != xb
| ~ aElement0(X274)
| sdtasdt0(xu,X274) != xa )
& ( ~ doDivides0(xu,xb)
| ~ aElement0(X274)
| sdtasdt0(xu,X274) != xa )
& ( ~ aDivisorOf0(xu,xb)
| ~ aElement0(X274)
| sdtasdt0(xu,X274) != xa )
& ( ~ aElement0(X275)
| sdtasdt0(xu,X275) != xb
| ~ doDivides0(xu,xa) )
& ( ~ doDivides0(xu,xb)
| ~ doDivides0(xu,xa) )
& ( ~ aDivisorOf0(xu,xb)
| ~ doDivides0(xu,xa) )
& ( ~ aElement0(X275)
| sdtasdt0(xu,X275) != xb
| ~ aDivisorOf0(xu,xa) )
& ( ~ doDivides0(xu,xb)
| ~ aDivisorOf0(xu,xa) )
& ( ~ aDivisorOf0(xu,xb)
| ~ aDivisorOf0(xu,xa) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2383])])])]) ).
fof(i_0_64,hypothesis,
( aElement0(esk39_0)
& aElement0(esk40_0)
& xu = sdtpldt0(sdtasdt0(xa,esk39_0),sdtasdt0(xb,esk40_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2416])]) ).
fof(i_0_65,plain,
! [X212,X213] :
( ( aElement0(X213)
| ~ aDivisorOf0(X213,X212)
| ~ aElement0(X212) )
& ( doDivides0(X213,X212)
| ~ aDivisorOf0(X213,X212)
| ~ aElement0(X212) )
& ( ~ aElement0(X213)
| ~ doDivides0(X213,X212)
| aDivisorOf0(X213,X212)
| ~ aElement0(X212) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDvs])])])]) ).
fof(i_0_66,hypothesis,
! [X261,X263,X264,X266] :
( ( aElement0(esk33_1(X261))
| ~ aElementOf0(X261,slsdtgt0(xa)) )
& ( sdtasdt0(xa,esk33_1(X261)) = X261
| ~ aElementOf0(X261,slsdtgt0(xa)) )
& ( ~ aElement0(X263)
| sdtasdt0(xa,X263) != X261
| aElementOf0(X261,slsdtgt0(xa)) )
& ( aElement0(esk34_1(X264))
| ~ aElementOf0(X264,slsdtgt0(xb)) )
& ( sdtasdt0(xb,esk34_1(X264)) = X264
| ~ aElementOf0(X264,slsdtgt0(xb)) )
& ( ~ aElement0(X266)
| sdtasdt0(xb,X266) != X264
| aElementOf0(X264,slsdtgt0(xb)) )
& aElementOf0(esk35_0,slsdtgt0(xa))
& aElementOf0(esk36_0,slsdtgt0(xb))
& sdtpldt0(esk35_0,esk36_0) = esk32_0
& aElementOf0(esk32_0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& esk32_0 != sz00 ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2228])])])])]) ).
fof(i_0_67,plain,
! [X192,X193] :
( ~ aIdeal0(X192)
| ~ aIdeal0(X193)
| aIdeal0(sdtasasdt0(X192,X193)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIdeInt])]) ).
fof(i_0_68,plain,
! [X190,X191] :
( ~ aIdeal0(X190)
| ~ aIdeal0(X191)
| aIdeal0(sdtpldt1(X190,X191)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIdeSum])]) ).
fof(i_0_69,plain,
! [X132,X133] :
( ~ aElement0(X132)
| ~ aElement0(X133)
| aElement0(sdtasdt0(X132,X133)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(i_0_70,plain,
! [X130,X131] :
( ~ aElement0(X130)
| ~ aElement0(X131)
| aElement0(sdtpldt0(X130,X131)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
fof(i_0_71,plain,
! [X141,X142] :
( ~ aElement0(X141)
| ~ aElement0(X142)
| sdtasdt0(X141,X142) = sdtasdt0(X142,X141) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
fof(i_0_72,plain,
! [X134,X135] :
( ~ aElement0(X134)
| ~ aElement0(X135)
| sdtpldt0(X134,X135) = sdtpldt0(X135,X134) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
fof(i_0_73,plain,
! [X152,X153] :
( ~ aElement0(X152)
| ~ aElement0(X153)
| sdtasdt0(X152,X153) != sz00
| X152 = sz00
| X153 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCancel])]) ).
fof(i_0_74,plain,
! [X154,X155] :
( ~ aSet0(X154)
| ~ aElementOf0(X155,X154)
| aElement0(X155) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
fof(i_0_75,plain,
! [X150] :
( ( sdtasdt0(smndt0(sz10),X150) = smndt0(X150)
| ~ aElement0(X150) )
& ( smndt0(X150) = sdtasdt0(X150,smndt0(sz10))
| ~ aElement0(X150) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMnOne])])]) ).
fof(i_0_76,plain,
! [X140] :
( ( sdtpldt0(X140,smndt0(X140)) = sz00
| ~ aElement0(X140) )
& ( sz00 = sdtpldt0(smndt0(X140),X140)
| ~ aElement0(X140) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddInvr])])]) ).
fof(i_0_77,plain,
! [X146] :
( ( sdtasdt0(X146,sz10) = X146
| ~ aElement0(X146) )
& ( X146 = sdtasdt0(sz10,X146)
| ~ aElement0(X146) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulUnit])])]) ).
fof(i_0_78,plain,
! [X139] :
( ( sdtpldt0(X139,sz00) = X139
| ~ aElement0(X139) )
& ( X139 = sdtpldt0(sz00,X139)
| ~ aElement0(X139) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).
fof(i_0_79,plain,
! [X151] :
( ( sdtasdt0(X151,sz00) = sz00
| ~ aElement0(X151) )
& ( sz00 = sdtasdt0(sz00,X151)
| ~ aElement0(X151) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulZero])])]) ).
fof(i_0_80,plain,
! [X203] :
( ~ aElement0(X203)
| X203 = sz00
| aNaturalNumber0(sbrdtbr0(X203)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEucSort])]) ).
fof(i_0_81,plain,
! [X232] :
( ~ aElement0(X232)
| aIdeal0(slsdtgt0(X232)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPrIdeal])]) ).
fof(i_0_82,plain,
! [X129] :
( ~ aElement0(X129)
| aElement0(smndt0(X129)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsU])]) ).
fof(i_0_83,hypothesis,
( aElement0(esk28_0)
& sdtasdt0(xa,esk28_0) = sz00
& aElementOf0(sz00,slsdtgt0(xa))
& aElement0(esk29_0)
& sdtasdt0(xa,esk29_0) = xa
& aElementOf0(xa,slsdtgt0(xa))
& aElement0(esk30_0)
& sdtasdt0(xb,esk30_0) = sz00
& aElementOf0(sz00,slsdtgt0(xb))
& aElement0(esk31_0)
& sdtasdt0(xb,esk31_0) = xb
& aElementOf0(xb,slsdtgt0(xb)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2203])]) ).
fof(i_0_84,hypothesis,
( aElement0(esk42_0)
& sdtasdt0(xu,esk42_0) = xb
& doDivides0(xu,xb) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2612])])]) ).
fof(i_0_85,hypothesis,
( aElement0(esk41_0)
& sdtasdt0(xu,esk41_0) = xa
& doDivides0(xu,xa) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2479])])]) ).
cnf(i_0_86,plain,
( sdtpldt0(esk3_4(X1,X2,X3,X4),esk4_4(X1,X2,X3,X4)) = X4
| ~ aElementOf0(X4,X3)
| X3 != sdtpldt1(X1,X2)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_87,plain,
( sdteqdtlpzmzozddtrp0(esk13_4(X1,X2,X3,X4),X3,X1)
| ~ aElement0(X3)
| ~ aElement0(X4)
| ~ aElementOf0(esk12_2(X1,X2),sdtpldt1(X1,X2))
| ~ aIdeal0(X1)
| ~ aIdeal0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_88,plain,
( sdteqdtlpzmzozddtrp0(esk13_4(X1,X2,X3,X4),X4,X2)
| ~ aElement0(X3)
| ~ aElement0(X4)
| ~ aElementOf0(esk12_2(X1,X2),sdtpldt1(X1,X2))
| ~ aIdeal0(X1)
| ~ aIdeal0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_89,plain,
( aElement0(esk13_4(X1,X2,X3,X4))
| ~ aElement0(X3)
| ~ aElement0(X4)
| ~ aElementOf0(esk12_2(X1,X2),sdtpldt1(X1,X2))
| ~ aIdeal0(X1)
| ~ aIdeal0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_90,plain,
( X3 = sdtasasdt0(X1,X2)
| ~ aElementOf0(esk8_3(X1,X2,X3),X3)
| ~ aElementOf0(esk8_3(X1,X2,X3),X1)
| ~ aElementOf0(esk8_3(X1,X2,X3),X2)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_91,plain,
( sdteqdtlpzmzozddtrp0(esk13_4(X1,X2,X3,X4),X3,X1)
| aElement0(esk12_2(X1,X2))
| ~ aElement0(X3)
| ~ aElement0(X4)
| ~ aIdeal0(X1)
| ~ aIdeal0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_92,plain,
( sdteqdtlpzmzozddtrp0(esk13_4(X1,X2,X3,X4),X4,X2)
| aElement0(esk12_2(X1,X2))
| ~ aElement0(X3)
| ~ aElement0(X4)
| ~ aIdeal0(X1)
| ~ aIdeal0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_93,plain,
( aElementOf0(esk4_4(X1,X2,X3,X4),X2)
| ~ aElementOf0(X4,X3)
| X3 != sdtpldt1(X1,X2)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_94,plain,
( aElementOf0(esk3_4(X1,X2,X3,X4),X1)
| ~ aElementOf0(X4,X3)
| X3 != sdtpldt1(X1,X2)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_95,plain,
( aElement0(esk13_4(X1,X2,X3,X4))
| aElement0(esk12_2(X1,X2))
| ~ aElement0(X3)
| ~ aElement0(X4)
| ~ aIdeal0(X1)
| ~ aIdeal0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_96,plain,
( sdtpldt0(esk6_3(X1,X2,X3),esk7_3(X1,X2,X3)) = esk5_3(X1,X2,X3)
| aElementOf0(esk5_3(X1,X2,X3),X3)
| X3 = sdtpldt1(X1,X2)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_97,plain,
( X3 = sdtpldt1(X1,X2)
| ~ aElementOf0(esk5_3(X1,X2,X3),X3)
| ~ aElementOf0(X4,X1)
| ~ aElementOf0(X5,X2)
| sdtpldt0(X4,X5) != esk5_3(X1,X2,X3)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_98,plain,
( aGcdOfAnd0(X3,X1,X2)
| ~ doDivides0(esk17_3(X1,X2,X3),X3)
| ~ aDivisorOf0(X3,X1)
| ~ aDivisorOf0(X3,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_99,plain,
( aElementOf0(esk8_3(X1,X2,X3),X1)
| aElementOf0(esk8_3(X1,X2,X3),X3)
| X3 = sdtasasdt0(X1,X2)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_100,plain,
( aElementOf0(esk8_3(X1,X2,X3),X2)
| aElementOf0(esk8_3(X1,X2,X3),X3)
| X3 = sdtasasdt0(X1,X2)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_101,plain,
( aElementOf0(esk7_3(X1,X2,X3),X2)
| aElementOf0(esk5_3(X1,X2,X3),X3)
| X3 = sdtpldt1(X1,X2)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_102,plain,
( aElementOf0(esk6_3(X1,X2,X3),X1)
| aElementOf0(esk5_3(X1,X2,X3),X3)
| X3 = sdtpldt1(X1,X2)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_103,plain,
( aDivisorOf0(esk17_3(X1,X2,X3),X1)
| aGcdOfAnd0(X3,X1,X2)
| ~ aDivisorOf0(X3,X1)
| ~ aDivisorOf0(X3,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_104,plain,
( aDivisorOf0(esk17_3(X1,X2,X3),X2)
| aGcdOfAnd0(X3,X1,X2)
| ~ aDivisorOf0(X3,X1)
| ~ aDivisorOf0(X3,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_105,plain,
( aIdeal0(X1)
| ~ aElementOf0(sdtasdt0(esk11_1(X1),esk9_1(X1)),X1)
| ~ aElementOf0(sdtpldt0(esk9_1(X1),esk10_1(X1)),X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_106,plain,
( doDivides0(X1,X4)
| ~ aDivisorOf0(X1,X2)
| ~ aDivisorOf0(X1,X3)
| ~ aGcdOfAnd0(X4,X2,X3)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_107,plain,
( aElementOf0(sdtpldt0(X1,smndt0(X2)),X3)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aIdeal0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_108,plain,
( sdtasdt0(X1,esk18_3(X1,X2,X3)) = X3
| ~ aElementOf0(X3,X2)
| X2 != slsdtgt0(X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_109,plain,
( sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ aElementOf0(sdtpldt0(X1,smndt0(X2)),X3)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aIdeal0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_110,plain,
( aElement0(esk18_3(X1,X2,X3))
| ~ aElementOf0(X3,X2)
| X2 != slsdtgt0(X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_111,plain,
( X1 = X2
| ~ aElementOf0(esk2_2(X1,X2),X1)
| ~ aElementOf0(esk1_2(X1,X2),X2)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_112,plain,
( X1 = sdtpldt0(sdtasdt0(esk14_2(X1,X2),X2),esk15_2(X1,X2))
| X2 = sz00
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_113,plain,
( X2 = slsdtgt0(X1)
| ~ aElementOf0(esk19_2(X1,X2),X2)
| ~ aElement0(X3)
| sdtasdt0(X1,X3) != esk19_2(X1,X2)
| ~ aSet0(X2)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_114,plain,
( aElementOf0(esk10_1(X1),X1)
| aIdeal0(X1)
| ~ aElementOf0(sdtasdt0(esk11_1(X1),esk9_1(X1)),X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_115,plain,
( sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3))
| ~ aElement0(X3)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_116,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_117,plain,
( aElement0(esk11_1(X1))
| aIdeal0(X1)
| ~ aElementOf0(sdtpldt0(esk9_1(X1),esk10_1(X1)),X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_118,plain,
( aElementOf0(X5,X6)
| ~ aElementOf0(X1,X2)
| ~ aElementOf0(X3,X4)
| sdtpldt0(X1,X3) != X5
| X6 != sdtpldt1(X2,X4)
| ~ aSet0(X2)
| ~ aSet0(X4) ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_119,plain,
( aElementOf0(esk2_2(X1,X2),X2)
| X1 = X2
| ~ aElementOf0(esk1_2(X1,X2),X2)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_120,plain,
( aElementOf0(esk1_2(X1,X2),X1)
| X1 = X2
| ~ aElementOf0(esk2_2(X1,X2),X1)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_121,hypothesis,
( X3 = sz00
| ~ aElementOf0(X1,slsdtgt0(xa))
| ~ aElementOf0(X2,slsdtgt0(xb))
| sdtpldt0(X1,X2) != X3
| ~ iLess0(sbrdtbr0(X3),sbrdtbr0(xu)) ),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_122,plain,
( aDivisorOf0(X1,X2)
| ~ aGcdOfAnd0(X1,X2,X3)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_123,plain,
( aDivisorOf0(X1,X2)
| ~ aGcdOfAnd0(X1,X3,X2)
| ~ aElement0(X3)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_124,plain,
( sdtasdt0(X1,esk20_2(X1,X2)) = esk19_2(X1,X2)
| aElementOf0(esk19_2(X1,X2),X2)
| X2 = slsdtgt0(X1)
| ~ aSet0(X2)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_125,plain,
( misRelativelyPrime0(X1,X2)
| ~ aGcdOfAnd0(sz10,X1,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_126,plain,
( esk15_2(X1,X2) = sz00
| iLess0(sbrdtbr0(esk15_2(X1,X2)),sbrdtbr0(X2))
| X2 = sz00
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_127,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_128,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_129,plain,
( aElementOf0(X1,X4)
| ~ aElementOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| X4 != sdtasasdt0(X2,X3)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_130,plain,
( aElementOf0(esk2_2(X1,X2),X2)
| aElementOf0(esk1_2(X1,X2),X1)
| X1 = X2
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_131,plain,
( aElementOf0(sdtpldt0(X3,X1),X2)
| ~ aElementOf0(X1,X2)
| ~ aElementOf0(X3,X2)
| ~ aIdeal0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_132,hypothesis,
( aElementOf0(X3,xI)
| ~ aElementOf0(X1,slsdtgt0(xa))
| ~ aElementOf0(X2,slsdtgt0(xb))
| sdtpldt0(X1,X2) != X3 ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_133,plain,
( aElement0(esk20_2(X1,X2))
| aElementOf0(esk19_2(X1,X2),X2)
| X2 = slsdtgt0(X1)
| ~ aSet0(X2)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_134,plain,
( aGcdOfAnd0(sz10,X1,X2)
| ~ misRelativelyPrime0(X1,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_135,hypothesis,
( sdtasdt0(X1,esk23_1(X1)) = xc
| ~ aElement0(X2)
| sdtasdt0(X1,X2) != xb
| ~ aElement0(X3)
| sdtasdt0(X1,X3) != xa
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_136,hypothesis,
( doDivides0(X1,xc)
| ~ aElement0(X2)
| sdtasdt0(X1,X2) != xb
| ~ aElement0(X3)
| sdtasdt0(X1,X3) != xa
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_137,hypothesis,
( aElementOf0(sdtpldt0(X2,X1),xI)
| ~ aElementOf0(X1,xI)
| ~ aElementOf0(X2,xI) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_138,plain,
( sdtasdt0(X1,esk16_2(X1,X2)) = X2
| ~ doDivides0(X1,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_139,hypothesis,
( sdtasdt0(X1,esk23_1(X1)) = xc
| ~ aElement0(X2)
| sdtasdt0(X1,X2) != xb
| ~ doDivides0(X1,xa)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_140,hypothesis,
( sdtasdt0(X1,esk23_1(X1)) = xc
| ~ aDivisorOf0(X1,xb)
| ~ aElement0(X2)
| sdtasdt0(X1,X2) != xa
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_141,hypothesis,
( sdtasdt0(X1,esk23_1(X1)) = xc
| ~ doDivides0(X1,xb)
| ~ aElement0(X2)
| sdtasdt0(X1,X2) != xa
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_142,hypothesis,
( aElement0(esk23_1(X1))
| ~ aElement0(X2)
| sdtasdt0(X1,X2) != xb
| ~ aElement0(X3)
| sdtasdt0(X1,X3) != xa
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_143,plain,
( aElementOf0(sdtasdt0(X1,X2),X3)
| ~ aElement0(X1)
| ~ aElementOf0(X2,X3)
| ~ aIdeal0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_144,plain,
( aElementOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| X3 != sdtasasdt0(X2,X4)
| ~ aSet0(X2)
| ~ aSet0(X4) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_145,plain,
( aElementOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| X3 != sdtasasdt0(X4,X2)
| ~ aSet0(X4)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_146,hypothesis,
( sdtasdt0(X1,esk23_1(X1)) = xc
| ~ aElement0(X2)
| sdtasdt0(X1,X2) != xb
| ~ aDivisorOf0(X1,xa) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_147,hypothesis,
( doDivides0(X1,xc)
| ~ aElement0(X2)
| sdtasdt0(X1,X2) != xb
| ~ doDivides0(X1,xa)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_148,hypothesis,
( doDivides0(X1,xc)
| ~ aDivisorOf0(X1,xb)
| ~ aElement0(X2)
| sdtasdt0(X1,X2) != xa
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_149,hypothesis,
( doDivides0(X1,xc)
| ~ doDivides0(X1,xb)
| ~ aElement0(X2)
| sdtasdt0(X1,X2) != xa
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_150,hypothesis,
( sdtasdt0(X1,esk23_1(X1)) = xc
| ~ aDivisorOf0(X1,xb)
| ~ doDivides0(X1,xa)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_151,hypothesis,
( sdtasdt0(X1,esk23_1(X1)) = xc
| ~ doDivides0(X1,xb)
| ~ doDivides0(X1,xa)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_152,hypothesis,
( aElement0(esk23_1(X1))
| ~ aElement0(X2)
| sdtasdt0(X1,X2) != xb
| ~ doDivides0(X1,xa)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_153,hypothesis,
( aElement0(esk23_1(X1))
| ~ aDivisorOf0(X1,xb)
| ~ aElement0(X2)
| sdtasdt0(X1,X2) != xa
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_154,hypothesis,
( aElement0(esk23_1(X1))
| ~ doDivides0(X1,xb)
| ~ aElement0(X2)
| sdtasdt0(X1,X2) != xa
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_155,plain,
( aElement0(esk16_2(X1,X2))
| ~ doDivides0(X1,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_156,hypothesis,
( aElementOf0(sdtasdt0(X1,X2),xI)
| ~ aElement0(X1)
| ~ aElementOf0(X2,xI) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_157,hypothesis,
( doDivides0(X1,xc)
| ~ aElement0(X2)
| sdtasdt0(X1,X2) != xb
| ~ aDivisorOf0(X1,xa) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_158,hypothesis,
( sdtasdt0(X1,esk23_1(X1)) = xc
| ~ aDivisorOf0(X1,xb)
| ~ aDivisorOf0(X1,xa) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_159,hypothesis,
( sdtasdt0(X1,esk23_1(X1)) = xc
| ~ doDivides0(X1,xb)
| ~ aDivisorOf0(X1,xa) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_160,plain,
( aElementOf0(X3,X4)
| ~ aElement0(X1)
| sdtasdt0(X2,X1) != X3
| X4 != slsdtgt0(X2)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_161,hypothesis,
( aElement0(esk23_1(X1))
| ~ aElement0(X2)
| sdtasdt0(X1,X2) != xb
| ~ aDivisorOf0(X1,xa) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_162,hypothesis,
( doDivides0(X1,xc)
| ~ aDivisorOf0(X1,xb)
| ~ doDivides0(X1,xa)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_163,hypothesis,
( doDivides0(X1,xc)
| ~ doDivides0(X1,xb)
| ~ doDivides0(X1,xa)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_164,plain,
( doDivides0(X2,X3)
| ~ aElement0(X1)
| sdtasdt0(X2,X1) != X3
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_165,hypothesis,
( X1 = sz00
| ~ aElementOf0(X1,xI)
| ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_166,hypothesis,
( aElement0(esk23_1(X1))
| ~ aDivisorOf0(X1,xb)
| ~ doDivides0(X1,xa)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_167,hypothesis,
( aElement0(esk23_1(X1))
| ~ doDivides0(X1,xb)
| ~ doDivides0(X1,xa)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_168,hypothesis,
( ~ aElement0(X1)
| sdtasdt0(xu,X1) != xb
| ~ aElement0(X2)
| sdtasdt0(xu,X2) != xa ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_169,hypothesis,
xu = sdtpldt0(sdtasdt0(xa,esk39_0),sdtasdt0(xb,esk40_0)),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_170,hypothesis,
( doDivides0(X1,xc)
| ~ aDivisorOf0(X1,xb)
| ~ aDivisorOf0(X1,xa) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_171,hypothesis,
( doDivides0(X1,xc)
| ~ doDivides0(X1,xb)
| ~ aDivisorOf0(X1,xa) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_172,plain,
( aDivisorOf0(X1,X2)
| ~ aElement0(X1)
| ~ doDivides0(X1,X2)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_173,hypothesis,
( aElement0(esk23_1(X1))
| ~ aDivisorOf0(X1,xb)
| ~ aDivisorOf0(X1,xa) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_174,hypothesis,
( aElement0(esk23_1(X1))
| ~ doDivides0(X1,xb)
| ~ aDivisorOf0(X1,xa) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_175,hypothesis,
aElementOf0(esk32_0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_176,hypothesis,
aGcdOfAnd0(xc,xa,xb),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_177,hypothesis,
( sdtpldt0(esk26_1(X1),esk27_1(X1)) = X1
| ~ aElementOf0(X1,xI) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_178,hypothesis,
( sdtasdt0(xb,esk34_1(X1)) = X1
| ~ aElementOf0(X1,slsdtgt0(xb)) ),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_179,hypothesis,
( sdtasdt0(xb,esk25_1(X1)) = X1
| ~ aElementOf0(X1,slsdtgt0(xb)) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_180,hypothesis,
( sdtasdt0(xa,esk33_1(X1)) = X1
| ~ aElementOf0(X1,slsdtgt0(xa)) ),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_181,hypothesis,
( sdtasdt0(xa,esk24_1(X1)) = X1
| ~ aElementOf0(X1,slsdtgt0(xa)) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_182,plain,
( aElement0(esk15_2(X1,X2))
| X2 = sz00
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_183,plain,
( aElement0(esk14_2(X1,X2))
| X2 = sz00
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_184,hypothesis,
( aElementOf0(X2,slsdtgt0(xb))
| ~ aElement0(X1)
| sdtasdt0(xb,X1) != X2 ),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_185,hypothesis,
( aElementOf0(X2,slsdtgt0(xb))
| ~ aElement0(X1)
| sdtasdt0(xb,X1) != X2 ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_186,hypothesis,
( aElementOf0(X2,slsdtgt0(xa))
| ~ aElement0(X1)
| sdtasdt0(xa,X1) != X2 ),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_187,hypothesis,
( aElementOf0(X2,slsdtgt0(xa))
| ~ aElement0(X1)
| sdtasdt0(xa,X1) != X2 ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_188,hypothesis,
( ~ aElement0(X1)
| sdtasdt0(xu,X1) != xb
| ~ aDivisorOf0(xu,xa) ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_189,hypothesis,
( ~ aElement0(X1)
| sdtasdt0(xu,X1) != xb
| ~ doDivides0(xu,xa) ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_190,hypothesis,
( ~ aDivisorOf0(xu,xb)
| ~ aElement0(X1)
| sdtasdt0(xu,X1) != xa ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_191,hypothesis,
( ~ doDivides0(xu,xb)
| ~ aElement0(X1)
| sdtasdt0(xu,X1) != xa ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_192,plain,
( aIdeal0(sdtasasdt0(X1,X2))
| ~ aIdeal0(X1)
| ~ aIdeal0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_193,plain,
( aIdeal0(sdtpldt1(X1,X2))
| ~ aIdeal0(X1)
| ~ aIdeal0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_194,plain,
( aElement0(sdtasdt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_195,plain,
( aElement0(sdtpldt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_196,plain,
( doDivides0(X1,X2)
| ~ aDivisorOf0(X1,X2)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_197,hypothesis,
( aElementOf0(esk27_1(X1),slsdtgt0(xb))
| ~ aElementOf0(X1,xI) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_198,hypothesis,
( aElementOf0(esk26_1(X1),slsdtgt0(xa))
| ~ aElementOf0(X1,xI) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_199,plain,
( aElement0(esk11_1(X1))
| aElementOf0(esk10_1(X1),X1)
| aIdeal0(X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_200,plain,
( aSet0(X1)
| X1 != sdtasasdt0(X2,X3)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_201,plain,
( aSet0(X1)
| X1 != sdtpldt1(X2,X3)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_202,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_203,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_204,plain,
( X1 = sz00
| X2 = sz00
| ~ aElement0(X1)
| ~ aElement0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[i_0_73]),
[final] ).
cnf(i_0_205,hypothesis,
( aElement0(esk34_1(X1))
| ~ aElementOf0(X1,slsdtgt0(xb)) ),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_206,hypothesis,
( aElement0(esk33_1(X1))
| ~ aElementOf0(X1,slsdtgt0(xa)) ),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_207,hypothesis,
( aElement0(esk25_1(X1))
| ~ aElementOf0(X1,slsdtgt0(xb)) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_208,hypothesis,
( aElement0(esk24_1(X1))
| ~ aElementOf0(X1,slsdtgt0(xa)) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_209,hypothesis,
( ~ aDivisorOf0(xu,xb)
| ~ aDivisorOf0(xu,xa) ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_210,hypothesis,
( ~ doDivides0(xu,xb)
| ~ aDivisorOf0(xu,xa) ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_211,hypothesis,
( ~ aDivisorOf0(xu,xb)
| ~ doDivides0(xu,xa) ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_212,hypothesis,
( ~ doDivides0(xu,xb)
| ~ doDivides0(xu,xa) ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_213,plain,
( aElement0(X1)
| ~ aDivisorOf0(X1,X2)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_214,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_74]),
[final] ).
cnf(i_0_215,plain,
( aElementOf0(esk9_1(X1),X1)
| aIdeal0(X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_216,plain,
( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_75]),
[final] ).
cnf(i_0_217,plain,
( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_75]),
[final] ).
cnf(i_0_218,plain,
( sdtpldt0(X1,smndt0(X1)) = sz00
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_76]),
[final] ).
cnf(i_0_219,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_76]),
[final] ).
cnf(i_0_220,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_77]),
[final] ).
cnf(i_0_221,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_78]),
[final] ).
cnf(i_0_222,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_77]),
[final] ).
cnf(i_0_223,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_78]),
[final] ).
cnf(i_0_224,hypothesis,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_225,plain,
( aSet0(X1)
| X1 != slsdtgt0(X2)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_226,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_79]),
[final] ).
cnf(i_0_227,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_79]),
[final] ).
cnf(i_0_228,plain,
( X1 = sz00
| aNaturalNumber0(sbrdtbr0(X1))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_80]),
[final] ).
cnf(i_0_229,plain,
( aIdeal0(slsdtgt0(X1))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_81]),
[final] ).
cnf(i_0_230,plain,
( aElement0(smndt0(X1))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_82]),
[final] ).
cnf(i_0_231,hypothesis,
aElementOf0(esk38_0,slsdtgt0(xb)),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_232,hypothesis,
aElementOf0(esk37_0,slsdtgt0(xa)),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_233,hypothesis,
aElementOf0(esk36_0,slsdtgt0(xb)),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_234,hypothesis,
aElementOf0(esk35_0,slsdtgt0(xa)),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_235,hypothesis,
aElementOf0(xb,slsdtgt0(xb)),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_236,hypothesis,
aElementOf0(xa,slsdtgt0(xa)),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_237,hypothesis,
aElementOf0(sz00,slsdtgt0(xb)),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_238,hypothesis,
aElementOf0(sz00,slsdtgt0(xa)),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_239,plain,
( aSet0(X1)
| ~ aIdeal0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_240,hypothesis,
aDivisorOf0(xc,xb),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_241,hypothesis,
aDivisorOf0(xc,xa),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_242,hypothesis,
doDivides0(xu,xb),
inference(split_conjunct,[status(thm)],[i_0_84]),
[final] ).
cnf(i_0_243,hypothesis,
doDivides0(xu,xa),
inference(split_conjunct,[status(thm)],[i_0_85]),
[final] ).
cnf(i_0_244,hypothesis,
doDivides0(xc,xb),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_245,hypothesis,
doDivides0(xc,xa),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_246,hypothesis,
aElementOf0(xu,xI),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_247,hypothesis,
sdtasdt0(xu,esk42_0) = xb,
inference(split_conjunct,[status(thm)],[i_0_84]),
[final] ).
cnf(i_0_248,hypothesis,
sdtasdt0(xu,esk41_0) = xa,
inference(split_conjunct,[status(thm)],[i_0_85]),
[final] ).
cnf(i_0_249,hypothesis,
sdtasdt0(xc,esk22_0) = xb,
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_250,hypothesis,
sdtasdt0(xc,esk21_0) = xa,
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_251,hypothesis,
sdtasdt0(xb,esk31_0) = xb,
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_252,hypothesis,
sdtasdt0(xb,esk30_0) = sz00,
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_253,hypothesis,
sdtasdt0(xa,esk29_0) = xa,
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_254,hypothesis,
sdtasdt0(xa,esk28_0) = sz00,
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_255,hypothesis,
sdtpldt0(esk37_0,esk38_0) = xu,
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_256,hypothesis,
sdtpldt0(esk35_0,esk36_0) = esk32_0,
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_257,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_258,hypothesis,
aSet0(xI),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_259,hypothesis,
aElement0(esk42_0),
inference(split_conjunct,[status(thm)],[i_0_84]),
[final] ).
cnf(i_0_260,hypothesis,
aElement0(esk41_0),
inference(split_conjunct,[status(thm)],[i_0_85]),
[final] ).
cnf(i_0_261,hypothesis,
aElement0(esk40_0),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_262,hypothesis,
aElement0(esk39_0),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_263,hypothesis,
aElement0(esk31_0),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_264,hypothesis,
aElement0(esk30_0),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_265,hypothesis,
aElement0(esk29_0),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_266,hypothesis,
aElement0(esk28_0),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_267,hypothesis,
aElement0(esk22_0),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_268,hypothesis,
aElement0(esk21_0),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_269,hypothesis,
aElement0(xc),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_270,hypothesis,
aElement0(xc),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_271,hypothesis,
aElement0(xb),
inference(split_conjunct,[status(thm)],[m__2091]),
[final] ).
cnf(i_0_272,hypothesis,
aElement0(xa),
inference(split_conjunct,[status(thm)],[m__2091]),
[final] ).
cnf(i_0_273,plain,
aElement0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]),
[final] ).
cnf(i_0_274,plain,
aElement0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]),
[final] ).
cnf(i_0_275,hypothesis,
( xa != sz00
| xb != sz00 ),
inference(split_conjunct,[status(thm)],[m__2110]),
[final] ).
cnf(i_0_276,hypothesis,
esk32_0 != sz00,
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_277,hypothesis,
xu != sz00,
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_278,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mUnNeZr]),
[final] ).
cnf(i_0_279,axiom,
X1 = X1 ).
cnf(i_0_280,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_281,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_282,axiom,
( X1 != X2
| sdtpldt0(X1,X3) = sdtpldt0(X2,X3) ) ).
cnf(i_0_283,axiom,
( X1 != X2
| sdtpldt0(X3,X1) = sdtpldt0(X3,X2) ) ).
cnf(i_0_284,axiom,
( X1 != X2
| esk5_3(X1,X3,X4) = esk5_3(X2,X3,X4) ) ).
cnf(i_0_285,axiom,
( X1 != X2
| esk5_3(X3,X1,X4) = esk5_3(X3,X2,X4) ) ).
cnf(i_0_286,axiom,
( X1 != X2
| esk5_3(X3,X4,X1) = esk5_3(X3,X4,X2) ) ).
cnf(i_0_287,axiom,
( X1 != X2
| sdtasdt0(X1,X3) = sdtasdt0(X2,X3) ) ).
cnf(i_0_288,axiom,
( X1 != X2
| sdtasdt0(X3,X1) = sdtasdt0(X3,X2) ) ).
cnf(i_0_289,axiom,
( X1 != X2
| smndt0(X1) = smndt0(X2) ) ).
cnf(i_0_290,axiom,
( X1 != X2
| slsdtgt0(X1) = slsdtgt0(X2) ) ).
cnf(i_0_291,axiom,
( X1 != X2
| esk15_2(X1,X3) = esk15_2(X2,X3) ) ).
cnf(i_0_292,axiom,
( X1 != X2
| esk15_2(X3,X1) = esk15_2(X3,X2) ) ).
cnf(i_0_293,axiom,
( X1 != X2
| esk19_2(X1,X3) = esk19_2(X2,X3) ) ).
cnf(i_0_294,axiom,
( X1 != X2
| esk19_2(X3,X1) = esk19_2(X3,X2) ) ).
cnf(i_0_295,axiom,
( X1 != X2
| sdtpldt1(X1,X3) = sdtpldt1(X2,X3) ) ).
cnf(i_0_296,axiom,
( X1 != X2
| sdtpldt1(X3,X1) = sdtpldt1(X3,X2) ) ).
cnf(i_0_297,axiom,
( X1 != X2
| sdtasasdt0(X1,X3) = sdtasasdt0(X2,X3) ) ).
cnf(i_0_298,axiom,
( X1 != X2
| sdtasasdt0(X3,X1) = sdtasasdt0(X3,X2) ) ).
cnf(i_0_299,axiom,
( X1 != X2
| ~ aElementOf0(X1,X3)
| aElementOf0(X2,X3) ) ).
cnf(i_0_300,axiom,
( X1 != X2
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X2) ) ).
cnf(i_0_301,axiom,
( X1 != X2
| ~ misRelativelyPrime0(X1,X3)
| misRelativelyPrime0(X2,X3) ) ).
cnf(i_0_302,axiom,
( X1 != X2
| ~ misRelativelyPrime0(X3,X1)
| misRelativelyPrime0(X3,X2) ) ).
cnf(i_0_303,axiom,
( X1 != X2
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(X2) ) ).
cnf(i_0_304,axiom,
( X1 != X2
| ~ aSet0(X1)
| aSet0(X2) ) ).
cnf(i_0_305,axiom,
( X1 != X2
| ~ sdteqdtlpzmzozddtrp0(X1,X3,X4)
| sdteqdtlpzmzozddtrp0(X2,X3,X4) ) ).
cnf(i_0_306,axiom,
( X1 != X2
| ~ sdteqdtlpzmzozddtrp0(X3,X1,X4)
| sdteqdtlpzmzozddtrp0(X3,X2,X4) ) ).
cnf(i_0_307,axiom,
( X1 != X2
| ~ sdteqdtlpzmzozddtrp0(X3,X4,X1)
| sdteqdtlpzmzozddtrp0(X3,X4,X2) ) ).
cnf(i_0_308,axiom,
( X1 != X2
| ~ aElement0(X1)
| aElement0(X2) ) ).
cnf(i_0_309,axiom,
( X1 != X2
| ~ aIdeal0(X1)
| aIdeal0(X2) ) ).
cnf(i_0_310,axiom,
( X1 != X2
| ~ aGcdOfAnd0(X1,X3,X4)
| aGcdOfAnd0(X2,X3,X4) ) ).
cnf(i_0_311,axiom,
( X1 != X2
| ~ aGcdOfAnd0(X3,X1,X4)
| aGcdOfAnd0(X3,X2,X4) ) ).
cnf(i_0_312,axiom,
( X1 != X2
| ~ aGcdOfAnd0(X3,X4,X1)
| aGcdOfAnd0(X3,X4,X2) ) ).
cnf(i_0_313,axiom,
( X1 != X2
| ~ doDivides0(X1,X3)
| doDivides0(X2,X3) ) ).
cnf(i_0_314,axiom,
( X1 != X2
| ~ doDivides0(X3,X1)
| doDivides0(X3,X2) ) ).
cnf(i_0_315,axiom,
( X1 != X2
| ~ aDivisorOf0(X1,X3)
| aDivisorOf0(X2,X3) ) ).
cnf(i_0_316,axiom,
( X1 != X2
| ~ aDivisorOf0(X3,X1)
| aDivisorOf0(X3,X2) ) ).
cnf(i_0_317,axiom,
( X1 != X2
| ~ iLess0(X1,X3)
| iLess0(X2,X3) ) ).
cnf(i_0_318,axiom,
( X1 != X2
| ~ iLess0(X3,X1)
| iLess0(X3,X2) ) ).
cnf(i_0_279_001,axiom,
X1 = X1 ).
cnf(i_0_280_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_281_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_282_004,axiom,
( X1 != X2
| sdtpldt0(X1,X3) = sdtpldt0(X2,X3) ) ).
cnf(i_0_283_005,axiom,
( X1 != X2
| sdtpldt0(X3,X1) = sdtpldt0(X3,X2) ) ).
cnf(i_0_284_006,axiom,
( X1 != X2
| esk5_3(X1,X3,X4) = esk5_3(X2,X3,X4) ) ).
cnf(i_0_285_007,axiom,
( X1 != X2
| esk5_3(X3,X1,X4) = esk5_3(X3,X2,X4) ) ).
cnf(i_0_286_008,axiom,
( X1 != X2
| esk5_3(X3,X4,X1) = esk5_3(X3,X4,X2) ) ).
cnf(i_0_287_009,axiom,
( X1 != X2
| sdtasdt0(X1,X3) = sdtasdt0(X2,X3) ) ).
cnf(i_0_288_010,axiom,
( X1 != X2
| sdtasdt0(X3,X1) = sdtasdt0(X3,X2) ) ).
cnf(i_0_289_011,axiom,
( X1 != X2
| smndt0(X1) = smndt0(X2) ) ).
cnf(i_0_290_012,axiom,
( X1 != X2
| slsdtgt0(X1) = slsdtgt0(X2) ) ).
cnf(i_0_291_013,axiom,
( X1 != X2
| esk15_2(X1,X3) = esk15_2(X2,X3) ) ).
cnf(i_0_292_014,axiom,
( X1 != X2
| esk15_2(X3,X1) = esk15_2(X3,X2) ) ).
cnf(i_0_293_015,axiom,
( X1 != X2
| esk19_2(X1,X3) = esk19_2(X2,X3) ) ).
cnf(i_0_294_016,axiom,
( X1 != X2
| esk19_2(X3,X1) = esk19_2(X3,X2) ) ).
cnf(i_0_295_017,axiom,
( X1 != X2
| sdtpldt1(X1,X3) = sdtpldt1(X2,X3) ) ).
cnf(i_0_296_018,axiom,
( X1 != X2
| sdtpldt1(X3,X1) = sdtpldt1(X3,X2) ) ).
cnf(i_0_297_019,axiom,
( X1 != X2
| sdtasasdt0(X1,X3) = sdtasasdt0(X2,X3) ) ).
cnf(i_0_298_020,axiom,
( X1 != X2
| sdtasasdt0(X3,X1) = sdtasasdt0(X3,X2) ) ).
cnf(i_0_299_021,axiom,
( X1 != X2
| ~ aElementOf0(X1,X3)
| aElementOf0(X2,X3) ) ).
cnf(i_0_300_022,axiom,
( X1 != X2
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X2) ) ).
cnf(i_0_301_023,axiom,
( X1 != X2
| ~ misRelativelyPrime0(X1,X3)
| misRelativelyPrime0(X2,X3) ) ).
cnf(i_0_302_024,axiom,
( X1 != X2
| ~ misRelativelyPrime0(X3,X1)
| misRelativelyPrime0(X3,X2) ) ).
cnf(i_0_303_025,axiom,
( X1 != X2
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(X2) ) ).
cnf(i_0_304_026,axiom,
( X1 != X2
| ~ aSet0(X1)
| aSet0(X2) ) ).
cnf(i_0_305_027,axiom,
( X1 != X2
| ~ sdteqdtlpzmzozddtrp0(X1,X3,X4)
| sdteqdtlpzmzozddtrp0(X2,X3,X4) ) ).
cnf(i_0_306_028,axiom,
( X1 != X2
| ~ sdteqdtlpzmzozddtrp0(X3,X1,X4)
| sdteqdtlpzmzozddtrp0(X3,X2,X4) ) ).
cnf(i_0_307_029,axiom,
( X1 != X2
| ~ sdteqdtlpzmzozddtrp0(X3,X4,X1)
| sdteqdtlpzmzozddtrp0(X3,X4,X2) ) ).
cnf(i_0_308_030,axiom,
( X1 != X2
| ~ aElement0(X1)
| aElement0(X2) ) ).
cnf(i_0_309_031,axiom,
( X1 != X2
| ~ aIdeal0(X1)
| aIdeal0(X2) ) ).
cnf(i_0_310_032,axiom,
( X1 != X2
| ~ aGcdOfAnd0(X1,X3,X4)
| aGcdOfAnd0(X2,X3,X4) ) ).
cnf(i_0_311_033,axiom,
( X1 != X2
| ~ aGcdOfAnd0(X3,X1,X4)
| aGcdOfAnd0(X3,X2,X4) ) ).
cnf(i_0_312_034,axiom,
( X1 != X2
| ~ aGcdOfAnd0(X3,X4,X1)
| aGcdOfAnd0(X3,X4,X2) ) ).
cnf(i_0_313_035,axiom,
( X1 != X2
| ~ doDivides0(X1,X3)
| doDivides0(X2,X3) ) ).
cnf(i_0_314_036,axiom,
( X1 != X2
| ~ doDivides0(X3,X1)
| doDivides0(X3,X2) ) ).
cnf(i_0_315_037,axiom,
( X1 != X2
| ~ aDivisorOf0(X1,X3)
| aDivisorOf0(X2,X3) ) ).
cnf(i_0_316_038,axiom,
( X1 != X2
| ~ aDivisorOf0(X3,X1)
| aDivisorOf0(X3,X2) ) ).
cnf(i_0_317_039,axiom,
( X1 != X2
| ~ iLess0(X1,X3)
| iLess0(X2,X3) ) ).
cnf(i_0_318_040,axiom,
( X1 != X2
| ~ iLess0(X3,X1)
| iLess0(X3,X2) ) ).
cnf(i_0_319,plain,
( ~ aElementOf0(X1,sdtpldt1(X2,X3))
| ~ aSet0(X2)
| ~ aSet0(X3)
| sdtpldt0(esk3_4(X2,X3,sdtpldt1(X2,X3),X1),esk4_4(X2,X3,sdtpldt1(X2,X3),X1)) = X1 ),
inference(equality_inference,[],[86]) ).
cnf(i_0_320,plain,
( ~ aElementOf0(X1,sdtpldt1(X2,X3))
| ~ aSet0(X2)
| ~ aSet0(X3)
| aElementOf0(esk4_4(X2,X3,sdtpldt1(X2,X3),X1),X3) ),
inference(equality_inference,[],[93]) ).
cnf(i_0_321,plain,
( ~ aElementOf0(X1,sdtpldt1(X2,X3))
| ~ aSet0(X2)
| ~ aSet0(X3)
| aElementOf0(esk3_4(X2,X3,sdtpldt1(X2,X3),X1),X2) ),
inference(equality_inference,[],[94]) ).
cnf(i_0_322,plain,
( ~ aElementOf0(X1,slsdtgt0(X2))
| ~ aElement0(X2)
| sdtasdt0(X2,esk18_3(X2,slsdtgt0(X2),X1)) = X1 ),
inference(equality_inference,[],[108]) ).
cnf(i_0_323,plain,
( ~ aElementOf0(X1,slsdtgt0(X2))
| ~ aElement0(X2)
| aElement0(esk18_3(X2,slsdtgt0(X2),X1)) ),
inference(equality_inference,[],[110]) ).
cnf(i_0_324,plain,
( sdtpldt0(X1,X2) = sz00
| ~ iLess0(sbrdtbr0(sdtpldt0(X1,X2)),sbrdtbr0(xu))
| ~ aElementOf0(X1,slsdtgt0(xa))
| ~ aElementOf0(X2,slsdtgt0(xb)) ),
inference(equality_inference,[],[121]) ).
cnf(i_0_325,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aElementOf0(X3,sdtasasdt0(X1,X2))
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X2) ),
inference(equality_inference,[],[129]) ).
cnf(i_0_326,plain,
( aElementOf0(sdtpldt0(X1,X2),xI)
| ~ aElementOf0(X1,slsdtgt0(xa))
| ~ aElementOf0(X2,slsdtgt0(xb)) ),
inference(equality_inference,[],[132]) ).
cnf(i_0_327,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aElementOf0(X3,X1)
| ~ aElementOf0(X3,sdtasasdt0(X1,X2)) ),
inference(equality_inference,[],[144]) ).
cnf(i_0_328,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aElementOf0(X3,X2)
| ~ aElementOf0(X3,sdtasasdt0(X1,X2)) ),
inference(equality_inference,[],[145]) ).
cnf(i_0_329,plain,
( ~ aElement0(X1)
| ~ aElement0(sdtasdt0(X1,X2))
| doDivides0(X1,sdtasdt0(X1,X2))
| ~ aElement0(X2) ),
inference(equality_inference,[],[164]) ).
cnf(i_0_330,plain,
( ~ aElement0(X1)
| aElementOf0(sdtasdt0(xb,X1),slsdtgt0(xb)) ),
inference(equality_inference,[],[185]) ).
cnf(i_0_331,plain,
( ~ aElement0(X1)
| aElementOf0(sdtasdt0(xa,X1),slsdtgt0(xa)) ),
inference(equality_inference,[],[187]) ).
cnf(i_0_332,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aSet0(sdtasasdt0(X1,X2)) ),
inference(equality_inference,[],[200]) ).
cnf(i_0_333,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aSet0(sdtpldt1(X1,X2)) ),
inference(equality_inference,[],[201]) ).
cnf(i_0_334,plain,
( ~ aElement0(X1)
| aSet0(slsdtgt0(X1)) ),
inference(equality_inference,[],[225]) ).
cnf(i_0_335,plain,
$false,
inference(scs_inference,[],[i_0_259,i_0_247,i_0_243,i_0_189]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : RNG125+4 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n004.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 01:52:17 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 0.34/5.61 % Version : CSE_E---1.7
% 0.34/5.61 % Problem : theBenchmark.p
% 0.34/5.61 % SZS status Theorem for theBenchmark.p
% 0.34/5.61 % SZS output start CNFRefutation
% See solution above
% 0.34/5.65 % Total time : 5.282s
%------------------------------------------------------------------------------