%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG124+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n006.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 05:05:25 PM UTC 2026
% Result : Theorem 0.32s 5.62s
% Output : CNFRefutation 0.42s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 96)
% Comments :
%------------------------------------------------------------------------------
fof(m__2273,hypothesis,
( aElementOf0(xu,xI)
& xu != sz00
& ! [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(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__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] :
( 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(m__2383,hypothesis,
~ ( aDivisorOf0(xu,xa)
& aDivisorOf0(xu,xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2383) ).
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(m__2612,hypothesis,
~ doDivides0(xu,xb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2612) ).
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__2479,hypothesis,
~ ~ doDivides0(xu,xa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2479) ).
fof(m__2690,hypothesis,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2690) ).
fof(m__2718,hypothesis,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2718) ).
fof(m__2129,hypothesis,
aGcdOfAnd0(xc,xa,xb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2129) ).
fof(m__2666,hypothesis,
( aElement0(xq)
& aElement0(xr)
& xb = sdtpldt0(sdtasdt0(xq,xu),xr)
& ( xr = sz00
| iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2666) ).
fof(m__2174,hypothesis,
( aIdeal0(xI)
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).
fof(m__2203,hypothesis,
( aElementOf0(sz00,slsdtgt0(xa))
& aElementOf0(xa,slsdtgt0(xa))
& aElementOf0(sz00,slsdtgt0(xb))
& aElementOf0(xb,slsdtgt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2203) ).
fof(m__2729,hypothesis,
aElementOf0(xr,xI),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2729) ).
fof(m__2699,hypothesis,
aElementOf0(xb,xI),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2699) ).
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(m__2673,hypothesis,
xr != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2673) ).
fof(mUnNeZr,axiom,
sz10 != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mUnNeZr) ).
fof(i_0_51,hypothesis,
( aElementOf0(xu,xI)
& xu != sz00
& ! [X1] :
( ( aElementOf0(X1,xI)
& X1 != sz00 )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
inference(fof_simplification,[status(thm)],[m__2273]) ).
fof(i_0_52,plain,
! [X126,X127,X128,X129,X132,X133,X134,X135,X137,X138] :
( ( aSet0(X128)
| X128 != sdtpldt1(X126,X127)
| ~ aSet0(X126)
| ~ aSet0(X127) )
& ( aElementOf0(esk3_4(X126,X127,X128,X129),X126)
| ~ aElementOf0(X129,X128)
| X128 != sdtpldt1(X126,X127)
| ~ aSet0(X126)
| ~ aSet0(X127) )
& ( aElementOf0(esk4_4(X126,X127,X128,X129),X127)
| ~ aElementOf0(X129,X128)
| X128 != sdtpldt1(X126,X127)
| ~ aSet0(X126)
| ~ aSet0(X127) )
& ( sdtpldt0(esk3_4(X126,X127,X128,X129),esk4_4(X126,X127,X128,X129)) = X129
| ~ aElementOf0(X129,X128)
| X128 != sdtpldt1(X126,X127)
| ~ aSet0(X126)
| ~ aSet0(X127) )
& ( ~ aElementOf0(X133,X126)
| ~ aElementOf0(X134,X127)
| sdtpldt0(X133,X134) != X132
| aElementOf0(X132,X128)
| X128 != sdtpldt1(X126,X127)
| ~ aSet0(X126)
| ~ aSet0(X127) )
& ( ~ aElementOf0(esk5_3(X126,X127,X135),X135)
| ~ aElementOf0(X137,X126)
| ~ aElementOf0(X138,X127)
| sdtpldt0(X137,X138) != esk5_3(X126,X127,X135)
| ~ aSet0(X135)
| X135 = sdtpldt1(X126,X127)
| ~ aSet0(X126)
| ~ aSet0(X127) )
& ( aElementOf0(esk6_3(X126,X127,X135),X126)
| aElementOf0(esk5_3(X126,X127,X135),X135)
| ~ aSet0(X135)
| X135 = sdtpldt1(X126,X127)
| ~ aSet0(X126)
| ~ aSet0(X127) )
& ( aElementOf0(esk7_3(X126,X127,X135),X127)
| aElementOf0(esk5_3(X126,X127,X135),X135)
| ~ aSet0(X135)
| X135 = sdtpldt1(X126,X127)
| ~ aSet0(X126)
| ~ aSet0(X127) )
& ( sdtpldt0(esk6_3(X126,X127,X135),esk7_3(X126,X127,X135)) = esk5_3(X126,X127,X135)
| aElementOf0(esk5_3(X126,X127,X135),X135)
| ~ aSet0(X135)
| X135 = sdtpldt1(X126,X127)
| ~ aSet0(X126)
| ~ aSet0(X127) ) ),
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_53,plain,
! [X163,X164,X166,X167] :
( ( aElement0(esk13_4(X163,X164,X166,X167))
| ~ aElement0(X166)
| ~ aElement0(X167)
| aElement0(esk12_2(X163,X164))
| ~ aIdeal0(X163)
| ~ aIdeal0(X164) )
& ( sdteqdtlpzmzozddtrp0(esk13_4(X163,X164,X166,X167),X166,X163)
| ~ aElement0(X166)
| ~ aElement0(X167)
| aElement0(esk12_2(X163,X164))
| ~ aIdeal0(X163)
| ~ aIdeal0(X164) )
& ( sdteqdtlpzmzozddtrp0(esk13_4(X163,X164,X166,X167),X167,X164)
| ~ aElement0(X166)
| ~ aElement0(X167)
| aElement0(esk12_2(X163,X164))
| ~ aIdeal0(X163)
| ~ aIdeal0(X164) )
& ( aElement0(esk13_4(X163,X164,X166,X167))
| ~ aElement0(X166)
| ~ aElement0(X167)
| ~ aElementOf0(esk12_2(X163,X164),sdtpldt1(X163,X164))
| ~ aIdeal0(X163)
| ~ aIdeal0(X164) )
& ( sdteqdtlpzmzozddtrp0(esk13_4(X163,X164,X166,X167),X166,X163)
| ~ aElement0(X166)
| ~ aElement0(X167)
| ~ aElementOf0(esk12_2(X163,X164),sdtpldt1(X163,X164))
| ~ aIdeal0(X163)
| ~ aIdeal0(X164) )
& ( sdteqdtlpzmzozddtrp0(esk13_4(X163,X164,X166,X167),X167,X164)
| ~ aElement0(X166)
| ~ aElement0(X167)
| ~ aElementOf0(esk12_2(X163,X164),sdtpldt1(X163,X164))
| ~ aIdeal0(X163)
| ~ aIdeal0(X164) ) ),
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_54,plain,
! [X141,X142,X143,X144,X145,X146] :
( ( aSet0(X143)
| X143 != sdtasasdt0(X141,X142)
| ~ aSet0(X141)
| ~ aSet0(X142) )
& ( aElementOf0(X144,X141)
| ~ aElementOf0(X144,X143)
| X143 != sdtasasdt0(X141,X142)
| ~ aSet0(X141)
| ~ aSet0(X142) )
& ( aElementOf0(X144,X142)
| ~ aElementOf0(X144,X143)
| X143 != sdtasasdt0(X141,X142)
| ~ aSet0(X141)
| ~ aSet0(X142) )
& ( ~ aElementOf0(X145,X141)
| ~ aElementOf0(X145,X142)
| aElementOf0(X145,X143)
| X143 != sdtasasdt0(X141,X142)
| ~ aSet0(X141)
| ~ aSet0(X142) )
& ( ~ aElementOf0(esk8_3(X141,X142,X146),X146)
| ~ aElementOf0(esk8_3(X141,X142,X146),X141)
| ~ aElementOf0(esk8_3(X141,X142,X146),X142)
| ~ aSet0(X146)
| X146 = sdtasasdt0(X141,X142)
| ~ aSet0(X141)
| ~ aSet0(X142) )
& ( aElementOf0(esk8_3(X141,X142,X146),X141)
| aElementOf0(esk8_3(X141,X142,X146),X146)
| ~ aSet0(X146)
| X146 = sdtasasdt0(X141,X142)
| ~ aSet0(X141)
| ~ aSet0(X142) )
& ( aElementOf0(esk8_3(X141,X142,X146),X142)
| aElementOf0(esk8_3(X141,X142,X146),X146)
| ~ aSet0(X146)
| X146 = sdtasasdt0(X141,X142)
| ~ aSet0(X141)
| ~ aSet0(X142) ) ),
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_55,plain,
! [X180,X181,X182,X183,X184] :
( ( aDivisorOf0(X182,X180)
| ~ aGcdOfAnd0(X182,X180,X181)
| ~ aElement0(X180)
| ~ aElement0(X181) )
& ( aDivisorOf0(X182,X181)
| ~ aGcdOfAnd0(X182,X180,X181)
| ~ aElement0(X180)
| ~ aElement0(X181) )
& ( ~ aDivisorOf0(X183,X180)
| ~ aDivisorOf0(X183,X181)
| doDivides0(X183,X182)
| ~ aGcdOfAnd0(X182,X180,X181)
| ~ aElement0(X180)
| ~ aElement0(X181) )
& ( aDivisorOf0(esk17_3(X180,X181,X184),X180)
| ~ aDivisorOf0(X184,X180)
| ~ aDivisorOf0(X184,X181)
| aGcdOfAnd0(X184,X180,X181)
| ~ aElement0(X180)
| ~ aElement0(X181) )
& ( aDivisorOf0(esk17_3(X180,X181,X184),X181)
| ~ aDivisorOf0(X184,X180)
| ~ aDivisorOf0(X184,X181)
| aGcdOfAnd0(X184,X180,X181)
| ~ aElement0(X180)
| ~ aElement0(X181) )
& ( ~ doDivides0(esk17_3(X180,X181,X184),X184)
| ~ aDivisorOf0(X184,X180)
| ~ aDivisorOf0(X184,X181)
| aGcdOfAnd0(X184,X180,X181)
| ~ aElement0(X180)
| ~ aElement0(X181) ) ),
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_56,plain,
! [X148,X149,X150,X151,X152] :
( ( aSet0(X148)
| ~ aIdeal0(X148) )
& ( ~ aElementOf0(X150,X148)
| aElementOf0(sdtpldt0(X149,X150),X148)
| ~ aElementOf0(X149,X148)
| ~ aIdeal0(X148) )
& ( ~ aElement0(X151)
| aElementOf0(sdtasdt0(X151,X149),X148)
| ~ aElementOf0(X149,X148)
| ~ aIdeal0(X148) )
& ( aElementOf0(esk9_1(X152),X152)
| ~ aSet0(X152)
| aIdeal0(X152) )
& ( aElement0(esk11_1(X152))
| aElementOf0(esk10_1(X152),X152)
| ~ aSet0(X152)
| aIdeal0(X152) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X152),esk9_1(X152)),X152)
| aElementOf0(esk10_1(X152),X152)
| ~ aSet0(X152)
| aIdeal0(X152) )
& ( aElement0(esk11_1(X152))
| ~ aElementOf0(sdtpldt0(esk9_1(X152),esk10_1(X152)),X152)
| ~ aSet0(X152)
| aIdeal0(X152) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X152),esk9_1(X152)),X152)
| ~ aElementOf0(sdtpldt0(esk9_1(X152),esk10_1(X152)),X152)
| ~ aSet0(X152)
| aIdeal0(X152) ) ),
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_57,plain,
! [X160,X161,X162] :
( ( ~ sdteqdtlpzmzozddtrp0(X160,X161,X162)
| aElementOf0(sdtpldt0(X160,smndt0(X161)),X162)
| ~ aElement0(X160)
| ~ aElement0(X161)
| ~ aIdeal0(X162) )
& ( ~ aElementOf0(sdtpldt0(X160,smndt0(X161)),X162)
| sdteqdtlpzmzozddtrp0(X160,X161,X162)
| ~ aElement0(X160)
| ~ aElement0(X161)
| ~ aIdeal0(X162) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefMod])])]) ).
fof(i_0_58,plain,
! [X188,X189,X190,X192,X193,X194,X196] :
( ( aSet0(X189)
| X189 != slsdtgt0(X188)
| ~ aElement0(X188) )
& ( aElement0(esk18_3(X188,X189,X190))
| ~ aElementOf0(X190,X189)
| X189 != slsdtgt0(X188)
| ~ aElement0(X188) )
& ( sdtasdt0(X188,esk18_3(X188,X189,X190)) = X190
| ~ aElementOf0(X190,X189)
| X189 != slsdtgt0(X188)
| ~ aElement0(X188) )
& ( ~ aElement0(X193)
| sdtasdt0(X188,X193) != X192
| aElementOf0(X192,X189)
| X189 != slsdtgt0(X188)
| ~ aElement0(X188) )
& ( ~ aElementOf0(esk19_2(X188,X194),X194)
| ~ aElement0(X196)
| sdtasdt0(X188,X196) != esk19_2(X188,X194)
| ~ aSet0(X194)
| X194 = slsdtgt0(X188)
| ~ aElement0(X188) )
& ( aElement0(esk20_2(X188,X194))
| aElementOf0(esk19_2(X188,X194),X194)
| ~ aSet0(X194)
| X194 = slsdtgt0(X188)
| ~ aElement0(X188) )
& ( sdtasdt0(X188,esk20_2(X188,X194)) = esk19_2(X188,X194)
| aElementOf0(esk19_2(X188,X194),X194)
| ~ aSet0(X194)
| X194 = slsdtgt0(X188)
| ~ aElement0(X188) ) ),
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_59,plain,
! [X122,X123] :
( ( aElementOf0(esk2_2(X122,X123),X123)
| aElementOf0(esk1_2(X122,X123),X122)
| X122 = X123
| ~ aSet0(X122)
| ~ aSet0(X123) )
& ( ~ aElementOf0(esk2_2(X122,X123),X122)
| aElementOf0(esk1_2(X122,X123),X122)
| X122 = X123
| ~ aSet0(X122)
| ~ aSet0(X123) )
& ( aElementOf0(esk2_2(X122,X123),X123)
| ~ aElementOf0(esk1_2(X122,X123),X123)
| X122 = X123
| ~ aSet0(X122)
| ~ aSet0(X123) )
& ( ~ aElementOf0(esk2_2(X122,X123),X122)
| ~ aElementOf0(esk1_2(X122,X123),X123)
| X122 = X123
| ~ aSet0(X122)
| ~ aSet0(X123) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSetEq])])])]) ).
fof(i_0_60,plain,
! [X170,X171] :
( ( aElement0(esk14_2(X170,X171))
| ~ aElement0(X170)
| ~ aElement0(X171)
| X171 = sz00 )
& ( aElement0(esk15_2(X170,X171))
| ~ aElement0(X170)
| ~ aElement0(X171)
| X171 = sz00 )
& ( X170 = sdtpldt0(sdtasdt0(esk14_2(X170,X171),X171),esk15_2(X170,X171))
| ~ aElement0(X170)
| ~ aElement0(X171)
| X171 = sz00 )
& ( esk15_2(X170,X171) = sz00
| iLess0(sbrdtbr0(esk15_2(X170,X171)),sbrdtbr0(X171))
| ~ aElement0(X170)
| ~ aElement0(X171)
| X171 = sz00 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivision])])])]) ).
fof(i_0_61,plain,
! [X113,X114,X115] :
( ( sdtasdt0(X113,sdtpldt0(X114,X115)) = sdtpldt0(sdtasdt0(X113,X114),sdtasdt0(X113,X115))
| ~ aElement0(X113)
| ~ aElement0(X114)
| ~ aElement0(X115) )
& ( sdtasdt0(sdtpldt0(X114,X115),X113) = sdtpldt0(sdtasdt0(X114,X113),sdtasdt0(X115,X113))
| ~ aElement0(X113)
| ~ aElement0(X114)
| ~ aElement0(X115) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])]) ).
fof(i_0_62,plain,
! [X186,X187] :
( ( ~ misRelativelyPrime0(X186,X187)
| aGcdOfAnd0(sz10,X186,X187)
| ~ aElement0(X186)
| ~ aElement0(X187) )
& ( ~ aGcdOfAnd0(sz10,X186,X187)
| misRelativelyPrime0(X186,X187)
| ~ aElement0(X186)
| ~ aElement0(X187) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefRel])])]) ).
fof(i_0_63,plain,
! [X109,X110,X111] :
( ~ aElement0(X109)
| ~ aElement0(X110)
| ~ aElement0(X111)
| sdtasdt0(sdtasdt0(X109,X110),X111) = sdtasdt0(X109,sdtasdt0(X110,X111)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
fof(i_0_64,plain,
! [X102,X103,X104] :
( ~ aElement0(X102)
| ~ aElement0(X103)
| ~ aElement0(X104)
| sdtpldt0(sdtpldt0(X102,X103),X104) = sdtpldt0(X102,sdtpldt0(X103,X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
fof(i_0_65,plain,
! [X174,X175,X177] :
( ( aElement0(esk16_2(X174,X175))
| ~ doDivides0(X174,X175)
| ~ aElement0(X174)
| ~ aElement0(X175) )
& ( sdtasdt0(X174,esk16_2(X174,X175)) = X175
| ~ doDivides0(X174,X175)
| ~ aElement0(X174)
| ~ aElement0(X175) )
& ( ~ aElement0(X177)
| sdtasdt0(X174,X177) != X175
| doDivides0(X174,X175)
| ~ aElement0(X174)
| ~ aElement0(X175) ) ),
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_66,hypothesis,
! [X200] :
( aElementOf0(xu,xI)
& xu != sz00
& ( ~ aElementOf0(X200,xI)
| X200 = sz00
| ~ iLess0(sbrdtbr0(X200),sbrdtbr0(xu)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_51])])]) ).
fof(i_0_67,hypothesis,
( aElement0(esk22_0)
& aElement0(esk23_0)
& xu = sdtpldt0(sdtasdt0(xa,esk22_0),sdtasdt0(xb,esk23_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2416])]) ).
fof(i_0_68,plain,
! [X178,X179] :
( ( aElement0(X179)
| ~ aDivisorOf0(X179,X178)
| ~ aElement0(X178) )
& ( doDivides0(X179,X178)
| ~ aDivisorOf0(X179,X178)
| ~ aElement0(X178) )
& ( ~ aElement0(X179)
| ~ doDivides0(X179,X178)
| aDivisorOf0(X179,X178)
| ~ aElement0(X178) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDvs])])])]) ).
fof(i_0_69,hypothesis,
( aElementOf0(esk21_0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& esk21_0 != sz00 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2228])]) ).
fof(i_0_70,plain,
! [X158,X159] :
( ~ aIdeal0(X158)
| ~ aIdeal0(X159)
| aIdeal0(sdtasasdt0(X158,X159)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIdeInt])]) ).
fof(i_0_71,plain,
! [X156,X157] :
( ~ aIdeal0(X156)
| ~ aIdeal0(X157)
| aIdeal0(sdtpldt1(X156,X157)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIdeSum])]) ).
fof(i_0_72,plain,
! [X98,X99] :
( ~ aElement0(X98)
| ~ aElement0(X99)
| aElement0(sdtasdt0(X98,X99)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(i_0_73,plain,
! [X96,X97] :
( ~ aElement0(X96)
| ~ aElement0(X97)
| aElement0(sdtpldt0(X96,X97)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
fof(i_0_74,plain,
! [X107,X108] :
( ~ aElement0(X107)
| ~ aElement0(X108)
| sdtasdt0(X107,X108) = sdtasdt0(X108,X107) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
fof(i_0_75,plain,
! [X100,X101] :
( ~ aElement0(X100)
| ~ aElement0(X101)
| sdtpldt0(X100,X101) = sdtpldt0(X101,X100) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
fof(i_0_76,plain,
! [X118,X119] :
( ~ aElement0(X118)
| ~ aElement0(X119)
| sdtasdt0(X118,X119) != sz00
| X118 = sz00
| X119 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCancel])]) ).
fof(i_0_77,hypothesis,
( ~ aDivisorOf0(xu,xa)
| ~ aDivisorOf0(xu,xb) ),
inference(fof_nnf,[status(thm)],[m__2383]) ).
fof(i_0_78,plain,
! [X120,X121] :
( ~ aSet0(X120)
| ~ aElementOf0(X121,X120)
| aElement0(X121) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
fof(i_0_79,plain,
! [X116] :
( ( sdtasdt0(smndt0(sz10),X116) = smndt0(X116)
| ~ aElement0(X116) )
& ( smndt0(X116) = sdtasdt0(X116,smndt0(sz10))
| ~ aElement0(X116) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMnOne])])]) ).
fof(i_0_80,plain,
! [X106] :
( ( sdtpldt0(X106,smndt0(X106)) = sz00
| ~ aElement0(X106) )
& ( sz00 = sdtpldt0(smndt0(X106),X106)
| ~ aElement0(X106) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddInvr])])]) ).
fof(i_0_81,plain,
! [X112] :
( ( sdtasdt0(X112,sz10) = X112
| ~ aElement0(X112) )
& ( X112 = sdtasdt0(sz10,X112)
| ~ aElement0(X112) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulUnit])])]) ).
fof(i_0_82,plain,
! [X105] :
( ( sdtpldt0(X105,sz00) = X105
| ~ aElement0(X105) )
& ( X105 = sdtpldt0(sz00,X105)
| ~ aElement0(X105) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).
fof(i_0_83,plain,
! [X117] :
( ( sdtasdt0(X117,sz00) = sz00
| ~ aElement0(X117) )
& ( sz00 = sdtasdt0(sz00,X117)
| ~ aElement0(X117) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulZero])])]) ).
fof(i_0_84,plain,
! [X169] :
( ~ aElement0(X169)
| X169 = sz00
| aNaturalNumber0(sbrdtbr0(X169)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEucSort])]) ).
fof(i_0_85,hypothesis,
~ doDivides0(xu,xb),
inference(fof_simplification,[status(thm)],[m__2612]) ).
fof(i_0_86,plain,
! [X198] :
( ~ aElement0(X198)
| aIdeal0(slsdtgt0(X198)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPrIdeal])]) ).
fof(i_0_87,plain,
! [X95] :
( ~ aElement0(X95)
| aElement0(smndt0(X95)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsU])]) ).
fof(i_0_88,hypothesis,
doDivides0(xu,xa),
inference(fof_simplification,[status(thm)],[m__2479]) ).
cnf(i_0_89,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_52]),
[final] ).
cnf(i_0_90,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_53]),
[final] ).
cnf(i_0_91,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_53]),
[final] ).
cnf(i_0_92,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_53]),
[final] ).
cnf(i_0_93,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_54]),
[final] ).
cnf(i_0_94,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_53]),
[final] ).
cnf(i_0_95,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_53]),
[final] ).
cnf(i_0_96,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_52]),
[final] ).
cnf(i_0_97,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_52]),
[final] ).
cnf(i_0_98,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_53]),
[final] ).
cnf(i_0_99,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_52]),
[final] ).
cnf(i_0_100,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_52]),
[final] ).
cnf(i_0_101,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_55]),
[final] ).
cnf(i_0_102,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_54]),
[final] ).
cnf(i_0_103,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_54]),
[final] ).
cnf(i_0_104,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_52]),
[final] ).
cnf(i_0_105,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_52]),
[final] ).
cnf(i_0_106,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_55]),
[final] ).
cnf(i_0_107,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_55]),
[final] ).
cnf(i_0_108,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_56]),
[final] ).
cnf(i_0_109,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_55]),
[final] ).
cnf(i_0_110,plain,
( aElementOf0(sdtpldt0(X1,smndt0(X2)),X3)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aIdeal0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_111,plain,
( sdtasdt0(X1,esk18_3(X1,X2,X3)) = X3
| ~ aElementOf0(X3,X2)
| X2 != slsdtgt0(X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_112,plain,
( sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ aElementOf0(sdtpldt0(X1,smndt0(X2)),X3)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aIdeal0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_113,plain,
( aElement0(esk18_3(X1,X2,X3))
| ~ aElementOf0(X3,X2)
| X2 != slsdtgt0(X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_114,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_59]),
[final] ).
cnf(i_0_115,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_60]),
[final] ).
cnf(i_0_116,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_58]),
[final] ).
cnf(i_0_117,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_56]),
[final] ).
cnf(i_0_118,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_61]),
[final] ).
cnf(i_0_119,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_61]),
[final] ).
cnf(i_0_120,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_56]),
[final] ).
cnf(i_0_121,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_52]),
[final] ).
cnf(i_0_122,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_59]),
[final] ).
cnf(i_0_123,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_59]),
[final] ).
cnf(i_0_124,plain,
( aDivisorOf0(X1,X2)
| ~ aGcdOfAnd0(X1,X2,X3)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_125,plain,
( aDivisorOf0(X1,X2)
| ~ aGcdOfAnd0(X1,X3,X2)
| ~ aElement0(X3)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_126,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_58]),
[final] ).
cnf(i_0_127,plain,
( misRelativelyPrime0(X1,X2)
| ~ aGcdOfAnd0(sz10,X1,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_128,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_60]),
[final] ).
cnf(i_0_129,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_130,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_131,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_54]),
[final] ).
cnf(i_0_132,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_59]),
[final] ).
cnf(i_0_133,plain,
( aElementOf0(sdtpldt0(X3,X1),X2)
| ~ aElementOf0(X1,X2)
| ~ aElementOf0(X3,X2)
| ~ aIdeal0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_134,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_58]),
[final] ).
cnf(i_0_135,plain,
( aGcdOfAnd0(sz10,X1,X2)
| ~ misRelativelyPrime0(X1,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_136,plain,
( sdtasdt0(X1,esk16_2(X1,X2)) = X2
| ~ doDivides0(X1,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_137,plain,
( aElementOf0(sdtasdt0(X1,X2),X3)
| ~ aElement0(X1)
| ~ aElementOf0(X2,X3)
| ~ aIdeal0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_138,plain,
( aElementOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| X3 != sdtasasdt0(X2,X4)
| ~ aSet0(X2)
| ~ aSet0(X4) ),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_139,plain,
( aElementOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| X3 != sdtasasdt0(X4,X2)
| ~ aSet0(X4)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_140,plain,
( aElement0(esk16_2(X1,X2))
| ~ doDivides0(X1,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_141,plain,
( aElementOf0(X3,X4)
| ~ aElement0(X1)
| sdtasdt0(X2,X1) != X3
| X4 != slsdtgt0(X2)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_142,plain,
( doDivides0(X2,X3)
| ~ aElement0(X1)
| sdtasdt0(X2,X1) != X3
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_143,hypothesis,
( X1 = sz00
| ~ aElementOf0(X1,xI)
| ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_144,hypothesis,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(split_conjunct,[status(thm)],[m__2690]),
[final] ).
cnf(i_0_145,hypothesis,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
inference(split_conjunct,[status(thm)],[m__2718]),
[final] ).
cnf(i_0_146,hypothesis,
xu = sdtpldt0(sdtasdt0(xa,esk22_0),sdtasdt0(xb,esk23_0)),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_147,plain,
( aDivisorOf0(X1,X2)
| ~ aElement0(X1)
| ~ doDivides0(X1,X2)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_148,hypothesis,
aElementOf0(esk21_0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_149,hypothesis,
aGcdOfAnd0(xc,xa,xb),
inference(split_conjunct,[status(thm)],[m__2129]),
[final] ).
cnf(i_0_150,plain,
( aElement0(esk15_2(X1,X2))
| X2 = sz00
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_151,plain,
( aElement0(esk14_2(X1,X2))
| X2 = sz00
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_152,plain,
( aIdeal0(sdtasasdt0(X1,X2))
| ~ aIdeal0(X1)
| ~ aIdeal0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_153,plain,
( aIdeal0(sdtpldt1(X1,X2))
| ~ aIdeal0(X1)
| ~ aIdeal0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_154,plain,
( aElement0(sdtasdt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_155,plain,
( aElement0(sdtpldt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_73]),
[final] ).
cnf(i_0_156,plain,
( doDivides0(X1,X2)
| ~ aDivisorOf0(X1,X2)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_157,plain,
( aElement0(esk11_1(X1))
| aElementOf0(esk10_1(X1),X1)
| aIdeal0(X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_158,plain,
( aSet0(X1)
| X1 != sdtasasdt0(X2,X3)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_159,plain,
( aSet0(X1)
| X1 != sdtpldt1(X2,X3)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_160,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_74]),
[final] ).
cnf(i_0_161,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_75]),
[final] ).
cnf(i_0_162,plain,
( X1 = sz00
| X2 = sz00
| ~ aElement0(X1)
| ~ aElement0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[i_0_76]),
[final] ).
cnf(i_0_163,hypothesis,
( ~ aDivisorOf0(xu,xa)
| ~ aDivisorOf0(xu,xb) ),
inference(split_conjunct,[status(thm)],[i_0_77]),
[final] ).
cnf(i_0_164,plain,
( aElement0(X1)
| ~ aDivisorOf0(X1,X2)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_165,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_78]),
[final] ).
cnf(i_0_166,hypothesis,
xb = sdtpldt0(sdtasdt0(xq,xu),xr),
inference(split_conjunct,[status(thm)],[m__2666]),
[final] ).
cnf(i_0_167,plain,
( aElementOf0(esk9_1(X1),X1)
| aIdeal0(X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_168,plain,
( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_79]),
[final] ).
cnf(i_0_169,plain,
( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_79]),
[final] ).
cnf(i_0_170,plain,
( sdtpldt0(X1,smndt0(X1)) = sz00
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_80]),
[final] ).
cnf(i_0_171,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_80]),
[final] ).
cnf(i_0_172,hypothesis,
( xr = sz00
| iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ),
inference(split_conjunct,[status(thm)],[m__2666]),
[final] ).
cnf(i_0_173,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_81]),
[final] ).
cnf(i_0_174,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_82]),
[final] ).
cnf(i_0_175,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_81]),
[final] ).
cnf(i_0_176,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_82]),
[final] ).
cnf(i_0_177,hypothesis,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(split_conjunct,[status(thm)],[m__2174]),
[final] ).
cnf(i_0_178,plain,
( aSet0(X1)
| X1 != slsdtgt0(X2)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_179,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_180,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_181,plain,
( X1 = sz00
| aNaturalNumber0(sbrdtbr0(X1))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_84]),
[final] ).
cnf(i_0_182,hypothesis,
~ doDivides0(xu,xb),
inference(split_conjunct,[status(thm)],[i_0_85]),
[final] ).
cnf(i_0_183,plain,
( aIdeal0(slsdtgt0(X1))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_86]),
[final] ).
cnf(i_0_184,plain,
( aElement0(smndt0(X1))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_185,hypothesis,
aElementOf0(xb,slsdtgt0(xb)),
inference(split_conjunct,[status(thm)],[m__2203]),
[final] ).
cnf(i_0_186,hypothesis,
aElementOf0(xa,slsdtgt0(xa)),
inference(split_conjunct,[status(thm)],[m__2203]),
[final] ).
cnf(i_0_187,hypothesis,
aElementOf0(sz00,slsdtgt0(xb)),
inference(split_conjunct,[status(thm)],[m__2203]),
[final] ).
cnf(i_0_188,hypothesis,
aElementOf0(sz00,slsdtgt0(xa)),
inference(split_conjunct,[status(thm)],[m__2203]),
[final] ).
cnf(i_0_189,plain,
( aSet0(X1)
| ~ aIdeal0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_190,hypothesis,
doDivides0(xu,xa),
inference(split_conjunct,[status(thm)],[i_0_88]),
[final] ).
cnf(i_0_191,hypothesis,
aElementOf0(xr,xI),
inference(split_conjunct,[status(thm)],[m__2729]),
[final] ).
cnf(i_0_192,hypothesis,
aElementOf0(xu,xI),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_193,hypothesis,
aElementOf0(xb,xI),
inference(split_conjunct,[status(thm)],[m__2699]),
[final] ).
cnf(i_0_194,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[m__2174]),
[final] ).
cnf(i_0_195,hypothesis,
aElement0(esk23_0),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_196,hypothesis,
aElement0(esk22_0),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_197,hypothesis,
aElement0(xr),
inference(split_conjunct,[status(thm)],[m__2666]),
[final] ).
cnf(i_0_198,hypothesis,
aElement0(xq),
inference(split_conjunct,[status(thm)],[m__2666]),
[final] ).
cnf(i_0_199,hypothesis,
aElement0(xb),
inference(split_conjunct,[status(thm)],[m__2091]),
[final] ).
cnf(i_0_200,hypothesis,
aElement0(xa),
inference(split_conjunct,[status(thm)],[m__2091]),
[final] ).
cnf(i_0_201,plain,
aElement0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]),
[final] ).
cnf(i_0_202,plain,
aElement0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]),
[final] ).
cnf(i_0_203,hypothesis,
( xa != sz00
| xb != sz00 ),
inference(split_conjunct,[status(thm)],[m__2110]),
[final] ).
cnf(i_0_204,hypothesis,
esk21_0 != sz00,
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_205,hypothesis,
xr != sz00,
inference(split_conjunct,[status(thm)],[m__2673]),
[final] ).
cnf(i_0_206,hypothesis,
xu != sz00,
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_207,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mUnNeZr]),
[final] ).
cnf(i_0_208,axiom,
X1 = X1 ).
cnf(i_0_209,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_210,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_211,axiom,
( X1 != X2
| sdtpldt0(X1,X3) = sdtpldt0(X2,X3) ) ).
cnf(i_0_212,axiom,
( X1 != X2
| sdtpldt0(X3,X1) = sdtpldt0(X3,X2) ) ).
cnf(i_0_213,axiom,
( X1 != X2
| esk5_3(X1,X3,X4) = esk5_3(X2,X3,X4) ) ).
cnf(i_0_214,axiom,
( X1 != X2
| esk5_3(X3,X1,X4) = esk5_3(X3,X2,X4) ) ).
cnf(i_0_215,axiom,
( X1 != X2
| esk5_3(X3,X4,X1) = esk5_3(X3,X4,X2) ) ).
cnf(i_0_216,axiom,
( X1 != X2
| sdtasdt0(X1,X3) = sdtasdt0(X2,X3) ) ).
cnf(i_0_217,axiom,
( X1 != X2
| sdtasdt0(X3,X1) = sdtasdt0(X3,X2) ) ).
cnf(i_0_218,axiom,
( X1 != X2
| smndt0(X1) = smndt0(X2) ) ).
cnf(i_0_219,axiom,
( X1 != X2
| slsdtgt0(X1) = slsdtgt0(X2) ) ).
cnf(i_0_220,axiom,
( X1 != X2
| esk15_2(X1,X3) = esk15_2(X2,X3) ) ).
cnf(i_0_221,axiom,
( X1 != X2
| esk15_2(X3,X1) = esk15_2(X3,X2) ) ).
cnf(i_0_222,axiom,
( X1 != X2
| esk19_2(X1,X3) = esk19_2(X2,X3) ) ).
cnf(i_0_223,axiom,
( X1 != X2
| esk19_2(X3,X1) = esk19_2(X3,X2) ) ).
cnf(i_0_224,axiom,
( X1 != X2
| sdtpldt1(X1,X3) = sdtpldt1(X2,X3) ) ).
cnf(i_0_225,axiom,
( X1 != X2
| sdtpldt1(X3,X1) = sdtpldt1(X3,X2) ) ).
cnf(i_0_226,axiom,
( X1 != X2
| sdtasasdt0(X1,X3) = sdtasasdt0(X2,X3) ) ).
cnf(i_0_227,axiom,
( X1 != X2
| sdtasasdt0(X3,X1) = sdtasasdt0(X3,X2) ) ).
cnf(i_0_228,axiom,
( X1 != X2
| ~ aElementOf0(X1,X3)
| aElementOf0(X2,X3) ) ).
cnf(i_0_229,axiom,
( X1 != X2
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X2) ) ).
cnf(i_0_230,axiom,
( X1 != X2
| ~ iLess0(X1,X3)
| iLess0(X2,X3) ) ).
cnf(i_0_231,axiom,
( X1 != X2
| ~ iLess0(X3,X1)
| iLess0(X3,X2) ) ).
cnf(i_0_232,axiom,
( X1 != X2
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(X2) ) ).
cnf(i_0_233,axiom,
( X1 != X2
| ~ aSet0(X1)
| aSet0(X2) ) ).
cnf(i_0_234,axiom,
( X1 != X2
| ~ sdteqdtlpzmzozddtrp0(X1,X3,X4)
| sdteqdtlpzmzozddtrp0(X2,X3,X4) ) ).
cnf(i_0_235,axiom,
( X1 != X2
| ~ sdteqdtlpzmzozddtrp0(X3,X1,X4)
| sdteqdtlpzmzozddtrp0(X3,X2,X4) ) ).
cnf(i_0_236,axiom,
( X1 != X2
| ~ sdteqdtlpzmzozddtrp0(X3,X4,X1)
| sdteqdtlpzmzozddtrp0(X3,X4,X2) ) ).
cnf(i_0_237,axiom,
( X1 != X2
| ~ aElement0(X1)
| aElement0(X2) ) ).
cnf(i_0_238,axiom,
( X1 != X2
| ~ aIdeal0(X1)
| aIdeal0(X2) ) ).
cnf(i_0_239,axiom,
( X1 != X2
| ~ aGcdOfAnd0(X1,X3,X4)
| aGcdOfAnd0(X2,X3,X4) ) ).
cnf(i_0_240,axiom,
( X1 != X2
| ~ aGcdOfAnd0(X3,X1,X4)
| aGcdOfAnd0(X3,X2,X4) ) ).
cnf(i_0_241,axiom,
( X1 != X2
| ~ aGcdOfAnd0(X3,X4,X1)
| aGcdOfAnd0(X3,X4,X2) ) ).
cnf(i_0_242,axiom,
( X1 != X2
| ~ doDivides0(X1,X3)
| doDivides0(X2,X3) ) ).
cnf(i_0_243,axiom,
( X1 != X2
| ~ doDivides0(X3,X1)
| doDivides0(X3,X2) ) ).
cnf(i_0_244,axiom,
( X1 != X2
| ~ aDivisorOf0(X1,X3)
| aDivisorOf0(X2,X3) ) ).
cnf(i_0_245,axiom,
( X1 != X2
| ~ aDivisorOf0(X3,X1)
| aDivisorOf0(X3,X2) ) ).
cnf(i_0_246,axiom,
( X1 != X2
| ~ misRelativelyPrime0(X1,X3)
| misRelativelyPrime0(X2,X3) ) ).
cnf(i_0_247,axiom,
( X1 != X2
| ~ misRelativelyPrime0(X3,X1)
| misRelativelyPrime0(X3,X2) ) ).
cnf(i_0_208_001,axiom,
X1 = X1 ).
cnf(i_0_209_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_210_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_211_004,axiom,
( X1 != X2
| sdtpldt0(X1,X3) = sdtpldt0(X2,X3) ) ).
cnf(i_0_212_005,axiom,
( X1 != X2
| sdtpldt0(X3,X1) = sdtpldt0(X3,X2) ) ).
cnf(i_0_213_006,axiom,
( X1 != X2
| esk5_3(X1,X3,X4) = esk5_3(X2,X3,X4) ) ).
cnf(i_0_214_007,axiom,
( X1 != X2
| esk5_3(X3,X1,X4) = esk5_3(X3,X2,X4) ) ).
cnf(i_0_215_008,axiom,
( X1 != X2
| esk5_3(X3,X4,X1) = esk5_3(X3,X4,X2) ) ).
cnf(i_0_216_009,axiom,
( X1 != X2
| sdtasdt0(X1,X3) = sdtasdt0(X2,X3) ) ).
cnf(i_0_217_010,axiom,
( X1 != X2
| sdtasdt0(X3,X1) = sdtasdt0(X3,X2) ) ).
cnf(i_0_218_011,axiom,
( X1 != X2
| smndt0(X1) = smndt0(X2) ) ).
cnf(i_0_219_012,axiom,
( X1 != X2
| slsdtgt0(X1) = slsdtgt0(X2) ) ).
cnf(i_0_220_013,axiom,
( X1 != X2
| esk15_2(X1,X3) = esk15_2(X2,X3) ) ).
cnf(i_0_221_014,axiom,
( X1 != X2
| esk15_2(X3,X1) = esk15_2(X3,X2) ) ).
cnf(i_0_222_015,axiom,
( X1 != X2
| esk19_2(X1,X3) = esk19_2(X2,X3) ) ).
cnf(i_0_223_016,axiom,
( X1 != X2
| esk19_2(X3,X1) = esk19_2(X3,X2) ) ).
cnf(i_0_224_017,axiom,
( X1 != X2
| sdtpldt1(X1,X3) = sdtpldt1(X2,X3) ) ).
cnf(i_0_225_018,axiom,
( X1 != X2
| sdtpldt1(X3,X1) = sdtpldt1(X3,X2) ) ).
cnf(i_0_226_019,axiom,
( X1 != X2
| sdtasasdt0(X1,X3) = sdtasasdt0(X2,X3) ) ).
cnf(i_0_227_020,axiom,
( X1 != X2
| sdtasasdt0(X3,X1) = sdtasasdt0(X3,X2) ) ).
cnf(i_0_228_021,axiom,
( X1 != X2
| ~ aElementOf0(X1,X3)
| aElementOf0(X2,X3) ) ).
cnf(i_0_229_022,axiom,
( X1 != X2
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X2) ) ).
cnf(i_0_230_023,axiom,
( X1 != X2
| ~ iLess0(X1,X3)
| iLess0(X2,X3) ) ).
cnf(i_0_231_024,axiom,
( X1 != X2
| ~ iLess0(X3,X1)
| iLess0(X3,X2) ) ).
cnf(i_0_232_025,axiom,
( X1 != X2
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(X2) ) ).
cnf(i_0_233_026,axiom,
( X1 != X2
| ~ aSet0(X1)
| aSet0(X2) ) ).
cnf(i_0_234_027,axiom,
( X1 != X2
| ~ sdteqdtlpzmzozddtrp0(X1,X3,X4)
| sdteqdtlpzmzozddtrp0(X2,X3,X4) ) ).
cnf(i_0_235_028,axiom,
( X1 != X2
| ~ sdteqdtlpzmzozddtrp0(X3,X1,X4)
| sdteqdtlpzmzozddtrp0(X3,X2,X4) ) ).
cnf(i_0_236_029,axiom,
( X1 != X2
| ~ sdteqdtlpzmzozddtrp0(X3,X4,X1)
| sdteqdtlpzmzozddtrp0(X3,X4,X2) ) ).
cnf(i_0_237_030,axiom,
( X1 != X2
| ~ aElement0(X1)
| aElement0(X2) ) ).
cnf(i_0_238_031,axiom,
( X1 != X2
| ~ aIdeal0(X1)
| aIdeal0(X2) ) ).
cnf(i_0_239_032,axiom,
( X1 != X2
| ~ aGcdOfAnd0(X1,X3,X4)
| aGcdOfAnd0(X2,X3,X4) ) ).
cnf(i_0_240_033,axiom,
( X1 != X2
| ~ aGcdOfAnd0(X3,X1,X4)
| aGcdOfAnd0(X3,X2,X4) ) ).
cnf(i_0_241_034,axiom,
( X1 != X2
| ~ aGcdOfAnd0(X3,X4,X1)
| aGcdOfAnd0(X3,X4,X2) ) ).
cnf(i_0_242_035,axiom,
( X1 != X2
| ~ doDivides0(X1,X3)
| doDivides0(X2,X3) ) ).
cnf(i_0_243_036,axiom,
( X1 != X2
| ~ doDivides0(X3,X1)
| doDivides0(X3,X2) ) ).
cnf(i_0_244_037,axiom,
( X1 != X2
| ~ aDivisorOf0(X1,X3)
| aDivisorOf0(X2,X3) ) ).
cnf(i_0_245_038,axiom,
( X1 != X2
| ~ aDivisorOf0(X3,X1)
| aDivisorOf0(X3,X2) ) ).
cnf(i_0_246_039,axiom,
( X1 != X2
| ~ misRelativelyPrime0(X1,X3)
| misRelativelyPrime0(X2,X3) ) ).
cnf(i_0_247_040,axiom,
( X1 != X2
| ~ misRelativelyPrime0(X3,X1)
| misRelativelyPrime0(X3,X2) ) ).
cnf(i_0_248,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,[],[89]) ).
cnf(i_0_249,plain,
( ~ aElementOf0(X1,sdtpldt1(X2,X3))
| ~ aSet0(X2)
| ~ aSet0(X3)
| aElementOf0(esk4_4(X2,X3,sdtpldt1(X2,X3),X1),X3) ),
inference(equality_inference,[],[96]) ).
cnf(i_0_250,plain,
( ~ aElementOf0(X1,sdtpldt1(X2,X3))
| ~ aSet0(X2)
| ~ aSet0(X3)
| aElementOf0(esk3_4(X2,X3,sdtpldt1(X2,X3),X1),X2) ),
inference(equality_inference,[],[97]) ).
cnf(i_0_251,plain,
( ~ aElementOf0(X1,slsdtgt0(X2))
| ~ aElement0(X2)
| sdtasdt0(X2,esk18_3(X2,slsdtgt0(X2),X1)) = X1 ),
inference(equality_inference,[],[111]) ).
cnf(i_0_252,plain,
( ~ aElementOf0(X1,slsdtgt0(X2))
| ~ aElement0(X2)
| aElement0(esk18_3(X2,slsdtgt0(X2),X1)) ),
inference(equality_inference,[],[113]) ).
cnf(i_0_253,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aElementOf0(X3,sdtasasdt0(X1,X2))
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X2) ),
inference(equality_inference,[],[131]) ).
cnf(i_0_254,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aElementOf0(X3,X1)
| ~ aElementOf0(X3,sdtasasdt0(X1,X2)) ),
inference(equality_inference,[],[138]) ).
cnf(i_0_255,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aElementOf0(X3,X2)
| ~ aElementOf0(X3,sdtasasdt0(X1,X2)) ),
inference(equality_inference,[],[139]) ).
cnf(i_0_256,plain,
( ~ aElement0(X1)
| ~ aElement0(sdtasdt0(X1,X2))
| doDivides0(X1,sdtasdt0(X1,X2))
| ~ aElement0(X2) ),
inference(equality_inference,[],[142]) ).
cnf(i_0_257,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aSet0(sdtasasdt0(X1,X2)) ),
inference(equality_inference,[],[158]) ).
cnf(i_0_258,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aSet0(sdtpldt1(X1,X2)) ),
inference(equality_inference,[],[159]) ).
cnf(i_0_259,plain,
( ~ aElement0(X1)
| aSet0(slsdtgt0(X1)) ),
inference(equality_inference,[],[178]) ).
cnf(i_0_260,plain,
iLess0(sbrdtbr0(xr),sbrdtbr0(xu)),
inference(scs_inference,[],[i_0_205,i_0_172]) ).
cnf(i_0_261,plain,
aSet0(xI),
inference(scs_inference,[],[i_0_194,i_0_189]) ).
cnf(i_0_262,plain,
( ~ aIdeal0(X1)
| aSet0(X1) ),
inference(rename_variables,[],[i_0_189]) ).
cnf(i_0_263,plain,
sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) = xI,
inference(scs_inference,[],[i_0_194,i_0_177,i_0_189,i_0_209]) ).
cnf(i_0_264,plain,
aElement0(smndt0(sdtasdt0(xq,xu))),
inference(scs_inference,[],[i_0_144,i_0_194,i_0_177,i_0_189,i_0_209,i_0_165]) ).
cnf(i_0_265,plain,
( ~ aElementOf0(X1,X2)
| aElement0(X1)
| ~ aSet0(X2) ),
inference(rename_variables,[],[i_0_165]) ).
cnf(i_0_266,plain,
sdtasdt0(xb,esk18_3(xb,slsdtgt0(xb),xb)) = xb,
inference(scs_inference,[],[i_0_144,i_0_194,i_0_199,i_0_185,i_0_177,i_0_189,i_0_209,i_0_165,i_0_251]) ).
cnf(i_0_267,plain,
( ~ aElement0(X1)
| sdtasdt0(X1,esk18_3(X1,slsdtgt0(X1),X2)) = X2
| ~ aElementOf0(X2,slsdtgt0(X1)) ),
inference(rename_variables,[],[i_0_251]) ).
cnf(i_0_268,plain,
aElement0(esk18_3(xb,slsdtgt0(xb),xb)),
inference(scs_inference,[],[i_0_144,i_0_194,i_0_199,i_0_185,i_0_177,i_0_189,i_0_209,i_0_165,i_0_251,i_0_252]) ).
cnf(i_0_269,plain,
( ~ aElement0(X1)
| aElement0(esk18_3(X1,slsdtgt0(X1),X2))
| ~ aElementOf0(X2,slsdtgt0(X1)) ),
inference(rename_variables,[],[i_0_252]) ).
cnf(i_0_270,plain,
sdtasdt0(xb,esk18_3(xb,slsdtgt0(xb),xb)) = sdtpldt0(sdtasdt0(xq,xu),xr),
inference(scs_inference,[],[i_0_144,i_0_194,i_0_199,i_0_185,i_0_177,i_0_166,i_0_189,i_0_209,i_0_165,i_0_251,i_0_252,i_0_210]) ).
cnf(i_0_271,plain,
aSet0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(scs_inference,[],[i_0_144,i_0_194,i_0_199,i_0_185,i_0_177,i_0_166,i_0_189,i_0_209,i_0_165,i_0_251,i_0_252,i_0_210,i_0_233]) ).
cnf(i_0_272,plain,
aElement0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),
inference(scs_inference,[],[i_0_144,i_0_194,i_0_197,i_0_199,i_0_185,i_0_177,i_0_166,i_0_145,i_0_189,i_0_209,i_0_165,i_0_251,i_0_252,i_0_210,i_0_233,i_0_237]) ).
cnf(i_0_273,plain,
aIdeal0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(scs_inference,[],[i_0_144,i_0_194,i_0_197,i_0_199,i_0_185,i_0_177,i_0_166,i_0_145,i_0_189,i_0_209,i_0_165,i_0_251,i_0_252,i_0_210,i_0_233,i_0_237,i_0_238]) ).
cnf(i_0_274,plain,
~ doDivides0(xu,sdtasdt0(xb,esk18_3(xb,slsdtgt0(xb),xb))),
inference(scs_inference,[],[i_0_144,i_0_182,i_0_194,i_0_197,i_0_199,i_0_185,i_0_177,i_0_166,i_0_145,i_0_189,i_0_209,i_0_165,i_0_251,i_0_252,i_0_210,i_0_233,i_0_237,i_0_238,i_0_243]) ).
cnf(i_0_275,plain,
doDivides0(xb,xb),
inference(scs_inference,[],[i_0_144,i_0_182,i_0_194,i_0_197,i_0_199,i_0_185,i_0_177,i_0_166,i_0_145,i_0_189,i_0_209,i_0_165,i_0_251,i_0_252,i_0_210,i_0_233,i_0_237,i_0_238,i_0_243,i_0_142]) ).
cnf(i_0_276,plain,
( sdtasdt0(X1,X2) != X3
| ~ aElement0(X1)
| ~ aElement0(X3)
| doDivides0(X1,X3)
| ~ aElement0(X2) ),
inference(rename_variables,[],[i_0_142]) ).
cnf(i_0_277,plain,
aElementOf0(smndt0(sdtasdt0(xq,xu)),sdtasasdt0(xI,xI)),
inference(scs_inference,[],[i_0_144,i_0_182,i_0_194,i_0_197,i_0_199,i_0_185,i_0_177,i_0_166,i_0_145,i_0_189,i_0_209,i_0_165,i_0_251,i_0_252,i_0_210,i_0_233,i_0_237,i_0_238,i_0_243,i_0_142,i_0_253]) ).
cnf(i_0_278,plain,
( ~ aElementOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| ~ aSet0(X2)
| aElementOf0(X1,sdtasasdt0(X2,X3))
| ~ aSet0(X3) ),
inference(rename_variables,[],[i_0_253]) ).
cnf(i_0_279,plain,
( aElement0(X1)
| ~ aDivisorOf0(X1,esk23_0) ),
inference(scs_inference,[],[i_0_144,i_0_182,i_0_194,i_0_195,i_0_197,i_0_199,i_0_185,i_0_177,i_0_166,i_0_145,i_0_189,i_0_209,i_0_165,i_0_251,i_0_252,i_0_210,i_0_233,i_0_237,i_0_238,i_0_243,i_0_142,i_0_253,i_0_164]) ).
cnf(i_0_280,plain,
( ~ aElement0(X1)
| aElement0(X2)
| ~ aDivisorOf0(X2,X1) ),
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_281,plain,
xb != xu,
inference(scs_inference,[],[i_0_144,i_0_182,i_0_194,i_0_195,i_0_197,i_0_199,i_0_185,i_0_177,i_0_166,i_0_145,i_0_189,i_0_209,i_0_165,i_0_251,i_0_252,i_0_210,i_0_233,i_0_237,i_0_238,i_0_243,i_0_142,i_0_253,i_0_164,i_0_242]) ).
cnf(i_0_282,plain,
aDivisorOf0(xb,xb),
inference(scs_inference,[],[i_0_144,i_0_182,i_0_194,i_0_195,i_0_197,i_0_199,i_0_185,i_0_177,i_0_166,i_0_145,i_0_189,i_0_209,i_0_165,i_0_251,i_0_252,i_0_210,i_0_233,i_0_237,i_0_238,i_0_243,i_0_142,i_0_253,i_0_164,i_0_242,i_0_147]) ).
cnf(i_0_283,plain,
( ~ aElement0(X1)
| ~ doDivides0(X1,X2)
| ~ aElement0(X2)
| aDivisorOf0(X1,X2) ),
inference(rename_variables,[],[i_0_147]) ).
cnf(i_0_284,plain,
( doDivides0(esk23_0,sdtasdt0(esk23_0,esk23_0))
| ~ aDivisorOf0(sdtasdt0(esk23_0,esk23_0),esk23_0) ),
inference(scs_inference,[],[i_0_144,i_0_182,i_0_194,i_0_195,i_0_197,i_0_199,i_0_185,i_0_177,i_0_166,i_0_145,i_0_189,i_0_209,i_0_165,i_0_251,i_0_252,i_0_210,i_0_233,i_0_237,i_0_238,i_0_243,i_0_142,i_0_253,i_0_164,i_0_242,i_0_147,i_0_256]) ).
cnf(i_0_285,plain,
( ~ aElement0(X1)
| doDivides0(X2,sdtasdt0(X2,X1))
| ~ aElement0(X2)
| ~ aElement0(sdtasdt0(X2,X1)) ),
inference(rename_variables,[],[i_0_256]) ).
cnf(i_0_286,plain,
( ~ aSet0(slsdtgt0(xb))
| ~ aSet0(slsdtgt0(xa))
| sdtpldt0(esk3_4(xI,xI,sdtpldt1(xI,xI),X1),esk4_4(xI,xI,sdtpldt1(xI,xI),X1)) = X1
| ~ aDivisorOf0(sdtasdt0(esk23_0,esk23_0),esk23_0)
| ~ aElementOf0(X1,sdtpldt1(xI,xI)) ),
inference(scs_inference,[],[i_0_144,i_0_182,i_0_194,i_0_195,i_0_197,i_0_199,i_0_185,i_0_177,i_0_166,i_0_145,i_0_189,i_0_209,i_0_165,i_0_251,i_0_252,i_0_210,i_0_233,i_0_237,i_0_238,i_0_243,i_0_142,i_0_253,i_0_164,i_0_242,i_0_147,i_0_256,i_0_159,i_0_248]) ).
cnf(i_0_287,plain,
sdtpldt0(sdtasdt0(xq,xu),xr) = sdtasdt0(xb,esk18_3(xb,slsdtgt0(xb),xb)),
inference(scs_inference,[],[i_0_270,i_0_209]) ).
cnf(i_0_288,plain,
$false,
inference(scs_inference,[],[i_0_270,i_0_191,i_0_205,i_0_260,i_0_209,i_0_143]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG124+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n006.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 01:52:16 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 0.32/5.62 % Version : CSE_E---1.7
% 0.32/5.62 % Problem : theBenchmark.p
% 0.32/5.62 % SZS status Theorem for theBenchmark.p
% 0.32/5.62 % SZS output start CNFRefutation
% See solution above
% 0.42/5.77 % Total time : 5.279s
%------------------------------------------------------------------------------