%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG101+2 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n008.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 05:05:20 PM UTC 2026
% Result : Theorem 0.30s 1.61s
% Output : CNFRefutation 0.30s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 69)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
? [X1] :
( aElement0(X1)
& sdtasdt0(xc,X1) = xx ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
fof(mDefRel,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> ( misRelativelyPrime0(X1,X2)
<=> aGcdOfAnd0(sz10,X1,X2) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(mDefDvs,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( aDivisorOf0(X2,X1)
<=> ( aElement0(X2)
& doDivides0(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDvs) ).
fof(mIdeInt,axiom,
! [X1,X2] :
( ( aIdeal0(X1)
& aIdeal0(X2) )
=> aIdeal0(sdtasasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIdeInt) ).
fof(mIdeSum,axiom,
! [X1,X2] :
( ( aIdeal0(X1)
& aIdeal0(X2) )
=> aIdeal0(sdtpldt1(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIdeSum) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(mCancel,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCancel) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mMulMnOne) ).
fof(mAddInvr,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddInvr) ).
fof(mMulUnit,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulUnit) ).
fof(mAddZero,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(mMulZero,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
fof(mEucSort,axiom,
! [X1] :
( ( aElement0(X1)
& X1 != sz00 )
=> aNaturalNumber0(sbrdtbr0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEucSort) ).
fof(mSortsU,axiom,
! [X1] :
( aElement0(X1)
=> aElement0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsU) ).
fof(m__1933,hypothesis,
( ? [X1] :
( aElement0(X1)
& sdtasdt0(xc,X1) = xx )
& aElementOf0(xx,slsdtgt0(xc))
& ? [X1] :
( aElement0(X1)
& sdtasdt0(xc,X1) = xy )
& aElementOf0(xy,slsdtgt0(xc))
& aElement0(xz) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1933) ).
fof(m__1905,hypothesis,
aElement0(xc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1905) ).
fof(mSortsC_01,axiom,
aElement0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(mSortsC,axiom,
aElement0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(mUnNeZr,axiom,
sz10 != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mUnNeZr) ).
fof(i_0_36,negated_conjecture,
~ ? [X1] :
( aElement0(X1)
& sdtasdt0(xc,X1) = xx ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(i_0_37,plain,
! [X124,X125,X126,X127,X130,X131,X132,X133,X135,X136] :
( ( aSet0(X126)
| X126 != sdtpldt1(X124,X125)
| ~ aSet0(X124)
| ~ aSet0(X125) )
& ( aElementOf0(esk3_4(X124,X125,X126,X127),X124)
| ~ aElementOf0(X127,X126)
| X126 != sdtpldt1(X124,X125)
| ~ aSet0(X124)
| ~ aSet0(X125) )
& ( aElementOf0(esk4_4(X124,X125,X126,X127),X125)
| ~ aElementOf0(X127,X126)
| X126 != sdtpldt1(X124,X125)
| ~ aSet0(X124)
| ~ aSet0(X125) )
& ( sdtpldt0(esk3_4(X124,X125,X126,X127),esk4_4(X124,X125,X126,X127)) = X127
| ~ aElementOf0(X127,X126)
| X126 != sdtpldt1(X124,X125)
| ~ aSet0(X124)
| ~ aSet0(X125) )
& ( ~ aElementOf0(X131,X124)
| ~ aElementOf0(X132,X125)
| sdtpldt0(X131,X132) != X130
| aElementOf0(X130,X126)
| X126 != sdtpldt1(X124,X125)
| ~ aSet0(X124)
| ~ aSet0(X125) )
& ( ~ aElementOf0(esk5_3(X124,X125,X133),X133)
| ~ aElementOf0(X135,X124)
| ~ aElementOf0(X136,X125)
| sdtpldt0(X135,X136) != esk5_3(X124,X125,X133)
| ~ aSet0(X133)
| X133 = sdtpldt1(X124,X125)
| ~ aSet0(X124)
| ~ aSet0(X125) )
& ( aElementOf0(esk6_3(X124,X125,X133),X124)
| aElementOf0(esk5_3(X124,X125,X133),X133)
| ~ aSet0(X133)
| X133 = sdtpldt1(X124,X125)
| ~ aSet0(X124)
| ~ aSet0(X125) )
& ( aElementOf0(esk7_3(X124,X125,X133),X125)
| aElementOf0(esk5_3(X124,X125,X133),X133)
| ~ aSet0(X133)
| X133 = sdtpldt1(X124,X125)
| ~ aSet0(X124)
| ~ aSet0(X125) )
& ( sdtpldt0(esk6_3(X124,X125,X133),esk7_3(X124,X125,X133)) = esk5_3(X124,X125,X133)
| aElementOf0(esk5_3(X124,X125,X133),X133)
| ~ aSet0(X133)
| X133 = sdtpldt1(X124,X125)
| ~ aSet0(X124)
| ~ aSet0(X125) ) ),
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_38,plain,
! [X161,X162,X164,X165] :
( ( aElement0(esk13_4(X161,X162,X164,X165))
| ~ aElement0(X164)
| ~ aElement0(X165)
| aElement0(esk12_2(X161,X162))
| ~ aIdeal0(X161)
| ~ aIdeal0(X162) )
& ( sdteqdtlpzmzozddtrp0(esk13_4(X161,X162,X164,X165),X164,X161)
| ~ aElement0(X164)
| ~ aElement0(X165)
| aElement0(esk12_2(X161,X162))
| ~ aIdeal0(X161)
| ~ aIdeal0(X162) )
& ( sdteqdtlpzmzozddtrp0(esk13_4(X161,X162,X164,X165),X165,X162)
| ~ aElement0(X164)
| ~ aElement0(X165)
| aElement0(esk12_2(X161,X162))
| ~ aIdeal0(X161)
| ~ aIdeal0(X162) )
& ( aElement0(esk13_4(X161,X162,X164,X165))
| ~ aElement0(X164)
| ~ aElement0(X165)
| ~ aElementOf0(esk12_2(X161,X162),sdtpldt1(X161,X162))
| ~ aIdeal0(X161)
| ~ aIdeal0(X162) )
& ( sdteqdtlpzmzozddtrp0(esk13_4(X161,X162,X164,X165),X164,X161)
| ~ aElement0(X164)
| ~ aElement0(X165)
| ~ aElementOf0(esk12_2(X161,X162),sdtpldt1(X161,X162))
| ~ aIdeal0(X161)
| ~ aIdeal0(X162) )
& ( sdteqdtlpzmzozddtrp0(esk13_4(X161,X162,X164,X165),X165,X162)
| ~ aElement0(X164)
| ~ aElement0(X165)
| ~ aElementOf0(esk12_2(X161,X162),sdtpldt1(X161,X162))
| ~ aIdeal0(X161)
| ~ aIdeal0(X162) ) ),
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_39,plain,
! [X139,X140,X141,X142,X143,X144] :
( ( aSet0(X141)
| X141 != sdtasasdt0(X139,X140)
| ~ aSet0(X139)
| ~ aSet0(X140) )
& ( aElementOf0(X142,X139)
| ~ aElementOf0(X142,X141)
| X141 != sdtasasdt0(X139,X140)
| ~ aSet0(X139)
| ~ aSet0(X140) )
& ( aElementOf0(X142,X140)
| ~ aElementOf0(X142,X141)
| X141 != sdtasasdt0(X139,X140)
| ~ aSet0(X139)
| ~ aSet0(X140) )
& ( ~ aElementOf0(X143,X139)
| ~ aElementOf0(X143,X140)
| aElementOf0(X143,X141)
| X141 != sdtasasdt0(X139,X140)
| ~ aSet0(X139)
| ~ aSet0(X140) )
& ( ~ aElementOf0(esk8_3(X139,X140,X144),X144)
| ~ aElementOf0(esk8_3(X139,X140,X144),X139)
| ~ aElementOf0(esk8_3(X139,X140,X144),X140)
| ~ aSet0(X144)
| X144 = sdtasasdt0(X139,X140)
| ~ aSet0(X139)
| ~ aSet0(X140) )
& ( aElementOf0(esk8_3(X139,X140,X144),X139)
| aElementOf0(esk8_3(X139,X140,X144),X144)
| ~ aSet0(X144)
| X144 = sdtasasdt0(X139,X140)
| ~ aSet0(X139)
| ~ aSet0(X140) )
& ( aElementOf0(esk8_3(X139,X140,X144),X140)
| aElementOf0(esk8_3(X139,X140,X144),X144)
| ~ aSet0(X144)
| X144 = sdtasasdt0(X139,X140)
| ~ aSet0(X139)
| ~ aSet0(X140) ) ),
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_40,plain,
! [X178,X179,X180,X181,X182] :
( ( aDivisorOf0(X180,X178)
| ~ aGcdOfAnd0(X180,X178,X179)
| ~ aElement0(X178)
| ~ aElement0(X179) )
& ( aDivisorOf0(X180,X179)
| ~ aGcdOfAnd0(X180,X178,X179)
| ~ aElement0(X178)
| ~ aElement0(X179) )
& ( ~ aDivisorOf0(X181,X178)
| ~ aDivisorOf0(X181,X179)
| doDivides0(X181,X180)
| ~ aGcdOfAnd0(X180,X178,X179)
| ~ aElement0(X178)
| ~ aElement0(X179) )
& ( aDivisorOf0(esk17_3(X178,X179,X182),X178)
| ~ aDivisorOf0(X182,X178)
| ~ aDivisorOf0(X182,X179)
| aGcdOfAnd0(X182,X178,X179)
| ~ aElement0(X178)
| ~ aElement0(X179) )
& ( aDivisorOf0(esk17_3(X178,X179,X182),X179)
| ~ aDivisorOf0(X182,X178)
| ~ aDivisorOf0(X182,X179)
| aGcdOfAnd0(X182,X178,X179)
| ~ aElement0(X178)
| ~ aElement0(X179) )
& ( ~ doDivides0(esk17_3(X178,X179,X182),X182)
| ~ aDivisorOf0(X182,X178)
| ~ aDivisorOf0(X182,X179)
| aGcdOfAnd0(X182,X178,X179)
| ~ aElement0(X178)
| ~ aElement0(X179) ) ),
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_41,plain,
! [X146,X147,X148,X149,X150] :
( ( aSet0(X146)
| ~ aIdeal0(X146) )
& ( ~ aElementOf0(X148,X146)
| aElementOf0(sdtpldt0(X147,X148),X146)
| ~ aElementOf0(X147,X146)
| ~ aIdeal0(X146) )
& ( ~ aElement0(X149)
| aElementOf0(sdtasdt0(X149,X147),X146)
| ~ aElementOf0(X147,X146)
| ~ aIdeal0(X146) )
& ( aElementOf0(esk9_1(X150),X150)
| ~ aSet0(X150)
| aIdeal0(X150) )
& ( aElement0(esk11_1(X150))
| aElementOf0(esk10_1(X150),X150)
| ~ aSet0(X150)
| aIdeal0(X150) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X150),esk9_1(X150)),X150)
| aElementOf0(esk10_1(X150),X150)
| ~ aSet0(X150)
| aIdeal0(X150) )
& ( aElement0(esk11_1(X150))
| ~ aElementOf0(sdtpldt0(esk9_1(X150),esk10_1(X150)),X150)
| ~ aSet0(X150)
| aIdeal0(X150) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X150),esk9_1(X150)),X150)
| ~ aElementOf0(sdtpldt0(esk9_1(X150),esk10_1(X150)),X150)
| ~ aSet0(X150)
| aIdeal0(X150) ) ),
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_42,plain,
! [X158,X159,X160] :
( ( ~ sdteqdtlpzmzozddtrp0(X158,X159,X160)
| aElementOf0(sdtpldt0(X158,smndt0(X159)),X160)
| ~ aElement0(X158)
| ~ aElement0(X159)
| ~ aIdeal0(X160) )
& ( ~ aElementOf0(sdtpldt0(X158,smndt0(X159)),X160)
| sdteqdtlpzmzozddtrp0(X158,X159,X160)
| ~ aElement0(X158)
| ~ aElement0(X159)
| ~ aIdeal0(X160) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefMod])])]) ).
fof(i_0_43,plain,
! [X186,X187,X188,X190,X191,X192,X194] :
( ( aSet0(X187)
| X187 != slsdtgt0(X186)
| ~ aElement0(X186) )
& ( aElement0(esk18_3(X186,X187,X188))
| ~ aElementOf0(X188,X187)
| X187 != slsdtgt0(X186)
| ~ aElement0(X186) )
& ( sdtasdt0(X186,esk18_3(X186,X187,X188)) = X188
| ~ aElementOf0(X188,X187)
| X187 != slsdtgt0(X186)
| ~ aElement0(X186) )
& ( ~ aElement0(X191)
| sdtasdt0(X186,X191) != X190
| aElementOf0(X190,X187)
| X187 != slsdtgt0(X186)
| ~ aElement0(X186) )
& ( ~ aElementOf0(esk19_2(X186,X192),X192)
| ~ aElement0(X194)
| sdtasdt0(X186,X194) != esk19_2(X186,X192)
| ~ aSet0(X192)
| X192 = slsdtgt0(X186)
| ~ aElement0(X186) )
& ( aElement0(esk20_2(X186,X192))
| aElementOf0(esk19_2(X186,X192),X192)
| ~ aSet0(X192)
| X192 = slsdtgt0(X186)
| ~ aElement0(X186) )
& ( sdtasdt0(X186,esk20_2(X186,X192)) = esk19_2(X186,X192)
| aElementOf0(esk19_2(X186,X192),X192)
| ~ aSet0(X192)
| X192 = slsdtgt0(X186)
| ~ aElement0(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)],[mDefPrIdeal])])])])])]) ).
fof(i_0_44,plain,
! [X120,X121] :
( ( aElementOf0(esk2_2(X120,X121),X121)
| aElementOf0(esk1_2(X120,X121),X120)
| X120 = X121
| ~ aSet0(X120)
| ~ aSet0(X121) )
& ( ~ aElementOf0(esk2_2(X120,X121),X120)
| aElementOf0(esk1_2(X120,X121),X120)
| X120 = X121
| ~ aSet0(X120)
| ~ aSet0(X121) )
& ( aElementOf0(esk2_2(X120,X121),X121)
| ~ aElementOf0(esk1_2(X120,X121),X121)
| X120 = X121
| ~ aSet0(X120)
| ~ aSet0(X121) )
& ( ~ aElementOf0(esk2_2(X120,X121),X120)
| ~ aElementOf0(esk1_2(X120,X121),X121)
| X120 = X121
| ~ aSet0(X120)
| ~ aSet0(X121) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSetEq])])])]) ).
fof(i_0_45,plain,
! [X168,X169] :
( ( aElement0(esk14_2(X168,X169))
| ~ aElement0(X168)
| ~ aElement0(X169)
| X169 = sz00 )
& ( aElement0(esk15_2(X168,X169))
| ~ aElement0(X168)
| ~ aElement0(X169)
| X169 = sz00 )
& ( X168 = sdtpldt0(sdtasdt0(esk14_2(X168,X169),X169),esk15_2(X168,X169))
| ~ aElement0(X168)
| ~ aElement0(X169)
| X169 = sz00 )
& ( esk15_2(X168,X169) = sz00
| iLess0(sbrdtbr0(esk15_2(X168,X169)),sbrdtbr0(X169))
| ~ aElement0(X168)
| ~ aElement0(X169)
| X169 = sz00 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivision])])])]) ).
fof(i_0_46,plain,
! [X111,X112,X113] :
( ( sdtasdt0(X111,sdtpldt0(X112,X113)) = sdtpldt0(sdtasdt0(X111,X112),sdtasdt0(X111,X113))
| ~ aElement0(X111)
| ~ aElement0(X112)
| ~ aElement0(X113) )
& ( sdtasdt0(sdtpldt0(X112,X113),X111) = sdtpldt0(sdtasdt0(X112,X111),sdtasdt0(X113,X111))
| ~ aElement0(X111)
| ~ aElement0(X112)
| ~ aElement0(X113) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])]) ).
fof(i_0_47,plain,
! [X184,X185] :
( ( ~ misRelativelyPrime0(X184,X185)
| aGcdOfAnd0(sz10,X184,X185)
| ~ aElement0(X184)
| ~ aElement0(X185) )
& ( ~ aGcdOfAnd0(sz10,X184,X185)
| misRelativelyPrime0(X184,X185)
| ~ aElement0(X184)
| ~ aElement0(X185) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefRel])])]) ).
fof(i_0_48,plain,
! [X107,X108,X109] :
( ~ aElement0(X107)
| ~ aElement0(X108)
| ~ aElement0(X109)
| sdtasdt0(sdtasdt0(X107,X108),X109) = sdtasdt0(X107,sdtasdt0(X108,X109)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
fof(i_0_49,plain,
! [X100,X101,X102] :
( ~ aElement0(X100)
| ~ aElement0(X101)
| ~ aElement0(X102)
| sdtpldt0(sdtpldt0(X100,X101),X102) = sdtpldt0(X100,sdtpldt0(X101,X102)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
fof(i_0_50,plain,
! [X172,X173,X175] :
( ( aElement0(esk16_2(X172,X173))
| ~ doDivides0(X172,X173)
| ~ aElement0(X172)
| ~ aElement0(X173) )
& ( sdtasdt0(X172,esk16_2(X172,X173)) = X173
| ~ doDivides0(X172,X173)
| ~ aElement0(X172)
| ~ aElement0(X173) )
& ( ~ aElement0(X175)
| sdtasdt0(X172,X175) != X173
| doDivides0(X172,X173)
| ~ aElement0(X172)
| ~ aElement0(X173) ) ),
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_51,plain,
! [X176,X177] :
( ( aElement0(X177)
| ~ aDivisorOf0(X177,X176)
| ~ aElement0(X176) )
& ( doDivides0(X177,X176)
| ~ aDivisorOf0(X177,X176)
| ~ aElement0(X176) )
& ( ~ aElement0(X177)
| ~ doDivides0(X177,X176)
| aDivisorOf0(X177,X176)
| ~ aElement0(X176) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDvs])])])]) ).
fof(i_0_52,plain,
! [X156,X157] :
( ~ aIdeal0(X156)
| ~ aIdeal0(X157)
| aIdeal0(sdtasasdt0(X156,X157)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIdeInt])]) ).
fof(i_0_53,plain,
! [X154,X155] :
( ~ aIdeal0(X154)
| ~ aIdeal0(X155)
| aIdeal0(sdtpldt1(X154,X155)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIdeSum])]) ).
fof(i_0_54,plain,
! [X96,X97] :
( ~ aElement0(X96)
| ~ aElement0(X97)
| aElement0(sdtasdt0(X96,X97)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(i_0_55,plain,
! [X94,X95] :
( ~ aElement0(X94)
| ~ aElement0(X95)
| aElement0(sdtpldt0(X94,X95)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
fof(i_0_56,plain,
! [X105,X106] :
( ~ aElement0(X105)
| ~ aElement0(X106)
| sdtasdt0(X105,X106) = sdtasdt0(X106,X105) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
fof(i_0_57,plain,
! [X98,X99] :
( ~ aElement0(X98)
| ~ aElement0(X99)
| sdtpldt0(X98,X99) = sdtpldt0(X99,X98) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
fof(i_0_58,plain,
! [X116,X117] :
( ~ aElement0(X116)
| ~ aElement0(X117)
| sdtasdt0(X116,X117) != sz00
| X116 = sz00
| X117 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCancel])]) ).
fof(i_0_59,plain,
! [X118,X119] :
( ~ aSet0(X118)
| ~ aElementOf0(X119,X118)
| aElement0(X119) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
fof(i_0_60,plain,
! [X114] :
( ( sdtasdt0(smndt0(sz10),X114) = smndt0(X114)
| ~ aElement0(X114) )
& ( smndt0(X114) = sdtasdt0(X114,smndt0(sz10))
| ~ aElement0(X114) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMnOne])])]) ).
fof(i_0_61,plain,
! [X104] :
( ( sdtpldt0(X104,smndt0(X104)) = sz00
| ~ aElement0(X104) )
& ( sz00 = sdtpldt0(smndt0(X104),X104)
| ~ aElement0(X104) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddInvr])])]) ).
fof(i_0_62,negated_conjecture,
! [X198] :
( ~ aElement0(X198)
| sdtasdt0(xc,X198) != xx ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_36])]) ).
fof(i_0_63,plain,
! [X110] :
( ( sdtasdt0(X110,sz10) = X110
| ~ aElement0(X110) )
& ( X110 = sdtasdt0(sz10,X110)
| ~ aElement0(X110) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulUnit])])]) ).
fof(i_0_64,plain,
! [X103] :
( ( sdtpldt0(X103,sz00) = X103
| ~ aElement0(X103) )
& ( X103 = sdtpldt0(sz00,X103)
| ~ aElement0(X103) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).
fof(i_0_65,plain,
! [X115] :
( ( sdtasdt0(X115,sz00) = sz00
| ~ aElement0(X115) )
& ( sz00 = sdtasdt0(sz00,X115)
| ~ aElement0(X115) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulZero])])]) ).
fof(i_0_66,plain,
! [X167] :
( ~ aElement0(X167)
| X167 = sz00
| aNaturalNumber0(sbrdtbr0(X167)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEucSort])]) ).
fof(i_0_67,plain,
! [X93] :
( ~ aElement0(X93)
| aElement0(smndt0(X93)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsU])]) ).
fof(i_0_68,hypothesis,
( aElement0(esk21_0)
& sdtasdt0(xc,esk21_0) = xx
& aElementOf0(xx,slsdtgt0(xc))
& aElement0(esk22_0)
& sdtasdt0(xc,esk22_0) = xy
& aElementOf0(xy,slsdtgt0(xc))
& aElement0(xz) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__1933])]) ).
cnf(i_0_69,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_37]),
[final] ).
cnf(i_0_70,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_38]),
[final] ).
cnf(i_0_71,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_38]),
[final] ).
cnf(i_0_72,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_38]),
[final] ).
cnf(i_0_73,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_39]),
[final] ).
cnf(i_0_74,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_38]),
[final] ).
cnf(i_0_75,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_38]),
[final] ).
cnf(i_0_76,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_37]),
[final] ).
cnf(i_0_77,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_37]),
[final] ).
cnf(i_0_78,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_38]),
[final] ).
cnf(i_0_79,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_37]),
[final] ).
cnf(i_0_80,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_37]),
[final] ).
cnf(i_0_81,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_40]),
[final] ).
cnf(i_0_82,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_39]),
[final] ).
cnf(i_0_83,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_39]),
[final] ).
cnf(i_0_84,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_37]),
[final] ).
cnf(i_0_85,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_37]),
[final] ).
cnf(i_0_86,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_40]),
[final] ).
cnf(i_0_87,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_40]),
[final] ).
cnf(i_0_88,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_41]),
[final] ).
cnf(i_0_89,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_40]),
[final] ).
cnf(i_0_90,plain,
( aElementOf0(sdtpldt0(X1,smndt0(X2)),X3)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aIdeal0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_91,plain,
( sdtasdt0(X1,esk18_3(X1,X2,X3)) = X3
| ~ aElementOf0(X3,X2)
| X2 != slsdtgt0(X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_92,plain,
( sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ aElementOf0(sdtpldt0(X1,smndt0(X2)),X3)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aIdeal0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_93,plain,
( aElement0(esk18_3(X1,X2,X3))
| ~ aElementOf0(X3,X2)
| X2 != slsdtgt0(X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_94,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_44]),
[final] ).
cnf(i_0_95,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_45]),
[final] ).
cnf(i_0_96,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_43]),
[final] ).
cnf(i_0_97,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_41]),
[final] ).
cnf(i_0_98,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_46]),
[final] ).
cnf(i_0_99,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_46]),
[final] ).
cnf(i_0_100,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_41]),
[final] ).
cnf(i_0_101,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_37]),
[final] ).
cnf(i_0_102,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_44]),
[final] ).
cnf(i_0_103,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_44]),
[final] ).
cnf(i_0_104,plain,
( aDivisorOf0(X1,X2)
| ~ aGcdOfAnd0(X1,X2,X3)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_40]),
[final] ).
cnf(i_0_105,plain,
( aDivisorOf0(X1,X2)
| ~ aGcdOfAnd0(X1,X3,X2)
| ~ aElement0(X3)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_40]),
[final] ).
cnf(i_0_106,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_43]),
[final] ).
cnf(i_0_107,plain,
( misRelativelyPrime0(X1,X2)
| ~ aGcdOfAnd0(sz10,X1,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_108,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_45]),
[final] ).
cnf(i_0_109,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_110,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_111,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_39]),
[final] ).
cnf(i_0_112,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_44]),
[final] ).
cnf(i_0_113,plain,
( aElementOf0(sdtpldt0(X3,X1),X2)
| ~ aElementOf0(X1,X2)
| ~ aElementOf0(X3,X2)
| ~ aIdeal0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_114,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_43]),
[final] ).
cnf(i_0_115,plain,
( aGcdOfAnd0(sz10,X1,X2)
| ~ misRelativelyPrime0(X1,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_116,plain,
( sdtasdt0(X1,esk16_2(X1,X2)) = X2
| ~ doDivides0(X1,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_117,plain,
( aElementOf0(sdtasdt0(X1,X2),X3)
| ~ aElement0(X1)
| ~ aElementOf0(X2,X3)
| ~ aIdeal0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_118,plain,
( aElementOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| X3 != sdtasasdt0(X2,X4)
| ~ aSet0(X2)
| ~ aSet0(X4) ),
inference(split_conjunct,[status(thm)],[i_0_39]),
[final] ).
cnf(i_0_119,plain,
( aElementOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| X3 != sdtasasdt0(X4,X2)
| ~ aSet0(X4)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_39]),
[final] ).
cnf(i_0_120,plain,
( aElement0(esk16_2(X1,X2))
| ~ doDivides0(X1,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_121,plain,
( aElementOf0(X3,X4)
| ~ aElement0(X1)
| sdtasdt0(X2,X1) != X3
| X4 != slsdtgt0(X2)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_122,plain,
( doDivides0(X2,X3)
| ~ aElement0(X1)
| sdtasdt0(X2,X1) != X3
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_123,plain,
( aDivisorOf0(X1,X2)
| ~ aElement0(X1)
| ~ doDivides0(X1,X2)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_124,plain,
( aElement0(esk15_2(X1,X2))
| X2 = sz00
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_125,plain,
( aElement0(esk14_2(X1,X2))
| X2 = sz00
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_126,plain,
( aIdeal0(sdtasasdt0(X1,X2))
| ~ aIdeal0(X1)
| ~ aIdeal0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_127,plain,
( aIdeal0(sdtpldt1(X1,X2))
| ~ aIdeal0(X1)
| ~ aIdeal0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_128,plain,
( aElement0(sdtasdt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_129,plain,
( aElement0(sdtpldt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_130,plain,
( doDivides0(X1,X2)
| ~ aDivisorOf0(X1,X2)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_131,plain,
( aElement0(esk11_1(X1))
| aElementOf0(esk10_1(X1),X1)
| aIdeal0(X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_132,plain,
( aSet0(X1)
| X1 != sdtasasdt0(X2,X3)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_39]),
[final] ).
cnf(i_0_133,plain,
( aSet0(X1)
| X1 != sdtpldt1(X2,X3)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_134,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_135,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_136,plain,
( X1 = sz00
| X2 = sz00
| ~ aElement0(X1)
| ~ aElement0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_137,plain,
( aElement0(X1)
| ~ aDivisorOf0(X1,X2)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_138,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_139,plain,
( aElementOf0(esk9_1(X1),X1)
| aIdeal0(X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_140,plain,
( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_141,plain,
( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_142,plain,
( sdtpldt0(X1,smndt0(X1)) = sz00
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_143,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_144,negated_conjecture,
( ~ aElement0(X1)
| sdtasdt0(xc,X1) != xx ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_145,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_146,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_147,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_148,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_149,plain,
( aSet0(X1)
| X1 != slsdtgt0(X2)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_150,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_151,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_152,plain,
( X1 = sz00
| aNaturalNumber0(sbrdtbr0(X1))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_153,plain,
( aElement0(smndt0(X1))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_154,hypothesis,
aElementOf0(xy,slsdtgt0(xc)),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_155,hypothesis,
aElementOf0(xx,slsdtgt0(xc)),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_156,plain,
( aSet0(X1)
| ~ aIdeal0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_157,hypothesis,
sdtasdt0(xc,esk22_0) = xy,
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_158,hypothesis,
sdtasdt0(xc,esk21_0) = xx,
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_159,hypothesis,
aElement0(esk22_0),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_160,hypothesis,
aElement0(esk21_0),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_161,hypothesis,
aElement0(xz),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_162,hypothesis,
aElement0(xc),
inference(split_conjunct,[status(thm)],[m__1905]),
[final] ).
cnf(i_0_163,plain,
aElement0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]),
[final] ).
cnf(i_0_164,plain,
aElement0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]),
[final] ).
cnf(i_0_165,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mUnNeZr]),
[final] ).
cnf(i_0_166,axiom,
X1 = X1 ).
cnf(i_0_167,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_168,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_169,axiom,
( X1 != X2
| sdtpldt0(X1,X3) = sdtpldt0(X2,X3) ) ).
cnf(i_0_170,axiom,
( X1 != X2
| sdtpldt0(X3,X1) = sdtpldt0(X3,X2) ) ).
cnf(i_0_171,axiom,
( X1 != X2
| esk5_3(X1,X3,X4) = esk5_3(X2,X3,X4) ) ).
cnf(i_0_172,axiom,
( X1 != X2
| esk5_3(X3,X1,X4) = esk5_3(X3,X2,X4) ) ).
cnf(i_0_173,axiom,
( X1 != X2
| esk5_3(X3,X4,X1) = esk5_3(X3,X4,X2) ) ).
cnf(i_0_174,axiom,
( X1 != X2
| sdtasdt0(X1,X3) = sdtasdt0(X2,X3) ) ).
cnf(i_0_175,axiom,
( X1 != X2
| sdtasdt0(X3,X1) = sdtasdt0(X3,X2) ) ).
cnf(i_0_176,axiom,
( X1 != X2
| smndt0(X1) = smndt0(X2) ) ).
cnf(i_0_177,axiom,
( X1 != X2
| slsdtgt0(X1) = slsdtgt0(X2) ) ).
cnf(i_0_178,axiom,
( X1 != X2
| esk15_2(X1,X3) = esk15_2(X2,X3) ) ).
cnf(i_0_179,axiom,
( X1 != X2
| esk15_2(X3,X1) = esk15_2(X3,X2) ) ).
cnf(i_0_180,axiom,
( X1 != X2
| esk19_2(X1,X3) = esk19_2(X2,X3) ) ).
cnf(i_0_181,axiom,
( X1 != X2
| esk19_2(X3,X1) = esk19_2(X3,X2) ) ).
cnf(i_0_182,axiom,
( X1 != X2
| sdtpldt1(X1,X3) = sdtpldt1(X2,X3) ) ).
cnf(i_0_183,axiom,
( X1 != X2
| sdtpldt1(X3,X1) = sdtpldt1(X3,X2) ) ).
cnf(i_0_184,axiom,
( X1 != X2
| sdtasasdt0(X1,X3) = sdtasasdt0(X2,X3) ) ).
cnf(i_0_185,axiom,
( X1 != X2
| sdtasasdt0(X3,X1) = sdtasasdt0(X3,X2) ) ).
cnf(i_0_186,axiom,
( X1 != X2
| ~ aElementOf0(X1,X3)
| aElementOf0(X2,X3) ) ).
cnf(i_0_187,axiom,
( X1 != X2
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X2) ) ).
cnf(i_0_188,axiom,
( X1 != X2
| ~ iLess0(X1,X3)
| iLess0(X2,X3) ) ).
cnf(i_0_189,axiom,
( X1 != X2
| ~ iLess0(X3,X1)
| iLess0(X3,X2) ) ).
cnf(i_0_190,axiom,
( X1 != X2
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(X2) ) ).
cnf(i_0_191,axiom,
( X1 != X2
| ~ aSet0(X1)
| aSet0(X2) ) ).
cnf(i_0_192,axiom,
( X1 != X2
| ~ sdteqdtlpzmzozddtrp0(X1,X3,X4)
| sdteqdtlpzmzozddtrp0(X2,X3,X4) ) ).
cnf(i_0_193,axiom,
( X1 != X2
| ~ sdteqdtlpzmzozddtrp0(X3,X1,X4)
| sdteqdtlpzmzozddtrp0(X3,X2,X4) ) ).
cnf(i_0_194,axiom,
( X1 != X2
| ~ sdteqdtlpzmzozddtrp0(X3,X4,X1)
| sdteqdtlpzmzozddtrp0(X3,X4,X2) ) ).
cnf(i_0_195,axiom,
( X1 != X2
| ~ aElement0(X1)
| aElement0(X2) ) ).
cnf(i_0_196,axiom,
( X1 != X2
| ~ aIdeal0(X1)
| aIdeal0(X2) ) ).
cnf(i_0_197,axiom,
( X1 != X2
| ~ aGcdOfAnd0(X1,X3,X4)
| aGcdOfAnd0(X2,X3,X4) ) ).
cnf(i_0_198,axiom,
( X1 != X2
| ~ aGcdOfAnd0(X3,X1,X4)
| aGcdOfAnd0(X3,X2,X4) ) ).
cnf(i_0_199,axiom,
( X1 != X2
| ~ aGcdOfAnd0(X3,X4,X1)
| aGcdOfAnd0(X3,X4,X2) ) ).
cnf(i_0_200,axiom,
( X1 != X2
| ~ doDivides0(X1,X3)
| doDivides0(X2,X3) ) ).
cnf(i_0_201,axiom,
( X1 != X2
| ~ doDivides0(X3,X1)
| doDivides0(X3,X2) ) ).
cnf(i_0_202,axiom,
( X1 != X2
| ~ aDivisorOf0(X1,X3)
| aDivisorOf0(X2,X3) ) ).
cnf(i_0_203,axiom,
( X1 != X2
| ~ aDivisorOf0(X3,X1)
| aDivisorOf0(X3,X2) ) ).
cnf(i_0_204,axiom,
( X1 != X2
| ~ misRelativelyPrime0(X1,X3)
| misRelativelyPrime0(X2,X3) ) ).
cnf(i_0_205,axiom,
( X1 != X2
| ~ misRelativelyPrime0(X3,X1)
| misRelativelyPrime0(X3,X2) ) ).
cnf(i_0_166_001,axiom,
X1 = X1 ).
cnf(i_0_167_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_168_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_169_004,axiom,
( X1 != X2
| sdtpldt0(X1,X3) = sdtpldt0(X2,X3) ) ).
cnf(i_0_170_005,axiom,
( X1 != X2
| sdtpldt0(X3,X1) = sdtpldt0(X3,X2) ) ).
cnf(i_0_171_006,axiom,
( X1 != X2
| esk5_3(X1,X3,X4) = esk5_3(X2,X3,X4) ) ).
cnf(i_0_172_007,axiom,
( X1 != X2
| esk5_3(X3,X1,X4) = esk5_3(X3,X2,X4) ) ).
cnf(i_0_173_008,axiom,
( X1 != X2
| esk5_3(X3,X4,X1) = esk5_3(X3,X4,X2) ) ).
cnf(i_0_174_009,axiom,
( X1 != X2
| sdtasdt0(X1,X3) = sdtasdt0(X2,X3) ) ).
cnf(i_0_175_010,axiom,
( X1 != X2
| sdtasdt0(X3,X1) = sdtasdt0(X3,X2) ) ).
cnf(i_0_176_011,axiom,
( X1 != X2
| smndt0(X1) = smndt0(X2) ) ).
cnf(i_0_177_012,axiom,
( X1 != X2
| slsdtgt0(X1) = slsdtgt0(X2) ) ).
cnf(i_0_178_013,axiom,
( X1 != X2
| esk15_2(X1,X3) = esk15_2(X2,X3) ) ).
cnf(i_0_179_014,axiom,
( X1 != X2
| esk15_2(X3,X1) = esk15_2(X3,X2) ) ).
cnf(i_0_180_015,axiom,
( X1 != X2
| esk19_2(X1,X3) = esk19_2(X2,X3) ) ).
cnf(i_0_181_016,axiom,
( X1 != X2
| esk19_2(X3,X1) = esk19_2(X3,X2) ) ).
cnf(i_0_182_017,axiom,
( X1 != X2
| sdtpldt1(X1,X3) = sdtpldt1(X2,X3) ) ).
cnf(i_0_183_018,axiom,
( X1 != X2
| sdtpldt1(X3,X1) = sdtpldt1(X3,X2) ) ).
cnf(i_0_184_019,axiom,
( X1 != X2
| sdtasasdt0(X1,X3) = sdtasasdt0(X2,X3) ) ).
cnf(i_0_185_020,axiom,
( X1 != X2
| sdtasasdt0(X3,X1) = sdtasasdt0(X3,X2) ) ).
cnf(i_0_186_021,axiom,
( X1 != X2
| ~ aElementOf0(X1,X3)
| aElementOf0(X2,X3) ) ).
cnf(i_0_187_022,axiom,
( X1 != X2
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X2) ) ).
cnf(i_0_188_023,axiom,
( X1 != X2
| ~ iLess0(X1,X3)
| iLess0(X2,X3) ) ).
cnf(i_0_189_024,axiom,
( X1 != X2
| ~ iLess0(X3,X1)
| iLess0(X3,X2) ) ).
cnf(i_0_190_025,axiom,
( X1 != X2
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(X2) ) ).
cnf(i_0_191_026,axiom,
( X1 != X2
| ~ aSet0(X1)
| aSet0(X2) ) ).
cnf(i_0_192_027,axiom,
( X1 != X2
| ~ sdteqdtlpzmzozddtrp0(X1,X3,X4)
| sdteqdtlpzmzozddtrp0(X2,X3,X4) ) ).
cnf(i_0_193_028,axiom,
( X1 != X2
| ~ sdteqdtlpzmzozddtrp0(X3,X1,X4)
| sdteqdtlpzmzozddtrp0(X3,X2,X4) ) ).
cnf(i_0_194_029,axiom,
( X1 != X2
| ~ sdteqdtlpzmzozddtrp0(X3,X4,X1)
| sdteqdtlpzmzozddtrp0(X3,X4,X2) ) ).
cnf(i_0_195_030,axiom,
( X1 != X2
| ~ aElement0(X1)
| aElement0(X2) ) ).
cnf(i_0_196_031,axiom,
( X1 != X2
| ~ aIdeal0(X1)
| aIdeal0(X2) ) ).
cnf(i_0_197_032,axiom,
( X1 != X2
| ~ aGcdOfAnd0(X1,X3,X4)
| aGcdOfAnd0(X2,X3,X4) ) ).
cnf(i_0_198_033,axiom,
( X1 != X2
| ~ aGcdOfAnd0(X3,X1,X4)
| aGcdOfAnd0(X3,X2,X4) ) ).
cnf(i_0_199_034,axiom,
( X1 != X2
| ~ aGcdOfAnd0(X3,X4,X1)
| aGcdOfAnd0(X3,X4,X2) ) ).
cnf(i_0_200_035,axiom,
( X1 != X2
| ~ doDivides0(X1,X3)
| doDivides0(X2,X3) ) ).
cnf(i_0_201_036,axiom,
( X1 != X2
| ~ doDivides0(X3,X1)
| doDivides0(X3,X2) ) ).
cnf(i_0_202_037,axiom,
( X1 != X2
| ~ aDivisorOf0(X1,X3)
| aDivisorOf0(X2,X3) ) ).
cnf(i_0_203_038,axiom,
( X1 != X2
| ~ aDivisorOf0(X3,X1)
| aDivisorOf0(X3,X2) ) ).
cnf(i_0_204_039,axiom,
( X1 != X2
| ~ misRelativelyPrime0(X1,X3)
| misRelativelyPrime0(X2,X3) ) ).
cnf(i_0_205_040,axiom,
( X1 != X2
| ~ misRelativelyPrime0(X3,X1)
| misRelativelyPrime0(X3,X2) ) ).
cnf(i_0_206,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,[],[69]) ).
cnf(i_0_207,plain,
( ~ aElementOf0(X1,sdtpldt1(X2,X3))
| ~ aSet0(X2)
| ~ aSet0(X3)
| aElementOf0(esk4_4(X2,X3,sdtpldt1(X2,X3),X1),X3) ),
inference(equality_inference,[],[76]) ).
cnf(i_0_208,plain,
( ~ aElementOf0(X1,sdtpldt1(X2,X3))
| ~ aSet0(X2)
| ~ aSet0(X3)
| aElementOf0(esk3_4(X2,X3,sdtpldt1(X2,X3),X1),X2) ),
inference(equality_inference,[],[77]) ).
cnf(i_0_209,plain,
( ~ aElementOf0(X1,slsdtgt0(X2))
| ~ aElement0(X2)
| sdtasdt0(X2,esk18_3(X2,slsdtgt0(X2),X1)) = X1 ),
inference(equality_inference,[],[91]) ).
cnf(i_0_210,plain,
( ~ aElementOf0(X1,slsdtgt0(X2))
| ~ aElement0(X2)
| aElement0(esk18_3(X2,slsdtgt0(X2),X1)) ),
inference(equality_inference,[],[93]) ).
cnf(i_0_211,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aElementOf0(X3,sdtasasdt0(X1,X2))
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X2) ),
inference(equality_inference,[],[111]) ).
cnf(i_0_212,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aElementOf0(X3,X1)
| ~ aElementOf0(X3,sdtasasdt0(X1,X2)) ),
inference(equality_inference,[],[118]) ).
cnf(i_0_213,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aElementOf0(X3,X2)
| ~ aElementOf0(X3,sdtasasdt0(X1,X2)) ),
inference(equality_inference,[],[119]) ).
cnf(i_0_214,plain,
( ~ aElement0(X1)
| ~ aElement0(sdtasdt0(X1,X2))
| doDivides0(X1,sdtasdt0(X1,X2))
| ~ aElement0(X2) ),
inference(equality_inference,[],[122]) ).
cnf(i_0_215,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aSet0(sdtasasdt0(X1,X2)) ),
inference(equality_inference,[],[132]) ).
cnf(i_0_216,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aSet0(sdtpldt1(X1,X2)) ),
inference(equality_inference,[],[133]) ).
cnf(i_0_217,plain,
( ~ aElement0(X1)
| aSet0(slsdtgt0(X1)) ),
inference(equality_inference,[],[149]) ).
cnf(i_0_218,plain,
$false,
inference(scs_inference,[],[i_0_160,i_0_158,i_0_144]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG101+2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n008.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 01:51:13 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.30/1.61 % Version : CSE_E---1.7
% 0.30/1.61 % Problem : theBenchmark.p
% 0.30/1.61 % SZS status Theorem for theBenchmark.p
% 0.30/1.61 % SZS output start CNFRefutation
% See solution above
% 0.30/1.65 % Total time : 1.272s
%------------------------------------------------------------------------------