%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : RNG111+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:55:13 AM UTC 2026
% Result : Theorem 256.18s 271.31s
% Output : Proof 256.44s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(mElmSort,axiom,
! [W0] :
( aElement0(W0)
=> $true ),
file('theBenchmark.p',mElmSort) ).
fof(mSortsC,axiom,
aElement0(sz00),
file('theBenchmark.p',mSortsC) ).
fof(mSortsC_01,axiom,
aElement0(sz10),
file('theBenchmark.p',mSortsC_01) ).
fof(mSortsU,axiom,
! [W0] :
( aElement0(W0)
=> aElement0(smndt0(W0)) ),
file('theBenchmark.p',mSortsU) ).
fof(mSortsB,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> aElement0(sdtpldt0(W0,W1)) ),
file('theBenchmark.p',mSortsB) ).
fof(mSortsB_02,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> aElement0(sdtasdt0(W0,W1)) ),
file('theBenchmark.p',mSortsB_02) ).
fof(mAddComm,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
file('theBenchmark.p',mAddComm) ).
fof(mAddAsso,axiom,
! [W0,W1,W2] :
( ( aElement0(W2)
& aElement0(W1)
& aElement0(W0) )
=> sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ),
file('theBenchmark.p',mAddAsso) ).
fof(mAddZero,axiom,
! [W0] :
( aElement0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
file('theBenchmark.p',mAddZero) ).
fof(mAddInvr,axiom,
! [W0] :
( aElement0(W0)
=> ( sz00 = sdtpldt0(smndt0(W0),W0)
& sdtpldt0(W0,smndt0(W0)) = sz00 ) ),
file('theBenchmark.p',mAddInvr) ).
fof(mMulComm,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('theBenchmark.p',mMulComm) ).
fof(mMulAsso,axiom,
! [W0,W1,W2] :
( ( aElement0(W2)
& aElement0(W1)
& aElement0(W0) )
=> sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ),
file('theBenchmark.p',mMulAsso) ).
fof(mMulUnit,axiom,
! [W0] :
( aElement0(W0)
=> ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 ) ),
file('theBenchmark.p',mMulUnit) ).
fof(mAMDistr,axiom,
! [W0,W1,W2] :
( ( aElement0(W2)
& aElement0(W1)
& aElement0(W0) )
=> ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) ) ),
file('theBenchmark.p',mAMDistr) ).
fof(mMulMnOne,axiom,
! [W0] :
( aElement0(W0)
=> ( smndt0(W0) = sdtasdt0(W0,smndt0(sz10))
& sdtasdt0(smndt0(sz10),W0) = smndt0(W0) ) ),
file('theBenchmark.p',mMulMnOne) ).
fof(mMulZero,axiom,
! [W0] :
( aElement0(W0)
=> ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 ) ),
file('theBenchmark.p',mMulZero) ).
fof(mCancel,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> ( sdtasdt0(W0,W1) = sz00
=> ( W1 = sz00
| W0 = sz00 ) ) ),
file('theBenchmark.p',mCancel) ).
fof(mUnNeZr,axiom,
sz10 != sz00,
file('theBenchmark.p',mUnNeZr) ).
fof(mSetSort,axiom,
! [W0] :
( aSet0(W0)
=> $true ),
file('theBenchmark.p',mSetSort) ).
fof(mEOfElem,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('theBenchmark.p',mEOfElem) ).
fof(mSetEq,axiom,
! [W0,W1] :
( ( aSet0(W1)
& aSet0(W0) )
=> ( ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& ! [W2] :
( aElementOf0(W2,W0)
=> aElementOf0(W2,W1) ) )
=> W0 = W1 ) ),
file('theBenchmark.p',mSetEq) ).
fof(mDefSSum,definition,
! [W0,W1] :
( ( aSet0(W1)
& aSet0(W0) )
=> ! [W2] :
( W2 = sdtpldt1(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ? [W4,W5] :
( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) ) )
& aSet0(W2) ) ) ),
file('theBenchmark.p',mDefSSum) ).
fof(mDefSInt,definition,
! [W0,W1] :
( ( aSet0(W1)
& aSet0(W0) )
=> ! [W2] :
( W2 = sdtasasdt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( aElementOf0(W3,W1)
& aElementOf0(W3,W0) ) )
& aSet0(W2) ) ) ),
file('theBenchmark.p',mDefSInt) ).
fof(mDefIdeal,definition,
! [W0] :
( aIdeal0(W0)
<=> ( ! [W1] :
( aElementOf0(W1,W0)
=> ( ! [W2] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) )
& ! [W2] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) ) ) )
& aSet0(W0) ) ),
file('theBenchmark.p',mDefIdeal) ).
fof(mIdeSum,axiom,
! [W0,W1] :
( ( aIdeal0(W1)
& aIdeal0(W0) )
=> aIdeal0(sdtpldt1(W0,W1)) ),
file('theBenchmark.p',mIdeSum) ).
fof(mIdeInt,axiom,
! [W0,W1] :
( ( aIdeal0(W1)
& aIdeal0(W0) )
=> aIdeal0(sdtasasdt0(W0,W1)) ),
file('theBenchmark.p',mIdeInt) ).
fof(mDefMod,definition,
! [W0,W1,W2] :
( ( aIdeal0(W2)
& aElement0(W1)
& aElement0(W0) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) ) ),
file('theBenchmark.p',mDefMod) ).
fof(mChineseRemainder,axiom,
! [W0,W1] :
( ( aIdeal0(W1)
& aIdeal0(W0) )
=> ( ! [W2] :
( aElement0(W2)
=> aElementOf0(W2,sdtpldt1(W0,W1)) )
=> ! [W2,W3] :
( ( aElement0(W3)
& aElement0(W2) )
=> ? [W4] :
( sdteqdtlpzmzozddtrp0(W4,W3,W1)
& sdteqdtlpzmzozddtrp0(W4,W2,W0)
& aElement0(W4) ) ) ) ),
file('theBenchmark.p',mChineseRemainder) ).
fof(mNatSort,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> $true ),
file('theBenchmark.p',mNatSort) ).
fof(mEucSort,axiom,
! [W0] :
( ( W0 != sz00
& aElement0(W0) )
=> aNaturalNumber0(sbrdtbr0(W0)) ),
file('theBenchmark.p',mEucSort) ).
fof(mNatLess,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( iLess0(W0,W1)
=> $true ) ),
file('theBenchmark.p',mNatLess) ).
fof(mDivision,axiom,
! [W0,W1] :
( ( W1 != sz00
& aElement0(W1)
& aElement0(W0) )
=> ? [W2,W3] :
( ( W3 != sz00
=> iLess0(sbrdtbr0(W3),sbrdtbr0(W1)) )
& W0 = sdtpldt0(sdtasdt0(W2,W1),W3)
& aElement0(W3)
& aElement0(W2) ) ),
file('theBenchmark.p',mDivision) ).
fof(mDefDiv,definition,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> ( doDivides0(W0,W1)
<=> ? [W2] :
( sdtasdt0(W0,W2) = W1
& aElement0(W2) ) ) ),
file('theBenchmark.p',mDefDiv) ).
fof(mDefDvs,definition,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( doDivides0(W1,W0)
& aElement0(W1) ) ) ),
file('theBenchmark.p',mDefDvs) ).
fof(mDefGCD,definition,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> ! [W2] :
( aGcdOfAnd0(W2,W0,W1)
<=> ( ! [W3] :
( ( aDivisorOf0(W3,W1)
& aDivisorOf0(W3,W0) )
=> doDivides0(W3,W2) )
& aDivisorOf0(W2,W1)
& aDivisorOf0(W2,W0) ) ) ),
file('theBenchmark.p',mDefGCD) ).
fof(mDefRel,definition,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> ( misRelativelyPrime0(W0,W1)
<=> aGcdOfAnd0(sz10,W0,W1) ) ),
file('theBenchmark.p',mDefRel) ).
fof(mDefPrIdeal,definition,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( W1 = slsdtgt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) ) )
& aSet0(W1) ) ) ),
file('theBenchmark.p',mDefPrIdeal) ).
fof(mPrIdeal,axiom,
! [W0] :
( aElement0(W0)
=> aIdeal0(slsdtgt0(W0)) ),
file('theBenchmark.p',mPrIdeal) ).
fof(m__2091,hypothesis,
( aElement0(xb)
& aElement0(xa) ),
file('theBenchmark.p',m__2091) ).
fof(m__2110,hypothesis,
( xb != sz00
| xa != sz00 ),
file('theBenchmark.p',m__2110) ).
fof(m__2129,hypothesis,
( aGcdOfAnd0(xc,xa,xb)
& ! [W0] :
( ( ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ? [W1] :
( sdtasdt0(W0,W1) = xb
& aElement0(W1) ) )
& ( aDivisorOf0(W0,xa)
| ( ( doDivides0(W0,xa)
| ? [W1] :
( sdtasdt0(W0,W1) = xa
& aElement0(W1) ) )
& aElement0(W0) ) ) )
=> ( doDivides0(W0,xc)
& ? [W1] :
( sdtasdt0(W0,W1) = xc
& aElement0(W1) ) ) )
& aDivisorOf0(xc,xb)
& doDivides0(xc,xb)
& ? [W0] :
( sdtasdt0(xc,W0) = xb
& aElement0(W0) )
& aElement0(xc)
& aDivisorOf0(xc,xa)
& doDivides0(xc,xa)
& ? [W0] :
( sdtasdt0(xc,W0) = xa
& aElement0(W0) )
& aElement0(xc) ),
file('theBenchmark.p',m__2129) ).
fof(m__2174,hypothesis,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [W0] :
( aElementOf0(W0,xI)
<=> ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) ) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xb))
<=> ? [W1] :
( sdtasdt0(xb,W1) = W0
& aElement0(W1) ) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xa))
<=> ? [W1] :
( sdtasdt0(xa,W1) = W0
& aElement0(W1) ) )
& aIdeal0(xI)
& ! [W0] :
( aElementOf0(W0,xI)
=> ( ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) )
& ! [W1] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) ) ) )
& aSet0(xI) ),
file('theBenchmark.p',m__2174) ).
fof(m__2203,hypothesis,
( aElementOf0(xb,slsdtgt0(xb))
& ? [W0] :
( sdtasdt0(xb,W0) = xb
& aElement0(W0) )
& aElementOf0(sz00,slsdtgt0(xb))
& ? [W0] :
( sdtasdt0(xb,W0) = sz00
& aElement0(W0) )
& aElementOf0(xa,slsdtgt0(xa))
& ? [W0] :
( sdtasdt0(xa,W0) = xa
& aElement0(W0) )
& aElementOf0(sz00,slsdtgt0(xa))
& ? [W0] :
( sdtasdt0(xa,W0) = sz00
& aElement0(W0) ) ),
file('theBenchmark.p',m__2203) ).
fof(m__2228,hypothesis,
? [W0] :
( W0 != sz00
& aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) )
& ! [W1] :
( aElementOf0(W1,slsdtgt0(xb))
<=> ? [W2] :
( sdtasdt0(xb,W2) = W1
& aElement0(W2) ) )
& ! [W1] :
( aElementOf0(W1,slsdtgt0(xa))
<=> ? [W2] :
( sdtasdt0(xa,W2) = W1
& aElement0(W2) ) ) ),
file('theBenchmark.p',m__2228) ).
fof(m__,conjecture,
! [W0] :
( ( W0 != sz00
& aElementOf0(W0,xI)
& ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) ) )
=> ( ! [W1] :
( ( W1 != sz00
& ( aElementOf0(W1,xI)
| ? [W2,W3] :
( sdtpldt0(W2,W3) = W1
& aElementOf0(W3,slsdtgt0(xb))
& aElementOf0(W2,slsdtgt0(xa)) ) ) )
=> ( iLess0(sbrdtbr0(W1),sbrdtbr0(W0))
=> ? [W2] :
( ! [W3] :
( ( W3 != sz00
& ( aElementOf0(W3,xI)
| ? [W4,W5] :
( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,slsdtgt0(xb))
& aElementOf0(W4,slsdtgt0(xa)) ) ) )
=> ~ iLess0(sbrdtbr0(W3),sbrdtbr0(W2)) )
& W2 != sz00
& aElementOf0(W2,xI)
& ? [W3,W4] :
( sdtpldt0(W3,W4) = W2
& aElementOf0(W4,slsdtgt0(xb))
& aElementOf0(W3,slsdtgt0(xa)) ) ) ) )
=> ? [W1] :
( ! [W2] :
( ( W2 != sz00
& aElementOf0(W2,xI)
& ? [W3,W4] :
( sdtpldt0(W3,W4) = W2
& aElementOf0(W4,slsdtgt0(xb))
& aElementOf0(W3,slsdtgt0(xa)) ) )
=> ~ iLess0(sbrdtbr0(W2),sbrdtbr0(W1)) )
& W1 != sz00
& ( aElementOf0(W1,xI)
| ? [W2,W3] :
( sdtpldt0(W2,W3) = W1
& aElementOf0(W3,slsdtgt0(xb))
& aElementOf0(W2,slsdtgt0(xa)) ) ) ) ) ),
file('theBenchmark.p',m__) ).
fof(f_1_1,plain,
! [W0] :
( $true
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mElmSort]) ).
fof(f_1_2,plain,
! [U_0] :
( $true
| ~ aElement0(U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ! [U_0] : ~ aElement0(U_0)
| $true ),
inference(miniscope,[status(thm)],[f_1_2]) ).
cnf(f_1_4,plain,
( ~ aElement0(U_0)
| $true ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
aElement0(sz00),
inference(fof_nnf,[status(thm)],[mSortsC]) ).
cnf(f_2_2,plain,
aElement0(sz00),
inference(clausify,[status(thm)],[f_2_1]) ).
fof(f_3_1,plain,
aElement0(sz10),
inference(fof_nnf,[status(thm)],[mSortsC_01]) ).
cnf(f_3_2,plain,
aElement0(sz10),
inference(clausify,[status(thm)],[f_3_1]) ).
fof(f_4_1,plain,
! [W0] :
( aElement0(smndt0(W0))
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mSortsU]) ).
fof(f_4_2,plain,
! [U_1] :
( aElement0(smndt0(U_1))
| ~ aElement0(U_1) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( aElement0(smndt0(U_1))
| ~ aElement0(U_1) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [W0,W1] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mSortsB]) ).
fof(f_5_2,plain,
! [U_3,U_2] :
( aElement0(sdtpldt0(U_3,U_2))
| ~ aElement0(U_2)
| ~ aElement0(U_3) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( aElement0(sdtpldt0(U_3,U_2))
| ~ aElement0(U_2)
| ~ aElement0(U_3) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [W0,W1] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mSortsB_02]) ).
fof(f_6_2,plain,
! [U_5,U_4] :
( aElement0(sdtasdt0(U_5,U_4))
| ~ aElement0(U_4)
| ~ aElement0(U_5) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( aElement0(sdtasdt0(U_5,U_4))
| ~ aElement0(U_4)
| ~ aElement0(U_5) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [W0,W1] :
( sdtpldt0(W0,W1) = sdtpldt0(W1,W0)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mAddComm]) ).
fof(f_7_2,plain,
! [U_7,U_6] :
( sdtpldt0(U_7,U_6) = sdtpldt0(U_6,U_7)
| ~ aElement0(U_6)
| ~ aElement0(U_7) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( sdtpldt0(U_7,U_6) = sdtpldt0(U_6,U_7)
| ~ aElement0(U_6)
| ~ aElement0(U_7) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [W0,W1,W2] :
( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2))
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mAddAsso]) ).
fof(f_8_2,plain,
! [U_10,U_9,U_8] :
( sdtpldt0(sdtpldt0(U_10,U_9),U_8) = sdtpldt0(U_10,sdtpldt0(U_9,U_8))
| ~ aElement0(U_8)
| ~ aElement0(U_9)
| ~ aElement0(U_10) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( sdtpldt0(sdtpldt0(U_10,U_9),U_8) = sdtpldt0(U_10,sdtpldt0(U_9,U_8))
| ~ aElement0(U_8)
| ~ aElement0(U_9)
| ~ aElement0(U_10) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [W0] :
( ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 )
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mAddZero]) ).
fof(f_9_2,plain,
! [U_11] :
( ( U_11 = sdtpldt0(sz00,U_11)
& sdtpldt0(U_11,sz00) = U_11 )
| ~ aElement0(U_11) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( sdtpldt0(U_11,sz00) = U_11
| ~ aElement0(U_11) ),
inference(clausify,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( U_11 = sdtpldt0(sz00,U_11)
| ~ aElement0(U_11) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [W0] :
( ( sz00 = sdtpldt0(smndt0(W0),W0)
& sdtpldt0(W0,smndt0(W0)) = sz00 )
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mAddInvr]) ).
fof(f_10_2,plain,
! [U_12] :
( ( sz00 = sdtpldt0(smndt0(U_12),U_12)
& sdtpldt0(U_12,smndt0(U_12)) = sz00 )
| ~ aElement0(U_12) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( sdtpldt0(U_12,smndt0(U_12)) = sz00
| ~ aElement0(U_12) ),
inference(clausify,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
( sz00 = sdtpldt0(smndt0(U_12),U_12)
| ~ aElement0(U_12) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [W0,W1] :
( sdtasdt0(W0,W1) = sdtasdt0(W1,W0)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mMulComm]) ).
fof(f_11_2,plain,
! [U_14,U_13] :
( sdtasdt0(U_14,U_13) = sdtasdt0(U_13,U_14)
| ~ aElement0(U_13)
| ~ aElement0(U_14) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( sdtasdt0(U_14,U_13) = sdtasdt0(U_13,U_14)
| ~ aElement0(U_13)
| ~ aElement0(U_14) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [W0,W1,W2] :
( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2))
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mMulAsso]) ).
fof(f_12_2,plain,
! [U_17,U_16,U_15] :
( sdtasdt0(sdtasdt0(U_17,U_16),U_15) = sdtasdt0(U_17,sdtasdt0(U_16,U_15))
| ~ aElement0(U_15)
| ~ aElement0(U_16)
| ~ aElement0(U_17) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( sdtasdt0(sdtasdt0(U_17,U_16),U_15) = sdtasdt0(U_17,sdtasdt0(U_16,U_15))
| ~ aElement0(U_15)
| ~ aElement0(U_16)
| ~ aElement0(U_17) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [W0] :
( ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 )
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mMulUnit]) ).
fof(f_13_2,plain,
! [U_18] :
( ( U_18 = sdtasdt0(sz10,U_18)
& sdtasdt0(U_18,sz10) = U_18 )
| ~ aElement0(U_18) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( sdtasdt0(U_18,sz10) = U_18
| ~ aElement0(U_18) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
( U_18 = sdtasdt0(sz10,U_18)
| ~ aElement0(U_18) ),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
! [W0,W1,W2] :
( ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mAMDistr]) ).
fof(f_14_2,plain,
! [U_21,U_20,U_19] :
( ( sdtasdt0(sdtpldt0(U_20,U_19),U_21) = sdtpldt0(sdtasdt0(U_20,U_21),sdtasdt0(U_19,U_21))
& sdtasdt0(U_21,sdtpldt0(U_20,U_19)) = sdtpldt0(sdtasdt0(U_21,U_20),sdtasdt0(U_21,U_19)) )
| ~ aElement0(U_19)
| ~ aElement0(U_20)
| ~ aElement0(U_21) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( sdtasdt0(U_21,sdtpldt0(U_20,U_19)) = sdtpldt0(sdtasdt0(U_21,U_20),sdtasdt0(U_21,U_19))
| ~ aElement0(U_19)
| ~ aElement0(U_20)
| ~ aElement0(U_21) ),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( sdtasdt0(sdtpldt0(U_20,U_19),U_21) = sdtpldt0(sdtasdt0(U_20,U_21),sdtasdt0(U_19,U_21))
| ~ aElement0(U_19)
| ~ aElement0(U_20)
| ~ aElement0(U_21) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [W0] :
( ( smndt0(W0) = sdtasdt0(W0,smndt0(sz10))
& sdtasdt0(smndt0(sz10),W0) = smndt0(W0) )
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mMulMnOne]) ).
fof(f_15_2,plain,
! [U_22] :
( ( smndt0(U_22) = sdtasdt0(U_22,smndt0(sz10))
& sdtasdt0(smndt0(sz10),U_22) = smndt0(U_22) )
| ~ aElement0(U_22) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( sdtasdt0(smndt0(sz10),U_22) = smndt0(U_22)
| ~ aElement0(U_22) ),
inference(clausify,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
( smndt0(U_22) = sdtasdt0(U_22,smndt0(sz10))
| ~ aElement0(U_22) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [W0] :
( ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 )
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mMulZero]) ).
fof(f_16_2,plain,
! [U_23] :
( ( sz00 = sdtasdt0(sz00,U_23)
& sdtasdt0(U_23,sz00) = sz00 )
| ~ aElement0(U_23) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( sdtasdt0(U_23,sz00) = sz00
| ~ aElement0(U_23) ),
inference(clausify,[status(thm)],[f_16_2]) ).
cnf(f_16_4,plain,
( sz00 = sdtasdt0(sz00,U_23)
| ~ aElement0(U_23) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [W0,W1] :
( W1 = sz00
| W0 = sz00
| sdtasdt0(W0,W1) != sz00
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mCancel]) ).
fof(f_17_2,plain,
! [U_25,U_24] :
( U_24 = sz00
| U_25 = sz00
| sdtasdt0(U_25,U_24) != sz00
| ~ aElement0(U_24)
| ~ aElement0(U_25) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( U_24 = sz00
| U_25 = sz00
| sdtasdt0(U_25,U_24) != sz00
| ~ aElement0(U_24)
| ~ aElement0(U_25) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
sz10 != sz00,
inference(fof_nnf,[status(thm)],[mUnNeZr]) ).
cnf(f_18_2,plain,
sz10 != sz00,
inference(clausify,[status(thm)],[f_18_1]) ).
fof(f_19_1,plain,
! [W0] :
( $true
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mSetSort]) ).
fof(f_19_2,plain,
! [U_26] :
( $true
| ~ aSet0(U_26) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( ! [U_26] : ~ aSet0(U_26)
| $true ),
inference(miniscope,[status(thm)],[f_19_2]) ).
cnf(f_19_4,plain,
( ~ aSet0(U_26)
| $true ),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mEOfElem]) ).
fof(f_20_2,plain,
! [U_28] :
( ! [U_27] :
( aElement0(U_27)
| ~ aElementOf0(U_27,U_28) )
| ~ aSet0(U_28) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( aElement0(U_27)
| ~ aElementOf0(U_27,U_28)
| ~ aSet0(U_28) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
! [W0,W1] :
( W0 = W1
| ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ? [W2] :
( ~ aElementOf0(W2,W1)
& aElementOf0(W2,W0) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mSetEq]) ).
fof(f_21_2,plain,
! [U_32,U_31] :
( U_32 = U_31
| ? [U_30] :
( ~ aElementOf0(U_30,U_32)
& aElementOf0(U_30,U_31) )
| ? [U_29] :
( ~ aElementOf0(U_29,U_31)
& aElementOf0(U_29,U_32) )
| ~ aSet0(U_31)
| ~ aSet0(U_32) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_32,U_31] :
( U_32 = U_31
| ? [U_30] :
( ~ aElementOf0(U_30,U_32)
& aElementOf0(U_30,U_31) )
| ( ~ aElementOf0(sK1(U_32,U_31),U_31)
& aElementOf0(sK1(U_32,U_31),U_32) )
| ~ aSet0(U_31)
| ~ aSet0(U_32) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_29,sK1(U_32,U_31))],[f_21_2]) ).
fof(f_21_4,plain,
! [U_32,U_31] :
( U_32 = U_31
| ( ~ aElementOf0(sK2(U_32,U_31),U_32)
& aElementOf0(sK2(U_32,U_31),U_31) )
| ( ~ aElementOf0(sK1(U_32,U_31),U_31)
& aElementOf0(sK1(U_32,U_31),U_32) )
| ~ aSet0(U_31)
| ~ aSet0(U_32) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_30,sK2(U_32,U_31))],[f_21_3]) ).
cnf(f_21_5,plain,
( aElementOf0(sK2(U_32,U_31),U_31)
| aElementOf0(sK1(U_32,U_31),U_32)
| U_32 = U_31
| ~ aSet0(U_31)
| ~ aSet0(U_32) ),
inference(clausify,[status(thm)],[f_21_4]) ).
cnf(f_21_6,plain,
( ~ aElementOf0(sK2(U_32,U_31),U_32)
| aElementOf0(sK1(U_32,U_31),U_32)
| U_32 = U_31
| ~ aSet0(U_31)
| ~ aSet0(U_32) ),
inference(clausify,[status(thm)],[f_21_4]) ).
cnf(f_21_7,plain,
( aElementOf0(sK2(U_32,U_31),U_31)
| ~ aElementOf0(sK1(U_32,U_31),U_31)
| U_32 = U_31
| ~ aSet0(U_31)
| ~ aSet0(U_32) ),
inference(clausify,[status(thm)],[f_21_4]) ).
cnf(f_21_8,plain,
( ~ aElementOf0(sK2(U_32,U_31),U_32)
| ~ aElementOf0(sK1(U_32,U_31),U_31)
| U_32 = U_31
| ~ aSet0(U_31)
| ~ aSet0(U_32) ),
inference(clausify,[status(thm)],[f_21_4]) ).
fof(f_22_1,plain,
! [W0,W1] :
( ! [W2] :
( ( W2 = sdtpldt1(W0,W1)
| ? [W3] :
( ( ~ aElementOf0(W3,W2)
& ? [W4,W5] :
( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) ) )
| ( ! [W4,W5] :
( sdtpldt0(W4,W5) != W3
| ~ aElementOf0(W5,W1)
| ~ aElementOf0(W4,W0) )
& aElementOf0(W3,W2) ) )
| ~ aSet0(W2) )
& ( ( ! [W3] :
( ( aElementOf0(W3,W2)
| ! [W4,W5] :
( sdtpldt0(W4,W5) != W3
| ~ aElementOf0(W5,W1)
| ~ aElementOf0(W4,W0) ) )
& ( ? [W4,W5] :
( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtpldt1(W0,W1) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mDefSSum]) ).
fof(f_22_2,plain,
! [U_45,U_44] :
( ! [U_43] :
( ( U_43 = sdtpldt1(U_45,U_44)
| ? [U_42] :
( ( ~ aElementOf0(U_42,U_43)
& ? [U_41,U_40] :
( sdtpldt0(U_41,U_40) = U_42
& aElementOf0(U_40,U_44)
& aElementOf0(U_41,U_45) ) )
| ( ! [U_39,U_38] :
( sdtpldt0(U_39,U_38) != U_42
| ~ aElementOf0(U_38,U_44)
| ~ aElementOf0(U_39,U_45) )
& aElementOf0(U_42,U_43) ) )
| ~ aSet0(U_43) )
& ( ( ! [U_37] :
( ( aElementOf0(U_37,U_43)
| ! [U_36,U_35] :
( sdtpldt0(U_36,U_35) != U_37
| ~ aElementOf0(U_35,U_44)
| ~ aElementOf0(U_36,U_45) ) )
& ( ? [U_34,U_33] :
( sdtpldt0(U_34,U_33) = U_37
& aElementOf0(U_33,U_44)
& aElementOf0(U_34,U_45) )
| ~ aElementOf0(U_37,U_43) ) )
& aSet0(U_43) )
| U_43 != sdtpldt1(U_45,U_44) ) )
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_45,U_44] :
( ( ! [U_51] :
( U_51 = sdtpldt1(U_45,U_44)
| ? [U_49] :
( ~ aElementOf0(U_49,U_51)
& ? [U_41] :
( ? [U_40] :
( sdtpldt0(U_41,U_40) = U_49
& aElementOf0(U_40,U_44) )
& aElementOf0(U_41,U_45) ) )
| ? [U_48] :
( ! [U_39] :
( ! [U_38] :
( sdtpldt0(U_39,U_38) != U_48
| ~ aElementOf0(U_38,U_44) )
| ~ aElementOf0(U_39,U_45) )
& aElementOf0(U_48,U_51) )
| ~ aSet0(U_51) )
& ! [U_50] :
( ( ! [U_47] :
( aElementOf0(U_47,U_50)
| ! [U_36] :
( ! [U_35] :
( sdtpldt0(U_36,U_35) != U_47
| ~ aElementOf0(U_35,U_44) )
| ~ aElementOf0(U_36,U_45) ) )
& ! [U_46] :
( ? [U_34] :
( ? [U_33] :
( sdtpldt0(U_34,U_33) = U_46
& aElementOf0(U_33,U_44) )
& aElementOf0(U_34,U_45) )
| ~ aElementOf0(U_46,U_50) )
& aSet0(U_50) )
| U_50 != sdtpldt1(U_45,U_44) ) )
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(miniscope,[status(thm)],[f_22_2]) ).
fof(f_22_4,plain,
! [U_45,U_44] :
( ( ! [U_51] :
( U_51 = sdtpldt1(U_45,U_44)
| ? [U_49] :
( ~ aElementOf0(U_49,U_51)
& ? [U_41] :
( ? [U_40] :
( sdtpldt0(U_41,U_40) = U_49
& aElementOf0(U_40,U_44) )
& aElementOf0(U_41,U_45) ) )
| ? [U_48] :
( ! [U_39] :
( ! [U_38] :
( sdtpldt0(U_39,U_38) != U_48
| ~ aElementOf0(U_38,U_44) )
| ~ aElementOf0(U_39,U_45) )
& aElementOf0(U_48,U_51) )
| ~ aSet0(U_51) )
& ! [U_50] :
( ( ! [U_47] :
( aElementOf0(U_47,U_50)
| ! [U_36] :
( ! [U_35] :
( sdtpldt0(U_36,U_35) != U_47
| ~ aElementOf0(U_35,U_44) )
| ~ aElementOf0(U_36,U_45) ) )
& ! [U_46] :
( ( ? [U_33] :
( sdtpldt0(sK3(U_45,U_44,U_50,U_46),U_33) = U_46
& aElementOf0(U_33,U_44) )
& aElementOf0(sK3(U_45,U_44,U_50,U_46),U_45) )
| ~ aElementOf0(U_46,U_50) )
& aSet0(U_50) )
| U_50 != sdtpldt1(U_45,U_44) ) )
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_34,sK3(U_45,U_44,U_50,U_46))],[f_22_3]) ).
fof(f_22_5,plain,
! [U_45,U_44] :
( ( ! [U_51] :
( U_51 = sdtpldt1(U_45,U_44)
| ? [U_49] :
( ~ aElementOf0(U_49,U_51)
& ? [U_41] :
( ? [U_40] :
( sdtpldt0(U_41,U_40) = U_49
& aElementOf0(U_40,U_44) )
& aElementOf0(U_41,U_45) ) )
| ? [U_48] :
( ! [U_39] :
( ! [U_38] :
( sdtpldt0(U_39,U_38) != U_48
| ~ aElementOf0(U_38,U_44) )
| ~ aElementOf0(U_39,U_45) )
& aElementOf0(U_48,U_51) )
| ~ aSet0(U_51) )
& ! [U_50] :
( ( ! [U_47] :
( aElementOf0(U_47,U_50)
| ! [U_36] :
( ! [U_35] :
( sdtpldt0(U_36,U_35) != U_47
| ~ aElementOf0(U_35,U_44) )
| ~ aElementOf0(U_36,U_45) ) )
& ! [U_46] :
( ( sdtpldt0(sK3(U_45,U_44,U_50,U_46),sK4(U_45,U_44,U_50,U_46)) = U_46
& aElementOf0(sK4(U_45,U_44,U_50,U_46),U_44)
& aElementOf0(sK3(U_45,U_44,U_50,U_46),U_45) )
| ~ aElementOf0(U_46,U_50) )
& aSet0(U_50) )
| U_50 != sdtpldt1(U_45,U_44) ) )
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_33,sK4(U_45,U_44,U_50,U_46))],[f_22_4]) ).
fof(f_22_6,plain,
! [U_45,U_44] :
( ( ! [U_51] :
( U_51 = sdtpldt1(U_45,U_44)
| ? [U_49] :
( ~ aElementOf0(U_49,U_51)
& ? [U_41] :
( ? [U_40] :
( sdtpldt0(U_41,U_40) = U_49
& aElementOf0(U_40,U_44) )
& aElementOf0(U_41,U_45) ) )
| ( ! [U_39] :
( ! [U_38] :
( sdtpldt0(U_39,U_38) != sK5(U_45,U_44,U_51)
| ~ aElementOf0(U_38,U_44) )
| ~ aElementOf0(U_39,U_45) )
& aElementOf0(sK5(U_45,U_44,U_51),U_51) )
| ~ aSet0(U_51) )
& ! [U_50] :
( ( ! [U_47] :
( aElementOf0(U_47,U_50)
| ! [U_36] :
( ! [U_35] :
( sdtpldt0(U_36,U_35) != U_47
| ~ aElementOf0(U_35,U_44) )
| ~ aElementOf0(U_36,U_45) ) )
& ! [U_46] :
( ( sdtpldt0(sK3(U_45,U_44,U_50,U_46),sK4(U_45,U_44,U_50,U_46)) = U_46
& aElementOf0(sK4(U_45,U_44,U_50,U_46),U_44)
& aElementOf0(sK3(U_45,U_44,U_50,U_46),U_45) )
| ~ aElementOf0(U_46,U_50) )
& aSet0(U_50) )
| U_50 != sdtpldt1(U_45,U_44) ) )
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_48,sK5(U_45,U_44,U_51))],[f_22_5]) ).
fof(f_22_7,plain,
! [U_45,U_44] :
( ( ! [U_51] :
( U_51 = sdtpldt1(U_45,U_44)
| ( ~ aElementOf0(sK6(U_45,U_44,U_51),U_51)
& ? [U_41] :
( ? [U_40] :
( sdtpldt0(U_41,U_40) = sK6(U_45,U_44,U_51)
& aElementOf0(U_40,U_44) )
& aElementOf0(U_41,U_45) ) )
| ( ! [U_39] :
( ! [U_38] :
( sdtpldt0(U_39,U_38) != sK5(U_45,U_44,U_51)
| ~ aElementOf0(U_38,U_44) )
| ~ aElementOf0(U_39,U_45) )
& aElementOf0(sK5(U_45,U_44,U_51),U_51) )
| ~ aSet0(U_51) )
& ! [U_50] :
( ( ! [U_47] :
( aElementOf0(U_47,U_50)
| ! [U_36] :
( ! [U_35] :
( sdtpldt0(U_36,U_35) != U_47
| ~ aElementOf0(U_35,U_44) )
| ~ aElementOf0(U_36,U_45) ) )
& ! [U_46] :
( ( sdtpldt0(sK3(U_45,U_44,U_50,U_46),sK4(U_45,U_44,U_50,U_46)) = U_46
& aElementOf0(sK4(U_45,U_44,U_50,U_46),U_44)
& aElementOf0(sK3(U_45,U_44,U_50,U_46),U_45) )
| ~ aElementOf0(U_46,U_50) )
& aSet0(U_50) )
| U_50 != sdtpldt1(U_45,U_44) ) )
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_49,sK6(U_45,U_44,U_51))],[f_22_6]) ).
fof(f_22_8,plain,
! [U_45,U_44] :
( ( ! [U_51] :
( U_51 = sdtpldt1(U_45,U_44)
| ( ~ aElementOf0(sK6(U_45,U_44,U_51),U_51)
& ? [U_40] :
( sdtpldt0(sK7(U_45,U_44,U_51),U_40) = sK6(U_45,U_44,U_51)
& aElementOf0(U_40,U_44) )
& aElementOf0(sK7(U_45,U_44,U_51),U_45) )
| ( ! [U_39] :
( ! [U_38] :
( sdtpldt0(U_39,U_38) != sK5(U_45,U_44,U_51)
| ~ aElementOf0(U_38,U_44) )
| ~ aElementOf0(U_39,U_45) )
& aElementOf0(sK5(U_45,U_44,U_51),U_51) )
| ~ aSet0(U_51) )
& ! [U_50] :
( ( ! [U_47] :
( aElementOf0(U_47,U_50)
| ! [U_36] :
( ! [U_35] :
( sdtpldt0(U_36,U_35) != U_47
| ~ aElementOf0(U_35,U_44) )
| ~ aElementOf0(U_36,U_45) ) )
& ! [U_46] :
( ( sdtpldt0(sK3(U_45,U_44,U_50,U_46),sK4(U_45,U_44,U_50,U_46)) = U_46
& aElementOf0(sK4(U_45,U_44,U_50,U_46),U_44)
& aElementOf0(sK3(U_45,U_44,U_50,U_46),U_45) )
| ~ aElementOf0(U_46,U_50) )
& aSet0(U_50) )
| U_50 != sdtpldt1(U_45,U_44) ) )
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_41,sK7(U_45,U_44,U_51))],[f_22_7]) ).
fof(f_22_9,plain,
! [U_45,U_44] :
( ( ! [U_51] :
( U_51 = sdtpldt1(U_45,U_44)
| ( ~ aElementOf0(sK6(U_45,U_44,U_51),U_51)
& sdtpldt0(sK7(U_45,U_44,U_51),sK8(U_45,U_44,U_51)) = sK6(U_45,U_44,U_51)
& aElementOf0(sK8(U_45,U_44,U_51),U_44)
& aElementOf0(sK7(U_45,U_44,U_51),U_45) )
| ( ! [U_39] :
( ! [U_38] :
( sdtpldt0(U_39,U_38) != sK5(U_45,U_44,U_51)
| ~ aElementOf0(U_38,U_44) )
| ~ aElementOf0(U_39,U_45) )
& aElementOf0(sK5(U_45,U_44,U_51),U_51) )
| ~ aSet0(U_51) )
& ! [U_50] :
( ( ! [U_47] :
( aElementOf0(U_47,U_50)
| ! [U_36] :
( ! [U_35] :
( sdtpldt0(U_36,U_35) != U_47
| ~ aElementOf0(U_35,U_44) )
| ~ aElementOf0(U_36,U_45) ) )
& ! [U_46] :
( ( sdtpldt0(sK3(U_45,U_44,U_50,U_46),sK4(U_45,U_44,U_50,U_46)) = U_46
& aElementOf0(sK4(U_45,U_44,U_50,U_46),U_44)
& aElementOf0(sK3(U_45,U_44,U_50,U_46),U_45) )
| ~ aElementOf0(U_46,U_50) )
& aSet0(U_50) )
| U_50 != sdtpldt1(U_45,U_44) ) )
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_40,sK8(U_45,U_44,U_51))],[f_22_8]) ).
cnf(f_22_10,plain,
( aSet0(U_50)
| U_50 != sdtpldt1(U_45,U_44)
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_11,plain,
( aElementOf0(sK3(U_45,U_44,U_50,U_46),U_45)
| ~ aElementOf0(U_46,U_50)
| U_50 != sdtpldt1(U_45,U_44)
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_12,plain,
( aElementOf0(sK4(U_45,U_44,U_50,U_46),U_44)
| ~ aElementOf0(U_46,U_50)
| U_50 != sdtpldt1(U_45,U_44)
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_13,plain,
( sdtpldt0(sK3(U_45,U_44,U_50,U_46),sK4(U_45,U_44,U_50,U_46)) = U_46
| ~ aElementOf0(U_46,U_50)
| U_50 != sdtpldt1(U_45,U_44)
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_14,plain,
( aElementOf0(U_47,U_50)
| sdtpldt0(U_36,U_35) != U_47
| ~ aElementOf0(U_35,U_44)
| ~ aElementOf0(U_36,U_45)
| U_50 != sdtpldt1(U_45,U_44)
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_15,plain,
( aElementOf0(sK7(U_45,U_44,U_51),U_45)
| aElementOf0(sK5(U_45,U_44,U_51),U_51)
| ~ aSet0(U_51)
| U_51 = sdtpldt1(U_45,U_44)
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_16,plain,
( aElementOf0(sK8(U_45,U_44,U_51),U_44)
| aElementOf0(sK5(U_45,U_44,U_51),U_51)
| ~ aSet0(U_51)
| U_51 = sdtpldt1(U_45,U_44)
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_17,plain,
( sdtpldt0(sK7(U_45,U_44,U_51),sK8(U_45,U_44,U_51)) = sK6(U_45,U_44,U_51)
| aElementOf0(sK5(U_45,U_44,U_51),U_51)
| ~ aSet0(U_51)
| U_51 = sdtpldt1(U_45,U_44)
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_18,plain,
( ~ aElementOf0(sK6(U_45,U_44,U_51),U_51)
| aElementOf0(sK5(U_45,U_44,U_51),U_51)
| ~ aSet0(U_51)
| U_51 = sdtpldt1(U_45,U_44)
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_19,plain,
( aElementOf0(sK7(U_45,U_44,U_51),U_45)
| sdtpldt0(U_39,U_38) != sK5(U_45,U_44,U_51)
| ~ aElementOf0(U_38,U_44)
| ~ aElementOf0(U_39,U_45)
| ~ aSet0(U_51)
| U_51 = sdtpldt1(U_45,U_44)
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_20,plain,
( aElementOf0(sK8(U_45,U_44,U_51),U_44)
| sdtpldt0(U_39,U_38) != sK5(U_45,U_44,U_51)
| ~ aElementOf0(U_38,U_44)
| ~ aElementOf0(U_39,U_45)
| ~ aSet0(U_51)
| U_51 = sdtpldt1(U_45,U_44)
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_21,plain,
( sdtpldt0(sK7(U_45,U_44,U_51),sK8(U_45,U_44,U_51)) = sK6(U_45,U_44,U_51)
| sdtpldt0(U_39,U_38) != sK5(U_45,U_44,U_51)
| ~ aElementOf0(U_38,U_44)
| ~ aElementOf0(U_39,U_45)
| ~ aSet0(U_51)
| U_51 = sdtpldt1(U_45,U_44)
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_22,plain,
( ~ aElementOf0(sK6(U_45,U_44,U_51),U_51)
| sdtpldt0(U_39,U_38) != sK5(U_45,U_44,U_51)
| ~ aElementOf0(U_38,U_44)
| ~ aElementOf0(U_39,U_45)
| ~ aSet0(U_51)
| U_51 = sdtpldt1(U_45,U_44)
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(clausify,[status(thm)],[f_22_9]) ).
fof(f_23_1,plain,
! [W0,W1] :
( ! [W2] :
( ( W2 = sdtasasdt0(W0,W1)
| ? [W3] :
( ( ~ aElementOf0(W3,W2)
& aElementOf0(W3,W1)
& aElementOf0(W3,W0) )
| ( ( ~ aElementOf0(W3,W1)
| ~ aElementOf0(W3,W0) )
& aElementOf0(W3,W2) ) )
| ~ aSet0(W2) )
& ( ( ! [W3] :
( ( aElementOf0(W3,W2)
| ~ aElementOf0(W3,W1)
| ~ aElementOf0(W3,W0) )
& ( ( aElementOf0(W3,W1)
& aElementOf0(W3,W0) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtasasdt0(W0,W1) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mDefSInt]) ).
fof(f_23_2,plain,
! [U_56,U_55] :
( ! [U_54] :
( ( U_54 = sdtasasdt0(U_56,U_55)
| ? [U_53] :
( ( ~ aElementOf0(U_53,U_54)
& aElementOf0(U_53,U_55)
& aElementOf0(U_53,U_56) )
| ( ( ~ aElementOf0(U_53,U_55)
| ~ aElementOf0(U_53,U_56) )
& aElementOf0(U_53,U_54) ) )
| ~ aSet0(U_54) )
& ( ( ! [U_52] :
( ( aElementOf0(U_52,U_54)
| ~ aElementOf0(U_52,U_55)
| ~ aElementOf0(U_52,U_56) )
& ( ( aElementOf0(U_52,U_55)
& aElementOf0(U_52,U_56) )
| ~ aElementOf0(U_52,U_54) ) )
& aSet0(U_54) )
| U_54 != sdtasasdt0(U_56,U_55) ) )
| ~ aSet0(U_55)
| ~ aSet0(U_56) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_56,U_55] :
( ( ! [U_62] :
( U_62 = sdtasasdt0(U_56,U_55)
| ? [U_60] :
( ~ aElementOf0(U_60,U_62)
& aElementOf0(U_60,U_55)
& aElementOf0(U_60,U_56) )
| ? [U_59] :
( ( ~ aElementOf0(U_59,U_55)
| ~ aElementOf0(U_59,U_56) )
& aElementOf0(U_59,U_62) )
| ~ aSet0(U_62) )
& ! [U_61] :
( ( ! [U_58] :
( aElementOf0(U_58,U_61)
| ~ aElementOf0(U_58,U_55)
| ~ aElementOf0(U_58,U_56) )
& ! [U_57] :
( ( aElementOf0(U_57,U_55)
& aElementOf0(U_57,U_56) )
| ~ aElementOf0(U_57,U_61) )
& aSet0(U_61) )
| U_61 != sdtasasdt0(U_56,U_55) ) )
| ~ aSet0(U_55)
| ~ aSet0(U_56) ),
inference(miniscope,[status(thm)],[f_23_2]) ).
fof(f_23_4,plain,
! [U_56,U_55] :
( ( ! [U_62] :
( U_62 = sdtasasdt0(U_56,U_55)
| ? [U_60] :
( ~ aElementOf0(U_60,U_62)
& aElementOf0(U_60,U_55)
& aElementOf0(U_60,U_56) )
| ( ( ~ aElementOf0(sK9(U_56,U_55,U_62),U_55)
| ~ aElementOf0(sK9(U_56,U_55,U_62),U_56) )
& aElementOf0(sK9(U_56,U_55,U_62),U_62) )
| ~ aSet0(U_62) )
& ! [U_61] :
( ( ! [U_58] :
( aElementOf0(U_58,U_61)
| ~ aElementOf0(U_58,U_55)
| ~ aElementOf0(U_58,U_56) )
& ! [U_57] :
( ( aElementOf0(U_57,U_55)
& aElementOf0(U_57,U_56) )
| ~ aElementOf0(U_57,U_61) )
& aSet0(U_61) )
| U_61 != sdtasasdt0(U_56,U_55) ) )
| ~ aSet0(U_55)
| ~ aSet0(U_56) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_59,sK9(U_56,U_55,U_62))],[f_23_3]) ).
fof(f_23_5,plain,
! [U_56,U_55] :
( ( ! [U_62] :
( U_62 = sdtasasdt0(U_56,U_55)
| ( ~ aElementOf0(sK10(U_56,U_55,U_62),U_62)
& aElementOf0(sK10(U_56,U_55,U_62),U_55)
& aElementOf0(sK10(U_56,U_55,U_62),U_56) )
| ( ( ~ aElementOf0(sK9(U_56,U_55,U_62),U_55)
| ~ aElementOf0(sK9(U_56,U_55,U_62),U_56) )
& aElementOf0(sK9(U_56,U_55,U_62),U_62) )
| ~ aSet0(U_62) )
& ! [U_61] :
( ( ! [U_58] :
( aElementOf0(U_58,U_61)
| ~ aElementOf0(U_58,U_55)
| ~ aElementOf0(U_58,U_56) )
& ! [U_57] :
( ( aElementOf0(U_57,U_55)
& aElementOf0(U_57,U_56) )
| ~ aElementOf0(U_57,U_61) )
& aSet0(U_61) )
| U_61 != sdtasasdt0(U_56,U_55) ) )
| ~ aSet0(U_55)
| ~ aSet0(U_56) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_60,sK10(U_56,U_55,U_62))],[f_23_4]) ).
cnf(f_23_6,plain,
( aSet0(U_61)
| U_61 != sdtasasdt0(U_56,U_55)
| ~ aSet0(U_55)
| ~ aSet0(U_56) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_7,plain,
( aElementOf0(U_57,U_56)
| ~ aElementOf0(U_57,U_61)
| U_61 != sdtasasdt0(U_56,U_55)
| ~ aSet0(U_55)
| ~ aSet0(U_56) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_8,plain,
( aElementOf0(U_57,U_55)
| ~ aElementOf0(U_57,U_61)
| U_61 != sdtasasdt0(U_56,U_55)
| ~ aSet0(U_55)
| ~ aSet0(U_56) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_9,plain,
( aElementOf0(U_58,U_61)
| ~ aElementOf0(U_58,U_55)
| ~ aElementOf0(U_58,U_56)
| U_61 != sdtasasdt0(U_56,U_55)
| ~ aSet0(U_55)
| ~ aSet0(U_56) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_10,plain,
( aElementOf0(sK10(U_56,U_55,U_62),U_56)
| aElementOf0(sK9(U_56,U_55,U_62),U_62)
| ~ aSet0(U_62)
| U_62 = sdtasasdt0(U_56,U_55)
| ~ aSet0(U_55)
| ~ aSet0(U_56) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_11,plain,
( aElementOf0(sK10(U_56,U_55,U_62),U_55)
| aElementOf0(sK9(U_56,U_55,U_62),U_62)
| ~ aSet0(U_62)
| U_62 = sdtasasdt0(U_56,U_55)
| ~ aSet0(U_55)
| ~ aSet0(U_56) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_12,plain,
( ~ aElementOf0(sK10(U_56,U_55,U_62),U_62)
| aElementOf0(sK9(U_56,U_55,U_62),U_62)
| ~ aSet0(U_62)
| U_62 = sdtasasdt0(U_56,U_55)
| ~ aSet0(U_55)
| ~ aSet0(U_56) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_13,plain,
( aElementOf0(sK10(U_56,U_55,U_62),U_56)
| ~ aElementOf0(sK9(U_56,U_55,U_62),U_55)
| ~ aElementOf0(sK9(U_56,U_55,U_62),U_56)
| ~ aSet0(U_62)
| U_62 = sdtasasdt0(U_56,U_55)
| ~ aSet0(U_55)
| ~ aSet0(U_56) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_14,plain,
( aElementOf0(sK10(U_56,U_55,U_62),U_55)
| ~ aElementOf0(sK9(U_56,U_55,U_62),U_55)
| ~ aElementOf0(sK9(U_56,U_55,U_62),U_56)
| ~ aSet0(U_62)
| U_62 = sdtasasdt0(U_56,U_55)
| ~ aSet0(U_55)
| ~ aSet0(U_56) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_15,plain,
( ~ aElementOf0(sK10(U_56,U_55,U_62),U_62)
| ~ aElementOf0(sK9(U_56,U_55,U_62),U_55)
| ~ aElementOf0(sK9(U_56,U_55,U_62),U_56)
| ~ aSet0(U_62)
| U_62 = sdtasasdt0(U_56,U_55)
| ~ aSet0(U_55)
| ~ aSet0(U_56) ),
inference(clausify,[status(thm)],[f_23_5]) ).
fof(f_24_1,plain,
! [W0] :
( ( aIdeal0(W0)
| ? [W1] :
( ( ? [W2] :
( ~ aElementOf0(sdtasdt0(W2,W1),W0)
& aElement0(W2) )
| ? [W2] :
( ~ aElementOf0(sdtpldt0(W1,W2),W0)
& aElementOf0(W2,W0) ) )
& aElementOf0(W1,W0) )
| ~ aSet0(W0) )
& ( ( ! [W1] :
( ( ! [W2] :
( aElementOf0(sdtasdt0(W2,W1),W0)
| ~ aElement0(W2) )
& ! [W2] :
( aElementOf0(sdtpldt0(W1,W2),W0)
| ~ aElementOf0(W2,W0) ) )
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aIdeal0(W0) ) ),
inference(fof_nnf,[status(thm)],[mDefIdeal]) ).
fof(f_24_2,plain,
! [U_69] :
( ( aIdeal0(U_69)
| ? [U_68] :
( ( ? [U_67] :
( ~ aElementOf0(sdtasdt0(U_67,U_68),U_69)
& aElement0(U_67) )
| ? [U_66] :
( ~ aElementOf0(sdtpldt0(U_68,U_66),U_69)
& aElementOf0(U_66,U_69) ) )
& aElementOf0(U_68,U_69) )
| ~ aSet0(U_69) )
& ( ( ! [U_65] :
( ( ! [U_64] :
( aElementOf0(sdtasdt0(U_64,U_65),U_69)
| ~ aElement0(U_64) )
& ! [U_63] :
( aElementOf0(sdtpldt0(U_65,U_63),U_69)
| ~ aElementOf0(U_63,U_69) ) )
| ~ aElementOf0(U_65,U_69) )
& aSet0(U_69) )
| ~ aIdeal0(U_69) ) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( ! [U_71] :
( aIdeal0(U_71)
| ? [U_68] :
( ( ? [U_67] :
( ~ aElementOf0(sdtasdt0(U_67,U_68),U_71)
& aElement0(U_67) )
| ? [U_66] :
( ~ aElementOf0(sdtpldt0(U_68,U_66),U_71)
& aElementOf0(U_66,U_71) ) )
& aElementOf0(U_68,U_71) )
| ~ aSet0(U_71) )
& ! [U_70] :
( ( ! [U_65] :
( ( ! [U_64] :
( aElementOf0(sdtasdt0(U_64,U_65),U_70)
| ~ aElement0(U_64) )
& ! [U_63] :
( aElementOf0(sdtpldt0(U_65,U_63),U_70)
| ~ aElementOf0(U_63,U_70) ) )
| ~ aElementOf0(U_65,U_70) )
& aSet0(U_70) )
| ~ aIdeal0(U_70) ) ),
inference(miniscope,[status(thm)],[f_24_2]) ).
fof(f_24_4,plain,
( ! [U_71] :
( aIdeal0(U_71)
| ( ( ? [U_67] :
( ~ aElementOf0(sdtasdt0(U_67,sK11(U_71)),U_71)
& aElement0(U_67) )
| ? [U_66] :
( ~ aElementOf0(sdtpldt0(sK11(U_71),U_66),U_71)
& aElementOf0(U_66,U_71) ) )
& aElementOf0(sK11(U_71),U_71) )
| ~ aSet0(U_71) )
& ! [U_70] :
( ( ! [U_65] :
( ( ! [U_64] :
( aElementOf0(sdtasdt0(U_64,U_65),U_70)
| ~ aElement0(U_64) )
& ! [U_63] :
( aElementOf0(sdtpldt0(U_65,U_63),U_70)
| ~ aElementOf0(U_63,U_70) ) )
| ~ aElementOf0(U_65,U_70) )
& aSet0(U_70) )
| ~ aIdeal0(U_70) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_68,sK11(U_71))],[f_24_3]) ).
fof(f_24_5,plain,
( ! [U_71] :
( aIdeal0(U_71)
| ( ( ? [U_67] :
( ~ aElementOf0(sdtasdt0(U_67,sK11(U_71)),U_71)
& aElement0(U_67) )
| ( ~ aElementOf0(sdtpldt0(sK11(U_71),sK12(U_71)),U_71)
& aElementOf0(sK12(U_71),U_71) ) )
& aElementOf0(sK11(U_71),U_71) )
| ~ aSet0(U_71) )
& ! [U_70] :
( ( ! [U_65] :
( ( ! [U_64] :
( aElementOf0(sdtasdt0(U_64,U_65),U_70)
| ~ aElement0(U_64) )
& ! [U_63] :
( aElementOf0(sdtpldt0(U_65,U_63),U_70)
| ~ aElementOf0(U_63,U_70) ) )
| ~ aElementOf0(U_65,U_70) )
& aSet0(U_70) )
| ~ aIdeal0(U_70) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_66,sK12(U_71))],[f_24_4]) ).
fof(f_24_6,plain,
( ! [U_71] :
( aIdeal0(U_71)
| ( ( ( ~ aElementOf0(sdtasdt0(sK13(U_71),sK11(U_71)),U_71)
& aElement0(sK13(U_71)) )
| ( ~ aElementOf0(sdtpldt0(sK11(U_71),sK12(U_71)),U_71)
& aElementOf0(sK12(U_71),U_71) ) )
& aElementOf0(sK11(U_71),U_71) )
| ~ aSet0(U_71) )
& ! [U_70] :
( ( ! [U_65] :
( ( ! [U_64] :
( aElementOf0(sdtasdt0(U_64,U_65),U_70)
| ~ aElement0(U_64) )
& ! [U_63] :
( aElementOf0(sdtpldt0(U_65,U_63),U_70)
| ~ aElementOf0(U_63,U_70) ) )
| ~ aElementOf0(U_65,U_70) )
& aSet0(U_70) )
| ~ aIdeal0(U_70) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_67,sK13(U_71))],[f_24_5]) ).
cnf(f_24_7,plain,
( aSet0(U_70)
| ~ aIdeal0(U_70) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_8,plain,
( aElementOf0(sdtpldt0(U_65,U_63),U_70)
| ~ aElementOf0(U_63,U_70)
| ~ aElementOf0(U_65,U_70)
| ~ aIdeal0(U_70) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_9,plain,
( aElementOf0(sdtasdt0(U_64,U_65),U_70)
| ~ aElement0(U_64)
| ~ aElementOf0(U_65,U_70)
| ~ aIdeal0(U_70) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_10,plain,
( aElementOf0(sK11(U_71),U_71)
| ~ aSet0(U_71)
| aIdeal0(U_71) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_11,plain,
( aElement0(sK13(U_71))
| aElementOf0(sK12(U_71),U_71)
| ~ aSet0(U_71)
| aIdeal0(U_71) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_12,plain,
( ~ aElementOf0(sdtasdt0(sK13(U_71),sK11(U_71)),U_71)
| aElementOf0(sK12(U_71),U_71)
| ~ aSet0(U_71)
| aIdeal0(U_71) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_13,plain,
( aElement0(sK13(U_71))
| ~ aElementOf0(sdtpldt0(sK11(U_71),sK12(U_71)),U_71)
| ~ aSet0(U_71)
| aIdeal0(U_71) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_14,plain,
( ~ aElementOf0(sdtasdt0(sK13(U_71),sK11(U_71)),U_71)
| ~ aElementOf0(sdtpldt0(sK11(U_71),sK12(U_71)),U_71)
| ~ aSet0(U_71)
| aIdeal0(U_71) ),
inference(clausify,[status(thm)],[f_24_6]) ).
fof(f_25_1,plain,
! [W0,W1] :
( aIdeal0(sdtpldt1(W0,W1))
| ~ aIdeal0(W1)
| ~ aIdeal0(W0) ),
inference(fof_nnf,[status(thm)],[mIdeSum]) ).
fof(f_25_2,plain,
! [U_73,U_72] :
( aIdeal0(sdtpldt1(U_73,U_72))
| ~ aIdeal0(U_72)
| ~ aIdeal0(U_73) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( aIdeal0(sdtpldt1(U_73,U_72))
| ~ aIdeal0(U_72)
| ~ aIdeal0(U_73) ),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
! [W0,W1] :
( aIdeal0(sdtasasdt0(W0,W1))
| ~ aIdeal0(W1)
| ~ aIdeal0(W0) ),
inference(fof_nnf,[status(thm)],[mIdeInt]) ).
fof(f_26_2,plain,
! [U_75,U_74] :
( aIdeal0(sdtasasdt0(U_75,U_74))
| ~ aIdeal0(U_74)
| ~ aIdeal0(U_75) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
( aIdeal0(sdtasasdt0(U_75,U_74))
| ~ aIdeal0(U_74)
| ~ aIdeal0(U_75) ),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
! [W0,W1,W2] :
( ( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) )
& ( aElementOf0(sdtpldt0(W0,smndt0(W1)),W2)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2) ) )
| ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mDefMod]) ).
fof(f_27_2,plain,
! [U_78,U_77,U_76] :
( ( ( sdteqdtlpzmzozddtrp0(U_78,U_77,U_76)
| ~ aElementOf0(sdtpldt0(U_78,smndt0(U_77)),U_76) )
& ( aElementOf0(sdtpldt0(U_78,smndt0(U_77)),U_76)
| ~ sdteqdtlpzmzozddtrp0(U_78,U_77,U_76) ) )
| ~ aIdeal0(U_76)
| ~ aElement0(U_77)
| ~ aElement0(U_78) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( aElementOf0(sdtpldt0(U_78,smndt0(U_77)),U_76)
| ~ sdteqdtlpzmzozddtrp0(U_78,U_77,U_76)
| ~ aIdeal0(U_76)
| ~ aElement0(U_77)
| ~ aElement0(U_78) ),
inference(clausify,[status(thm)],[f_27_2]) ).
cnf(f_27_4,plain,
( sdteqdtlpzmzozddtrp0(U_78,U_77,U_76)
| ~ aElementOf0(sdtpldt0(U_78,smndt0(U_77)),U_76)
| ~ aIdeal0(U_76)
| ~ aElement0(U_77)
| ~ aElement0(U_78) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_1,plain,
! [W0,W1] :
( ! [W2,W3] :
( ? [W4] :
( sdteqdtlpzmzozddtrp0(W4,W3,W1)
& sdteqdtlpzmzozddtrp0(W4,W2,W0)
& aElement0(W4) )
| ~ aElement0(W3)
| ~ aElement0(W2) )
| ? [W2] :
( ~ aElementOf0(W2,sdtpldt1(W0,W1))
& aElement0(W2) )
| ~ aIdeal0(W1)
| ~ aIdeal0(W0) ),
inference(fof_nnf,[status(thm)],[mChineseRemainder]) ).
fof(f_28_2,plain,
! [U_84,U_83] :
( ! [U_82,U_81] :
( ? [U_80] :
( sdteqdtlpzmzozddtrp0(U_80,U_81,U_83)
& sdteqdtlpzmzozddtrp0(U_80,U_82,U_84)
& aElement0(U_80) )
| ~ aElement0(U_81)
| ~ aElement0(U_82) )
| ? [U_79] :
( ~ aElementOf0(U_79,sdtpldt1(U_84,U_83))
& aElement0(U_79) )
| ~ aIdeal0(U_83)
| ~ aIdeal0(U_84) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_84,U_83] :
( ! [U_82,U_81] :
( ? [U_80] :
( sdteqdtlpzmzozddtrp0(U_80,U_81,U_83)
& sdteqdtlpzmzozddtrp0(U_80,U_82,U_84)
& aElement0(U_80) )
| ~ aElement0(U_81)
| ~ aElement0(U_82) )
| ( ~ aElementOf0(sK14(U_84,U_83),sdtpldt1(U_84,U_83))
& aElement0(sK14(U_84,U_83)) )
| ~ aIdeal0(U_83)
| ~ aIdeal0(U_84) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_79,sK14(U_84,U_83))],[f_28_2]) ).
fof(f_28_4,plain,
! [U_84,U_83] :
( ! [U_82,U_81] :
( ( sdteqdtlpzmzozddtrp0(sK15(U_84,U_83,U_82,U_81),U_81,U_83)
& sdteqdtlpzmzozddtrp0(sK15(U_84,U_83,U_82,U_81),U_82,U_84)
& aElement0(sK15(U_84,U_83,U_82,U_81)) )
| ~ aElement0(U_81)
| ~ aElement0(U_82) )
| ( ~ aElementOf0(sK14(U_84,U_83),sdtpldt1(U_84,U_83))
& aElement0(sK14(U_84,U_83)) )
| ~ aIdeal0(U_83)
| ~ aIdeal0(U_84) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_80,sK15(U_84,U_83,U_82,U_81))],[f_28_3]) ).
cnf(f_28_5,plain,
( aElement0(sK15(U_84,U_83,U_82,U_81))
| ~ aElement0(U_81)
| ~ aElement0(U_82)
| aElement0(sK14(U_84,U_83))
| ~ aIdeal0(U_83)
| ~ aIdeal0(U_84) ),
inference(clausify,[status(thm)],[f_28_4]) ).
cnf(f_28_6,plain,
( sdteqdtlpzmzozddtrp0(sK15(U_84,U_83,U_82,U_81),U_82,U_84)
| ~ aElement0(U_81)
| ~ aElement0(U_82)
| aElement0(sK14(U_84,U_83))
| ~ aIdeal0(U_83)
| ~ aIdeal0(U_84) ),
inference(clausify,[status(thm)],[f_28_4]) ).
cnf(f_28_7,plain,
( sdteqdtlpzmzozddtrp0(sK15(U_84,U_83,U_82,U_81),U_81,U_83)
| ~ aElement0(U_81)
| ~ aElement0(U_82)
| aElement0(sK14(U_84,U_83))
| ~ aIdeal0(U_83)
| ~ aIdeal0(U_84) ),
inference(clausify,[status(thm)],[f_28_4]) ).
cnf(f_28_8,plain,
( aElement0(sK15(U_84,U_83,U_82,U_81))
| ~ aElement0(U_81)
| ~ aElement0(U_82)
| ~ aElementOf0(sK14(U_84,U_83),sdtpldt1(U_84,U_83))
| ~ aIdeal0(U_83)
| ~ aIdeal0(U_84) ),
inference(clausify,[status(thm)],[f_28_4]) ).
cnf(f_28_9,plain,
( sdteqdtlpzmzozddtrp0(sK15(U_84,U_83,U_82,U_81),U_82,U_84)
| ~ aElement0(U_81)
| ~ aElement0(U_82)
| ~ aElementOf0(sK14(U_84,U_83),sdtpldt1(U_84,U_83))
| ~ aIdeal0(U_83)
| ~ aIdeal0(U_84) ),
inference(clausify,[status(thm)],[f_28_4]) ).
cnf(f_28_10,plain,
( sdteqdtlpzmzozddtrp0(sK15(U_84,U_83,U_82,U_81),U_81,U_83)
| ~ aElement0(U_81)
| ~ aElement0(U_82)
| ~ aElementOf0(sK14(U_84,U_83),sdtpldt1(U_84,U_83))
| ~ aIdeal0(U_83)
| ~ aIdeal0(U_84) ),
inference(clausify,[status(thm)],[f_28_4]) ).
fof(f_29_1,plain,
! [W0] :
( $true
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mNatSort]) ).
fof(f_29_2,plain,
! [U_85] :
( $true
| ~ aNaturalNumber0(U_85) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
( ! [U_85] : ~ aNaturalNumber0(U_85)
| $true ),
inference(miniscope,[status(thm)],[f_29_2]) ).
cnf(f_29_4,plain,
( ~ aNaturalNumber0(U_85)
| $true ),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_1,plain,
! [W0] :
( aNaturalNumber0(sbrdtbr0(W0))
| W0 = sz00
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mEucSort]) ).
fof(f_30_2,plain,
! [U_86] :
( aNaturalNumber0(sbrdtbr0(U_86))
| U_86 = sz00
| ~ aElement0(U_86) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( aNaturalNumber0(sbrdtbr0(U_86))
| U_86 = sz00
| ~ aElement0(U_86) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
! [W0,W1] :
( $true
| ~ iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mNatLess]) ).
fof(f_31_2,plain,
! [U_88,U_87] :
( $true
| ~ iLess0(U_88,U_87)
| ~ aNaturalNumber0(U_87)
| ~ aNaturalNumber0(U_88) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( $true
| ~ iLess0(U_88,U_87)
| ~ aNaturalNumber0(U_87)
| ~ aNaturalNumber0(U_88) ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
! [W0,W1] :
( ? [W2,W3] :
( ( iLess0(sbrdtbr0(W3),sbrdtbr0(W1))
| W3 = sz00 )
& W0 = sdtpldt0(sdtasdt0(W2,W1),W3)
& aElement0(W3)
& aElement0(W2) )
| W1 = sz00
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mDivision]) ).
fof(f_32_2,plain,
! [U_92,U_91] :
( ? [U_90,U_89] :
( ( iLess0(sbrdtbr0(U_89),sbrdtbr0(U_91))
| U_89 = sz00 )
& U_92 = sdtpldt0(sdtasdt0(U_90,U_91),U_89)
& aElement0(U_89)
& aElement0(U_90) )
| U_91 = sz00
| ~ aElement0(U_91)
| ~ aElement0(U_92) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_92,U_91] :
( ? [U_90] :
( ? [U_89] :
( ( iLess0(sbrdtbr0(U_89),sbrdtbr0(U_91))
| U_89 = sz00 )
& U_92 = sdtpldt0(sdtasdt0(U_90,U_91),U_89)
& aElement0(U_89) )
& aElement0(U_90) )
| U_91 = sz00
| ~ aElement0(U_91)
| ~ aElement0(U_92) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
fof(f_32_4,plain,
! [U_92,U_91] :
( ( ? [U_89] :
( ( iLess0(sbrdtbr0(U_89),sbrdtbr0(U_91))
| U_89 = sz00 )
& U_92 = sdtpldt0(sdtasdt0(sK16(U_92,U_91),U_91),U_89)
& aElement0(U_89) )
& aElement0(sK16(U_92,U_91)) )
| U_91 = sz00
| ~ aElement0(U_91)
| ~ aElement0(U_92) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_90,sK16(U_92,U_91))],[f_32_3]) ).
fof(f_32_5,plain,
! [U_92,U_91] :
( ( ( iLess0(sbrdtbr0(sK17(U_92,U_91)),sbrdtbr0(U_91))
| sK17(U_92,U_91) = sz00 )
& U_92 = sdtpldt0(sdtasdt0(sK16(U_92,U_91),U_91),sK17(U_92,U_91))
& aElement0(sK17(U_92,U_91))
& aElement0(sK16(U_92,U_91)) )
| U_91 = sz00
| ~ aElement0(U_91)
| ~ aElement0(U_92) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_89,sK17(U_92,U_91))],[f_32_4]) ).
cnf(f_32_6,plain,
( aElement0(sK16(U_92,U_91))
| U_91 = sz00
| ~ aElement0(U_91)
| ~ aElement0(U_92) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_7,plain,
( aElement0(sK17(U_92,U_91))
| U_91 = sz00
| ~ aElement0(U_91)
| ~ aElement0(U_92) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_8,plain,
( U_92 = sdtpldt0(sdtasdt0(sK16(U_92,U_91),U_91),sK17(U_92,U_91))
| U_91 = sz00
| ~ aElement0(U_91)
| ~ aElement0(U_92) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_9,plain,
( iLess0(sbrdtbr0(sK17(U_92,U_91)),sbrdtbr0(U_91))
| sK17(U_92,U_91) = sz00
| U_91 = sz00
| ~ aElement0(U_91)
| ~ aElement0(U_92) ),
inference(clausify,[status(thm)],[f_32_5]) ).
fof(f_33_1,plain,
! [W0,W1] :
( ( ( doDivides0(W0,W1)
| ! [W2] :
( sdtasdt0(W0,W2) != W1
| ~ aElement0(W2) ) )
& ( ? [W2] :
( sdtasdt0(W0,W2) = W1
& aElement0(W2) )
| ~ doDivides0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mDefDiv]) ).
fof(f_33_2,plain,
! [U_96,U_95] :
( ( ( doDivides0(U_96,U_95)
| ! [U_94] :
( sdtasdt0(U_96,U_94) != U_95
| ~ aElement0(U_94) ) )
& ( ? [U_93] :
( sdtasdt0(U_96,U_93) = U_95
& aElement0(U_93) )
| ~ doDivides0(U_96,U_95) ) )
| ~ aElement0(U_95)
| ~ aElement0(U_96) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_96,U_95] :
( ( ( doDivides0(U_96,U_95)
| ! [U_94] :
( sdtasdt0(U_96,U_94) != U_95
| ~ aElement0(U_94) ) )
& ( ( sdtasdt0(U_96,sK18(U_96,U_95)) = U_95
& aElement0(sK18(U_96,U_95)) )
| ~ doDivides0(U_96,U_95) ) )
| ~ aElement0(U_95)
| ~ aElement0(U_96) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_93,sK18(U_96,U_95))],[f_33_2]) ).
cnf(f_33_4,plain,
( aElement0(sK18(U_96,U_95))
| ~ doDivides0(U_96,U_95)
| ~ aElement0(U_95)
| ~ aElement0(U_96) ),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_5,plain,
( sdtasdt0(U_96,sK18(U_96,U_95)) = U_95
| ~ doDivides0(U_96,U_95)
| ~ aElement0(U_95)
| ~ aElement0(U_96) ),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_6,plain,
( doDivides0(U_96,U_95)
| sdtasdt0(U_96,U_94) != U_95
| ~ aElement0(U_94)
| ~ aElement0(U_95)
| ~ aElement0(U_96) ),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
! [W0] :
( ! [W1] :
( ( aDivisorOf0(W1,W0)
| ~ doDivides0(W1,W0)
| ~ aElement0(W1) )
& ( ( doDivides0(W1,W0)
& aElement0(W1) )
| ~ aDivisorOf0(W1,W0) ) )
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mDefDvs]) ).
fof(f_34_2,plain,
! [U_98] :
( ! [U_97] :
( ( aDivisorOf0(U_97,U_98)
| ~ doDivides0(U_97,U_98)
| ~ aElement0(U_97) )
& ( ( doDivides0(U_97,U_98)
& aElement0(U_97) )
| ~ aDivisorOf0(U_97,U_98) ) )
| ~ aElement0(U_98) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_98] :
( ( ! [U_100] :
( aDivisorOf0(U_100,U_98)
| ~ doDivides0(U_100,U_98)
| ~ aElement0(U_100) )
& ! [U_99] :
( ( doDivides0(U_99,U_98)
& aElement0(U_99) )
| ~ aDivisorOf0(U_99,U_98) ) )
| ~ aElement0(U_98) ),
inference(miniscope,[status(thm)],[f_34_2]) ).
cnf(f_34_4,plain,
( aElement0(U_99)
| ~ aDivisorOf0(U_99,U_98)
| ~ aElement0(U_98) ),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_34_5,plain,
( doDivides0(U_99,U_98)
| ~ aDivisorOf0(U_99,U_98)
| ~ aElement0(U_98) ),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_34_6,plain,
( aDivisorOf0(U_100,U_98)
| ~ doDivides0(U_100,U_98)
| ~ aElement0(U_100)
| ~ aElement0(U_98) ),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
! [W0,W1] :
( ! [W2] :
( ( aGcdOfAnd0(W2,W0,W1)
| ? [W3] :
( ~ doDivides0(W3,W2)
& aDivisorOf0(W3,W1)
& aDivisorOf0(W3,W0) )
| ~ aDivisorOf0(W2,W1)
| ~ aDivisorOf0(W2,W0) )
& ( ( ! [W3] :
( doDivides0(W3,W2)
| ~ aDivisorOf0(W3,W1)
| ~ aDivisorOf0(W3,W0) )
& aDivisorOf0(W2,W1)
& aDivisorOf0(W2,W0) )
| ~ aGcdOfAnd0(W2,W0,W1) ) )
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mDefGCD]) ).
fof(f_35_2,plain,
! [U_105,U_104] :
( ! [U_103] :
( ( aGcdOfAnd0(U_103,U_105,U_104)
| ? [U_102] :
( ~ doDivides0(U_102,U_103)
& aDivisorOf0(U_102,U_104)
& aDivisorOf0(U_102,U_105) )
| ~ aDivisorOf0(U_103,U_104)
| ~ aDivisorOf0(U_103,U_105) )
& ( ( ! [U_101] :
( doDivides0(U_101,U_103)
| ~ aDivisorOf0(U_101,U_104)
| ~ aDivisorOf0(U_101,U_105) )
& aDivisorOf0(U_103,U_104)
& aDivisorOf0(U_103,U_105) )
| ~ aGcdOfAnd0(U_103,U_105,U_104) ) )
| ~ aElement0(U_104)
| ~ aElement0(U_105) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_105,U_104] :
( ( ! [U_107] :
( aGcdOfAnd0(U_107,U_105,U_104)
| ? [U_102] :
( ~ doDivides0(U_102,U_107)
& aDivisorOf0(U_102,U_104)
& aDivisorOf0(U_102,U_105) )
| ~ aDivisorOf0(U_107,U_104)
| ~ aDivisorOf0(U_107,U_105) )
& ! [U_106] :
( ( ! [U_101] :
( doDivides0(U_101,U_106)
| ~ aDivisorOf0(U_101,U_104)
| ~ aDivisorOf0(U_101,U_105) )
& aDivisorOf0(U_106,U_104)
& aDivisorOf0(U_106,U_105) )
| ~ aGcdOfAnd0(U_106,U_105,U_104) ) )
| ~ aElement0(U_104)
| ~ aElement0(U_105) ),
inference(miniscope,[status(thm)],[f_35_2]) ).
fof(f_35_4,plain,
! [U_105,U_104] :
( ( ! [U_107] :
( aGcdOfAnd0(U_107,U_105,U_104)
| ( ~ doDivides0(sK19(U_105,U_104,U_107),U_107)
& aDivisorOf0(sK19(U_105,U_104,U_107),U_104)
& aDivisorOf0(sK19(U_105,U_104,U_107),U_105) )
| ~ aDivisorOf0(U_107,U_104)
| ~ aDivisorOf0(U_107,U_105) )
& ! [U_106] :
( ( ! [U_101] :
( doDivides0(U_101,U_106)
| ~ aDivisorOf0(U_101,U_104)
| ~ aDivisorOf0(U_101,U_105) )
& aDivisorOf0(U_106,U_104)
& aDivisorOf0(U_106,U_105) )
| ~ aGcdOfAnd0(U_106,U_105,U_104) ) )
| ~ aElement0(U_104)
| ~ aElement0(U_105) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_102,sK19(U_105,U_104,U_107))],[f_35_3]) ).
cnf(f_35_5,plain,
( aDivisorOf0(U_106,U_105)
| ~ aGcdOfAnd0(U_106,U_105,U_104)
| ~ aElement0(U_104)
| ~ aElement0(U_105) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_6,plain,
( aDivisorOf0(U_106,U_104)
| ~ aGcdOfAnd0(U_106,U_105,U_104)
| ~ aElement0(U_104)
| ~ aElement0(U_105) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_7,plain,
( doDivides0(U_101,U_106)
| ~ aDivisorOf0(U_101,U_104)
| ~ aDivisorOf0(U_101,U_105)
| ~ aGcdOfAnd0(U_106,U_105,U_104)
| ~ aElement0(U_104)
| ~ aElement0(U_105) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_8,plain,
( aDivisorOf0(sK19(U_105,U_104,U_107),U_105)
| ~ aDivisorOf0(U_107,U_104)
| ~ aDivisorOf0(U_107,U_105)
| aGcdOfAnd0(U_107,U_105,U_104)
| ~ aElement0(U_104)
| ~ aElement0(U_105) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_9,plain,
( aDivisorOf0(sK19(U_105,U_104,U_107),U_104)
| ~ aDivisorOf0(U_107,U_104)
| ~ aDivisorOf0(U_107,U_105)
| aGcdOfAnd0(U_107,U_105,U_104)
| ~ aElement0(U_104)
| ~ aElement0(U_105) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_10,plain,
( ~ doDivides0(sK19(U_105,U_104,U_107),U_107)
| ~ aDivisorOf0(U_107,U_104)
| ~ aDivisorOf0(U_107,U_105)
| aGcdOfAnd0(U_107,U_105,U_104)
| ~ aElement0(U_104)
| ~ aElement0(U_105) ),
inference(clausify,[status(thm)],[f_35_4]) ).
fof(f_36_1,plain,
! [W0,W1] :
( ( ( misRelativelyPrime0(W0,W1)
| ~ aGcdOfAnd0(sz10,W0,W1) )
& ( aGcdOfAnd0(sz10,W0,W1)
| ~ misRelativelyPrime0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mDefRel]) ).
fof(f_36_2,plain,
! [U_109,U_108] :
( ( ( misRelativelyPrime0(U_109,U_108)
| ~ aGcdOfAnd0(sz10,U_109,U_108) )
& ( aGcdOfAnd0(sz10,U_109,U_108)
| ~ misRelativelyPrime0(U_109,U_108) ) )
| ~ aElement0(U_108)
| ~ aElement0(U_109) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
cnf(f_36_3,plain,
( aGcdOfAnd0(sz10,U_109,U_108)
| ~ misRelativelyPrime0(U_109,U_108)
| ~ aElement0(U_108)
| ~ aElement0(U_109) ),
inference(clausify,[status(thm)],[f_36_2]) ).
cnf(f_36_4,plain,
( misRelativelyPrime0(U_109,U_108)
| ~ aGcdOfAnd0(sz10,U_109,U_108)
| ~ aElement0(U_108)
| ~ aElement0(U_109) ),
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,plain,
! [W0] :
( ! [W1] :
( ( W1 = slsdtgt0(W0)
| ? [W2] :
( ( ~ aElementOf0(W2,W1)
& ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) ) )
| ( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
& aElementOf0(W2,W1) ) )
| ~ aSet0(W1) )
& ( ( ! [W2] :
( ( aElementOf0(W2,W1)
| ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) ) )
& ( ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) )
| ~ aElementOf0(W2,W1) ) )
& aSet0(W1) )
| W1 != slsdtgt0(W0) ) )
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mDefPrIdeal]) ).
fof(f_37_2,plain,
! [U_117] :
( ! [U_116] :
( ( U_116 = slsdtgt0(U_117)
| ? [U_115] :
( ( ~ aElementOf0(U_115,U_116)
& ? [U_114] :
( sdtasdt0(U_117,U_114) = U_115
& aElement0(U_114) ) )
| ( ! [U_113] :
( sdtasdt0(U_117,U_113) != U_115
| ~ aElement0(U_113) )
& aElementOf0(U_115,U_116) ) )
| ~ aSet0(U_116) )
& ( ( ! [U_112] :
( ( aElementOf0(U_112,U_116)
| ! [U_111] :
( sdtasdt0(U_117,U_111) != U_112
| ~ aElement0(U_111) ) )
& ( ? [U_110] :
( sdtasdt0(U_117,U_110) = U_112
& aElement0(U_110) )
| ~ aElementOf0(U_112,U_116) ) )
& aSet0(U_116) )
| U_116 != slsdtgt0(U_117) ) )
| ~ aElement0(U_117) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_117] :
( ( ! [U_123] :
( U_123 = slsdtgt0(U_117)
| ? [U_121] :
( ~ aElementOf0(U_121,U_123)
& ? [U_114] :
( sdtasdt0(U_117,U_114) = U_121
& aElement0(U_114) ) )
| ? [U_120] :
( ! [U_113] :
( sdtasdt0(U_117,U_113) != U_120
| ~ aElement0(U_113) )
& aElementOf0(U_120,U_123) )
| ~ aSet0(U_123) )
& ! [U_122] :
( ( ! [U_119] :
( aElementOf0(U_119,U_122)
| ! [U_111] :
( sdtasdt0(U_117,U_111) != U_119
| ~ aElement0(U_111) ) )
& ! [U_118] :
( ? [U_110] :
( sdtasdt0(U_117,U_110) = U_118
& aElement0(U_110) )
| ~ aElementOf0(U_118,U_122) )
& aSet0(U_122) )
| U_122 != slsdtgt0(U_117) ) )
| ~ aElement0(U_117) ),
inference(miniscope,[status(thm)],[f_37_2]) ).
fof(f_37_4,plain,
! [U_117] :
( ( ! [U_123] :
( U_123 = slsdtgt0(U_117)
| ? [U_121] :
( ~ aElementOf0(U_121,U_123)
& ? [U_114] :
( sdtasdt0(U_117,U_114) = U_121
& aElement0(U_114) ) )
| ? [U_120] :
( ! [U_113] :
( sdtasdt0(U_117,U_113) != U_120
| ~ aElement0(U_113) )
& aElementOf0(U_120,U_123) )
| ~ aSet0(U_123) )
& ! [U_122] :
( ( ! [U_119] :
( aElementOf0(U_119,U_122)
| ! [U_111] :
( sdtasdt0(U_117,U_111) != U_119
| ~ aElement0(U_111) ) )
& ! [U_118] :
( ( sdtasdt0(U_117,sK20(U_117,U_122,U_118)) = U_118
& aElement0(sK20(U_117,U_122,U_118)) )
| ~ aElementOf0(U_118,U_122) )
& aSet0(U_122) )
| U_122 != slsdtgt0(U_117) ) )
| ~ aElement0(U_117) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_110,sK20(U_117,U_122,U_118))],[f_37_3]) ).
fof(f_37_5,plain,
! [U_117] :
( ( ! [U_123] :
( U_123 = slsdtgt0(U_117)
| ? [U_121] :
( ~ aElementOf0(U_121,U_123)
& ? [U_114] :
( sdtasdt0(U_117,U_114) = U_121
& aElement0(U_114) ) )
| ( ! [U_113] :
( sdtasdt0(U_117,U_113) != sK21(U_117,U_123)
| ~ aElement0(U_113) )
& aElementOf0(sK21(U_117,U_123),U_123) )
| ~ aSet0(U_123) )
& ! [U_122] :
( ( ! [U_119] :
( aElementOf0(U_119,U_122)
| ! [U_111] :
( sdtasdt0(U_117,U_111) != U_119
| ~ aElement0(U_111) ) )
& ! [U_118] :
( ( sdtasdt0(U_117,sK20(U_117,U_122,U_118)) = U_118
& aElement0(sK20(U_117,U_122,U_118)) )
| ~ aElementOf0(U_118,U_122) )
& aSet0(U_122) )
| U_122 != slsdtgt0(U_117) ) )
| ~ aElement0(U_117) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_120,sK21(U_117,U_123))],[f_37_4]) ).
fof(f_37_6,plain,
! [U_117] :
( ( ! [U_123] :
( U_123 = slsdtgt0(U_117)
| ( ~ aElementOf0(sK22(U_117,U_123),U_123)
& ? [U_114] :
( sdtasdt0(U_117,U_114) = sK22(U_117,U_123)
& aElement0(U_114) ) )
| ( ! [U_113] :
( sdtasdt0(U_117,U_113) != sK21(U_117,U_123)
| ~ aElement0(U_113) )
& aElementOf0(sK21(U_117,U_123),U_123) )
| ~ aSet0(U_123) )
& ! [U_122] :
( ( ! [U_119] :
( aElementOf0(U_119,U_122)
| ! [U_111] :
( sdtasdt0(U_117,U_111) != U_119
| ~ aElement0(U_111) ) )
& ! [U_118] :
( ( sdtasdt0(U_117,sK20(U_117,U_122,U_118)) = U_118
& aElement0(sK20(U_117,U_122,U_118)) )
| ~ aElementOf0(U_118,U_122) )
& aSet0(U_122) )
| U_122 != slsdtgt0(U_117) ) )
| ~ aElement0(U_117) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_121,sK22(U_117,U_123))],[f_37_5]) ).
fof(f_37_7,plain,
! [U_117] :
( ( ! [U_123] :
( U_123 = slsdtgt0(U_117)
| ( ~ aElementOf0(sK22(U_117,U_123),U_123)
& sdtasdt0(U_117,sK23(U_117,U_123)) = sK22(U_117,U_123)
& aElement0(sK23(U_117,U_123)) )
| ( ! [U_113] :
( sdtasdt0(U_117,U_113) != sK21(U_117,U_123)
| ~ aElement0(U_113) )
& aElementOf0(sK21(U_117,U_123),U_123) )
| ~ aSet0(U_123) )
& ! [U_122] :
( ( ! [U_119] :
( aElementOf0(U_119,U_122)
| ! [U_111] :
( sdtasdt0(U_117,U_111) != U_119
| ~ aElement0(U_111) ) )
& ! [U_118] :
( ( sdtasdt0(U_117,sK20(U_117,U_122,U_118)) = U_118
& aElement0(sK20(U_117,U_122,U_118)) )
| ~ aElementOf0(U_118,U_122) )
& aSet0(U_122) )
| U_122 != slsdtgt0(U_117) ) )
| ~ aElement0(U_117) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_114,sK23(U_117,U_123))],[f_37_6]) ).
cnf(f_37_8,plain,
( aSet0(U_122)
| U_122 != slsdtgt0(U_117)
| ~ aElement0(U_117) ),
inference(clausify,[status(thm)],[f_37_7]) ).
cnf(f_37_9,plain,
( aElement0(sK20(U_117,U_122,U_118))
| ~ aElementOf0(U_118,U_122)
| U_122 != slsdtgt0(U_117)
| ~ aElement0(U_117) ),
inference(clausify,[status(thm)],[f_37_7]) ).
cnf(f_37_10,plain,
( sdtasdt0(U_117,sK20(U_117,U_122,U_118)) = U_118
| ~ aElementOf0(U_118,U_122)
| U_122 != slsdtgt0(U_117)
| ~ aElement0(U_117) ),
inference(clausify,[status(thm)],[f_37_7]) ).
cnf(f_37_11,plain,
( aElementOf0(U_119,U_122)
| sdtasdt0(U_117,U_111) != U_119
| ~ aElement0(U_111)
| U_122 != slsdtgt0(U_117)
| ~ aElement0(U_117) ),
inference(clausify,[status(thm)],[f_37_7]) ).
cnf(f_37_12,plain,
( aElement0(sK23(U_117,U_123))
| aElementOf0(sK21(U_117,U_123),U_123)
| ~ aSet0(U_123)
| U_123 = slsdtgt0(U_117)
| ~ aElement0(U_117) ),
inference(clausify,[status(thm)],[f_37_7]) ).
cnf(f_37_13,plain,
( sdtasdt0(U_117,sK23(U_117,U_123)) = sK22(U_117,U_123)
| aElementOf0(sK21(U_117,U_123),U_123)
| ~ aSet0(U_123)
| U_123 = slsdtgt0(U_117)
| ~ aElement0(U_117) ),
inference(clausify,[status(thm)],[f_37_7]) ).
cnf(f_37_14,plain,
( ~ aElementOf0(sK22(U_117,U_123),U_123)
| aElementOf0(sK21(U_117,U_123),U_123)
| ~ aSet0(U_123)
| U_123 = slsdtgt0(U_117)
| ~ aElement0(U_117) ),
inference(clausify,[status(thm)],[f_37_7]) ).
cnf(f_37_15,plain,
( aElement0(sK23(U_117,U_123))
| sdtasdt0(U_117,U_113) != sK21(U_117,U_123)
| ~ aElement0(U_113)
| ~ aSet0(U_123)
| U_123 = slsdtgt0(U_117)
| ~ aElement0(U_117) ),
inference(clausify,[status(thm)],[f_37_7]) ).
cnf(f_37_16,plain,
( sdtasdt0(U_117,sK23(U_117,U_123)) = sK22(U_117,U_123)
| sdtasdt0(U_117,U_113) != sK21(U_117,U_123)
| ~ aElement0(U_113)
| ~ aSet0(U_123)
| U_123 = slsdtgt0(U_117)
| ~ aElement0(U_117) ),
inference(clausify,[status(thm)],[f_37_7]) ).
cnf(f_37_17,plain,
( ~ aElementOf0(sK22(U_117,U_123),U_123)
| sdtasdt0(U_117,U_113) != sK21(U_117,U_123)
| ~ aElement0(U_113)
| ~ aSet0(U_123)
| U_123 = slsdtgt0(U_117)
| ~ aElement0(U_117) ),
inference(clausify,[status(thm)],[f_37_7]) ).
fof(f_38_1,plain,
! [W0] :
( aIdeal0(slsdtgt0(W0))
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mPrIdeal]) ).
fof(f_38_2,plain,
! [U_124] :
( aIdeal0(slsdtgt0(U_124))
| ~ aElement0(U_124) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
cnf(f_38_3,plain,
( aIdeal0(slsdtgt0(U_124))
| ~ aElement0(U_124) ),
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_1,plain,
( aElement0(xb)
& aElement0(xa) ),
inference(fof_nnf,[status(thm)],[m__2091]) ).
cnf(f_39_2,plain,
aElement0(xa),
inference(clausify,[status(thm)],[f_39_1]) ).
cnf(f_39_3,plain,
aElement0(xb),
inference(clausify,[status(thm)],[f_39_1]) ).
fof(f_40_1,plain,
( xb != sz00
| xa != sz00 ),
inference(fof_nnf,[status(thm)],[m__2110]) ).
cnf(f_40_2,plain,
( xb != sz00
| xa != sz00 ),
inference(clausify,[status(thm)],[f_40_1]) ).
fof(f_41_1,plain,
( aGcdOfAnd0(xc,xa,xb)
& ! [W0] :
( ( doDivides0(W0,xc)
& ? [W1] :
( sdtasdt0(W0,W1) = xc
& aElement0(W1) ) )
| ( ~ aDivisorOf0(W0,xb)
& ~ doDivides0(W0,xb)
& ! [W1] :
( sdtasdt0(W0,W1) != xb
| ~ aElement0(W1) ) )
| ( ~ aDivisorOf0(W0,xa)
& ( ( ~ doDivides0(W0,xa)
& ! [W1] :
( sdtasdt0(W0,W1) != xa
| ~ aElement0(W1) ) )
| ~ aElement0(W0) ) ) )
& aDivisorOf0(xc,xb)
& doDivides0(xc,xb)
& ? [W0] :
( sdtasdt0(xc,W0) = xb
& aElement0(W0) )
& aElement0(xc)
& aDivisorOf0(xc,xa)
& doDivides0(xc,xa)
& ? [W0] :
( sdtasdt0(xc,W0) = xa
& aElement0(W0) )
& aElement0(xc) ),
inference(fof_nnf,[status(thm)],[m__2129]) ).
fof(f_41_2,plain,
( aGcdOfAnd0(xc,xa,xb)
& ! [U_130] :
( ( doDivides0(U_130,xc)
& ? [U_129] :
( sdtasdt0(U_130,U_129) = xc
& aElement0(U_129) ) )
| ( ~ aDivisorOf0(U_130,xb)
& ~ doDivides0(U_130,xb)
& ! [U_128] :
( sdtasdt0(U_130,U_128) != xb
| ~ aElement0(U_128) ) )
| ( ~ aDivisorOf0(U_130,xa)
& ( ( ~ doDivides0(U_130,xa)
& ! [U_127] :
( sdtasdt0(U_130,U_127) != xa
| ~ aElement0(U_127) ) )
| ~ aElement0(U_130) ) ) )
& aDivisorOf0(xc,xb)
& doDivides0(xc,xb)
& ? [U_126] :
( sdtasdt0(xc,U_126) = xb
& aElement0(U_126) )
& aElement0(xc)
& aDivisorOf0(xc,xa)
& doDivides0(xc,xa)
& ? [U_125] :
( sdtasdt0(xc,U_125) = xa
& aElement0(U_125) )
& aElement0(xc) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
( aGcdOfAnd0(xc,xa,xb)
& ! [U_130] :
( ( doDivides0(U_130,xc)
& ? [U_129] :
( sdtasdt0(U_130,U_129) = xc
& aElement0(U_129) ) )
| ( ~ aDivisorOf0(U_130,xb)
& ~ doDivides0(U_130,xb)
& ! [U_128] :
( sdtasdt0(U_130,U_128) != xb
| ~ aElement0(U_128) ) )
| ( ~ aDivisorOf0(U_130,xa)
& ( ( ~ doDivides0(U_130,xa)
& ! [U_127] :
( sdtasdt0(U_130,U_127) != xa
| ~ aElement0(U_127) ) )
| ~ aElement0(U_130) ) ) )
& aDivisorOf0(xc,xb)
& doDivides0(xc,xb)
& ? [U_126] :
( sdtasdt0(xc,U_126) = xb
& aElement0(U_126) )
& aElement0(xc)
& aDivisorOf0(xc,xa)
& doDivides0(xc,xa)
& sdtasdt0(xc,sK24) = xa
& aElement0(sK24)
& aElement0(xc) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_125,sK24)],[f_41_2]) ).
fof(f_41_4,plain,
( aGcdOfAnd0(xc,xa,xb)
& ! [U_130] :
( ( doDivides0(U_130,xc)
& ? [U_129] :
( sdtasdt0(U_130,U_129) = xc
& aElement0(U_129) ) )
| ( ~ aDivisorOf0(U_130,xb)
& ~ doDivides0(U_130,xb)
& ! [U_128] :
( sdtasdt0(U_130,U_128) != xb
| ~ aElement0(U_128) ) )
| ( ~ aDivisorOf0(U_130,xa)
& ( ( ~ doDivides0(U_130,xa)
& ! [U_127] :
( sdtasdt0(U_130,U_127) != xa
| ~ aElement0(U_127) ) )
| ~ aElement0(U_130) ) ) )
& aDivisorOf0(xc,xb)
& doDivides0(xc,xb)
& sdtasdt0(xc,sK25) = xb
& aElement0(sK25)
& aElement0(xc)
& aDivisorOf0(xc,xa)
& doDivides0(xc,xa)
& sdtasdt0(xc,sK24) = xa
& aElement0(sK24)
& aElement0(xc) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_126,sK25)],[f_41_3]) ).
fof(f_41_5,plain,
( aGcdOfAnd0(xc,xa,xb)
& ! [U_130] :
( ( doDivides0(U_130,xc)
& sdtasdt0(U_130,sK26(U_130)) = xc
& aElement0(sK26(U_130)) )
| ( ~ aDivisorOf0(U_130,xb)
& ~ doDivides0(U_130,xb)
& ! [U_128] :
( sdtasdt0(U_130,U_128) != xb
| ~ aElement0(U_128) ) )
| ( ~ aDivisorOf0(U_130,xa)
& ( ( ~ doDivides0(U_130,xa)
& ! [U_127] :
( sdtasdt0(U_130,U_127) != xa
| ~ aElement0(U_127) ) )
| ~ aElement0(U_130) ) ) )
& aDivisorOf0(xc,xb)
& doDivides0(xc,xb)
& sdtasdt0(xc,sK25) = xb
& aElement0(sK25)
& aElement0(xc)
& aDivisorOf0(xc,xa)
& doDivides0(xc,xa)
& sdtasdt0(xc,sK24) = xa
& aElement0(sK24)
& aElement0(xc) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_129,sK26(U_130))],[f_41_4]) ).
cnf(f_41_6,plain,
aElement0(xc),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_7,plain,
aElement0(sK24),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_8,plain,
sdtasdt0(xc,sK24) = xa,
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_9,plain,
doDivides0(xc,xa),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_10,plain,
aDivisorOf0(xc,xa),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_11,plain,
aElement0(xc),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_12,plain,
aElement0(sK25),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_13,plain,
sdtasdt0(xc,sK25) = xb,
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_14,plain,
doDivides0(xc,xb),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_15,plain,
aDivisorOf0(xc,xb),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_16,plain,
( sdtasdt0(U_130,U_127) != xa
| ~ aElement0(U_127)
| ~ aElement0(U_130)
| sdtasdt0(U_130,U_128) != xb
| ~ aElement0(U_128)
| aElement0(sK26(U_130)) ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_17,plain,
( ~ doDivides0(U_130,xa)
| ~ aElement0(U_130)
| sdtasdt0(U_130,U_128) != xb
| ~ aElement0(U_128)
| aElement0(sK26(U_130)) ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_18,plain,
( sdtasdt0(U_130,U_127) != xa
| ~ aElement0(U_127)
| ~ aElement0(U_130)
| ~ doDivides0(U_130,xb)
| aElement0(sK26(U_130)) ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_19,plain,
( ~ doDivides0(U_130,xa)
| ~ aElement0(U_130)
| ~ doDivides0(U_130,xb)
| aElement0(sK26(U_130)) ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_20,plain,
( sdtasdt0(U_130,U_127) != xa
| ~ aElement0(U_127)
| ~ aElement0(U_130)
| ~ aDivisorOf0(U_130,xb)
| aElement0(sK26(U_130)) ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_21,plain,
( ~ doDivides0(U_130,xa)
| ~ aElement0(U_130)
| ~ aDivisorOf0(U_130,xb)
| aElement0(sK26(U_130)) ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_22,plain,
( sdtasdt0(U_130,U_128) != xb
| ~ aElement0(U_128)
| ~ aDivisorOf0(U_130,xa)
| aElement0(sK26(U_130)) ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_23,plain,
( ~ doDivides0(U_130,xb)
| ~ aDivisorOf0(U_130,xa)
| aElement0(sK26(U_130)) ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_24,plain,
( ~ aDivisorOf0(U_130,xb)
| ~ aDivisorOf0(U_130,xa)
| aElement0(sK26(U_130)) ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_25,plain,
( sdtasdt0(U_130,U_127) != xa
| ~ aElement0(U_127)
| ~ aElement0(U_130)
| sdtasdt0(U_130,U_128) != xb
| ~ aElement0(U_128)
| sdtasdt0(U_130,sK26(U_130)) = xc ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_26,plain,
( ~ doDivides0(U_130,xa)
| ~ aElement0(U_130)
| sdtasdt0(U_130,U_128) != xb
| ~ aElement0(U_128)
| sdtasdt0(U_130,sK26(U_130)) = xc ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_27,plain,
( sdtasdt0(U_130,U_127) != xa
| ~ aElement0(U_127)
| ~ aElement0(U_130)
| ~ doDivides0(U_130,xb)
| sdtasdt0(U_130,sK26(U_130)) = xc ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_28,plain,
( ~ doDivides0(U_130,xa)
| ~ aElement0(U_130)
| ~ doDivides0(U_130,xb)
| sdtasdt0(U_130,sK26(U_130)) = xc ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_29,plain,
( sdtasdt0(U_130,U_127) != xa
| ~ aElement0(U_127)
| ~ aElement0(U_130)
| ~ aDivisorOf0(U_130,xb)
| sdtasdt0(U_130,sK26(U_130)) = xc ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_30,plain,
( ~ doDivides0(U_130,xa)
| ~ aElement0(U_130)
| ~ aDivisorOf0(U_130,xb)
| sdtasdt0(U_130,sK26(U_130)) = xc ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_31,plain,
( sdtasdt0(U_130,U_128) != xb
| ~ aElement0(U_128)
| ~ aDivisorOf0(U_130,xa)
| sdtasdt0(U_130,sK26(U_130)) = xc ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_32,plain,
( ~ doDivides0(U_130,xb)
| ~ aDivisorOf0(U_130,xa)
| sdtasdt0(U_130,sK26(U_130)) = xc ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_33,plain,
( ~ aDivisorOf0(U_130,xb)
| ~ aDivisorOf0(U_130,xa)
| sdtasdt0(U_130,sK26(U_130)) = xc ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_34,plain,
( sdtasdt0(U_130,U_127) != xa
| ~ aElement0(U_127)
| ~ aElement0(U_130)
| sdtasdt0(U_130,U_128) != xb
| ~ aElement0(U_128)
| doDivides0(U_130,xc) ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_35,plain,
( ~ doDivides0(U_130,xa)
| ~ aElement0(U_130)
| sdtasdt0(U_130,U_128) != xb
| ~ aElement0(U_128)
| doDivides0(U_130,xc) ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_36,plain,
( sdtasdt0(U_130,U_127) != xa
| ~ aElement0(U_127)
| ~ aElement0(U_130)
| ~ doDivides0(U_130,xb)
| doDivides0(U_130,xc) ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_37,plain,
( ~ doDivides0(U_130,xa)
| ~ aElement0(U_130)
| ~ doDivides0(U_130,xb)
| doDivides0(U_130,xc) ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_38,plain,
( sdtasdt0(U_130,U_127) != xa
| ~ aElement0(U_127)
| ~ aElement0(U_130)
| ~ aDivisorOf0(U_130,xb)
| doDivides0(U_130,xc) ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_39,plain,
( ~ doDivides0(U_130,xa)
| ~ aElement0(U_130)
| ~ aDivisorOf0(U_130,xb)
| doDivides0(U_130,xc) ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_40,plain,
( sdtasdt0(U_130,U_128) != xb
| ~ aElement0(U_128)
| ~ aDivisorOf0(U_130,xa)
| doDivides0(U_130,xc) ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_41,plain,
( ~ doDivides0(U_130,xb)
| ~ aDivisorOf0(U_130,xa)
| doDivides0(U_130,xc) ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_42,plain,
( ~ aDivisorOf0(U_130,xb)
| ~ aDivisorOf0(U_130,xa)
| doDivides0(U_130,xc) ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_43,plain,
aGcdOfAnd0(xc,xa,xb),
inference(clausify,[status(thm)],[f_41_5]) ).
fof(f_42_1,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [W0] :
( ( aElementOf0(W0,xI)
| ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) ) )
& ( ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) )
| ~ aElementOf0(W0,xI) ) )
& ! [W0] :
( ( aElementOf0(W0,slsdtgt0(xb))
| ! [W1] :
( sdtasdt0(xb,W1) != W0
| ~ aElement0(W1) ) )
& ( ? [W1] :
( sdtasdt0(xb,W1) = W0
& aElement0(W1) )
| ~ aElementOf0(W0,slsdtgt0(xb)) ) )
& ! [W0] :
( ( aElementOf0(W0,slsdtgt0(xa))
| ! [W1] :
( sdtasdt0(xa,W1) != W0
| ~ aElement0(W1) ) )
& ( ? [W1] :
( sdtasdt0(xa,W1) = W0
& aElement0(W1) )
| ~ aElementOf0(W0,slsdtgt0(xa)) ) )
& aIdeal0(xI)
& ! [W0] :
( ( ! [W1] :
( aElementOf0(sdtasdt0(W1,W0),xI)
| ~ aElement0(W1) )
& ! [W1] :
( aElementOf0(sdtpldt0(W0,W1),xI)
| ~ aElementOf0(W1,xI) ) )
| ~ aElementOf0(W0,xI) )
& aSet0(xI) ),
inference(fof_nnf,[status(thm)],[m__2174]) ).
fof(f_42_2,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [U_144] :
( ( aElementOf0(U_144,xI)
| ! [U_143,U_142] :
( sdtpldt0(U_143,U_142) != U_144
| ~ aElementOf0(U_142,slsdtgt0(xb))
| ~ aElementOf0(U_143,slsdtgt0(xa)) ) )
& ( ? [U_141,U_140] :
( sdtpldt0(U_141,U_140) = U_144
& aElementOf0(U_140,slsdtgt0(xb))
& aElementOf0(U_141,slsdtgt0(xa)) )
| ~ aElementOf0(U_144,xI) ) )
& ! [U_139] :
( ( aElementOf0(U_139,slsdtgt0(xb))
| ! [U_138] :
( sdtasdt0(xb,U_138) != U_139
| ~ aElement0(U_138) ) )
& ( ? [U_137] :
( sdtasdt0(xb,U_137) = U_139
& aElement0(U_137) )
| ~ aElementOf0(U_139,slsdtgt0(xb)) ) )
& ! [U_136] :
( ( aElementOf0(U_136,slsdtgt0(xa))
| ! [U_135] :
( sdtasdt0(xa,U_135) != U_136
| ~ aElement0(U_135) ) )
& ( ? [U_134] :
( sdtasdt0(xa,U_134) = U_136
& aElement0(U_134) )
| ~ aElementOf0(U_136,slsdtgt0(xa)) ) )
& aIdeal0(xI)
& ! [U_133] :
( ( ! [U_132] :
( aElementOf0(sdtasdt0(U_132,U_133),xI)
| ~ aElement0(U_132) )
& ! [U_131] :
( aElementOf0(sdtpldt0(U_133,U_131),xI)
| ~ aElementOf0(U_131,xI) ) )
| ~ aElementOf0(U_133,xI) )
& aSet0(xI) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [U_150] :
( aElementOf0(U_150,xI)
| ! [U_143] :
( ! [U_142] :
( sdtpldt0(U_143,U_142) != U_150
| ~ aElementOf0(U_142,slsdtgt0(xb)) )
| ~ aElementOf0(U_143,slsdtgt0(xa)) ) )
& ! [U_149] :
( ? [U_141] :
( ? [U_140] :
( sdtpldt0(U_141,U_140) = U_149
& aElementOf0(U_140,slsdtgt0(xb)) )
& aElementOf0(U_141,slsdtgt0(xa)) )
| ~ aElementOf0(U_149,xI) )
& ! [U_148] :
( aElementOf0(U_148,slsdtgt0(xb))
| ! [U_138] :
( sdtasdt0(xb,U_138) != U_148
| ~ aElement0(U_138) ) )
& ! [U_147] :
( ? [U_137] :
( sdtasdt0(xb,U_137) = U_147
& aElement0(U_137) )
| ~ aElementOf0(U_147,slsdtgt0(xb)) )
& ! [U_146] :
( aElementOf0(U_146,slsdtgt0(xa))
| ! [U_135] :
( sdtasdt0(xa,U_135) != U_146
| ~ aElement0(U_135) ) )
& ! [U_145] :
( ? [U_134] :
( sdtasdt0(xa,U_134) = U_145
& aElement0(U_134) )
| ~ aElementOf0(U_145,slsdtgt0(xa)) )
& aIdeal0(xI)
& ! [U_133] :
( ( ! [U_132] :
( aElementOf0(sdtasdt0(U_132,U_133),xI)
| ~ aElement0(U_132) )
& ! [U_131] :
( aElementOf0(sdtpldt0(U_133,U_131),xI)
| ~ aElementOf0(U_131,xI) ) )
| ~ aElementOf0(U_133,xI) )
& aSet0(xI) ),
inference(miniscope,[status(thm)],[f_42_2]) ).
fof(f_42_4,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [U_150] :
( aElementOf0(U_150,xI)
| ! [U_143] :
( ! [U_142] :
( sdtpldt0(U_143,U_142) != U_150
| ~ aElementOf0(U_142,slsdtgt0(xb)) )
| ~ aElementOf0(U_143,slsdtgt0(xa)) ) )
& ! [U_149] :
( ? [U_141] :
( ? [U_140] :
( sdtpldt0(U_141,U_140) = U_149
& aElementOf0(U_140,slsdtgt0(xb)) )
& aElementOf0(U_141,slsdtgt0(xa)) )
| ~ aElementOf0(U_149,xI) )
& ! [U_148] :
( aElementOf0(U_148,slsdtgt0(xb))
| ! [U_138] :
( sdtasdt0(xb,U_138) != U_148
| ~ aElement0(U_138) ) )
& ! [U_147] :
( ? [U_137] :
( sdtasdt0(xb,U_137) = U_147
& aElement0(U_137) )
| ~ aElementOf0(U_147,slsdtgt0(xb)) )
& ! [U_146] :
( aElementOf0(U_146,slsdtgt0(xa))
| ! [U_135] :
( sdtasdt0(xa,U_135) != U_146
| ~ aElement0(U_135) ) )
& ! [U_145] :
( ( sdtasdt0(xa,sK27(U_145)) = U_145
& aElement0(sK27(U_145)) )
| ~ aElementOf0(U_145,slsdtgt0(xa)) )
& aIdeal0(xI)
& ! [U_133] :
( ( ! [U_132] :
( aElementOf0(sdtasdt0(U_132,U_133),xI)
| ~ aElement0(U_132) )
& ! [U_131] :
( aElementOf0(sdtpldt0(U_133,U_131),xI)
| ~ aElementOf0(U_131,xI) ) )
| ~ aElementOf0(U_133,xI) )
& aSet0(xI) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_134,sK27(U_145))],[f_42_3]) ).
fof(f_42_5,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [U_150] :
( aElementOf0(U_150,xI)
| ! [U_143] :
( ! [U_142] :
( sdtpldt0(U_143,U_142) != U_150
| ~ aElementOf0(U_142,slsdtgt0(xb)) )
| ~ aElementOf0(U_143,slsdtgt0(xa)) ) )
& ! [U_149] :
( ? [U_141] :
( ? [U_140] :
( sdtpldt0(U_141,U_140) = U_149
& aElementOf0(U_140,slsdtgt0(xb)) )
& aElementOf0(U_141,slsdtgt0(xa)) )
| ~ aElementOf0(U_149,xI) )
& ! [U_148] :
( aElementOf0(U_148,slsdtgt0(xb))
| ! [U_138] :
( sdtasdt0(xb,U_138) != U_148
| ~ aElement0(U_138) ) )
& ! [U_147] :
( ( sdtasdt0(xb,sK28(U_147)) = U_147
& aElement0(sK28(U_147)) )
| ~ aElementOf0(U_147,slsdtgt0(xb)) )
& ! [U_146] :
( aElementOf0(U_146,slsdtgt0(xa))
| ! [U_135] :
( sdtasdt0(xa,U_135) != U_146
| ~ aElement0(U_135) ) )
& ! [U_145] :
( ( sdtasdt0(xa,sK27(U_145)) = U_145
& aElement0(sK27(U_145)) )
| ~ aElementOf0(U_145,slsdtgt0(xa)) )
& aIdeal0(xI)
& ! [U_133] :
( ( ! [U_132] :
( aElementOf0(sdtasdt0(U_132,U_133),xI)
| ~ aElement0(U_132) )
& ! [U_131] :
( aElementOf0(sdtpldt0(U_133,U_131),xI)
| ~ aElementOf0(U_131,xI) ) )
| ~ aElementOf0(U_133,xI) )
& aSet0(xI) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_137,sK28(U_147))],[f_42_4]) ).
fof(f_42_6,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [U_150] :
( aElementOf0(U_150,xI)
| ! [U_143] :
( ! [U_142] :
( sdtpldt0(U_143,U_142) != U_150
| ~ aElementOf0(U_142,slsdtgt0(xb)) )
| ~ aElementOf0(U_143,slsdtgt0(xa)) ) )
& ! [U_149] :
( ( ? [U_140] :
( sdtpldt0(sK29(U_149),U_140) = U_149
& aElementOf0(U_140,slsdtgt0(xb)) )
& aElementOf0(sK29(U_149),slsdtgt0(xa)) )
| ~ aElementOf0(U_149,xI) )
& ! [U_148] :
( aElementOf0(U_148,slsdtgt0(xb))
| ! [U_138] :
( sdtasdt0(xb,U_138) != U_148
| ~ aElement0(U_138) ) )
& ! [U_147] :
( ( sdtasdt0(xb,sK28(U_147)) = U_147
& aElement0(sK28(U_147)) )
| ~ aElementOf0(U_147,slsdtgt0(xb)) )
& ! [U_146] :
( aElementOf0(U_146,slsdtgt0(xa))
| ! [U_135] :
( sdtasdt0(xa,U_135) != U_146
| ~ aElement0(U_135) ) )
& ! [U_145] :
( ( sdtasdt0(xa,sK27(U_145)) = U_145
& aElement0(sK27(U_145)) )
| ~ aElementOf0(U_145,slsdtgt0(xa)) )
& aIdeal0(xI)
& ! [U_133] :
( ( ! [U_132] :
( aElementOf0(sdtasdt0(U_132,U_133),xI)
| ~ aElement0(U_132) )
& ! [U_131] :
( aElementOf0(sdtpldt0(U_133,U_131),xI)
| ~ aElementOf0(U_131,xI) ) )
| ~ aElementOf0(U_133,xI) )
& aSet0(xI) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_141,sK29(U_149))],[f_42_5]) ).
fof(f_42_7,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [U_150] :
( aElementOf0(U_150,xI)
| ! [U_143] :
( ! [U_142] :
( sdtpldt0(U_143,U_142) != U_150
| ~ aElementOf0(U_142,slsdtgt0(xb)) )
| ~ aElementOf0(U_143,slsdtgt0(xa)) ) )
& ! [U_149] :
( ( sdtpldt0(sK29(U_149),sK30(U_149)) = U_149
& aElementOf0(sK30(U_149),slsdtgt0(xb))
& aElementOf0(sK29(U_149),slsdtgt0(xa)) )
| ~ aElementOf0(U_149,xI) )
& ! [U_148] :
( aElementOf0(U_148,slsdtgt0(xb))
| ! [U_138] :
( sdtasdt0(xb,U_138) != U_148
| ~ aElement0(U_138) ) )
& ! [U_147] :
( ( sdtasdt0(xb,sK28(U_147)) = U_147
& aElement0(sK28(U_147)) )
| ~ aElementOf0(U_147,slsdtgt0(xb)) )
& ! [U_146] :
( aElementOf0(U_146,slsdtgt0(xa))
| ! [U_135] :
( sdtasdt0(xa,U_135) != U_146
| ~ aElement0(U_135) ) )
& ! [U_145] :
( ( sdtasdt0(xa,sK27(U_145)) = U_145
& aElement0(sK27(U_145)) )
| ~ aElementOf0(U_145,slsdtgt0(xa)) )
& aIdeal0(xI)
& ! [U_133] :
( ( ! [U_132] :
( aElementOf0(sdtasdt0(U_132,U_133),xI)
| ~ aElement0(U_132) )
& ! [U_131] :
( aElementOf0(sdtpldt0(U_133,U_131),xI)
| ~ aElementOf0(U_131,xI) ) )
| ~ aElementOf0(U_133,xI) )
& aSet0(xI) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_140,sK30(U_149))],[f_42_6]) ).
cnf(f_42_8,plain,
aSet0(xI),
inference(clausify,[status(thm)],[f_42_7]) ).
cnf(f_42_9,plain,
( aElementOf0(sdtpldt0(U_133,U_131),xI)
| ~ aElementOf0(U_131,xI)
| ~ aElementOf0(U_133,xI) ),
inference(clausify,[status(thm)],[f_42_7]) ).
cnf(f_42_10,plain,
( aElementOf0(sdtasdt0(U_132,U_133),xI)
| ~ aElement0(U_132)
| ~ aElementOf0(U_133,xI) ),
inference(clausify,[status(thm)],[f_42_7]) ).
cnf(f_42_11,plain,
aIdeal0(xI),
inference(clausify,[status(thm)],[f_42_7]) ).
cnf(f_42_12,plain,
( aElement0(sK27(U_145))
| ~ aElementOf0(U_145,slsdtgt0(xa)) ),
inference(clausify,[status(thm)],[f_42_7]) ).
cnf(f_42_13,plain,
( sdtasdt0(xa,sK27(U_145)) = U_145
| ~ aElementOf0(U_145,slsdtgt0(xa)) ),
inference(clausify,[status(thm)],[f_42_7]) ).
cnf(f_42_14,plain,
( aElementOf0(U_146,slsdtgt0(xa))
| sdtasdt0(xa,U_135) != U_146
| ~ aElement0(U_135) ),
inference(clausify,[status(thm)],[f_42_7]) ).
cnf(f_42_15,plain,
( aElement0(sK28(U_147))
| ~ aElementOf0(U_147,slsdtgt0(xb)) ),
inference(clausify,[status(thm)],[f_42_7]) ).
cnf(f_42_16,plain,
( sdtasdt0(xb,sK28(U_147)) = U_147
| ~ aElementOf0(U_147,slsdtgt0(xb)) ),
inference(clausify,[status(thm)],[f_42_7]) ).
cnf(f_42_17,plain,
( aElementOf0(U_148,slsdtgt0(xb))
| sdtasdt0(xb,U_138) != U_148
| ~ aElement0(U_138) ),
inference(clausify,[status(thm)],[f_42_7]) ).
cnf(f_42_18,plain,
( aElementOf0(sK29(U_149),slsdtgt0(xa))
| ~ aElementOf0(U_149,xI) ),
inference(clausify,[status(thm)],[f_42_7]) ).
cnf(f_42_19,plain,
( aElementOf0(sK30(U_149),slsdtgt0(xb))
| ~ aElementOf0(U_149,xI) ),
inference(clausify,[status(thm)],[f_42_7]) ).
cnf(f_42_20,plain,
( sdtpldt0(sK29(U_149),sK30(U_149)) = U_149
| ~ aElementOf0(U_149,xI) ),
inference(clausify,[status(thm)],[f_42_7]) ).
cnf(f_42_21,plain,
( aElementOf0(U_150,xI)
| sdtpldt0(U_143,U_142) != U_150
| ~ aElementOf0(U_142,slsdtgt0(xb))
| ~ aElementOf0(U_143,slsdtgt0(xa)) ),
inference(clausify,[status(thm)],[f_42_7]) ).
cnf(f_42_22,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(clausify,[status(thm)],[f_42_7]) ).
fof(f_43_1,plain,
( aElementOf0(xb,slsdtgt0(xb))
& ? [W0] :
( sdtasdt0(xb,W0) = xb
& aElement0(W0) )
& aElementOf0(sz00,slsdtgt0(xb))
& ? [W0] :
( sdtasdt0(xb,W0) = sz00
& aElement0(W0) )
& aElementOf0(xa,slsdtgt0(xa))
& ? [W0] :
( sdtasdt0(xa,W0) = xa
& aElement0(W0) )
& aElementOf0(sz00,slsdtgt0(xa))
& ? [W0] :
( sdtasdt0(xa,W0) = sz00
& aElement0(W0) ) ),
inference(fof_nnf,[status(thm)],[m__2203]) ).
fof(f_43_2,plain,
( aElementOf0(xb,slsdtgt0(xb))
& ? [U_154] :
( sdtasdt0(xb,U_154) = xb
& aElement0(U_154) )
& aElementOf0(sz00,slsdtgt0(xb))
& ? [U_153] :
( sdtasdt0(xb,U_153) = sz00
& aElement0(U_153) )
& aElementOf0(xa,slsdtgt0(xa))
& ? [U_152] :
( sdtasdt0(xa,U_152) = xa
& aElement0(U_152) )
& aElementOf0(sz00,slsdtgt0(xa))
& ? [U_151] :
( sdtasdt0(xa,U_151) = sz00
& aElement0(U_151) ) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
( aElementOf0(xb,slsdtgt0(xb))
& ? [U_154] :
( sdtasdt0(xb,U_154) = xb
& aElement0(U_154) )
& aElementOf0(sz00,slsdtgt0(xb))
& ? [U_153] :
( sdtasdt0(xb,U_153) = sz00
& aElement0(U_153) )
& aElementOf0(xa,slsdtgt0(xa))
& ? [U_152] :
( sdtasdt0(xa,U_152) = xa
& aElement0(U_152) )
& aElementOf0(sz00,slsdtgt0(xa))
& sdtasdt0(xa,sK31) = sz00
& aElement0(sK31) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_151,sK31)],[f_43_2]) ).
fof(f_43_4,plain,
( aElementOf0(xb,slsdtgt0(xb))
& ? [U_154] :
( sdtasdt0(xb,U_154) = xb
& aElement0(U_154) )
& aElementOf0(sz00,slsdtgt0(xb))
& ? [U_153] :
( sdtasdt0(xb,U_153) = sz00
& aElement0(U_153) )
& aElementOf0(xa,slsdtgt0(xa))
& sdtasdt0(xa,sK32) = xa
& aElement0(sK32)
& aElementOf0(sz00,slsdtgt0(xa))
& sdtasdt0(xa,sK31) = sz00
& aElement0(sK31) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_152,sK32)],[f_43_3]) ).
fof(f_43_5,plain,
( aElementOf0(xb,slsdtgt0(xb))
& ? [U_154] :
( sdtasdt0(xb,U_154) = xb
& aElement0(U_154) )
& aElementOf0(sz00,slsdtgt0(xb))
& sdtasdt0(xb,sK33) = sz00
& aElement0(sK33)
& aElementOf0(xa,slsdtgt0(xa))
& sdtasdt0(xa,sK32) = xa
& aElement0(sK32)
& aElementOf0(sz00,slsdtgt0(xa))
& sdtasdt0(xa,sK31) = sz00
& aElement0(sK31) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_153,sK33)],[f_43_4]) ).
fof(f_43_6,plain,
( aElementOf0(xb,slsdtgt0(xb))
& sdtasdt0(xb,sK34) = xb
& aElement0(sK34)
& aElementOf0(sz00,slsdtgt0(xb))
& sdtasdt0(xb,sK33) = sz00
& aElement0(sK33)
& aElementOf0(xa,slsdtgt0(xa))
& sdtasdt0(xa,sK32) = xa
& aElement0(sK32)
& aElementOf0(sz00,slsdtgt0(xa))
& sdtasdt0(xa,sK31) = sz00
& aElement0(sK31) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_154,sK34)],[f_43_5]) ).
cnf(f_43_7,plain,
aElement0(sK31),
inference(clausify,[status(thm)],[f_43_6]) ).
cnf(f_43_8,plain,
sdtasdt0(xa,sK31) = sz00,
inference(clausify,[status(thm)],[f_43_6]) ).
cnf(f_43_9,plain,
aElementOf0(sz00,slsdtgt0(xa)),
inference(clausify,[status(thm)],[f_43_6]) ).
cnf(f_43_10,plain,
aElement0(sK32),
inference(clausify,[status(thm)],[f_43_6]) ).
cnf(f_43_11,plain,
sdtasdt0(xa,sK32) = xa,
inference(clausify,[status(thm)],[f_43_6]) ).
cnf(f_43_12,plain,
aElementOf0(xa,slsdtgt0(xa)),
inference(clausify,[status(thm)],[f_43_6]) ).
cnf(f_43_13,plain,
aElement0(sK33),
inference(clausify,[status(thm)],[f_43_6]) ).
cnf(f_43_14,plain,
sdtasdt0(xb,sK33) = sz00,
inference(clausify,[status(thm)],[f_43_6]) ).
cnf(f_43_15,plain,
aElementOf0(sz00,slsdtgt0(xb)),
inference(clausify,[status(thm)],[f_43_6]) ).
cnf(f_43_16,plain,
aElement0(sK34),
inference(clausify,[status(thm)],[f_43_6]) ).
cnf(f_43_17,plain,
sdtasdt0(xb,sK34) = xb,
inference(clausify,[status(thm)],[f_43_6]) ).
cnf(f_43_18,plain,
aElementOf0(xb,slsdtgt0(xb)),
inference(clausify,[status(thm)],[f_43_6]) ).
fof(f_44_1,plain,
? [W0] :
( W0 != sz00
& aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) )
& ! [W1] :
( ( aElementOf0(W1,slsdtgt0(xb))
| ! [W2] :
( sdtasdt0(xb,W2) != W1
| ~ aElement0(W2) ) )
& ( ? [W2] :
( sdtasdt0(xb,W2) = W1
& aElement0(W2) )
| ~ aElementOf0(W1,slsdtgt0(xb)) ) )
& ! [W1] :
( ( aElementOf0(W1,slsdtgt0(xa))
| ! [W2] :
( sdtasdt0(xa,W2) != W1
| ~ aElement0(W2) ) )
& ( ? [W2] :
( sdtasdt0(xa,W2) = W1
& aElement0(W2) )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ),
inference(fof_nnf,[status(thm)],[m__2228]) ).
fof(f_44_2,plain,
? [U_163] :
( U_163 != sz00
& aElementOf0(U_163,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [U_162,U_161] :
( sdtpldt0(U_162,U_161) = U_163
& aElementOf0(U_161,slsdtgt0(xb))
& aElementOf0(U_162,slsdtgt0(xa)) )
& ! [U_160] :
( ( aElementOf0(U_160,slsdtgt0(xb))
| ! [U_159] :
( sdtasdt0(xb,U_159) != U_160
| ~ aElement0(U_159) ) )
& ( ? [U_158] :
( sdtasdt0(xb,U_158) = U_160
& aElement0(U_158) )
| ~ aElementOf0(U_160,slsdtgt0(xb)) ) )
& ! [U_157] :
( ( aElementOf0(U_157,slsdtgt0(xa))
| ! [U_156] :
( sdtasdt0(xa,U_156) != U_157
| ~ aElement0(U_156) ) )
& ( ? [U_155] :
( sdtasdt0(xa,U_155) = U_157
& aElement0(U_155) )
| ~ aElementOf0(U_157,slsdtgt0(xa)) ) ) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
( ? [U_163] :
( U_163 != sz00
& aElementOf0(U_163,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [U_162] :
( ? [U_161] :
( sdtpldt0(U_162,U_161) = U_163
& aElementOf0(U_161,slsdtgt0(xb)) )
& aElementOf0(U_162,slsdtgt0(xa)) ) )
& ! [U_167] :
( aElementOf0(U_167,slsdtgt0(xb))
| ! [U_159] :
( sdtasdt0(xb,U_159) != U_167
| ~ aElement0(U_159) ) )
& ! [U_166] :
( ? [U_158] :
( sdtasdt0(xb,U_158) = U_166
& aElement0(U_158) )
| ~ aElementOf0(U_166,slsdtgt0(xb)) )
& ! [U_165] :
( aElementOf0(U_165,slsdtgt0(xa))
| ! [U_156] :
( sdtasdt0(xa,U_156) != U_165
| ~ aElement0(U_156) ) )
& ! [U_164] :
( ? [U_155] :
( sdtasdt0(xa,U_155) = U_164
& aElement0(U_155) )
| ~ aElementOf0(U_164,slsdtgt0(xa)) ) ),
inference(miniscope,[status(thm)],[f_44_2]) ).
fof(f_44_4,plain,
( ? [U_163] :
( U_163 != sz00
& aElementOf0(U_163,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [U_162] :
( ? [U_161] :
( sdtpldt0(U_162,U_161) = U_163
& aElementOf0(U_161,slsdtgt0(xb)) )
& aElementOf0(U_162,slsdtgt0(xa)) ) )
& ! [U_167] :
( aElementOf0(U_167,slsdtgt0(xb))
| ! [U_159] :
( sdtasdt0(xb,U_159) != U_167
| ~ aElement0(U_159) ) )
& ! [U_166] :
( ? [U_158] :
( sdtasdt0(xb,U_158) = U_166
& aElement0(U_158) )
| ~ aElementOf0(U_166,slsdtgt0(xb)) )
& ! [U_165] :
( aElementOf0(U_165,slsdtgt0(xa))
| ! [U_156] :
( sdtasdt0(xa,U_156) != U_165
| ~ aElement0(U_156) ) )
& ! [U_164] :
( ( sdtasdt0(xa,sK35(U_164)) = U_164
& aElement0(sK35(U_164)) )
| ~ aElementOf0(U_164,slsdtgt0(xa)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_155,sK35(U_164))],[f_44_3]) ).
fof(f_44_5,plain,
( ? [U_163] :
( U_163 != sz00
& aElementOf0(U_163,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [U_162] :
( ? [U_161] :
( sdtpldt0(U_162,U_161) = U_163
& aElementOf0(U_161,slsdtgt0(xb)) )
& aElementOf0(U_162,slsdtgt0(xa)) ) )
& ! [U_167] :
( aElementOf0(U_167,slsdtgt0(xb))
| ! [U_159] :
( sdtasdt0(xb,U_159) != U_167
| ~ aElement0(U_159) ) )
& ! [U_166] :
( ( sdtasdt0(xb,sK36(U_166)) = U_166
& aElement0(sK36(U_166)) )
| ~ aElementOf0(U_166,slsdtgt0(xb)) )
& ! [U_165] :
( aElementOf0(U_165,slsdtgt0(xa))
| ! [U_156] :
( sdtasdt0(xa,U_156) != U_165
| ~ aElement0(U_156) ) )
& ! [U_164] :
( ( sdtasdt0(xa,sK35(U_164)) = U_164
& aElement0(sK35(U_164)) )
| ~ aElementOf0(U_164,slsdtgt0(xa)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_158,sK36(U_166))],[f_44_4]) ).
fof(f_44_6,plain,
( sK37 != sz00
& aElementOf0(sK37,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [U_162] :
( ? [U_161] :
( sdtpldt0(U_162,U_161) = sK37
& aElementOf0(U_161,slsdtgt0(xb)) )
& aElementOf0(U_162,slsdtgt0(xa)) )
& ! [U_167] :
( aElementOf0(U_167,slsdtgt0(xb))
| ! [U_159] :
( sdtasdt0(xb,U_159) != U_167
| ~ aElement0(U_159) ) )
& ! [U_166] :
( ( sdtasdt0(xb,sK36(U_166)) = U_166
& aElement0(sK36(U_166)) )
| ~ aElementOf0(U_166,slsdtgt0(xb)) )
& ! [U_165] :
( aElementOf0(U_165,slsdtgt0(xa))
| ! [U_156] :
( sdtasdt0(xa,U_156) != U_165
| ~ aElement0(U_156) ) )
& ! [U_164] :
( ( sdtasdt0(xa,sK35(U_164)) = U_164
& aElement0(sK35(U_164)) )
| ~ aElementOf0(U_164,slsdtgt0(xa)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_163,sK37)],[f_44_5]) ).
fof(f_44_7,plain,
( sK37 != sz00
& aElementOf0(sK37,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [U_161] :
( sdtpldt0(sK38,U_161) = sK37
& aElementOf0(U_161,slsdtgt0(xb)) )
& aElementOf0(sK38,slsdtgt0(xa))
& ! [U_167] :
( aElementOf0(U_167,slsdtgt0(xb))
| ! [U_159] :
( sdtasdt0(xb,U_159) != U_167
| ~ aElement0(U_159) ) )
& ! [U_166] :
( ( sdtasdt0(xb,sK36(U_166)) = U_166
& aElement0(sK36(U_166)) )
| ~ aElementOf0(U_166,slsdtgt0(xb)) )
& ! [U_165] :
( aElementOf0(U_165,slsdtgt0(xa))
| ! [U_156] :
( sdtasdt0(xa,U_156) != U_165
| ~ aElement0(U_156) ) )
& ! [U_164] :
( ( sdtasdt0(xa,sK35(U_164)) = U_164
& aElement0(sK35(U_164)) )
| ~ aElementOf0(U_164,slsdtgt0(xa)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_162,sK38)],[f_44_6]) ).
fof(f_44_8,plain,
( sK37 != sz00
& aElementOf0(sK37,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& sdtpldt0(sK38,sK39) = sK37
& aElementOf0(sK39,slsdtgt0(xb))
& aElementOf0(sK38,slsdtgt0(xa))
& ! [U_167] :
( aElementOf0(U_167,slsdtgt0(xb))
| ! [U_159] :
( sdtasdt0(xb,U_159) != U_167
| ~ aElement0(U_159) ) )
& ! [U_166] :
( ( sdtasdt0(xb,sK36(U_166)) = U_166
& aElement0(sK36(U_166)) )
| ~ aElementOf0(U_166,slsdtgt0(xb)) )
& ! [U_165] :
( aElementOf0(U_165,slsdtgt0(xa))
| ! [U_156] :
( sdtasdt0(xa,U_156) != U_165
| ~ aElement0(U_156) ) )
& ! [U_164] :
( ( sdtasdt0(xa,sK35(U_164)) = U_164
& aElement0(sK35(U_164)) )
| ~ aElementOf0(U_164,slsdtgt0(xa)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_161,sK39)],[f_44_7]) ).
cnf(f_44_9,plain,
( aElement0(sK35(U_164))
| ~ aElementOf0(U_164,slsdtgt0(xa)) ),
inference(clausify,[status(thm)],[f_44_8]) ).
cnf(f_44_10,plain,
( sdtasdt0(xa,sK35(U_164)) = U_164
| ~ aElementOf0(U_164,slsdtgt0(xa)) ),
inference(clausify,[status(thm)],[f_44_8]) ).
cnf(f_44_11,plain,
( aElementOf0(U_165,slsdtgt0(xa))
| sdtasdt0(xa,U_156) != U_165
| ~ aElement0(U_156) ),
inference(clausify,[status(thm)],[f_44_8]) ).
cnf(f_44_12,plain,
( aElement0(sK36(U_166))
| ~ aElementOf0(U_166,slsdtgt0(xb)) ),
inference(clausify,[status(thm)],[f_44_8]) ).
cnf(f_44_13,plain,
( sdtasdt0(xb,sK36(U_166)) = U_166
| ~ aElementOf0(U_166,slsdtgt0(xb)) ),
inference(clausify,[status(thm)],[f_44_8]) ).
cnf(f_44_14,plain,
( aElementOf0(U_167,slsdtgt0(xb))
| sdtasdt0(xb,U_159) != U_167
| ~ aElement0(U_159) ),
inference(clausify,[status(thm)],[f_44_8]) ).
cnf(f_44_15,plain,
aElementOf0(sK38,slsdtgt0(xa)),
inference(clausify,[status(thm)],[f_44_8]) ).
cnf(f_44_16,plain,
aElementOf0(sK39,slsdtgt0(xb)),
inference(clausify,[status(thm)],[f_44_8]) ).
cnf(f_44_17,plain,
sdtpldt0(sK38,sK39) = sK37,
inference(clausify,[status(thm)],[f_44_8]) ).
cnf(f_44_18,plain,
aElementOf0(sK37,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(clausify,[status(thm)],[f_44_8]) ).
cnf(f_44_19,plain,
sK37 != sz00,
inference(clausify,[status(thm)],[f_44_8]) ).
fof(f_45_1,negated_conjecture,
~ ! [W0] :
( ( W0 != sz00
& aElementOf0(W0,xI)
& ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) ) )
=> ( ! [W1] :
( ( W1 != sz00
& ( aElementOf0(W1,xI)
| ? [W2,W3] :
( sdtpldt0(W2,W3) = W1
& aElementOf0(W3,slsdtgt0(xb))
& aElementOf0(W2,slsdtgt0(xa)) ) ) )
=> ( iLess0(sbrdtbr0(W1),sbrdtbr0(W0))
=> ? [W2] :
( ! [W3] :
( ( W3 != sz00
& ( aElementOf0(W3,xI)
| ? [W4,W5] :
( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,slsdtgt0(xb))
& aElementOf0(W4,slsdtgt0(xa)) ) ) )
=> ~ iLess0(sbrdtbr0(W3),sbrdtbr0(W2)) )
& W2 != sz00
& aElementOf0(W2,xI)
& ? [W3,W4] :
( sdtpldt0(W3,W4) = W2
& aElementOf0(W4,slsdtgt0(xb))
& aElementOf0(W3,slsdtgt0(xa)) ) ) ) )
=> ? [W1] :
( ! [W2] :
( ( W2 != sz00
& aElementOf0(W2,xI)
& ? [W3,W4] :
( sdtpldt0(W3,W4) = W2
& aElementOf0(W4,slsdtgt0(xb))
& aElementOf0(W3,slsdtgt0(xa)) ) )
=> ~ iLess0(sbrdtbr0(W2),sbrdtbr0(W1)) )
& W1 != sz00
& ( aElementOf0(W1,xI)
| ? [W2,W3] :
( sdtpldt0(W2,W3) = W1
& aElementOf0(W3,slsdtgt0(xb))
& aElementOf0(W2,slsdtgt0(xa)) ) ) ) ) ),
inference(negate,[status(cth)],[m__]) ).
fof(f_45_2,negated_conjecture,
? [W0] :
( ! [W1] :
( ? [W2] :
( iLess0(sbrdtbr0(W2),sbrdtbr0(W1))
& W2 != sz00
& aElementOf0(W2,xI)
& ? [W3,W4] :
( sdtpldt0(W3,W4) = W2
& aElementOf0(W4,slsdtgt0(xb))
& aElementOf0(W3,slsdtgt0(xa)) ) )
| W1 = sz00
| ( ~ aElementOf0(W1,xI)
& ! [W2,W3] :
( sdtpldt0(W2,W3) != W1
| ~ aElementOf0(W3,slsdtgt0(xb))
| ~ aElementOf0(W2,slsdtgt0(xa)) ) ) )
& ! [W1] :
( ? [W2] :
( ! [W3] :
( ~ iLess0(sbrdtbr0(W3),sbrdtbr0(W2))
| W3 = sz00
| ( ~ aElementOf0(W3,xI)
& ! [W4,W5] :
( sdtpldt0(W4,W5) != W3
| ~ aElementOf0(W5,slsdtgt0(xb))
| ~ aElementOf0(W4,slsdtgt0(xa)) ) ) )
& W2 != sz00
& aElementOf0(W2,xI)
& ? [W3,W4] :
( sdtpldt0(W3,W4) = W2
& aElementOf0(W4,slsdtgt0(xb))
& aElementOf0(W3,slsdtgt0(xa)) ) )
| ~ iLess0(sbrdtbr0(W1),sbrdtbr0(W0))
| W1 = sz00
| ( ~ aElementOf0(W1,xI)
& ! [W2,W3] :
( sdtpldt0(W2,W3) != W1
| ~ aElementOf0(W3,slsdtgt0(xb))
| ~ aElementOf0(W2,slsdtgt0(xa)) ) ) )
& W0 != sz00
& aElementOf0(W0,xI)
& ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) ) ),
inference(fof_nnf,[status(thm)],[f_45_1]) ).
fof(f_45_3,negated_conjecture,
? [U_185] :
( ! [U_184] :
( ? [U_183] :
( iLess0(sbrdtbr0(U_183),sbrdtbr0(U_184))
& U_183 != sz00
& aElementOf0(U_183,xI)
& ? [U_182,U_181] :
( sdtpldt0(U_182,U_181) = U_183
& aElementOf0(U_181,slsdtgt0(xb))
& aElementOf0(U_182,slsdtgt0(xa)) ) )
| U_184 = sz00
| ( ~ aElementOf0(U_184,xI)
& ! [U_180,U_179] :
( sdtpldt0(U_180,U_179) != U_184
| ~ aElementOf0(U_179,slsdtgt0(xb))
| ~ aElementOf0(U_180,slsdtgt0(xa)) ) ) )
& ! [U_178] :
( ? [U_177] :
( ! [U_176] :
( ~ iLess0(sbrdtbr0(U_176),sbrdtbr0(U_177))
| U_176 = sz00
| ( ~ aElementOf0(U_176,xI)
& ! [U_175,U_174] :
( sdtpldt0(U_175,U_174) != U_176
| ~ aElementOf0(U_174,slsdtgt0(xb))
| ~ aElementOf0(U_175,slsdtgt0(xa)) ) ) )
& U_177 != sz00
& aElementOf0(U_177,xI)
& ? [U_173,U_172] :
( sdtpldt0(U_173,U_172) = U_177
& aElementOf0(U_172,slsdtgt0(xb))
& aElementOf0(U_173,slsdtgt0(xa)) ) )
| ~ iLess0(sbrdtbr0(U_178),sbrdtbr0(U_185))
| U_178 = sz00
| ( ~ aElementOf0(U_178,xI)
& ! [U_171,U_170] :
( sdtpldt0(U_171,U_170) != U_178
| ~ aElementOf0(U_170,slsdtgt0(xb))
| ~ aElementOf0(U_171,slsdtgt0(xa)) ) ) )
& U_185 != sz00
& aElementOf0(U_185,xI)
& ? [U_169,U_168] :
( sdtpldt0(U_169,U_168) = U_185
& aElementOf0(U_168,slsdtgt0(xb))
& aElementOf0(U_169,slsdtgt0(xa)) ) ),
inference(variable_rename,[status(thm)],[f_45_2]) ).
fof(f_45_4,negated_conjecture,
? [U_185] :
( ! [U_184] :
( ? [U_183] :
( iLess0(sbrdtbr0(U_183),sbrdtbr0(U_184))
& U_183 != sz00
& aElementOf0(U_183,xI)
& ? [U_182] :
( ? [U_181] :
( sdtpldt0(U_182,U_181) = U_183
& aElementOf0(U_181,slsdtgt0(xb)) )
& aElementOf0(U_182,slsdtgt0(xa)) ) )
| U_184 = sz00
| ( ~ aElementOf0(U_184,xI)
& ! [U_180] :
( ! [U_179] :
( sdtpldt0(U_180,U_179) != U_184
| ~ aElementOf0(U_179,slsdtgt0(xb)) )
| ~ aElementOf0(U_180,slsdtgt0(xa)) ) ) )
& ! [U_178] :
( ? [U_177] :
( ! [U_176] :
( ~ iLess0(sbrdtbr0(U_176),sbrdtbr0(U_177))
| U_176 = sz00
| ( ~ aElementOf0(U_176,xI)
& ! [U_175] :
( ! [U_174] :
( sdtpldt0(U_175,U_174) != U_176
| ~ aElementOf0(U_174,slsdtgt0(xb)) )
| ~ aElementOf0(U_175,slsdtgt0(xa)) ) ) )
& U_177 != sz00
& aElementOf0(U_177,xI)
& ? [U_173] :
( ? [U_172] :
( sdtpldt0(U_173,U_172) = U_177
& aElementOf0(U_172,slsdtgt0(xb)) )
& aElementOf0(U_173,slsdtgt0(xa)) ) )
| ~ iLess0(sbrdtbr0(U_178),sbrdtbr0(U_185))
| U_178 = sz00
| ( ~ aElementOf0(U_178,xI)
& ! [U_171] :
( ! [U_170] :
( sdtpldt0(U_171,U_170) != U_178
| ~ aElementOf0(U_170,slsdtgt0(xb)) )
| ~ aElementOf0(U_171,slsdtgt0(xa)) ) ) )
& U_185 != sz00
& aElementOf0(U_185,xI)
& ? [U_169] :
( ? [U_168] :
( sdtpldt0(U_169,U_168) = U_185
& aElementOf0(U_168,slsdtgt0(xb)) )
& aElementOf0(U_169,slsdtgt0(xa)) ) ),
inference(miniscope,[status(thm)],[f_45_3]) ).
fof(f_45_5,negated_conjecture,
( ! [U_184] :
( ? [U_183] :
( iLess0(sbrdtbr0(U_183),sbrdtbr0(U_184))
& U_183 != sz00
& aElementOf0(U_183,xI)
& ? [U_182] :
( ? [U_181] :
( sdtpldt0(U_182,U_181) = U_183
& aElementOf0(U_181,slsdtgt0(xb)) )
& aElementOf0(U_182,slsdtgt0(xa)) ) )
| U_184 = sz00
| ( ~ aElementOf0(U_184,xI)
& ! [U_180] :
( ! [U_179] :
( sdtpldt0(U_180,U_179) != U_184
| ~ aElementOf0(U_179,slsdtgt0(xb)) )
| ~ aElementOf0(U_180,slsdtgt0(xa)) ) ) )
& ! [U_178] :
( ? [U_177] :
( ! [U_176] :
( ~ iLess0(sbrdtbr0(U_176),sbrdtbr0(U_177))
| U_176 = sz00
| ( ~ aElementOf0(U_176,xI)
& ! [U_175] :
( ! [U_174] :
( sdtpldt0(U_175,U_174) != U_176
| ~ aElementOf0(U_174,slsdtgt0(xb)) )
| ~ aElementOf0(U_175,slsdtgt0(xa)) ) ) )
& U_177 != sz00
& aElementOf0(U_177,xI)
& ? [U_173] :
( ? [U_172] :
( sdtpldt0(U_173,U_172) = U_177
& aElementOf0(U_172,slsdtgt0(xb)) )
& aElementOf0(U_173,slsdtgt0(xa)) ) )
| ~ iLess0(sbrdtbr0(U_178),sbrdtbr0(sK40))
| U_178 = sz00
| ( ~ aElementOf0(U_178,xI)
& ! [U_171] :
( ! [U_170] :
( sdtpldt0(U_171,U_170) != U_178
| ~ aElementOf0(U_170,slsdtgt0(xb)) )
| ~ aElementOf0(U_171,slsdtgt0(xa)) ) ) )
& sK40 != sz00
& aElementOf0(sK40,xI)
& ? [U_169] :
( ? [U_168] :
( sdtpldt0(U_169,U_168) = sK40
& aElementOf0(U_168,slsdtgt0(xb)) )
& aElementOf0(U_169,slsdtgt0(xa)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_185,sK40)],[f_45_4]) ).
fof(f_45_6,negated_conjecture,
( ! [U_184] :
( ? [U_183] :
( iLess0(sbrdtbr0(U_183),sbrdtbr0(U_184))
& U_183 != sz00
& aElementOf0(U_183,xI)
& ? [U_182] :
( ? [U_181] :
( sdtpldt0(U_182,U_181) = U_183
& aElementOf0(U_181,slsdtgt0(xb)) )
& aElementOf0(U_182,slsdtgt0(xa)) ) )
| U_184 = sz00
| ( ~ aElementOf0(U_184,xI)
& ! [U_180] :
( ! [U_179] :
( sdtpldt0(U_180,U_179) != U_184
| ~ aElementOf0(U_179,slsdtgt0(xb)) )
| ~ aElementOf0(U_180,slsdtgt0(xa)) ) ) )
& ! [U_178] :
( ? [U_177] :
( ! [U_176] :
( ~ iLess0(sbrdtbr0(U_176),sbrdtbr0(U_177))
| U_176 = sz00
| ( ~ aElementOf0(U_176,xI)
& ! [U_175] :
( ! [U_174] :
( sdtpldt0(U_175,U_174) != U_176
| ~ aElementOf0(U_174,slsdtgt0(xb)) )
| ~ aElementOf0(U_175,slsdtgt0(xa)) ) ) )
& U_177 != sz00
& aElementOf0(U_177,xI)
& ? [U_173] :
( ? [U_172] :
( sdtpldt0(U_173,U_172) = U_177
& aElementOf0(U_172,slsdtgt0(xb)) )
& aElementOf0(U_173,slsdtgt0(xa)) ) )
| ~ iLess0(sbrdtbr0(U_178),sbrdtbr0(sK40))
| U_178 = sz00
| ( ~ aElementOf0(U_178,xI)
& ! [U_171] :
( ! [U_170] :
( sdtpldt0(U_171,U_170) != U_178
| ~ aElementOf0(U_170,slsdtgt0(xb)) )
| ~ aElementOf0(U_171,slsdtgt0(xa)) ) ) )
& sK40 != sz00
& aElementOf0(sK40,xI)
& ? [U_168] :
( sdtpldt0(sK41,U_168) = sK40
& aElementOf0(U_168,slsdtgt0(xb)) )
& aElementOf0(sK41,slsdtgt0(xa)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_169,sK41)],[f_45_5]) ).
fof(f_45_7,negated_conjecture,
( ! [U_184] :
( ? [U_183] :
( iLess0(sbrdtbr0(U_183),sbrdtbr0(U_184))
& U_183 != sz00
& aElementOf0(U_183,xI)
& ? [U_182] :
( ? [U_181] :
( sdtpldt0(U_182,U_181) = U_183
& aElementOf0(U_181,slsdtgt0(xb)) )
& aElementOf0(U_182,slsdtgt0(xa)) ) )
| U_184 = sz00
| ( ~ aElementOf0(U_184,xI)
& ! [U_180] :
( ! [U_179] :
( sdtpldt0(U_180,U_179) != U_184
| ~ aElementOf0(U_179,slsdtgt0(xb)) )
| ~ aElementOf0(U_180,slsdtgt0(xa)) ) ) )
& ! [U_178] :
( ? [U_177] :
( ! [U_176] :
( ~ iLess0(sbrdtbr0(U_176),sbrdtbr0(U_177))
| U_176 = sz00
| ( ~ aElementOf0(U_176,xI)
& ! [U_175] :
( ! [U_174] :
( sdtpldt0(U_175,U_174) != U_176
| ~ aElementOf0(U_174,slsdtgt0(xb)) )
| ~ aElementOf0(U_175,slsdtgt0(xa)) ) ) )
& U_177 != sz00
& aElementOf0(U_177,xI)
& ? [U_173] :
( ? [U_172] :
( sdtpldt0(U_173,U_172) = U_177
& aElementOf0(U_172,slsdtgt0(xb)) )
& aElementOf0(U_173,slsdtgt0(xa)) ) )
| ~ iLess0(sbrdtbr0(U_178),sbrdtbr0(sK40))
| U_178 = sz00
| ( ~ aElementOf0(U_178,xI)
& ! [U_171] :
( ! [U_170] :
( sdtpldt0(U_171,U_170) != U_178
| ~ aElementOf0(U_170,slsdtgt0(xb)) )
| ~ aElementOf0(U_171,slsdtgt0(xa)) ) ) )
& sK40 != sz00
& aElementOf0(sK40,xI)
& sdtpldt0(sK41,sK42) = sK40
& aElementOf0(sK42,slsdtgt0(xb))
& aElementOf0(sK41,slsdtgt0(xa)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_168,sK42)],[f_45_6]) ).
fof(f_45_8,negated_conjecture,
( ! [U_184] :
( ? [U_183] :
( iLess0(sbrdtbr0(U_183),sbrdtbr0(U_184))
& U_183 != sz00
& aElementOf0(U_183,xI)
& ? [U_182] :
( ? [U_181] :
( sdtpldt0(U_182,U_181) = U_183
& aElementOf0(U_181,slsdtgt0(xb)) )
& aElementOf0(U_182,slsdtgt0(xa)) ) )
| U_184 = sz00
| ( ~ aElementOf0(U_184,xI)
& ! [U_180] :
( ! [U_179] :
( sdtpldt0(U_180,U_179) != U_184
| ~ aElementOf0(U_179,slsdtgt0(xb)) )
| ~ aElementOf0(U_180,slsdtgt0(xa)) ) ) )
& ! [U_178] :
( ( ! [U_176] :
( ~ iLess0(sbrdtbr0(U_176),sbrdtbr0(sK43(U_178)))
| U_176 = sz00
| ( ~ aElementOf0(U_176,xI)
& ! [U_175] :
( ! [U_174] :
( sdtpldt0(U_175,U_174) != U_176
| ~ aElementOf0(U_174,slsdtgt0(xb)) )
| ~ aElementOf0(U_175,slsdtgt0(xa)) ) ) )
& sK43(U_178) != sz00
& aElementOf0(sK43(U_178),xI)
& ? [U_173] :
( ? [U_172] :
( sdtpldt0(U_173,U_172) = sK43(U_178)
& aElementOf0(U_172,slsdtgt0(xb)) )
& aElementOf0(U_173,slsdtgt0(xa)) ) )
| ~ iLess0(sbrdtbr0(U_178),sbrdtbr0(sK40))
| U_178 = sz00
| ( ~ aElementOf0(U_178,xI)
& ! [U_171] :
( ! [U_170] :
( sdtpldt0(U_171,U_170) != U_178
| ~ aElementOf0(U_170,slsdtgt0(xb)) )
| ~ aElementOf0(U_171,slsdtgt0(xa)) ) ) )
& sK40 != sz00
& aElementOf0(sK40,xI)
& sdtpldt0(sK41,sK42) = sK40
& aElementOf0(sK42,slsdtgt0(xb))
& aElementOf0(sK41,slsdtgt0(xa)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_177,sK43(U_178))],[f_45_7]) ).
fof(f_45_9,negated_conjecture,
( ! [U_184] :
( ? [U_183] :
( iLess0(sbrdtbr0(U_183),sbrdtbr0(U_184))
& U_183 != sz00
& aElementOf0(U_183,xI)
& ? [U_182] :
( ? [U_181] :
( sdtpldt0(U_182,U_181) = U_183
& aElementOf0(U_181,slsdtgt0(xb)) )
& aElementOf0(U_182,slsdtgt0(xa)) ) )
| U_184 = sz00
| ( ~ aElementOf0(U_184,xI)
& ! [U_180] :
( ! [U_179] :
( sdtpldt0(U_180,U_179) != U_184
| ~ aElementOf0(U_179,slsdtgt0(xb)) )
| ~ aElementOf0(U_180,slsdtgt0(xa)) ) ) )
& ! [U_178] :
( ( ! [U_176] :
( ~ iLess0(sbrdtbr0(U_176),sbrdtbr0(sK43(U_178)))
| U_176 = sz00
| ( ~ aElementOf0(U_176,xI)
& ! [U_175] :
( ! [U_174] :
( sdtpldt0(U_175,U_174) != U_176
| ~ aElementOf0(U_174,slsdtgt0(xb)) )
| ~ aElementOf0(U_175,slsdtgt0(xa)) ) ) )
& sK43(U_178) != sz00
& aElementOf0(sK43(U_178),xI)
& ? [U_172] :
( sdtpldt0(sK44(U_178),U_172) = sK43(U_178)
& aElementOf0(U_172,slsdtgt0(xb)) )
& aElementOf0(sK44(U_178),slsdtgt0(xa)) )
| ~ iLess0(sbrdtbr0(U_178),sbrdtbr0(sK40))
| U_178 = sz00
| ( ~ aElementOf0(U_178,xI)
& ! [U_171] :
( ! [U_170] :
( sdtpldt0(U_171,U_170) != U_178
| ~ aElementOf0(U_170,slsdtgt0(xb)) )
| ~ aElementOf0(U_171,slsdtgt0(xa)) ) ) )
& sK40 != sz00
& aElementOf0(sK40,xI)
& sdtpldt0(sK41,sK42) = sK40
& aElementOf0(sK42,slsdtgt0(xb))
& aElementOf0(sK41,slsdtgt0(xa)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_173,sK44(U_178))],[f_45_8]) ).
fof(f_45_10,negated_conjecture,
( ! [U_184] :
( ? [U_183] :
( iLess0(sbrdtbr0(U_183),sbrdtbr0(U_184))
& U_183 != sz00
& aElementOf0(U_183,xI)
& ? [U_182] :
( ? [U_181] :
( sdtpldt0(U_182,U_181) = U_183
& aElementOf0(U_181,slsdtgt0(xb)) )
& aElementOf0(U_182,slsdtgt0(xa)) ) )
| U_184 = sz00
| ( ~ aElementOf0(U_184,xI)
& ! [U_180] :
( ! [U_179] :
( sdtpldt0(U_180,U_179) != U_184
| ~ aElementOf0(U_179,slsdtgt0(xb)) )
| ~ aElementOf0(U_180,slsdtgt0(xa)) ) ) )
& ! [U_178] :
( ( ! [U_176] :
( ~ iLess0(sbrdtbr0(U_176),sbrdtbr0(sK43(U_178)))
| U_176 = sz00
| ( ~ aElementOf0(U_176,xI)
& ! [U_175] :
( ! [U_174] :
( sdtpldt0(U_175,U_174) != U_176
| ~ aElementOf0(U_174,slsdtgt0(xb)) )
| ~ aElementOf0(U_175,slsdtgt0(xa)) ) ) )
& sK43(U_178) != sz00
& aElementOf0(sK43(U_178),xI)
& sdtpldt0(sK44(U_178),sK45(U_178)) = sK43(U_178)
& aElementOf0(sK45(U_178),slsdtgt0(xb))
& aElementOf0(sK44(U_178),slsdtgt0(xa)) )
| ~ iLess0(sbrdtbr0(U_178),sbrdtbr0(sK40))
| U_178 = sz00
| ( ~ aElementOf0(U_178,xI)
& ! [U_171] :
( ! [U_170] :
( sdtpldt0(U_171,U_170) != U_178
| ~ aElementOf0(U_170,slsdtgt0(xb)) )
| ~ aElementOf0(U_171,slsdtgt0(xa)) ) ) )
& sK40 != sz00
& aElementOf0(sK40,xI)
& sdtpldt0(sK41,sK42) = sK40
& aElementOf0(sK42,slsdtgt0(xb))
& aElementOf0(sK41,slsdtgt0(xa)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_172,sK45(U_178))],[f_45_9]) ).
fof(f_45_11,negated_conjecture,
( ! [U_184] :
( ( iLess0(sbrdtbr0(sK46(U_184)),sbrdtbr0(U_184))
& sK46(U_184) != sz00
& aElementOf0(sK46(U_184),xI)
& ? [U_182] :
( ? [U_181] :
( sdtpldt0(U_182,U_181) = sK46(U_184)
& aElementOf0(U_181,slsdtgt0(xb)) )
& aElementOf0(U_182,slsdtgt0(xa)) ) )
| U_184 = sz00
| ( ~ aElementOf0(U_184,xI)
& ! [U_180] :
( ! [U_179] :
( sdtpldt0(U_180,U_179) != U_184
| ~ aElementOf0(U_179,slsdtgt0(xb)) )
| ~ aElementOf0(U_180,slsdtgt0(xa)) ) ) )
& ! [U_178] :
( ( ! [U_176] :
( ~ iLess0(sbrdtbr0(U_176),sbrdtbr0(sK43(U_178)))
| U_176 = sz00
| ( ~ aElementOf0(U_176,xI)
& ! [U_175] :
( ! [U_174] :
( sdtpldt0(U_175,U_174) != U_176
| ~ aElementOf0(U_174,slsdtgt0(xb)) )
| ~ aElementOf0(U_175,slsdtgt0(xa)) ) ) )
& sK43(U_178) != sz00
& aElementOf0(sK43(U_178),xI)
& sdtpldt0(sK44(U_178),sK45(U_178)) = sK43(U_178)
& aElementOf0(sK45(U_178),slsdtgt0(xb))
& aElementOf0(sK44(U_178),slsdtgt0(xa)) )
| ~ iLess0(sbrdtbr0(U_178),sbrdtbr0(sK40))
| U_178 = sz00
| ( ~ aElementOf0(U_178,xI)
& ! [U_171] :
( ! [U_170] :
( sdtpldt0(U_171,U_170) != U_178
| ~ aElementOf0(U_170,slsdtgt0(xb)) )
| ~ aElementOf0(U_171,slsdtgt0(xa)) ) ) )
& sK40 != sz00
& aElementOf0(sK40,xI)
& sdtpldt0(sK41,sK42) = sK40
& aElementOf0(sK42,slsdtgt0(xb))
& aElementOf0(sK41,slsdtgt0(xa)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_183,sK46(U_184))],[f_45_10]) ).
fof(f_45_12,negated_conjecture,
( ! [U_184] :
( ( iLess0(sbrdtbr0(sK46(U_184)),sbrdtbr0(U_184))
& sK46(U_184) != sz00
& aElementOf0(sK46(U_184),xI)
& ? [U_181] :
( sdtpldt0(sK47(U_184),U_181) = sK46(U_184)
& aElementOf0(U_181,slsdtgt0(xb)) )
& aElementOf0(sK47(U_184),slsdtgt0(xa)) )
| U_184 = sz00
| ( ~ aElementOf0(U_184,xI)
& ! [U_180] :
( ! [U_179] :
( sdtpldt0(U_180,U_179) != U_184
| ~ aElementOf0(U_179,slsdtgt0(xb)) )
| ~ aElementOf0(U_180,slsdtgt0(xa)) ) ) )
& ! [U_178] :
( ( ! [U_176] :
( ~ iLess0(sbrdtbr0(U_176),sbrdtbr0(sK43(U_178)))
| U_176 = sz00
| ( ~ aElementOf0(U_176,xI)
& ! [U_175] :
( ! [U_174] :
( sdtpldt0(U_175,U_174) != U_176
| ~ aElementOf0(U_174,slsdtgt0(xb)) )
| ~ aElementOf0(U_175,slsdtgt0(xa)) ) ) )
& sK43(U_178) != sz00
& aElementOf0(sK43(U_178),xI)
& sdtpldt0(sK44(U_178),sK45(U_178)) = sK43(U_178)
& aElementOf0(sK45(U_178),slsdtgt0(xb))
& aElementOf0(sK44(U_178),slsdtgt0(xa)) )
| ~ iLess0(sbrdtbr0(U_178),sbrdtbr0(sK40))
| U_178 = sz00
| ( ~ aElementOf0(U_178,xI)
& ! [U_171] :
( ! [U_170] :
( sdtpldt0(U_171,U_170) != U_178
| ~ aElementOf0(U_170,slsdtgt0(xb)) )
| ~ aElementOf0(U_171,slsdtgt0(xa)) ) ) )
& sK40 != sz00
& aElementOf0(sK40,xI)
& sdtpldt0(sK41,sK42) = sK40
& aElementOf0(sK42,slsdtgt0(xb))
& aElementOf0(sK41,slsdtgt0(xa)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_182,sK47(U_184))],[f_45_11]) ).
fof(f_45_13,negated_conjecture,
( ! [U_184] :
( ( iLess0(sbrdtbr0(sK46(U_184)),sbrdtbr0(U_184))
& sK46(U_184) != sz00
& aElementOf0(sK46(U_184),xI)
& sdtpldt0(sK47(U_184),sK48(U_184)) = sK46(U_184)
& aElementOf0(sK48(U_184),slsdtgt0(xb))
& aElementOf0(sK47(U_184),slsdtgt0(xa)) )
| U_184 = sz00
| ( ~ aElementOf0(U_184,xI)
& ! [U_180] :
( ! [U_179] :
( sdtpldt0(U_180,U_179) != U_184
| ~ aElementOf0(U_179,slsdtgt0(xb)) )
| ~ aElementOf0(U_180,slsdtgt0(xa)) ) ) )
& ! [U_178] :
( ( ! [U_176] :
( ~ iLess0(sbrdtbr0(U_176),sbrdtbr0(sK43(U_178)))
| U_176 = sz00
| ( ~ aElementOf0(U_176,xI)
& ! [U_175] :
( ! [U_174] :
( sdtpldt0(U_175,U_174) != U_176
| ~ aElementOf0(U_174,slsdtgt0(xb)) )
| ~ aElementOf0(U_175,slsdtgt0(xa)) ) ) )
& sK43(U_178) != sz00
& aElementOf0(sK43(U_178),xI)
& sdtpldt0(sK44(U_178),sK45(U_178)) = sK43(U_178)
& aElementOf0(sK45(U_178),slsdtgt0(xb))
& aElementOf0(sK44(U_178),slsdtgt0(xa)) )
| ~ iLess0(sbrdtbr0(U_178),sbrdtbr0(sK40))
| U_178 = sz00
| ( ~ aElementOf0(U_178,xI)
& ! [U_171] :
( ! [U_170] :
( sdtpldt0(U_171,U_170) != U_178
| ~ aElementOf0(U_170,slsdtgt0(xb)) )
| ~ aElementOf0(U_171,slsdtgt0(xa)) ) ) )
& sK40 != sz00
& aElementOf0(sK40,xI)
& sdtpldt0(sK41,sK42) = sK40
& aElementOf0(sK42,slsdtgt0(xb))
& aElementOf0(sK41,slsdtgt0(xa)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_181,sK48(U_184))],[f_45_12]) ).
cnf(f_45_14,negated_conjecture,
aElementOf0(sK41,slsdtgt0(xa)),
inference(clausify,[status(thm)],[f_45_13]) ).
cnf(f_45_15,negated_conjecture,
aElementOf0(sK42,slsdtgt0(xb)),
inference(clausify,[status(thm)],[f_45_13]) ).
cnf(f_45_16,negated_conjecture,
sdtpldt0(sK41,sK42) = sK40,
inference(clausify,[status(thm)],[f_45_13]) ).
cnf(f_45_17,negated_conjecture,
aElementOf0(sK40,xI),
inference(clausify,[status(thm)],[f_45_13]) ).
cnf(f_45_18,negated_conjecture,
sK40 != sz00,
inference(clausify,[status(thm)],[f_45_13]) ).
cnf(f_45_19,negated_conjecture,
( aElementOf0(sK44(U_178),slsdtgt0(xa))
| ~ iLess0(sbrdtbr0(U_178),sbrdtbr0(sK40))
| sdtpldt0(U_171,U_170) != U_178
| ~ aElementOf0(U_170,slsdtgt0(xb))
| ~ aElementOf0(U_171,slsdtgt0(xa))
| U_178 = sz00 ),
inference(clausify,[status(thm)],[f_45_13]) ).
cnf(f_45_20,negated_conjecture,
( aElementOf0(sK45(U_178),slsdtgt0(xb))
| ~ iLess0(sbrdtbr0(U_178),sbrdtbr0(sK40))
| sdtpldt0(U_171,U_170) != U_178
| ~ aElementOf0(U_170,slsdtgt0(xb))
| ~ aElementOf0(U_171,slsdtgt0(xa))
| U_178 = sz00 ),
inference(clausify,[status(thm)],[f_45_13]) ).
cnf(f_45_21,negated_conjecture,
( sdtpldt0(sK44(U_178),sK45(U_178)) = sK43(U_178)
| ~ iLess0(sbrdtbr0(U_178),sbrdtbr0(sK40))
| sdtpldt0(U_171,U_170) != U_178
| ~ aElementOf0(U_170,slsdtgt0(xb))
| ~ aElementOf0(U_171,slsdtgt0(xa))
| U_178 = sz00 ),
inference(clausify,[status(thm)],[f_45_13]) ).
cnf(f_45_22,negated_conjecture,
( aElementOf0(sK43(U_178),xI)
| ~ iLess0(sbrdtbr0(U_178),sbrdtbr0(sK40))
| sdtpldt0(U_171,U_170) != U_178
| ~ aElementOf0(U_170,slsdtgt0(xb))
| ~ aElementOf0(U_171,slsdtgt0(xa))
| U_178 = sz00 ),
inference(clausify,[status(thm)],[f_45_13]) ).
cnf(f_45_23,negated_conjecture,
( sK43(U_178) != sz00
| ~ iLess0(sbrdtbr0(U_178),sbrdtbr0(sK40))
| sdtpldt0(U_171,U_170) != U_178
| ~ aElementOf0(U_170,slsdtgt0(xb))
| ~ aElementOf0(U_171,slsdtgt0(xa))
| U_178 = sz00 ),
inference(clausify,[status(thm)],[f_45_13]) ).
cnf(f_45_24,negated_conjecture,
( sdtpldt0(U_175,U_174) != U_176
| ~ aElementOf0(U_174,slsdtgt0(xb))
| ~ aElementOf0(U_175,slsdtgt0(xa))
| U_176 = sz00
| ~ iLess0(sbrdtbr0(U_176),sbrdtbr0(sK43(U_178)))
| ~ iLess0(sbrdtbr0(U_178),sbrdtbr0(sK40))
| sdtpldt0(U_171,U_170) != U_178
| ~ aElementOf0(U_170,slsdtgt0(xb))
| ~ aElementOf0(U_171,slsdtgt0(xa))
| U_178 = sz00 ),
inference(clausify,[status(thm)],[f_45_13]) ).
cnf(f_45_25,negated_conjecture,
( ~ aElementOf0(U_176,xI)
| U_176 = sz00
| ~ iLess0(sbrdtbr0(U_176),sbrdtbr0(sK43(U_178)))
| ~ iLess0(sbrdtbr0(U_178),sbrdtbr0(sK40))
| sdtpldt0(U_171,U_170) != U_178
| ~ aElementOf0(U_170,slsdtgt0(xb))
| ~ aElementOf0(U_171,slsdtgt0(xa))
| U_178 = sz00 ),
inference(clausify,[status(thm)],[f_45_13]) ).
cnf(f_45_26,negated_conjecture,
( aElementOf0(sK44(U_178),slsdtgt0(xa))
| ~ iLess0(sbrdtbr0(U_178),sbrdtbr0(sK40))
| ~ aElementOf0(U_178,xI)
| U_178 = sz00 ),
inference(clausify,[status(thm)],[f_45_13]) ).
cnf(f_45_27,negated_conjecture,
( aElementOf0(sK45(U_178),slsdtgt0(xb))
| ~ iLess0(sbrdtbr0(U_178),sbrdtbr0(sK40))
| ~ aElementOf0(U_178,xI)
| U_178 = sz00 ),
inference(clausify,[status(thm)],[f_45_13]) ).
cnf(f_45_28,negated_conjecture,
( sdtpldt0(sK44(U_178),sK45(U_178)) = sK43(U_178)
| ~ iLess0(sbrdtbr0(U_178),sbrdtbr0(sK40))
| ~ aElementOf0(U_178,xI)
| U_178 = sz00 ),
inference(clausify,[status(thm)],[f_45_13]) ).
cnf(f_45_29,negated_conjecture,
( aElementOf0(sK43(U_178),xI)
| ~ iLess0(sbrdtbr0(U_178),sbrdtbr0(sK40))
| ~ aElementOf0(U_178,xI)
| U_178 = sz00 ),
inference(clausify,[status(thm)],[f_45_13]) ).
cnf(f_45_30,negated_conjecture,
( sK43(U_178) != sz00
| ~ iLess0(sbrdtbr0(U_178),sbrdtbr0(sK40))
| ~ aElementOf0(U_178,xI)
| U_178 = sz00 ),
inference(clausify,[status(thm)],[f_45_13]) ).
cnf(f_45_31,negated_conjecture,
( sdtpldt0(U_175,U_174) != U_176
| ~ aElementOf0(U_174,slsdtgt0(xb))
| ~ aElementOf0(U_175,slsdtgt0(xa))
| U_176 = sz00
| ~ iLess0(sbrdtbr0(U_176),sbrdtbr0(sK43(U_178)))
| ~ iLess0(sbrdtbr0(U_178),sbrdtbr0(sK40))
| ~ aElementOf0(U_178,xI)
| U_178 = sz00 ),
inference(clausify,[status(thm)],[f_45_13]) ).
cnf(f_45_32,negated_conjecture,
( ~ aElementOf0(U_176,xI)
| U_176 = sz00
| ~ iLess0(sbrdtbr0(U_176),sbrdtbr0(sK43(U_178)))
| ~ iLess0(sbrdtbr0(U_178),sbrdtbr0(sK40))
| ~ aElementOf0(U_178,xI)
| U_178 = sz00 ),
inference(clausify,[status(thm)],[f_45_13]) ).
cnf(f_45_33,negated_conjecture,
( aElementOf0(sK47(U_184),slsdtgt0(xa))
| sdtpldt0(U_180,U_179) != U_184
| ~ aElementOf0(U_179,slsdtgt0(xb))
| ~ aElementOf0(U_180,slsdtgt0(xa))
| U_184 = sz00 ),
inference(clausify,[status(thm)],[f_45_13]) ).
cnf(f_45_34,negated_conjecture,
( aElementOf0(sK48(U_184),slsdtgt0(xb))
| sdtpldt0(U_180,U_179) != U_184
| ~ aElementOf0(U_179,slsdtgt0(xb))
| ~ aElementOf0(U_180,slsdtgt0(xa))
| U_184 = sz00 ),
inference(clausify,[status(thm)],[f_45_13]) ).
cnf(f_45_35,negated_conjecture,
( sdtpldt0(sK47(U_184),sK48(U_184)) = sK46(U_184)
| sdtpldt0(U_180,U_179) != U_184
| ~ aElementOf0(U_179,slsdtgt0(xb))
| ~ aElementOf0(U_180,slsdtgt0(xa))
| U_184 = sz00 ),
inference(clausify,[status(thm)],[f_45_13]) ).
cnf(f_45_36,negated_conjecture,
( aElementOf0(sK46(U_184),xI)
| sdtpldt0(U_180,U_179) != U_184
| ~ aElementOf0(U_179,slsdtgt0(xb))
| ~ aElementOf0(U_180,slsdtgt0(xa))
| U_184 = sz00 ),
inference(clausify,[status(thm)],[f_45_13]) ).
cnf(f_45_37,negated_conjecture,
( sK46(U_184) != sz00
| sdtpldt0(U_180,U_179) != U_184
| ~ aElementOf0(U_179,slsdtgt0(xb))
| ~ aElementOf0(U_180,slsdtgt0(xa))
| U_184 = sz00 ),
inference(clausify,[status(thm)],[f_45_13]) ).
cnf(f_45_38,negated_conjecture,
( aElementOf0(sK47(U_184),slsdtgt0(xa))
| ~ aElementOf0(U_184,xI)
| U_184 = sz00 ),
inference(clausify,[status(thm)],[f_45_13]) ).
cnf(f_45_39,negated_conjecture,
( aElementOf0(sK48(U_184),slsdtgt0(xb))
| ~ aElementOf0(U_184,xI)
| U_184 = sz00 ),
inference(clausify,[status(thm)],[f_45_13]) ).
cnf(f_45_40,negated_conjecture,
( sdtpldt0(sK47(U_184),sK48(U_184)) = sK46(U_184)
| ~ aElementOf0(U_184,xI)
| U_184 = sz00 ),
inference(clausify,[status(thm)],[f_45_13]) ).
cnf(f_45_41,negated_conjecture,
( aElementOf0(sK46(U_184),xI)
| ~ aElementOf0(U_184,xI)
| U_184 = sz00 ),
inference(clausify,[status(thm)],[f_45_13]) ).
cnf(f_45_42,negated_conjecture,
( sK46(U_184) != sz00
| ~ aElementOf0(U_184,xI)
| U_184 = sz00 ),
inference(clausify,[status(thm)],[f_45_13]) ).
cnf(f_45_43,negated_conjecture,
( sdtpldt0(U_180,U_179) != U_184
| ~ aElementOf0(U_179,slsdtgt0(xb))
| ~ aElementOf0(U_180,slsdtgt0(xa))
| U_184 = sz00
| iLess0(sbrdtbr0(sK46(U_184)),sbrdtbr0(U_184)) ),
inference(clausify,[status(thm)],[f_45_13]) ).
cnf(f_45_44,negated_conjecture,
( ~ aElementOf0(U_184,xI)
| U_184 = sz00
| iLess0(sbrdtbr0(sK46(U_184)),sbrdtbr0(U_184)) ),
inference(clausify,[status(thm)],[f_45_13]) ).
cnf(f_1_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1_4]) ).
cnf(f_19_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_19_4]) ).
cnf(f_29_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_29_4]) ).
cnf(f_31_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_31_3]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( smndt0(Eq_x_0) = smndt0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( sdtpldt0(Eq_x_0,Eq_x_1) = sdtpldt0(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( sdtasdt0(Eq_x_0,Eq_x_1) = sdtasdt0(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sdtpldt1(Eq_x_0,Eq_x_1) = sdtpldt1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sdtasasdt0(Eq_x_0,Eq_x_1) = sdtasasdt0(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sbrdtbr0(Eq_x_0) = sbrdtbr0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( slsdtgt0(Eq_x_0) = slsdtgt0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK1(Eq_x_0,Eq_x_1) = sK1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK2(Eq_x_0,Eq_x_1) = sK2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK3(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK3(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK4(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK4(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK5(Eq_x_0,Eq_x_1,Eq_x_2) = sK5(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK6(Eq_x_0,Eq_x_1,Eq_x_2) = sK6(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( sK7(Eq_x_0,Eq_x_1,Eq_x_2) = sK7(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( sK8(Eq_x_0,Eq_x_1,Eq_x_2) = sK8(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( sK9(Eq_x_0,Eq_x_1,Eq_x_2) = sK9(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( sK10(Eq_x_0,Eq_x_1,Eq_x_2) = sK10(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( sK11(Eq_x_0) = sK11(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( sK12(Eq_x_0) = sK12(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( sK13(Eq_x_0) = sK13(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_24,axiom,
( sK14(Eq_x_0,Eq_x_1) = sK14(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,axiom,
( sK15(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK15(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,axiom,
( sK16(Eq_x_0,Eq_x_1) = sK16(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_27,axiom,
( sK17(Eq_x_0,Eq_x_1) = sK17(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_28,axiom,
( sK18(Eq_x_0,Eq_x_1) = sK18(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_29,axiom,
( sK19(Eq_x_0,Eq_x_1,Eq_x_2) = sK19(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_30,axiom,
( sK20(Eq_x_0,Eq_x_1,Eq_x_2) = sK20(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_31,axiom,
( sK21(Eq_x_0,Eq_x_1) = sK21(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_32,axiom,
( sK22(Eq_x_0,Eq_x_1) = sK22(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_33,axiom,
( sK23(Eq_x_0,Eq_x_1) = sK23(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_34,axiom,
( sK26(Eq_x_0) = sK26(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_35,axiom,
( sK27(Eq_x_0) = sK27(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_36,axiom,
( sK28(Eq_x_0) = sK28(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_37,axiom,
( sK29(Eq_x_0) = sK29(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_38,axiom,
( sK30(Eq_x_0) = sK30(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_39,axiom,
( sK35(Eq_x_0) = sK35(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_40,axiom,
( sK36(Eq_x_0) = sK36(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_41,axiom,
( sK43(Eq_x_0) = sK43(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_42,axiom,
( sK44(Eq_x_0) = sK44(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_43,axiom,
( sK45(Eq_x_0) = sK45(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_44,axiom,
( sK46(Eq_x_0) = sK46(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_45,axiom,
( sK47(Eq_x_0) = sK47(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_46,axiom,
( sK48(Eq_x_0) = sK48(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_47,axiom,
( aElement0(Eq_y_0)
| ~ aElement0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_48,axiom,
( aSet0(Eq_y_0)
| ~ aSet0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_49,axiom,
( aElementOf0(Eq_y_0,Eq_y_1)
| ~ aElementOf0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_50,axiom,
( aIdeal0(Eq_y_0)
| ~ aIdeal0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_51,axiom,
( sdteqdtlpzmzozddtrp0(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sdteqdtlpzmzozddtrp0(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_52,axiom,
( aNaturalNumber0(Eq_y_0)
| ~ aNaturalNumber0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_53,axiom,
( iLess0(Eq_y_0,Eq_y_1)
| ~ iLess0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_54,axiom,
( doDivides0(Eq_y_0,Eq_y_1)
| ~ doDivides0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_55,axiom,
( aDivisorOf0(Eq_y_0,Eq_y_1)
| ~ aDivisorOf0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_56,axiom,
( aGcdOfAnd0(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ aGcdOfAnd0(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_57,axiom,
( misRelativelyPrime0(Eq_y_0,Eq_y_1)
| ~ misRelativelyPrime0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG111+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/15.43 % CPULimit : 300
% 0.08/15.43 % WCLimit : 300
% 0.08/15.43 % DateTime : Sat Sep 19 20:56:10 UTC 2026
% 0.08/15.43 % CPUTime :
% 256.18/271.31 % SZS status Theorem for theBenchmark
% 256.18/271.31 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------