%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : RNG103+2 : 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 : n012.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 08:55:11 AM UTC 2026
% Result : Theorem 35.65s 35.98s
% Output : Proof 35.77s
% 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(m__1905,hypothesis,
aElement0(xc),
file('theBenchmark.p',m__1905) ).
fof(m__1933,hypothesis,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& ? [W0] :
( sdtasdt0(xc,W0) = xy
& aElement0(W0) )
& aElementOf0(xx,slsdtgt0(xc))
& ? [W0] :
( sdtasdt0(xc,W0) = xx
& aElement0(W0) ) ),
file('theBenchmark.p',m__1933) ).
fof(m__1956,hypothesis,
( sdtasdt0(xc,xu) = xx
& aElement0(xu) ),
file('theBenchmark.p',m__1956) ).
fof(m__1979,hypothesis,
( sdtasdt0(xc,xv) = xy
& aElement0(xv) ),
file('theBenchmark.p',m__1979) ).
fof(m__,conjecture,
sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
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]) ).
fof(f_1_4,plain,
! [U_0] :
( ~ aElement0(U_0)
| $true ),
inference(definitional_conversion,[status(esa)],[f_1_3]) ).
cnf(f_1_5,plain,
( ~ aElement0(U_0)
| $true ),
inference(clausify,[status(thm)],[f_1_4]) ).
fof(f_2_1,plain,
aElement0(sz00),
inference(fof_nnf,[status(thm)],[mSortsC]) ).
fof(f_2_2,plain,
aElement0(sz00),
inference(definitional_conversion,[status(esa)],[f_2_1]) ).
cnf(f_2_3,plain,
aElement0(sz00),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
aElement0(sz10),
inference(fof_nnf,[status(thm)],[mSortsC_01]) ).
fof(f_3_2,plain,
aElement0(sz10),
inference(definitional_conversion,[status(esa)],[f_3_1]) ).
cnf(f_3_3,plain,
aElement0(sz10),
inference(clausify,[status(thm)],[f_3_2]) ).
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]) ).
fof(f_4_3,plain,
! [U_1] :
( aElement0(smndt0(U_1))
| ~ aElement0(U_1) ),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
( aElement0(smndt0(U_1))
| ~ aElement0(U_1) ),
inference(clausify,[status(thm)],[f_4_3]) ).
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]) ).
fof(f_5_3,plain,
! [U_3,U_2] :
( aElement0(sdtpldt0(U_3,U_2))
| ~ aElement0(U_2)
| ~ aElement0(U_3) ),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
( aElement0(sdtpldt0(U_3,U_2))
| ~ aElement0(U_2)
| ~ aElement0(U_3) ),
inference(clausify,[status(thm)],[f_5_3]) ).
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]) ).
fof(f_6_3,plain,
! [U_5,U_4] :
( aElement0(sdtasdt0(U_5,U_4))
| ~ aElement0(U_4)
| ~ aElement0(U_5) ),
inference(definitional_conversion,[status(esa)],[f_6_2]) ).
cnf(f_6_4,plain,
( aElement0(sdtasdt0(U_5,U_4))
| ~ aElement0(U_4)
| ~ aElement0(U_5) ),
inference(clausify,[status(thm)],[f_6_3]) ).
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]) ).
fof(f_7_3,plain,
! [U_6,U_7] :
( sdtpldt0(U_7,U_6) = sdtpldt0(U_6,U_7)
| ~ aElement0(U_6)
| ~ aElement0(U_7) ),
inference(definitional_conversion,[status(esa)],[f_7_2]) ).
cnf(f_7_4,plain,
( sdtpldt0(U_7,U_6) = sdtpldt0(U_6,U_7)
| ~ aElement0(U_6)
| ~ aElement0(U_7) ),
inference(clausify,[status(thm)],[f_7_3]) ).
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]) ).
fof(f_8_3,plain,
! [U_9,U_10,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(definitional_conversion,[status(esa)],[f_8_2]) ).
cnf(f_8_4,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_3]) ).
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]) ).
fof(f_9_3,plain,
( ! [U_11] :
( U_11 = sdtpldt0(sz00,U_11)
| ~ sP0(U_11) )
& ! [U_11] :
( sdtpldt0(U_11,sz00) = U_11
| ~ sP0(U_11) )
& ! [U_11] :
( sP0(U_11)
| ~ aElement0(U_11) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_9_2]) ).
cnf(f_9_4,plain,
( sP0(U_11)
| ~ aElement0(U_11) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_5,plain,
( sdtpldt0(U_11,sz00) = U_11
| ~ sP0(U_11) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_6,plain,
( U_11 = sdtpldt0(sz00,U_11)
| ~ sP0(U_11) ),
inference(clausify,[status(thm)],[f_9_3]) ).
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]) ).
fof(f_10_3,plain,
( ! [U_12] :
( sz00 = sdtpldt0(smndt0(U_12),U_12)
| ~ sP1(U_12) )
& ! [U_12] :
( sdtpldt0(U_12,smndt0(U_12)) = sz00
| ~ sP1(U_12) )
& ! [U_12] :
( sP1(U_12)
| ~ aElement0(U_12) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_10_2]) ).
cnf(f_10_4,plain,
( sP1(U_12)
| ~ aElement0(U_12) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_5,plain,
( sdtpldt0(U_12,smndt0(U_12)) = sz00
| ~ sP1(U_12) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_6,plain,
( sz00 = sdtpldt0(smndt0(U_12),U_12)
| ~ sP1(U_12) ),
inference(clausify,[status(thm)],[f_10_3]) ).
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]) ).
fof(f_11_3,plain,
! [U_13,U_14] :
( sdtasdt0(U_14,U_13) = sdtasdt0(U_13,U_14)
| ~ aElement0(U_13)
| ~ aElement0(U_14) ),
inference(definitional_conversion,[status(esa)],[f_11_2]) ).
cnf(f_11_4,plain,
( sdtasdt0(U_14,U_13) = sdtasdt0(U_13,U_14)
| ~ aElement0(U_13)
| ~ aElement0(U_14) ),
inference(clausify,[status(thm)],[f_11_3]) ).
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]) ).
fof(f_12_3,plain,
! [U_15,U_16,U_17] :
( 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(definitional_conversion,[status(esa)],[f_12_2]) ).
cnf(f_12_4,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_3]) ).
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]) ).
fof(f_13_3,plain,
( ! [U_18] :
( U_18 = sdtasdt0(sz10,U_18)
| ~ sP2(U_18) )
& ! [U_18] :
( sdtasdt0(U_18,sz10) = U_18
| ~ sP2(U_18) )
& ! [U_18] :
( sP2(U_18)
| ~ aElement0(U_18) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_13_2]) ).
cnf(f_13_4,plain,
( sP2(U_18)
| ~ aElement0(U_18) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_5,plain,
( sdtasdt0(U_18,sz10) = U_18
| ~ sP2(U_18) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_6,plain,
( U_18 = sdtasdt0(sz10,U_18)
| ~ sP2(U_18) ),
inference(clausify,[status(thm)],[f_13_3]) ).
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]) ).
fof(f_14_3,plain,
( ! [U_20,U_21,U_19] :
( sdtasdt0(sdtpldt0(U_20,U_19),U_21) = sdtpldt0(sdtasdt0(U_20,U_21),sdtasdt0(U_19,U_21))
| ~ sP3(U_20,U_21,U_19) )
& ! [U_20,U_21,U_19] :
( sdtasdt0(U_21,sdtpldt0(U_20,U_19)) = sdtpldt0(sdtasdt0(U_21,U_20),sdtasdt0(U_21,U_19))
| ~ sP3(U_20,U_21,U_19) )
& ! [U_20,U_21,U_19] :
( sP3(U_20,U_21,U_19)
| ~ aElement0(U_19)
| ~ aElement0(U_20)
| ~ aElement0(U_21) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_14_2]) ).
cnf(f_14_4,plain,
( sP3(U_20,U_21,U_19)
| ~ aElement0(U_19)
| ~ aElement0(U_20)
| ~ aElement0(U_21) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_5,plain,
( sdtasdt0(U_21,sdtpldt0(U_20,U_19)) = sdtpldt0(sdtasdt0(U_21,U_20),sdtasdt0(U_21,U_19))
| ~ sP3(U_20,U_21,U_19) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_6,plain,
( sdtasdt0(sdtpldt0(U_20,U_19),U_21) = sdtpldt0(sdtasdt0(U_20,U_21),sdtasdt0(U_19,U_21))
| ~ sP3(U_20,U_21,U_19) ),
inference(clausify,[status(thm)],[f_14_3]) ).
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]) ).
fof(f_15_3,plain,
( ! [U_22] :
( smndt0(U_22) = sdtasdt0(U_22,smndt0(sz10))
| ~ sP4(U_22) )
& ! [U_22] :
( sdtasdt0(smndt0(sz10),U_22) = smndt0(U_22)
| ~ sP4(U_22) )
& ! [U_22] :
( sP4(U_22)
| ~ aElement0(U_22) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_15_2]) ).
cnf(f_15_4,plain,
( sP4(U_22)
| ~ aElement0(U_22) ),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_5,plain,
( sdtasdt0(smndt0(sz10),U_22) = smndt0(U_22)
| ~ sP4(U_22) ),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_6,plain,
( smndt0(U_22) = sdtasdt0(U_22,smndt0(sz10))
| ~ sP4(U_22) ),
inference(clausify,[status(thm)],[f_15_3]) ).
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]) ).
fof(f_16_3,plain,
( ! [U_23] :
( sz00 = sdtasdt0(sz00,U_23)
| ~ sP5(U_23) )
& ! [U_23] :
( sdtasdt0(U_23,sz00) = sz00
| ~ sP5(U_23) )
& ! [U_23] :
( sP5(U_23)
| ~ aElement0(U_23) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_16_2]) ).
cnf(f_16_4,plain,
( sP5(U_23)
| ~ aElement0(U_23) ),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_5,plain,
( sdtasdt0(U_23,sz00) = sz00
| ~ sP5(U_23) ),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_6,plain,
( sz00 = sdtasdt0(sz00,U_23)
| ~ sP5(U_23) ),
inference(clausify,[status(thm)],[f_16_3]) ).
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]) ).
fof(f_17_3,plain,
! [U_25,U_24] :
( U_24 = sz00
| U_25 = sz00
| sdtasdt0(U_25,U_24) != sz00
| ~ aElement0(U_24)
| ~ aElement0(U_25) ),
inference(definitional_conversion,[status(esa)],[f_17_2]) ).
cnf(f_17_4,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_3]) ).
fof(f_18_1,plain,
sz10 != sz00,
inference(fof_nnf,[status(thm)],[mUnNeZr]) ).
fof(f_18_2,plain,
sz10 != sz00,
inference(definitional_conversion,[status(esa)],[f_18_1]) ).
cnf(f_18_3,plain,
sz10 != sz00,
inference(clausify,[status(thm)],[f_18_2]) ).
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]) ).
fof(f_19_4,plain,
! [U_26] :
( ~ aSet0(U_26)
| $true ),
inference(definitional_conversion,[status(esa)],[f_19_3]) ).
cnf(f_19_5,plain,
( ~ aSet0(U_26)
| $true ),
inference(clausify,[status(thm)],[f_19_4]) ).
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]) ).
fof(f_20_3,plain,
! [U_27,U_28] :
( aElement0(U_27)
| ~ aElementOf0(U_27,U_28)
| ~ aSet0(U_28) ),
inference(definitional_conversion,[status(esa)],[f_20_2]) ).
cnf(f_20_4,plain,
( aElement0(U_27)
| ~ aElementOf0(U_27,U_28)
| ~ aSet0(U_28) ),
inference(clausify,[status(thm)],[f_20_3]) ).
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]) ).
fof(f_21_5,plain,
( ! [U_31,U_32] :
( ~ aElementOf0(sK2(U_32,U_31),U_32)
| ~ sP7(U_31,U_32) )
& ! [U_31,U_32] :
( aElementOf0(sK2(U_32,U_31),U_31)
| ~ sP7(U_31,U_32) )
& ! [U_31,U_32] :
( ~ aElementOf0(sK1(U_32,U_31),U_31)
| ~ sP6(U_31,U_32) )
& ! [U_31,U_32] :
( aElementOf0(sK1(U_32,U_31),U_32)
| ~ sP6(U_31,U_32) )
& ! [U_31,U_32] :
( U_32 = U_31
| sP7(U_31,U_32)
| sP6(U_31,U_32)
| ~ aSet0(U_31)
| ~ aSet0(U_32) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6,sP7])],[f_21_4]) ).
cnf(f_21_6,plain,
( U_32 = U_31
| sP7(U_31,U_32)
| sP6(U_31,U_32)
| ~ aSet0(U_31)
| ~ aSet0(U_32) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_7,plain,
( aElementOf0(sK1(U_32,U_31),U_32)
| ~ sP6(U_31,U_32) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_8,plain,
( ~ aElementOf0(sK1(U_32,U_31),U_31)
| ~ sP6(U_31,U_32) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_9,plain,
( aElementOf0(sK2(U_32,U_31),U_31)
| ~ sP7(U_31,U_32) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_10,plain,
( ~ aElementOf0(sK2(U_32,U_31),U_32)
| ~ sP7(U_31,U_32) ),
inference(clausify,[status(thm)],[f_21_5]) ).
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]) ).
fof(f_22_10,plain,
( ! [U_44,U_45,U_51] :
( ~ aElementOf0(sK6(U_45,U_44,U_51),U_51)
| ~ sP11(U_44,U_45,U_51) )
& ! [U_44,U_45,U_51] :
( sdtpldt0(sK7(U_45,U_44,U_51),sK8(U_45,U_44,U_51)) = sK6(U_45,U_44,U_51)
| ~ sP11(U_44,U_45,U_51) )
& ! [U_44,U_45,U_51] :
( aElementOf0(sK8(U_45,U_44,U_51),U_44)
| ~ sP11(U_44,U_45,U_51) )
& ! [U_44,U_45,U_51] :
( aElementOf0(sK7(U_45,U_44,U_51),U_45)
| ~ sP11(U_44,U_45,U_51) )
& ! [U_38,U_39,U_44,U_45,U_51] :
( sdtpldt0(U_39,U_38) != sK5(U_45,U_44,U_51)
| ~ aElementOf0(U_38,U_44)
| ~ aElementOf0(U_39,U_45)
| ~ sP10(U_38,U_39,U_44,U_45,U_51) )
& ! [U_38,U_39,U_44,U_45,U_51] :
( aElementOf0(sK5(U_45,U_44,U_51),U_51)
| ~ sP10(U_38,U_39,U_44,U_45,U_51) )
& ! [U_44,U_45,U_46,U_50] :
( sdtpldt0(sK3(U_45,U_44,U_50,U_46),sK4(U_45,U_44,U_50,U_46)) = U_46
| ~ sP8(U_44,U_45,U_46,U_50) )
& ! [U_44,U_45,U_46,U_50] :
( aElementOf0(sK4(U_45,U_44,U_50,U_46),U_44)
| ~ sP8(U_44,U_45,U_46,U_50) )
& ! [U_44,U_45,U_46,U_50] :
( aElementOf0(sK3(U_45,U_44,U_50,U_46),U_45)
| ~ sP8(U_44,U_45,U_46,U_50) )
& ! [U_35,U_36,U_44,U_45,U_46,U_47,U_50] :
( aElementOf0(U_47,U_50)
| sdtpldt0(U_36,U_35) != U_47
| ~ aElementOf0(U_35,U_44)
| ~ aElementOf0(U_36,U_45)
| ~ sP9(U_35,U_36,U_44,U_45,U_46,U_47,U_50) )
& ! [U_35,U_36,U_44,U_45,U_46,U_47,U_50] :
( sP8(U_44,U_45,U_46,U_50)
| ~ aElementOf0(U_46,U_50)
| ~ sP9(U_35,U_36,U_44,U_45,U_46,U_47,U_50) )
& ! [U_35,U_36,U_44,U_45,U_46,U_47,U_50] :
( aSet0(U_50)
| ~ sP9(U_35,U_36,U_44,U_45,U_46,U_47,U_50) )
& ! [U_35,U_36,U_38,U_39,U_44,U_45,U_46,U_47,U_51,U_50] :
( U_51 = sdtpldt1(U_45,U_44)
| sP11(U_44,U_45,U_51)
| sP10(U_38,U_39,U_44,U_45,U_51)
| ~ aSet0(U_51)
| ~ sP12(U_35,U_36,U_38,U_39,U_44,U_45,U_46,U_47,U_51,U_50) )
& ! [U_35,U_36,U_38,U_39,U_44,U_45,U_46,U_47,U_51,U_50] :
( sP9(U_35,U_36,U_44,U_45,U_46,U_47,U_50)
| U_50 != sdtpldt1(U_45,U_44)
| ~ sP12(U_35,U_36,U_38,U_39,U_44,U_45,U_46,U_47,U_51,U_50) )
& ! [U_35,U_36,U_38,U_39,U_44,U_45,U_46,U_47,U_51,U_50] :
( sP12(U_35,U_36,U_38,U_39,U_44,U_45,U_46,U_47,U_51,U_50)
| ~ aSet0(U_44)
| ~ aSet0(U_45) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8,sP9,sP10,sP11,sP12])],[f_22_9]) ).
cnf(f_22_11,plain,
( sP12(U_35,U_36,U_38,U_39,U_44,U_45,U_46,U_47,U_51,U_50)
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(clausify,[status(thm)],[f_22_10]) ).
cnf(f_22_12,plain,
( sP9(U_35,U_36,U_44,U_45,U_46,U_47,U_50)
| U_50 != sdtpldt1(U_45,U_44)
| ~ sP12(U_35,U_36,U_38,U_39,U_44,U_45,U_46,U_47,U_51,U_50) ),
inference(clausify,[status(thm)],[f_22_10]) ).
cnf(f_22_13,plain,
( U_51 = sdtpldt1(U_45,U_44)
| sP11(U_44,U_45,U_51)
| sP10(U_38,U_39,U_44,U_45,U_51)
| ~ aSet0(U_51)
| ~ sP12(U_35,U_36,U_38,U_39,U_44,U_45,U_46,U_47,U_51,U_50) ),
inference(clausify,[status(thm)],[f_22_10]) ).
cnf(f_22_14,plain,
( aSet0(U_50)
| ~ sP9(U_35,U_36,U_44,U_45,U_46,U_47,U_50) ),
inference(clausify,[status(thm)],[f_22_10]) ).
cnf(f_22_15,plain,
( sP8(U_44,U_45,U_46,U_50)
| ~ aElementOf0(U_46,U_50)
| ~ sP9(U_35,U_36,U_44,U_45,U_46,U_47,U_50) ),
inference(clausify,[status(thm)],[f_22_10]) ).
cnf(f_22_16,plain,
( aElementOf0(U_47,U_50)
| sdtpldt0(U_36,U_35) != U_47
| ~ aElementOf0(U_35,U_44)
| ~ aElementOf0(U_36,U_45)
| ~ sP9(U_35,U_36,U_44,U_45,U_46,U_47,U_50) ),
inference(clausify,[status(thm)],[f_22_10]) ).
cnf(f_22_17,plain,
( aElementOf0(sK3(U_45,U_44,U_50,U_46),U_45)
| ~ sP8(U_44,U_45,U_46,U_50) ),
inference(clausify,[status(thm)],[f_22_10]) ).
cnf(f_22_18,plain,
( aElementOf0(sK4(U_45,U_44,U_50,U_46),U_44)
| ~ sP8(U_44,U_45,U_46,U_50) ),
inference(clausify,[status(thm)],[f_22_10]) ).
cnf(f_22_19,plain,
( sdtpldt0(sK3(U_45,U_44,U_50,U_46),sK4(U_45,U_44,U_50,U_46)) = U_46
| ~ sP8(U_44,U_45,U_46,U_50) ),
inference(clausify,[status(thm)],[f_22_10]) ).
cnf(f_22_20,plain,
( aElementOf0(sK5(U_45,U_44,U_51),U_51)
| ~ sP10(U_38,U_39,U_44,U_45,U_51) ),
inference(clausify,[status(thm)],[f_22_10]) ).
cnf(f_22_21,plain,
( sdtpldt0(U_39,U_38) != sK5(U_45,U_44,U_51)
| ~ aElementOf0(U_38,U_44)
| ~ aElementOf0(U_39,U_45)
| ~ sP10(U_38,U_39,U_44,U_45,U_51) ),
inference(clausify,[status(thm)],[f_22_10]) ).
cnf(f_22_22,plain,
( aElementOf0(sK7(U_45,U_44,U_51),U_45)
| ~ sP11(U_44,U_45,U_51) ),
inference(clausify,[status(thm)],[f_22_10]) ).
cnf(f_22_23,plain,
( aElementOf0(sK8(U_45,U_44,U_51),U_44)
| ~ sP11(U_44,U_45,U_51) ),
inference(clausify,[status(thm)],[f_22_10]) ).
cnf(f_22_24,plain,
( sdtpldt0(sK7(U_45,U_44,U_51),sK8(U_45,U_44,U_51)) = sK6(U_45,U_44,U_51)
| ~ sP11(U_44,U_45,U_51) ),
inference(clausify,[status(thm)],[f_22_10]) ).
cnf(f_22_25,plain,
( ~ aElementOf0(sK6(U_45,U_44,U_51),U_51)
| ~ sP11(U_44,U_45,U_51) ),
inference(clausify,[status(thm)],[f_22_10]) ).
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]) ).
fof(f_23_6,plain,
( ! [U_55,U_62,U_56] :
( ~ aElementOf0(sK10(U_56,U_55,U_62),U_62)
| ~ sP16(U_55,U_62,U_56) )
& ! [U_55,U_62,U_56] :
( aElementOf0(sK10(U_56,U_55,U_62),U_55)
| ~ sP16(U_55,U_62,U_56) )
& ! [U_55,U_62,U_56] :
( aElementOf0(sK10(U_56,U_55,U_62),U_56)
| ~ sP16(U_55,U_62,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)
| ~ sP15(U_55,U_62,U_56) )
& ! [U_55,U_62,U_56] :
( aElementOf0(sK9(U_56,U_55,U_62),U_62)
| ~ sP15(U_55,U_62,U_56) )
& ! [U_55,U_56,U_57] :
( aElementOf0(U_57,U_55)
| ~ sP13(U_55,U_56,U_57) )
& ! [U_55,U_56,U_57] :
( aElementOf0(U_57,U_56)
| ~ sP13(U_55,U_56,U_57) )
& ! [U_55,U_58,U_56,U_57,U_61] :
( aElementOf0(U_58,U_61)
| ~ aElementOf0(U_58,U_55)
| ~ aElementOf0(U_58,U_56)
| ~ sP14(U_55,U_58,U_56,U_57,U_61) )
& ! [U_55,U_58,U_56,U_57,U_61] :
( sP13(U_55,U_56,U_57)
| ~ aElementOf0(U_57,U_61)
| ~ sP14(U_55,U_58,U_56,U_57,U_61) )
& ! [U_55,U_58,U_56,U_57,U_61] :
( aSet0(U_61)
| ~ sP14(U_55,U_58,U_56,U_57,U_61) )
& ! [U_55,U_62,U_58,U_56,U_57,U_61] :
( U_62 = sdtasasdt0(U_56,U_55)
| sP16(U_55,U_62,U_56)
| sP15(U_55,U_62,U_56)
| ~ aSet0(U_62)
| ~ sP17(U_55,U_62,U_58,U_56,U_57,U_61) )
& ! [U_55,U_62,U_58,U_56,U_57,U_61] :
( sP14(U_55,U_58,U_56,U_57,U_61)
| U_61 != sdtasasdt0(U_56,U_55)
| ~ sP17(U_55,U_62,U_58,U_56,U_57,U_61) )
& ! [U_55,U_62,U_58,U_56,U_57,U_61] :
( sP17(U_55,U_62,U_58,U_56,U_57,U_61)
| ~ aSet0(U_55)
| ~ aSet0(U_56) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP13,sP14,sP15,sP16,sP17])],[f_23_5]) ).
cnf(f_23_7,plain,
( sP17(U_55,U_62,U_58,U_56,U_57,U_61)
| ~ aSet0(U_55)
| ~ aSet0(U_56) ),
inference(clausify,[status(thm)],[f_23_6]) ).
cnf(f_23_8,plain,
( sP14(U_55,U_58,U_56,U_57,U_61)
| U_61 != sdtasasdt0(U_56,U_55)
| ~ sP17(U_55,U_62,U_58,U_56,U_57,U_61) ),
inference(clausify,[status(thm)],[f_23_6]) ).
cnf(f_23_9,plain,
( U_62 = sdtasasdt0(U_56,U_55)
| sP16(U_55,U_62,U_56)
| sP15(U_55,U_62,U_56)
| ~ aSet0(U_62)
| ~ sP17(U_55,U_62,U_58,U_56,U_57,U_61) ),
inference(clausify,[status(thm)],[f_23_6]) ).
cnf(f_23_10,plain,
( aSet0(U_61)
| ~ sP14(U_55,U_58,U_56,U_57,U_61) ),
inference(clausify,[status(thm)],[f_23_6]) ).
cnf(f_23_11,plain,
( sP13(U_55,U_56,U_57)
| ~ aElementOf0(U_57,U_61)
| ~ sP14(U_55,U_58,U_56,U_57,U_61) ),
inference(clausify,[status(thm)],[f_23_6]) ).
cnf(f_23_12,plain,
( aElementOf0(U_58,U_61)
| ~ aElementOf0(U_58,U_55)
| ~ aElementOf0(U_58,U_56)
| ~ sP14(U_55,U_58,U_56,U_57,U_61) ),
inference(clausify,[status(thm)],[f_23_6]) ).
cnf(f_23_13,plain,
( aElementOf0(U_57,U_56)
| ~ sP13(U_55,U_56,U_57) ),
inference(clausify,[status(thm)],[f_23_6]) ).
cnf(f_23_14,plain,
( aElementOf0(U_57,U_55)
| ~ sP13(U_55,U_56,U_57) ),
inference(clausify,[status(thm)],[f_23_6]) ).
cnf(f_23_15,plain,
( aElementOf0(sK9(U_56,U_55,U_62),U_62)
| ~ sP15(U_55,U_62,U_56) ),
inference(clausify,[status(thm)],[f_23_6]) ).
cnf(f_23_16,plain,
( ~ aElementOf0(sK9(U_56,U_55,U_62),U_55)
| ~ aElementOf0(sK9(U_56,U_55,U_62),U_56)
| ~ sP15(U_55,U_62,U_56) ),
inference(clausify,[status(thm)],[f_23_6]) ).
cnf(f_23_17,plain,
( aElementOf0(sK10(U_56,U_55,U_62),U_56)
| ~ sP16(U_55,U_62,U_56) ),
inference(clausify,[status(thm)],[f_23_6]) ).
cnf(f_23_18,plain,
( aElementOf0(sK10(U_56,U_55,U_62),U_55)
| ~ sP16(U_55,U_62,U_56) ),
inference(clausify,[status(thm)],[f_23_6]) ).
cnf(f_23_19,plain,
( ~ aElementOf0(sK10(U_56,U_55,U_62),U_62)
| ~ sP16(U_55,U_62,U_56) ),
inference(clausify,[status(thm)],[f_23_6]) ).
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]) ).
fof(f_24_7,plain,
( ! [U_71] :
( ~ aElementOf0(sdtasdt0(sK13(U_71),sK11(U_71)),U_71)
| ~ sP21(U_71) )
& ! [U_71] :
( aElement0(sK13(U_71))
| ~ sP21(U_71) )
& ! [U_71] :
( ~ aElementOf0(sdtpldt0(sK11(U_71),sK12(U_71)),U_71)
| ~ sP20(U_71) )
& ! [U_71] :
( aElementOf0(sK12(U_71),U_71)
| ~ sP20(U_71) )
& ! [U_71] :
( sP21(U_71)
| sP20(U_71)
| ~ sP22(U_71) )
& ! [U_71] :
( aElementOf0(sK11(U_71),U_71)
| ~ sP22(U_71) )
& ! [U_70,U_65,U_64,U_63] :
( aElementOf0(sdtasdt0(U_64,U_65),U_70)
| ~ aElement0(U_64)
| ~ sP18(U_70,U_65,U_64,U_63) )
& ! [U_70,U_65,U_64,U_63] :
( aElementOf0(sdtpldt0(U_65,U_63),U_70)
| ~ aElementOf0(U_63,U_70)
| ~ sP18(U_70,U_65,U_64,U_63) )
& ! [U_70,U_65,U_64,U_63] :
( sP18(U_70,U_65,U_64,U_63)
| ~ aElementOf0(U_65,U_70)
| ~ sP19(U_70,U_65,U_64,U_63) )
& ! [U_70,U_65,U_64,U_63] :
( aSet0(U_70)
| ~ sP19(U_70,U_65,U_64,U_63) )
& ! [U_71] :
( aIdeal0(U_71)
| sP22(U_71)
| ~ aSet0(U_71) )
& ! [U_70,U_65,U_64,U_63] :
( sP19(U_70,U_65,U_64,U_63)
| ~ aIdeal0(U_70) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP18,sP19,sP20,sP21,sP22])],[f_24_6]) ).
cnf(f_24_8,plain,
( sP19(U_70,U_65,U_64,U_63)
| ~ aIdeal0(U_70) ),
inference(clausify,[status(thm)],[f_24_7]) ).
cnf(f_24_9,plain,
( aIdeal0(U_71)
| sP22(U_71)
| ~ aSet0(U_71) ),
inference(clausify,[status(thm)],[f_24_7]) ).
cnf(f_24_10,plain,
( aSet0(U_70)
| ~ sP19(U_70,U_65,U_64,U_63) ),
inference(clausify,[status(thm)],[f_24_7]) ).
cnf(f_24_11,plain,
( sP18(U_70,U_65,U_64,U_63)
| ~ aElementOf0(U_65,U_70)
| ~ sP19(U_70,U_65,U_64,U_63) ),
inference(clausify,[status(thm)],[f_24_7]) ).
cnf(f_24_12,plain,
( aElementOf0(sdtpldt0(U_65,U_63),U_70)
| ~ aElementOf0(U_63,U_70)
| ~ sP18(U_70,U_65,U_64,U_63) ),
inference(clausify,[status(thm)],[f_24_7]) ).
cnf(f_24_13,plain,
( aElementOf0(sdtasdt0(U_64,U_65),U_70)
| ~ aElement0(U_64)
| ~ sP18(U_70,U_65,U_64,U_63) ),
inference(clausify,[status(thm)],[f_24_7]) ).
cnf(f_24_14,plain,
( aElementOf0(sK11(U_71),U_71)
| ~ sP22(U_71) ),
inference(clausify,[status(thm)],[f_24_7]) ).
cnf(f_24_15,plain,
( sP21(U_71)
| sP20(U_71)
| ~ sP22(U_71) ),
inference(clausify,[status(thm)],[f_24_7]) ).
cnf(f_24_16,plain,
( aElementOf0(sK12(U_71),U_71)
| ~ sP20(U_71) ),
inference(clausify,[status(thm)],[f_24_7]) ).
cnf(f_24_17,plain,
( ~ aElementOf0(sdtpldt0(sK11(U_71),sK12(U_71)),U_71)
| ~ sP20(U_71) ),
inference(clausify,[status(thm)],[f_24_7]) ).
cnf(f_24_18,plain,
( aElement0(sK13(U_71))
| ~ sP21(U_71) ),
inference(clausify,[status(thm)],[f_24_7]) ).
cnf(f_24_19,plain,
( ~ aElementOf0(sdtasdt0(sK13(U_71),sK11(U_71)),U_71)
| ~ sP21(U_71) ),
inference(clausify,[status(thm)],[f_24_7]) ).
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]) ).
fof(f_25_3,plain,
! [U_73,U_72] :
( aIdeal0(sdtpldt1(U_73,U_72))
| ~ aIdeal0(U_72)
| ~ aIdeal0(U_73) ),
inference(definitional_conversion,[status(esa)],[f_25_2]) ).
cnf(f_25_4,plain,
( aIdeal0(sdtpldt1(U_73,U_72))
| ~ aIdeal0(U_72)
| ~ aIdeal0(U_73) ),
inference(clausify,[status(thm)],[f_25_3]) ).
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]) ).
fof(f_26_3,plain,
! [U_75,U_74] :
( aIdeal0(sdtasasdt0(U_75,U_74))
| ~ aIdeal0(U_74)
| ~ aIdeal0(U_75) ),
inference(definitional_conversion,[status(esa)],[f_26_2]) ).
cnf(f_26_4,plain,
( aIdeal0(sdtasasdt0(U_75,U_74))
| ~ aIdeal0(U_74)
| ~ aIdeal0(U_75) ),
inference(clausify,[status(thm)],[f_26_3]) ).
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]) ).
fof(f_27_3,plain,
( ! [U_78,U_77,U_76] :
( sdteqdtlpzmzozddtrp0(U_78,U_77,U_76)
| ~ aElementOf0(sdtpldt0(U_78,smndt0(U_77)),U_76)
| ~ sP23(U_78,U_77,U_76) )
& ! [U_78,U_77,U_76] :
( aElementOf0(sdtpldt0(U_78,smndt0(U_77)),U_76)
| ~ sdteqdtlpzmzozddtrp0(U_78,U_77,U_76)
| ~ sP23(U_78,U_77,U_76) )
& ! [U_78,U_77,U_76] :
( sP23(U_78,U_77,U_76)
| ~ aIdeal0(U_76)
| ~ aElement0(U_77)
| ~ aElement0(U_78) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP23])],[f_27_2]) ).
cnf(f_27_4,plain,
( sP23(U_78,U_77,U_76)
| ~ aIdeal0(U_76)
| ~ aElement0(U_77)
| ~ aElement0(U_78) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_5,plain,
( aElementOf0(sdtpldt0(U_78,smndt0(U_77)),U_76)
| ~ sdteqdtlpzmzozddtrp0(U_78,U_77,U_76)
| ~ sP23(U_78,U_77,U_76) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_6,plain,
( sdteqdtlpzmzozddtrp0(U_78,U_77,U_76)
| ~ aElementOf0(sdtpldt0(U_78,smndt0(U_77)),U_76)
| ~ sP23(U_78,U_77,U_76) ),
inference(clausify,[status(thm)],[f_27_3]) ).
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]) ).
fof(f_28_5,plain,
( ! [U_83,U_82,U_81,U_84] :
( sdteqdtlpzmzozddtrp0(sK15(U_84,U_83,U_82,U_81),U_81,U_83)
| ~ sP25(U_83,U_82,U_81,U_84) )
& ! [U_83,U_82,U_81,U_84] :
( sdteqdtlpzmzozddtrp0(sK15(U_84,U_83,U_82,U_81),U_82,U_84)
| ~ sP25(U_83,U_82,U_81,U_84) )
& ! [U_83,U_82,U_81,U_84] :
( aElement0(sK15(U_84,U_83,U_82,U_81))
| ~ sP25(U_83,U_82,U_81,U_84) )
& ! [U_83,U_84] :
( ~ aElementOf0(sK14(U_84,U_83),sdtpldt1(U_84,U_83))
| ~ sP24(U_83,U_84) )
& ! [U_83,U_84] :
( aElement0(sK14(U_84,U_83))
| ~ sP24(U_83,U_84) )
& ! [U_83,U_82,U_81,U_84] :
( sP25(U_83,U_82,U_81,U_84)
| ~ aElement0(U_81)
| ~ aElement0(U_82)
| sP24(U_83,U_84)
| ~ aIdeal0(U_83)
| ~ aIdeal0(U_84) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP24,sP25])],[f_28_4]) ).
cnf(f_28_6,plain,
( sP25(U_83,U_82,U_81,U_84)
| ~ aElement0(U_81)
| ~ aElement0(U_82)
| sP24(U_83,U_84)
| ~ aIdeal0(U_83)
| ~ aIdeal0(U_84) ),
inference(clausify,[status(thm)],[f_28_5]) ).
cnf(f_28_7,plain,
( aElement0(sK14(U_84,U_83))
| ~ sP24(U_83,U_84) ),
inference(clausify,[status(thm)],[f_28_5]) ).
cnf(f_28_8,plain,
( ~ aElementOf0(sK14(U_84,U_83),sdtpldt1(U_84,U_83))
| ~ sP24(U_83,U_84) ),
inference(clausify,[status(thm)],[f_28_5]) ).
cnf(f_28_9,plain,
( aElement0(sK15(U_84,U_83,U_82,U_81))
| ~ sP25(U_83,U_82,U_81,U_84) ),
inference(clausify,[status(thm)],[f_28_5]) ).
cnf(f_28_10,plain,
( sdteqdtlpzmzozddtrp0(sK15(U_84,U_83,U_82,U_81),U_82,U_84)
| ~ sP25(U_83,U_82,U_81,U_84) ),
inference(clausify,[status(thm)],[f_28_5]) ).
cnf(f_28_11,plain,
( sdteqdtlpzmzozddtrp0(sK15(U_84,U_83,U_82,U_81),U_81,U_83)
| ~ sP25(U_83,U_82,U_81,U_84) ),
inference(clausify,[status(thm)],[f_28_5]) ).
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]) ).
fof(f_29_4,plain,
! [U_85] :
( ~ aNaturalNumber0(U_85)
| $true ),
inference(definitional_conversion,[status(esa)],[f_29_3]) ).
cnf(f_29_5,plain,
( ~ aNaturalNumber0(U_85)
| $true ),
inference(clausify,[status(thm)],[f_29_4]) ).
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]) ).
fof(f_30_3,plain,
! [U_86] :
( aNaturalNumber0(sbrdtbr0(U_86))
| U_86 = sz00
| ~ aElement0(U_86) ),
inference(definitional_conversion,[status(esa)],[f_30_2]) ).
cnf(f_30_4,plain,
( aNaturalNumber0(sbrdtbr0(U_86))
| U_86 = sz00
| ~ aElement0(U_86) ),
inference(clausify,[status(thm)],[f_30_3]) ).
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]) ).
fof(f_31_3,plain,
! [U_88,U_87] :
( $true
| ~ iLess0(U_88,U_87)
| ~ aNaturalNumber0(U_87)
| ~ aNaturalNumber0(U_88) ),
inference(definitional_conversion,[status(esa)],[f_31_2]) ).
cnf(f_31_4,plain,
( $true
| ~ iLess0(U_88,U_87)
| ~ aNaturalNumber0(U_87)
| ~ aNaturalNumber0(U_88) ),
inference(clausify,[status(thm)],[f_31_3]) ).
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]) ).
fof(f_32_6,plain,
( ! [U_92,U_91] :
( iLess0(sbrdtbr0(sK17(U_92,U_91)),sbrdtbr0(U_91))
| sK17(U_92,U_91) = sz00
| ~ sP26(U_92,U_91) )
& ! [U_92,U_91] :
( U_92 = sdtpldt0(sdtasdt0(sK16(U_92,U_91),U_91),sK17(U_92,U_91))
| ~ sP26(U_92,U_91) )
& ! [U_92,U_91] :
( aElement0(sK17(U_92,U_91))
| ~ sP26(U_92,U_91) )
& ! [U_92,U_91] :
( aElement0(sK16(U_92,U_91))
| ~ sP26(U_92,U_91) )
& ! [U_92,U_91] :
( sP26(U_92,U_91)
| U_91 = sz00
| ~ aElement0(U_91)
| ~ aElement0(U_92) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP26])],[f_32_5]) ).
cnf(f_32_7,plain,
( sP26(U_92,U_91)
| U_91 = sz00
| ~ aElement0(U_91)
| ~ aElement0(U_92) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_8,plain,
( aElement0(sK16(U_92,U_91))
| ~ sP26(U_92,U_91) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_9,plain,
( aElement0(sK17(U_92,U_91))
| ~ sP26(U_92,U_91) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_10,plain,
( U_92 = sdtpldt0(sdtasdt0(sK16(U_92,U_91),U_91),sK17(U_92,U_91))
| ~ sP26(U_92,U_91) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_11,plain,
( iLess0(sbrdtbr0(sK17(U_92,U_91)),sbrdtbr0(U_91))
| sK17(U_92,U_91) = sz00
| ~ sP26(U_92,U_91) ),
inference(clausify,[status(thm)],[f_32_6]) ).
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]) ).
fof(f_33_4,plain,
( ! [U_95,U_96] :
( sdtasdt0(U_96,sK18(U_96,U_95)) = U_95
| ~ sP27(U_95,U_96) )
& ! [U_95,U_96] :
( aElement0(sK18(U_96,U_95))
| ~ sP27(U_95,U_96) )
& ! [U_95,U_94,U_96] :
( doDivides0(U_96,U_95)
| sdtasdt0(U_96,U_94) != U_95
| ~ aElement0(U_94)
| ~ sP28(U_95,U_94,U_96) )
& ! [U_95,U_94,U_96] :
( sP27(U_95,U_96)
| ~ doDivides0(U_96,U_95)
| ~ sP28(U_95,U_94,U_96) )
& ! [U_95,U_94,U_96] :
( sP28(U_95,U_94,U_96)
| ~ aElement0(U_95)
| ~ aElement0(U_96) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP27,sP28])],[f_33_3]) ).
cnf(f_33_5,plain,
( sP28(U_95,U_94,U_96)
| ~ aElement0(U_95)
| ~ aElement0(U_96) ),
inference(clausify,[status(thm)],[f_33_4]) ).
cnf(f_33_6,plain,
( sP27(U_95,U_96)
| ~ doDivides0(U_96,U_95)
| ~ sP28(U_95,U_94,U_96) ),
inference(clausify,[status(thm)],[f_33_4]) ).
cnf(f_33_7,plain,
( doDivides0(U_96,U_95)
| sdtasdt0(U_96,U_94) != U_95
| ~ aElement0(U_94)
| ~ sP28(U_95,U_94,U_96) ),
inference(clausify,[status(thm)],[f_33_4]) ).
cnf(f_33_8,plain,
( aElement0(sK18(U_96,U_95))
| ~ sP27(U_95,U_96) ),
inference(clausify,[status(thm)],[f_33_4]) ).
cnf(f_33_9,plain,
( sdtasdt0(U_96,sK18(U_96,U_95)) = U_95
| ~ sP27(U_95,U_96) ),
inference(clausify,[status(thm)],[f_33_4]) ).
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]) ).
fof(f_34_4,plain,
( ! [U_99,U_98] :
( doDivides0(U_99,U_98)
| ~ sP29(U_99,U_98) )
& ! [U_99,U_98] :
( aElement0(U_99)
| ~ sP29(U_99,U_98) )
& ! [U_100,U_99,U_98] :
( aDivisorOf0(U_100,U_98)
| ~ doDivides0(U_100,U_98)
| ~ aElement0(U_100)
| ~ sP30(U_100,U_99,U_98) )
& ! [U_100,U_99,U_98] :
( sP29(U_99,U_98)
| ~ aDivisorOf0(U_99,U_98)
| ~ sP30(U_100,U_99,U_98) )
& ! [U_100,U_99,U_98] :
( sP30(U_100,U_99,U_98)
| ~ aElement0(U_98) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP29,sP30])],[f_34_3]) ).
cnf(f_34_5,plain,
( sP30(U_100,U_99,U_98)
| ~ aElement0(U_98) ),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_6,plain,
( sP29(U_99,U_98)
| ~ aDivisorOf0(U_99,U_98)
| ~ sP30(U_100,U_99,U_98) ),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_7,plain,
( aDivisorOf0(U_100,U_98)
| ~ doDivides0(U_100,U_98)
| ~ aElement0(U_100)
| ~ sP30(U_100,U_99,U_98) ),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_8,plain,
( aElement0(U_99)
| ~ sP29(U_99,U_98) ),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_9,plain,
( doDivides0(U_99,U_98)
| ~ sP29(U_99,U_98) ),
inference(clausify,[status(thm)],[f_34_4]) ).
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]) ).
fof(f_35_5,plain,
( ! [U_105,U_104,U_107] :
( ~ doDivides0(sK19(U_105,U_104,U_107),U_107)
| ~ sP32(U_105,U_104,U_107) )
& ! [U_105,U_104,U_107] :
( aDivisorOf0(sK19(U_105,U_104,U_107),U_104)
| ~ sP32(U_105,U_104,U_107) )
& ! [U_105,U_104,U_107] :
( aDivisorOf0(sK19(U_105,U_104,U_107),U_105)
| ~ sP32(U_105,U_104,U_107) )
& ! [U_105,U_106,U_104,U_101] :
( doDivides0(U_101,U_106)
| ~ aDivisorOf0(U_101,U_104)
| ~ aDivisorOf0(U_101,U_105)
| ~ sP31(U_105,U_106,U_104,U_101) )
& ! [U_105,U_106,U_104,U_101] :
( aDivisorOf0(U_106,U_104)
| ~ sP31(U_105,U_106,U_104,U_101) )
& ! [U_105,U_106,U_104,U_101] :
( aDivisorOf0(U_106,U_105)
| ~ sP31(U_105,U_106,U_104,U_101) )
& ! [U_105,U_106,U_104,U_101,U_107] :
( aGcdOfAnd0(U_107,U_105,U_104)
| sP32(U_105,U_104,U_107)
| ~ aDivisorOf0(U_107,U_104)
| ~ aDivisorOf0(U_107,U_105)
| ~ sP33(U_105,U_106,U_104,U_101,U_107) )
& ! [U_105,U_106,U_104,U_101,U_107] :
( sP31(U_105,U_106,U_104,U_101)
| ~ aGcdOfAnd0(U_106,U_105,U_104)
| ~ sP33(U_105,U_106,U_104,U_101,U_107) )
& ! [U_105,U_106,U_104,U_101,U_107] :
( sP33(U_105,U_106,U_104,U_101,U_107)
| ~ aElement0(U_104)
| ~ aElement0(U_105) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP31,sP32,sP33])],[f_35_4]) ).
cnf(f_35_6,plain,
( sP33(U_105,U_106,U_104,U_101,U_107)
| ~ aElement0(U_104)
| ~ aElement0(U_105) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_7,plain,
( sP31(U_105,U_106,U_104,U_101)
| ~ aGcdOfAnd0(U_106,U_105,U_104)
| ~ sP33(U_105,U_106,U_104,U_101,U_107) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_8,plain,
( aGcdOfAnd0(U_107,U_105,U_104)
| sP32(U_105,U_104,U_107)
| ~ aDivisorOf0(U_107,U_104)
| ~ aDivisorOf0(U_107,U_105)
| ~ sP33(U_105,U_106,U_104,U_101,U_107) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_9,plain,
( aDivisorOf0(U_106,U_105)
| ~ sP31(U_105,U_106,U_104,U_101) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_10,plain,
( aDivisorOf0(U_106,U_104)
| ~ sP31(U_105,U_106,U_104,U_101) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_11,plain,
( doDivides0(U_101,U_106)
| ~ aDivisorOf0(U_101,U_104)
| ~ aDivisorOf0(U_101,U_105)
| ~ sP31(U_105,U_106,U_104,U_101) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_12,plain,
( aDivisorOf0(sK19(U_105,U_104,U_107),U_105)
| ~ sP32(U_105,U_104,U_107) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_13,plain,
( aDivisorOf0(sK19(U_105,U_104,U_107),U_104)
| ~ sP32(U_105,U_104,U_107) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_14,plain,
( ~ doDivides0(sK19(U_105,U_104,U_107),U_107)
| ~ sP32(U_105,U_104,U_107) ),
inference(clausify,[status(thm)],[f_35_5]) ).
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]) ).
fof(f_36_3,plain,
( ! [U_108,U_109] :
( misRelativelyPrime0(U_109,U_108)
| ~ aGcdOfAnd0(sz10,U_109,U_108)
| ~ sP34(U_108,U_109) )
& ! [U_108,U_109] :
( aGcdOfAnd0(sz10,U_109,U_108)
| ~ misRelativelyPrime0(U_109,U_108)
| ~ sP34(U_108,U_109) )
& ! [U_108,U_109] :
( sP34(U_108,U_109)
| ~ aElement0(U_108)
| ~ aElement0(U_109) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP34])],[f_36_2]) ).
cnf(f_36_4,plain,
( sP34(U_108,U_109)
| ~ aElement0(U_108)
| ~ aElement0(U_109) ),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_36_5,plain,
( aGcdOfAnd0(sz10,U_109,U_108)
| ~ misRelativelyPrime0(U_109,U_108)
| ~ sP34(U_108,U_109) ),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_36_6,plain,
( misRelativelyPrime0(U_109,U_108)
| ~ aGcdOfAnd0(sz10,U_109,U_108)
| ~ sP34(U_108,U_109) ),
inference(clausify,[status(thm)],[f_36_3]) ).
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]) ).
fof(f_37_8,plain,
( ! [U_117,U_123] :
( ~ aElementOf0(sK22(U_117,U_123),U_123)
| ~ sP38(U_117,U_123) )
& ! [U_117,U_123] :
( sdtasdt0(U_117,sK23(U_117,U_123)) = sK22(U_117,U_123)
| ~ sP38(U_117,U_123) )
& ! [U_117,U_123] :
( aElement0(sK23(U_117,U_123))
| ~ sP38(U_117,U_123) )
& ! [U_117,U_113,U_123] :
( sdtasdt0(U_117,U_113) != sK21(U_117,U_123)
| ~ aElement0(U_113)
| ~ sP37(U_117,U_113,U_123) )
& ! [U_117,U_113,U_123] :
( aElementOf0(sK21(U_117,U_123),U_123)
| ~ sP37(U_117,U_113,U_123) )
& ! [U_117,U_118,U_122] :
( sdtasdt0(U_117,sK20(U_117,U_122,U_118)) = U_118
| ~ sP35(U_117,U_118,U_122) )
& ! [U_117,U_118,U_122] :
( aElement0(sK20(U_117,U_122,U_118))
| ~ sP35(U_117,U_118,U_122) )
& ! [U_111,U_117,U_118,U_119,U_122] :
( aElementOf0(U_119,U_122)
| sdtasdt0(U_117,U_111) != U_119
| ~ aElement0(U_111)
| ~ sP36(U_111,U_117,U_118,U_119,U_122) )
& ! [U_111,U_117,U_118,U_119,U_122] :
( sP35(U_117,U_118,U_122)
| ~ aElementOf0(U_118,U_122)
| ~ sP36(U_111,U_117,U_118,U_119,U_122) )
& ! [U_111,U_117,U_118,U_119,U_122] :
( aSet0(U_122)
| ~ sP36(U_111,U_117,U_118,U_119,U_122) )
& ! [U_111,U_117,U_118,U_119,U_113,U_122,U_123] :
( U_123 = slsdtgt0(U_117)
| sP38(U_117,U_123)
| sP37(U_117,U_113,U_123)
| ~ aSet0(U_123)
| ~ sP39(U_111,U_117,U_118,U_119,U_113,U_122,U_123) )
& ! [U_111,U_117,U_118,U_119,U_113,U_122,U_123] :
( sP36(U_111,U_117,U_118,U_119,U_122)
| U_122 != slsdtgt0(U_117)
| ~ sP39(U_111,U_117,U_118,U_119,U_113,U_122,U_123) )
& ! [U_111,U_117,U_118,U_119,U_113,U_122,U_123] :
( sP39(U_111,U_117,U_118,U_119,U_113,U_122,U_123)
| ~ aElement0(U_117) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP35,sP36,sP37,sP38,sP39])],[f_37_7]) ).
cnf(f_37_9,plain,
( sP39(U_111,U_117,U_118,U_119,U_113,U_122,U_123)
| ~ aElement0(U_117) ),
inference(clausify,[status(thm)],[f_37_8]) ).
cnf(f_37_10,plain,
( sP36(U_111,U_117,U_118,U_119,U_122)
| U_122 != slsdtgt0(U_117)
| ~ sP39(U_111,U_117,U_118,U_119,U_113,U_122,U_123) ),
inference(clausify,[status(thm)],[f_37_8]) ).
cnf(f_37_11,plain,
( U_123 = slsdtgt0(U_117)
| sP38(U_117,U_123)
| sP37(U_117,U_113,U_123)
| ~ aSet0(U_123)
| ~ sP39(U_111,U_117,U_118,U_119,U_113,U_122,U_123) ),
inference(clausify,[status(thm)],[f_37_8]) ).
cnf(f_37_12,plain,
( aSet0(U_122)
| ~ sP36(U_111,U_117,U_118,U_119,U_122) ),
inference(clausify,[status(thm)],[f_37_8]) ).
cnf(f_37_13,plain,
( sP35(U_117,U_118,U_122)
| ~ aElementOf0(U_118,U_122)
| ~ sP36(U_111,U_117,U_118,U_119,U_122) ),
inference(clausify,[status(thm)],[f_37_8]) ).
cnf(f_37_14,plain,
( aElementOf0(U_119,U_122)
| sdtasdt0(U_117,U_111) != U_119
| ~ aElement0(U_111)
| ~ sP36(U_111,U_117,U_118,U_119,U_122) ),
inference(clausify,[status(thm)],[f_37_8]) ).
cnf(f_37_15,plain,
( aElement0(sK20(U_117,U_122,U_118))
| ~ sP35(U_117,U_118,U_122) ),
inference(clausify,[status(thm)],[f_37_8]) ).
cnf(f_37_16,plain,
( sdtasdt0(U_117,sK20(U_117,U_122,U_118)) = U_118
| ~ sP35(U_117,U_118,U_122) ),
inference(clausify,[status(thm)],[f_37_8]) ).
cnf(f_37_17,plain,
( aElementOf0(sK21(U_117,U_123),U_123)
| ~ sP37(U_117,U_113,U_123) ),
inference(clausify,[status(thm)],[f_37_8]) ).
cnf(f_37_18,plain,
( sdtasdt0(U_117,U_113) != sK21(U_117,U_123)
| ~ aElement0(U_113)
| ~ sP37(U_117,U_113,U_123) ),
inference(clausify,[status(thm)],[f_37_8]) ).
cnf(f_37_19,plain,
( aElement0(sK23(U_117,U_123))
| ~ sP38(U_117,U_123) ),
inference(clausify,[status(thm)],[f_37_8]) ).
cnf(f_37_20,plain,
( sdtasdt0(U_117,sK23(U_117,U_123)) = sK22(U_117,U_123)
| ~ sP38(U_117,U_123) ),
inference(clausify,[status(thm)],[f_37_8]) ).
cnf(f_37_21,plain,
( ~ aElementOf0(sK22(U_117,U_123),U_123)
| ~ sP38(U_117,U_123) ),
inference(clausify,[status(thm)],[f_37_8]) ).
fof(f_38_1,plain,
aElement0(xc),
inference(fof_nnf,[status(thm)],[m__1905]) ).
fof(f_38_2,plain,
aElement0(xc),
inference(definitional_conversion,[status(esa)],[f_38_1]) ).
cnf(f_38_3,plain,
aElement0(xc),
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_1,plain,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& ? [W0] :
( sdtasdt0(xc,W0) = xy
& aElement0(W0) )
& aElementOf0(xx,slsdtgt0(xc))
& ? [W0] :
( sdtasdt0(xc,W0) = xx
& aElement0(W0) ) ),
inference(fof_nnf,[status(thm)],[m__1933]) ).
fof(f_39_2,plain,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& ? [U_125] :
( sdtasdt0(xc,U_125) = xy
& aElement0(U_125) )
& aElementOf0(xx,slsdtgt0(xc))
& ? [U_124] :
( sdtasdt0(xc,U_124) = xx
& aElement0(U_124) ) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& ? [U_125] :
( sdtasdt0(xc,U_125) = xy
& aElement0(U_125) )
& aElementOf0(xx,slsdtgt0(xc))
& sdtasdt0(xc,sK24) = xx
& aElement0(sK24) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_124,sK24)],[f_39_2]) ).
fof(f_39_4,plain,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& sdtasdt0(xc,sK25) = xy
& aElement0(sK25)
& aElementOf0(xx,slsdtgt0(xc))
& sdtasdt0(xc,sK24) = xx
& aElement0(sK24) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_125,sK25)],[f_39_3]) ).
fof(f_39_5,plain,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& sdtasdt0(xc,sK25) = xy
& aElement0(sK25)
& aElementOf0(xx,slsdtgt0(xc))
& sdtasdt0(xc,sK24) = xx
& aElement0(sK24) ),
inference(definitional_conversion,[status(esa)],[f_39_4]) ).
cnf(f_39_6,plain,
aElement0(sK24),
inference(clausify,[status(thm)],[f_39_5]) ).
cnf(f_39_7,plain,
sdtasdt0(xc,sK24) = xx,
inference(clausify,[status(thm)],[f_39_5]) ).
cnf(f_39_8,plain,
aElementOf0(xx,slsdtgt0(xc)),
inference(clausify,[status(thm)],[f_39_5]) ).
cnf(f_39_9,plain,
aElement0(sK25),
inference(clausify,[status(thm)],[f_39_5]) ).
cnf(f_39_10,plain,
sdtasdt0(xc,sK25) = xy,
inference(clausify,[status(thm)],[f_39_5]) ).
cnf(f_39_11,plain,
aElementOf0(xy,slsdtgt0(xc)),
inference(clausify,[status(thm)],[f_39_5]) ).
cnf(f_39_12,plain,
aElement0(xz),
inference(clausify,[status(thm)],[f_39_5]) ).
fof(f_40_1,plain,
( sdtasdt0(xc,xu) = xx
& aElement0(xu) ),
inference(fof_nnf,[status(thm)],[m__1956]) ).
fof(f_40_2,plain,
( sdtasdt0(xc,xu) = xx
& aElement0(xu) ),
inference(definitional_conversion,[status(esa)],[f_40_1]) ).
cnf(f_40_3,plain,
aElement0(xu),
inference(clausify,[status(thm)],[f_40_2]) ).
cnf(f_40_4,plain,
sdtasdt0(xc,xu) = xx,
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_1,plain,
( sdtasdt0(xc,xv) = xy
& aElement0(xv) ),
inference(fof_nnf,[status(thm)],[m__1979]) ).
fof(f_41_2,plain,
( sdtasdt0(xc,xv) = xy
& aElement0(xv) ),
inference(definitional_conversion,[status(esa)],[f_41_1]) ).
cnf(f_41_3,plain,
aElement0(xv),
inference(clausify,[status(thm)],[f_41_2]) ).
cnf(f_41_4,plain,
sdtasdt0(xc,xv) = xy,
inference(clausify,[status(thm)],[f_41_2]) ).
fof(f_42_1,negated_conjecture,
sdtpldt0(xx,xy) != sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(negate,[status(cth)],[m__]) ).
fof(f_42_2,negated_conjecture,
sdtpldt0(xx,xy) != sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(definitional_conversion,[status(esa)],[f_42_1]) ).
cnf(f_42_3,negated_conjecture,
sdtpldt0(xx,xy) != sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(clausify,[status(thm)],[f_42_2]) ).
cnf(f_1_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1_5]) ).
cnf(f_19_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_19_5]) ).
cnf(f_29_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_29_5]) ).
cnf(f_31_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_31_4]) ).
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,
( aElement0(Eq_y_0)
| ~ aElement0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_35,axiom,
( aSet0(Eq_y_0)
| ~ aSet0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_36,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_37,axiom,
( aIdeal0(Eq_y_0)
| ~ aIdeal0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_38,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_39,axiom,
( aNaturalNumber0(Eq_y_0)
| ~ aNaturalNumber0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_40,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_41,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_42,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_43,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_44,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(equality_45,axiom,
( sP0(Eq_y_0)
| ~ sP0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_46,axiom,
( sP1(Eq_y_0)
| ~ sP1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_47,axiom,
( sP2(Eq_y_0)
| ~ sP2(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_48,axiom,
( sP3(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP3(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_49,axiom,
( sP4(Eq_y_0)
| ~ sP4(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_50,axiom,
( sP5(Eq_y_0)
| ~ sP5(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_51,axiom,
( sP6(Eq_y_0,Eq_y_1)
| ~ sP6(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_52,axiom,
( sP7(Eq_y_0,Eq_y_1)
| ~ sP7(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_53,axiom,
( sP8(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP8(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_54,axiom,
( sP9(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP9(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(equality_55,axiom,
( sP10(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP10(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(equality_56,axiom,
( sP11(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP11(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,
( sP12(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8,Eq_y_9)
| ~ sP12(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8,Eq_x_9)
| Eq_x_9 != Eq_y_9
| Eq_x_8 != Eq_y_8
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(equality_58,axiom,
( sP13(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP13(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_59,axiom,
( sP14(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP14(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(equality_60,axiom,
( sP15(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP15(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_61,axiom,
( sP16(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP16(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_62,axiom,
( sP17(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP17(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(equality_63,axiom,
( sP18(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP18(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_64,axiom,
( sP19(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP19(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_65,axiom,
( sP20(Eq_y_0)
| ~ sP20(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_66,axiom,
( sP21(Eq_y_0)
| ~ sP21(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_67,axiom,
( sP22(Eq_y_0)
| ~ sP22(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_68,axiom,
( sP23(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP23(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_69,axiom,
( sP24(Eq_y_0,Eq_y_1)
| ~ sP24(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_70,axiom,
( sP25(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP25(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_71,axiom,
( sP26(Eq_y_0,Eq_y_1)
| ~ sP26(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_72,axiom,
( sP27(Eq_y_0,Eq_y_1)
| ~ sP27(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_73,axiom,
( sP28(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP28(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_74,axiom,
( sP29(Eq_y_0,Eq_y_1)
| ~ sP29(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_75,axiom,
( sP30(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP30(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_76,axiom,
( sP31(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP31(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_77,axiom,
( sP32(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP32(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_78,axiom,
( sP33(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP33(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(equality_79,axiom,
( sP34(Eq_y_0,Eq_y_1)
| ~ sP34(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_80,axiom,
( sP35(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP35(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_81,axiom,
( sP36(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP36(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(equality_82,axiom,
( sP37(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP37(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_83,axiom,
( sP38(Eq_y_0,Eq_y_1)
| ~ sP38(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_84,axiom,
( sP39(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP39(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : RNG103+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.01 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.02 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.29 % Computer : n012.cluster.edu
% 0.04/0.29 % Model : x86_64 x86_64
% 0.04/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.29 % Memory : 8046.5625MB
% 0.04/0.29 % OS : Linux 6.8.0-71-generic
% 0.04/0.29 % CPULimit : 300
% 0.04/0.29 % WCLimit : 300
% 0.04/0.29 % DateTime : Sat Sep 19 20:54:37 UTC 2026
% 0.04/0.29 % CPUTime :
% 35.65/35.98 % SZS status Theorem for theBenchmark
% 35.65/35.98 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------