%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : RNG073+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 : n019.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 08:55:05 AM UTC 2026
% Result : Theorem 30.46s 30.78s
% Output : Proof 30.56s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(mNatSort,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> $true ),
file('theBenchmark.p',mNatSort) ).
fof(mZeroNat,axiom,
aNaturalNumber0(sz00),
file('theBenchmark.p',mZeroNat) ).
fof(mSuccNat,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( szszuzczcdt0(W0) != sz00
& aNaturalNumber0(szszuzczcdt0(W0)) ) ),
file('theBenchmark.p',mSuccNat) ).
fof(mNatExtr,axiom,
! [W0] :
( ( W0 != sz00
& aNaturalNumber0(W0) )
=> ? [W1] :
( W0 = szszuzczcdt0(W1)
& aNaturalNumber0(W1) ) ),
file('theBenchmark.p',mNatExtr) ).
fof(mSuccEqu,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( szszuzczcdt0(W0) = szszuzczcdt0(W1)
=> W0 = W1 ) ),
file('theBenchmark.p',mSuccEqu) ).
fof(mIHOrd,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( iLess0(W0,W1)
=> $true ) ),
file('theBenchmark.p',mIHOrd) ).
fof(mIH,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> iLess0(W0,szszuzczcdt0(W0)) ),
file('theBenchmark.p',mIH) ).
fof(mScSort,axiom,
! [W0] :
( aScalar0(W0)
=> $true ),
file('theBenchmark.p',mScSort) ).
fof(mSZeroSc,axiom,
aScalar0(sz0z00),
file('theBenchmark.p',mSZeroSc) ).
fof(mSumSc,axiom,
! [W0,W1] :
( ( aScalar0(W1)
& aScalar0(W0) )
=> aScalar0(sdtpldt0(W0,W1)) ),
file('theBenchmark.p',mSumSc) ).
fof(mMulSc,axiom,
! [W0,W1] :
( ( aScalar0(W1)
& aScalar0(W0) )
=> aScalar0(sdtasdt0(W0,W1)) ),
file('theBenchmark.p',mMulSc) ).
fof(mNegSc,axiom,
! [W0] :
( aScalar0(W0)
=> aScalar0(smndt0(W0)) ),
file('theBenchmark.p',mNegSc) ).
fof(mScZero,axiom,
! [W0] :
( aScalar0(W0)
=> ( smndt0(sz0z00) = sz0z00
& smndt0(smndt0(W0)) = W0
& sdtpldt0(smndt0(W0),W0) = sz0z00
& sdtpldt0(W0,smndt0(W0)) = sz0z00
& sdtasdt0(sz0z00,W0) = sz0z00
& sdtasdt0(W0,sz0z00) = sz0z00
& sdtpldt0(sz0z00,W0) = W0
& sdtpldt0(W0,sz0z00) = W0 ) ),
file('theBenchmark.p',mScZero) ).
fof(mArith,axiom,
! [W0,W1,W2] :
( ( aScalar0(W2)
& aScalar0(W1)
& aScalar0(W0) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0)
& sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2))
& sdtpldt0(W0,W1) = sdtpldt0(W1,W0)
& sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ),
file('theBenchmark.p',mArith) ).
fof(mDistr,axiom,
! [W0,W1,W2] :
( ( aScalar0(W2)
& aScalar0(W1)
& aScalar0(W0) )
=> ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) ) ),
file('theBenchmark.p',mDistr) ).
fof(mDistr2,axiom,
! [W0,W1,W2,W3] :
( ( aScalar0(W3)
& aScalar0(W2)
& aScalar0(W1)
& aScalar0(W0) )
=> sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) ),
file('theBenchmark.p',mDistr2) ).
fof(mMNeg,axiom,
! [W0,W1] :
( ( aScalar0(W1)
& aScalar0(W0) )
=> ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1))
& sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) ) ),
file('theBenchmark.p',mMNeg) ).
fof(mMDNeg,axiom,
! [W0,W1] :
( ( aScalar0(W1)
& aScalar0(W0) )
=> sdtasdt0(smndt0(W0),smndt0(W1)) = sdtasdt0(W0,W1) ),
file('theBenchmark.p',mMDNeg) ).
fof(mLess,axiom,
! [W0,W1] :
( ( aScalar0(W1)
& aScalar0(W0) )
=> ( sdtlseqdt0(W0,W1)
=> $true ) ),
file('theBenchmark.p',mLess) ).
fof(mLERef,axiom,
! [W0] :
( aScalar0(W0)
=> sdtlseqdt0(W0,W0) ),
file('theBenchmark.p',mLERef) ).
fof(mLEASm,axiom,
! [W0,W1] :
( ( aScalar0(W1)
& aScalar0(W0) )
=> ( ( sdtlseqdt0(W1,W0)
& sdtlseqdt0(W0,W1) )
=> W0 = W1 ) ),
file('theBenchmark.p',mLEASm) ).
fof(mLETrn,axiom,
! [W0,W1,W2] :
( ( aScalar0(W2)
& aScalar0(W1)
& aScalar0(W0) )
=> ( ( sdtlseqdt0(W1,W2)
& sdtlseqdt0(W0,W1) )
=> sdtlseqdt0(W0,W2) ) ),
file('theBenchmark.p',mLETrn) ).
fof(mLEMon,axiom,
! [W0,W1,W2,W3] :
( ( aScalar0(W3)
& aScalar0(W2)
& aScalar0(W1)
& aScalar0(W0) )
=> ( ( sdtlseqdt0(W2,W3)
& sdtlseqdt0(W0,W1) )
=> sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3)) ) ),
file('theBenchmark.p',mLEMon) ).
fof(mLEMonM,axiom,
! [W0,W1,W2,W3] :
( ( aScalar0(W3)
& aScalar0(W2)
& aScalar0(W1)
& aScalar0(W0) )
=> ( ( sdtlseqdt0(W2,W3)
& sdtlseqdt0(sz0z00,W2)
& sdtlseqdt0(W0,W1) )
=> sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3)) ) ),
file('theBenchmark.p',mLEMonM) ).
fof(mLETot,axiom,
! [W0,W1] :
( ( aScalar0(W1)
& aScalar0(W0) )
=> ( sdtlseqdt0(W1,W0)
| sdtlseqdt0(W0,W1) ) ),
file('theBenchmark.p',mLETot) ).
fof(mPosMon,axiom,
! [W0,W1] :
( ( aScalar0(W1)
& aScalar0(W0) )
=> ( ( sdtlseqdt0(sz0z00,W1)
& sdtlseqdt0(sz0z00,W0) )
=> ( sdtlseqdt0(sz0z00,sdtasdt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtpldt0(W0,W1)) ) ) ),
file('theBenchmark.p',mPosMon) ).
fof(mSqPos,axiom,
! [W0] :
( aScalar0(W0)
=> sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) ),
file('theBenchmark.p',mSqPos) ).
fof(mSqrt,axiom,
! [W0,W1] :
( ( aScalar0(W1)
& aScalar0(W0) )
=> ( ( sdtasdt0(W0,W0) = sdtasdt0(W1,W1)
& sdtlseqdt0(sz0z00,W1)
& sdtlseqdt0(sz0z00,W0) )
=> W0 = W1 ) ),
file('theBenchmark.p',mSqrt) ).
fof(mVcSort,axiom,
! [W0] :
( aVector0(W0)
=> $true ),
file('theBenchmark.p',mVcSort) ).
fof(mDimNat,axiom,
! [W0] :
( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) ),
file('theBenchmark.p',mDimNat) ).
fof(mElmSc,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aVector0(W0) )
=> aScalar0(sdtlbdtrb0(W0,W1)) ),
file('theBenchmark.p',mElmSc) ).
fof(mDefInit,definition,
! [W0] :
( aVector0(W0)
=> ( aDimensionOf0(W0) != sz00
=> ! [W1] :
( W1 = sziznziztdt0(W0)
<=> ( ! [W2] :
( aNaturalNumber0(W2)
=> sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) )
& szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0)
& aVector0(W1) ) ) ) ),
file('theBenchmark.p',mDefInit) ).
fof(mEqInit,axiom,
! [W0,W1] :
( ( aVector0(W1)
& aVector0(W0) )
=> ( ( aDimensionOf0(W1) != sz00
& aDimensionOf0(W0) = aDimensionOf0(W1) )
=> aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) ) ),
file('theBenchmark.p',mEqInit) ).
fof(mScPr,axiom,
! [W0,W1] :
( ( aVector0(W1)
& aVector0(W0) )
=> ( aDimensionOf0(W0) = aDimensionOf0(W1)
=> aScalar0(sdtasasdt0(W0,W1)) ) ),
file('theBenchmark.p',mScPr) ).
fof(mDefSPZ,axiom,
! [W0,W1] :
( ( aVector0(W1)
& aVector0(W0) )
=> ( ( aDimensionOf0(W1) = sz00
& aDimensionOf0(W0) = aDimensionOf0(W1) )
=> sdtasasdt0(W0,W1) = sz0z00 ) ),
file('theBenchmark.p',mDefSPZ) ).
fof(mDefSPN,axiom,
! [W0,W1] :
( ( aVector0(W1)
& aVector0(W0) )
=> ( ( aDimensionOf0(W1) != sz00
& aDimensionOf0(W0) = aDimensionOf0(W1) )
=> sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) ) ),
file('theBenchmark.p',mDefSPN) ).
fof(mScSqPos,axiom,
! [W0] :
( aVector0(W0)
=> sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ),
file('theBenchmark.p',mScSqPos) ).
fof(m__1678,hypothesis,
( aVector0(xt)
& aVector0(xs) ),
file('theBenchmark.p',m__1678) ).
fof(m__1652,hypothesis,
! [W0,W1] :
( ( aVector0(W1)
& aVector0(W0) )
=> ( aDimensionOf0(W0) = aDimensionOf0(W1)
=> ( iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
=> sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1))) ) ) ),
file('theBenchmark.p',m__1652) ).
fof(m__1678_01,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
file('theBenchmark.p',m__1678_01) ).
fof(m__1692,hypothesis,
aDimensionOf0(xs) != sz00,
file('theBenchmark.p',m__1692) ).
fof(m__1709,hypothesis,
( xp = sziznziztdt0(xs)
& ! [W0] :
( aNaturalNumber0(W0)
=> sdtlbdtrb0(xp,W0) = sdtlbdtrb0(xs,W0) )
& szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs)
& aVector0(xp) ),
file('theBenchmark.p',m__1709) ).
fof(m__1726,hypothesis,
( xq = sziznziztdt0(xt)
& ! [W0] :
( aNaturalNumber0(W0)
=> sdtlbdtrb0(xq,W0) = sdtlbdtrb0(xt,W0) )
& szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt)
& aVector0(xq) ),
file('theBenchmark.p',m__1726) ).
fof(m__1746,hypothesis,
( xA = sdtlbdtrb0(xs,aDimensionOf0(xs))
& aScalar0(xA) ),
file('theBenchmark.p',m__1746) ).
fof(m__1766,hypothesis,
( xB = sdtlbdtrb0(xt,aDimensionOf0(xt))
& aScalar0(xB) ),
file('theBenchmark.p',m__1766) ).
fof(m__1783,hypothesis,
( xC = sdtasasdt0(xp,xp)
& aScalar0(xC) ),
file('theBenchmark.p',m__1783) ).
fof(m__1800,hypothesis,
( xD = sdtasasdt0(xq,xq)
& aScalar0(xD) ),
file('theBenchmark.p',m__1800) ).
fof(m__1820,hypothesis,
( xE = sdtasasdt0(xp,xq)
& aScalar0(xE) ),
file('theBenchmark.p',m__1820) ).
fof(m__1837,hypothesis,
( xF = sdtasdt0(xA,xA)
& aScalar0(xF) ),
file('theBenchmark.p',m__1837) ).
fof(m__1854,hypothesis,
( xG = sdtasdt0(xB,xB)
& aScalar0(xG) ),
file('theBenchmark.p',m__1854) ).
fof(m__1873,hypothesis,
( xH = sdtasdt0(xA,xB)
& aScalar0(xH) ),
file('theBenchmark.p',m__1873) ).
fof(m__1892,hypothesis,
( xR = sdtasdt0(xC,xG)
& aScalar0(xR) ),
file('theBenchmark.p',m__1892) ).
fof(m__1911,hypothesis,
( xP = sdtasdt0(xE,xH)
& aScalar0(xP) ),
file('theBenchmark.p',m__1911) ).
fof(m__1930,hypothesis,
( xS = sdtasdt0(xF,xD)
& aScalar0(xS) ),
file('theBenchmark.p',m__1930) ).
fof(m__1949,hypothesis,
( xN = sdtasdt0(xR,xS)
& aScalar0(xN) ),
file('theBenchmark.p',m__1949) ).
fof(m__1967,hypothesis,
sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
file('theBenchmark.p',m__1967) ).
fof(m__2004,hypothesis,
sdtlseqdt0(sdtasdt0(xP,xP),xN),
file('theBenchmark.p',m__2004) ).
fof(m__2104,hypothesis,
sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
file('theBenchmark.p',m__2104) ).
fof(m__2405,hypothesis,
sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
file('theBenchmark.p',m__2405) ).
fof(m__2590,hypothesis,
~ sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)),
file('theBenchmark.p',m__2590) ).
fof(m__2610,hypothesis,
sdtlseqdt0(sdtpldt0(xR,xS),sdtpldt0(xP,xP)),
file('theBenchmark.p',m__2610) ).
fof(m__2628,hypothesis,
( sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
& sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)) ),
file('theBenchmark.p',m__2628) ).
fof(m__2654,hypothesis,
sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))),
file('theBenchmark.p',m__2654) ).
fof(m__,conjecture,
sdtpldt0(xR,xS) = sdtpldt0(xP,xP),
file('theBenchmark.p',m__) ).
fof(f_1_1,plain,
! [W0] :
( $true
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mNatSort]) ).
fof(f_1_2,plain,
! [U_0] :
( $true
| ~ aNaturalNumber0(U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ! [U_0] : ~ aNaturalNumber0(U_0)
| $true ),
inference(miniscope,[status(thm)],[f_1_2]) ).
fof(f_1_4,plain,
! [U_0] :
( ~ aNaturalNumber0(U_0)
| $true ),
inference(definitional_conversion,[status(esa)],[f_1_3]) ).
cnf(f_1_5,plain,
( ~ aNaturalNumber0(U_0)
| $true ),
inference(clausify,[status(thm)],[f_1_4]) ).
fof(f_2_1,plain,
aNaturalNumber0(sz00),
inference(fof_nnf,[status(thm)],[mZeroNat]) ).
fof(f_2_2,plain,
aNaturalNumber0(sz00),
inference(definitional_conversion,[status(esa)],[f_2_1]) ).
cnf(f_2_3,plain,
aNaturalNumber0(sz00),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [W0] :
( ( szszuzczcdt0(W0) != sz00
& aNaturalNumber0(szszuzczcdt0(W0)) )
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mSuccNat]) ).
fof(f_3_2,plain,
! [U_1] :
( ( szszuzczcdt0(U_1) != sz00
& aNaturalNumber0(szszuzczcdt0(U_1)) )
| ~ aNaturalNumber0(U_1) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_1] :
( szszuzczcdt0(U_1) != sz00
| ~ sP0(U_1) )
& ! [U_1] :
( aNaturalNumber0(szszuzczcdt0(U_1))
| ~ sP0(U_1) )
& ! [U_1] :
( sP0(U_1)
| ~ aNaturalNumber0(U_1) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_3_2]) ).
cnf(f_3_4,plain,
( sP0(U_1)
| ~ aNaturalNumber0(U_1) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_5,plain,
( aNaturalNumber0(szszuzczcdt0(U_1))
| ~ sP0(U_1) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_6,plain,
( szszuzczcdt0(U_1) != sz00
| ~ sP0(U_1) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [W0] :
( ? [W1] :
( W0 = szszuzczcdt0(W1)
& aNaturalNumber0(W1) )
| W0 = sz00
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mNatExtr]) ).
fof(f_4_2,plain,
! [U_3] :
( ? [U_2] :
( U_3 = szszuzczcdt0(U_2)
& aNaturalNumber0(U_2) )
| U_3 = sz00
| ~ aNaturalNumber0(U_3) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_3] :
( ( U_3 = szszuzczcdt0(sK1(U_3))
& aNaturalNumber0(sK1(U_3)) )
| U_3 = sz00
| ~ aNaturalNumber0(U_3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_2,sK1(U_3))],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_3] :
( U_3 = szszuzczcdt0(sK1(U_3))
| ~ sP1(U_3) )
& ! [U_3] :
( aNaturalNumber0(sK1(U_3))
| ~ sP1(U_3) )
& ! [U_3] :
( sP1(U_3)
| U_3 = sz00
| ~ aNaturalNumber0(U_3) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_4_3]) ).
cnf(f_4_5,plain,
( sP1(U_3)
| U_3 = sz00
| ~ aNaturalNumber0(U_3) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_6,plain,
( aNaturalNumber0(sK1(U_3))
| ~ sP1(U_3) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_7,plain,
( U_3 = szszuzczcdt0(sK1(U_3))
| ~ sP1(U_3) ),
inference(clausify,[status(thm)],[f_4_4]) ).
fof(f_5_1,plain,
! [W0,W1] :
( W0 = W1
| szszuzczcdt0(W0) != szszuzczcdt0(W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mSuccEqu]) ).
fof(f_5_2,plain,
! [U_5,U_4] :
( U_5 = U_4
| szszuzczcdt0(U_5) != szszuzczcdt0(U_4)
| ~ aNaturalNumber0(U_4)
| ~ aNaturalNumber0(U_5) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_5,U_4] :
( U_5 = U_4
| szszuzczcdt0(U_5) != szszuzczcdt0(U_4)
| ~ aNaturalNumber0(U_4)
| ~ aNaturalNumber0(U_5) ),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
( U_5 = U_4
| szszuzczcdt0(U_5) != szszuzczcdt0(U_4)
| ~ aNaturalNumber0(U_4)
| ~ aNaturalNumber0(U_5) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [W0,W1] :
( $true
| ~ iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mIHOrd]) ).
fof(f_6_2,plain,
! [U_7,U_6] :
( $true
| ~ iLess0(U_7,U_6)
| ~ aNaturalNumber0(U_6)
| ~ aNaturalNumber0(U_7) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_7,U_6] :
( $true
| ~ iLess0(U_7,U_6)
| ~ aNaturalNumber0(U_6)
| ~ aNaturalNumber0(U_7) ),
inference(definitional_conversion,[status(esa)],[f_6_2]) ).
cnf(f_6_4,plain,
( $true
| ~ iLess0(U_7,U_6)
| ~ aNaturalNumber0(U_6)
| ~ aNaturalNumber0(U_7) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [W0] :
( iLess0(W0,szszuzczcdt0(W0))
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mIH]) ).
fof(f_7_2,plain,
! [U_8] :
( iLess0(U_8,szszuzczcdt0(U_8))
| ~ aNaturalNumber0(U_8) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_8] :
( iLess0(U_8,szszuzczcdt0(U_8))
| ~ aNaturalNumber0(U_8) ),
inference(definitional_conversion,[status(esa)],[f_7_2]) ).
cnf(f_7_4,plain,
( iLess0(U_8,szszuzczcdt0(U_8))
| ~ aNaturalNumber0(U_8) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [W0] :
( $true
| ~ aScalar0(W0) ),
inference(fof_nnf,[status(thm)],[mScSort]) ).
fof(f_8_2,plain,
! [U_9] :
( $true
| ~ aScalar0(U_9) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_9] : ~ aScalar0(U_9)
| $true ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
! [U_9] :
( ~ aScalar0(U_9)
| $true ),
inference(definitional_conversion,[status(esa)],[f_8_3]) ).
cnf(f_8_5,plain,
( ~ aScalar0(U_9)
| $true ),
inference(clausify,[status(thm)],[f_8_4]) ).
fof(f_9_1,plain,
aScalar0(sz0z00),
inference(fof_nnf,[status(thm)],[mSZeroSc]) ).
fof(f_9_2,plain,
aScalar0(sz0z00),
inference(definitional_conversion,[status(esa)],[f_9_1]) ).
cnf(f_9_3,plain,
aScalar0(sz0z00),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [W0,W1] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(fof_nnf,[status(thm)],[mSumSc]) ).
fof(f_10_2,plain,
! [U_11,U_10] :
( aScalar0(sdtpldt0(U_11,U_10))
| ~ aScalar0(U_10)
| ~ aScalar0(U_11) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_10,U_11] :
( aScalar0(sdtpldt0(U_11,U_10))
| ~ aScalar0(U_10)
| ~ aScalar0(U_11) ),
inference(definitional_conversion,[status(esa)],[f_10_2]) ).
cnf(f_10_4,plain,
( aScalar0(sdtpldt0(U_11,U_10))
| ~ aScalar0(U_10)
| ~ aScalar0(U_11) ),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
! [W0,W1] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(fof_nnf,[status(thm)],[mMulSc]) ).
fof(f_11_2,plain,
! [U_13,U_12] :
( aScalar0(sdtasdt0(U_13,U_12))
| ~ aScalar0(U_12)
| ~ aScalar0(U_13) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_13,U_12] :
( aScalar0(sdtasdt0(U_13,U_12))
| ~ aScalar0(U_12)
| ~ aScalar0(U_13) ),
inference(definitional_conversion,[status(esa)],[f_11_2]) ).
cnf(f_11_4,plain,
( aScalar0(sdtasdt0(U_13,U_12))
| ~ aScalar0(U_12)
| ~ aScalar0(U_13) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [W0] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) ),
inference(fof_nnf,[status(thm)],[mNegSc]) ).
fof(f_12_2,plain,
! [U_14] :
( aScalar0(smndt0(U_14))
| ~ aScalar0(U_14) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_14] :
( aScalar0(smndt0(U_14))
| ~ aScalar0(U_14) ),
inference(definitional_conversion,[status(esa)],[f_12_2]) ).
cnf(f_12_4,plain,
( aScalar0(smndt0(U_14))
| ~ aScalar0(U_14) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [W0] :
( ( smndt0(sz0z00) = sz0z00
& smndt0(smndt0(W0)) = W0
& sdtpldt0(smndt0(W0),W0) = sz0z00
& sdtpldt0(W0,smndt0(W0)) = sz0z00
& sdtasdt0(sz0z00,W0) = sz0z00
& sdtasdt0(W0,sz0z00) = sz0z00
& sdtpldt0(sz0z00,W0) = W0
& sdtpldt0(W0,sz0z00) = W0 )
| ~ aScalar0(W0) ),
inference(fof_nnf,[status(thm)],[mScZero]) ).
fof(f_13_2,plain,
! [U_15] :
( ( smndt0(sz0z00) = sz0z00
& smndt0(smndt0(U_15)) = U_15
& sdtpldt0(smndt0(U_15),U_15) = sz0z00
& sdtpldt0(U_15,smndt0(U_15)) = sz0z00
& sdtasdt0(sz0z00,U_15) = sz0z00
& sdtasdt0(U_15,sz0z00) = sz0z00
& sdtpldt0(sz0z00,U_15) = U_15
& sdtpldt0(U_15,sz0z00) = U_15 )
| ~ aScalar0(U_15) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_15] :
( smndt0(sz0z00) = sz0z00
| ~ sP2(U_15) )
& ! [U_15] :
( smndt0(smndt0(U_15)) = U_15
| ~ sP2(U_15) )
& ! [U_15] :
( sdtpldt0(smndt0(U_15),U_15) = sz0z00
| ~ sP2(U_15) )
& ! [U_15] :
( sdtpldt0(U_15,smndt0(U_15)) = sz0z00
| ~ sP2(U_15) )
& ! [U_15] :
( sdtasdt0(sz0z00,U_15) = sz0z00
| ~ sP2(U_15) )
& ! [U_15] :
( sdtasdt0(U_15,sz0z00) = sz0z00
| ~ sP2(U_15) )
& ! [U_15] :
( sdtpldt0(sz0z00,U_15) = U_15
| ~ sP2(U_15) )
& ! [U_15] :
( sdtpldt0(U_15,sz0z00) = U_15
| ~ sP2(U_15) )
& ! [U_15] :
( sP2(U_15)
| ~ aScalar0(U_15) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_13_2]) ).
cnf(f_13_4,plain,
( sP2(U_15)
| ~ aScalar0(U_15) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_5,plain,
( sdtpldt0(U_15,sz0z00) = U_15
| ~ sP2(U_15) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_6,plain,
( sdtpldt0(sz0z00,U_15) = U_15
| ~ sP2(U_15) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_7,plain,
( sdtasdt0(U_15,sz0z00) = sz0z00
| ~ sP2(U_15) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_8,plain,
( sdtasdt0(sz0z00,U_15) = sz0z00
| ~ sP2(U_15) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_9,plain,
( sdtpldt0(U_15,smndt0(U_15)) = sz0z00
| ~ sP2(U_15) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_10,plain,
( sdtpldt0(smndt0(U_15),U_15) = sz0z00
| ~ sP2(U_15) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_11,plain,
( smndt0(smndt0(U_15)) = U_15
| ~ sP2(U_15) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_12,plain,
( smndt0(sz0z00) = sz0z00
| ~ sP2(U_15) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [W0,W1,W2] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0)
& sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2))
& sdtpldt0(W0,W1) = sdtpldt0(W1,W0)
& sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(fof_nnf,[status(thm)],[mArith]) ).
fof(f_14_2,plain,
! [U_18,U_17,U_16] :
( ( sdtasdt0(U_18,U_17) = sdtasdt0(U_17,U_18)
& sdtasdt0(sdtasdt0(U_18,U_17),U_16) = sdtasdt0(U_18,sdtasdt0(U_17,U_16))
& sdtpldt0(U_18,U_17) = sdtpldt0(U_17,U_18)
& sdtpldt0(sdtpldt0(U_18,U_17),U_16) = sdtpldt0(U_18,sdtpldt0(U_17,U_16)) )
| ~ aScalar0(U_16)
| ~ aScalar0(U_17)
| ~ aScalar0(U_18) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_18,U_16,U_17] :
( sdtasdt0(U_18,U_17) = sdtasdt0(U_17,U_18)
| ~ sP3(U_18,U_16,U_17) )
& ! [U_18,U_16,U_17] :
( sdtasdt0(sdtasdt0(U_18,U_17),U_16) = sdtasdt0(U_18,sdtasdt0(U_17,U_16))
| ~ sP3(U_18,U_16,U_17) )
& ! [U_18,U_16,U_17] :
( sdtpldt0(U_18,U_17) = sdtpldt0(U_17,U_18)
| ~ sP3(U_18,U_16,U_17) )
& ! [U_18,U_16,U_17] :
( sdtpldt0(sdtpldt0(U_18,U_17),U_16) = sdtpldt0(U_18,sdtpldt0(U_17,U_16))
| ~ sP3(U_18,U_16,U_17) )
& ! [U_18,U_16,U_17] :
( sP3(U_18,U_16,U_17)
| ~ aScalar0(U_16)
| ~ aScalar0(U_17)
| ~ aScalar0(U_18) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_14_2]) ).
cnf(f_14_4,plain,
( sP3(U_18,U_16,U_17)
| ~ aScalar0(U_16)
| ~ aScalar0(U_17)
| ~ aScalar0(U_18) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_5,plain,
( sdtpldt0(sdtpldt0(U_18,U_17),U_16) = sdtpldt0(U_18,sdtpldt0(U_17,U_16))
| ~ sP3(U_18,U_16,U_17) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_6,plain,
( sdtpldt0(U_18,U_17) = sdtpldt0(U_17,U_18)
| ~ sP3(U_18,U_16,U_17) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_7,plain,
( sdtasdt0(sdtasdt0(U_18,U_17),U_16) = sdtasdt0(U_18,sdtasdt0(U_17,U_16))
| ~ sP3(U_18,U_16,U_17) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_8,plain,
( sdtasdt0(U_18,U_17) = sdtasdt0(U_17,U_18)
| ~ sP3(U_18,U_16,U_17) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
! [W0,W1,W2] :
( ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(fof_nnf,[status(thm)],[mDistr]) ).
fof(f_15_2,plain,
! [U_21,U_20,U_19] :
( ( sdtasdt0(sdtpldt0(U_21,U_20),U_19) = sdtpldt0(sdtasdt0(U_21,U_19),sdtasdt0(U_20,U_19))
& sdtasdt0(U_21,sdtpldt0(U_20,U_19)) = sdtpldt0(sdtasdt0(U_21,U_20),sdtasdt0(U_21,U_19)) )
| ~ aScalar0(U_19)
| ~ aScalar0(U_20)
| ~ aScalar0(U_21) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( ! [U_20,U_19,U_21] :
( sdtasdt0(sdtpldt0(U_21,U_20),U_19) = sdtpldt0(sdtasdt0(U_21,U_19),sdtasdt0(U_20,U_19))
| ~ sP4(U_20,U_19,U_21) )
& ! [U_20,U_19,U_21] :
( sdtasdt0(U_21,sdtpldt0(U_20,U_19)) = sdtpldt0(sdtasdt0(U_21,U_20),sdtasdt0(U_21,U_19))
| ~ sP4(U_20,U_19,U_21) )
& ! [U_20,U_19,U_21] :
( sP4(U_20,U_19,U_21)
| ~ aScalar0(U_19)
| ~ aScalar0(U_20)
| ~ aScalar0(U_21) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_15_2]) ).
cnf(f_15_4,plain,
( sP4(U_20,U_19,U_21)
| ~ aScalar0(U_19)
| ~ aScalar0(U_20)
| ~ aScalar0(U_21) ),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_5,plain,
( sdtasdt0(U_21,sdtpldt0(U_20,U_19)) = sdtpldt0(sdtasdt0(U_21,U_20),sdtasdt0(U_21,U_19))
| ~ sP4(U_20,U_19,U_21) ),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_6,plain,
( sdtasdt0(sdtpldt0(U_21,U_20),U_19) = sdtpldt0(sdtasdt0(U_21,U_19),sdtasdt0(U_20,U_19))
| ~ sP4(U_20,U_19,U_21) ),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
! [W0,W1,W2,W3] :
( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3)))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(fof_nnf,[status(thm)],[mDistr2]) ).
fof(f_16_2,plain,
! [U_25,U_24,U_23,U_22] :
( sdtasdt0(sdtpldt0(U_25,U_24),sdtpldt0(U_23,U_22)) = sdtpldt0(sdtpldt0(sdtasdt0(U_25,U_23),sdtasdt0(U_25,U_22)),sdtpldt0(sdtasdt0(U_24,U_23),sdtasdt0(U_24,U_22)))
| ~ aScalar0(U_22)
| ~ aScalar0(U_23)
| ~ aScalar0(U_24)
| ~ aScalar0(U_25) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_23,U_22,U_24,U_25] :
( sdtasdt0(sdtpldt0(U_25,U_24),sdtpldt0(U_23,U_22)) = sdtpldt0(sdtpldt0(sdtasdt0(U_25,U_23),sdtasdt0(U_25,U_22)),sdtpldt0(sdtasdt0(U_24,U_23),sdtasdt0(U_24,U_22)))
| ~ aScalar0(U_22)
| ~ aScalar0(U_23)
| ~ aScalar0(U_24)
| ~ aScalar0(U_25) ),
inference(definitional_conversion,[status(esa)],[f_16_2]) ).
cnf(f_16_4,plain,
( sdtasdt0(sdtpldt0(U_25,U_24),sdtpldt0(U_23,U_22)) = sdtpldt0(sdtpldt0(sdtasdt0(U_25,U_23),sdtasdt0(U_25,U_22)),sdtpldt0(sdtasdt0(U_24,U_23),sdtasdt0(U_24,U_22)))
| ~ aScalar0(U_22)
| ~ aScalar0(U_23)
| ~ aScalar0(U_24)
| ~ aScalar0(U_25) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
! [W0,W1] :
( ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1))
& sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) )
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(fof_nnf,[status(thm)],[mMNeg]) ).
fof(f_17_2,plain,
! [U_27,U_26] :
( ( sdtasdt0(smndt0(U_27),U_26) = smndt0(sdtasdt0(U_27,U_26))
& sdtasdt0(U_27,smndt0(U_26)) = smndt0(sdtasdt0(U_27,U_26)) )
| ~ aScalar0(U_26)
| ~ aScalar0(U_27) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
( ! [U_27,U_26] :
( sdtasdt0(smndt0(U_27),U_26) = smndt0(sdtasdt0(U_27,U_26))
| ~ sP5(U_27,U_26) )
& ! [U_27,U_26] :
( sdtasdt0(U_27,smndt0(U_26)) = smndt0(sdtasdt0(U_27,U_26))
| ~ sP5(U_27,U_26) )
& ! [U_27,U_26] :
( sP5(U_27,U_26)
| ~ aScalar0(U_26)
| ~ aScalar0(U_27) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_17_2]) ).
cnf(f_17_4,plain,
( sP5(U_27,U_26)
| ~ aScalar0(U_26)
| ~ aScalar0(U_27) ),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_5,plain,
( sdtasdt0(U_27,smndt0(U_26)) = smndt0(sdtasdt0(U_27,U_26))
| ~ sP5(U_27,U_26) ),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_6,plain,
( sdtasdt0(smndt0(U_27),U_26) = smndt0(sdtasdt0(U_27,U_26))
| ~ sP5(U_27,U_26) ),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
! [W0,W1] :
( sdtasdt0(smndt0(W0),smndt0(W1)) = sdtasdt0(W0,W1)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(fof_nnf,[status(thm)],[mMDNeg]) ).
fof(f_18_2,plain,
! [U_29,U_28] :
( sdtasdt0(smndt0(U_29),smndt0(U_28)) = sdtasdt0(U_29,U_28)
| ~ aScalar0(U_28)
| ~ aScalar0(U_29) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_28,U_29] :
( sdtasdt0(smndt0(U_29),smndt0(U_28)) = sdtasdt0(U_29,U_28)
| ~ aScalar0(U_28)
| ~ aScalar0(U_29) ),
inference(definitional_conversion,[status(esa)],[f_18_2]) ).
cnf(f_18_4,plain,
( sdtasdt0(smndt0(U_29),smndt0(U_28)) = sdtasdt0(U_29,U_28)
| ~ aScalar0(U_28)
| ~ aScalar0(U_29) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
! [W0,W1] :
( $true
| ~ sdtlseqdt0(W0,W1)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(fof_nnf,[status(thm)],[mLess]) ).
fof(f_19_2,plain,
! [U_31,U_30] :
( $true
| ~ sdtlseqdt0(U_31,U_30)
| ~ aScalar0(U_30)
| ~ aScalar0(U_31) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_30,U_31] :
( $true
| ~ sdtlseqdt0(U_31,U_30)
| ~ aScalar0(U_30)
| ~ aScalar0(U_31) ),
inference(definitional_conversion,[status(esa)],[f_19_2]) ).
cnf(f_19_4,plain,
( $true
| ~ sdtlseqdt0(U_31,U_30)
| ~ aScalar0(U_30)
| ~ aScalar0(U_31) ),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
! [W0] :
( sdtlseqdt0(W0,W0)
| ~ aScalar0(W0) ),
inference(fof_nnf,[status(thm)],[mLERef]) ).
fof(f_20_2,plain,
! [U_32] :
( sdtlseqdt0(U_32,U_32)
| ~ aScalar0(U_32) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_32] :
( sdtlseqdt0(U_32,U_32)
| ~ aScalar0(U_32) ),
inference(definitional_conversion,[status(esa)],[f_20_2]) ).
cnf(f_20_4,plain,
( sdtlseqdt0(U_32,U_32)
| ~ aScalar0(U_32) ),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
! [W0,W1] :
( W0 = W1
| ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(fof_nnf,[status(thm)],[mLEASm]) ).
fof(f_21_2,plain,
! [U_34,U_33] :
( U_34 = U_33
| ~ sdtlseqdt0(U_33,U_34)
| ~ sdtlseqdt0(U_34,U_33)
| ~ aScalar0(U_33)
| ~ aScalar0(U_34) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_34,U_33] :
( U_34 = U_33
| ~ sdtlseqdt0(U_33,U_34)
| ~ sdtlseqdt0(U_34,U_33)
| ~ aScalar0(U_33)
| ~ aScalar0(U_34) ),
inference(definitional_conversion,[status(esa)],[f_21_2]) ).
cnf(f_21_4,plain,
( U_34 = U_33
| ~ sdtlseqdt0(U_33,U_34)
| ~ sdtlseqdt0(U_34,U_33)
| ~ aScalar0(U_33)
| ~ aScalar0(U_34) ),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
! [W0,W1,W2] :
( sdtlseqdt0(W0,W2)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(fof_nnf,[status(thm)],[mLETrn]) ).
fof(f_22_2,plain,
! [U_37,U_36,U_35] :
( sdtlseqdt0(U_37,U_35)
| ~ sdtlseqdt0(U_36,U_35)
| ~ sdtlseqdt0(U_37,U_36)
| ~ aScalar0(U_35)
| ~ aScalar0(U_36)
| ~ aScalar0(U_37) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_37,U_36,U_35] :
( sdtlseqdt0(U_37,U_35)
| ~ sdtlseqdt0(U_36,U_35)
| ~ sdtlseqdt0(U_37,U_36)
| ~ aScalar0(U_35)
| ~ aScalar0(U_36)
| ~ aScalar0(U_37) ),
inference(definitional_conversion,[status(esa)],[f_22_2]) ).
cnf(f_22_4,plain,
( sdtlseqdt0(U_37,U_35)
| ~ sdtlseqdt0(U_36,U_35)
| ~ sdtlseqdt0(U_37,U_36)
| ~ aScalar0(U_35)
| ~ aScalar0(U_36)
| ~ aScalar0(U_37) ),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
! [W0,W1,W2,W3] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1)
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(fof_nnf,[status(thm)],[mLEMon]) ).
fof(f_23_2,plain,
! [U_41,U_40,U_39,U_38] :
( sdtlseqdt0(sdtpldt0(U_41,U_39),sdtpldt0(U_40,U_38))
| ~ sdtlseqdt0(U_39,U_38)
| ~ sdtlseqdt0(U_41,U_40)
| ~ aScalar0(U_38)
| ~ aScalar0(U_39)
| ~ aScalar0(U_40)
| ~ aScalar0(U_41) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_41,U_40,U_39,U_38] :
( sdtlseqdt0(sdtpldt0(U_41,U_39),sdtpldt0(U_40,U_38))
| ~ sdtlseqdt0(U_39,U_38)
| ~ sdtlseqdt0(U_41,U_40)
| ~ aScalar0(U_38)
| ~ aScalar0(U_39)
| ~ aScalar0(U_40)
| ~ aScalar0(U_41) ),
inference(definitional_conversion,[status(esa)],[f_23_2]) ).
cnf(f_23_4,plain,
( sdtlseqdt0(sdtpldt0(U_41,U_39),sdtpldt0(U_40,U_38))
| ~ sdtlseqdt0(U_39,U_38)
| ~ sdtlseqdt0(U_41,U_40)
| ~ aScalar0(U_38)
| ~ aScalar0(U_39)
| ~ aScalar0(U_40)
| ~ aScalar0(U_41) ),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
! [W0,W1,W2,W3] :
( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(sz0z00,W2)
| ~ sdtlseqdt0(W0,W1)
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(fof_nnf,[status(thm)],[mLEMonM]) ).
fof(f_24_2,plain,
! [U_45,U_44,U_43,U_42] :
( sdtlseqdt0(sdtasdt0(U_45,U_43),sdtasdt0(U_44,U_42))
| ~ sdtlseqdt0(U_43,U_42)
| ~ sdtlseqdt0(sz0z00,U_43)
| ~ sdtlseqdt0(U_45,U_44)
| ~ aScalar0(U_42)
| ~ aScalar0(U_43)
| ~ aScalar0(U_44)
| ~ aScalar0(U_45) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_45,U_42,U_43,U_44] :
( sdtlseqdt0(sdtasdt0(U_45,U_43),sdtasdt0(U_44,U_42))
| ~ sdtlseqdt0(U_43,U_42)
| ~ sdtlseqdt0(sz0z00,U_43)
| ~ sdtlseqdt0(U_45,U_44)
| ~ aScalar0(U_42)
| ~ aScalar0(U_43)
| ~ aScalar0(U_44)
| ~ aScalar0(U_45) ),
inference(definitional_conversion,[status(esa)],[f_24_2]) ).
cnf(f_24_4,plain,
( sdtlseqdt0(sdtasdt0(U_45,U_43),sdtasdt0(U_44,U_42))
| ~ sdtlseqdt0(U_43,U_42)
| ~ sdtlseqdt0(sz0z00,U_43)
| ~ sdtlseqdt0(U_45,U_44)
| ~ aScalar0(U_42)
| ~ aScalar0(U_43)
| ~ aScalar0(U_44)
| ~ aScalar0(U_45) ),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
! [W0,W1] :
( sdtlseqdt0(W1,W0)
| sdtlseqdt0(W0,W1)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(fof_nnf,[status(thm)],[mLETot]) ).
fof(f_25_2,plain,
! [U_47,U_46] :
( sdtlseqdt0(U_46,U_47)
| sdtlseqdt0(U_47,U_46)
| ~ aScalar0(U_46)
| ~ aScalar0(U_47) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_46,U_47] :
( sdtlseqdt0(U_46,U_47)
| sdtlseqdt0(U_47,U_46)
| ~ aScalar0(U_46)
| ~ aScalar0(U_47) ),
inference(definitional_conversion,[status(esa)],[f_25_2]) ).
cnf(f_25_4,plain,
( sdtlseqdt0(U_46,U_47)
| sdtlseqdt0(U_47,U_46)
| ~ aScalar0(U_46)
| ~ aScalar0(U_47) ),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
! [W0,W1] :
( ( sdtlseqdt0(sz0z00,sdtasdt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtpldt0(W0,W1)) )
| ~ sdtlseqdt0(sz0z00,W1)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(fof_nnf,[status(thm)],[mPosMon]) ).
fof(f_26_2,plain,
! [U_49,U_48] :
( ( sdtlseqdt0(sz0z00,sdtasdt0(U_49,U_48))
& sdtlseqdt0(sz0z00,sdtpldt0(U_49,U_48)) )
| ~ sdtlseqdt0(sz0z00,U_48)
| ~ sdtlseqdt0(sz0z00,U_49)
| ~ aScalar0(U_48)
| ~ aScalar0(U_49) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( ! [U_48,U_49] :
( sdtlseqdt0(sz0z00,sdtasdt0(U_49,U_48))
| ~ sP6(U_48,U_49) )
& ! [U_48,U_49] :
( sdtlseqdt0(sz0z00,sdtpldt0(U_49,U_48))
| ~ sP6(U_48,U_49) )
& ! [U_48,U_49] :
( sP6(U_48,U_49)
| ~ sdtlseqdt0(sz0z00,U_48)
| ~ sdtlseqdt0(sz0z00,U_49)
| ~ aScalar0(U_48)
| ~ aScalar0(U_49) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_26_2]) ).
cnf(f_26_4,plain,
( sP6(U_48,U_49)
| ~ sdtlseqdt0(sz0z00,U_48)
| ~ sdtlseqdt0(sz0z00,U_49)
| ~ aScalar0(U_48)
| ~ aScalar0(U_49) ),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_5,plain,
( sdtlseqdt0(sz0z00,sdtpldt0(U_49,U_48))
| ~ sP6(U_48,U_49) ),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_6,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(U_49,U_48))
| ~ sP6(U_48,U_49) ),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [W0] :
( sdtlseqdt0(sz0z00,sdtasdt0(W0,W0))
| ~ aScalar0(W0) ),
inference(fof_nnf,[status(thm)],[mSqPos]) ).
fof(f_27_2,plain,
! [U_50] :
( sdtlseqdt0(sz0z00,sdtasdt0(U_50,U_50))
| ~ aScalar0(U_50) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_50] :
( sdtlseqdt0(sz0z00,sdtasdt0(U_50,U_50))
| ~ aScalar0(U_50) ),
inference(definitional_conversion,[status(esa)],[f_27_2]) ).
cnf(f_27_4,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(U_50,U_50))
| ~ aScalar0(U_50) ),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
! [W0,W1] :
( W0 = W1
| sdtasdt0(W0,W0) != sdtasdt0(W1,W1)
| ~ sdtlseqdt0(sz0z00,W1)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(fof_nnf,[status(thm)],[mSqrt]) ).
fof(f_28_2,plain,
! [U_52,U_51] :
( U_52 = U_51
| sdtasdt0(U_52,U_52) != sdtasdt0(U_51,U_51)
| ~ sdtlseqdt0(sz0z00,U_51)
| ~ sdtlseqdt0(sz0z00,U_52)
| ~ aScalar0(U_51)
| ~ aScalar0(U_52) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_51,U_52] :
( U_52 = U_51
| sdtasdt0(U_52,U_52) != sdtasdt0(U_51,U_51)
| ~ sdtlseqdt0(sz0z00,U_51)
| ~ sdtlseqdt0(sz0z00,U_52)
| ~ aScalar0(U_51)
| ~ aScalar0(U_52) ),
inference(definitional_conversion,[status(esa)],[f_28_2]) ).
cnf(f_28_4,plain,
( U_52 = U_51
| sdtasdt0(U_52,U_52) != sdtasdt0(U_51,U_51)
| ~ sdtlseqdt0(sz0z00,U_51)
| ~ sdtlseqdt0(sz0z00,U_52)
| ~ aScalar0(U_51)
| ~ aScalar0(U_52) ),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
! [W0] :
( $true
| ~ aVector0(W0) ),
inference(fof_nnf,[status(thm)],[mVcSort]) ).
fof(f_29_2,plain,
! [U_53] :
( $true
| ~ aVector0(U_53) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
( ! [U_53] : ~ aVector0(U_53)
| $true ),
inference(miniscope,[status(thm)],[f_29_2]) ).
fof(f_29_4,plain,
! [U_53] :
( ~ aVector0(U_53)
| $true ),
inference(definitional_conversion,[status(esa)],[f_29_3]) ).
cnf(f_29_5,plain,
( ~ aVector0(U_53)
| $true ),
inference(clausify,[status(thm)],[f_29_4]) ).
fof(f_30_1,plain,
! [W0] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(fof_nnf,[status(thm)],[mDimNat]) ).
fof(f_30_2,plain,
! [U_54] :
( aNaturalNumber0(aDimensionOf0(U_54))
| ~ aVector0(U_54) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_54] :
( aNaturalNumber0(aDimensionOf0(U_54))
| ~ aVector0(U_54) ),
inference(definitional_conversion,[status(esa)],[f_30_2]) ).
cnf(f_30_4,plain,
( aNaturalNumber0(aDimensionOf0(U_54))
| ~ aVector0(U_54) ),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
! [W0,W1] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) ),
inference(fof_nnf,[status(thm)],[mElmSc]) ).
fof(f_31_2,plain,
! [U_56,U_55] :
( aScalar0(sdtlbdtrb0(U_56,U_55))
| ~ aNaturalNumber0(U_55)
| ~ aVector0(U_56) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_56,U_55] :
( aScalar0(sdtlbdtrb0(U_56,U_55))
| ~ aNaturalNumber0(U_55)
| ~ aVector0(U_56) ),
inference(definitional_conversion,[status(esa)],[f_31_2]) ).
cnf(f_31_4,plain,
( aScalar0(sdtlbdtrb0(U_56,U_55))
| ~ aNaturalNumber0(U_55)
| ~ aVector0(U_56) ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [W0] :
( ! [W1] :
( ( W1 = sziznziztdt0(W0)
| ? [W2] :
( sdtlbdtrb0(W1,W2) != sdtlbdtrb0(W0,W2)
& aNaturalNumber0(W2) )
| szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0)
| ~ aVector0(W1) )
& ( ( ! [W2] :
( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2)
| ~ aNaturalNumber0(W2) )
& szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0)
& aVector0(W1) )
| W1 != sziznziztdt0(W0) ) )
| aDimensionOf0(W0) = sz00
| ~ aVector0(W0) ),
inference(fof_nnf,[status(thm)],[mDefInit]) ).
fof(f_32_2,plain,
! [U_60] :
( ! [U_59] :
( ( U_59 = sziznziztdt0(U_60)
| ? [U_58] :
( sdtlbdtrb0(U_59,U_58) != sdtlbdtrb0(U_60,U_58)
& aNaturalNumber0(U_58) )
| szszuzczcdt0(aDimensionOf0(U_59)) != aDimensionOf0(U_60)
| ~ aVector0(U_59) )
& ( ( ! [U_57] :
( sdtlbdtrb0(U_59,U_57) = sdtlbdtrb0(U_60,U_57)
| ~ aNaturalNumber0(U_57) )
& szszuzczcdt0(aDimensionOf0(U_59)) = aDimensionOf0(U_60)
& aVector0(U_59) )
| U_59 != sziznziztdt0(U_60) ) )
| aDimensionOf0(U_60) = sz00
| ~ aVector0(U_60) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_60] :
( ( ! [U_62] :
( U_62 = sziznziztdt0(U_60)
| ? [U_58] :
( sdtlbdtrb0(U_62,U_58) != sdtlbdtrb0(U_60,U_58)
& aNaturalNumber0(U_58) )
| szszuzczcdt0(aDimensionOf0(U_62)) != aDimensionOf0(U_60)
| ~ aVector0(U_62) )
& ! [U_61] :
( ( ! [U_57] :
( sdtlbdtrb0(U_61,U_57) = sdtlbdtrb0(U_60,U_57)
| ~ aNaturalNumber0(U_57) )
& szszuzczcdt0(aDimensionOf0(U_61)) = aDimensionOf0(U_60)
& aVector0(U_61) )
| U_61 != sziznziztdt0(U_60) ) )
| aDimensionOf0(U_60) = sz00
| ~ aVector0(U_60) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
fof(f_32_4,plain,
! [U_60] :
( ( ! [U_62] :
( U_62 = sziznziztdt0(U_60)
| ( sdtlbdtrb0(U_62,sK2(U_60,U_62)) != sdtlbdtrb0(U_60,sK2(U_60,U_62))
& aNaturalNumber0(sK2(U_60,U_62)) )
| szszuzczcdt0(aDimensionOf0(U_62)) != aDimensionOf0(U_60)
| ~ aVector0(U_62) )
& ! [U_61] :
( ( ! [U_57] :
( sdtlbdtrb0(U_61,U_57) = sdtlbdtrb0(U_60,U_57)
| ~ aNaturalNumber0(U_57) )
& szszuzczcdt0(aDimensionOf0(U_61)) = aDimensionOf0(U_60)
& aVector0(U_61) )
| U_61 != sziznziztdt0(U_60) ) )
| aDimensionOf0(U_60) = sz00
| ~ aVector0(U_60) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_58,sK2(U_60,U_62))],[f_32_3]) ).
fof(f_32_5,plain,
( ! [U_60,U_62] :
( sdtlbdtrb0(U_62,sK2(U_60,U_62)) != sdtlbdtrb0(U_60,sK2(U_60,U_62))
| ~ sP8(U_60,U_62) )
& ! [U_60,U_62] :
( aNaturalNumber0(sK2(U_60,U_62))
| ~ sP8(U_60,U_62) )
& ! [U_61,U_57,U_60] :
( sdtlbdtrb0(U_61,U_57) = sdtlbdtrb0(U_60,U_57)
| ~ aNaturalNumber0(U_57)
| ~ sP7(U_61,U_57,U_60) )
& ! [U_61,U_57,U_60] :
( szszuzczcdt0(aDimensionOf0(U_61)) = aDimensionOf0(U_60)
| ~ sP7(U_61,U_57,U_60) )
& ! [U_61,U_57,U_60] :
( aVector0(U_61)
| ~ sP7(U_61,U_57,U_60) )
& ! [U_61,U_57,U_60,U_62] :
( U_62 = sziznziztdt0(U_60)
| sP8(U_60,U_62)
| szszuzczcdt0(aDimensionOf0(U_62)) != aDimensionOf0(U_60)
| ~ aVector0(U_62)
| ~ sP9(U_61,U_57,U_60,U_62) )
& ! [U_61,U_57,U_60,U_62] :
( sP7(U_61,U_57,U_60)
| U_61 != sziznziztdt0(U_60)
| ~ sP9(U_61,U_57,U_60,U_62) )
& ! [U_61,U_57,U_60,U_62] :
( sP9(U_61,U_57,U_60,U_62)
| aDimensionOf0(U_60) = sz00
| ~ aVector0(U_60) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7,sP8,sP9])],[f_32_4]) ).
cnf(f_32_6,plain,
( sP9(U_61,U_57,U_60,U_62)
| aDimensionOf0(U_60) = sz00
| ~ aVector0(U_60) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_7,plain,
( sP7(U_61,U_57,U_60)
| U_61 != sziznziztdt0(U_60)
| ~ sP9(U_61,U_57,U_60,U_62) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_8,plain,
( U_62 = sziznziztdt0(U_60)
| sP8(U_60,U_62)
| szszuzczcdt0(aDimensionOf0(U_62)) != aDimensionOf0(U_60)
| ~ aVector0(U_62)
| ~ sP9(U_61,U_57,U_60,U_62) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_9,plain,
( aVector0(U_61)
| ~ sP7(U_61,U_57,U_60) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_10,plain,
( szszuzczcdt0(aDimensionOf0(U_61)) = aDimensionOf0(U_60)
| ~ sP7(U_61,U_57,U_60) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_11,plain,
( sdtlbdtrb0(U_61,U_57) = sdtlbdtrb0(U_60,U_57)
| ~ aNaturalNumber0(U_57)
| ~ sP7(U_61,U_57,U_60) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_12,plain,
( aNaturalNumber0(sK2(U_60,U_62))
| ~ sP8(U_60,U_62) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_13,plain,
( sdtlbdtrb0(U_62,sK2(U_60,U_62)) != sdtlbdtrb0(U_60,sK2(U_60,U_62))
| ~ sP8(U_60,U_62) ),
inference(clausify,[status(thm)],[f_32_5]) ).
fof(f_33_1,plain,
! [W0,W1] :
( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1))
| aDimensionOf0(W1) = sz00
| aDimensionOf0(W0) != aDimensionOf0(W1)
| ~ aVector0(W1)
| ~ aVector0(W0) ),
inference(fof_nnf,[status(thm)],[mEqInit]) ).
fof(f_33_2,plain,
! [U_64,U_63] :
( aDimensionOf0(sziznziztdt0(U_64)) = aDimensionOf0(sziznziztdt0(U_63))
| aDimensionOf0(U_63) = sz00
| aDimensionOf0(U_64) != aDimensionOf0(U_63)
| ~ aVector0(U_63)
| ~ aVector0(U_64) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_64,U_63] :
( aDimensionOf0(sziznziztdt0(U_64)) = aDimensionOf0(sziznziztdt0(U_63))
| aDimensionOf0(U_63) = sz00
| aDimensionOf0(U_64) != aDimensionOf0(U_63)
| ~ aVector0(U_63)
| ~ aVector0(U_64) ),
inference(definitional_conversion,[status(esa)],[f_33_2]) ).
cnf(f_33_4,plain,
( aDimensionOf0(sziznziztdt0(U_64)) = aDimensionOf0(sziznziztdt0(U_63))
| aDimensionOf0(U_63) = sz00
| aDimensionOf0(U_64) != aDimensionOf0(U_63)
| ~ aVector0(U_63)
| ~ aVector0(U_64) ),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
! [W0,W1] :
( aScalar0(sdtasasdt0(W0,W1))
| aDimensionOf0(W0) != aDimensionOf0(W1)
| ~ aVector0(W1)
| ~ aVector0(W0) ),
inference(fof_nnf,[status(thm)],[mScPr]) ).
fof(f_34_2,plain,
! [U_66,U_65] :
( aScalar0(sdtasasdt0(U_66,U_65))
| aDimensionOf0(U_66) != aDimensionOf0(U_65)
| ~ aVector0(U_65)
| ~ aVector0(U_66) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_66,U_65] :
( aScalar0(sdtasasdt0(U_66,U_65))
| aDimensionOf0(U_66) != aDimensionOf0(U_65)
| ~ aVector0(U_65)
| ~ aVector0(U_66) ),
inference(definitional_conversion,[status(esa)],[f_34_2]) ).
cnf(f_34_4,plain,
( aScalar0(sdtasasdt0(U_66,U_65))
| aDimensionOf0(U_66) != aDimensionOf0(U_65)
| ~ aVector0(U_65)
| ~ aVector0(U_66) ),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
! [W0,W1] :
( sdtasasdt0(W0,W1) = sz0z00
| aDimensionOf0(W1) != sz00
| aDimensionOf0(W0) != aDimensionOf0(W1)
| ~ aVector0(W1)
| ~ aVector0(W0) ),
inference(fof_nnf,[status(thm)],[mDefSPZ]) ).
fof(f_35_2,plain,
! [U_68,U_67] :
( sdtasasdt0(U_68,U_67) = sz0z00
| aDimensionOf0(U_67) != sz00
| aDimensionOf0(U_68) != aDimensionOf0(U_67)
| ~ aVector0(U_67)
| ~ aVector0(U_68) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_67,U_68] :
( sdtasasdt0(U_68,U_67) = sz0z00
| aDimensionOf0(U_67) != sz00
| aDimensionOf0(U_68) != aDimensionOf0(U_67)
| ~ aVector0(U_67)
| ~ aVector0(U_68) ),
inference(definitional_conversion,[status(esa)],[f_35_2]) ).
cnf(f_35_4,plain,
( sdtasasdt0(U_68,U_67) = sz0z00
| aDimensionOf0(U_67) != sz00
| aDimensionOf0(U_68) != aDimensionOf0(U_67)
| ~ aVector0(U_67)
| ~ aVector0(U_68) ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
! [W0,W1] :
( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1))))
| aDimensionOf0(W1) = sz00
| aDimensionOf0(W0) != aDimensionOf0(W1)
| ~ aVector0(W1)
| ~ aVector0(W0) ),
inference(fof_nnf,[status(thm)],[mDefSPN]) ).
fof(f_36_2,plain,
! [U_70,U_69] :
( sdtasasdt0(U_70,U_69) = sdtpldt0(sdtasasdt0(sziznziztdt0(U_70),sziznziztdt0(U_69)),sdtasdt0(sdtlbdtrb0(U_70,aDimensionOf0(U_70)),sdtlbdtrb0(U_69,aDimensionOf0(U_69))))
| aDimensionOf0(U_69) = sz00
| aDimensionOf0(U_70) != aDimensionOf0(U_69)
| ~ aVector0(U_69)
| ~ aVector0(U_70) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_70,U_69] :
( sdtasasdt0(U_70,U_69) = sdtpldt0(sdtasasdt0(sziznziztdt0(U_70),sziznziztdt0(U_69)),sdtasdt0(sdtlbdtrb0(U_70,aDimensionOf0(U_70)),sdtlbdtrb0(U_69,aDimensionOf0(U_69))))
| aDimensionOf0(U_69) = sz00
| aDimensionOf0(U_70) != aDimensionOf0(U_69)
| ~ aVector0(U_69)
| ~ aVector0(U_70) ),
inference(definitional_conversion,[status(esa)],[f_36_2]) ).
cnf(f_36_4,plain,
( sdtasasdt0(U_70,U_69) = sdtpldt0(sdtasasdt0(sziznziztdt0(U_70),sziznziztdt0(U_69)),sdtasdt0(sdtlbdtrb0(U_70,aDimensionOf0(U_70)),sdtlbdtrb0(U_69,aDimensionOf0(U_69))))
| aDimensionOf0(U_69) = sz00
| aDimensionOf0(U_70) != aDimensionOf0(U_69)
| ~ aVector0(U_69)
| ~ aVector0(U_70) ),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
! [W0] :
( sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0))
| ~ aVector0(W0) ),
inference(fof_nnf,[status(thm)],[mScSqPos]) ).
fof(f_37_2,plain,
! [U_71] :
( sdtlseqdt0(sz0z00,sdtasasdt0(U_71,U_71))
| ~ aVector0(U_71) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_71] :
( sdtlseqdt0(sz0z00,sdtasasdt0(U_71,U_71))
| ~ aVector0(U_71) ),
inference(definitional_conversion,[status(esa)],[f_37_2]) ).
cnf(f_37_4,plain,
( sdtlseqdt0(sz0z00,sdtasasdt0(U_71,U_71))
| ~ aVector0(U_71) ),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
( aVector0(xt)
& aVector0(xs) ),
inference(fof_nnf,[status(thm)],[m__1678]) ).
fof(f_38_2,plain,
( aVector0(xt)
& aVector0(xs) ),
inference(definitional_conversion,[status(esa)],[f_38_1]) ).
cnf(f_38_3,plain,
aVector0(xs),
inference(clausify,[status(thm)],[f_38_2]) ).
cnf(f_38_4,plain,
aVector0(xt),
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_1,plain,
! [W0,W1] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
| aDimensionOf0(W0) != aDimensionOf0(W1)
| ~ aVector0(W1)
| ~ aVector0(W0) ),
inference(fof_nnf,[status(thm)],[m__1652]) ).
fof(f_39_2,plain,
! [U_73,U_72] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(U_73,U_72),sdtasasdt0(U_73,U_72)),sdtasdt0(sdtasasdt0(U_73,U_73),sdtasasdt0(U_72,U_72)))
| ~ iLess0(aDimensionOf0(U_73),aDimensionOf0(xs))
| aDimensionOf0(U_73) != aDimensionOf0(U_72)
| ~ aVector0(U_72)
| ~ aVector0(U_73) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_72,U_73] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(U_73,U_72),sdtasasdt0(U_73,U_72)),sdtasdt0(sdtasasdt0(U_73,U_73),sdtasasdt0(U_72,U_72)))
| ~ iLess0(aDimensionOf0(U_73),aDimensionOf0(xs))
| aDimensionOf0(U_73) != aDimensionOf0(U_72)
| ~ aVector0(U_72)
| ~ aVector0(U_73) ),
inference(definitional_conversion,[status(esa)],[f_39_2]) ).
cnf(f_39_4,plain,
( sdtlseqdt0(sdtasdt0(sdtasasdt0(U_73,U_72),sdtasasdt0(U_73,U_72)),sdtasdt0(sdtasasdt0(U_73,U_73),sdtasasdt0(U_72,U_72)))
| ~ iLess0(aDimensionOf0(U_73),aDimensionOf0(xs))
| aDimensionOf0(U_73) != aDimensionOf0(U_72)
| ~ aVector0(U_72)
| ~ aVector0(U_73) ),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(fof_nnf,[status(thm)],[m__1678_01]) ).
fof(f_40_2,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(definitional_conversion,[status(esa)],[f_40_1]) ).
cnf(f_40_3,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_1,plain,
aDimensionOf0(xs) != sz00,
inference(fof_nnf,[status(thm)],[m__1692]) ).
fof(f_41_2,plain,
aDimensionOf0(xs) != sz00,
inference(definitional_conversion,[status(esa)],[f_41_1]) ).
cnf(f_41_3,plain,
aDimensionOf0(xs) != sz00,
inference(clausify,[status(thm)],[f_41_2]) ).
fof(f_42_1,plain,
( xp = sziznziztdt0(xs)
& ! [W0] :
( sdtlbdtrb0(xp,W0) = sdtlbdtrb0(xs,W0)
| ~ aNaturalNumber0(W0) )
& szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs)
& aVector0(xp) ),
inference(fof_nnf,[status(thm)],[m__1709]) ).
fof(f_42_2,plain,
( xp = sziznziztdt0(xs)
& ! [U_74] :
( sdtlbdtrb0(xp,U_74) = sdtlbdtrb0(xs,U_74)
| ~ aNaturalNumber0(U_74) )
& szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs)
& aVector0(xp) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
( xp = sziznziztdt0(xs)
& ! [U_74] :
( sdtlbdtrb0(xp,U_74) = sdtlbdtrb0(xs,U_74)
| ~ aNaturalNumber0(U_74) )
& szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs)
& aVector0(xp) ),
inference(definitional_conversion,[status(esa)],[f_42_2]) ).
cnf(f_42_4,plain,
aVector0(xp),
inference(clausify,[status(thm)],[f_42_3]) ).
cnf(f_42_5,plain,
szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs),
inference(clausify,[status(thm)],[f_42_3]) ).
cnf(f_42_6,plain,
( sdtlbdtrb0(xp,U_74) = sdtlbdtrb0(xs,U_74)
| ~ aNaturalNumber0(U_74) ),
inference(clausify,[status(thm)],[f_42_3]) ).
cnf(f_42_7,plain,
xp = sziznziztdt0(xs),
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_43_1,plain,
( xq = sziznziztdt0(xt)
& ! [W0] :
( sdtlbdtrb0(xq,W0) = sdtlbdtrb0(xt,W0)
| ~ aNaturalNumber0(W0) )
& szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt)
& aVector0(xq) ),
inference(fof_nnf,[status(thm)],[m__1726]) ).
fof(f_43_2,plain,
( xq = sziznziztdt0(xt)
& ! [U_75] :
( sdtlbdtrb0(xq,U_75) = sdtlbdtrb0(xt,U_75)
| ~ aNaturalNumber0(U_75) )
& szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt)
& aVector0(xq) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
( xq = sziznziztdt0(xt)
& ! [U_75] :
( sdtlbdtrb0(xq,U_75) = sdtlbdtrb0(xt,U_75)
| ~ aNaturalNumber0(U_75) )
& szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt)
& aVector0(xq) ),
inference(definitional_conversion,[status(esa)],[f_43_2]) ).
cnf(f_43_4,plain,
aVector0(xq),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_5,plain,
szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_6,plain,
( sdtlbdtrb0(xq,U_75) = sdtlbdtrb0(xt,U_75)
| ~ aNaturalNumber0(U_75) ),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_7,plain,
xq = sziznziztdt0(xt),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
( xA = sdtlbdtrb0(xs,aDimensionOf0(xs))
& aScalar0(xA) ),
inference(fof_nnf,[status(thm)],[m__1746]) ).
fof(f_44_2,plain,
( xA = sdtlbdtrb0(xs,aDimensionOf0(xs))
& aScalar0(xA) ),
inference(definitional_conversion,[status(esa)],[f_44_1]) ).
cnf(f_44_3,plain,
aScalar0(xA),
inference(clausify,[status(thm)],[f_44_2]) ).
cnf(f_44_4,plain,
xA = sdtlbdtrb0(xs,aDimensionOf0(xs)),
inference(clausify,[status(thm)],[f_44_2]) ).
fof(f_45_1,plain,
( xB = sdtlbdtrb0(xt,aDimensionOf0(xt))
& aScalar0(xB) ),
inference(fof_nnf,[status(thm)],[m__1766]) ).
fof(f_45_2,plain,
( xB = sdtlbdtrb0(xt,aDimensionOf0(xt))
& aScalar0(xB) ),
inference(definitional_conversion,[status(esa)],[f_45_1]) ).
cnf(f_45_3,plain,
aScalar0(xB),
inference(clausify,[status(thm)],[f_45_2]) ).
cnf(f_45_4,plain,
xB = sdtlbdtrb0(xt,aDimensionOf0(xt)),
inference(clausify,[status(thm)],[f_45_2]) ).
fof(f_46_1,plain,
( xC = sdtasasdt0(xp,xp)
& aScalar0(xC) ),
inference(fof_nnf,[status(thm)],[m__1783]) ).
fof(f_46_2,plain,
( xC = sdtasasdt0(xp,xp)
& aScalar0(xC) ),
inference(definitional_conversion,[status(esa)],[f_46_1]) ).
cnf(f_46_3,plain,
aScalar0(xC),
inference(clausify,[status(thm)],[f_46_2]) ).
cnf(f_46_4,plain,
xC = sdtasasdt0(xp,xp),
inference(clausify,[status(thm)],[f_46_2]) ).
fof(f_47_1,plain,
( xD = sdtasasdt0(xq,xq)
& aScalar0(xD) ),
inference(fof_nnf,[status(thm)],[m__1800]) ).
fof(f_47_2,plain,
( xD = sdtasasdt0(xq,xq)
& aScalar0(xD) ),
inference(definitional_conversion,[status(esa)],[f_47_1]) ).
cnf(f_47_3,plain,
aScalar0(xD),
inference(clausify,[status(thm)],[f_47_2]) ).
cnf(f_47_4,plain,
xD = sdtasasdt0(xq,xq),
inference(clausify,[status(thm)],[f_47_2]) ).
fof(f_48_1,plain,
( xE = sdtasasdt0(xp,xq)
& aScalar0(xE) ),
inference(fof_nnf,[status(thm)],[m__1820]) ).
fof(f_48_2,plain,
( xE = sdtasasdt0(xp,xq)
& aScalar0(xE) ),
inference(definitional_conversion,[status(esa)],[f_48_1]) ).
cnf(f_48_3,plain,
aScalar0(xE),
inference(clausify,[status(thm)],[f_48_2]) ).
cnf(f_48_4,plain,
xE = sdtasasdt0(xp,xq),
inference(clausify,[status(thm)],[f_48_2]) ).
fof(f_49_1,plain,
( xF = sdtasdt0(xA,xA)
& aScalar0(xF) ),
inference(fof_nnf,[status(thm)],[m__1837]) ).
fof(f_49_2,plain,
( xF = sdtasdt0(xA,xA)
& aScalar0(xF) ),
inference(definitional_conversion,[status(esa)],[f_49_1]) ).
cnf(f_49_3,plain,
aScalar0(xF),
inference(clausify,[status(thm)],[f_49_2]) ).
cnf(f_49_4,plain,
xF = sdtasdt0(xA,xA),
inference(clausify,[status(thm)],[f_49_2]) ).
fof(f_50_1,plain,
( xG = sdtasdt0(xB,xB)
& aScalar0(xG) ),
inference(fof_nnf,[status(thm)],[m__1854]) ).
fof(f_50_2,plain,
( xG = sdtasdt0(xB,xB)
& aScalar0(xG) ),
inference(definitional_conversion,[status(esa)],[f_50_1]) ).
cnf(f_50_3,plain,
aScalar0(xG),
inference(clausify,[status(thm)],[f_50_2]) ).
cnf(f_50_4,plain,
xG = sdtasdt0(xB,xB),
inference(clausify,[status(thm)],[f_50_2]) ).
fof(f_51_1,plain,
( xH = sdtasdt0(xA,xB)
& aScalar0(xH) ),
inference(fof_nnf,[status(thm)],[m__1873]) ).
fof(f_51_2,plain,
( xH = sdtasdt0(xA,xB)
& aScalar0(xH) ),
inference(definitional_conversion,[status(esa)],[f_51_1]) ).
cnf(f_51_3,plain,
aScalar0(xH),
inference(clausify,[status(thm)],[f_51_2]) ).
cnf(f_51_4,plain,
xH = sdtasdt0(xA,xB),
inference(clausify,[status(thm)],[f_51_2]) ).
fof(f_52_1,plain,
( xR = sdtasdt0(xC,xG)
& aScalar0(xR) ),
inference(fof_nnf,[status(thm)],[m__1892]) ).
fof(f_52_2,plain,
( xR = sdtasdt0(xC,xG)
& aScalar0(xR) ),
inference(definitional_conversion,[status(esa)],[f_52_1]) ).
cnf(f_52_3,plain,
aScalar0(xR),
inference(clausify,[status(thm)],[f_52_2]) ).
cnf(f_52_4,plain,
xR = sdtasdt0(xC,xG),
inference(clausify,[status(thm)],[f_52_2]) ).
fof(f_53_1,plain,
( xP = sdtasdt0(xE,xH)
& aScalar0(xP) ),
inference(fof_nnf,[status(thm)],[m__1911]) ).
fof(f_53_2,plain,
( xP = sdtasdt0(xE,xH)
& aScalar0(xP) ),
inference(definitional_conversion,[status(esa)],[f_53_1]) ).
cnf(f_53_3,plain,
aScalar0(xP),
inference(clausify,[status(thm)],[f_53_2]) ).
cnf(f_53_4,plain,
xP = sdtasdt0(xE,xH),
inference(clausify,[status(thm)],[f_53_2]) ).
fof(f_54_1,plain,
( xS = sdtasdt0(xF,xD)
& aScalar0(xS) ),
inference(fof_nnf,[status(thm)],[m__1930]) ).
fof(f_54_2,plain,
( xS = sdtasdt0(xF,xD)
& aScalar0(xS) ),
inference(definitional_conversion,[status(esa)],[f_54_1]) ).
cnf(f_54_3,plain,
aScalar0(xS),
inference(clausify,[status(thm)],[f_54_2]) ).
cnf(f_54_4,plain,
xS = sdtasdt0(xF,xD),
inference(clausify,[status(thm)],[f_54_2]) ).
fof(f_55_1,plain,
( xN = sdtasdt0(xR,xS)
& aScalar0(xN) ),
inference(fof_nnf,[status(thm)],[m__1949]) ).
fof(f_55_2,plain,
( xN = sdtasdt0(xR,xS)
& aScalar0(xN) ),
inference(definitional_conversion,[status(esa)],[f_55_1]) ).
cnf(f_55_3,plain,
aScalar0(xN),
inference(clausify,[status(thm)],[f_55_2]) ).
cnf(f_55_4,plain,
xN = sdtasdt0(xR,xS),
inference(clausify,[status(thm)],[f_55_2]) ).
fof(f_56_1,plain,
sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
inference(fof_nnf,[status(thm)],[m__1967]) ).
fof(f_56_2,plain,
sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
inference(definitional_conversion,[status(esa)],[f_56_1]) ).
cnf(f_56_3,plain,
sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
inference(clausify,[status(thm)],[f_56_2]) ).
fof(f_57_1,plain,
sdtlseqdt0(sdtasdt0(xP,xP),xN),
inference(fof_nnf,[status(thm)],[m__2004]) ).
fof(f_57_2,plain,
sdtlseqdt0(sdtasdt0(xP,xP),xN),
inference(definitional_conversion,[status(esa)],[f_57_1]) ).
cnf(f_57_3,plain,
sdtlseqdt0(sdtasdt0(xP,xP),xN),
inference(clausify,[status(thm)],[f_57_2]) ).
fof(f_58_1,plain,
sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
inference(fof_nnf,[status(thm)],[m__2104]) ).
fof(f_58_2,plain,
sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
inference(definitional_conversion,[status(esa)],[f_58_1]) ).
cnf(f_58_3,plain,
sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
inference(clausify,[status(thm)],[f_58_2]) ).
fof(f_59_1,plain,
sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
inference(fof_nnf,[status(thm)],[m__2405]) ).
fof(f_59_2,plain,
sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
inference(definitional_conversion,[status(esa)],[f_59_1]) ).
cnf(f_59_3,plain,
sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
inference(clausify,[status(thm)],[f_59_2]) ).
fof(f_60_1,plain,
~ sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)),
inference(fof_nnf,[status(thm)],[m__2590]) ).
fof(f_60_2,plain,
~ sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)),
inference(definitional_conversion,[status(esa)],[f_60_1]) ).
cnf(f_60_3,plain,
~ sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)),
inference(clausify,[status(thm)],[f_60_2]) ).
fof(f_61_1,plain,
sdtlseqdt0(sdtpldt0(xR,xS),sdtpldt0(xP,xP)),
inference(fof_nnf,[status(thm)],[m__2610]) ).
fof(f_61_2,plain,
sdtlseqdt0(sdtpldt0(xR,xS),sdtpldt0(xP,xP)),
inference(definitional_conversion,[status(esa)],[f_61_1]) ).
cnf(f_61_3,plain,
sdtlseqdt0(sdtpldt0(xR,xS),sdtpldt0(xP,xP)),
inference(clausify,[status(thm)],[f_61_2]) ).
fof(f_62_1,plain,
( sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
& sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)) ),
inference(fof_nnf,[status(thm)],[m__2628]) ).
fof(f_62_2,plain,
( sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
& sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)) ),
inference(definitional_conversion,[status(esa)],[f_62_1]) ).
cnf(f_62_3,plain,
sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)),
inference(clausify,[status(thm)],[f_62_2]) ).
cnf(f_62_4,plain,
sdtlseqdt0(sz0z00,sdtpldt0(xP,xP)),
inference(clausify,[status(thm)],[f_62_2]) ).
fof(f_63_1,plain,
sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))),
inference(fof_nnf,[status(thm)],[m__2654]) ).
fof(f_63_2,plain,
sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))),
inference(definitional_conversion,[status(esa)],[f_63_1]) ).
cnf(f_63_3,plain,
sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))),
inference(clausify,[status(thm)],[f_63_2]) ).
fof(f_64_1,negated_conjecture,
sdtpldt0(xR,xS) != sdtpldt0(xP,xP),
inference(negate,[status(cth)],[m__]) ).
fof(f_64_2,negated_conjecture,
sdtpldt0(xR,xS) != sdtpldt0(xP,xP),
inference(definitional_conversion,[status(esa)],[f_64_1]) ).
cnf(f_64_3,negated_conjecture,
sdtpldt0(xR,xS) != sdtpldt0(xP,xP),
inference(clausify,[status(thm)],[f_64_2]) ).
cnf(f_1_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1_5]) ).
cnf(f_6_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_4]) ).
cnf(f_8_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_5]) ).
cnf(f_19_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_19_4]) ).
cnf(f_29_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_29_5]) ).
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,
( szszuzczcdt0(Eq_x_0) = szszuzczcdt0(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,
( smndt0(Eq_x_0) = smndt0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( aDimensionOf0(Eq_x_0) = aDimensionOf0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sdtlbdtrb0(Eq_x_0,Eq_x_1) = sdtlbdtrb0(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sziznziztdt0(Eq_x_0) = sziznziztdt0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,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_12,axiom,
( sK1(Eq_x_0) = sK1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,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_14,axiom,
( aNaturalNumber0(Eq_y_0)
| ~ aNaturalNumber0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_15,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_16,axiom,
( aScalar0(Eq_y_0)
| ~ aScalar0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,axiom,
( sdtlseqdt0(Eq_y_0,Eq_y_1)
| ~ sdtlseqdt0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,axiom,
( aVector0(Eq_y_0)
| ~ aVector0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,axiom,
( sP0(Eq_y_0)
| ~ sP0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,axiom,
( sP1(Eq_y_0)
| ~ sP1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( sP2(Eq_y_0)
| ~ sP2(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,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_23,axiom,
( sP4(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP4(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_24,axiom,
( sP5(Eq_y_0,Eq_y_1)
| ~ sP5(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,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_26,axiom,
( sP7(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP7(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_27,axiom,
( sP8(Eq_y_0,Eq_y_1)
| ~ sP8(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( sP9(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP9(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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG073+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 This is a FOF_CAX_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 19 20:49:49 UTC 2026
% 0.09/0.36 % CPUTime :
% 30.46/30.78 % SZS status Theorem for theBenchmark
% 30.46/30.78 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------