%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : RNG047+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 : n007.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 08:55:00 AM UTC 2026
% Result : Theorem 19.56s 19.87s
% Output : Proof 20.11s
% 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(m__1329,hypothesis,
( aVector0(xt)
& aVector0(xs) ),
file('theBenchmark.p',m__1329) ).
fof(m__1329_01,hypothesis,
( aDimensionOf0(xt) != sz00
& aDimensionOf0(xs) = aDimensionOf0(xt) ),
file('theBenchmark.p',m__1329_01) ).
fof(m__,conjecture,
( ( ! [W0] :
( aNaturalNumber0(W0)
=> sdtlbdtrb0(sziznziztdt0(xs),W0) = sdtlbdtrb0(xs,W0) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& aVector0(sziznziztdt0(xs)) )
=> ( ( ! [W0] :
( aNaturalNumber0(W0)
=> sdtlbdtrb0(sziznziztdt0(xt),W0) = sdtlbdtrb0(xt,W0) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt)
& aVector0(sziznziztdt0(xt)) )
=> aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) ) ),
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]) ).
cnf(f_1_4,plain,
( ~ aNaturalNumber0(U_0)
| $true ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
aNaturalNumber0(sz00),
inference(fof_nnf,[status(thm)],[mZeroNat]) ).
cnf(f_2_2,plain,
aNaturalNumber0(sz00),
inference(clausify,[status(thm)],[f_2_1]) ).
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]) ).
cnf(f_3_3,plain,
( aNaturalNumber0(szszuzczcdt0(U_1))
| ~ aNaturalNumber0(U_1) ),
inference(clausify,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( szszuzczcdt0(U_1) != sz00
| ~ aNaturalNumber0(U_1) ),
inference(clausify,[status(thm)],[f_3_2]) ).
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]) ).
cnf(f_4_4,plain,
( aNaturalNumber0(sK1(U_3))
| U_3 = sz00
| ~ aNaturalNumber0(U_3) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( U_3 = szszuzczcdt0(sK1(U_3))
| U_3 = sz00
| ~ aNaturalNumber0(U_3) ),
inference(clausify,[status(thm)],[f_4_3]) ).
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]) ).
cnf(f_5_3,plain,
( U_5 = U_4
| szszuzczcdt0(U_5) != szszuzczcdt0(U_4)
| ~ aNaturalNumber0(U_4)
| ~ aNaturalNumber0(U_5) ),
inference(clausify,[status(thm)],[f_5_2]) ).
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]) ).
cnf(f_6_3,plain,
( $true
| ~ iLess0(U_7,U_6)
| ~ aNaturalNumber0(U_6)
| ~ aNaturalNumber0(U_7) ),
inference(clausify,[status(thm)],[f_6_2]) ).
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]) ).
cnf(f_7_3,plain,
( iLess0(U_8,szszuzczcdt0(U_8))
| ~ aNaturalNumber0(U_8) ),
inference(clausify,[status(thm)],[f_7_2]) ).
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]) ).
cnf(f_8_4,plain,
( ~ aScalar0(U_9)
| $true ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
aScalar0(sz0z00),
inference(fof_nnf,[status(thm)],[mSZeroSc]) ).
cnf(f_9_2,plain,
aScalar0(sz0z00),
inference(clausify,[status(thm)],[f_9_1]) ).
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]) ).
cnf(f_10_3,plain,
( aScalar0(sdtpldt0(U_11,U_10))
| ~ aScalar0(U_10)
| ~ aScalar0(U_11) ),
inference(clausify,[status(thm)],[f_10_2]) ).
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]) ).
cnf(f_11_3,plain,
( aScalar0(sdtasdt0(U_13,U_12))
| ~ aScalar0(U_12)
| ~ aScalar0(U_13) ),
inference(clausify,[status(thm)],[f_11_2]) ).
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]) ).
cnf(f_12_3,plain,
( aScalar0(smndt0(U_14))
| ~ aScalar0(U_14) ),
inference(clausify,[status(thm)],[f_12_2]) ).
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]) ).
cnf(f_13_3,plain,
( sdtpldt0(U_15,sz0z00) = U_15
| ~ aScalar0(U_15) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
( sdtpldt0(sz0z00,U_15) = U_15
| ~ aScalar0(U_15) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_5,plain,
( sdtasdt0(U_15,sz0z00) = sz0z00
| ~ aScalar0(U_15) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_6,plain,
( sdtasdt0(sz0z00,U_15) = sz0z00
| ~ aScalar0(U_15) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_7,plain,
( sdtpldt0(U_15,smndt0(U_15)) = sz0z00
| ~ aScalar0(U_15) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_8,plain,
( sdtpldt0(smndt0(U_15),U_15) = sz0z00
| ~ aScalar0(U_15) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_9,plain,
( smndt0(smndt0(U_15)) = U_15
| ~ aScalar0(U_15) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_10,plain,
( smndt0(sz0z00) = sz0z00
| ~ aScalar0(U_15) ),
inference(clausify,[status(thm)],[f_13_2]) ).
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]) ).
cnf(f_14_3,plain,
( 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(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( sdtpldt0(U_18,U_17) = sdtpldt0(U_17,U_18)
| ~ aScalar0(U_16)
| ~ aScalar0(U_17)
| ~ aScalar0(U_18) ),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_5,plain,
( sdtasdt0(sdtasdt0(U_18,U_17),U_16) = sdtasdt0(U_18,sdtasdt0(U_17,U_16))
| ~ aScalar0(U_16)
| ~ aScalar0(U_17)
| ~ aScalar0(U_18) ),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_6,plain,
( sdtasdt0(U_18,U_17) = sdtasdt0(U_17,U_18)
| ~ aScalar0(U_16)
| ~ aScalar0(U_17)
| ~ aScalar0(U_18) ),
inference(clausify,[status(thm)],[f_14_2]) ).
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]) ).
cnf(f_15_3,plain,
( 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(clausify,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
( sdtasdt0(sdtpldt0(U_21,U_20),U_19) = sdtpldt0(sdtasdt0(U_21,U_19),sdtasdt0(U_20,U_19))
| ~ aScalar0(U_19)
| ~ aScalar0(U_20)
| ~ aScalar0(U_21) ),
inference(clausify,[status(thm)],[f_15_2]) ).
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]) ).
cnf(f_16_3,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_2]) ).
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]) ).
cnf(f_17_3,plain,
( sdtasdt0(U_27,smndt0(U_26)) = smndt0(sdtasdt0(U_27,U_26))
| ~ aScalar0(U_26)
| ~ aScalar0(U_27) ),
inference(clausify,[status(thm)],[f_17_2]) ).
cnf(f_17_4,plain,
( sdtasdt0(smndt0(U_27),U_26) = smndt0(sdtasdt0(U_27,U_26))
| ~ aScalar0(U_26)
| ~ aScalar0(U_27) ),
inference(clausify,[status(thm)],[f_17_2]) ).
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]) ).
cnf(f_18_3,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_2]) ).
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]) ).
cnf(f_19_3,plain,
( $true
| ~ sdtlseqdt0(U_31,U_30)
| ~ aScalar0(U_30)
| ~ aScalar0(U_31) ),
inference(clausify,[status(thm)],[f_19_2]) ).
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]) ).
cnf(f_20_3,plain,
( sdtlseqdt0(U_32,U_32)
| ~ aScalar0(U_32) ),
inference(clausify,[status(thm)],[f_20_2]) ).
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]) ).
cnf(f_21_3,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_2]) ).
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]) ).
cnf(f_22_3,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_2]) ).
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]) ).
cnf(f_23_3,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_2]) ).
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]) ).
cnf(f_24_3,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_2]) ).
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]) ).
cnf(f_25_3,plain,
( sdtlseqdt0(U_46,U_47)
| sdtlseqdt0(U_47,U_46)
| ~ aScalar0(U_46)
| ~ aScalar0(U_47) ),
inference(clausify,[status(thm)],[f_25_2]) ).
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]) ).
cnf(f_26_3,plain,
( sdtlseqdt0(sz0z00,sdtpldt0(U_49,U_48))
| ~ sdtlseqdt0(sz0z00,U_48)
| ~ sdtlseqdt0(sz0z00,U_49)
| ~ aScalar0(U_48)
| ~ aScalar0(U_49) ),
inference(clausify,[status(thm)],[f_26_2]) ).
cnf(f_26_4,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(U_49,U_48))
| ~ sdtlseqdt0(sz0z00,U_48)
| ~ sdtlseqdt0(sz0z00,U_49)
| ~ aScalar0(U_48)
| ~ aScalar0(U_49) ),
inference(clausify,[status(thm)],[f_26_2]) ).
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]) ).
cnf(f_27_3,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(U_50,U_50))
| ~ aScalar0(U_50) ),
inference(clausify,[status(thm)],[f_27_2]) ).
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]) ).
cnf(f_28_3,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_2]) ).
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]) ).
cnf(f_29_4,plain,
( ~ aVector0(U_53)
| $true ),
inference(clausify,[status(thm)],[f_29_3]) ).
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]) ).
cnf(f_30_3,plain,
( aNaturalNumber0(aDimensionOf0(U_54))
| ~ aVector0(U_54) ),
inference(clausify,[status(thm)],[f_30_2]) ).
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]) ).
cnf(f_31_3,plain,
( aScalar0(sdtlbdtrb0(U_56,U_55))
| ~ aNaturalNumber0(U_55)
| ~ aVector0(U_56) ),
inference(clausify,[status(thm)],[f_31_2]) ).
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]) ).
cnf(f_32_5,plain,
( aVector0(U_61)
| U_61 != sziznziztdt0(U_60)
| aDimensionOf0(U_60) = sz00
| ~ aVector0(U_60) ),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_6,plain,
( szszuzczcdt0(aDimensionOf0(U_61)) = aDimensionOf0(U_60)
| U_61 != sziznziztdt0(U_60)
| aDimensionOf0(U_60) = sz00
| ~ aVector0(U_60) ),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_7,plain,
( sdtlbdtrb0(U_61,U_57) = sdtlbdtrb0(U_60,U_57)
| ~ aNaturalNumber0(U_57)
| U_61 != sziznziztdt0(U_60)
| aDimensionOf0(U_60) = sz00
| ~ aVector0(U_60) ),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_8,plain,
( aNaturalNumber0(sK2(U_60,U_62))
| szszuzczcdt0(aDimensionOf0(U_62)) != aDimensionOf0(U_60)
| ~ aVector0(U_62)
| U_62 = sziznziztdt0(U_60)
| aDimensionOf0(U_60) = sz00
| ~ aVector0(U_60) ),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_9,plain,
( sdtlbdtrb0(U_62,sK2(U_60,U_62)) != sdtlbdtrb0(U_60,sK2(U_60,U_62))
| szszuzczcdt0(aDimensionOf0(U_62)) != aDimensionOf0(U_60)
| ~ aVector0(U_62)
| U_62 = sziznziztdt0(U_60)
| aDimensionOf0(U_60) = sz00
| ~ aVector0(U_60) ),
inference(clausify,[status(thm)],[f_32_4]) ).
fof(f_33_1,plain,
( aVector0(xt)
& aVector0(xs) ),
inference(fof_nnf,[status(thm)],[m__1329]) ).
cnf(f_33_2,plain,
aVector0(xs),
inference(clausify,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
aVector0(xt),
inference(clausify,[status(thm)],[f_33_1]) ).
fof(f_34_1,plain,
( aDimensionOf0(xt) != sz00
& aDimensionOf0(xs) = aDimensionOf0(xt) ),
inference(fof_nnf,[status(thm)],[m__1329_01]) ).
cnf(f_34_2,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(clausify,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
aDimensionOf0(xt) != sz00,
inference(clausify,[status(thm)],[f_34_1]) ).
fof(f_35_1,negated_conjecture,
( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt))
& ! [W0] :
( aNaturalNumber0(W0)
=> sdtlbdtrb0(sziznziztdt0(xt),W0) = sdtlbdtrb0(xt,W0) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt)
& aVector0(sziznziztdt0(xt))
& ! [W0] :
( aNaturalNumber0(W0)
=> sdtlbdtrb0(sziznziztdt0(xs),W0) = sdtlbdtrb0(xs,W0) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& aVector0(sziznziztdt0(xs)) ),
inference(negate,[status(cth)],[m__]) ).
fof(f_35_2,negated_conjecture,
( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt))
& ! [W0] :
( sdtlbdtrb0(sziznziztdt0(xt),W0) = sdtlbdtrb0(xt,W0)
| ~ aNaturalNumber0(W0) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt)
& aVector0(sziznziztdt0(xt))
& ! [W0] :
( sdtlbdtrb0(sziznziztdt0(xs),W0) = sdtlbdtrb0(xs,W0)
| ~ aNaturalNumber0(W0) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& aVector0(sziznziztdt0(xs)) ),
inference(fof_nnf,[status(thm)],[f_35_1]) ).
fof(f_35_3,negated_conjecture,
( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt))
& ! [U_64] :
( sdtlbdtrb0(sziznziztdt0(xt),U_64) = sdtlbdtrb0(xt,U_64)
| ~ aNaturalNumber0(U_64) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt)
& aVector0(sziznziztdt0(xt))
& ! [U_63] :
( sdtlbdtrb0(sziznziztdt0(xs),U_63) = sdtlbdtrb0(xs,U_63)
| ~ aNaturalNumber0(U_63) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& aVector0(sziznziztdt0(xs)) ),
inference(variable_rename,[status(thm)],[f_35_2]) ).
fof(f_35_4,negated_conjecture,
( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt))
& ! [U_64] :
( sdtlbdtrb0(sziznziztdt0(xt),U_64) = sdtlbdtrb0(xt,U_64)
| ~ aNaturalNumber0(U_64) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt)
& aVector0(sziznziztdt0(xt))
& ! [U_63] :
( sdtlbdtrb0(sziznziztdt0(xs),U_63) = sdtlbdtrb0(xs,U_63)
| ~ aNaturalNumber0(U_63) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& aVector0(sziznziztdt0(xs)) ),
inference(definitional_conversion,[status(esa)],[f_35_3]) ).
cnf(f_35_5,negated_conjecture,
aVector0(sziznziztdt0(xs)),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_6,negated_conjecture,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_7,negated_conjecture,
( sdtlbdtrb0(sziznziztdt0(xs),U_63) = sdtlbdtrb0(xs,U_63)
| ~ aNaturalNumber0(U_63) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_8,negated_conjecture,
aVector0(sziznziztdt0(xt)),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_9,negated_conjecture,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_10,negated_conjecture,
( sdtlbdtrb0(sziznziztdt0(xt),U_64) = sdtlbdtrb0(xt,U_64)
| ~ aNaturalNumber0(U_64) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_11,negated_conjecture,
aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_1_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1_4]) ).
cnf(f_6_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_3]) ).
cnf(f_8_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_4]) ).
cnf(f_19_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_19_3]) ).
cnf(f_29_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_29_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,
( 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,
( sK1(Eq_x_0) = sK1(Eq_y_0)
| 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,
( aNaturalNumber0(Eq_y_0)
| ~ aNaturalNumber0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_14,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_15,axiom,
( aScalar0(Eq_y_0)
| ~ aScalar0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_16,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_17,axiom,
( aVector0(Eq_y_0)
| ~ aVector0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG047+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.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 20:43:05 UTC 2026
% 0.09/0.36 % CPUTime :
% 19.56/19.87 % SZS status Theorem for theBenchmark
% 19.56/19.87 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------