TSTP Solution File: RNG081+2 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : RNG081+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n021.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 13:57:45 EDT 2023

% Result   : Theorem 11.48s 2.34s
% Output   : Proof 17.37s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : RNG081+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34  % Computer : n021.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Sun Aug 27 03:02:12 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.20/0.58  ________       _____
% 0.20/0.58  ___  __ \_________(_)________________________________
% 0.20/0.58  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.58  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.58  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.58  
% 0.20/0.58  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.58  (2023-06-19)
% 0.20/0.58  
% 0.20/0.58  (c) Philipp Rümmer, 2009-2023
% 0.20/0.58  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.58                Amanda Stjerna.
% 0.20/0.58  Free software under BSD-3-Clause.
% 0.20/0.58  
% 0.20/0.58  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.58  
% 0.20/0.59  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.60  Running up to 7 provers in parallel.
% 0.20/0.61  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.61  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.61  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.61  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.61  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.61  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.61  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.51/1.23  Prover 4: Preprocessing ...
% 3.51/1.23  Prover 1: Preprocessing ...
% 3.51/1.27  Prover 6: Preprocessing ...
% 3.51/1.27  Prover 2: Preprocessing ...
% 3.51/1.27  Prover 5: Preprocessing ...
% 3.51/1.27  Prover 0: Preprocessing ...
% 3.51/1.28  Prover 3: Preprocessing ...
% 9.24/2.02  Prover 1: Constructing countermodel ...
% 9.65/2.06  Prover 3: Constructing countermodel ...
% 9.65/2.07  Prover 6: Proving ...
% 10.80/2.32  Prover 3: proved (1711ms)
% 10.80/2.32  
% 11.48/2.34  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.48/2.34  
% 11.48/2.34  Prover 6: stopped
% 11.48/2.34  Prover 5: Constructing countermodel ...
% 11.48/2.34  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.48/2.34  Prover 5: stopped
% 11.48/2.35  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.48/2.35  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.48/2.35  Prover 4: Constructing countermodel ...
% 12.30/2.44  Prover 10: Preprocessing ...
% 12.30/2.44  Prover 7: Preprocessing ...
% 12.30/2.45  Prover 2: Proving ...
% 12.48/2.48  Prover 8: Preprocessing ...
% 12.48/2.48  Prover 2: stopped
% 12.48/2.48  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.48/2.49  Prover 0: Proving ...
% 12.48/2.49  Prover 0: stopped
% 12.48/2.50  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.15/2.57  Prover 11: Preprocessing ...
% 13.15/2.61  Prover 13: Preprocessing ...
% 13.74/2.64  Prover 8: Warning: ignoring some quantifiers
% 13.74/2.65  Prover 8: Constructing countermodel ...
% 14.08/2.70  Prover 10: Constructing countermodel ...
% 14.78/2.77  Prover 7: Constructing countermodel ...
% 14.78/2.91  Prover 13: Constructing countermodel ...
% 17.02/3.10  Prover 11: Constructing countermodel ...
% 17.02/3.11  Prover 10: Found proof (size 90)
% 17.02/3.11  Prover 10: proved (762ms)
% 17.02/3.11  Prover 13: stopped
% 17.02/3.11  Prover 7: stopped
% 17.02/3.11  Prover 8: stopped
% 17.02/3.11  Prover 4: stopped
% 17.27/3.11  Prover 1: stopped
% 17.27/3.11  Prover 11: stopped
% 17.27/3.11  
% 17.27/3.11  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.27/3.11  
% 17.27/3.13  % SZS output start Proof for theBenchmark
% 17.27/3.13  Assumptions after simplification:
% 17.27/3.13  ---------------------------------
% 17.27/3.13  
% 17.27/3.13    (mDefSPZ)
% 17.37/3.15    $i(sz0z00) & $i(sz00) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = sz0z00
% 17.37/3.15      |  ~ (sdtasasdt0(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ aVector0(v1) | 
% 17.37/3.15      ~ aVector0(v0) |  ? [v3: $i] :  ? [v4: $i] : (aDimensionOf0(v1) = v4 &
% 17.37/3.15        $i(v4) & ( ~ (v4 = sz00) | ( ~ (v3 = sz00) & aDimensionOf0(v0) = v3 &
% 17.37/3.15            $i(v3)))))
% 17.37/3.15  
% 17.37/3.16    (mLEMonM)
% 17.37/3.16    $i(sz0z00) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4:
% 17.37/3.16      $i] :  ! [v5: $i] : ( ~ (sdtasdt0(v1, v3) = v5) |  ~ (sdtasdt0(v0, v2) = v4)
% 17.37/3.16      |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ sdtlseqdt0(v2, v3) |  ~
% 17.37/3.16      sdtlseqdt0(v0, v1) |  ~ sdtlseqdt0(sz0z00, v2) |  ~ aScalar0(v3) |  ~
% 17.37/3.16      aScalar0(v2) |  ~ aScalar0(v1) |  ~ aScalar0(v0) | sdtlseqdt0(v4, v5))
% 17.37/3.16  
% 17.37/3.16    (mScPr)
% 17.37/3.16     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (sdtasasdt0(v0, v1) = v2) |  ~
% 17.37/3.16      $i(v1) |  ~ $i(v0) |  ~ aVector0(v1) |  ~ aVector0(v0) | aScalar0(v2) |  ?
% 17.37/3.16      [v3: $i] :  ? [v4: $i] : ( ~ (v4 = v3) & aDimensionOf0(v1) = v4 &
% 17.37/3.16        aDimensionOf0(v0) = v3 & $i(v4) & $i(v3)))
% 17.37/3.16  
% 17.37/3.16    (mScSqPos)
% 17.37/3.16    $i(sz0z00) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (sdtasasdt0(v0, v0) = v1) |  ~
% 17.37/3.16      $i(v0) |  ~ aVector0(v0) | sdtlseqdt0(sz0z00, v1))
% 17.37/3.16  
% 17.37/3.16    (m__)
% 17.37/3.16    $i(xt) & $i(xs) & $i(sz00) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3:
% 17.37/3.16      $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] : 
% 17.37/3.16    ? [v9: $i] :  ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ?
% 17.37/3.16    [v14: $i] :  ? [v15: $i] :  ? [v16: $i] :  ? [v17: $i] :  ? [v18: $i] :
% 17.37/3.16    (sdtasasdt0(xt, xt) = v3 & sdtasasdt0(xs, xt) = v0 & sdtasasdt0(xs, xs) = v2 &
% 17.37/3.16      aDimensionOf0(xs) = sz00 & sdtasdt0(v2, v3) = v4 & sdtasdt0(v0, v0) = v1 &
% 17.37/3.16      $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 17.37/3.16      $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 17.37/3.16      $i(v3) & $i(v2) & $i(v1) & $i(v0) &  ~ sdtlseqdt0(v1, v4))
% 17.37/3.16  
% 17.37/3.16    (m__1652)
% 17.37/3.16    $i(xs) &  ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) &  ! [v1: $i] :  !
% 17.37/3.16      [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :  ! [v5: $i] : ( ~ (sdtasasdt0(v2, v2)
% 17.37/3.16          = v4) |  ~ (sdtasasdt0(v1, v1) = v3) |  ~ (sdtasdt0(v3, v4) = v5) |  ~
% 17.37/3.16        $i(v2) |  ~ $i(v1) |  ~ aVector0(v2) |  ~ aVector0(v1) |  ? [v6: $i] :  ?
% 17.37/3.16        [v7: $i] :  ? [v8: $i] :  ? [v9: $i] : ((sdtasasdt0(v1, v2) = v8 &
% 17.37/3.16            sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8) & sdtlseqdt0(v9, v5)) |
% 17.37/3.16          (aDimensionOf0(v1) = v6 & $i(v6) & ( ~ iLess0(v6, v0) | ( ~ (v7 = v6) &
% 17.37/3.16                aDimensionOf0(v2) = v7 & $i(v7)))))))
% 17.37/3.16  
% 17.37/3.16    (m__1678)
% 17.37/3.16    $i(xt) & $i(xs) & aVector0(xt) & aVector0(xs)
% 17.37/3.16  
% 17.37/3.16    (m__1678_01)
% 17.37/3.17    $i(xt) & $i(xs) &  ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) =
% 17.37/3.17      v0 & $i(v0))
% 17.37/3.17  
% 17.37/3.17    (function-axioms)
% 17.37/3.17     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 17.37/3.17      (sdtasasdt0(v3, v2) = v1) |  ~ (sdtasasdt0(v3, v2) = v0)) &  ! [v0: $i] :  !
% 17.37/3.17    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (sdtlbdtrb0(v3, v2) = v1)
% 17.37/3.17      |  ~ (sdtlbdtrb0(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : 
% 17.37/3.17    ! [v3: $i] : (v1 = v0 |  ~ (sdtasdt0(v3, v2) = v1) |  ~ (sdtasdt0(v3, v2) =
% 17.37/3.17        v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 | 
% 17.37/3.17      ~ (sdtpldt0(v3, v2) = v1) |  ~ (sdtpldt0(v3, v2) = v0)) &  ! [v0: $i] :  !
% 17.37/3.17    [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (sziznziztdt0(v2) = v1) |  ~
% 17.37/3.17      (sziznziztdt0(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 =
% 17.37/3.17      v0 |  ~ (aDimensionOf0(v2) = v1) |  ~ (aDimensionOf0(v2) = v0)) &  ! [v0:
% 17.37/3.17      $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (smndt0(v2) = v1) |  ~
% 17.37/3.17      (smndt0(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 17.37/3.17      (szszuzczcdt0(v2) = v1) |  ~ (szszuzczcdt0(v2) = v0))
% 17.37/3.17  
% 17.37/3.17  Further assumptions not needed in the proof:
% 17.37/3.17  --------------------------------------------
% 17.37/3.17  mArith, mDefInit, mDefSPN, mDimNat, mDistr, mDistr2, mElmSc, mEqInit, mIH,
% 17.37/3.17  mIHOrd, mLEASm, mLEMon, mLERef, mLETot, mLETrn, mLess, mMDNeg, mMNeg, mMulSc,
% 17.37/3.17  mNatExtr, mNatSort, mNegSc, mPosMon, mSZeroSc, mScSort, mScZero, mSqPos, mSqrt,
% 17.37/3.17  mSuccEqu, mSuccNat, mSumSc, mVcSort, mZeroNat
% 17.37/3.17  
% 17.37/3.17  Those formulas are unsatisfiable:
% 17.37/3.17  ---------------------------------
% 17.37/3.17  
% 17.37/3.17  Begin of proof
% 17.37/3.17  | 
% 17.37/3.17  | ALPHA: (mLEMonM) implies:
% 17.37/3.17  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : 
% 17.37/3.17  |        ! [v5: $i] : ( ~ (sdtasdt0(v1, v3) = v5) |  ~ (sdtasdt0(v0, v2) = v4) |
% 17.37/3.17  |           ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ sdtlseqdt0(v2, v3)
% 17.37/3.17  |          |  ~ sdtlseqdt0(v0, v1) |  ~ sdtlseqdt0(sz0z00, v2) |  ~ aScalar0(v3)
% 17.37/3.17  |          |  ~ aScalar0(v2) |  ~ aScalar0(v1) |  ~ aScalar0(v0) |
% 17.37/3.17  |          sdtlseqdt0(v4, v5))
% 17.37/3.17  | 
% 17.37/3.17  | ALPHA: (mDefSPZ) implies:
% 17.37/3.17  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = sz0z00 |  ~
% 17.37/3.17  |          (sdtasasdt0(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ aVector0(v1) |
% 17.37/3.17  |           ~ aVector0(v0) |  ? [v3: $i] :  ? [v4: $i] : (aDimensionOf0(v1) = v4
% 17.37/3.17  |            & $i(v4) & ( ~ (v4 = sz00) | ( ~ (v3 = sz00) & aDimensionOf0(v0) =
% 17.37/3.17  |                v3 & $i(v3)))))
% 17.37/3.17  | 
% 17.37/3.17  | ALPHA: (mScSqPos) implies:
% 17.37/3.17  |   (3)   ! [v0: $i] :  ! [v1: $i] : ( ~ (sdtasasdt0(v0, v0) = v1) |  ~ $i(v0) |
% 17.37/3.17  |           ~ aVector0(v0) | sdtlseqdt0(sz0z00, v1))
% 17.37/3.17  | 
% 17.37/3.17  | ALPHA: (m__1678) implies:
% 17.37/3.17  |   (4)  aVector0(xs)
% 17.37/3.17  |   (5)  aVector0(xt)
% 17.37/3.17  | 
% 17.37/3.17  | ALPHA: (m__1652) implies:
% 17.37/3.18  |   (6)   ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) &  ! [v1: $i] :  ! [v2:
% 17.37/3.18  |            $i] :  ! [v3: $i] :  ! [v4: $i] :  ! [v5: $i] : ( ~ (sdtasasdt0(v2,
% 17.37/3.18  |                v2) = v4) |  ~ (sdtasasdt0(v1, v1) = v3) |  ~ (sdtasdt0(v3, v4)
% 17.37/3.18  |              = v5) |  ~ $i(v2) |  ~ $i(v1) |  ~ aVector0(v2) |  ~ aVector0(v1)
% 17.37/3.18  |            |  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] :
% 17.37/3.18  |            ((sdtasasdt0(v1, v2) = v8 & sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8)
% 17.37/3.18  |                & sdtlseqdt0(v9, v5)) | (aDimensionOf0(v1) = v6 & $i(v6) & ( ~
% 17.37/3.18  |                  iLess0(v6, v0) | ( ~ (v7 = v6) & aDimensionOf0(v2) = v7 &
% 17.37/3.18  |                    $i(v7)))))))
% 17.37/3.18  | 
% 17.37/3.18  | ALPHA: (m__1678_01) implies:
% 17.37/3.18  |   (7)   ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) = v0 &
% 17.37/3.18  |          $i(v0))
% 17.37/3.18  | 
% 17.37/3.18  | ALPHA: (m__) implies:
% 17.37/3.18  |   (8)  $i(xs)
% 17.37/3.18  |   (9)  $i(xt)
% 17.37/3.18  |   (10)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 17.37/3.18  |         ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] : 
% 17.37/3.18  |         ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14:
% 17.37/3.18  |           $i] :  ? [v15: $i] :  ? [v16: $i] :  ? [v17: $i] :  ? [v18: $i] :
% 17.37/3.18  |         (sdtasasdt0(xt, xt) = v3 & sdtasasdt0(xs, xt) = v0 & sdtasasdt0(xs,
% 17.37/3.18  |             xs) = v2 & aDimensionOf0(xs) = sz00 & sdtasdt0(v2, v3) = v4 &
% 17.37/3.18  |           sdtasdt0(v0, v0) = v1 & $i(v18) & $i(v17) & $i(v16) & $i(v15) &
% 17.37/3.18  |           $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) &
% 17.37/3.18  |           $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 17.37/3.18  |           $i(v0) &  ~ sdtlseqdt0(v1, v4))
% 17.37/3.18  | 
% 17.37/3.18  | ALPHA: (function-axioms) implies:
% 17.37/3.18  |   (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 17.37/3.18  |           (aDimensionOf0(v2) = v1) |  ~ (aDimensionOf0(v2) = v0))
% 17.37/3.18  |   (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 17.37/3.18  |           (sdtasdt0(v3, v2) = v1) |  ~ (sdtasdt0(v3, v2) = v0))
% 17.37/3.18  | 
% 17.37/3.18  | DELTA: instantiating (7) with fresh symbol all_33_0 gives:
% 17.37/3.18  |   (13)  aDimensionOf0(xt) = all_33_0 & aDimensionOf0(xs) = all_33_0 &
% 17.37/3.18  |         $i(all_33_0)
% 17.37/3.18  | 
% 17.37/3.18  | ALPHA: (13) implies:
% 17.37/3.18  |   (14)  aDimensionOf0(xs) = all_33_0
% 17.37/3.18  |   (15)  aDimensionOf0(xt) = all_33_0
% 17.37/3.18  | 
% 17.37/3.18  | DELTA: instantiating (6) with fresh symbol all_35_0 gives:
% 17.37/3.18  |   (16)  aDimensionOf0(xs) = all_35_0 & $i(all_35_0) &  ! [v0: $i] :  ! [v1:
% 17.37/3.18  |           $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : ( ~ (sdtasasdt0(v1,
% 17.37/3.18  |               v1) = v3) |  ~ (sdtasasdt0(v0, v0) = v2) |  ~ (sdtasdt0(v2, v3)
% 17.37/3.18  |             = v4) |  ~ $i(v1) |  ~ $i(v0) |  ~ aVector0(v1) |  ~ aVector0(v0)
% 17.37/3.18  |           |  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :
% 17.37/3.18  |           ((sdtasasdt0(v0, v1) = v7 & sdtasdt0(v7, v7) = v8 & $i(v8) & $i(v7)
% 17.37/3.18  |               & sdtlseqdt0(v8, v4)) | (aDimensionOf0(v0) = v5 & $i(v5) & ( ~
% 17.37/3.18  |                 iLess0(v5, all_35_0) | ( ~ (v6 = v5) & aDimensionOf0(v1) = v6
% 17.37/3.18  |                   & $i(v6))))))
% 17.37/3.18  | 
% 17.37/3.18  | ALPHA: (16) implies:
% 17.37/3.18  |   (17)  aDimensionOf0(xs) = all_35_0
% 17.37/3.18  | 
% 17.37/3.18  | DELTA: instantiating (10) with fresh symbols all_41_0, all_41_1, all_41_2,
% 17.37/3.18  |        all_41_3, all_41_4, all_41_5, all_41_6, all_41_7, all_41_8, all_41_9,
% 17.37/3.18  |        all_41_10, all_41_11, all_41_12, all_41_13, all_41_14, all_41_15,
% 17.37/3.18  |        all_41_16, all_41_17, all_41_18 gives:
% 17.37/3.18  |   (18)  sdtasasdt0(xt, xt) = all_41_15 & sdtasasdt0(xs, xt) = all_41_18 &
% 17.37/3.18  |         sdtasasdt0(xs, xs) = all_41_16 & aDimensionOf0(xs) = sz00 &
% 17.37/3.18  |         sdtasdt0(all_41_16, all_41_15) = all_41_14 & sdtasdt0(all_41_18,
% 17.37/3.18  |           all_41_18) = all_41_17 & $i(all_41_0) & $i(all_41_1) & $i(all_41_2)
% 17.37/3.18  |         & $i(all_41_3) & $i(all_41_4) & $i(all_41_5) & $i(all_41_6) &
% 17.37/3.18  |         $i(all_41_7) & $i(all_41_8) & $i(all_41_9) & $i(all_41_10) &
% 17.37/3.18  |         $i(all_41_11) & $i(all_41_12) & $i(all_41_13) & $i(all_41_14) &
% 17.37/3.18  |         $i(all_41_15) & $i(all_41_16) & $i(all_41_17) & $i(all_41_18) &  ~
% 17.37/3.18  |         sdtlseqdt0(all_41_17, all_41_14)
% 17.37/3.18  | 
% 17.37/3.18  | ALPHA: (18) implies:
% 17.37/3.18  |   (19)   ~ sdtlseqdt0(all_41_17, all_41_14)
% 17.37/3.18  |   (20)  $i(all_41_16)
% 17.37/3.19  |   (21)  sdtasdt0(all_41_18, all_41_18) = all_41_17
% 17.37/3.19  |   (22)  sdtasdt0(all_41_16, all_41_15) = all_41_14
% 17.37/3.19  |   (23)  aDimensionOf0(xs) = sz00
% 17.37/3.19  |   (24)  sdtasasdt0(xs, xs) = all_41_16
% 17.37/3.19  |   (25)  sdtasasdt0(xs, xt) = all_41_18
% 17.37/3.19  |   (26)  sdtasasdt0(xt, xt) = all_41_15
% 17.37/3.19  | 
% 17.37/3.19  | GROUND_INST: instantiating (11) with all_33_0, all_35_0, xs, simplifying with
% 17.37/3.19  |              (14), (17) gives:
% 17.37/3.19  |   (27)  all_35_0 = all_33_0
% 17.37/3.19  | 
% 17.37/3.19  | GROUND_INST: instantiating (11) with sz00, all_35_0, xs, simplifying with
% 17.37/3.19  |              (17), (23) gives:
% 17.37/3.19  |   (28)  all_35_0 = sz00
% 17.37/3.19  | 
% 17.37/3.19  | COMBINE_EQS: (27), (28) imply:
% 17.37/3.19  |   (29)  all_33_0 = sz00
% 17.37/3.19  | 
% 17.37/3.19  | SIMP: (29) implies:
% 17.37/3.19  |   (30)  all_33_0 = sz00
% 17.37/3.19  | 
% 17.37/3.19  | REDUCE: (15), (30) imply:
% 17.37/3.19  |   (31)  aDimensionOf0(xt) = sz00
% 17.37/3.19  | 
% 17.37/3.19  | GROUND_INST: instantiating (2) with xs, xs, all_41_16, simplifying with (4),
% 17.37/3.19  |              (8), (24) gives:
% 17.37/3.19  |   (32)  all_41_16 = sz0z00 |  ? [v0: $i] :  ? [v1: $i] : (aDimensionOf0(xs) =
% 17.37/3.19  |           v1 & $i(v1) & ( ~ (v1 = sz00) | ( ~ (v0 = sz00) & aDimensionOf0(xs)
% 17.37/3.19  |               = v0 & $i(v0))))
% 17.37/3.19  | 
% 17.37/3.19  | GROUND_INST: instantiating (mScPr) with xs, xs, all_41_16, simplifying with
% 17.37/3.19  |              (4), (8), (24) gives:
% 17.37/3.19  |   (33)  aScalar0(all_41_16) |  ? [v0: $i] :  ? [v1: $i] : ( ~ (v1 = v0) &
% 17.37/3.19  |           aDimensionOf0(xs) = v1 & aDimensionOf0(xs) = v0 & $i(v1) & $i(v0))
% 17.37/3.19  | 
% 17.37/3.19  | GROUND_INST: instantiating (3) with xs, all_41_16, simplifying with (4), (8),
% 17.37/3.19  |              (24) gives:
% 17.37/3.19  |   (34)  sdtlseqdt0(sz0z00, all_41_16)
% 17.37/3.19  | 
% 17.37/3.19  | GROUND_INST: instantiating (2) with xs, xt, all_41_18, simplifying with (4),
% 17.37/3.19  |              (5), (8), (9), (25) gives:
% 17.37/3.19  |   (35)  all_41_18 = sz0z00 |  ? [v0: $i] :  ? [v1: $i] : (aDimensionOf0(xt) =
% 17.37/3.19  |           v1 & $i(v1) & ( ~ (v1 = sz00) | ( ~ (v0 = sz00) & aDimensionOf0(xs)
% 17.37/3.19  |               = v0 & $i(v0))))
% 17.37/3.19  | 
% 17.37/3.19  | GROUND_INST: instantiating (2) with xt, xt, all_41_15, simplifying with (5),
% 17.37/3.19  |              (9), (26) gives:
% 17.37/3.19  |   (36)  all_41_15 = sz0z00 |  ? [v0: $i] :  ? [v1: $i] : (aDimensionOf0(xt) =
% 17.37/3.19  |           v1 & $i(v1) & ( ~ (v1 = sz00) | ( ~ (v0 = sz00) & aDimensionOf0(xt)
% 17.37/3.19  |               = v0 & $i(v0))))
% 17.37/3.19  | 
% 17.37/3.19  | BETA: splitting (33) gives:
% 17.37/3.19  | 
% 17.37/3.19  | Case 1:
% 17.37/3.19  | | 
% 17.37/3.19  | |   (37)  aScalar0(all_41_16)
% 17.37/3.19  | | 
% 17.37/3.19  | | BETA: splitting (36) gives:
% 17.37/3.19  | | 
% 17.37/3.19  | | Case 1:
% 17.37/3.19  | | | 
% 17.37/3.19  | | |   (38)  all_41_15 = sz0z00
% 17.37/3.19  | | | 
% 17.37/3.19  | | | REDUCE: (22), (38) imply:
% 17.37/3.19  | | |   (39)  sdtasdt0(all_41_16, sz0z00) = all_41_14
% 17.37/3.19  | | | 
% 17.37/3.19  | | | BETA: splitting (35) gives:
% 17.37/3.19  | | | 
% 17.37/3.19  | | | Case 1:
% 17.37/3.19  | | | | 
% 17.37/3.19  | | | |   (40)  all_41_18 = sz0z00
% 17.37/3.19  | | | | 
% 17.37/3.19  | | | | REDUCE: (21), (40) imply:
% 17.37/3.19  | | | |   (41)  sdtasdt0(sz0z00, sz0z00) = all_41_17
% 17.37/3.19  | | | | 
% 17.37/3.19  | | | | BETA: splitting (32) gives:
% 17.37/3.19  | | | | 
% 17.37/3.19  | | | | Case 1:
% 17.37/3.19  | | | | | 
% 17.37/3.19  | | | | |   (42)  all_41_16 = sz0z00
% 17.37/3.19  | | | | | 
% 17.37/3.19  | | | | | REDUCE: (39), (42) imply:
% 17.37/3.19  | | | | |   (43)  sdtasdt0(sz0z00, sz0z00) = all_41_14
% 17.37/3.19  | | | | | 
% 17.37/3.19  | | | | | REDUCE: (20), (42) imply:
% 17.37/3.19  | | | | |   (44)  $i(sz0z00)
% 17.37/3.19  | | | | | 
% 17.37/3.19  | | | | | REDUCE: (34), (42) imply:
% 17.37/3.19  | | | | |   (45)  sdtlseqdt0(sz0z00, sz0z00)
% 17.37/3.19  | | | | | 
% 17.37/3.19  | | | | | REDUCE: (37), (42) imply:
% 17.37/3.20  | | | | |   (46)  aScalar0(sz0z00)
% 17.37/3.20  | | | | | 
% 17.37/3.20  | | | | | GROUND_INST: instantiating (12) with all_41_17, all_41_14, sz0z00,
% 17.37/3.20  | | | | |              sz0z00, simplifying with (41), (43) gives:
% 17.37/3.20  | | | | |   (47)  all_41_14 = all_41_17
% 17.37/3.20  | | | | | 
% 17.37/3.20  | | | | | REDUCE: (19), (47) imply:
% 17.37/3.20  | | | | |   (48)   ~ sdtlseqdt0(all_41_17, all_41_17)
% 17.37/3.20  | | | | | 
% 17.37/3.20  | | | | | GROUND_INST: instantiating (1) with sz0z00, sz0z00, sz0z00, sz0z00,
% 17.37/3.20  | | | | |              all_41_17, all_41_17, simplifying with (41), (44), (45),
% 17.37/3.20  | | | | |              (46), (48) gives:
% 17.37/3.20  | | | | |   (49)  $false
% 17.37/3.20  | | | | | 
% 17.37/3.20  | | | | | CLOSE: (49) is inconsistent.
% 17.37/3.20  | | | | | 
% 17.37/3.20  | | | | Case 2:
% 17.37/3.20  | | | | | 
% 17.37/3.20  | | | | |   (50)   ? [v0: $i] :  ? [v1: $i] : (aDimensionOf0(xs) = v1 & $i(v1) &
% 17.37/3.20  | | | | |           ( ~ (v1 = sz00) | ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 &
% 17.37/3.20  | | | | |               $i(v0))))
% 17.37/3.20  | | | | | 
% 17.37/3.20  | | | | | DELTA: instantiating (50) with fresh symbols all_78_0, all_78_1 gives:
% 17.37/3.20  | | | | |   (51)  aDimensionOf0(xs) = all_78_0 & $i(all_78_0) & ( ~ (all_78_0 =
% 17.37/3.20  | | | | |             sz00) | ( ~ (all_78_1 = sz00) & aDimensionOf0(xs) =
% 17.37/3.20  | | | | |             all_78_1 & $i(all_78_1)))
% 17.37/3.20  | | | | | 
% 17.37/3.20  | | | | | ALPHA: (51) implies:
% 17.37/3.20  | | | | |   (52)  aDimensionOf0(xs) = all_78_0
% 17.37/3.20  | | | | |   (53)   ~ (all_78_0 = sz00) | ( ~ (all_78_1 = sz00) &
% 17.37/3.20  | | | | |           aDimensionOf0(xs) = all_78_1 & $i(all_78_1))
% 17.37/3.20  | | | | | 
% 17.37/3.20  | | | | | BETA: splitting (53) gives:
% 17.37/3.20  | | | | | 
% 17.37/3.20  | | | | | Case 1:
% 17.37/3.20  | | | | | | 
% 17.37/3.20  | | | | | |   (54)   ~ (all_78_0 = sz00)
% 17.37/3.20  | | | | | | 
% 17.37/3.20  | | | | | | GROUND_INST: instantiating (11) with sz00, all_78_0, xs, simplifying
% 17.37/3.20  | | | | | |              with (23), (52) gives:
% 17.37/3.20  | | | | | |   (55)  all_78_0 = sz00
% 17.37/3.20  | | | | | | 
% 17.37/3.20  | | | | | | REDUCE: (54), (55) imply:
% 17.37/3.20  | | | | | |   (56)  $false
% 17.37/3.20  | | | | | | 
% 17.37/3.20  | | | | | | CLOSE: (56) is inconsistent.
% 17.37/3.20  | | | | | | 
% 17.37/3.20  | | | | | Case 2:
% 17.37/3.20  | | | | | | 
% 17.37/3.20  | | | | | |   (57)  all_78_0 = sz00
% 17.37/3.20  | | | | | |   (58)   ~ (all_78_1 = sz00) & aDimensionOf0(xs) = all_78_1 &
% 17.37/3.20  | | | | | |         $i(all_78_1)
% 17.37/3.20  | | | | | | 
% 17.37/3.20  | | | | | | ALPHA: (58) implies:
% 17.37/3.20  | | | | | |   (59)   ~ (all_78_1 = sz00)
% 17.37/3.20  | | | | | |   (60)  aDimensionOf0(xs) = all_78_1
% 17.37/3.20  | | | | | | 
% 17.37/3.20  | | | | | | GROUND_INST: instantiating (11) with sz00, all_78_1, xs, simplifying
% 17.37/3.20  | | | | | |              with (23), (60) gives:
% 17.37/3.20  | | | | | |   (61)  all_78_1 = sz00
% 17.37/3.20  | | | | | | 
% 17.37/3.20  | | | | | | REDUCE: (59), (61) imply:
% 17.37/3.20  | | | | | |   (62)  $false
% 17.37/3.20  | | | | | | 
% 17.37/3.20  | | | | | | CLOSE: (62) is inconsistent.
% 17.37/3.20  | | | | | | 
% 17.37/3.20  | | | | | End of split
% 17.37/3.20  | | | | | 
% 17.37/3.20  | | | | End of split
% 17.37/3.20  | | | | 
% 17.37/3.20  | | | Case 2:
% 17.37/3.20  | | | | 
% 17.37/3.20  | | | |   (63)   ? [v0: $i] :  ? [v1: $i] : (aDimensionOf0(xt) = v1 & $i(v1) & (
% 17.37/3.20  | | | |             ~ (v1 = sz00) | ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 &
% 17.37/3.20  | | | |               $i(v0))))
% 17.37/3.20  | | | | 
% 17.37/3.20  | | | | DELTA: instantiating (63) with fresh symbols all_74_0, all_74_1 gives:
% 17.37/3.20  | | | |   (64)  aDimensionOf0(xt) = all_74_0 & $i(all_74_0) & ( ~ (all_74_0 =
% 17.37/3.20  | | | |             sz00) | ( ~ (all_74_1 = sz00) & aDimensionOf0(xs) = all_74_1
% 17.37/3.20  | | | |             & $i(all_74_1)))
% 17.37/3.20  | | | | 
% 17.37/3.20  | | | | ALPHA: (64) implies:
% 17.37/3.20  | | | |   (65)  aDimensionOf0(xt) = all_74_0
% 17.37/3.20  | | | |   (66)   ~ (all_74_0 = sz00) | ( ~ (all_74_1 = sz00) & aDimensionOf0(xs)
% 17.37/3.20  | | | |           = all_74_1 & $i(all_74_1))
% 17.37/3.20  | | | | 
% 17.37/3.20  | | | | BETA: splitting (66) gives:
% 17.37/3.20  | | | | 
% 17.37/3.20  | | | | Case 1:
% 17.37/3.20  | | | | | 
% 17.37/3.20  | | | | |   (67)   ~ (all_74_0 = sz00)
% 17.37/3.20  | | | | | 
% 17.37/3.20  | | | | | GROUND_INST: instantiating (11) with sz00, all_74_0, xt, simplifying
% 17.37/3.20  | | | | |              with (31), (65) gives:
% 17.37/3.20  | | | | |   (68)  all_74_0 = sz00
% 17.37/3.20  | | | | | 
% 17.37/3.20  | | | | | REDUCE: (67), (68) imply:
% 17.37/3.20  | | | | |   (69)  $false
% 17.37/3.20  | | | | | 
% 17.37/3.20  | | | | | CLOSE: (69) is inconsistent.
% 17.37/3.20  | | | | | 
% 17.37/3.20  | | | | Case 2:
% 17.37/3.20  | | | | | 
% 17.37/3.21  | | | | |   (70)   ~ (all_74_1 = sz00) & aDimensionOf0(xs) = all_74_1 &
% 17.37/3.21  | | | | |         $i(all_74_1)
% 17.37/3.21  | | | | | 
% 17.37/3.21  | | | | | ALPHA: (70) implies:
% 17.37/3.21  | | | | |   (71)   ~ (all_74_1 = sz00)
% 17.37/3.21  | | | | |   (72)  aDimensionOf0(xs) = all_74_1
% 17.37/3.21  | | | | | 
% 17.37/3.21  | | | | | GROUND_INST: instantiating (11) with sz00, all_74_1, xs, simplifying
% 17.37/3.21  | | | | |              with (23), (72) gives:
% 17.37/3.21  | | | | |   (73)  all_74_1 = sz00
% 17.37/3.21  | | | | | 
% 17.37/3.21  | | | | | REDUCE: (71), (73) imply:
% 17.37/3.21  | | | | |   (74)  $false
% 17.37/3.21  | | | | | 
% 17.37/3.21  | | | | | CLOSE: (74) is inconsistent.
% 17.37/3.21  | | | | | 
% 17.37/3.21  | | | | End of split
% 17.37/3.21  | | | | 
% 17.37/3.21  | | | End of split
% 17.37/3.21  | | | 
% 17.37/3.21  | | Case 2:
% 17.37/3.21  | | | 
% 17.37/3.21  | | |   (75)   ? [v0: $i] :  ? [v1: $i] : (aDimensionOf0(xt) = v1 & $i(v1) & ( ~
% 17.37/3.21  | | |             (v1 = sz00) | ( ~ (v0 = sz00) & aDimensionOf0(xt) = v0 &
% 17.37/3.21  | | |               $i(v0))))
% 17.37/3.21  | | | 
% 17.37/3.21  | | | DELTA: instantiating (75) with fresh symbols all_70_0, all_70_1 gives:
% 17.37/3.21  | | |   (76)  aDimensionOf0(xt) = all_70_0 & $i(all_70_0) & ( ~ (all_70_0 =
% 17.37/3.21  | | |             sz00) | ( ~ (all_70_1 = sz00) & aDimensionOf0(xt) = all_70_1 &
% 17.37/3.21  | | |             $i(all_70_1)))
% 17.37/3.21  | | | 
% 17.37/3.21  | | | ALPHA: (76) implies:
% 17.37/3.21  | | |   (77)  aDimensionOf0(xt) = all_70_0
% 17.37/3.21  | | |   (78)   ~ (all_70_0 = sz00) | ( ~ (all_70_1 = sz00) & aDimensionOf0(xt) =
% 17.37/3.21  | | |           all_70_1 & $i(all_70_1))
% 17.37/3.21  | | | 
% 17.37/3.21  | | | BETA: splitting (78) gives:
% 17.37/3.21  | | | 
% 17.37/3.21  | | | Case 1:
% 17.37/3.21  | | | | 
% 17.37/3.21  | | | |   (79)   ~ (all_70_0 = sz00)
% 17.37/3.21  | | | | 
% 17.37/3.21  | | | | GROUND_INST: instantiating (11) with sz00, all_70_0, xt, simplifying
% 17.37/3.21  | | | |              with (31), (77) gives:
% 17.37/3.21  | | | |   (80)  all_70_0 = sz00
% 17.37/3.21  | | | | 
% 17.37/3.21  | | | | REDUCE: (79), (80) imply:
% 17.37/3.21  | | | |   (81)  $false
% 17.37/3.21  | | | | 
% 17.37/3.21  | | | | CLOSE: (81) is inconsistent.
% 17.37/3.21  | | | | 
% 17.37/3.21  | | | Case 2:
% 17.37/3.21  | | | | 
% 17.37/3.21  | | | |   (82)  all_70_0 = sz00
% 17.37/3.21  | | | |   (83)   ~ (all_70_1 = sz00) & aDimensionOf0(xt) = all_70_1 &
% 17.37/3.21  | | | |         $i(all_70_1)
% 17.37/3.21  | | | | 
% 17.37/3.21  | | | | ALPHA: (83) implies:
% 17.37/3.21  | | | |   (84)   ~ (all_70_1 = sz00)
% 17.37/3.21  | | | |   (85)  aDimensionOf0(xt) = all_70_1
% 17.37/3.21  | | | | 
% 17.37/3.21  | | | | GROUND_INST: instantiating (11) with sz00, all_70_1, xt, simplifying
% 17.37/3.21  | | | |              with (31), (85) gives:
% 17.37/3.21  | | | |   (86)  all_70_1 = sz00
% 17.37/3.21  | | | | 
% 17.37/3.21  | | | | REDUCE: (84), (86) imply:
% 17.37/3.21  | | | |   (87)  $false
% 17.37/3.21  | | | | 
% 17.37/3.21  | | | | CLOSE: (87) is inconsistent.
% 17.37/3.21  | | | | 
% 17.37/3.21  | | | End of split
% 17.37/3.21  | | | 
% 17.37/3.21  | | End of split
% 17.37/3.21  | | 
% 17.37/3.21  | Case 2:
% 17.37/3.21  | | 
% 17.37/3.21  | |   (88)   ? [v0: $i] :  ? [v1: $i] : ( ~ (v1 = v0) & aDimensionOf0(xs) = v1 &
% 17.37/3.21  | |           aDimensionOf0(xs) = v0 & $i(v1) & $i(v0))
% 17.37/3.21  | | 
% 17.37/3.21  | | DELTA: instantiating (88) with fresh symbols all_62_0, all_62_1 gives:
% 17.37/3.21  | |   (89)   ~ (all_62_0 = all_62_1) & aDimensionOf0(xs) = all_62_0 &
% 17.37/3.21  | |         aDimensionOf0(xs) = all_62_1 & $i(all_62_0) & $i(all_62_1)
% 17.37/3.21  | | 
% 17.37/3.21  | | ALPHA: (89) implies:
% 17.37/3.21  | |   (90)   ~ (all_62_0 = all_62_1)
% 17.37/3.21  | |   (91)  aDimensionOf0(xs) = all_62_1
% 17.37/3.21  | |   (92)  aDimensionOf0(xs) = all_62_0
% 17.37/3.21  | | 
% 17.37/3.21  | | GROUND_INST: instantiating (11) with sz00, all_62_0, xs, simplifying with
% 17.37/3.21  | |              (23), (92) gives:
% 17.37/3.21  | |   (93)  all_62_0 = sz00
% 17.37/3.21  | | 
% 17.37/3.21  | | GROUND_INST: instantiating (11) with all_62_1, all_62_0, xs, simplifying
% 17.37/3.21  | |              with (91), (92) gives:
% 17.37/3.21  | |   (94)  all_62_0 = all_62_1
% 17.37/3.21  | | 
% 17.37/3.21  | | COMBINE_EQS: (93), (94) imply:
% 17.37/3.21  | |   (95)  all_62_1 = sz00
% 17.37/3.21  | | 
% 17.37/3.21  | | REDUCE: (90), (93), (95) imply:
% 17.37/3.21  | |   (96)  $false
% 17.37/3.21  | | 
% 17.37/3.21  | | CLOSE: (96) is inconsistent.
% 17.37/3.21  | | 
% 17.37/3.21  | End of split
% 17.37/3.21  | 
% 17.37/3.21  End of proof
% 17.37/3.21  % SZS output end Proof for theBenchmark
% 17.37/3.21  
% 17.37/3.21  2628ms
%------------------------------------------------------------------------------