TSTP Solution File: RNG047+2 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : RNG047+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 : n026.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 13:57:32 EDT 2023

% Result   : Theorem 10.30s 2.22s
% Output   : Proof 14.89s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : RNG047+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35  % Computer : n026.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Sun Aug 27 03:07:34 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.20/0.62  ________       _____
% 0.20/0.62  ___  __ \_________(_)________________________________
% 0.20/0.62  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.62  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.62  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62  
% 0.20/0.62  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62  (2023-06-19)
% 0.20/0.62  
% 0.20/0.62  (c) Philipp Rümmer, 2009-2023
% 0.20/0.62  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62                Amanda Stjerna.
% 0.20/0.62  Free software under BSD-3-Clause.
% 0.20/0.62  
% 0.20/0.62  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62  
% 0.20/0.62  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63  Running up to 7 provers in parallel.
% 0.20/0.65  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.34/1.19  Prover 1: Preprocessing ...
% 3.34/1.21  Prover 4: Preprocessing ...
% 3.84/1.26  Prover 5: Preprocessing ...
% 3.84/1.26  Prover 6: Preprocessing ...
% 3.84/1.26  Prover 2: Preprocessing ...
% 3.84/1.26  Prover 3: Preprocessing ...
% 3.84/1.26  Prover 0: Preprocessing ...
% 8.62/1.94  Prover 1: Constructing countermodel ...
% 8.76/1.95  Prover 3: Constructing countermodel ...
% 8.76/2.00  Prover 6: Proving ...
% 9.66/2.17  Prover 5: Constructing countermodel ...
% 10.30/2.22  Prover 3: proved (1577ms)
% 10.30/2.22  
% 10.30/2.22  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.30/2.22  
% 10.30/2.22  Prover 5: stopped
% 10.30/2.22  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.30/2.22  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.30/2.23  Prover 6: stopped
% 10.30/2.25  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.95/2.31  Prover 7: Preprocessing ...
% 11.18/2.32  Prover 8: Preprocessing ...
% 11.31/2.35  Prover 10: Preprocessing ...
% 11.31/2.36  Prover 4: Constructing countermodel ...
% 11.31/2.41  Prover 2: Proving ...
% 11.31/2.41  Prover 2: stopped
% 11.93/2.43  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.47/2.48  Prover 11: Preprocessing ...
% 12.47/2.50  Prover 10: Constructing countermodel ...
% 12.47/2.52  Prover 0: Proving ...
% 12.47/2.53  Prover 0: stopped
% 12.47/2.53  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.47/2.55  Prover 7: Constructing countermodel ...
% 13.10/2.57  Prover 8: Warning: ignoring some quantifiers
% 13.21/2.58  Prover 8: Constructing countermodel ...
% 13.39/2.62  Prover 13: Preprocessing ...
% 13.39/2.63  Prover 1: Found proof (size 68)
% 13.39/2.63  Prover 1: proved (1987ms)
% 13.39/2.63  Prover 4: stopped
% 13.39/2.63  Prover 8: stopped
% 13.39/2.63  Prover 10: stopped
% 13.39/2.63  Prover 7: stopped
% 13.39/2.66  Prover 13: stopped
% 13.95/2.78  Prover 11: Constructing countermodel ...
% 13.95/2.79  Prover 11: stopped
% 13.95/2.79  
% 13.95/2.80  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.95/2.80  
% 13.95/2.82  % SZS output start Proof for theBenchmark
% 13.95/2.82  Assumptions after simplification:
% 13.95/2.82  ---------------------------------
% 13.95/2.83  
% 13.95/2.83    (mDefInit)
% 14.55/2.87    $i(sz00) &  ! [v0: $i] : ( ~ (aVector0(v0) = 0) |  ~ $i(v0) |  ? [v1: $i] :  ?
% 14.55/2.87      [v2: $i] : (sziznziztdt0(v0) = v2 & aDimensionOf0(v0) = v1 & $i(v2) & $i(v1)
% 14.55/2.87        & (v1 = sz00 | ( ! [v3: $i] : (v3 = v2 |  ~ (aVector0(v3) = 0) |  ~ $i(v3)
% 14.55/2.87              |  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] : ( ~ (v6 = v5) &
% 14.55/2.87                sdtlbdtrb0(v3, v4) = v5 & sdtlbdtrb0(v0, v4) = v6 &
% 14.55/2.87                aNaturalNumber0(v4) = 0 & $i(v6) & $i(v5) & $i(v4)) |  ? [v4: $i]
% 14.55/2.87              :  ? [v5: $i] : ( ~ (v5 = v1) & aDimensionOf0(v3) = v4 &
% 14.55/2.87                szszuzczcdt0(v4) = v5 & $i(v5) & $i(v4))) &  ! [v3: any] : ( ~
% 14.55/2.87              (aVector0(v2) = v3) | (v3 = 0 &  ! [v4: $i] :  ! [v5: $i] : ( ~
% 14.55/2.87                  (sdtlbdtrb0(v0, v4) = v5) |  ~ $i(v4) |  ? [v6: any] :  ? [v7:
% 14.55/2.87                    $i] : (sdtlbdtrb0(v2, v4) = v7 & aNaturalNumber0(v4) = v6 &
% 14.55/2.87                    $i(v7) & ( ~ (v6 = 0) | v7 = v5))) &  ? [v4: $i] :
% 14.55/2.87                (aDimensionOf0(v2) = v4 & szszuzczcdt0(v4) = v1 & $i(v4))))))))
% 14.55/2.87  
% 14.55/2.87    (mDimNat)
% 14.55/2.87     ! [v0: $i] : ( ~ (aVector0(v0) = 0) |  ~ $i(v0) |  ? [v1: $i] :
% 14.55/2.87      (aDimensionOf0(v0) = v1 & aNaturalNumber0(v1) = 0 & $i(v1)))
% 14.55/2.87  
% 14.55/2.87    (mSuccEqu)
% 14.55/2.87     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (szszuzczcdt0(v1) =
% 14.55/2.87        v2) |  ~ (szszuzczcdt0(v0) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] : 
% 14.55/2.87      ? [v4: any] : (aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4
% 14.55/2.87            = 0) |  ~ (v3 = 0))))
% 14.55/2.87  
% 14.55/2.87    (mSuccNat)
% 14.55/2.88    $i(sz00) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) |  ~ $i(v0)
% 14.55/2.88      |  ? [v2: any] :  ? [v3: any] : (aNaturalNumber0(v1) = v3 &
% 14.55/2.88        aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = 0 &  ~ (v1 = sz00)))))
% 14.55/2.88  
% 14.55/2.88    (m__)
% 14.55/2.88    $i(xt) & $i(xs) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ?
% 14.55/2.88    [v4: $i] :  ? [v5: $i] : ( ~ (v4 = v1) & sziznziztdt0(xt) = v3 &
% 14.55/2.88      sziznziztdt0(xs) = v0 & aVector0(v3) = 0 & aVector0(v0) = 0 &
% 14.55/2.88      aDimensionOf0(v3) = v4 & aDimensionOf0(v0) = v1 & aDimensionOf0(xt) = v5 &
% 14.55/2.88      aDimensionOf0(xs) = v2 & szszuzczcdt0(v4) = v5 & szszuzczcdt0(v1) = v2 &
% 14.55/2.88      $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &  ! [v6: $i] :  ! [v7:
% 14.55/2.88        $i] : ( ~ (sdtlbdtrb0(v3, v6) = v7) |  ~ $i(v6) |  ? [v8: any] :  ? [v9:
% 14.55/2.88          $i] : (sdtlbdtrb0(xt, v6) = v9 & aNaturalNumber0(v6) = v8 & $i(v9) & ( ~
% 14.55/2.88            (v8 = 0) | v9 = v7))) &  ! [v6: $i] :  ! [v7: $i] : ( ~
% 14.55/2.88        (sdtlbdtrb0(v0, v6) = v7) |  ~ $i(v6) |  ? [v8: any] :  ? [v9: $i] :
% 14.55/2.88        (sdtlbdtrb0(xs, v6) = v9 & aNaturalNumber0(v6) = v8 & $i(v9) & ( ~ (v8 =
% 14.55/2.88              0) | v9 = v7))))
% 14.55/2.88  
% 14.55/2.88    (m__1329_01)
% 14.55/2.88    $i(xt) & $i(xs) & $i(sz00) &  ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xt)
% 14.55/2.88      = v0 & aDimensionOf0(xs) = v0 & $i(v0))
% 14.55/2.88  
% 14.55/2.88    (function-axioms)
% 14.55/2.88     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 14.55/2.88      (sdtlbdtrb0(v3, v2) = v1) |  ~ (sdtlbdtrb0(v3, v2) = v0)) &  ! [v0:
% 14.55/2.88      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 14.55/2.88    : (v1 = v0 |  ~ (sdtlseqdt0(v3, v2) = v1) |  ~ (sdtlseqdt0(v3, v2) = v0)) &  !
% 14.55/2.88    [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 14.55/2.88      (sdtasdt0(v3, v2) = v1) |  ~ (sdtasdt0(v3, v2) = v0)) &  ! [v0: $i] :  !
% 14.55/2.88    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (sdtpldt0(v3, v2) = v1) |
% 14.55/2.88       ~ (sdtpldt0(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 14.55/2.88      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (iLess0(v3,
% 14.55/2.88          v2) = v1) |  ~ (iLess0(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 14.55/2.88    [v2: $i] : (v1 = v0 |  ~ (sziznziztdt0(v2) = v1) |  ~ (sziznziztdt0(v2) = v0))
% 14.55/2.88    &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1
% 14.55/2.88      = v0 |  ~ (aVector0(v2) = v1) |  ~ (aVector0(v2) = v0)) &  ! [v0: $i] :  !
% 14.55/2.88    [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (aDimensionOf0(v2) = v1) |  ~
% 14.55/2.88      (aDimensionOf0(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 =
% 14.55/2.88      v0 |  ~ (smndt0(v2) = v1) |  ~ (smndt0(v2) = v0)) &  ! [v0:
% 14.55/2.88      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 14.55/2.88      ~ (aScalar0(v2) = v1) |  ~ (aScalar0(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i]
% 14.55/2.88    :  ! [v2: $i] : (v1 = v0 |  ~ (szszuzczcdt0(v2) = v1) |  ~ (szszuzczcdt0(v2) =
% 14.55/2.88        v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 14.55/2.88      $i] : (v1 = v0 |  ~ (aNaturalNumber0(v2) = v1) |  ~ (aNaturalNumber0(v2) =
% 14.55/2.88        v0))
% 14.55/2.88  
% 14.55/2.88  Further assumptions not needed in the proof:
% 14.55/2.88  --------------------------------------------
% 14.55/2.88  mArith, mDistr, mDistr2, mElmSc, mIH, mIHOrd, mLEASm, mLEMon, mLEMonM, mLERef,
% 14.55/2.88  mLETot, mLETrn, mLess, mMDNeg, mMNeg, mMulSc, mNatExtr, mNatSort, mNegSc,
% 14.55/2.88  mPosMon, mSZeroSc, mScSort, mScZero, mSqPos, mSqrt, mSumSc, mVcSort, mZeroNat,
% 14.55/2.88  m__1329
% 14.55/2.88  
% 14.55/2.88  Those formulas are unsatisfiable:
% 14.55/2.88  ---------------------------------
% 14.55/2.88  
% 14.55/2.88  Begin of proof
% 14.55/2.89  | 
% 14.55/2.89  | ALPHA: (mSuccNat) implies:
% 14.55/2.89  |   (1)   ! [v0: $i] :  ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) |  ~ $i(v0) | 
% 14.55/2.89  |          ? [v2: any] :  ? [v3: any] : (aNaturalNumber0(v1) = v3 &
% 14.55/2.89  |            aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = 0 &  ~ (v1 =
% 14.55/2.89  |                  sz00)))))
% 14.55/2.89  | 
% 14.55/2.89  | ALPHA: (mDefInit) implies:
% 14.55/2.89  |   (2)   ! [v0: $i] : ( ~ (aVector0(v0) = 0) |  ~ $i(v0) |  ? [v1: $i] :  ?
% 14.55/2.89  |          [v2: $i] : (sziznziztdt0(v0) = v2 & aDimensionOf0(v0) = v1 & $i(v2) &
% 14.55/2.89  |            $i(v1) & (v1 = sz00 | ( ! [v3: $i] : (v3 = v2 |  ~ (aVector0(v3) =
% 14.55/2.89  |                    0) |  ~ $i(v3) |  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :
% 14.55/2.89  |                  ( ~ (v6 = v5) & sdtlbdtrb0(v3, v4) = v5 & sdtlbdtrb0(v0, v4)
% 14.55/2.89  |                    = v6 & aNaturalNumber0(v4) = 0 & $i(v6) & $i(v5) & $i(v4))
% 14.55/2.89  |                  |  ? [v4: $i] :  ? [v5: $i] : ( ~ (v5 = v1) &
% 14.55/2.89  |                    aDimensionOf0(v3) = v4 & szszuzczcdt0(v4) = v5 & $i(v5) &
% 14.55/2.89  |                    $i(v4))) &  ! [v3: any] : ( ~ (aVector0(v2) = v3) | (v3 = 0
% 14.55/2.89  |                    &  ! [v4: $i] :  ! [v5: $i] : ( ~ (sdtlbdtrb0(v0, v4) = v5)
% 14.55/2.89  |                      |  ~ $i(v4) |  ? [v6: any] :  ? [v7: $i] :
% 14.55/2.89  |                      (sdtlbdtrb0(v2, v4) = v7 & aNaturalNumber0(v4) = v6 &
% 14.55/2.89  |                        $i(v7) & ( ~ (v6 = 0) | v7 = v5))) &  ? [v4: $i] :
% 14.55/2.89  |                    (aDimensionOf0(v2) = v4 & szszuzczcdt0(v4) = v1 &
% 14.55/2.89  |                      $i(v4))))))))
% 14.55/2.89  | 
% 14.55/2.89  | ALPHA: (m__1329_01) implies:
% 14.55/2.89  |   (3)   ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xt) = v0 &
% 14.55/2.89  |          aDimensionOf0(xs) = v0 & $i(v0))
% 14.55/2.89  | 
% 14.55/2.89  | ALPHA: (m__) implies:
% 14.55/2.89  |   (4)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 14.55/2.89  |        ? [v5: $i] : ( ~ (v4 = v1) & sziznziztdt0(xt) = v3 & sziznziztdt0(xs) =
% 14.55/2.89  |          v0 & aVector0(v3) = 0 & aVector0(v0) = 0 & aDimensionOf0(v3) = v4 &
% 14.55/2.89  |          aDimensionOf0(v0) = v1 & aDimensionOf0(xt) = v5 & aDimensionOf0(xs) =
% 14.55/2.89  |          v2 & szszuzczcdt0(v4) = v5 & szszuzczcdt0(v1) = v2 & $i(v5) & $i(v4)
% 14.55/2.89  |          & $i(v3) & $i(v2) & $i(v1) & $i(v0) &  ! [v6: $i] :  ! [v7: $i] : ( ~
% 14.55/2.89  |            (sdtlbdtrb0(v3, v6) = v7) |  ~ $i(v6) |  ? [v8: any] :  ? [v9: $i]
% 14.55/2.89  |            : (sdtlbdtrb0(xt, v6) = v9 & aNaturalNumber0(v6) = v8 & $i(v9) & (
% 14.55/2.89  |                ~ (v8 = 0) | v9 = v7))) &  ! [v6: $i] :  ! [v7: $i] : ( ~
% 14.55/2.89  |            (sdtlbdtrb0(v0, v6) = v7) |  ~ $i(v6) |  ? [v8: any] :  ? [v9: $i]
% 14.55/2.89  |            : (sdtlbdtrb0(xs, v6) = v9 & aNaturalNumber0(v6) = v8 & $i(v9) & (
% 14.55/2.89  |                ~ (v8 = 0) | v9 = v7))))
% 14.55/2.89  | 
% 14.55/2.89  | ALPHA: (function-axioms) implies:
% 14.55/2.89  |   (5)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 14.55/2.89  |        (v1 = v0 |  ~ (aNaturalNumber0(v2) = v1) |  ~ (aNaturalNumber0(v2) =
% 14.55/2.89  |            v0))
% 14.55/2.89  |   (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 14.55/2.89  |          (aDimensionOf0(v2) = v1) |  ~ (aDimensionOf0(v2) = v0))
% 14.55/2.89  | 
% 14.55/2.90  | DELTA: instantiating (3) with fresh symbol all_28_0 gives:
% 14.55/2.90  |   (7)   ~ (all_28_0 = sz00) & aDimensionOf0(xt) = all_28_0 & aDimensionOf0(xs)
% 14.55/2.90  |        = all_28_0 & $i(all_28_0)
% 14.55/2.90  | 
% 14.55/2.90  | ALPHA: (7) implies:
% 14.55/2.90  |   (8)  aDimensionOf0(xs) = all_28_0
% 14.55/2.90  |   (9)  aDimensionOf0(xt) = all_28_0
% 14.55/2.90  | 
% 14.55/2.90  | DELTA: instantiating (4) with fresh symbols all_33_0, all_33_1, all_33_2,
% 14.55/2.90  |        all_33_3, all_33_4, all_33_5 gives:
% 14.55/2.90  |   (10)   ~ (all_33_1 = all_33_4) & sziznziztdt0(xt) = all_33_2 &
% 14.55/2.90  |         sziznziztdt0(xs) = all_33_5 & aVector0(all_33_2) = 0 &
% 14.55/2.90  |         aVector0(all_33_5) = 0 & aDimensionOf0(all_33_2) = all_33_1 &
% 14.55/2.90  |         aDimensionOf0(all_33_5) = all_33_4 & aDimensionOf0(xt) = all_33_0 &
% 14.55/2.90  |         aDimensionOf0(xs) = all_33_3 & szszuzczcdt0(all_33_1) = all_33_0 &
% 14.55/2.90  |         szszuzczcdt0(all_33_4) = all_33_3 & $i(all_33_0) & $i(all_33_1) &
% 14.55/2.90  |         $i(all_33_2) & $i(all_33_3) & $i(all_33_4) & $i(all_33_5) &  ! [v0:
% 14.55/2.90  |           $i] :  ! [v1: $i] : ( ~ (sdtlbdtrb0(all_33_2, v0) = v1) |  ~ $i(v0)
% 14.55/2.90  |           |  ? [v2: any] :  ? [v3: $i] : (sdtlbdtrb0(xt, v0) = v3 &
% 14.55/2.90  |             aNaturalNumber0(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = v1))) &  !
% 14.55/2.90  |         [v0: $i] :  ! [v1: $i] : ( ~ (sdtlbdtrb0(all_33_5, v0) = v1) |  ~
% 14.55/2.90  |           $i(v0) |  ? [v2: any] :  ? [v3: $i] : (sdtlbdtrb0(xs, v0) = v3 &
% 14.55/2.90  |             aNaturalNumber0(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = v1)))
% 14.55/2.90  | 
% 14.55/2.90  | ALPHA: (10) implies:
% 14.55/2.90  |   (11)   ~ (all_33_1 = all_33_4)
% 14.55/2.90  |   (12)  $i(all_33_5)
% 14.55/2.90  |   (13)  $i(all_33_4)
% 14.55/2.90  |   (14)  $i(all_33_2)
% 14.55/2.90  |   (15)  $i(all_33_1)
% 14.55/2.90  |   (16)  szszuzczcdt0(all_33_4) = all_33_3
% 14.55/2.90  |   (17)  szszuzczcdt0(all_33_1) = all_33_0
% 14.55/2.90  |   (18)  aDimensionOf0(xs) = all_33_3
% 14.55/2.90  |   (19)  aDimensionOf0(xt) = all_33_0
% 14.55/2.90  |   (20)  aDimensionOf0(all_33_5) = all_33_4
% 14.55/2.90  |   (21)  aDimensionOf0(all_33_2) = all_33_1
% 14.55/2.90  |   (22)  aVector0(all_33_5) = 0
% 14.55/2.90  |   (23)  aVector0(all_33_2) = 0
% 14.55/2.90  | 
% 14.55/2.90  | GROUND_INST: instantiating (6) with all_28_0, all_33_3, xs, simplifying with
% 14.55/2.90  |              (8), (18) gives:
% 14.55/2.90  |   (24)  all_33_3 = all_28_0
% 14.55/2.90  | 
% 14.55/2.90  | GROUND_INST: instantiating (6) with all_28_0, all_33_0, xt, simplifying with
% 14.55/2.90  |              (9), (19) gives:
% 14.55/2.90  |   (25)  all_33_0 = all_28_0
% 14.55/2.90  | 
% 14.55/2.90  | REDUCE: (17), (25) imply:
% 14.55/2.90  |   (26)  szszuzczcdt0(all_33_1) = all_28_0
% 14.55/2.90  | 
% 14.55/2.90  | REDUCE: (16), (24) imply:
% 14.55/2.90  |   (27)  szszuzczcdt0(all_33_4) = all_28_0
% 14.55/2.90  | 
% 14.89/2.90  | GROUND_INST: instantiating (1) with all_33_4, all_28_0, simplifying with (13),
% 14.89/2.90  |              (27) gives:
% 14.89/2.90  |   (28)   ? [v0: any] :  ? [v1: any] : (aNaturalNumber0(all_33_4) = v0 &
% 14.89/2.90  |           aNaturalNumber0(all_28_0) = v1 & ( ~ (v0 = 0) | (v1 = 0 &  ~
% 14.89/2.90  |               (all_28_0 = sz00))))
% 14.89/2.90  | 
% 14.89/2.90  | GROUND_INST: instantiating (mSuccEqu) with all_33_4, all_33_1, all_28_0,
% 14.89/2.90  |              simplifying with (13), (15), (26), (27) gives:
% 14.89/2.90  |   (29)  all_33_1 = all_33_4 |  ? [v0: any] :  ? [v1: any] :
% 14.89/2.90  |         (aNaturalNumber0(all_33_1) = v1 & aNaturalNumber0(all_33_4) = v0 & ( ~
% 14.89/2.90  |             (v1 = 0) |  ~ (v0 = 0)))
% 14.89/2.90  | 
% 14.89/2.91  | GROUND_INST: instantiating (mSuccEqu) with all_33_1, all_33_4, all_28_0,
% 14.89/2.91  |              simplifying with (13), (15), (26), (27) gives:
% 14.89/2.91  |   (30)  all_33_1 = all_33_4 |  ? [v0: any] :  ? [v1: any] :
% 14.89/2.91  |         (aNaturalNumber0(all_33_1) = v0 & aNaturalNumber0(all_33_4) = v1 & ( ~
% 14.89/2.91  |             (v1 = 0) |  ~ (v0 = 0)))
% 14.89/2.91  | 
% 14.89/2.91  | GROUND_INST: instantiating (1) with all_33_1, all_28_0, simplifying with (15),
% 14.89/2.91  |              (26) gives:
% 14.89/2.91  |   (31)   ? [v0: any] :  ? [v1: any] : (aNaturalNumber0(all_33_1) = v0 &
% 14.89/2.91  |           aNaturalNumber0(all_28_0) = v1 & ( ~ (v0 = 0) | (v1 = 0 &  ~
% 14.89/2.91  |               (all_28_0 = sz00))))
% 14.89/2.91  | 
% 14.89/2.91  | GROUND_INST: instantiating (2) with all_33_5, simplifying with (12), (22)
% 14.89/2.91  |              gives:
% 14.89/2.91  |   (32)   ? [v0: $i] :  ? [v1: $i] : (sziznziztdt0(all_33_5) = v1 &
% 14.89/2.91  |           aDimensionOf0(all_33_5) = v0 & $i(v1) & $i(v0) & (v0 = sz00 | ( !
% 14.89/2.91  |               [v2: $i] : (v2 = v1 |  ~ (aVector0(v2) = 0) |  ~ $i(v2) |  ?
% 14.89/2.91  |                 [v3: $i] :  ? [v4: $i] :  ? [v5: $i] : ( ~ (v5 = v4) &
% 14.89/2.91  |                   sdtlbdtrb0(v2, v3) = v4 & sdtlbdtrb0(all_33_5, v3) = v5 &
% 14.89/2.91  |                   aNaturalNumber0(v3) = 0 & $i(v5) & $i(v4) & $i(v3)) |  ?
% 14.89/2.91  |                 [v3: $i] :  ? [v4: $i] : ( ~ (v4 = v0) & aDimensionOf0(v2) =
% 14.89/2.91  |                   v3 & szszuzczcdt0(v3) = v4 & $i(v4) & $i(v3))) &  ! [v2:
% 14.89/2.91  |                 any] : ( ~ (aVector0(v1) = v2) | (v2 = 0 &  ! [v3: $i] :  !
% 14.89/2.91  |                   [v4: $i] : ( ~ (sdtlbdtrb0(all_33_5, v3) = v4) |  ~ $i(v3) |
% 14.89/2.91  |                      ? [v5: any] :  ? [v6: $i] : (sdtlbdtrb0(v1, v3) = v6 &
% 14.89/2.91  |                       aNaturalNumber0(v3) = v5 & $i(v6) & ( ~ (v5 = 0) | v6 =
% 14.89/2.91  |                         v4))) &  ? [v3: $i] : (aDimensionOf0(v1) = v3 &
% 14.89/2.91  |                     szszuzczcdt0(v3) = v0 & $i(v3)))))))
% 14.89/2.91  | 
% 14.89/2.91  | GROUND_INST: instantiating (mDimNat) with all_33_5, simplifying with (12),
% 14.89/2.91  |              (22) gives:
% 14.89/2.91  |   (33)   ? [v0: $i] : (aDimensionOf0(all_33_5) = v0 & aNaturalNumber0(v0) = 0
% 14.89/2.91  |           & $i(v0))
% 14.89/2.91  | 
% 14.89/2.91  | GROUND_INST: instantiating (2) with all_33_2, simplifying with (14), (23)
% 14.89/2.91  |              gives:
% 14.89/2.91  |   (34)   ? [v0: $i] :  ? [v1: $i] : (sziznziztdt0(all_33_2) = v1 &
% 14.89/2.91  |           aDimensionOf0(all_33_2) = v0 & $i(v1) & $i(v0) & (v0 = sz00 | ( !
% 14.89/2.91  |               [v2: $i] : (v2 = v1 |  ~ (aVector0(v2) = 0) |  ~ $i(v2) |  ?
% 14.89/2.91  |                 [v3: $i] :  ? [v4: $i] :  ? [v5: $i] : ( ~ (v5 = v4) &
% 14.89/2.91  |                   sdtlbdtrb0(v2, v3) = v4 & sdtlbdtrb0(all_33_2, v3) = v5 &
% 14.89/2.91  |                   aNaturalNumber0(v3) = 0 & $i(v5) & $i(v4) & $i(v3)) |  ?
% 14.89/2.91  |                 [v3: $i] :  ? [v4: $i] : ( ~ (v4 = v0) & aDimensionOf0(v2) =
% 14.89/2.91  |                   v3 & szszuzczcdt0(v3) = v4 & $i(v4) & $i(v3))) &  ! [v2:
% 14.89/2.91  |                 any] : ( ~ (aVector0(v1) = v2) | (v2 = 0 &  ! [v3: $i] :  !
% 14.89/2.91  |                   [v4: $i] : ( ~ (sdtlbdtrb0(all_33_2, v3) = v4) |  ~ $i(v3) |
% 14.89/2.91  |                      ? [v5: any] :  ? [v6: $i] : (sdtlbdtrb0(v1, v3) = v6 &
% 14.89/2.91  |                       aNaturalNumber0(v3) = v5 & $i(v6) & ( ~ (v5 = 0) | v6 =
% 14.89/2.91  |                         v4))) &  ? [v3: $i] : (aDimensionOf0(v1) = v3 &
% 14.89/2.91  |                     szszuzczcdt0(v3) = v0 & $i(v3)))))))
% 14.89/2.91  | 
% 14.89/2.91  | GROUND_INST: instantiating (mDimNat) with all_33_2, simplifying with (14),
% 14.89/2.91  |              (23) gives:
% 14.89/2.91  |   (35)   ? [v0: $i] : (aDimensionOf0(all_33_2) = v0 & aNaturalNumber0(v0) = 0
% 14.89/2.91  |           & $i(v0))
% 14.89/2.91  | 
% 14.89/2.91  | DELTA: instantiating (35) with fresh symbol all_45_0 gives:
% 14.89/2.91  |   (36)  aDimensionOf0(all_33_2) = all_45_0 & aNaturalNumber0(all_45_0) = 0 &
% 14.89/2.91  |         $i(all_45_0)
% 14.89/2.91  | 
% 14.89/2.91  | ALPHA: (36) implies:
% 14.89/2.91  |   (37)  aNaturalNumber0(all_45_0) = 0
% 14.89/2.91  |   (38)  aDimensionOf0(all_33_2) = all_45_0
% 14.89/2.91  | 
% 14.89/2.91  | DELTA: instantiating (33) with fresh symbol all_49_0 gives:
% 14.89/2.91  |   (39)  aDimensionOf0(all_33_5) = all_49_0 & aNaturalNumber0(all_49_0) = 0 &
% 14.89/2.91  |         $i(all_49_0)
% 14.89/2.91  | 
% 14.89/2.91  | ALPHA: (39) implies:
% 14.89/2.91  |   (40)  aNaturalNumber0(all_49_0) = 0
% 14.89/2.91  |   (41)  aDimensionOf0(all_33_5) = all_49_0
% 14.89/2.91  | 
% 14.89/2.91  | DELTA: instantiating (31) with fresh symbols all_55_0, all_55_1 gives:
% 14.89/2.91  |   (42)  aNaturalNumber0(all_33_1) = all_55_1 & aNaturalNumber0(all_28_0) =
% 14.89/2.91  |         all_55_0 & ( ~ (all_55_1 = 0) | (all_55_0 = 0 &  ~ (all_28_0 = sz00)))
% 14.89/2.91  | 
% 14.89/2.91  | ALPHA: (42) implies:
% 14.89/2.92  |   (43)  aNaturalNumber0(all_33_1) = all_55_1
% 14.89/2.92  | 
% 14.89/2.92  | DELTA: instantiating (28) with fresh symbols all_57_0, all_57_1 gives:
% 14.89/2.92  |   (44)  aNaturalNumber0(all_33_4) = all_57_1 & aNaturalNumber0(all_28_0) =
% 14.89/2.92  |         all_57_0 & ( ~ (all_57_1 = 0) | (all_57_0 = 0 &  ~ (all_28_0 = sz00)))
% 14.89/2.92  | 
% 14.89/2.92  | ALPHA: (44) implies:
% 14.89/2.92  |   (45)  aNaturalNumber0(all_33_4) = all_57_1
% 14.89/2.92  | 
% 14.89/2.92  | DELTA: instantiating (34) with fresh symbols all_59_0, all_59_1 gives:
% 14.89/2.92  |   (46)  sziznziztdt0(all_33_2) = all_59_0 & aDimensionOf0(all_33_2) = all_59_1
% 14.89/2.92  |         & $i(all_59_0) & $i(all_59_1) & (all_59_1 = sz00 | ( ! [v0: any] : (v0
% 14.89/2.92  |               = all_59_0 |  ~ (aVector0(v0) = 0) |  ~ $i(v0) |  ? [v1: $i] : 
% 14.89/2.92  |               ? [v2: $i] :  ? [v3: $i] : ( ~ (v3 = v2) & sdtlbdtrb0(v0, v1) =
% 14.89/2.92  |                 v2 & sdtlbdtrb0(all_33_2, v1) = v3 & aNaturalNumber0(v1) = 0 &
% 14.89/2.92  |                 $i(v3) & $i(v2) & $i(v1)) |  ? [v1: $i] :  ? [v2: any] : ( ~
% 14.89/2.92  |                 (v2 = all_59_1) & aDimensionOf0(v0) = v1 & szszuzczcdt0(v1) =
% 14.89/2.92  |                 v2 & $i(v2) & $i(v1))) &  ! [v0: any] : ( ~
% 14.89/2.92  |               (aVector0(all_59_0) = v0) | (v0 = 0 &  ! [v1: $i] :  ! [v2: $i]
% 14.89/2.92  |                 : ( ~ (sdtlbdtrb0(all_33_2, v1) = v2) |  ~ $i(v1) |  ? [v3:
% 14.89/2.92  |                     any] :  ? [v4: $i] : (sdtlbdtrb0(all_59_0, v1) = v4 &
% 14.89/2.92  |                     aNaturalNumber0(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 =
% 14.89/2.92  |                       v2))) &  ? [v1: $i] : (aDimensionOf0(all_59_0) = v1 &
% 14.89/2.92  |                   szszuzczcdt0(v1) = all_59_1 & $i(v1))))))
% 14.89/2.92  | 
% 14.89/2.92  | ALPHA: (46) implies:
% 14.89/2.92  |   (47)  aDimensionOf0(all_33_2) = all_59_1
% 14.89/2.92  | 
% 14.89/2.92  | DELTA: instantiating (32) with fresh symbols all_63_0, all_63_1 gives:
% 14.89/2.92  |   (48)  sziznziztdt0(all_33_5) = all_63_0 & aDimensionOf0(all_33_5) = all_63_1
% 14.89/2.92  |         & $i(all_63_0) & $i(all_63_1) & (all_63_1 = sz00 | ( ! [v0: any] : (v0
% 14.89/2.92  |               = all_63_0 |  ~ (aVector0(v0) = 0) |  ~ $i(v0) |  ? [v1: $i] : 
% 14.89/2.92  |               ? [v2: $i] :  ? [v3: $i] : ( ~ (v3 = v2) & sdtlbdtrb0(v0, v1) =
% 14.89/2.92  |                 v2 & sdtlbdtrb0(all_33_5, v1) = v3 & aNaturalNumber0(v1) = 0 &
% 14.89/2.92  |                 $i(v3) & $i(v2) & $i(v1)) |  ? [v1: $i] :  ? [v2: any] : ( ~
% 14.89/2.92  |                 (v2 = all_63_1) & aDimensionOf0(v0) = v1 & szszuzczcdt0(v1) =
% 14.89/2.92  |                 v2 & $i(v2) & $i(v1))) &  ! [v0: any] : ( ~
% 14.89/2.92  |               (aVector0(all_63_0) = v0) | (v0 = 0 &  ! [v1: $i] :  ! [v2: $i]
% 14.89/2.92  |                 : ( ~ (sdtlbdtrb0(all_33_5, v1) = v2) |  ~ $i(v1) |  ? [v3:
% 14.89/2.92  |                     any] :  ? [v4: $i] : (sdtlbdtrb0(all_63_0, v1) = v4 &
% 14.89/2.92  |                     aNaturalNumber0(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 =
% 14.89/2.92  |                       v2))) &  ? [v1: $i] : (aDimensionOf0(all_63_0) = v1 &
% 14.89/2.92  |                   szszuzczcdt0(v1) = all_63_1 & $i(v1))))))
% 14.89/2.92  | 
% 14.89/2.92  | ALPHA: (48) implies:
% 14.89/2.92  |   (49)  aDimensionOf0(all_33_5) = all_63_1
% 14.89/2.92  | 
% 14.89/2.92  | GROUND_INST: instantiating (6) with all_33_4, all_63_1, all_33_5, simplifying
% 14.89/2.92  |              with (20), (49) gives:
% 14.89/2.92  |   (50)  all_63_1 = all_33_4
% 14.89/2.92  | 
% 14.89/2.92  | GROUND_INST: instantiating (6) with all_49_0, all_63_1, all_33_5, simplifying
% 14.89/2.92  |              with (41), (49) gives:
% 14.89/2.92  |   (51)  all_63_1 = all_49_0
% 14.89/2.92  | 
% 14.89/2.92  | GROUND_INST: instantiating (6) with all_33_1, all_59_1, all_33_2, simplifying
% 14.89/2.92  |              with (21), (47) gives:
% 14.89/2.92  |   (52)  all_59_1 = all_33_1
% 14.89/2.92  | 
% 14.89/2.92  | GROUND_INST: instantiating (6) with all_45_0, all_59_1, all_33_2, simplifying
% 14.89/2.92  |              with (38), (47) gives:
% 14.89/2.92  |   (53)  all_59_1 = all_45_0
% 14.89/2.92  | 
% 14.89/2.92  | COMBINE_EQS: (50), (51) imply:
% 14.89/2.92  |   (54)  all_49_0 = all_33_4
% 14.89/2.92  | 
% 14.89/2.92  | COMBINE_EQS: (52), (53) imply:
% 14.89/2.92  |   (55)  all_45_0 = all_33_1
% 14.89/2.92  | 
% 14.89/2.92  | SIMP: (55) implies:
% 14.89/2.92  |   (56)  all_45_0 = all_33_1
% 14.89/2.92  | 
% 14.89/2.92  | REDUCE: (40), (54) imply:
% 14.89/2.92  |   (57)  aNaturalNumber0(all_33_4) = 0
% 14.89/2.92  | 
% 14.89/2.92  | REDUCE: (37), (56) imply:
% 14.89/2.92  |   (58)  aNaturalNumber0(all_33_1) = 0
% 14.89/2.92  | 
% 14.89/2.92  | GROUND_INST: instantiating (5) with all_57_1, 0, all_33_4, simplifying with
% 14.89/2.92  |              (45), (57) gives:
% 14.89/2.92  |   (59)  all_57_1 = 0
% 14.89/2.92  | 
% 14.89/2.93  | GROUND_INST: instantiating (5) with all_55_1, 0, all_33_1, simplifying with
% 14.89/2.93  |              (43), (58) gives:
% 14.89/2.93  |   (60)  all_55_1 = 0
% 14.89/2.93  | 
% 14.89/2.93  | BETA: splitting (29) gives:
% 14.89/2.93  | 
% 14.89/2.93  | Case 1:
% 14.89/2.93  | | 
% 14.89/2.93  | |   (61)  all_33_1 = all_33_4
% 14.89/2.93  | | 
% 14.89/2.93  | | REDUCE: (11), (61) imply:
% 14.89/2.93  | |   (62)  $false
% 14.89/2.93  | | 
% 14.89/2.93  | | CLOSE: (62) is inconsistent.
% 14.89/2.93  | | 
% 14.89/2.93  | Case 2:
% 14.89/2.93  | | 
% 14.89/2.93  | |   (63)   ? [v0: any] :  ? [v1: any] : (aNaturalNumber0(all_33_1) = v1 &
% 14.89/2.93  | |           aNaturalNumber0(all_33_4) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 14.89/2.93  | | 
% 14.89/2.93  | | DELTA: instantiating (63) with fresh symbols all_92_0, all_92_1 gives:
% 14.89/2.93  | |   (64)  aNaturalNumber0(all_33_1) = all_92_0 & aNaturalNumber0(all_33_4) =
% 14.89/2.93  | |         all_92_1 & ( ~ (all_92_0 = 0) |  ~ (all_92_1 = 0))
% 14.89/2.93  | | 
% 14.89/2.93  | | ALPHA: (64) implies:
% 14.89/2.93  | |   (65)  aNaturalNumber0(all_33_4) = all_92_1
% 14.89/2.93  | |   (66)  aNaturalNumber0(all_33_1) = all_92_0
% 14.89/2.93  | |   (67)   ~ (all_92_0 = 0) |  ~ (all_92_1 = 0)
% 14.89/2.93  | | 
% 14.89/2.93  | | BETA: splitting (30) gives:
% 14.89/2.93  | | 
% 14.89/2.93  | | Case 1:
% 14.89/2.93  | | | 
% 14.89/2.93  | | |   (68)  all_33_1 = all_33_4
% 14.89/2.93  | | | 
% 14.89/2.93  | | | REDUCE: (11), (68) imply:
% 14.89/2.93  | | |   (69)  $false
% 14.89/2.93  | | | 
% 14.89/2.93  | | | CLOSE: (69) is inconsistent.
% 14.89/2.93  | | | 
% 14.89/2.93  | | Case 2:
% 14.89/2.93  | | | 
% 14.89/2.93  | | |   (70)   ? [v0: any] :  ? [v1: any] : (aNaturalNumber0(all_33_1) = v0 &
% 14.89/2.93  | | |           aNaturalNumber0(all_33_4) = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 14.89/2.93  | | | 
% 14.89/2.93  | | | DELTA: instantiating (70) with fresh symbols all_98_0, all_98_1 gives:
% 14.89/2.93  | | |   (71)  aNaturalNumber0(all_33_1) = all_98_1 & aNaturalNumber0(all_33_4) =
% 14.89/2.93  | | |         all_98_0 & ( ~ (all_98_0 = 0) |  ~ (all_98_1 = 0))
% 14.89/2.93  | | | 
% 14.89/2.93  | | | ALPHA: (71) implies:
% 14.89/2.93  | | |   (72)  aNaturalNumber0(all_33_4) = all_98_0
% 14.89/2.93  | | |   (73)  aNaturalNumber0(all_33_1) = all_98_1
% 14.89/2.93  | | | 
% 14.89/2.93  | | | GROUND_INST: instantiating (5) with 0, all_98_0, all_33_4, simplifying
% 14.89/2.93  | | |              with (57), (72) gives:
% 14.89/2.93  | | |   (74)  all_98_0 = 0
% 14.89/2.93  | | | 
% 14.89/2.93  | | | GROUND_INST: instantiating (5) with all_92_1, all_98_0, all_33_4,
% 14.89/2.93  | | |              simplifying with (65), (72) gives:
% 14.89/2.93  | | |   (75)  all_98_0 = all_92_1
% 14.89/2.93  | | | 
% 14.89/2.93  | | | GROUND_INST: instantiating (5) with 0, all_98_1, all_33_1, simplifying
% 14.89/2.93  | | |              with (58), (73) gives:
% 14.89/2.93  | | |   (76)  all_98_1 = 0
% 14.89/2.93  | | | 
% 14.89/2.93  | | | GROUND_INST: instantiating (5) with all_92_0, all_98_1, all_33_1,
% 14.89/2.93  | | |              simplifying with (66), (73) gives:
% 14.89/2.93  | | |   (77)  all_98_1 = all_92_0
% 14.89/2.93  | | | 
% 14.89/2.93  | | | COMBINE_EQS: (74), (75) imply:
% 14.89/2.93  | | |   (78)  all_92_1 = 0
% 14.89/2.93  | | | 
% 14.89/2.93  | | | COMBINE_EQS: (76), (77) imply:
% 14.89/2.93  | | |   (79)  all_92_0 = 0
% 14.89/2.93  | | | 
% 14.89/2.93  | | | BETA: splitting (67) gives:
% 14.89/2.93  | | | 
% 14.89/2.93  | | | Case 1:
% 14.89/2.93  | | | | 
% 14.89/2.93  | | | |   (80)   ~ (all_92_0 = 0)
% 14.89/2.93  | | | | 
% 14.89/2.93  | | | | REDUCE: (79), (80) imply:
% 14.89/2.93  | | | |   (81)  $false
% 14.89/2.93  | | | | 
% 14.89/2.93  | | | | CLOSE: (81) is inconsistent.
% 14.89/2.93  | | | | 
% 14.89/2.93  | | | Case 2:
% 14.89/2.93  | | | | 
% 14.89/2.93  | | | |   (82)   ~ (all_92_1 = 0)
% 14.89/2.93  | | | | 
% 14.89/2.93  | | | | REDUCE: (78), (82) imply:
% 14.89/2.93  | | | |   (83)  $false
% 14.89/2.93  | | | | 
% 14.89/2.93  | | | | CLOSE: (83) is inconsistent.
% 14.89/2.93  | | | | 
% 14.89/2.93  | | | End of split
% 14.89/2.93  | | | 
% 14.89/2.93  | | End of split
% 14.89/2.93  | | 
% 14.89/2.93  | End of split
% 14.89/2.93  | 
% 14.89/2.93  End of proof
% 14.89/2.93  % SZS output end Proof for theBenchmark
% 14.89/2.93  
% 14.89/2.93  2314ms
%------------------------------------------------------------------------------