%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : NUM475+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n028.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 11:48:00 EDT 2023

% Result   : Theorem 11.39s 2.25s
% Output   : Proof 22.34s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM475+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n028.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Fri Aug 25 09:50:36 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.56  ________       _____
% 0.19/0.56  ___  __ \_________(_)________________________________
% 0.19/0.56  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.19/0.56  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.19/0.56  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.19/0.56  
% 0.19/0.56  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.56  (2023-06-19)
% 0.19/0.56  
% 0.19/0.56  (c) Philipp Rümmer, 2009-2023
% 0.19/0.56  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.56                Amanda Stjerna.
% 0.19/0.56  Free software under BSD-3-Clause.
% 0.19/0.56  
% 0.19/0.56  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.56  
% 0.19/0.56  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.57  Running up to 7 provers in parallel.
% 0.19/0.58  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.58  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.58  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.58  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.58  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.58  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.58  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.92/1.14  Prover 4: Preprocessing ...
% 3.48/1.15  Prover 1: Preprocessing ...
% 3.70/1.19  Prover 3: Preprocessing ...
% 3.70/1.19  Prover 0: Preprocessing ...
% 3.70/1.19  Prover 2: Preprocessing ...
% 3.70/1.19  Prover 6: Preprocessing ...
% 3.70/1.19  Prover 5: Preprocessing ...
% 8.02/1.80  Prover 1: Constructing countermodel ...
% 8.02/1.81  Prover 3: Constructing countermodel ...
% 8.02/1.83  Prover 6: Proving ...
% 8.69/1.96  Prover 5: Constructing countermodel ...
% 10.02/2.08  Prover 2: Proving ...
% 10.59/2.16  Prover 4: Constructing countermodel ...
% 10.89/2.22  Prover 6: proved (1637ms)
% 11.39/2.24  
% 11.39/2.25  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.39/2.25  
% 11.39/2.25  Prover 5: stopped
% 11.39/2.26  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.39/2.26  Prover 3: stopped
% 11.58/2.27  Prover 2: stopped
% 11.58/2.28  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.58/2.28  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.58/2.29  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.58/2.31  Prover 7: Preprocessing ...
% 12.00/2.33  Prover 0: Proving ...
% 12.00/2.34  Prover 0: stopped
% 12.00/2.35  Prover 8: Preprocessing ...
% 12.00/2.35  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.26/2.38  Prover 11: Preprocessing ...
% 12.26/2.39  Prover 10: Preprocessing ...
% 12.26/2.42  Prover 13: Preprocessing ...
% 13.16/2.52  Prover 8: Warning: ignoring some quantifiers
% 13.64/2.54  Prover 8: Constructing countermodel ...
% 13.64/2.56  Prover 7: Constructing countermodel ...
% 13.64/2.57  Prover 10: Constructing countermodel ...
% 13.64/2.67  Prover 13: Constructing countermodel ...
% 15.33/2.80  Prover 11: Constructing countermodel ...
% 21.23/3.59  Prover 1: Found proof (size 326)
% 21.23/3.59  Prover 1: proved (3011ms)
% 21.23/3.59  Prover 7: stopped
% 21.23/3.59  Prover 13: stopped
% 21.23/3.59  Prover 10: stopped
% 21.23/3.59  Prover 8: stopped
% 21.23/3.59  Prover 11: stopped
% 21.23/3.60  Prover 4: stopped
% 21.23/3.60  
% 21.23/3.60  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.23/3.60  
% 21.69/3.64  % SZS output start Proof for theBenchmark
% 21.69/3.65  Assumptions after simplification:
% 21.69/3.65  ---------------------------------
% 21.69/3.65  
% 21.69/3.65    (mAMDistr)
% 21.69/3.67     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :  ! [v5:
% 21.69/3.67      $i] : ( ~ (sdtasdt0(v0, v2) = v4) |  ~ (sdtasdt0(v0, v1) = v3) |  ~
% 21.69/3.67      (sdtpldt0(v3, v4) = v5) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v6: any] :
% 21.69/3.67       ? [v7: any] :  ? [v8: any] :  ? [v9: $i] :  ? [v10: $i] :  ? [v11: $i] :  ?
% 21.69/3.67      [v12: $i] :  ? [v13: $i] :  ? [v14: $i] : (sdtasdt0(v9, v0) = v11 &
% 21.69/3.67        sdtasdt0(v2, v0) = v13 & sdtasdt0(v1, v0) = v12 & sdtasdt0(v0, v9) = v10 &
% 21.69/3.67        sdtpldt0(v12, v13) = v14 & sdtpldt0(v1, v2) = v9 & aNaturalNumber0(v2) =
% 21.69/3.67        v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & $i(v14) &
% 21.69/3.67        $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & ( ~ (v8 = 0) |  ~ (v7 =
% 21.69/3.67            0) |  ~ (v6 = 0) | (v14 = v11 & v10 = v5))))
% 21.69/3.67  
% 21.69/3.67    (mAddCanc)
% 21.69/3.68     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v2 = v1
% 21.69/3.68      |  ~ (sdtpldt0(v0, v2) = v4) |  ~ (sdtpldt0(v0, v1) = v3) |  ~ $i(v2) |  ~
% 21.69/3.68      $i(v1) |  ~ $i(v0) |  ? [v5: any] :  ? [v6: any] :  ? [v7: any] :  ? [v8:
% 21.69/3.68        $i] :  ? [v9: $i] : (sdtpldt0(v2, v0) = v9 & sdtpldt0(v1, v0) = v8 &
% 21.69/3.68        aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0)
% 21.69/3.68        = v5 & $i(v9) & $i(v8) & ( ~ (v7 = 0) |  ~ (v6 = 0) |  ~ (v5 = 0) | ( ~
% 21.69/3.68            (v9 = v8) &  ~ (v4 = v3)))))
% 21.69/3.68  
% 21.69/3.68    (mAddComm)
% 21.91/3.68     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) |  ~
% 21.91/3.68      $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] :  ? [v5: $i] :
% 21.91/3.68      (sdtpldt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3
% 21.91/3.68        & $i(v5) & ( ~ (v4 = 0) |  ~ (v3 = 0) | v5 = v2)))
% 21.91/3.68  
% 21.91/3.68    (mDefDiff)
% 21.91/3.68     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (sdtmndt0(v1, v0) = v2) |  ~
% 21.91/3.68      $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] :  ? [v5: any] :
% 21.91/3.68      (sdtlseqdt0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) =
% 21.91/3.68        v3 & ( ~ (v5 = 0) |  ~ (v4 = 0) |  ~ (v3 = 0))) | ( ! [v3: $i] : (v3 = v2
% 21.91/3.68          |  ~ (sdtpldt0(v0, v3) = v1) |  ~ $i(v3) |  ? [v4: int] : ( ~ (v4 = 0) &
% 21.91/3.68            aNaturalNumber0(v3) = v4)) &  ! [v3: $i] : ( ~ (sdtpldt0(v0, v2) = v3)
% 21.91/3.68          |  ~ $i(v2) | (v3 = v1 & aNaturalNumber0(v2) = 0))))
% 21.91/3.68  
% 21.91/3.68    (mDefDiv)
% 21.91/3.68     ! [v0: $i] :  ! [v1: $i] :  ! [v2: any] : ( ~ (doDivides0(v0, v1) = v2) |  ~
% 21.91/3.68      $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] : (aNaturalNumber0(v1) = v4
% 21.91/3.68        & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0))) | (( ~ (v2 = 0)
% 21.91/3.68          |  ? [v3: $i] : (sdtasdt0(v0, v3) = v1 & aNaturalNumber0(v3) = 0 &
% 21.91/3.68            $i(v3))) & (v2 = 0 |  ! [v3: $i] : ( ~ (sdtasdt0(v0, v3) = v1) |  ~
% 21.91/3.68            $i(v3) |  ? [v4: int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4)))))
% 21.91/3.68  
% 21.91/3.68    (mDefQuot)
% 21.91/3.68    $i(sz00) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v0 = sz00 |  ~
% 21.91/3.68      (sdtsldt0(v1, v0) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4:
% 21.91/3.68        any] :  ? [v5: any] : (doDivides0(v0, v1) = v5 & aNaturalNumber0(v1) = v4
% 21.91/3.68        & aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) |  ~ (v4 = 0) |  ~ (v3 = 0))) |
% 21.91/3.68      ( ! [v3: $i] : (v3 = v2 |  ~ (sdtasdt0(v0, v3) = v1) |  ~ $i(v3) |  ? [v4:
% 21.91/3.68            int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4)) &  ! [v3: $i] : ( ~
% 21.91/3.68          (sdtasdt0(v0, v2) = v3) |  ~ $i(v2) | (v3 = v1 & aNaturalNumber0(v2) =
% 21.91/3.68            0))))
% 21.91/3.68  
% 21.91/3.68    (mMulComm)
% 21.91/3.68     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) |  ~
% 21.91/3.68      $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] :  ? [v5: $i] :
% 21.91/3.68      (sdtasdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3
% 21.91/3.68        & $i(v5) & ( ~ (v4 = 0) |  ~ (v3 = 0) | v5 = v2)))
% 21.91/3.68  
% 21.91/3.68    (mSortsB)
% 21.91/3.68     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) |  ~
% 21.91/3.68      $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] :  ? [v5: any] :
% 21.91/3.69      (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) =
% 21.91/3.69        v3 & ( ~ (v4 = 0) |  ~ (v3 = 0) | v5 = 0)))
% 21.91/3.69  
% 21.91/3.69    (mSortsB_02)
% 21.91/3.69     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) |  ~
% 21.91/3.69      $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] :  ? [v5: any] :
% 21.91/3.69      (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) =
% 21.91/3.69        v3 & ( ~ (v4 = 0) |  ~ (v3 = 0) | v5 = 0)))
% 21.91/3.69  
% 21.91/3.69    (m__)
% 21.91/3.69    $i(xr) & $i(xn) & $i(xl) &  ? [v0: $i] : ( ~ (v0 = xn) & sdtasdt0(xl, xr) = v0
% 21.91/3.69      & $i(v0))
% 21.91/3.69  
% 21.91/3.69    (m__1324)
% 21.91/3.69    aNaturalNumber0(xn) = 0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(xl) = 0 &
% 21.91/3.69    $i(xn) & $i(xm) & $i(xl)
% 21.91/3.69  
% 21.91/3.69    (m__1324_04)
% 21.91/3.69    $i(xn) & $i(xm) & $i(xl) &  ? [v0: $i] : (doDivides0(xl, v0) = 0 &
% 21.91/3.69      doDivides0(xl, xm) = 0 & sdtpldt0(xm, xn) = v0 & $i(v0))
% 21.91/3.69  
% 21.91/3.69    (m__1347)
% 21.91/3.69     ~ (xl = sz00) & $i(xl) & $i(sz00)
% 21.91/3.69  
% 21.91/3.69    (m__1360)
% 21.91/3.69    sdtsldt0(xm, xl) = xp & $i(xp) & $i(xm) & $i(xl)
% 21.91/3.69  
% 21.91/3.69    (m__1379)
% 21.91/3.69    $i(xq) & $i(xn) & $i(xm) & $i(xl) &  ? [v0: $i] : (sdtsldt0(v0, xl) = xq &
% 21.91/3.69      sdtpldt0(xm, xn) = v0 & $i(v0))
% 21.91/3.69  
% 21.91/3.69    (m__1395)
% 21.91/3.69    sdtlseqdt0(xp, xq) = 0 & $i(xq) & $i(xp)
% 21.91/3.69  
% 21.91/3.69    (m__1422)
% 21.91/3.69    sdtmndt0(xq, xp) = xr & $i(xr) & $i(xq) & $i(xp)
% 21.91/3.69  
% 21.91/3.69    (m__1459)
% 21.91/3.69    $i(xr) & $i(xp) & $i(xn) & $i(xl) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 21.91/3.69    (sdtasdt0(xl, xr) = v1 & sdtasdt0(xl, xp) = v0 & sdtpldt0(v0, v1) = v2 &
% 21.91/3.69      sdtpldt0(v0, xn) = v2 & $i(v2) & $i(v1) & $i(v0))
% 21.91/3.69  
% 21.91/3.69    (function-axioms)
% 21.91/3.69     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 21.91/3.69      (sdtsldt0(v3, v2) = v1) |  ~ (sdtsldt0(v3, v2) = v0)) &  ! [v0:
% 21.91/3.69      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 21.91/3.69    : (v1 = v0 |  ~ (doDivides0(v3, v2) = v1) |  ~ (doDivides0(v3, v2) = v0)) &  !
% 21.91/3.69    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 21.91/3.69      $i] : (v1 = v0 |  ~ (iLess0(v3, v2) = v1) |  ~ (iLess0(v3, v2) = v0)) &  !
% 21.91/3.69    [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 21.91/3.69      (sdtmndt0(v3, v2) = v1) |  ~ (sdtmndt0(v3, v2) = v0)) &  ! [v0:
% 21.91/3.69      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 21.91/3.69    : (v1 = v0 |  ~ (sdtlseqdt0(v3, v2) = v1) |  ~ (sdtlseqdt0(v3, v2) = v0)) &  !
% 21.91/3.69    [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 21.91/3.69      (sdtasdt0(v3, v2) = v1) |  ~ (sdtasdt0(v3, v2) = v0)) &  ! [v0: $i] :  !
% 21.91/3.69    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (sdtpldt0(v3, v2) = v1) |
% 21.91/3.69       ~ (sdtpldt0(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 21.91/3.69      MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (aNaturalNumber0(v2) = v1)
% 21.91/3.69      |  ~ (aNaturalNumber0(v2) = v0))
% 21.91/3.69  
% 21.91/3.69  Further assumptions not needed in the proof:
% 21.91/3.69  --------------------------------------------
% 21.91/3.69  mAddAsso, mDefLE, mDivSum, mDivTrans, mIH, mIH_03, mLEAsym, mLENTr, mLERefl,
% 21.91/3.69  mLETotal, mLETran, mMonAdd, mMonMul, mMonMul2, mMulAsso, mMulCanc, mNatSort,
% 21.91/3.69  mSortsC, mSortsC_01, mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, m_MulZero
% 21.91/3.69  
% 21.91/3.69  Those formulas are unsatisfiable:
% 21.91/3.69  ---------------------------------
% 21.91/3.69  
% 21.91/3.69  Begin of proof
% 21.91/3.69  | 
% 21.91/3.69  | ALPHA: (mDefQuot) implies:
% 21.91/3.70  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v0 = sz00 |  ~ (sdtsldt0(v1,
% 21.91/3.70  |              v0) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] :
% 21.91/3.70  |           ? [v5: any] : (doDivides0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 &
% 21.91/3.70  |            aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) |  ~ (v4 = 0) |  ~ (v3 =
% 21.91/3.70  |                0))) | ( ! [v3: $i] : (v3 = v2 |  ~ (sdtasdt0(v0, v3) = v1) | 
% 21.91/3.70  |              ~ $i(v3) |  ? [v4: int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) =
% 21.91/3.70  |                v4)) &  ! [v3: $i] : ( ~ (sdtasdt0(v0, v2) = v3) |  ~ $i(v2) |
% 21.91/3.70  |              (v3 = v1 & aNaturalNumber0(v2) = 0))))
% 21.91/3.70  | 
% 21.91/3.70  | ALPHA: (m__1324) implies:
% 21.91/3.70  |   (2)  aNaturalNumber0(xl) = 0
% 21.91/3.70  |   (3)  aNaturalNumber0(xm) = 0
% 21.91/3.70  |   (4)  aNaturalNumber0(xn) = 0
% 21.91/3.70  | 
% 21.91/3.70  | ALPHA: (m__1324_04) implies:
% 21.91/3.70  |   (5)   ? [v0: $i] : (doDivides0(xl, v0) = 0 & doDivides0(xl, xm) = 0 &
% 21.91/3.70  |          sdtpldt0(xm, xn) = v0 & $i(v0))
% 21.91/3.70  | 
% 21.91/3.70  | ALPHA: (m__1347) implies:
% 21.91/3.70  |   (6)   ~ (xl = sz00)
% 21.91/3.70  | 
% 21.91/3.70  | ALPHA: (m__1360) implies:
% 21.91/3.70  |   (7)  sdtsldt0(xm, xl) = xp
% 21.91/3.70  | 
% 21.91/3.70  | ALPHA: (m__1379) implies:
% 21.91/3.70  |   (8)  $i(xm)
% 21.91/3.70  |   (9)   ? [v0: $i] : (sdtsldt0(v0, xl) = xq & sdtpldt0(xm, xn) = v0 & $i(v0))
% 21.91/3.70  | 
% 21.91/3.70  | ALPHA: (m__1395) implies:
% 21.91/3.70  |   (10)  sdtlseqdt0(xp, xq) = 0
% 21.91/3.70  | 
% 21.91/3.70  | ALPHA: (m__1422) implies:
% 21.91/3.70  |   (11)  $i(xq)
% 21.91/3.70  |   (12)  sdtmndt0(xq, xp) = xr
% 21.91/3.70  | 
% 21.91/3.70  | ALPHA: (m__1459) implies:
% 21.91/3.70  |   (13)  $i(xp)
% 21.91/3.70  |   (14)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (sdtasdt0(xl, xr) = v1 &
% 21.91/3.70  |           sdtasdt0(xl, xp) = v0 & sdtpldt0(v0, v1) = v2 & sdtpldt0(v0, xn) =
% 21.91/3.70  |           v2 & $i(v2) & $i(v1) & $i(v0))
% 21.91/3.70  | 
% 21.91/3.70  | ALPHA: (m__) implies:
% 21.91/3.70  |   (15)  $i(xl)
% 21.91/3.70  |   (16)  $i(xn)
% 21.91/3.70  |   (17)  $i(xr)
% 21.91/3.70  |   (18)   ? [v0: $i] : ( ~ (v0 = xn) & sdtasdt0(xl, xr) = v0 & $i(v0))
% 21.91/3.70  | 
% 21.91/3.70  | ALPHA: (function-axioms) implies:
% 21.91/3.70  |   (19)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i]
% 21.91/3.70  |         : (v1 = v0 |  ~ (aNaturalNumber0(v2) = v1) |  ~ (aNaturalNumber0(v2) =
% 21.91/3.70  |             v0))
% 21.91/3.70  |   (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 21.91/3.70  |           (sdtpldt0(v3, v2) = v1) |  ~ (sdtpldt0(v3, v2) = v0))
% 21.91/3.70  |   (21)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 21.91/3.70  |           (sdtasdt0(v3, v2) = v1) |  ~ (sdtasdt0(v3, v2) = v0))
% 21.91/3.70  |   (22)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i]
% 21.91/3.70  |         :  ! [v3: $i] : (v1 = v0 |  ~ (sdtlseqdt0(v3, v2) = v1) |  ~
% 21.91/3.70  |           (sdtlseqdt0(v3, v2) = v0))
% 21.91/3.70  |   (23)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i]
% 21.91/3.70  |         :  ! [v3: $i] : (v1 = v0 |  ~ (doDivides0(v3, v2) = v1) |  ~
% 21.91/3.70  |           (doDivides0(v3, v2) = v0))
% 21.91/3.70  | 
% 21.91/3.70  | DELTA: instantiating (9) with fresh symbol all_33_0 gives:
% 21.91/3.70  |   (24)  sdtsldt0(all_33_0, xl) = xq & sdtpldt0(xm, xn) = all_33_0 &
% 21.91/3.70  |         $i(all_33_0)
% 21.91/3.70  | 
% 21.91/3.70  | ALPHA: (24) implies:
% 21.91/3.70  |   (25)  sdtpldt0(xm, xn) = all_33_0
% 21.91/3.71  |   (26)  sdtsldt0(all_33_0, xl) = xq
% 21.91/3.71  | 
% 21.91/3.71  | DELTA: instantiating (18) with fresh symbol all_35_0 gives:
% 21.91/3.71  |   (27)   ~ (all_35_0 = xn) & sdtasdt0(xl, xr) = all_35_0 & $i(all_35_0)
% 21.91/3.71  | 
% 21.91/3.71  | ALPHA: (27) implies:
% 21.91/3.71  |   (28)   ~ (all_35_0 = xn)
% 21.91/3.71  |   (29)  sdtasdt0(xl, xr) = all_35_0
% 21.91/3.71  | 
% 21.91/3.71  | DELTA: instantiating (5) with fresh symbol all_37_0 gives:
% 21.91/3.71  |   (30)  doDivides0(xl, all_37_0) = 0 & doDivides0(xl, xm) = 0 & sdtpldt0(xm,
% 21.91/3.71  |           xn) = all_37_0 & $i(all_37_0)
% 21.91/3.71  | 
% 21.91/3.71  | ALPHA: (30) implies:
% 21.91/3.71  |   (31)  $i(all_37_0)
% 21.91/3.71  |   (32)  sdtpldt0(xm, xn) = all_37_0
% 21.91/3.71  |   (33)  doDivides0(xl, xm) = 0
% 21.91/3.71  |   (34)  doDivides0(xl, all_37_0) = 0
% 21.91/3.71  | 
% 21.91/3.71  | DELTA: instantiating (14) with fresh symbols all_39_0, all_39_1, all_39_2
% 21.91/3.71  |        gives:
% 21.91/3.71  |   (35)  sdtasdt0(xl, xr) = all_39_1 & sdtasdt0(xl, xp) = all_39_2 &
% 21.91/3.71  |         sdtpldt0(all_39_2, all_39_1) = all_39_0 & sdtpldt0(all_39_2, xn) =
% 21.91/3.71  |         all_39_0 & $i(all_39_0) & $i(all_39_1) & $i(all_39_2)
% 21.91/3.71  | 
% 21.91/3.71  | ALPHA: (35) implies:
% 21.91/3.71  |   (36)  $i(all_39_2)
% 21.91/3.71  |   (37)  $i(all_39_1)
% 21.91/3.71  |   (38)  sdtpldt0(all_39_2, xn) = all_39_0
% 21.91/3.71  |   (39)  sdtpldt0(all_39_2, all_39_1) = all_39_0
% 21.91/3.71  |   (40)  sdtasdt0(xl, xp) = all_39_2
% 21.91/3.71  |   (41)  sdtasdt0(xl, xr) = all_39_1
% 21.91/3.71  | 
% 21.91/3.71  | GROUND_INST: instantiating (20) with all_33_0, all_37_0, xn, xm, simplifying
% 21.91/3.71  |              with (25), (32) gives:
% 21.91/3.71  |   (42)  all_37_0 = all_33_0
% 21.91/3.71  | 
% 21.91/3.71  | GROUND_INST: instantiating (21) with all_35_0, all_39_1, xr, xl, simplifying
% 21.91/3.71  |              with (29), (41) gives:
% 21.91/3.71  |   (43)  all_39_1 = all_35_0
% 21.91/3.71  | 
% 21.91/3.71  | REDUCE: (34), (42) imply:
% 21.91/3.71  |   (44)  doDivides0(xl, all_33_0) = 0
% 21.91/3.71  | 
% 21.91/3.71  | REDUCE: (39), (43) imply:
% 21.91/3.71  |   (45)  sdtpldt0(all_39_2, all_35_0) = all_39_0
% 21.91/3.71  | 
% 21.91/3.71  | REDUCE: (37), (43) imply:
% 21.91/3.71  |   (46)  $i(all_35_0)
% 21.91/3.71  | 
% 21.91/3.71  | REDUCE: (31), (42) imply:
% 21.91/3.71  |   (47)  $i(all_33_0)
% 21.91/3.71  | 
% 21.91/3.71  | GROUND_INST: instantiating (mAddComm) with xm, xn, all_33_0, simplifying with
% 21.91/3.71  |              (8), (16), (25) gives:
% 21.91/3.71  |   (48)   ? [v0: any] :  ? [v1: any] :  ? [v2: $i] : (sdtpldt0(xn, xm) = v2 &
% 21.91/3.71  |           aNaturalNumber0(xn) = v1 & aNaturalNumber0(xm) = v0 & $i(v2) & ( ~
% 21.91/3.71  |             (v1 = 0) |  ~ (v0 = 0) | v2 = all_33_0))
% 21.91/3.71  | 
% 21.91/3.71  | GROUND_INST: instantiating (mSortsB) with xm, xn, all_33_0, simplifying with
% 21.91/3.71  |              (8), (16), (25) gives:
% 21.91/3.71  |   (49)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :
% 21.91/3.71  |         (aNaturalNumber0(all_33_0) = v2 & aNaturalNumber0(xn) = v1 &
% 21.91/3.71  |           aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = 0))
% 21.91/3.71  | 
% 21.91/3.71  | GROUND_INST: instantiating (mAddComm) with all_39_2, xn, all_39_0, simplifying
% 21.91/3.71  |              with (16), (36), (38) gives:
% 21.91/3.71  |   (50)   ? [v0: any] :  ? [v1: any] :  ? [v2: $i] : (sdtpldt0(xn, all_39_2) =
% 21.91/3.71  |           v2 & aNaturalNumber0(all_39_2) = v0 & aNaturalNumber0(xn) = v1 &
% 21.91/3.71  |           $i(v2) & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = all_39_0))
% 21.91/3.71  | 
% 21.91/3.71  | GROUND_INST: instantiating (mSortsB) with all_39_2, xn, all_39_0, simplifying
% 21.91/3.71  |              with (16), (36), (38) gives:
% 21.91/3.71  |   (51)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :
% 21.91/3.71  |         (aNaturalNumber0(all_39_0) = v2 & aNaturalNumber0(all_39_2) = v0 &
% 21.91/3.71  |           aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = 0))
% 21.91/3.71  | 
% 21.91/3.72  | GROUND_INST: instantiating (mAddCanc) with all_39_2, xn, all_35_0, all_39_0,
% 21.91/3.72  |              all_39_0, simplifying with (16), (36), (38), (45), (46) gives:
% 21.91/3.72  |   (52)  all_35_0 = xn |  ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ? [v3:
% 21.91/3.72  |           $i] :  ? [v4: $i] : (sdtpldt0(all_35_0, all_39_2) = v4 &
% 21.91/3.72  |           sdtpldt0(xn, all_39_2) = v3 & aNaturalNumber0(all_39_2) = v0 &
% 21.91/3.72  |           aNaturalNumber0(all_35_0) = v2 & aNaturalNumber0(xn) = v1 & $i(v4) &
% 21.91/3.72  |           $i(v3) & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 21.91/3.72  | 
% 21.91/3.72  | GROUND_INST: instantiating (mAddCanc) with all_39_2, all_35_0, xn, all_39_0,
% 21.91/3.72  |              all_39_0, simplifying with (16), (36), (38), (45), (46) gives:
% 21.91/3.72  |   (53)  all_35_0 = xn |  ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ? [v3:
% 21.91/3.72  |           $i] :  ? [v4: $i] : (sdtpldt0(all_35_0, all_39_2) = v3 &
% 21.91/3.72  |           sdtpldt0(xn, all_39_2) = v4 & aNaturalNumber0(all_39_2) = v0 &
% 21.91/3.72  |           aNaturalNumber0(all_35_0) = v1 & aNaturalNumber0(xn) = v2 & $i(v4) &
% 21.91/3.72  |           $i(v3) & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 21.91/3.72  | 
% 21.91/3.72  | GROUND_INST: instantiating (mAddComm) with all_39_2, all_35_0, all_39_0,
% 21.91/3.72  |              simplifying with (36), (45), (46) gives:
% 21.91/3.72  |   (54)   ? [v0: any] :  ? [v1: any] :  ? [v2: $i] : (sdtpldt0(all_35_0,
% 21.91/3.72  |             all_39_2) = v2 & aNaturalNumber0(all_39_2) = v0 &
% 21.91/3.72  |           aNaturalNumber0(all_35_0) = v1 & $i(v2) & ( ~ (v1 = 0) |  ~ (v0 = 0)
% 21.91/3.72  |             | v2 = all_39_0))
% 21.91/3.72  | 
% 21.91/3.72  | GROUND_INST: instantiating (mSortsB) with all_39_2, all_35_0, all_39_0,
% 21.91/3.72  |              simplifying with (36), (45), (46) gives:
% 21.91/3.72  |   (55)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :
% 21.91/3.72  |         (aNaturalNumber0(all_39_0) = v2 & aNaturalNumber0(all_39_2) = v0 &
% 21.91/3.72  |           aNaturalNumber0(all_35_0) = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 =
% 21.91/3.72  |             0))
% 21.91/3.72  | 
% 21.91/3.72  | GROUND_INST: instantiating (mMulComm) with xl, xp, all_39_2, simplifying with
% 21.91/3.72  |              (13), (15), (40) gives:
% 21.91/3.72  |   (56)   ? [v0: any] :  ? [v1: any] :  ? [v2: $i] : (sdtasdt0(xp, xl) = v2 &
% 21.91/3.72  |           aNaturalNumber0(xp) = v1 & aNaturalNumber0(xl) = v0 & $i(v2) & ( ~
% 21.91/3.72  |             (v1 = 0) |  ~ (v0 = 0) | v2 = all_39_2))
% 21.91/3.72  | 
% 21.91/3.72  | GROUND_INST: instantiating (mSortsB_02) with xl, xp, all_39_2, simplifying
% 21.91/3.72  |              with (13), (15), (40) gives:
% 21.91/3.72  |   (57)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :
% 21.91/3.72  |         (aNaturalNumber0(all_39_2) = v2 & aNaturalNumber0(xp) = v1 &
% 21.91/3.72  |           aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = 0))
% 21.91/3.72  | 
% 21.91/3.72  | GROUND_INST: instantiating (mAMDistr) with xl, xp, xr, all_39_2, all_35_0,
% 21.91/3.72  |              all_39_0, simplifying with (13), (15), (17), (29), (40), (45)
% 21.91/3.72  |              gives:
% 21.91/3.72  |   (58)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ? [v3: $i] :  ? [v4: $i]
% 21.91/3.72  |         :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :
% 21.91/3.72  |         (sdtasdt0(v3, xl) = v5 & sdtasdt0(xr, xl) = v7 & sdtasdt0(xp, xl) = v6
% 21.91/3.72  |           & sdtasdt0(xl, v3) = v4 & sdtpldt0(v6, v7) = v8 & sdtpldt0(xp, xr) =
% 21.91/3.72  |           v3 & aNaturalNumber0(xr) = v2 & aNaturalNumber0(xp) = v1 &
% 21.91/3.72  |           aNaturalNumber0(xl) = v0 & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 21.91/3.72  |           $i(v4) & $i(v3) & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0) | (v8 =
% 21.91/3.72  |               v5 & v4 = all_39_0)))
% 21.91/3.72  | 
% 21.91/3.72  | GROUND_INST: instantiating (mMulComm) with xl, xr, all_35_0, simplifying with
% 21.91/3.72  |              (15), (17), (29) gives:
% 21.91/3.72  |   (59)   ? [v0: any] :  ? [v1: any] :  ? [v2: $i] : (sdtasdt0(xr, xl) = v2 &
% 21.91/3.73  |           aNaturalNumber0(xr) = v1 & aNaturalNumber0(xl) = v0 & $i(v2) & ( ~
% 21.91/3.73  |             (v1 = 0) |  ~ (v0 = 0) | v2 = all_35_0))
% 21.91/3.73  | 
% 21.91/3.73  | GROUND_INST: instantiating (mSortsB_02) with xl, xr, all_35_0, simplifying
% 21.91/3.73  |              with (15), (17), (29) gives:
% 21.91/3.73  |   (60)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :
% 21.91/3.73  |         (aNaturalNumber0(all_35_0) = v2 & aNaturalNumber0(xr) = v1 &
% 21.91/3.73  |           aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = 0))
% 21.91/3.73  | 
% 21.91/3.73  | GROUND_INST: instantiating (mDefDiff) with xp, xq, xr, simplifying with (11),
% 21.91/3.73  |              (12), (13) gives:
% 21.91/3.73  |   (61)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] : (sdtlseqdt0(xp, xq) = v2
% 21.91/3.73  |           & aNaturalNumber0(xq) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0)
% 21.91/3.73  |             |  ~ (v1 = 0) |  ~ (v0 = 0))) | ( ! [v0: $i] : (v0 = xr |  ~
% 21.91/3.73  |             (sdtpldt0(xp, v0) = xq) |  ~ $i(v0) |  ? [v1: int] : ( ~ (v1 = 0)
% 21.91/3.73  |               & aNaturalNumber0(v0) = v1)) &  ! [v0: $i] : ( ~ (sdtpldt0(xp,
% 21.91/3.73  |                 xr) = v0) |  ~ $i(xr) | (v0 = xq & aNaturalNumber0(xr) = 0)))
% 21.91/3.73  | 
% 21.91/3.73  | GROUND_INST: instantiating (mDefDiv) with xl, xm, 0, simplifying with (8),
% 21.91/3.73  |              (15), (33) gives:
% 21.91/3.73  |   (62)   ? [v0: any] :  ? [v1: any] : (aNaturalNumber0(xm) = v1 &
% 21.91/3.73  |           aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0))) |  ? [v0:
% 21.91/3.73  |           $i] : (sdtasdt0(xl, v0) = xm & aNaturalNumber0(v0) = 0 & $i(v0))
% 21.91/3.73  | 
% 21.91/3.73  | GROUND_INST: instantiating (mDefDiv) with xl, all_33_0, 0, simplifying with
% 21.91/3.73  |              (15), (44), (47) gives:
% 21.91/3.73  |   (63)   ? [v0: any] :  ? [v1: any] : (aNaturalNumber0(all_33_0) = v1 &
% 21.91/3.73  |           aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0))) |  ? [v0:
% 21.91/3.73  |           $i] : (sdtasdt0(xl, v0) = all_33_0 & aNaturalNumber0(v0) = 0 &
% 21.91/3.73  |           $i(v0))
% 21.91/3.73  | 
% 21.91/3.73  | GROUND_INST: instantiating (1) with xl, xm, xp, simplifying with (7), (8),
% 21.91/3.73  |              (15) gives:
% 21.91/3.73  |   (64)  xl = sz00 |  ? [v0: any] :  ? [v1: any] :  ? [v2: any] :
% 21.91/3.73  |         (doDivides0(xl, xm) = v2 & aNaturalNumber0(xm) = v1 &
% 21.91/3.73  |           aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 =
% 21.91/3.73  |               0))) | ( ! [v0: $i] : (v0 = xp |  ~ (sdtasdt0(xl, v0) = xm) |  ~
% 21.91/3.73  |             $i(v0) |  ? [v1: int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1))
% 21.91/3.73  |           &  ! [v0: $i] : ( ~ (sdtasdt0(xl, xp) = v0) |  ~ $i(xp) | (v0 = xm &
% 21.91/3.73  |               aNaturalNumber0(xp) = 0)))
% 21.91/3.73  | 
% 21.91/3.73  | GROUND_INST: instantiating (1) with xl, all_33_0, xq, simplifying with (15),
% 21.91/3.73  |              (26), (47) gives:
% 21.91/3.73  |   (65)  xl = sz00 |  ? [v0: any] :  ? [v1: any] :  ? [v2: any] :
% 21.91/3.73  |         (doDivides0(xl, all_33_0) = v2 & aNaturalNumber0(all_33_0) = v1 &
% 21.91/3.73  |           aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 =
% 21.91/3.73  |               0))) | ( ! [v0: $i] : (v0 = xq |  ~ (sdtasdt0(xl, v0) =
% 21.91/3.73  |               all_33_0) |  ~ $i(v0) |  ? [v1: int] : ( ~ (v1 = 0) &
% 21.91/3.73  |               aNaturalNumber0(v0) = v1)) &  ! [v0: $i] : ( ~ (sdtasdt0(xl, xq)
% 21.91/3.73  |               = v0) |  ~ $i(xq) | (v0 = all_33_0 & aNaturalNumber0(xq) = 0)))
% 21.91/3.73  | 
% 21.91/3.73  | DELTA: instantiating (60) with fresh symbols all_50_0, all_50_1, all_50_2
% 21.91/3.73  |        gives:
% 21.91/3.73  |   (66)  aNaturalNumber0(all_35_0) = all_50_0 & aNaturalNumber0(xr) = all_50_1
% 21.91/3.73  |         & aNaturalNumber0(xl) = all_50_2 & ( ~ (all_50_1 = 0) |  ~ (all_50_2 =
% 21.91/3.73  |             0) | all_50_0 = 0)
% 21.91/3.73  | 
% 21.91/3.73  | ALPHA: (66) implies:
% 21.91/3.73  |   (67)  aNaturalNumber0(xl) = all_50_2
% 21.91/3.73  |   (68)  aNaturalNumber0(xr) = all_50_1
% 21.91/3.73  |   (69)  aNaturalNumber0(all_35_0) = all_50_0
% 21.91/3.73  |   (70)   ~ (all_50_1 = 0) |  ~ (all_50_2 = 0) | all_50_0 = 0
% 21.91/3.73  | 
% 21.91/3.73  | DELTA: instantiating (57) with fresh symbols all_52_0, all_52_1, all_52_2
% 21.91/3.73  |        gives:
% 21.91/3.73  |   (71)  aNaturalNumber0(all_39_2) = all_52_0 & aNaturalNumber0(xp) = all_52_1
% 21.91/3.73  |         & aNaturalNumber0(xl) = all_52_2 & ( ~ (all_52_1 = 0) |  ~ (all_52_2 =
% 21.91/3.73  |             0) | all_52_0 = 0)
% 21.91/3.73  | 
% 21.91/3.73  | ALPHA: (71) implies:
% 21.91/3.73  |   (72)  aNaturalNumber0(xl) = all_52_2
% 21.91/3.73  |   (73)  aNaturalNumber0(xp) = all_52_1
% 21.91/3.73  |   (74)  aNaturalNumber0(all_39_2) = all_52_0
% 21.91/3.73  | 
% 21.91/3.73  | DELTA: instantiating (51) with fresh symbols all_54_0, all_54_1, all_54_2
% 21.91/3.73  |        gives:
% 21.91/3.73  |   (75)  aNaturalNumber0(all_39_0) = all_54_0 & aNaturalNumber0(all_39_2) =
% 21.91/3.73  |         all_54_2 & aNaturalNumber0(xn) = all_54_1 & ( ~ (all_54_1 = 0) |  ~
% 21.91/3.73  |           (all_54_2 = 0) | all_54_0 = 0)
% 21.91/3.73  | 
% 21.91/3.73  | ALPHA: (75) implies:
% 21.91/3.74  |   (76)  aNaturalNumber0(xn) = all_54_1
% 21.91/3.74  |   (77)  aNaturalNumber0(all_39_2) = all_54_2
% 21.91/3.74  | 
% 21.91/3.74  | DELTA: instantiating (49) with fresh symbols all_56_0, all_56_1, all_56_2
% 21.91/3.74  |        gives:
% 21.91/3.74  |   (78)  aNaturalNumber0(all_33_0) = all_56_0 & aNaturalNumber0(xn) = all_56_1
% 21.91/3.74  |         & aNaturalNumber0(xm) = all_56_2 & ( ~ (all_56_1 = 0) |  ~ (all_56_2 =
% 21.91/3.74  |             0) | all_56_0 = 0)
% 21.91/3.74  | 
% 21.91/3.74  | ALPHA: (78) implies:
% 21.91/3.74  |   (79)  aNaturalNumber0(xm) = all_56_2
% 21.91/3.74  |   (80)  aNaturalNumber0(xn) = all_56_1
% 21.91/3.74  |   (81)  aNaturalNumber0(all_33_0) = all_56_0
% 21.91/3.74  |   (82)   ~ (all_56_1 = 0) |  ~ (all_56_2 = 0) | all_56_0 = 0
% 21.91/3.74  | 
% 21.91/3.74  | DELTA: instantiating (55) with fresh symbols all_58_0, all_58_1, all_58_2
% 21.91/3.74  |        gives:
% 21.91/3.74  |   (83)  aNaturalNumber0(all_39_0) = all_58_0 & aNaturalNumber0(all_39_2) =
% 21.91/3.74  |         all_58_2 & aNaturalNumber0(all_35_0) = all_58_1 & ( ~ (all_58_1 = 0) |
% 21.91/3.74  |            ~ (all_58_2 = 0) | all_58_0 = 0)
% 21.91/3.74  | 
% 21.91/3.74  | ALPHA: (83) implies:
% 21.91/3.74  |   (84)  aNaturalNumber0(all_35_0) = all_58_1
% 21.91/3.74  |   (85)  aNaturalNumber0(all_39_2) = all_58_2
% 21.91/3.74  | 
% 21.91/3.74  | DELTA: instantiating (59) with fresh symbols all_60_0, all_60_1, all_60_2
% 21.91/3.74  |        gives:
% 21.91/3.74  |   (86)  sdtasdt0(xr, xl) = all_60_0 & aNaturalNumber0(xr) = all_60_1 &
% 21.91/3.74  |         aNaturalNumber0(xl) = all_60_2 & $i(all_60_0) & ( ~ (all_60_1 = 0) | 
% 21.91/3.74  |           ~ (all_60_2 = 0) | all_60_0 = all_35_0)
% 21.91/3.74  | 
% 21.91/3.74  | ALPHA: (86) implies:
% 21.91/3.74  |   (87)  aNaturalNumber0(xl) = all_60_2
% 21.91/3.74  |   (88)  aNaturalNumber0(xr) = all_60_1
% 21.91/3.74  |   (89)  sdtasdt0(xr, xl) = all_60_0
% 21.91/3.74  | 
% 21.91/3.74  | DELTA: instantiating (56) with fresh symbols all_62_0, all_62_1, all_62_2
% 21.91/3.74  |        gives:
% 21.91/3.74  |   (90)  sdtasdt0(xp, xl) = all_62_0 & aNaturalNumber0(xp) = all_62_1 &
% 21.91/3.74  |         aNaturalNumber0(xl) = all_62_2 & $i(all_62_0) & ( ~ (all_62_1 = 0) | 
% 21.91/3.74  |           ~ (all_62_2 = 0) | all_62_0 = all_39_2)
% 21.91/3.74  | 
% 21.91/3.74  | ALPHA: (90) implies:
% 21.91/3.74  |   (91)  aNaturalNumber0(xl) = all_62_2
% 21.91/3.74  |   (92)  aNaturalNumber0(xp) = all_62_1
% 21.91/3.74  | 
% 21.91/3.74  | DELTA: instantiating (54) with fresh symbols all_64_0, all_64_1, all_64_2
% 21.91/3.74  |        gives:
% 21.91/3.74  |   (93)  sdtpldt0(all_35_0, all_39_2) = all_64_0 & aNaturalNumber0(all_39_2) =
% 21.91/3.74  |         all_64_2 & aNaturalNumber0(all_35_0) = all_64_1 & $i(all_64_0) & ( ~
% 21.91/3.74  |           (all_64_1 = 0) |  ~ (all_64_2 = 0) | all_64_0 = all_39_0)
% 21.91/3.74  | 
% 21.91/3.74  | ALPHA: (93) implies:
% 21.91/3.74  |   (94)  aNaturalNumber0(all_35_0) = all_64_1
% 21.91/3.74  |   (95)  aNaturalNumber0(all_39_2) = all_64_2
% 21.91/3.74  |   (96)  sdtpldt0(all_35_0, all_39_2) = all_64_0
% 21.91/3.74  | 
% 21.91/3.74  | DELTA: instantiating (48) with fresh symbols all_66_0, all_66_1, all_66_2
% 21.91/3.74  |        gives:
% 21.91/3.74  |   (97)  sdtpldt0(xn, xm) = all_66_0 & aNaturalNumber0(xn) = all_66_1 &
% 21.91/3.74  |         aNaturalNumber0(xm) = all_66_2 & $i(all_66_0) & ( ~ (all_66_1 = 0) | 
% 21.91/3.74  |           ~ (all_66_2 = 0) | all_66_0 = all_33_0)
% 21.91/3.74  | 
% 21.91/3.74  | ALPHA: (97) implies:
% 21.91/3.74  |   (98)  aNaturalNumber0(xm) = all_66_2
% 21.91/3.74  |   (99)  aNaturalNumber0(xn) = all_66_1
% 21.91/3.74  | 
% 21.91/3.74  | DELTA: instantiating (50) with fresh symbols all_68_0, all_68_1, all_68_2
% 21.91/3.74  |        gives:
% 21.91/3.74  |   (100)  sdtpldt0(xn, all_39_2) = all_68_0 & aNaturalNumber0(all_39_2) =
% 21.91/3.74  |          all_68_2 & aNaturalNumber0(xn) = all_68_1 & $i(all_68_0) & ( ~
% 21.91/3.74  |            (all_68_1 = 0) |  ~ (all_68_2 = 0) | all_68_0 = all_39_0)
% 21.91/3.74  | 
% 21.91/3.74  | ALPHA: (100) implies:
% 21.91/3.74  |   (101)  aNaturalNumber0(xn) = all_68_1
% 21.91/3.74  |   (102)  aNaturalNumber0(all_39_2) = all_68_2
% 21.91/3.74  | 
% 21.91/3.74  | DELTA: instantiating (58) with fresh symbols all_70_0, all_70_1, all_70_2,
% 21.91/3.74  |        all_70_3, all_70_4, all_70_5, all_70_6, all_70_7, all_70_8 gives:
% 21.91/3.74  |   (103)  sdtasdt0(all_70_5, xl) = all_70_3 & sdtasdt0(xr, xl) = all_70_1 &
% 21.91/3.74  |          sdtasdt0(xp, xl) = all_70_2 & sdtasdt0(xl, all_70_5) = all_70_4 &
% 21.91/3.74  |          sdtpldt0(all_70_2, all_70_1) = all_70_0 & sdtpldt0(xp, xr) = all_70_5
% 21.91/3.74  |          & aNaturalNumber0(xr) = all_70_6 & aNaturalNumber0(xp) = all_70_7 &
% 21.91/3.74  |          aNaturalNumber0(xl) = all_70_8 & $i(all_70_0) & $i(all_70_1) &
% 21.91/3.74  |          $i(all_70_2) & $i(all_70_3) & $i(all_70_4) & $i(all_70_5) & ( ~
% 21.91/3.74  |            (all_70_6 = 0) |  ~ (all_70_7 = 0) |  ~ (all_70_8 = 0) | (all_70_0
% 21.91/3.74  |              = all_70_3 & all_70_4 = all_39_0))
% 21.91/3.74  | 
% 21.91/3.74  | ALPHA: (103) implies:
% 21.91/3.74  |   (104)  aNaturalNumber0(xl) = all_70_8
% 21.91/3.74  |   (105)  aNaturalNumber0(xp) = all_70_7
% 21.91/3.74  |   (106)  aNaturalNumber0(xr) = all_70_6
% 21.91/3.74  |   (107)  sdtpldt0(xp, xr) = all_70_5
% 21.91/3.74  |   (108)  sdtasdt0(xr, xl) = all_70_1
% 21.91/3.74  | 
% 21.91/3.74  | GROUND_INST: instantiating (19) with 0, all_52_2, xl, simplifying with (2),
% 21.91/3.74  |              (72) gives:
% 21.91/3.74  |   (109)  all_52_2 = 0
% 21.91/3.74  | 
% 21.91/3.74  | GROUND_INST: instantiating (19) with all_60_2, all_62_2, xl, simplifying with
% 21.91/3.74  |              (87), (91) gives:
% 21.91/3.74  |   (110)  all_62_2 = all_60_2
% 21.91/3.74  | 
% 21.91/3.74  | GROUND_INST: instantiating (19) with all_52_2, all_62_2, xl, simplifying with
% 21.91/3.74  |              (72), (91) gives:
% 21.91/3.74  |   (111)  all_62_2 = all_52_2
% 21.91/3.74  | 
% 21.91/3.74  | GROUND_INST: instantiating (19) with all_62_2, all_70_8, xl, simplifying with
% 21.91/3.74  |              (91), (104) gives:
% 21.91/3.74  |   (112)  all_70_8 = all_62_2
% 21.91/3.74  | 
% 21.91/3.74  | GROUND_INST: instantiating (19) with all_50_2, all_70_8, xl, simplifying with
% 21.91/3.74  |              (67), (104) gives:
% 21.91/3.74  |   (113)  all_70_8 = all_50_2
% 21.91/3.74  | 
% 21.91/3.74  | GROUND_INST: instantiating (19) with 0, all_66_2, xm, simplifying with (3),
% 21.91/3.74  |              (98) gives:
% 21.91/3.74  |   (114)  all_66_2 = 0
% 21.91/3.74  | 
% 21.91/3.74  | GROUND_INST: instantiating (19) with all_56_2, all_66_2, xm, simplifying with
% 21.91/3.74  |              (79), (98) gives:
% 22.25/3.74  |   (115)  all_66_2 = all_56_2
% 22.25/3.74  | 
% 22.25/3.74  | GROUND_INST: instantiating (19) with 0, all_68_1, xn, simplifying with (4),
% 22.25/3.74  |              (101) gives:
% 22.25/3.74  |   (116)  all_68_1 = 0
% 22.25/3.74  | 
% 22.25/3.74  | GROUND_INST: instantiating (19) with all_66_1, all_68_1, xn, simplifying with
% 22.25/3.74  |              (99), (101) gives:
% 22.25/3.74  |   (117)  all_68_1 = all_66_1
% 22.25/3.74  | 
% 22.25/3.74  | GROUND_INST: instantiating (19) with all_56_1, all_68_1, xn, simplifying with
% 22.25/3.74  |              (80), (101) gives:
% 22.25/3.74  |   (118)  all_68_1 = all_56_1
% 22.25/3.74  | 
% 22.25/3.75  | GROUND_INST: instantiating (19) with all_54_1, all_68_1, xn, simplifying with
% 22.25/3.75  |              (76), (101) gives:
% 22.25/3.75  |   (119)  all_68_1 = all_54_1
% 22.25/3.75  | 
% 22.25/3.75  | GROUND_INST: instantiating (19) with all_62_1, all_70_7, xp, simplifying with
% 22.25/3.75  |              (92), (105) gives:
% 22.25/3.75  |   (120)  all_70_7 = all_62_1
% 22.25/3.75  | 
% 22.25/3.75  | GROUND_INST: instantiating (19) with all_52_1, all_70_7, xp, simplifying with
% 22.25/3.75  |              (73), (105) gives:
% 22.25/3.75  |   (121)  all_70_7 = all_52_1
% 22.25/3.75  | 
% 22.25/3.75  | GROUND_INST: instantiating (19) with all_60_1, all_70_6, xr, simplifying with
% 22.25/3.75  |              (88), (106) gives:
% 22.25/3.75  |   (122)  all_70_6 = all_60_1
% 22.25/3.75  | 
% 22.25/3.75  | GROUND_INST: instantiating (19) with all_50_1, all_70_6, xr, simplifying with
% 22.25/3.75  |              (68), (106) gives:
% 22.25/3.75  |   (123)  all_70_6 = all_50_1
% 22.25/3.75  | 
% 22.25/3.75  | GROUND_INST: instantiating (19) with all_58_1, all_64_1, all_35_0, simplifying
% 22.25/3.75  |              with (84), (94) gives:
% 22.25/3.75  |   (124)  all_64_1 = all_58_1
% 22.25/3.75  | 
% 22.25/3.75  | GROUND_INST: instantiating (19) with all_50_0, all_64_1, all_35_0, simplifying
% 22.25/3.75  |              with (69), (94) gives:
% 22.25/3.75  |   (125)  all_64_1 = all_50_0
% 22.25/3.75  | 
% 22.25/3.75  | GROUND_INST: instantiating (19) with all_58_2, all_64_2, all_39_2, simplifying
% 22.25/3.75  |              with (85), (95) gives:
% 22.25/3.75  |   (126)  all_64_2 = all_58_2
% 22.25/3.75  | 
% 22.25/3.75  | GROUND_INST: instantiating (19) with all_52_0, all_64_2, all_39_2, simplifying
% 22.25/3.75  |              with (74), (95) gives:
% 22.25/3.75  |   (127)  all_64_2 = all_52_0
% 22.25/3.75  | 
% 22.25/3.75  | GROUND_INST: instantiating (19) with all_58_2, all_68_2, all_39_2, simplifying
% 22.25/3.75  |              with (85), (102) gives:
% 22.25/3.75  |   (128)  all_68_2 = all_58_2
% 22.25/3.75  | 
% 22.25/3.75  | GROUND_INST: instantiating (19) with all_54_2, all_68_2, all_39_2, simplifying
% 22.25/3.75  |              with (77), (102) gives:
% 22.25/3.75  |   (129)  all_68_2 = all_54_2
% 22.25/3.75  | 
% 22.25/3.75  | GROUND_INST: instantiating (21) with all_60_0, all_70_1, xl, xr, simplifying
% 22.25/3.75  |              with (89), (108) gives:
% 22.25/3.75  |   (130)  all_70_1 = all_60_0
% 22.25/3.75  | 
% 22.25/3.75  | COMBINE_EQS: (122), (123) imply:
% 22.25/3.75  |   (131)  all_60_1 = all_50_1
% 22.25/3.75  | 
% 22.25/3.75  | SIMP: (131) implies:
% 22.25/3.75  |   (132)  all_60_1 = all_50_1
% 22.25/3.75  | 
% 22.25/3.75  | COMBINE_EQS: (120), (121) imply:
% 22.25/3.75  |   (133)  all_62_1 = all_52_1
% 22.25/3.75  | 
% 22.25/3.75  | COMBINE_EQS: (112), (113) imply:
% 22.25/3.75  |   (134)  all_62_2 = all_50_2
% 22.25/3.75  | 
% 22.25/3.75  | SIMP: (134) implies:
% 22.25/3.75  |   (135)  all_62_2 = all_50_2
% 22.25/3.75  | 
% 22.25/3.75  | COMBINE_EQS: (117), (119) imply:
% 22.25/3.75  |   (136)  all_66_1 = all_54_1
% 22.25/3.75  | 
% 22.25/3.75  | COMBINE_EQS: (116), (117) imply:
% 22.25/3.75  |   (137)  all_66_1 = 0
% 22.25/3.75  | 
% 22.25/3.75  | COMBINE_EQS: (117), (118) imply:
% 22.25/3.75  |   (138)  all_66_1 = all_56_1
% 22.25/3.75  | 
% 22.25/3.75  | COMBINE_EQS: (128), (129) imply:
% 22.25/3.75  |   (139)  all_58_2 = all_54_2
% 22.25/3.75  | 
% 22.25/3.75  | SIMP: (139) implies:
% 22.25/3.75  |   (140)  all_58_2 = all_54_2
% 22.25/3.75  | 
% 22.25/3.75  | COMBINE_EQS: (137), (138) imply:
% 22.25/3.75  |   (141)  all_56_1 = 0
% 22.25/3.75  | 
% 22.25/3.75  | COMBINE_EQS: (136), (138) imply:
% 22.25/3.75  |   (142)  all_56_1 = all_54_1
% 22.25/3.75  | 
% 22.25/3.75  | COMBINE_EQS: (114), (115) imply:
% 22.25/3.75  |   (143)  all_56_2 = 0
% 22.25/3.75  | 
% 22.25/3.75  | COMBINE_EQS: (124), (125) imply:
% 22.25/3.75  |   (144)  all_58_1 = all_50_0
% 22.25/3.75  | 
% 22.25/3.75  | SIMP: (144) implies:
% 22.25/3.75  |   (145)  all_58_1 = all_50_0
% 22.25/3.75  | 
% 22.25/3.75  | COMBINE_EQS: (126), (127) imply:
% 22.25/3.75  |   (146)  all_58_2 = all_52_0
% 22.25/3.75  | 
% 22.25/3.75  | SIMP: (146) implies:
% 22.25/3.75  |   (147)  all_58_2 = all_52_0
% 22.25/3.75  | 
% 22.25/3.75  | COMBINE_EQS: (110), (135) imply:
% 22.25/3.75  |   (148)  all_60_2 = all_50_2
% 22.25/3.75  | 
% 22.25/3.75  | COMBINE_EQS: (110), (111) imply:
% 22.25/3.75  |   (149)  all_60_2 = all_52_2
% 22.25/3.75  | 
% 22.25/3.75  | COMBINE_EQS: (148), (149) imply:
% 22.25/3.75  |   (150)  all_52_2 = all_50_2
% 22.25/3.75  | 
% 22.25/3.75  | SIMP: (150) implies:
% 22.25/3.75  |   (151)  all_52_2 = all_50_2
% 22.25/3.75  | 
% 22.25/3.75  | COMBINE_EQS: (140), (147) imply:
% 22.25/3.75  |   (152)  all_54_2 = all_52_0
% 22.25/3.75  | 
% 22.25/3.75  | SIMP: (152) implies:
% 22.25/3.75  |   (153)  all_54_2 = all_52_0
% 22.25/3.75  | 
% 22.25/3.75  | COMBINE_EQS: (141), (142) imply:
% 22.25/3.75  |   (154)  all_54_1 = 0
% 22.25/3.75  | 
% 22.25/3.75  | SIMP: (154) implies:
% 22.25/3.75  |   (155)  all_54_1 = 0
% 22.25/3.75  | 
% 22.25/3.75  | COMBINE_EQS: (109), (151) imply:
% 22.25/3.75  |   (156)  all_50_2 = 0
% 22.25/3.75  | 
% 22.25/3.75  | BETA: splitting (64) gives:
% 22.25/3.75  | 
% 22.25/3.75  | Case 1:
% 22.25/3.75  | | 
% 22.25/3.75  | |   (157)  xl = sz00
% 22.25/3.75  | | 
% 22.25/3.75  | | REDUCE: (6), (157) imply:
% 22.25/3.75  | |   (158)  $false
% 22.25/3.75  | | 
% 22.25/3.75  | | CLOSE: (158) is inconsistent.
% 22.25/3.75  | | 
% 22.25/3.75  | Case 2:
% 22.25/3.75  | | 
% 22.25/3.75  | |   (159)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] : (doDivides0(xl, xm) =
% 22.25/3.75  | |            v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xl) = v0 & ( ~
% 22.25/3.75  | |              (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0))) | ( ! [v0: $i] : (v0 =
% 22.25/3.75  | |              xp |  ~ (sdtasdt0(xl, v0) = xm) |  ~ $i(v0) |  ? [v1: int] : (
% 22.25/3.75  | |                ~ (v1 = 0) & aNaturalNumber0(v0) = v1)) &  ! [v0: $i] : ( ~
% 22.25/3.75  | |              (sdtasdt0(xl, xp) = v0) |  ~ $i(xp) | (v0 = xm &
% 22.25/3.75  | |                aNaturalNumber0(xp) = 0)))
% 22.25/3.75  | | 
% 22.25/3.75  | | BETA: splitting (82) gives:
% 22.25/3.75  | | 
% 22.25/3.75  | | Case 1:
% 22.25/3.75  | | | 
% 22.25/3.75  | | |   (160)   ~ (all_56_1 = 0)
% 22.25/3.75  | | | 
% 22.25/3.75  | | | REDUCE: (141), (160) imply:
% 22.25/3.76  | | |   (161)  $false
% 22.25/3.76  | | | 
% 22.25/3.76  | | | CLOSE: (161) is inconsistent.
% 22.25/3.76  | | | 
% 22.25/3.76  | | Case 2:
% 22.25/3.76  | | | 
% 22.25/3.76  | | |   (162)   ~ (all_56_2 = 0) | all_56_0 = 0
% 22.25/3.76  | | | 
% 22.25/3.76  | | | BETA: splitting (162) gives:
% 22.25/3.76  | | | 
% 22.25/3.76  | | | Case 1:
% 22.25/3.76  | | | | 
% 22.25/3.76  | | | |   (163)   ~ (all_56_2 = 0)
% 22.25/3.76  | | | | 
% 22.25/3.76  | | | | REDUCE: (143), (163) imply:
% 22.25/3.76  | | | |   (164)  $false
% 22.25/3.76  | | | | 
% 22.25/3.76  | | | | CLOSE: (164) is inconsistent.
% 22.25/3.76  | | | | 
% 22.25/3.76  | | | Case 2:
% 22.25/3.76  | | | | 
% 22.25/3.76  | | | |   (165)  all_56_0 = 0
% 22.25/3.76  | | | | 
% 22.25/3.76  | | | | REDUCE: (81), (165) imply:
% 22.25/3.76  | | | |   (166)  aNaturalNumber0(all_33_0) = 0
% 22.25/3.76  | | | | 
% 22.25/3.76  | | | | BETA: splitting (65) gives:
% 22.25/3.76  | | | | 
% 22.25/3.76  | | | | Case 1:
% 22.25/3.76  | | | | | 
% 22.25/3.76  | | | | |   (167)  xl = sz00
% 22.25/3.76  | | | | | 
% 22.25/3.76  | | | | | REDUCE: (6), (167) imply:
% 22.25/3.76  | | | | |   (168)  $false
% 22.25/3.76  | | | | | 
% 22.25/3.76  | | | | | CLOSE: (168) is inconsistent.
% 22.25/3.76  | | | | | 
% 22.25/3.76  | | | | Case 2:
% 22.25/3.76  | | | | | 
% 22.25/3.76  | | | | |   (169)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] : (doDivides0(xl,
% 22.25/3.76  | | | | |              all_33_0) = v2 & aNaturalNumber0(all_33_0) = v1 &
% 22.25/3.76  | | | | |            aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~
% 22.25/3.76  | | | | |              (v0 = 0))) | ( ! [v0: $i] : (v0 = xq |  ~ (sdtasdt0(xl,
% 22.25/3.76  | | | | |                  v0) = all_33_0) |  ~ $i(v0) |  ? [v1: int] : ( ~ (v1
% 22.25/3.76  | | | | |                  = 0) & aNaturalNumber0(v0) = v1)) &  ! [v0: $i] : ( ~
% 22.25/3.76  | | | | |              (sdtasdt0(xl, xq) = v0) |  ~ $i(xq) | (v0 = all_33_0 &
% 22.25/3.76  | | | | |                aNaturalNumber0(xq) = 0)))
% 22.25/3.76  | | | | | 
% 22.25/3.76  | | | | | BETA: splitting (63) gives:
% 22.25/3.76  | | | | | 
% 22.25/3.76  | | | | | Case 1:
% 22.25/3.76  | | | | | | 
% 22.25/3.76  | | | | | |   (170)   ? [v0: any] :  ? [v1: any] : (aNaturalNumber0(all_33_0) =
% 22.25/3.76  | | | | | |            v1 & aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) |  ~ (v0 =
% 22.25/3.76  | | | | | |                0)))
% 22.25/3.76  | | | | | | 
% 22.25/3.76  | | | | | | DELTA: instantiating (170) with fresh symbols all_110_0, all_110_1
% 22.25/3.76  | | | | | |        gives:
% 22.25/3.76  | | | | | |   (171)  aNaturalNumber0(all_33_0) = all_110_0 & aNaturalNumber0(xl)
% 22.25/3.76  | | | | | |          = all_110_1 & ( ~ (all_110_0 = 0) |  ~ (all_110_1 = 0))
% 22.25/3.76  | | | | | | 
% 22.25/3.76  | | | | | | ALPHA: (171) implies:
% 22.25/3.76  | | | | | |   (172)  aNaturalNumber0(xl) = all_110_1
% 22.25/3.76  | | | | | |   (173)  aNaturalNumber0(all_33_0) = all_110_0
% 22.25/3.76  | | | | | |   (174)   ~ (all_110_0 = 0) |  ~ (all_110_1 = 0)
% 22.25/3.76  | | | | | | 
% 22.25/3.76  | | | | | | GROUND_INST: instantiating (19) with 0, all_110_1, xl, simplifying
% 22.25/3.76  | | | | | |              with (2), (172) gives:
% 22.25/3.76  | | | | | |   (175)  all_110_1 = 0
% 22.25/3.76  | | | | | | 
% 22.25/3.76  | | | | | | GROUND_INST: instantiating (19) with 0, all_110_0, all_33_0,
% 22.25/3.76  | | | | | |              simplifying with (166), (173) gives:
% 22.25/3.76  | | | | | |   (176)  all_110_0 = 0
% 22.25/3.76  | | | | | | 
% 22.25/3.76  | | | | | | BETA: splitting (174) gives:
% 22.25/3.76  | | | | | | 
% 22.25/3.76  | | | | | | Case 1:
% 22.25/3.76  | | | | | | | 
% 22.25/3.76  | | | | | | |   (177)   ~ (all_110_0 = 0)
% 22.25/3.76  | | | | | | | 
% 22.25/3.76  | | | | | | | REDUCE: (176), (177) imply:
% 22.25/3.76  | | | | | | |   (178)  $false
% 22.25/3.76  | | | | | | | 
% 22.25/3.76  | | | | | | | CLOSE: (178) is inconsistent.
% 22.25/3.76  | | | | | | | 
% 22.25/3.76  | | | | | | Case 2:
% 22.25/3.76  | | | | | | | 
% 22.25/3.76  | | | | | | |   (179)   ~ (all_110_1 = 0)
% 22.25/3.76  | | | | | | | 
% 22.25/3.76  | | | | | | | REDUCE: (175), (179) imply:
% 22.25/3.76  | | | | | | |   (180)  $false
% 22.25/3.76  | | | | | | | 
% 22.25/3.76  | | | | | | | CLOSE: (180) is inconsistent.
% 22.25/3.76  | | | | | | | 
% 22.25/3.76  | | | | | | End of split
% 22.25/3.76  | | | | | | 
% 22.25/3.76  | | | | | Case 2:
% 22.25/3.76  | | | | | | 
% 22.25/3.76  | | | | | |   (181)   ? [v0: $i] : (sdtasdt0(xl, v0) = all_33_0 &
% 22.25/3.76  | | | | | |            aNaturalNumber0(v0) = 0 & $i(v0))
% 22.25/3.76  | | | | | | 
% 22.25/3.76  | | | | | | DELTA: instantiating (181) with fresh symbol all_110_0 gives:
% 22.25/3.76  | | | | | |   (182)  sdtasdt0(xl, all_110_0) = all_33_0 &
% 22.25/3.76  | | | | | |          aNaturalNumber0(all_110_0) = 0 & $i(all_110_0)
% 22.25/3.76  | | | | | | 
% 22.25/3.76  | | | | | | ALPHA: (182) implies:
% 22.25/3.76  | | | | | |   (183)  $i(all_110_0)
% 22.25/3.76  | | | | | |   (184)  aNaturalNumber0(all_110_0) = 0
% 22.25/3.76  | | | | | |   (185)  sdtasdt0(xl, all_110_0) = all_33_0
% 22.25/3.76  | | | | | | 
% 22.25/3.76  | | | | | | BETA: splitting (62) gives:
% 22.25/3.76  | | | | | | 
% 22.25/3.76  | | | | | | Case 1:
% 22.25/3.76  | | | | | | | 
% 22.25/3.76  | | | | | | |   (186)   ? [v0: any] :  ? [v1: any] : (aNaturalNumber0(xm) = v1 &
% 22.25/3.76  | | | | | | |            aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 22.25/3.76  | | | | | | | 
% 22.25/3.76  | | | | | | | DELTA: instantiating (186) with fresh symbols all_114_0, all_114_1
% 22.25/3.76  | | | | | | |        gives:
% 22.25/3.76  | | | | | | |   (187)  aNaturalNumber0(xm) = all_114_0 & aNaturalNumber0(xl) =
% 22.25/3.76  | | | | | | |          all_114_1 & ( ~ (all_114_0 = 0) |  ~ (all_114_1 = 0))
% 22.25/3.76  | | | | | | | 
% 22.25/3.76  | | | | | | | ALPHA: (187) implies:
% 22.25/3.76  | | | | | | |   (188)  aNaturalNumber0(xl) = all_114_1
% 22.25/3.76  | | | | | | |   (189)  aNaturalNumber0(xm) = all_114_0
% 22.25/3.76  | | | | | | |   (190)   ~ (all_114_0 = 0) |  ~ (all_114_1 = 0)
% 22.25/3.76  | | | | | | | 
% 22.25/3.76  | | | | | | | GROUND_INST: instantiating (19) with 0, all_114_1, xl, simplifying
% 22.25/3.76  | | | | | | |              with (2), (188) gives:
% 22.25/3.76  | | | | | | |   (191)  all_114_1 = 0
% 22.25/3.76  | | | | | | | 
% 22.25/3.76  | | | | | | | GROUND_INST: instantiating (19) with 0, all_114_0, xm, simplifying
% 22.25/3.76  | | | | | | |              with (3), (189) gives:
% 22.25/3.76  | | | | | | |   (192)  all_114_0 = 0
% 22.25/3.76  | | | | | | | 
% 22.25/3.76  | | | | | | | BETA: splitting (190) gives:
% 22.25/3.76  | | | | | | | 
% 22.25/3.76  | | | | | | | Case 1:
% 22.25/3.76  | | | | | | | | 
% 22.25/3.76  | | | | | | | |   (193)   ~ (all_114_0 = 0)
% 22.25/3.76  | | | | | | | | 
% 22.25/3.76  | | | | | | | | REDUCE: (192), (193) imply:
% 22.25/3.76  | | | | | | | |   (194)  $false
% 22.25/3.76  | | | | | | | | 
% 22.25/3.76  | | | | | | | | CLOSE: (194) is inconsistent.
% 22.25/3.76  | | | | | | | | 
% 22.25/3.76  | | | | | | | Case 2:
% 22.25/3.76  | | | | | | | | 
% 22.25/3.76  | | | | | | | |   (195)   ~ (all_114_1 = 0)
% 22.25/3.76  | | | | | | | | 
% 22.25/3.76  | | | | | | | | REDUCE: (191), (195) imply:
% 22.25/3.76  | | | | | | | |   (196)  $false
% 22.25/3.76  | | | | | | | | 
% 22.25/3.76  | | | | | | | | CLOSE: (196) is inconsistent.
% 22.25/3.76  | | | | | | | | 
% 22.25/3.76  | | | | | | | End of split
% 22.25/3.76  | | | | | | | 
% 22.25/3.76  | | | | | | Case 2:
% 22.25/3.76  | | | | | | | 
% 22.25/3.76  | | | | | | |   (197)   ? [v0: $i] : (sdtasdt0(xl, v0) = xm &
% 22.25/3.76  | | | | | | |            aNaturalNumber0(v0) = 0 & $i(v0))
% 22.25/3.76  | | | | | | | 
% 22.25/3.76  | | | | | | | DELTA: instantiating (197) with fresh symbol all_114_0 gives:
% 22.25/3.76  | | | | | | |   (198)  sdtasdt0(xl, all_114_0) = xm & aNaturalNumber0(all_114_0)
% 22.25/3.76  | | | | | | |          = 0 & $i(all_114_0)
% 22.25/3.76  | | | | | | | 
% 22.25/3.76  | | | | | | | ALPHA: (198) implies:
% 22.25/3.76  | | | | | | |   (199)  $i(all_114_0)
% 22.25/3.76  | | | | | | |   (200)  sdtasdt0(xl, all_114_0) = xm
% 22.25/3.76  | | | | | | | 
% 22.25/3.76  | | | | | | | BETA: splitting (159) gives:
% 22.25/3.76  | | | | | | | 
% 22.25/3.76  | | | | | | | Case 1:
% 22.25/3.76  | | | | | | | | 
% 22.25/3.76  | | | | | | | |   (201)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :
% 22.25/3.76  | | | | | | | |          (doDivides0(xl, xm) = v2 & aNaturalNumber0(xm) = v1 &
% 22.25/3.76  | | | | | | | |            aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0)
% 22.25/3.76  | | | | | | | |              |  ~ (v0 = 0)))
% 22.25/3.76  | | | | | | | | 
% 22.25/3.76  | | | | | | | | DELTA: instantiating (201) with fresh symbols all_121_0,
% 22.25/3.76  | | | | | | | |        all_121_1, all_121_2 gives:
% 22.25/3.76  | | | | | | | |   (202)  doDivides0(xl, xm) = all_121_0 & aNaturalNumber0(xm) =
% 22.25/3.76  | | | | | | | |          all_121_1 & aNaturalNumber0(xl) = all_121_2 & ( ~
% 22.25/3.76  | | | | | | | |            (all_121_0 = 0) |  ~ (all_121_1 = 0) |  ~ (all_121_2
% 22.25/3.76  | | | | | | | |              = 0))
% 22.25/3.76  | | | | | | | | 
% 22.25/3.76  | | | | | | | | ALPHA: (202) implies:
% 22.25/3.76  | | | | | | | |   (203)  aNaturalNumber0(xl) = all_121_2
% 22.25/3.76  | | | | | | | |   (204)  aNaturalNumber0(xm) = all_121_1
% 22.34/3.76  | | | | | | | |   (205)  doDivides0(xl, xm) = all_121_0
% 22.34/3.76  | | | | | | | |   (206)   ~ (all_121_0 = 0) |  ~ (all_121_1 = 0) |  ~ (all_121_2
% 22.34/3.76  | | | | | | | |            = 0)
% 22.34/3.76  | | | | | | | | 
% 22.34/3.76  | | | | | | | | GROUND_INST: instantiating (19) with 0, all_121_2, xl,
% 22.34/3.76  | | | | | | | |              simplifying with (2), (203) gives:
% 22.34/3.76  | | | | | | | |   (207)  all_121_2 = 0
% 22.34/3.76  | | | | | | | | 
% 22.34/3.76  | | | | | | | | GROUND_INST: instantiating (19) with 0, all_121_1, xm,
% 22.34/3.76  | | | | | | | |              simplifying with (3), (204) gives:
% 22.34/3.76  | | | | | | | |   (208)  all_121_1 = 0
% 22.34/3.76  | | | | | | | | 
% 22.34/3.76  | | | | | | | | GROUND_INST: instantiating (23) with 0, all_121_0, xm, xl,
% 22.34/3.76  | | | | | | | |              simplifying with (33), (205) gives:
% 22.34/3.76  | | | | | | | |   (209)  all_121_0 = 0
% 22.34/3.76  | | | | | | | | 
% 22.34/3.76  | | | | | | | | BETA: splitting (206) gives:
% 22.34/3.76  | | | | | | | | 
% 22.34/3.76  | | | | | | | | Case 1:
% 22.34/3.76  | | | | | | | | | 
% 22.34/3.76  | | | | | | | | |   (210)   ~ (all_121_0 = 0)
% 22.34/3.76  | | | | | | | | | 
% 22.34/3.76  | | | | | | | | | REDUCE: (209), (210) imply:
% 22.34/3.76  | | | | | | | | |   (211)  $false
% 22.34/3.76  | | | | | | | | | 
% 22.34/3.76  | | | | | | | | | CLOSE: (211) is inconsistent.
% 22.34/3.76  | | | | | | | | | 
% 22.34/3.76  | | | | | | | | Case 2:
% 22.34/3.76  | | | | | | | | | 
% 22.34/3.76  | | | | | | | | |   (212)   ~ (all_121_1 = 0) |  ~ (all_121_2 = 0)
% 22.34/3.76  | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | BETA: splitting (212) gives:
% 22.34/3.77  | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | Case 1:
% 22.34/3.77  | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | |   (213)   ~ (all_121_1 = 0)
% 22.34/3.77  | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | | REDUCE: (208), (213) imply:
% 22.34/3.77  | | | | | | | | | |   (214)  $false
% 22.34/3.77  | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | | CLOSE: (214) is inconsistent.
% 22.34/3.77  | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | Case 2:
% 22.34/3.77  | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | |   (215)   ~ (all_121_2 = 0)
% 22.34/3.77  | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | | REDUCE: (207), (215) imply:
% 22.34/3.77  | | | | | | | | | |   (216)  $false
% 22.34/3.77  | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | | CLOSE: (216) is inconsistent.
% 22.34/3.77  | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | End of split
% 22.34/3.77  | | | | | | | | | 
% 22.34/3.77  | | | | | | | | End of split
% 22.34/3.77  | | | | | | | | 
% 22.34/3.77  | | | | | | | Case 2:
% 22.34/3.77  | | | | | | | | 
% 22.34/3.77  | | | | | | | |   (217)   ! [v0: $i] : (v0 = xp |  ~ (sdtasdt0(xl, v0) = xm) | 
% 22.34/3.77  | | | | | | | |            ~ $i(v0) |  ? [v1: int] : ( ~ (v1 = 0) &
% 22.34/3.77  | | | | | | | |              aNaturalNumber0(v0) = v1)) &  ! [v0: $i] : ( ~
% 22.34/3.77  | | | | | | | |            (sdtasdt0(xl, xp) = v0) |  ~ $i(xp) | (v0 = xm &
% 22.34/3.77  | | | | | | | |              aNaturalNumber0(xp) = 0))
% 22.34/3.77  | | | | | | | | 
% 22.34/3.77  | | | | | | | | ALPHA: (217) implies:
% 22.34/3.77  | | | | | | | |   (218)   ! [v0: $i] : ( ~ (sdtasdt0(xl, xp) = v0) |  ~ $i(xp) |
% 22.34/3.77  | | | | | | | |            (v0 = xm & aNaturalNumber0(xp) = 0))
% 22.34/3.77  | | | | | | | | 
% 22.34/3.77  | | | | | | | | GROUND_INST: instantiating (218) with all_39_2, simplifying with
% 22.34/3.77  | | | | | | | |              (13), (40) gives:
% 22.34/3.77  | | | | | | | |   (219)  all_39_2 = xm & aNaturalNumber0(xp) = 0
% 22.34/3.77  | | | | | | | | 
% 22.34/3.77  | | | | | | | | ALPHA: (219) implies:
% 22.34/3.77  | | | | | | | |   (220)  all_39_2 = xm
% 22.34/3.77  | | | | | | | |   (221)  aNaturalNumber0(xp) = 0
% 22.34/3.77  | | | | | | | | 
% 22.34/3.77  | | | | | | | | REDUCE: (40), (220) imply:
% 22.34/3.77  | | | | | | | |   (222)  sdtasdt0(xl, xp) = xm
% 22.34/3.77  | | | | | | | | 
% 22.34/3.77  | | | | | | | | REDUCE: (45), (220) imply:
% 22.34/3.77  | | | | | | | |   (223)  sdtpldt0(xm, all_35_0) = all_39_0
% 22.34/3.77  | | | | | | | | 
% 22.34/3.77  | | | | | | | | REDUCE: (38), (220) imply:
% 22.34/3.77  | | | | | | | |   (224)  sdtpldt0(xm, xn) = all_39_0
% 22.34/3.77  | | | | | | | | 
% 22.34/3.77  | | | | | | | | REDUCE: (96), (220) imply:
% 22.34/3.77  | | | | | | | |   (225)  sdtpldt0(all_35_0, xm) = all_64_0
% 22.34/3.77  | | | | | | | | 
% 22.34/3.77  | | | | | | | | REDUCE: (74), (220) imply:
% 22.34/3.77  | | | | | | | |   (226)  aNaturalNumber0(xm) = all_52_0
% 22.34/3.77  | | | | | | | | 
% 22.34/3.77  | | | | | | | | BETA: splitting (169) gives:
% 22.34/3.77  | | | | | | | | 
% 22.34/3.77  | | | | | | | | Case 1:
% 22.34/3.77  | | | | | | | | | 
% 22.34/3.77  | | | | | | | | |   (227)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :
% 22.34/3.77  | | | | | | | | |          (doDivides0(xl, all_33_0) = v2 &
% 22.34/3.77  | | | | | | | | |            aNaturalNumber0(all_33_0) = v1 &
% 22.34/3.77  | | | | | | | | |            aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) |  ~ (v1 =
% 22.34/3.77  | | | | | | | | |                0) |  ~ (v0 = 0)))
% 22.34/3.77  | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | DELTA: instantiating (227) with fresh symbols all_123_0,
% 22.34/3.77  | | | | | | | | |        all_123_1, all_123_2 gives:
% 22.34/3.77  | | | | | | | | |   (228)  doDivides0(xl, all_33_0) = all_123_0 &
% 22.34/3.77  | | | | | | | | |          aNaturalNumber0(all_33_0) = all_123_1 &
% 22.34/3.77  | | | | | | | | |          aNaturalNumber0(xl) = all_123_2 & ( ~ (all_123_0 = 0)
% 22.34/3.77  | | | | | | | | |            |  ~ (all_123_1 = 0) |  ~ (all_123_2 = 0))
% 22.34/3.77  | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | ALPHA: (228) implies:
% 22.34/3.77  | | | | | | | | |   (229)  aNaturalNumber0(xl) = all_123_2
% 22.34/3.77  | | | | | | | | |   (230)  aNaturalNumber0(all_33_0) = all_123_1
% 22.34/3.77  | | | | | | | | |   (231)  doDivides0(xl, all_33_0) = all_123_0
% 22.34/3.77  | | | | | | | | |   (232)   ~ (all_123_0 = 0) |  ~ (all_123_1 = 0) |  ~
% 22.34/3.77  | | | | | | | | |          (all_123_2 = 0)
% 22.34/3.77  | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_123_2, xl,
% 22.34/3.77  | | | | | | | | |              simplifying with (2), (229) gives:
% 22.34/3.77  | | | | | | | | |   (233)  all_123_2 = 0
% 22.34/3.77  | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_123_1, all_33_0,
% 22.34/3.77  | | | | | | | | |              simplifying with (166), (230) gives:
% 22.34/3.77  | | | | | | | | |   (234)  all_123_1 = 0
% 22.34/3.77  | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | GROUND_INST: instantiating (23) with 0, all_123_0, all_33_0,
% 22.34/3.77  | | | | | | | | |              xl, simplifying with (44), (231) gives:
% 22.34/3.77  | | | | | | | | |   (235)  all_123_0 = 0
% 22.34/3.77  | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | BETA: splitting (232) gives:
% 22.34/3.77  | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | Case 1:
% 22.34/3.77  | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | |   (236)   ~ (all_123_0 = 0)
% 22.34/3.77  | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | | REDUCE: (235), (236) imply:
% 22.34/3.77  | | | | | | | | | |   (237)  $false
% 22.34/3.77  | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | | CLOSE: (237) is inconsistent.
% 22.34/3.77  | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | Case 2:
% 22.34/3.77  | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | |   (238)   ~ (all_123_1 = 0) |  ~ (all_123_2 = 0)
% 22.34/3.77  | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | | BETA: splitting (238) gives:
% 22.34/3.77  | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | | Case 1:
% 22.34/3.77  | | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | | |   (239)   ~ (all_123_1 = 0)
% 22.34/3.77  | | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | | | REDUCE: (234), (239) imply:
% 22.34/3.77  | | | | | | | | | | |   (240)  $false
% 22.34/3.77  | | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | | | CLOSE: (240) is inconsistent.
% 22.34/3.77  | | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | | Case 2:
% 22.34/3.77  | | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | | |   (241)   ~ (all_123_2 = 0)
% 22.34/3.77  | | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | | | REDUCE: (233), (241) imply:
% 22.34/3.77  | | | | | | | | | | |   (242)  $false
% 22.34/3.77  | | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | | | CLOSE: (242) is inconsistent.
% 22.34/3.77  | | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | | End of split
% 22.34/3.77  | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | End of split
% 22.34/3.77  | | | | | | | | | 
% 22.34/3.77  | | | | | | | | Case 2:
% 22.34/3.77  | | | | | | | | | 
% 22.34/3.77  | | | | | | | | |   (243)   ! [v0: $i] : (v0 = xq |  ~ (sdtasdt0(xl, v0) =
% 22.34/3.77  | | | | | | | | |              all_33_0) |  ~ $i(v0) |  ? [v1: int] : ( ~ (v1 =
% 22.34/3.77  | | | | | | | | |                0) & aNaturalNumber0(v0) = v1)) &  ! [v0: $i] :
% 22.34/3.77  | | | | | | | | |          ( ~ (sdtasdt0(xl, xq) = v0) |  ~ $i(xq) | (v0 =
% 22.34/3.77  | | | | | | | | |              all_33_0 & aNaturalNumber0(xq) = 0))
% 22.34/3.77  | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | ALPHA: (243) implies:
% 22.34/3.77  | | | | | | | | |   (244)   ! [v0: $i] : (v0 = xq |  ~ (sdtasdt0(xl, v0) =
% 22.34/3.77  | | | | | | | | |              all_33_0) |  ~ $i(v0) |  ? [v1: int] : ( ~ (v1 =
% 22.34/3.77  | | | | | | | | |                0) & aNaturalNumber0(v0) = v1))
% 22.34/3.77  | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_52_0, xm,
% 22.34/3.77  | | | | | | | | |              simplifying with (3), (226) gives:
% 22.34/3.77  | | | | | | | | |   (245)  all_52_0 = 0
% 22.34/3.77  | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | GROUND_INST: instantiating (19) with all_52_1, 0, xp,
% 22.34/3.77  | | | | | | | | |              simplifying with (73), (221) gives:
% 22.34/3.77  | | | | | | | | |   (246)  all_52_1 = 0
% 22.34/3.77  | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | GROUND_INST: instantiating (20) with all_33_0, all_39_0, xn,
% 22.34/3.77  | | | | | | | | |              xm, simplifying with (25), (224) gives:
% 22.34/3.77  | | | | | | | | |   (247)  all_39_0 = all_33_0
% 22.34/3.77  | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | REDUCE: (223), (247) imply:
% 22.34/3.77  | | | | | | | | |   (248)  sdtpldt0(xm, all_35_0) = all_33_0
% 22.34/3.77  | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | BETA: splitting (52) gives:
% 22.34/3.77  | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | Case 1:
% 22.34/3.77  | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | |   (249)  all_35_0 = xn
% 22.34/3.77  | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | | REDUCE: (28), (249) imply:
% 22.34/3.77  | | | | | | | | | |   (250)  $false
% 22.34/3.77  | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | | CLOSE: (250) is inconsistent.
% 22.34/3.77  | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | Case 2:
% 22.34/3.77  | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | |   (251)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ?
% 22.34/3.77  | | | | | | | | | |          [v3: $i] :  ? [v4: $i] : (sdtpldt0(all_35_0,
% 22.34/3.77  | | | | | | | | | |              all_39_2) = v4 & sdtpldt0(xn, all_39_2) = v3 &
% 22.34/3.77  | | | | | | | | | |            aNaturalNumber0(all_39_2) = v0 &
% 22.34/3.77  | | | | | | | | | |            aNaturalNumber0(all_35_0) = v2 &
% 22.34/3.77  | | | | | | | | | |            aNaturalNumber0(xn) = v1 & $i(v4) & $i(v3) & ( ~
% 22.34/3.77  | | | | | | | | | |              (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 22.34/3.77  | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | | DELTA: instantiating (251) with fresh symbols all_131_0,
% 22.34/3.77  | | | | | | | | | |        all_131_1, all_131_2, all_131_3, all_131_4 gives:
% 22.34/3.77  | | | | | | | | | |   (252)  sdtpldt0(all_35_0, all_39_2) = all_131_0 &
% 22.34/3.77  | | | | | | | | | |          sdtpldt0(xn, all_39_2) = all_131_1 &
% 22.34/3.77  | | | | | | | | | |          aNaturalNumber0(all_39_2) = all_131_4 &
% 22.34/3.77  | | | | | | | | | |          aNaturalNumber0(all_35_0) = all_131_2 &
% 22.34/3.77  | | | | | | | | | |          aNaturalNumber0(xn) = all_131_3 & $i(all_131_0) &
% 22.34/3.77  | | | | | | | | | |          $i(all_131_1) & ( ~ (all_131_2 = 0) |  ~ (all_131_3
% 22.34/3.77  | | | | | | | | | |              = 0) |  ~ (all_131_4 = 0))
% 22.34/3.77  | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | | ALPHA: (252) implies:
% 22.34/3.77  | | | | | | | | | |   (253)  aNaturalNumber0(xn) = all_131_3
% 22.34/3.77  | | | | | | | | | |   (254)  aNaturalNumber0(all_35_0) = all_131_2
% 22.34/3.77  | | | | | | | | | |   (255)  aNaturalNumber0(all_39_2) = all_131_4
% 22.34/3.77  | | | | | | | | | |   (256)  sdtpldt0(all_35_0, all_39_2) = all_131_0
% 22.34/3.77  | | | | | | | | | |   (257)   ~ (all_131_2 = 0) |  ~ (all_131_3 = 0) |  ~
% 22.34/3.77  | | | | | | | | | |          (all_131_4 = 0)
% 22.34/3.77  | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | | REDUCE: (220), (256) imply:
% 22.34/3.77  | | | | | | | | | |   (258)  sdtpldt0(all_35_0, xm) = all_131_0
% 22.34/3.77  | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | | REDUCE: (220), (255) imply:
% 22.34/3.77  | | | | | | | | | |   (259)  aNaturalNumber0(xm) = all_131_4
% 22.34/3.77  | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | | BETA: splitting (53) gives:
% 22.34/3.77  | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | | Case 1:
% 22.34/3.77  | | | | | | | | | | | 
% 22.34/3.77  | | | | | | | | | | |   (260)  all_35_0 = xn
% 22.34/3.78  | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | REDUCE: (28), (260) imply:
% 22.34/3.78  | | | | | | | | | | |   (261)  $false
% 22.34/3.78  | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | CLOSE: (261) is inconsistent.
% 22.34/3.78  | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | Case 2:
% 22.34/3.78  | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | |   (262)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ?
% 22.34/3.78  | | | | | | | | | | |          [v3: $i] :  ? [v4: $i] : (sdtpldt0(all_35_0,
% 22.34/3.78  | | | | | | | | | | |              all_39_2) = v3 & sdtpldt0(xn, all_39_2) = v4 &
% 22.34/3.78  | | | | | | | | | | |            aNaturalNumber0(all_39_2) = v0 &
% 22.34/3.78  | | | | | | | | | | |            aNaturalNumber0(all_35_0) = v1 &
% 22.34/3.78  | | | | | | | | | | |            aNaturalNumber0(xn) = v2 & $i(v4) & $i(v3) & ( ~
% 22.34/3.78  | | | | | | | | | | |              (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 22.34/3.78  | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | DELTA: instantiating (262) with fresh symbols all_137_0,
% 22.34/3.78  | | | | | | | | | | |        all_137_1, all_137_2, all_137_3, all_137_4 gives:
% 22.34/3.78  | | | | | | | | | | |   (263)  sdtpldt0(all_35_0, all_39_2) = all_137_1 &
% 22.34/3.78  | | | | | | | | | | |          sdtpldt0(xn, all_39_2) = all_137_0 &
% 22.34/3.78  | | | | | | | | | | |          aNaturalNumber0(all_39_2) = all_137_4 &
% 22.34/3.78  | | | | | | | | | | |          aNaturalNumber0(all_35_0) = all_137_3 &
% 22.34/3.78  | | | | | | | | | | |          aNaturalNumber0(xn) = all_137_2 & $i(all_137_0) &
% 22.34/3.78  | | | | | | | | | | |          $i(all_137_1) & ( ~ (all_137_2 = 0) |  ~
% 22.34/3.78  | | | | | | | | | | |            (all_137_3 = 0) |  ~ (all_137_4 = 0))
% 22.34/3.78  | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | ALPHA: (263) implies:
% 22.34/3.78  | | | | | | | | | | |   (264)  aNaturalNumber0(xn) = all_137_2
% 22.34/3.78  | | | | | | | | | | |   (265)  aNaturalNumber0(all_35_0) = all_137_3
% 22.34/3.78  | | | | | | | | | | |   (266)  aNaturalNumber0(all_39_2) = all_137_4
% 22.34/3.78  | | | | | | | | | | |   (267)  sdtpldt0(all_35_0, all_39_2) = all_137_1
% 22.34/3.78  | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | REDUCE: (220), (267) imply:
% 22.34/3.78  | | | | | | | | | | |   (268)  sdtpldt0(all_35_0, xm) = all_137_1
% 22.34/3.78  | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | REDUCE: (220), (266) imply:
% 22.34/3.78  | | | | | | | | | | |   (269)  aNaturalNumber0(xm) = all_137_4
% 22.34/3.78  | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_137_4, xm,
% 22.34/3.78  | | | | | | | | | | |              simplifying with (3), (269) gives:
% 22.34/3.78  | | | | | | | | | | |   (270)  all_137_4 = 0
% 22.34/3.78  | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | GROUND_INST: instantiating (19) with all_131_4, all_137_4, xm,
% 22.34/3.78  | | | | | | | | | | |              simplifying with (259), (269) gives:
% 22.34/3.78  | | | | | | | | | | |   (271)  all_137_4 = all_131_4
% 22.34/3.78  | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_137_2, xn,
% 22.34/3.78  | | | | | | | | | | |              simplifying with (4), (264) gives:
% 22.34/3.78  | | | | | | | | | | |   (272)  all_137_2 = 0
% 22.34/3.78  | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | GROUND_INST: instantiating (19) with all_131_3, all_137_2, xn,
% 22.34/3.78  | | | | | | | | | | |              simplifying with (253), (264) gives:
% 22.34/3.78  | | | | | | | | | | |   (273)  all_137_2 = all_131_3
% 22.34/3.78  | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | GROUND_INST: instantiating (19) with all_50_0, all_137_3,
% 22.34/3.78  | | | | | | | | | | |              all_35_0, simplifying with (69), (265) gives:
% 22.34/3.78  | | | | | | | | | | |   (274)  all_137_3 = all_50_0
% 22.34/3.78  | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | GROUND_INST: instantiating (19) with all_131_2, all_137_3,
% 22.34/3.78  | | | | | | | | | | |              all_35_0, simplifying with (254), (265) gives:
% 22.34/3.78  | | | | | | | | | | |   (275)  all_137_3 = all_131_2
% 22.34/3.78  | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | GROUND_INST: instantiating (20) with all_64_0, all_137_1, xm,
% 22.34/3.78  | | | | | | | | | | |              all_35_0, simplifying with (225), (268) gives:
% 22.34/3.78  | | | | | | | | | | |   (276)  all_137_1 = all_64_0
% 22.34/3.78  | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | GROUND_INST: instantiating (20) with all_131_0, all_137_1, xm,
% 22.34/3.78  | | | | | | | | | | |              all_35_0, simplifying with (258), (268) gives:
% 22.34/3.78  | | | | | | | | | | |   (277)  all_137_1 = all_131_0
% 22.34/3.78  | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | COMBINE_EQS: (276), (277) imply:
% 22.34/3.78  | | | | | | | | | | |   (278)  all_131_0 = all_64_0
% 22.34/3.78  | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | COMBINE_EQS: (272), (273) imply:
% 22.34/3.78  | | | | | | | | | | |   (279)  all_131_3 = 0
% 22.34/3.78  | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | COMBINE_EQS: (274), (275) imply:
% 22.34/3.78  | | | | | | | | | | |   (280)  all_131_2 = all_50_0
% 22.34/3.78  | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | SIMP: (280) implies:
% 22.34/3.78  | | | | | | | | | | |   (281)  all_131_2 = all_50_0
% 22.34/3.78  | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | COMBINE_EQS: (270), (271) imply:
% 22.34/3.78  | | | | | | | | | | |   (282)  all_131_4 = 0
% 22.34/3.78  | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | SIMP: (282) implies:
% 22.34/3.78  | | | | | | | | | | |   (283)  all_131_4 = 0
% 22.34/3.78  | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | BETA: splitting (257) gives:
% 22.34/3.78  | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | Case 1:
% 22.34/3.78  | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | |   (284)   ~ (all_131_2 = 0)
% 22.34/3.78  | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | REDUCE: (281), (284) imply:
% 22.34/3.78  | | | | | | | | | | | |   (285)   ~ (all_50_0 = 0)
% 22.34/3.78  | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | BETA: splitting (70) gives:
% 22.34/3.78  | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | Case 1:
% 22.34/3.78  | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | |   (286)   ~ (all_50_1 = 0)
% 22.34/3.78  | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | BETA: splitting (61) gives:
% 22.34/3.78  | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | Case 1:
% 22.34/3.78  | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | |   (287)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :
% 22.34/3.78  | | | | | | | | | | | | | |          (sdtlseqdt0(xp, xq) = v2 & aNaturalNumber0(xq) =
% 22.34/3.78  | | | | | | | | | | | | | |            v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | 
% 22.34/3.78  | | | | | | | | | | | | | |              ~ (v1 = 0) |  ~ (v0 = 0)))
% 22.34/3.78  | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | DELTA: instantiating (287) with fresh symbols all_170_0,
% 22.34/3.78  | | | | | | | | | | | | | |        all_170_1, all_170_2 gives:
% 22.34/3.78  | | | | | | | | | | | | | |   (288)  sdtlseqdt0(xp, xq) = all_170_0 &
% 22.34/3.78  | | | | | | | | | | | | | |          aNaturalNumber0(xq) = all_170_1 &
% 22.34/3.78  | | | | | | | | | | | | | |          aNaturalNumber0(xp) = all_170_2 & ( ~ (all_170_0 =
% 22.34/3.78  | | | | | | | | | | | | | |              0) |  ~ (all_170_1 = 0) |  ~ (all_170_2 = 0))
% 22.34/3.78  | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | ALPHA: (288) implies:
% 22.34/3.78  | | | | | | | | | | | | | |   (289)  aNaturalNumber0(xp) = all_170_2
% 22.34/3.78  | | | | | | | | | | | | | |   (290)  aNaturalNumber0(xq) = all_170_1
% 22.34/3.78  | | | | | | | | | | | | | |   (291)  sdtlseqdt0(xp, xq) = all_170_0
% 22.34/3.78  | | | | | | | | | | | | | |   (292)   ~ (all_170_0 = 0) |  ~ (all_170_1 = 0) |  ~
% 22.34/3.78  | | | | | | | | | | | | | |          (all_170_2 = 0)
% 22.34/3.78  | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_170_2, xp,
% 22.34/3.78  | | | | | | | | | | | | | |              simplifying with (221), (289) gives:
% 22.34/3.78  | | | | | | | | | | | | | |   (293)  all_170_2 = 0
% 22.34/3.78  | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | GROUND_INST: instantiating (22) with 0, all_170_0, xq, xp,
% 22.34/3.78  | | | | | | | | | | | | | |              simplifying with (10), (291) gives:
% 22.34/3.78  | | | | | | | | | | | | | |   (294)  all_170_0 = 0
% 22.34/3.78  | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | BETA: splitting (292) gives:
% 22.34/3.78  | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | Case 1:
% 22.34/3.78  | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | |   (295)   ~ (all_170_0 = 0)
% 22.34/3.78  | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | | REDUCE: (294), (295) imply:
% 22.34/3.78  | | | | | | | | | | | | | | |   (296)  $false
% 22.34/3.78  | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | | CLOSE: (296) is inconsistent.
% 22.34/3.78  | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | Case 2:
% 22.34/3.78  | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | |   (297)   ~ (all_170_1 = 0) |  ~ (all_170_2 = 0)
% 22.34/3.78  | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | | BETA: splitting (297) gives:
% 22.34/3.78  | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | | Case 1:
% 22.34/3.78  | | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | | |   (298)   ~ (all_170_1 = 0)
% 22.34/3.78  | | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (244) with all_110_0, simplifying
% 22.34/3.78  | | | | | | | | | | | | | | | |              with (183), (185) gives:
% 22.34/3.78  | | | | | | | | | | | | | | | |   (299)  all_110_0 = xq |  ? [v0: int] : ( ~ (v0 = 0) &
% 22.34/3.78  | | | | | | | | | | | | | | | |            aNaturalNumber0(all_110_0) = v0)
% 22.34/3.78  | | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with xl, all_110_0,
% 22.34/3.78  | | | | | | | | | | | | | | | |              all_33_0, simplifying with (15), (183), (185)
% 22.34/3.78  | | | | | | | | | | | | | | | |              gives:
% 22.34/3.78  | | | | | | | | | | | | | | | |   (300)   ? [v0: any] :  ? [v1: any] :  ? [v2: $i] :
% 22.34/3.78  | | | | | | | | | | | | | | | |          (sdtasdt0(all_110_0, xl) = v2 &
% 22.34/3.78  | | | | | | | | | | | | | | | |            aNaturalNumber0(all_110_0) = v1 &
% 22.34/3.78  | | | | | | | | | | | | | | | |            aNaturalNumber0(xl) = v0 & $i(v2) & ( ~ (v1 = 0)
% 22.34/3.78  | | | | | | | | | | | | | | | |              |  ~ (v0 = 0) | v2 = all_33_0))
% 22.34/3.78  | | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | | | DELTA: instantiating (300) with fresh symbols all_207_0,
% 22.34/3.78  | | | | | | | | | | | | | | | |        all_207_1, all_207_2 gives:
% 22.34/3.78  | | | | | | | | | | | | | | | |   (301)  sdtasdt0(all_110_0, xl) = all_207_0 &
% 22.34/3.78  | | | | | | | | | | | | | | | |          aNaturalNumber0(all_110_0) = all_207_1 &
% 22.34/3.78  | | | | | | | | | | | | | | | |          aNaturalNumber0(xl) = all_207_2 & $i(all_207_0) &
% 22.34/3.78  | | | | | | | | | | | | | | | |          ( ~ (all_207_1 = 0) |  ~ (all_207_2 = 0) |
% 22.34/3.78  | | | | | | | | | | | | | | | |            all_207_0 = all_33_0)
% 22.34/3.78  | | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | | | ALPHA: (301) implies:
% 22.34/3.78  | | | | | | | | | | | | | | | |   (302)  aNaturalNumber0(all_110_0) = all_207_1
% 22.34/3.78  | | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_207_1, all_110_0,
% 22.34/3.78  | | | | | | | | | | | | | | | |              simplifying with (184), (302) gives:
% 22.34/3.78  | | | | | | | | | | | | | | | |   (303)  all_207_1 = 0
% 22.34/3.78  | | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | | | BETA: splitting (299) gives:
% 22.34/3.78  | | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | | | Case 1:
% 22.34/3.78  | | | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | | | |   (304)  all_110_0 = xq
% 22.34/3.78  | | | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | | | | REDUCE: (184), (304) imply:
% 22.34/3.78  | | | | | | | | | | | | | | | | |   (305)  aNaturalNumber0(xq) = 0
% 22.34/3.78  | | | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_170_1, 0, xq,
% 22.34/3.78  | | | | | | | | | | | | | | | | |              simplifying with (290), (305) gives:
% 22.34/3.78  | | | | | | | | | | | | | | | | |   (306)  all_170_1 = 0
% 22.34/3.78  | | | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | | | | REDUCE: (298), (306) imply:
% 22.34/3.78  | | | | | | | | | | | | | | | | |   (307)  $false
% 22.34/3.78  | | | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | | | | CLOSE: (307) is inconsistent.
% 22.34/3.78  | | | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | | | Case 2:
% 22.34/3.78  | | | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | | | |   (308)   ? [v0: int] : ( ~ (v0 = 0) &
% 22.34/3.78  | | | | | | | | | | | | | | | | |            aNaturalNumber0(all_110_0) = v0)
% 22.34/3.78  | | | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | | | | DELTA: instantiating (308) with fresh symbol all_251_0
% 22.34/3.78  | | | | | | | | | | | | | | | | |        gives:
% 22.34/3.78  | | | | | | | | | | | | | | | | |   (309)   ~ (all_251_0 = 0) & aNaturalNumber0(all_110_0) =
% 22.34/3.78  | | | | | | | | | | | | | | | | |          all_251_0
% 22.34/3.78  | | | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | | | | ALPHA: (309) implies:
% 22.34/3.78  | | | | | | | | | | | | | | | | |   (310)   ~ (all_251_0 = 0)
% 22.34/3.78  | | | | | | | | | | | | | | | | |   (311)  aNaturalNumber0(all_110_0) = all_251_0
% 22.34/3.78  | | | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_251_0, all_110_0,
% 22.34/3.78  | | | | | | | | | | | | | | | | |              simplifying with (184), (311) gives:
% 22.34/3.78  | | | | | | | | | | | | | | | | |   (312)  all_251_0 = 0
% 22.34/3.78  | | | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | | | | REDUCE: (310), (312) imply:
% 22.34/3.78  | | | | | | | | | | | | | | | | |   (313)  $false
% 22.34/3.78  | | | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | | | | CLOSE: (313) is inconsistent.
% 22.34/3.78  | | | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | | | End of split
% 22.34/3.78  | | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | | Case 2:
% 22.34/3.78  | | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | | |   (314)   ~ (all_170_2 = 0)
% 22.34/3.78  | | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | | | REDUCE: (293), (314) imply:
% 22.34/3.78  | | | | | | | | | | | | | | | |   (315)  $false
% 22.34/3.78  | | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | | | CLOSE: (315) is inconsistent.
% 22.34/3.78  | | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | | End of split
% 22.34/3.78  | | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | End of split
% 22.34/3.78  | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | Case 2:
% 22.34/3.78  | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | |   (316)   ! [v0: $i] : (v0 = xr |  ~ (sdtpldt0(xp, v0) =
% 22.34/3.78  | | | | | | | | | | | | | |              xq) |  ~ $i(v0) |  ? [v1: int] : ( ~ (v1 = 0)
% 22.34/3.78  | | | | | | | | | | | | | |              & aNaturalNumber0(v0) = v1)) &  ! [v0: $i] : (
% 22.34/3.78  | | | | | | | | | | | | | |            ~ (sdtpldt0(xp, xr) = v0) |  ~ $i(xr) | (v0 = xq
% 22.34/3.78  | | | | | | | | | | | | | |              & aNaturalNumber0(xr) = 0))
% 22.34/3.78  | | | | | | | | | | | | | | 
% 22.34/3.78  | | | | | | | | | | | | | | ALPHA: (316) implies:
% 22.34/3.79  | | | | | | | | | | | | | |   (317)   ! [v0: $i] : ( ~ (sdtpldt0(xp, xr) = v0) |  ~
% 22.34/3.79  | | | | | | | | | | | | | |            $i(xr) | (v0 = xq & aNaturalNumber0(xr) = 0))
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | GROUND_INST: instantiating (317) with all_70_5, simplifying
% 22.34/3.79  | | | | | | | | | | | | | |              with (17), (107) gives:
% 22.34/3.79  | | | | | | | | | | | | | |   (318)  all_70_5 = xq & aNaturalNumber0(xr) = 0
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | ALPHA: (318) implies:
% 22.34/3.79  | | | | | | | | | | | | | |   (319)  aNaturalNumber0(xr) = 0
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | GROUND_INST: instantiating (mAddComm) with xp, xr, all_70_5,
% 22.34/3.79  | | | | | | | | | | | | | |              simplifying with (13), (17), (107) gives:
% 22.34/3.79  | | | | | | | | | | | | | |   (320)   ? [v0: any] :  ? [v1: any] :  ? [v2: $i] :
% 22.34/3.79  | | | | | | | | | | | | | |          (sdtpldt0(xr, xp) = v2 & aNaturalNumber0(xr) = v1
% 22.34/3.79  | | | | | | | | | | | | | |            & aNaturalNumber0(xp) = v0 & $i(v2) & ( ~ (v1 =
% 22.34/3.79  | | | | | | | | | | | | | |                0) |  ~ (v0 = 0) | v2 = all_70_5))
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | GROUND_INST: instantiating (mSortsB) with xp, xr, all_70_5,
% 22.34/3.79  | | | | | | | | | | | | | |              simplifying with (13), (17), (107) gives:
% 22.34/3.79  | | | | | | | | | | | | | |   (321)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :
% 22.34/3.79  | | | | | | | | | | | | | |          (aNaturalNumber0(all_70_5) = v2 &
% 22.34/3.79  | | | | | | | | | | | | | |            aNaturalNumber0(xr) = v1 & aNaturalNumber0(xp) =
% 22.34/3.79  | | | | | | | | | | | | | |            v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = 0))
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | GROUND_INST: instantiating (mAMDistr) with xl, xr, xp,
% 22.34/3.79  | | | | | | | | | | | | | |              all_35_0, xm, all_64_0, simplifying with (13),
% 22.34/3.79  | | | | | | | | | | | | | |              (15), (17), (29), (222), (225) gives:
% 22.34/3.79  | | | | | | | | | | | | | |   (322)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ?
% 22.34/3.79  | | | | | | | | | | | | | |          [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i]
% 22.34/3.79  | | | | | | | | | | | | | |          :  ? [v7: $i] :  ? [v8: $i] : (sdtasdt0(v3, xl) =
% 22.34/3.79  | | | | | | | | | | | | | |            v5 & sdtasdt0(xr, xl) = v6 & sdtasdt0(xp, xl) =
% 22.34/3.79  | | | | | | | | | | | | | |            v7 & sdtasdt0(xl, v3) = v4 & sdtpldt0(v6, v7) =
% 22.34/3.79  | | | | | | | | | | | | | |            v8 & sdtpldt0(xr, xp) = v3 & aNaturalNumber0(xr)
% 22.34/3.79  | | | | | | | | | | | | | |            = v1 & aNaturalNumber0(xp) = v2 &
% 22.34/3.79  | | | | | | | | | | | | | |            aNaturalNumber0(xl) = v0 & $i(v8) & $i(v7) &
% 22.34/3.79  | | | | | | | | | | | | | |            $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0)
% 22.34/3.79  | | | | | | | | | | | | | |              |  ~ (v1 = 0) |  ~ (v0 = 0) | (v8 = v5 & v4 =
% 22.34/3.79  | | | | | | | | | | | | | |                all_64_0)))
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | GROUND_INST: instantiating (mAMDistr) with xl, xr, all_114_0,
% 22.34/3.79  | | | | | | | | | | | | | |              all_35_0, xm, all_64_0, simplifying with (15),
% 22.34/3.79  | | | | | | | | | | | | | |              (17), (29), (199), (200), (225) gives:
% 22.34/3.79  | | | | | | | | | | | | | |   (323)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ?
% 22.34/3.79  | | | | | | | | | | | | | |          [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i]
% 22.34/3.79  | | | | | | | | | | | | | |          :  ? [v7: $i] :  ? [v8: $i] : (sdtasdt0(v3, xl) =
% 22.34/3.79  | | | | | | | | | | | | | |            v5 & sdtasdt0(all_114_0, xl) = v7 & sdtasdt0(xr,
% 22.34/3.79  | | | | | | | | | | | | | |              xl) = v6 & sdtasdt0(xl, v3) = v4 &
% 22.34/3.79  | | | | | | | | | | | | | |            sdtpldt0(v6, v7) = v8 & sdtpldt0(xr, all_114_0)
% 22.34/3.79  | | | | | | | | | | | | | |            = v3 & aNaturalNumber0(all_114_0) = v2 &
% 22.34/3.79  | | | | | | | | | | | | | |            aNaturalNumber0(xr) = v1 & aNaturalNumber0(xl) =
% 22.34/3.79  | | | | | | | | | | | | | |            v0 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4)
% 22.34/3.79  | | | | | | | | | | | | | |            & $i(v3) & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 =
% 22.34/3.79  | | | | | | | | | | | | | |                0) | (v8 = v5 & v4 = all_64_0)))
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | GROUND_INST: instantiating (mAMDistr) with xl, all_114_0, xr,
% 22.34/3.79  | | | | | | | | | | | | | |              xm, all_35_0, all_33_0, simplifying with (15),
% 22.34/3.79  | | | | | | | | | | | | | |              (17), (29), (199), (200), (248) gives:
% 22.34/3.79  | | | | | | | | | | | | | |   (324)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ?
% 22.34/3.79  | | | | | | | | | | | | | |          [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i]
% 22.34/3.79  | | | | | | | | | | | | | |          :  ? [v7: $i] :  ? [v8: $i] : (sdtasdt0(v3, xl) =
% 22.34/3.79  | | | | | | | | | | | | | |            v5 & sdtasdt0(all_114_0, xl) = v6 & sdtasdt0(xr,
% 22.34/3.79  | | | | | | | | | | | | | |              xl) = v7 & sdtasdt0(xl, v3) = v4 &
% 22.34/3.79  | | | | | | | | | | | | | |            sdtpldt0(v6, v7) = v8 & sdtpldt0(all_114_0, xr)
% 22.34/3.79  | | | | | | | | | | | | | |            = v3 & aNaturalNumber0(all_114_0) = v1 &
% 22.34/3.79  | | | | | | | | | | | | | |            aNaturalNumber0(xr) = v2 & aNaturalNumber0(xl) =
% 22.34/3.79  | | | | | | | | | | | | | |            v0 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4)
% 22.34/3.79  | | | | | | | | | | | | | |            & $i(v3) & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 =
% 22.34/3.79  | | | | | | | | | | | | | |                0) | (v8 = v5 & v4 = all_33_0)))
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | GROUND_INST: instantiating (mSortsB_02) with xr, xl, all_60_0,
% 22.34/3.79  | | | | | | | | | | | | | |              simplifying with (15), (17), (89) gives:
% 22.34/3.79  | | | | | | | | | | | | | |   (325)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :
% 22.34/3.79  | | | | | | | | | | | | | |          (aNaturalNumber0(all_60_0) = v2 &
% 22.34/3.79  | | | | | | | | | | | | | |            aNaturalNumber0(xr) = v0 & aNaturalNumber0(xl) =
% 22.34/3.79  | | | | | | | | | | | | | |            v1 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = 0))
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | DELTA: instantiating (325) with fresh symbols all_180_0,
% 22.34/3.79  | | | | | | | | | | | | | |        all_180_1, all_180_2 gives:
% 22.34/3.79  | | | | | | | | | | | | | |   (326)  aNaturalNumber0(all_60_0) = all_180_0 &
% 22.34/3.79  | | | | | | | | | | | | | |          aNaturalNumber0(xr) = all_180_2 &
% 22.34/3.79  | | | | | | | | | | | | | |          aNaturalNumber0(xl) = all_180_1 & ( ~ (all_180_1 =
% 22.34/3.79  | | | | | | | | | | | | | |              0) |  ~ (all_180_2 = 0) | all_180_0 = 0)
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | ALPHA: (326) implies:
% 22.34/3.79  | | | | | | | | | | | | | |   (327)  aNaturalNumber0(xr) = all_180_2
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | DELTA: instantiating (321) with fresh symbols all_186_0,
% 22.34/3.79  | | | | | | | | | | | | | |        all_186_1, all_186_2 gives:
% 22.34/3.79  | | | | | | | | | | | | | |   (328)  aNaturalNumber0(all_70_5) = all_186_0 &
% 22.34/3.79  | | | | | | | | | | | | | |          aNaturalNumber0(xr) = all_186_1 &
% 22.34/3.79  | | | | | | | | | | | | | |          aNaturalNumber0(xp) = all_186_2 & ( ~ (all_186_1 =
% 22.34/3.79  | | | | | | | | | | | | | |              0) |  ~ (all_186_2 = 0) | all_186_0 = 0)
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | ALPHA: (328) implies:
% 22.34/3.79  | | | | | | | | | | | | | |   (329)  aNaturalNumber0(xr) = all_186_1
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | DELTA: instantiating (320) with fresh symbols all_198_0,
% 22.34/3.79  | | | | | | | | | | | | | |        all_198_1, all_198_2 gives:
% 22.34/3.79  | | | | | | | | | | | | | |   (330)  sdtpldt0(xr, xp) = all_198_0 & aNaturalNumber0(xr)
% 22.34/3.79  | | | | | | | | | | | | | |          = all_198_1 & aNaturalNumber0(xp) = all_198_2 &
% 22.34/3.79  | | | | | | | | | | | | | |          $i(all_198_0) & ( ~ (all_198_1 = 0) |  ~
% 22.34/3.79  | | | | | | | | | | | | | |            (all_198_2 = 0) | all_198_0 = all_70_5)
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | ALPHA: (330) implies:
% 22.34/3.79  | | | | | | | | | | | | | |   (331)  aNaturalNumber0(xr) = all_198_1
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | DELTA: instantiating (324) with fresh symbols all_200_0,
% 22.34/3.79  | | | | | | | | | | | | | |        all_200_1, all_200_2, all_200_3, all_200_4,
% 22.34/3.79  | | | | | | | | | | | | | |        all_200_5, all_200_6, all_200_7, all_200_8 gives:
% 22.34/3.79  | | | | | | | | | | | | | |   (332)  sdtasdt0(all_200_5, xl) = all_200_3 &
% 22.34/3.79  | | | | | | | | | | | | | |          sdtasdt0(all_114_0, xl) = all_200_2 & sdtasdt0(xr,
% 22.34/3.79  | | | | | | | | | | | | | |            xl) = all_200_1 & sdtasdt0(xl, all_200_5) =
% 22.34/3.79  | | | | | | | | | | | | | |          all_200_4 & sdtpldt0(all_200_2, all_200_1) =
% 22.34/3.79  | | | | | | | | | | | | | |          all_200_0 & sdtpldt0(all_114_0, xr) = all_200_5 &
% 22.34/3.79  | | | | | | | | | | | | | |          aNaturalNumber0(all_114_0) = all_200_7 &
% 22.34/3.79  | | | | | | | | | | | | | |          aNaturalNumber0(xr) = all_200_6 &
% 22.34/3.79  | | | | | | | | | | | | | |          aNaturalNumber0(xl) = all_200_8 & $i(all_200_0) &
% 22.34/3.79  | | | | | | | | | | | | | |          $i(all_200_1) & $i(all_200_2) & $i(all_200_3) &
% 22.34/3.79  | | | | | | | | | | | | | |          $i(all_200_4) & $i(all_200_5) & ( ~ (all_200_6 =
% 22.34/3.79  | | | | | | | | | | | | | |              0) |  ~ (all_200_7 = 0) |  ~ (all_200_8 = 0) |
% 22.34/3.79  | | | | | | | | | | | | | |            (all_200_0 = all_200_3 & all_200_4 = all_33_0))
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | ALPHA: (332) implies:
% 22.34/3.79  | | | | | | | | | | | | | |   (333)  aNaturalNumber0(xr) = all_200_6
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | DELTA: instantiating (323) with fresh symbols all_202_0,
% 22.34/3.79  | | | | | | | | | | | | | |        all_202_1, all_202_2, all_202_3, all_202_4,
% 22.34/3.79  | | | | | | | | | | | | | |        all_202_5, all_202_6, all_202_7, all_202_8 gives:
% 22.34/3.79  | | | | | | | | | | | | | |   (334)  sdtasdt0(all_202_5, xl) = all_202_3 &
% 22.34/3.79  | | | | | | | | | | | | | |          sdtasdt0(all_114_0, xl) = all_202_1 & sdtasdt0(xr,
% 22.34/3.79  | | | | | | | | | | | | | |            xl) = all_202_2 & sdtasdt0(xl, all_202_5) =
% 22.34/3.79  | | | | | | | | | | | | | |          all_202_4 & sdtpldt0(all_202_2, all_202_1) =
% 22.34/3.79  | | | | | | | | | | | | | |          all_202_0 & sdtpldt0(xr, all_114_0) = all_202_5 &
% 22.34/3.79  | | | | | | | | | | | | | |          aNaturalNumber0(all_114_0) = all_202_6 &
% 22.34/3.79  | | | | | | | | | | | | | |          aNaturalNumber0(xr) = all_202_7 &
% 22.34/3.79  | | | | | | | | | | | | | |          aNaturalNumber0(xl) = all_202_8 & $i(all_202_0) &
% 22.34/3.79  | | | | | | | | | | | | | |          $i(all_202_1) & $i(all_202_2) & $i(all_202_3) &
% 22.34/3.79  | | | | | | | | | | | | | |          $i(all_202_4) & $i(all_202_5) & ( ~ (all_202_6 =
% 22.34/3.79  | | | | | | | | | | | | | |              0) |  ~ (all_202_7 = 0) |  ~ (all_202_8 = 0) |
% 22.34/3.79  | | | | | | | | | | | | | |            (all_202_0 = all_202_3 & all_202_4 = all_64_0))
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | ALPHA: (334) implies:
% 22.34/3.79  | | | | | | | | | | | | | |   (335)  aNaturalNumber0(xr) = all_202_7
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | DELTA: instantiating (322) with fresh symbols all_204_0,
% 22.34/3.79  | | | | | | | | | | | | | |        all_204_1, all_204_2, all_204_3, all_204_4,
% 22.34/3.79  | | | | | | | | | | | | | |        all_204_5, all_204_6, all_204_7, all_204_8 gives:
% 22.34/3.79  | | | | | | | | | | | | | |   (336)  sdtasdt0(all_204_5, xl) = all_204_3 & sdtasdt0(xr,
% 22.34/3.79  | | | | | | | | | | | | | |            xl) = all_204_2 & sdtasdt0(xp, xl) = all_204_1 &
% 22.34/3.79  | | | | | | | | | | | | | |          sdtasdt0(xl, all_204_5) = all_204_4 &
% 22.34/3.79  | | | | | | | | | | | | | |          sdtpldt0(all_204_2, all_204_1) = all_204_0 &
% 22.34/3.79  | | | | | | | | | | | | | |          sdtpldt0(xr, xp) = all_204_5 & aNaturalNumber0(xr)
% 22.34/3.79  | | | | | | | | | | | | | |          = all_204_7 & aNaturalNumber0(xp) = all_204_6 &
% 22.34/3.79  | | | | | | | | | | | | | |          aNaturalNumber0(xl) = all_204_8 & $i(all_204_0) &
% 22.34/3.79  | | | | | | | | | | | | | |          $i(all_204_1) & $i(all_204_2) & $i(all_204_3) &
% 22.34/3.79  | | | | | | | | | | | | | |          $i(all_204_4) & $i(all_204_5) & ( ~ (all_204_6 =
% 22.34/3.79  | | | | | | | | | | | | | |              0) |  ~ (all_204_7 = 0) |  ~ (all_204_8 = 0) |
% 22.34/3.79  | | | | | | | | | | | | | |            (all_204_0 = all_204_3 & all_204_4 = all_64_0))
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | ALPHA: (336) implies:
% 22.34/3.79  | | | | | | | | | | | | | |   (337)  aNaturalNumber0(xr) = all_204_7
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_198_1, all_200_6, xr,
% 22.34/3.79  | | | | | | | | | | | | | |              simplifying with (331), (333) gives:
% 22.34/3.79  | | | | | | | | | | | | | |   (338)  all_200_6 = all_198_1
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_186_1, all_200_6, xr,
% 22.34/3.79  | | | | | | | | | | | | | |              simplifying with (329), (333) gives:
% 22.34/3.79  | | | | | | | | | | | | | |   (339)  all_200_6 = all_186_1
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_200_6, all_202_7, xr,
% 22.34/3.79  | | | | | | | | | | | | | |              simplifying with (333), (335) gives:
% 22.34/3.79  | | | | | | | | | | | | | |   (340)  all_202_7 = all_200_6
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_180_2, all_202_7, xr,
% 22.34/3.79  | | | | | | | | | | | | | |              simplifying with (327), (335) gives:
% 22.34/3.79  | | | | | | | | | | | | | |   (341)  all_202_7 = all_180_2
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_202_7, xr,
% 22.34/3.79  | | | | | | | | | | | | | |              simplifying with (319), (335) gives:
% 22.34/3.79  | | | | | | | | | | | | | |   (342)  all_202_7 = 0
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_50_1, all_204_7, xr,
% 22.34/3.79  | | | | | | | | | | | | | |              simplifying with (68), (337) gives:
% 22.34/3.79  | | | | | | | | | | | | | |   (343)  all_204_7 = all_50_1
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_198_1, all_204_7, xr,
% 22.34/3.79  | | | | | | | | | | | | | |              simplifying with (331), (337) gives:
% 22.34/3.79  | | | | | | | | | | | | | |   (344)  all_204_7 = all_198_1
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | COMBINE_EQS: (343), (344) imply:
% 22.34/3.79  | | | | | | | | | | | | | |   (345)  all_198_1 = all_50_1
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | SIMP: (345) implies:
% 22.34/3.79  | | | | | | | | | | | | | |   (346)  all_198_1 = all_50_1
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | COMBINE_EQS: (340), (341) imply:
% 22.34/3.79  | | | | | | | | | | | | | |   (347)  all_200_6 = all_180_2
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | SIMP: (347) implies:
% 22.34/3.79  | | | | | | | | | | | | | |   (348)  all_200_6 = all_180_2
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | COMBINE_EQS: (341), (342) imply:
% 22.34/3.79  | | | | | | | | | | | | | |   (349)  all_180_2 = 0
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | COMBINE_EQS: (338), (339) imply:
% 22.34/3.79  | | | | | | | | | | | | | |   (350)  all_198_1 = all_186_1
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | SIMP: (350) implies:
% 22.34/3.79  | | | | | | | | | | | | | |   (351)  all_198_1 = all_186_1
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | COMBINE_EQS: (339), (348) imply:
% 22.34/3.79  | | | | | | | | | | | | | |   (352)  all_186_1 = all_180_2
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | COMBINE_EQS: (346), (351) imply:
% 22.34/3.79  | | | | | | | | | | | | | |   (353)  all_186_1 = all_50_1
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | SIMP: (353) implies:
% 22.34/3.79  | | | | | | | | | | | | | |   (354)  all_186_1 = all_50_1
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | COMBINE_EQS: (352), (354) imply:
% 22.34/3.79  | | | | | | | | | | | | | |   (355)  all_180_2 = all_50_1
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | SIMP: (355) implies:
% 22.34/3.79  | | | | | | | | | | | | | |   (356)  all_180_2 = all_50_1
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | COMBINE_EQS: (349), (356) imply:
% 22.34/3.79  | | | | | | | | | | | | | |   (357)  all_50_1 = 0
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | REDUCE: (286), (357) imply:
% 22.34/3.79  | | | | | | | | | | | | | |   (358)  $false
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | | CLOSE: (358) is inconsistent.
% 22.34/3.79  | | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | | End of split
% 22.34/3.79  | | | | | | | | | | | | | 
% 22.34/3.79  | | | | | | | | | | | | Case 2:
% 22.34/3.79  | | | | | | | | | | | | | 
% 22.34/3.80  | | | | | | | | | | | | |   (359)   ~ (all_50_2 = 0) | all_50_0 = 0
% 22.34/3.80  | | | | | | | | | | | | | 
% 22.34/3.80  | | | | | | | | | | | | | BETA: splitting (359) gives:
% 22.34/3.80  | | | | | | | | | | | | | 
% 22.34/3.80  | | | | | | | | | | | | | Case 1:
% 22.34/3.80  | | | | | | | | | | | | | | 
% 22.34/3.80  | | | | | | | | | | | | | |   (360)   ~ (all_50_2 = 0)
% 22.34/3.80  | | | | | | | | | | | | | | 
% 22.34/3.80  | | | | | | | | | | | | | | REDUCE: (156), (360) imply:
% 22.34/3.80  | | | | | | | | | | | | | |   (361)  $false
% 22.34/3.80  | | | | | | | | | | | | | | 
% 22.34/3.80  | | | | | | | | | | | | | | CLOSE: (361) is inconsistent.
% 22.34/3.80  | | | | | | | | | | | | | | 
% 22.34/3.80  | | | | | | | | | | | | | Case 2:
% 22.34/3.80  | | | | | | | | | | | | | | 
% 22.34/3.80  | | | | | | | | | | | | | |   (362)  all_50_0 = 0
% 22.34/3.80  | | | | | | | | | | | | | | 
% 22.34/3.80  | | | | | | | | | | | | | | REDUCE: (285), (362) imply:
% 22.34/3.80  | | | | | | | | | | | | | |   (363)  $false
% 22.34/3.80  | | | | | | | | | | | | | | 
% 22.34/3.80  | | | | | | | | | | | | | | CLOSE: (363) is inconsistent.
% 22.34/3.80  | | | | | | | | | | | | | | 
% 22.34/3.80  | | | | | | | | | | | | | End of split
% 22.34/3.80  | | | | | | | | | | | | | 
% 22.34/3.80  | | | | | | | | | | | | End of split
% 22.34/3.80  | | | | | | | | | | | | 
% 22.34/3.80  | | | | | | | | | | | Case 2:
% 22.34/3.80  | | | | | | | | | | | | 
% 22.34/3.80  | | | | | | | | | | | |   (364)   ~ (all_131_3 = 0) |  ~ (all_131_4 = 0)
% 22.34/3.80  | | | | | | | | | | | | 
% 22.34/3.80  | | | | | | | | | | | | BETA: splitting (364) gives:
% 22.34/3.80  | | | | | | | | | | | | 
% 22.34/3.80  | | | | | | | | | | | | Case 1:
% 22.34/3.80  | | | | | | | | | | | | | 
% 22.34/3.80  | | | | | | | | | | | | |   (365)   ~ (all_131_3 = 0)
% 22.34/3.80  | | | | | | | | | | | | | 
% 22.34/3.80  | | | | | | | | | | | | | REDUCE: (279), (365) imply:
% 22.34/3.80  | | | | | | | | | | | | |   (366)  $false
% 22.34/3.80  | | | | | | | | | | | | | 
% 22.34/3.80  | | | | | | | | | | | | | CLOSE: (366) is inconsistent.
% 22.34/3.80  | | | | | | | | | | | | | 
% 22.34/3.80  | | | | | | | | | | | | Case 2:
% 22.34/3.80  | | | | | | | | | | | | | 
% 22.34/3.80  | | | | | | | | | | | | |   (367)   ~ (all_131_4 = 0)
% 22.34/3.80  | | | | | | | | | | | | | 
% 22.34/3.80  | | | | | | | | | | | | | REDUCE: (283), (367) imply:
% 22.34/3.80  | | | | | | | | | | | | |   (368)  $false
% 22.34/3.80  | | | | | | | | | | | | | 
% 22.34/3.80  | | | | | | | | | | | | | CLOSE: (368) is inconsistent.
% 22.34/3.80  | | | | | | | | | | | | | 
% 22.34/3.80  | | | | | | | | | | | | End of split
% 22.34/3.80  | | | | | | | | | | | | 
% 22.34/3.80  | | | | | | | | | | | End of split
% 22.34/3.80  | | | | | | | | | | | 
% 22.34/3.80  | | | | | | | | | | End of split
% 22.34/3.80  | | | | | | | | | | 
% 22.34/3.80  | | | | | | | | | End of split
% 22.34/3.80  | | | | | | | | | 
% 22.34/3.80  | | | | | | | | End of split
% 22.34/3.80  | | | | | | | | 
% 22.34/3.80  | | | | | | | End of split
% 22.34/3.80  | | | | | | | 
% 22.34/3.80  | | | | | | End of split
% 22.34/3.80  | | | | | | 
% 22.34/3.80  | | | | | End of split
% 22.34/3.80  | | | | | 
% 22.34/3.80  | | | | End of split
% 22.34/3.80  | | | | 
% 22.34/3.80  | | | End of split
% 22.34/3.80  | | | 
% 22.34/3.80  | | End of split
% 22.34/3.80  | | 
% 22.34/3.80  | End of split
% 22.34/3.80  | 
% 22.34/3.80  End of proof
% 22.34/3.80  % SZS output end Proof for theBenchmark
% 22.34/3.80  
% 22.34/3.80  3237ms
%------------------------------------------------------------------------------