TSTP Solution File: NUM536+2 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : NUM536+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n019.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 11:48:27 EDT 2023

% Result   : Theorem 14.07s 2.58s
% Output   : Proof 15.64s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : NUM536+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.33  % Computer : n019.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Fri Aug 25 10:33:28 EDT 2023
% 0.11/0.33  % CPUTime  : 
% 0.18/0.61  ________       _____
% 0.18/0.61  ___  __ \_________(_)________________________________
% 0.18/0.61  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.18/0.61  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.18/0.61  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.18/0.61  
% 0.18/0.61  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.61  (2023-06-19)
% 0.18/0.61  
% 0.18/0.61  (c) Philipp Rümmer, 2009-2023
% 0.18/0.61  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.61                Amanda Stjerna.
% 0.18/0.61  Free software under BSD-3-Clause.
% 0.18/0.61  
% 0.18/0.61  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.61  
% 0.18/0.61  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.18/0.62  Running up to 7 provers in parallel.
% 0.18/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.22/1.03  Prover 1: Preprocessing ...
% 2.22/1.05  Prover 4: Preprocessing ...
% 2.89/1.07  Prover 3: Preprocessing ...
% 2.89/1.07  Prover 2: Preprocessing ...
% 2.89/1.07  Prover 0: Preprocessing ...
% 2.89/1.07  Prover 5: Preprocessing ...
% 2.89/1.07  Prover 6: Preprocessing ...
% 5.67/1.54  Prover 1: Constructing countermodel ...
% 5.67/1.54  Prover 5: Constructing countermodel ...
% 6.55/1.56  Prover 3: Constructing countermodel ...
% 6.55/1.58  Prover 2: Proving ...
% 6.55/1.58  Prover 6: Proving ...
% 7.89/1.75  Prover 4: Constructing countermodel ...
% 8.75/1.87  Prover 0: Proving ...
% 14.07/2.58  Prover 3: proved (1945ms)
% 14.07/2.58  
% 14.07/2.58  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.07/2.58  
% 14.07/2.58  Prover 6: stopped
% 14.07/2.59  Prover 5: stopped
% 14.07/2.60  Prover 2: stopped
% 14.07/2.60  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.07/2.60  Prover 0: stopped
% 14.07/2.62  Prover 1: Found proof (size 119)
% 14.07/2.62  Prover 1: proved (1964ms)
% 14.07/2.62  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.07/2.62  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 14.07/2.62  Prover 7: Preprocessing ...
% 14.07/2.62  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.07/2.62  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.07/2.62  Prover 4: stopped
% 14.07/2.62  Prover 7: stopped
% 14.07/2.62  Prover 10: Preprocessing ...
% 14.07/2.63  Prover 8: Preprocessing ...
% 14.07/2.64  Prover 10: stopped
% 14.64/2.66  Prover 11: Preprocessing ...
% 14.64/2.66  Prover 13: Preprocessing ...
% 14.77/2.68  Prover 13: stopped
% 14.77/2.70  Prover 11: stopped
% 14.77/2.71  Prover 8: Warning: ignoring some quantifiers
% 14.77/2.71  Prover 8: Constructing countermodel ...
% 14.77/2.71  Prover 8: stopped
% 14.77/2.71  
% 14.77/2.71  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.77/2.71  
% 14.77/2.72  % SZS output start Proof for theBenchmark
% 14.77/2.73  Assumptions after simplification:
% 14.77/2.73  ---------------------------------
% 14.77/2.73  
% 14.77/2.73    (mDefCons)
% 14.77/2.76     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) |  ~
% 14.77/2.76      $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] : (aSet0(v0) = v3 &
% 14.77/2.76        aElement0(v1) = v4 & ( ~ (v4 = 0) |  ~ (v3 = 0))) | ( ! [v3: $i] : (v3 =
% 14.77/2.76          v2 |  ~ (aSet0(v3) = 0) |  ~ $i(v3) |  ? [v4: $i] :  ? [v5: any] :  ?
% 14.77/2.76          [v6: any] :  ? [v7: any] : (aElement0(v4) = v6 & aElementOf0(v4, v3) =
% 14.77/2.76            v5 & aElementOf0(v4, v0) = v7 & $i(v4) & ( ~ (v6 = 0) |  ~ (v5 = 0) |
% 14.77/2.76              ( ~ (v7 = 0) &  ~ (v4 = v1))) & (v5 = 0 | (v6 = 0 & (v7 = 0 | v4 =
% 14.77/2.76                  v1))))) &  ! [v3: any] : ( ~ (aSet0(v2) = v3) |  ~ $i(v2) | (v3
% 14.77/2.76            = 0 &  ! [v4: $i] :  ! [v5: any] : ( ~ (aElement0(v4) = v5) |  ~
% 14.77/2.76              $i(v4) |  ? [v6: any] :  ? [v7: any] : (aElementOf0(v4, v2) = v6 &
% 14.77/2.76                aElementOf0(v4, v0) = v7 & ( ~ (v6 = 0) | (v5 = 0 & (v7 = 0 | v4 =
% 14.77/2.76                      v1))))) &  ! [v4: $i] : ( ~ (aElement0(v4) = 0) |  ~ $i(v4)
% 14.77/2.76              |  ? [v5: any] :  ? [v6: any] : (aElementOf0(v4, v2) = v6 &
% 14.77/2.76                aElementOf0(v4, v0) = v5 & (v6 = 0 | ( ~ (v5 = 0) &  ~ (v4 =
% 14.77/2.76                      v1)))))))))
% 14.77/2.76  
% 14.77/2.76    (mDefDiff)
% 14.77/2.77     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (sdtmndt0(v0, v1) = v2) |  ~
% 14.77/2.77      $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] : (aSet0(v0) = v3 &
% 14.77/2.77        aElement0(v1) = v4 & ( ~ (v4 = 0) |  ~ (v3 = 0))) | ( ! [v3: $i] : (v3 =
% 14.77/2.77          v2 |  ~ (aSet0(v3) = 0) |  ~ $i(v3) |  ? [v4: $i] :  ? [v5: any] :  ?
% 14.77/2.77          [v6: any] :  ? [v7: any] : (aElement0(v4) = v6 & aElementOf0(v4, v3) =
% 14.77/2.77            v5 & aElementOf0(v4, v0) = v7 & $i(v4) & ( ~ (v7 = 0) |  ~ (v6 = 0) | 
% 14.77/2.77              ~ (v5 = 0) | v4 = v1) & (v5 = 0 | (v7 = 0 & v6 = 0 &  ~ (v4 =
% 14.77/2.77                  v1))))) &  ! [v3: any] : ( ~ (aSet0(v2) = v3) |  ~ $i(v2) | (v3
% 14.77/2.77            = 0 &  ! [v4: $i] :  ! [v5: any] : ( ~ (aElement0(v4) = v5) |  ~
% 14.77/2.77              $i(v4) |  ? [v6: any] :  ? [v7: any] : (aElementOf0(v4, v2) = v6 &
% 14.77/2.77                aElementOf0(v4, v0) = v7 & ( ~ (v6 = 0) | (v7 = 0 & v5 = 0 &  ~
% 14.77/2.77                    (v4 = v1))))) &  ! [v4: $i] : (v4 = v1 |  ~ (aElement0(v4) =
% 14.77/2.77                0) |  ~ $i(v4) |  ? [v5: any] :  ? [v6: any] : (aElementOf0(v4,
% 14.77/2.77                  v2) = v6 & aElementOf0(v4, v0) = v5 & ( ~ (v5 = 0) | v6 =
% 14.77/2.77                  0)))))))
% 14.77/2.77  
% 14.77/2.77    (mEOfElem)
% 14.77/2.77     ! [v0: $i] : ( ~ (aSet0(v0) = 0) |  ~ $i(v0) |  ! [v1: $i] :  ! [v2: int] :
% 14.77/2.77      (v2 = 0 |  ~ (aElement0(v1) = v2) |  ~ $i(v1) |  ? [v3: int] : ( ~ (v3 = 0)
% 14.77/2.77          & aElementOf0(v1, v0) = v3)))
% 14.77/2.77  
% 14.77/2.77    (m__)
% 14.77/2.77    $i(xS) & $i(xx) &  ? [v0: $i] :  ? [v1: $i] : ( ~ (v1 = xS) & sdtmndt0(v0, xx)
% 14.77/2.77      = v1 & sdtpldt0(xS, xx) = v0 & aSet0(v1) = 0 & aSet0(v0) = 0 & $i(v1) &
% 14.77/2.77      $i(v0) &  ! [v2: $i] :  ! [v3: int] : (v3 = 0 | v2 = xx |  ~
% 14.77/2.77        (aElementOf0(v2, v1) = v3) |  ~ $i(v2) |  ? [v4: any] :  ? [v5: any] :
% 14.77/2.77        (aElement0(v2) = v4 & aElementOf0(v2, v0) = v5 & ( ~ (v5 = 0) |  ~ (v4 =
% 14.77/2.77              0)))) &  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~ (aElementOf0(v2,
% 14.77/2.77            v0) = v3) |  ~ $i(v2) |  ? [v4: any] :  ? [v5: any] : (aElement0(v2) =
% 14.77/2.77          v4 & aElementOf0(v2, xS) = v5 & ( ~ (v4 = 0) | ( ~ (v5 = 0) &  ~ (v2 =
% 14.77/2.77                xx))))) &  ! [v2: $i] : ( ~ (aElementOf0(v2, v1) = 0) |  ~ $i(v2)
% 14.77/2.77        | ( ~ (v2 = xx) & aElement0(v2) = 0 & aElementOf0(v2, v0) = 0)) &  ! [v2:
% 14.77/2.77        $i] : ( ~ (aElementOf0(v2, v0) = 0) |  ~ $i(v2) |  ? [v3: any] :
% 14.77/2.77        (aElement0(v2) = 0 & aElementOf0(v2, xS) = v3 & (v3 = 0 | v2 = xx))))
% 14.77/2.77  
% 14.77/2.77    (m__679)
% 14.77/2.77    aSet0(xS) = 0 & aElement0(xx) = 0 & $i(xS) & $i(xx)
% 14.77/2.77  
% 14.77/2.77    (m__679_02)
% 14.77/2.77    $i(xS) & $i(xx) &  ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(xx, xS) = v0)
% 14.77/2.77  
% 14.77/2.77    (function-axioms)
% 14.77/2.78     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 14.77/2.78      (sdtmndt0(v3, v2) = v1) |  ~ (sdtmndt0(v3, v2) = v0)) &  ! [v0: $i] :  !
% 14.77/2.78    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (sdtpldt0(v3, v2) = v1) |
% 14.77/2.78       ~ (sdtpldt0(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 14.77/2.78      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 14.77/2.78      (aSubsetOf0(v3, v2) = v1) |  ~ (aSubsetOf0(v3, v2) = v0)) &  ! [v0:
% 14.77/2.78      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 14.77/2.78    : (v1 = v0 |  ~ (aElementOf0(v3, v2) = v1) |  ~ (aElementOf0(v3, v2) = v0)) & 
% 14.77/2.78    ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 =
% 14.77/2.78      v0 |  ~ (isCountable0(v2) = v1) |  ~ (isCountable0(v2) = v0)) &  ! [v0:
% 14.77/2.78      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 14.77/2.78      ~ (isFinite0(v2) = v1) |  ~ (isFinite0(v2) = v0)) &  ! [v0:
% 14.77/2.78      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 14.77/2.78      ~ (aSet0(v2) = v1) |  ~ (aSet0(v2) = v0)) &  ! [v0: MultipleValueBool] :  !
% 14.77/2.78    [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (aElement0(v2) = v1) | 
% 14.77/2.78      ~ (aElement0(v2) = v0))
% 14.77/2.78  
% 14.77/2.78  Further assumptions not needed in the proof:
% 14.77/2.78  --------------------------------------------
% 14.77/2.78  mCntRel, mConsDiff, mCountNFin, mCountNFin_01, mDefEmp, mDefSub, mElmSort,
% 14.77/2.78  mEmpFin, mFinRel, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans
% 14.77/2.78  
% 14.77/2.78  Those formulas are unsatisfiable:
% 14.77/2.78  ---------------------------------
% 14.77/2.78  
% 14.77/2.78  Begin of proof
% 14.77/2.78  | 
% 14.77/2.78  | ALPHA: (m__679) implies:
% 14.77/2.78  |   (1)  aElement0(xx) = 0
% 14.77/2.78  |   (2)  aSet0(xS) = 0
% 14.77/2.78  | 
% 14.77/2.78  | ALPHA: (m__679_02) implies:
% 14.77/2.78  |   (3)   ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(xx, xS) = v0)
% 14.77/2.78  | 
% 14.77/2.78  | ALPHA: (m__) implies:
% 14.77/2.78  |   (4)  $i(xx)
% 14.77/2.78  |   (5)  $i(xS)
% 14.77/2.78  |   (6)   ? [v0: $i] :  ? [v1: $i] : ( ~ (v1 = xS) & sdtmndt0(v0, xx) = v1 &
% 14.77/2.78  |          sdtpldt0(xS, xx) = v0 & aSet0(v1) = 0 & aSet0(v0) = 0 & $i(v1) &
% 14.77/2.78  |          $i(v0) &  ! [v2: $i] :  ! [v3: int] : (v3 = 0 | v2 = xx |  ~
% 14.77/2.78  |            (aElementOf0(v2, v1) = v3) |  ~ $i(v2) |  ? [v4: any] :  ? [v5:
% 14.77/2.78  |              any] : (aElement0(v2) = v4 & aElementOf0(v2, v0) = v5 & ( ~ (v5 =
% 14.77/2.78  |                  0) |  ~ (v4 = 0)))) &  ! [v2: $i] :  ! [v3: int] : (v3 = 0 | 
% 14.77/2.78  |            ~ (aElementOf0(v2, v0) = v3) |  ~ $i(v2) |  ? [v4: any] :  ? [v5:
% 14.77/2.78  |              any] : (aElement0(v2) = v4 & aElementOf0(v2, xS) = v5 & ( ~ (v4 =
% 14.77/2.78  |                  0) | ( ~ (v5 = 0) &  ~ (v2 = xx))))) &  ! [v2: $i] : ( ~
% 14.77/2.78  |            (aElementOf0(v2, v1) = 0) |  ~ $i(v2) | ( ~ (v2 = xx) &
% 14.77/2.78  |              aElement0(v2) = 0 & aElementOf0(v2, v0) = 0)) &  ! [v2: $i] : ( ~
% 14.77/2.78  |            (aElementOf0(v2, v0) = 0) |  ~ $i(v2) |  ? [v3: any] :
% 14.77/2.78  |            (aElement0(v2) = 0 & aElementOf0(v2, xS) = v3 & (v3 = 0 | v2 =
% 14.77/2.78  |                xx))))
% 14.77/2.78  | 
% 14.77/2.78  | ALPHA: (function-axioms) implies:
% 14.77/2.79  |   (7)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 14.77/2.79  |        (v1 = v0 |  ~ (aElement0(v2) = v1) |  ~ (aElement0(v2) = v0))
% 14.77/2.79  |   (8)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 14.77/2.79  |        (v1 = v0 |  ~ (aSet0(v2) = v1) |  ~ (aSet0(v2) = v0))
% 14.77/2.79  |   (9)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 14.77/2.79  |         ! [v3: $i] : (v1 = v0 |  ~ (aElementOf0(v3, v2) = v1) |  ~
% 14.77/2.79  |          (aElementOf0(v3, v2) = v0))
% 14.77/2.79  | 
% 14.77/2.79  | DELTA: instantiating (3) with fresh symbol all_15_0 gives:
% 14.77/2.79  |   (10)   ~ (all_15_0 = 0) & aElementOf0(xx, xS) = all_15_0
% 14.77/2.79  | 
% 14.77/2.79  | ALPHA: (10) implies:
% 14.77/2.79  |   (11)   ~ (all_15_0 = 0)
% 14.77/2.79  |   (12)  aElementOf0(xx, xS) = all_15_0
% 14.77/2.79  | 
% 14.77/2.79  | DELTA: instantiating (6) with fresh symbols all_17_0, all_17_1 gives:
% 14.77/2.79  |   (13)   ~ (all_17_0 = xS) & sdtmndt0(all_17_1, xx) = all_17_0 & sdtpldt0(xS,
% 14.77/2.79  |           xx) = all_17_1 & aSet0(all_17_0) = 0 & aSet0(all_17_1) = 0 &
% 14.77/2.79  |         $i(all_17_0) & $i(all_17_1) &  ! [v0: $i] :  ! [v1: int] : (v1 = 0 |
% 14.77/2.79  |           v0 = xx |  ~ (aElementOf0(v0, all_17_0) = v1) |  ~ $i(v0) |  ? [v2:
% 14.77/2.79  |             any] :  ? [v3: any] : (aElement0(v0) = v2 & aElementOf0(v0,
% 14.77/2.79  |               all_17_1) = v3 & ( ~ (v3 = 0) |  ~ (v2 = 0)))) &  ! [v0: $i] : 
% 14.77/2.79  |         ! [v1: int] : (v1 = 0 |  ~ (aElementOf0(v0, all_17_1) = v1) |  ~
% 14.77/2.79  |           $i(v0) |  ? [v2: any] :  ? [v3: any] : (aElement0(v0) = v2 &
% 14.77/2.79  |             aElementOf0(v0, xS) = v3 & ( ~ (v2 = 0) | ( ~ (v3 = 0) &  ~ (v0 =
% 14.77/2.79  |                   xx))))) &  ! [v0: $i] : ( ~ (aElementOf0(v0, all_17_0) = 0)
% 14.77/2.79  |           |  ~ $i(v0) | ( ~ (v0 = xx) & aElement0(v0) = 0 & aElementOf0(v0,
% 14.77/2.79  |               all_17_1) = 0)) &  ! [v0: $i] : ( ~ (aElementOf0(v0, all_17_1) =
% 14.77/2.79  |             0) |  ~ $i(v0) |  ? [v1: any] : (aElement0(v0) = 0 &
% 14.77/2.79  |             aElementOf0(v0, xS) = v1 & (v1 = 0 | v0 = xx)))
% 14.77/2.79  | 
% 14.77/2.79  | ALPHA: (13) implies:
% 14.77/2.79  |   (14)   ~ (all_17_0 = xS)
% 14.77/2.79  |   (15)  $i(all_17_1)
% 14.77/2.79  |   (16)  $i(all_17_0)
% 14.77/2.79  |   (17)  aSet0(all_17_1) = 0
% 14.77/2.79  |   (18)  aSet0(all_17_0) = 0
% 14.77/2.79  |   (19)  sdtpldt0(xS, xx) = all_17_1
% 14.77/2.79  |   (20)  sdtmndt0(all_17_1, xx) = all_17_0
% 14.77/2.79  |   (21)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (aElementOf0(v0, all_17_1) =
% 14.77/2.79  |             v1) |  ~ $i(v0) |  ? [v2: any] :  ? [v3: any] : (aElement0(v0) =
% 14.77/2.79  |             v2 & aElementOf0(v0, xS) = v3 & ( ~ (v2 = 0) | ( ~ (v3 = 0) &  ~
% 14.77/2.79  |                 (v0 = xx)))))
% 14.77/2.79  | 
% 14.77/2.79  | GROUND_INST: instantiating (mEOfElem) with xS, simplifying with (2), (5)
% 14.77/2.79  |              gives:
% 14.77/2.79  |   (22)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (aElement0(v0) = v1) |  ~
% 14.77/2.79  |           $i(v0) |  ? [v2: int] : ( ~ (v2 = 0) & aElementOf0(v0, xS) = v2))
% 14.77/2.79  | 
% 14.77/2.79  | GROUND_INST: instantiating (mDefCons) with xS, xx, all_17_1, simplifying with
% 14.77/2.79  |              (4), (5), (19) gives:
% 14.77/2.80  |   (23)   ? [v0: any] :  ? [v1: any] : (aSet0(xS) = v0 & aElement0(xx) = v1 & (
% 14.77/2.80  |             ~ (v1 = 0) |  ~ (v0 = 0))) | ( ! [v0: any] : (v0 = all_17_1 |  ~
% 14.77/2.80  |             (aSet0(v0) = 0) |  ~ $i(v0) |  ? [v1: $i] :  ? [v2: any] :  ? [v3:
% 14.77/2.80  |               any] :  ? [v4: any] : (aElement0(v1) = v3 & aElementOf0(v1, v0)
% 14.77/2.80  |               = v2 & aElementOf0(v1, xS) = v4 & $i(v1) & ( ~ (v3 = 0) |  ~ (v2
% 14.77/2.80  |                   = 0) | ( ~ (v4 = 0) &  ~ (v1 = xx))) & (v2 = 0 | (v3 = 0 &
% 14.77/2.80  |                   (v4 = 0 | v1 = xx))))) &  ! [v0: any] : ( ~ (aSet0(all_17_1)
% 14.77/2.80  |               = v0) |  ~ $i(all_17_1) | (v0 = 0 &  ! [v1: $i] :  ! [v2: any] :
% 14.77/2.80  |               ( ~ (aElement0(v1) = v2) |  ~ $i(v1) |  ? [v3: any] :  ? [v4:
% 14.77/2.80  |                   any] : (aElementOf0(v1, all_17_1) = v3 & aElementOf0(v1, xS)
% 14.77/2.80  |                   = v4 & ( ~ (v3 = 0) | (v2 = 0 & (v4 = 0 | v1 = xx))))) &  !
% 14.77/2.80  |               [v1: $i] : ( ~ (aElement0(v1) = 0) |  ~ $i(v1) |  ? [v2: any] : 
% 14.77/2.80  |                 ? [v3: any] : (aElementOf0(v1, all_17_1) = v3 &
% 14.77/2.80  |                   aElementOf0(v1, xS) = v2 & (v3 = 0 | ( ~ (v2 = 0) &  ~ (v1 =
% 14.77/2.80  |                         xx))))))))
% 14.77/2.80  | 
% 14.77/2.80  | GROUND_INST: instantiating (mDefDiff) with all_17_1, xx, all_17_0, simplifying
% 14.77/2.80  |              with (4), (15), (20) gives:
% 14.77/2.80  |   (24)   ? [v0: any] :  ? [v1: any] : (aSet0(all_17_1) = v0 & aElement0(xx) =
% 14.77/2.80  |           v1 & ( ~ (v1 = 0) |  ~ (v0 = 0))) | ( ! [v0: any] : (v0 = all_17_0 |
% 14.77/2.80  |              ~ (aSet0(v0) = 0) |  ~ $i(v0) |  ? [v1: $i] :  ? [v2: any] :  ?
% 14.77/2.80  |             [v3: any] :  ? [v4: any] : (aElement0(v1) = v3 & aElementOf0(v1,
% 14.77/2.80  |                 v0) = v2 & aElementOf0(v1, all_17_1) = v4 & $i(v1) & ( ~ (v4 =
% 14.77/2.80  |                   0) |  ~ (v3 = 0) |  ~ (v2 = 0) | v1 = xx) & (v2 = 0 | (v4 =
% 14.77/2.80  |                   0 & v3 = 0 &  ~ (v1 = xx))))) &  ! [v0: any] : ( ~
% 14.77/2.80  |             (aSet0(all_17_0) = v0) |  ~ $i(all_17_0) | (v0 = 0 &  ! [v1: $i] :
% 14.77/2.80  |                ! [v2: any] : ( ~ (aElement0(v1) = v2) |  ~ $i(v1) |  ? [v3:
% 14.77/2.80  |                   any] :  ? [v4: any] : (aElementOf0(v1, all_17_0) = v3 &
% 14.77/2.80  |                   aElementOf0(v1, all_17_1) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2
% 14.77/2.80  |                       = 0 &  ~ (v1 = xx))))) &  ! [v1: $i] : (v1 = xx |  ~
% 14.77/2.80  |                 (aElement0(v1) = 0) |  ~ $i(v1) |  ? [v2: any] :  ? [v3: any]
% 14.77/2.80  |                 : (aElementOf0(v1, all_17_0) = v3 & aElementOf0(v1, all_17_1)
% 14.77/2.80  |                   = v2 & ( ~ (v2 = 0) | v3 = 0))))))
% 14.77/2.80  | 
% 14.77/2.80  | BETA: splitting (24) gives:
% 14.77/2.80  | 
% 14.77/2.80  | Case 1:
% 14.77/2.80  | | 
% 14.77/2.80  | |   (25)   ? [v0: any] :  ? [v1: any] : (aSet0(all_17_1) = v0 & aElement0(xx)
% 14.77/2.80  | |           = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 14.77/2.80  | | 
% 14.77/2.80  | | DELTA: instantiating (25) with fresh symbols all_39_0, all_39_1 gives:
% 14.77/2.80  | |   (26)  aSet0(all_17_1) = all_39_1 & aElement0(xx) = all_39_0 & ( ~
% 14.77/2.80  | |           (all_39_0 = 0) |  ~ (all_39_1 = 0))
% 14.77/2.80  | | 
% 14.77/2.80  | | ALPHA: (26) implies:
% 14.77/2.80  | |   (27)  aElement0(xx) = all_39_0
% 14.77/2.80  | |   (28)  aSet0(all_17_1) = all_39_1
% 14.77/2.80  | |   (29)   ~ (all_39_0 = 0) |  ~ (all_39_1 = 0)
% 14.77/2.80  | | 
% 14.77/2.80  | | GROUND_INST: instantiating (7) with 0, all_39_0, xx, simplifying with (1),
% 14.77/2.80  | |              (27) gives:
% 14.77/2.80  | |   (30)  all_39_0 = 0
% 14.77/2.80  | | 
% 14.77/2.80  | | GROUND_INST: instantiating (8) with 0, all_39_1, all_17_1, simplifying with
% 14.77/2.80  | |              (17), (28) gives:
% 14.77/2.80  | |   (31)  all_39_1 = 0
% 14.77/2.80  | | 
% 14.77/2.80  | | BETA: splitting (29) gives:
% 14.77/2.80  | | 
% 14.77/2.80  | | Case 1:
% 14.77/2.80  | | | 
% 14.77/2.80  | | |   (32)   ~ (all_39_0 = 0)
% 14.77/2.80  | | | 
% 14.77/2.80  | | | REDUCE: (30), (32) imply:
% 14.77/2.81  | | |   (33)  $false
% 14.77/2.81  | | | 
% 14.77/2.81  | | | CLOSE: (33) is inconsistent.
% 14.77/2.81  | | | 
% 14.77/2.81  | | Case 2:
% 14.77/2.81  | | | 
% 14.77/2.81  | | |   (34)   ~ (all_39_1 = 0)
% 14.77/2.81  | | | 
% 14.77/2.81  | | | REDUCE: (31), (34) imply:
% 14.77/2.81  | | |   (35)  $false
% 14.77/2.81  | | | 
% 14.77/2.81  | | | CLOSE: (35) is inconsistent.
% 14.77/2.81  | | | 
% 14.77/2.81  | | End of split
% 14.77/2.81  | | 
% 14.77/2.81  | Case 2:
% 14.77/2.81  | | 
% 14.77/2.81  | |   (36)   ! [v0: any] : (v0 = all_17_0 |  ~ (aSet0(v0) = 0) |  ~ $i(v0) |  ?
% 14.77/2.81  | |           [v1: $i] :  ? [v2: any] :  ? [v3: any] :  ? [v4: any] :
% 14.77/2.81  | |           (aElement0(v1) = v3 & aElementOf0(v1, v0) = v2 & aElementOf0(v1,
% 14.77/2.81  | |               all_17_1) = v4 & $i(v1) & ( ~ (v4 = 0) |  ~ (v3 = 0) |  ~ (v2
% 14.77/2.81  | |                 = 0) | v1 = xx) & (v2 = 0 | (v4 = 0 & v3 = 0 &  ~ (v1 =
% 14.77/2.81  | |                   xx))))) &  ! [v0: any] : ( ~ (aSet0(all_17_0) = v0) |  ~
% 14.77/2.81  | |           $i(all_17_0) | (v0 = 0 &  ! [v1: $i] :  ! [v2: any] : ( ~
% 14.77/2.81  | |               (aElement0(v1) = v2) |  ~ $i(v1) |  ? [v3: any] :  ? [v4: any]
% 14.77/2.81  | |               : (aElementOf0(v1, all_17_0) = v3 & aElementOf0(v1, all_17_1)
% 14.77/2.81  | |                 = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0 &  ~ (v1 = xx))))) & 
% 14.77/2.81  | |             ! [v1: $i] : (v1 = xx |  ~ (aElement0(v1) = 0) |  ~ $i(v1) |  ?
% 14.77/2.81  | |               [v2: any] :  ? [v3: any] : (aElementOf0(v1, all_17_0) = v3 &
% 14.77/2.81  | |                 aElementOf0(v1, all_17_1) = v2 & ( ~ (v2 = 0) | v3 = 0)))))
% 14.77/2.81  | | 
% 14.77/2.81  | | ALPHA: (36) implies:
% 14.77/2.81  | |   (37)   ! [v0: any] : ( ~ (aSet0(all_17_0) = v0) |  ~ $i(all_17_0) | (v0 =
% 14.77/2.81  | |             0 &  ! [v1: $i] :  ! [v2: any] : ( ~ (aElement0(v1) = v2) |  ~
% 14.77/2.81  | |               $i(v1) |  ? [v3: any] :  ? [v4: any] : (aElementOf0(v1,
% 14.77/2.81  | |                   all_17_0) = v3 & aElementOf0(v1, all_17_1) = v4 & ( ~ (v3
% 14.77/2.81  | |                     = 0) | (v4 = 0 & v2 = 0 &  ~ (v1 = xx))))) &  ! [v1: $i]
% 14.77/2.81  | |             : (v1 = xx |  ~ (aElement0(v1) = 0) |  ~ $i(v1) |  ? [v2: any] :
% 14.77/2.81  | |                ? [v3: any] : (aElementOf0(v1, all_17_0) = v3 &
% 14.77/2.81  | |                 aElementOf0(v1, all_17_1) = v2 & ( ~ (v2 = 0) | v3 = 0)))))
% 14.77/2.81  | |   (38)   ! [v0: any] : (v0 = all_17_0 |  ~ (aSet0(v0) = 0) |  ~ $i(v0) |  ?
% 14.77/2.81  | |           [v1: $i] :  ? [v2: any] :  ? [v3: any] :  ? [v4: any] :
% 14.77/2.81  | |           (aElement0(v1) = v3 & aElementOf0(v1, v0) = v2 & aElementOf0(v1,
% 14.77/2.81  | |               all_17_1) = v4 & $i(v1) & ( ~ (v4 = 0) |  ~ (v3 = 0) |  ~ (v2
% 14.77/2.81  | |                 = 0) | v1 = xx) & (v2 = 0 | (v4 = 0 & v3 = 0 &  ~ (v1 =
% 14.77/2.81  | |                   xx)))))
% 14.77/2.81  | | 
% 14.77/2.81  | | GROUND_INST: instantiating (38) with xS, simplifying with (2), (5) gives:
% 14.77/2.81  | |   (39)  all_17_0 = xS |  ? [v0: $i] :  ? [v1: any] :  ? [v2: any] :  ? [v3:
% 14.77/2.81  | |           any] : (aElement0(v0) = v2 & aElementOf0(v0, all_17_1) = v3 &
% 14.77/2.81  | |           aElementOf0(v0, xS) = v1 & $i(v0) & ( ~ (v3 = 0) |  ~ (v2 = 0) | 
% 14.77/2.81  | |             ~ (v1 = 0) | v0 = xx) & (v1 = 0 | (v3 = 0 & v2 = 0 &  ~ (v0 =
% 14.77/2.81  | |                 xx))))
% 14.77/2.81  | | 
% 14.77/2.81  | | GROUND_INST: instantiating (37) with 0, simplifying with (16), (18) gives:
% 14.77/2.82  | |   (40)   ! [v0: $i] :  ! [v1: any] : ( ~ (aElement0(v0) = v1) |  ~ $i(v0) | 
% 14.77/2.82  | |           ? [v2: any] :  ? [v3: any] : (aElementOf0(v0, all_17_0) = v2 &
% 14.77/2.82  | |             aElementOf0(v0, all_17_1) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0
% 14.77/2.82  | |                 &  ~ (v0 = xx))))) &  ! [v0: $i] : (v0 = xx |  ~
% 14.77/2.82  | |           (aElement0(v0) = 0) |  ~ $i(v0) |  ? [v1: any] :  ? [v2: any] :
% 14.77/2.82  | |           (aElementOf0(v0, all_17_0) = v2 & aElementOf0(v0, all_17_1) = v1 &
% 14.77/2.82  | |             ( ~ (v1 = 0) | v2 = 0)))
% 14.77/2.82  | | 
% 14.77/2.82  | | ALPHA: (40) implies:
% 14.77/2.82  | |   (41)   ! [v0: $i] :  ! [v1: any] : ( ~ (aElement0(v0) = v1) |  ~ $i(v0) | 
% 14.77/2.82  | |           ? [v2: any] :  ? [v3: any] : (aElementOf0(v0, all_17_0) = v2 &
% 14.77/2.82  | |             aElementOf0(v0, all_17_1) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0
% 14.77/2.82  | |                 &  ~ (v0 = xx)))))
% 14.77/2.82  | | 
% 14.77/2.82  | | BETA: splitting (23) gives:
% 14.77/2.82  | | 
% 14.77/2.82  | | Case 1:
% 14.77/2.82  | | | 
% 14.77/2.82  | | |   (42)   ? [v0: any] :  ? [v1: any] : (aSet0(xS) = v0 & aElement0(xx) = v1
% 14.77/2.82  | | |           & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 14.77/2.82  | | | 
% 14.77/2.82  | | | DELTA: instantiating (42) with fresh symbols all_41_0, all_41_1 gives:
% 14.77/2.82  | | |   (43)  aSet0(xS) = all_41_1 & aElement0(xx) = all_41_0 & ( ~ (all_41_0 =
% 14.77/2.82  | | |             0) |  ~ (all_41_1 = 0))
% 14.77/2.82  | | | 
% 14.77/2.82  | | | ALPHA: (43) implies:
% 14.77/2.82  | | |   (44)  aElement0(xx) = all_41_0
% 14.77/2.82  | | |   (45)  aSet0(xS) = all_41_1
% 14.77/2.82  | | |   (46)   ~ (all_41_0 = 0) |  ~ (all_41_1 = 0)
% 14.77/2.82  | | | 
% 14.77/2.82  | | | GROUND_INST: instantiating (7) with 0, all_41_0, xx, simplifying with (1),
% 14.77/2.82  | | |              (44) gives:
% 14.77/2.82  | | |   (47)  all_41_0 = 0
% 14.77/2.82  | | | 
% 14.77/2.82  | | | GROUND_INST: instantiating (8) with 0, all_41_1, xS, simplifying with (2),
% 14.77/2.82  | | |              (45) gives:
% 14.77/2.82  | | |   (48)  all_41_1 = 0
% 14.77/2.82  | | | 
% 14.77/2.82  | | | BETA: splitting (46) gives:
% 14.77/2.82  | | | 
% 14.77/2.82  | | | Case 1:
% 14.77/2.82  | | | | 
% 14.77/2.82  | | | |   (49)   ~ (all_41_0 = 0)
% 14.77/2.82  | | | | 
% 14.77/2.82  | | | | REDUCE: (47), (49) imply:
% 14.77/2.82  | | | |   (50)  $false
% 14.77/2.82  | | | | 
% 14.77/2.82  | | | | CLOSE: (50) is inconsistent.
% 14.77/2.82  | | | | 
% 14.77/2.82  | | | Case 2:
% 14.77/2.82  | | | | 
% 14.77/2.82  | | | |   (51)   ~ (all_41_1 = 0)
% 14.77/2.82  | | | | 
% 14.77/2.82  | | | | REDUCE: (48), (51) imply:
% 14.77/2.82  | | | |   (52)  $false
% 14.77/2.82  | | | | 
% 14.77/2.82  | | | | CLOSE: (52) is inconsistent.
% 14.77/2.82  | | | | 
% 14.77/2.82  | | | End of split
% 14.77/2.82  | | | 
% 14.77/2.82  | | Case 2:
% 14.77/2.82  | | | 
% 14.77/2.82  | | |   (53)   ! [v0: any] : (v0 = all_17_1 |  ~ (aSet0(v0) = 0) |  ~ $i(v0) | 
% 14.77/2.82  | | |           ? [v1: $i] :  ? [v2: any] :  ? [v3: any] :  ? [v4: any] :
% 14.77/2.82  | | |           (aElement0(v1) = v3 & aElementOf0(v1, v0) = v2 & aElementOf0(v1,
% 14.77/2.82  | | |               xS) = v4 & $i(v1) & ( ~ (v3 = 0) |  ~ (v2 = 0) | ( ~ (v4 =
% 14.77/2.82  | | |                   0) &  ~ (v1 = xx))) & (v2 = 0 | (v3 = 0 & (v4 = 0 | v1 =
% 14.77/2.82  | | |                   xx))))) &  ! [v0: any] : ( ~ (aSet0(all_17_1) = v0) |  ~
% 14.77/2.82  | | |           $i(all_17_1) | (v0 = 0 &  ! [v1: $i] :  ! [v2: any] : ( ~
% 14.77/2.82  | | |               (aElement0(v1) = v2) |  ~ $i(v1) |  ? [v3: any] :  ? [v4:
% 14.77/2.82  | | |                 any] : (aElementOf0(v1, all_17_1) = v3 & aElementOf0(v1,
% 14.77/2.82  | | |                   xS) = v4 & ( ~ (v3 = 0) | (v2 = 0 & (v4 = 0 | v1 =
% 14.77/2.82  | | |                       xx))))) &  ! [v1: $i] : ( ~ (aElement0(v1) = 0) |  ~
% 14.77/2.82  | | |               $i(v1) |  ? [v2: any] :  ? [v3: any] : (aElementOf0(v1,
% 14.77/2.82  | | |                   all_17_1) = v3 & aElementOf0(v1, xS) = v2 & (v3 = 0 | (
% 14.77/2.82  | | |                     ~ (v2 = 0) &  ~ (v1 = xx)))))))
% 14.77/2.82  | | | 
% 14.77/2.82  | | | ALPHA: (53) implies:
% 14.77/2.82  | | |   (54)   ! [v0: any] : ( ~ (aSet0(all_17_1) = v0) |  ~ $i(all_17_1) | (v0
% 14.77/2.82  | | |             = 0 &  ! [v1: $i] :  ! [v2: any] : ( ~ (aElement0(v1) = v2) | 
% 14.77/2.82  | | |               ~ $i(v1) |  ? [v3: any] :  ? [v4: any] : (aElementOf0(v1,
% 14.77/2.82  | | |                   all_17_1) = v3 & aElementOf0(v1, xS) = v4 & ( ~ (v3 = 0)
% 14.77/2.82  | | |                   | (v2 = 0 & (v4 = 0 | v1 = xx))))) &  ! [v1: $i] : ( ~
% 14.77/2.82  | | |               (aElement0(v1) = 0) |  ~ $i(v1) |  ? [v2: any] :  ? [v3:
% 14.77/2.82  | | |                 any] : (aElementOf0(v1, all_17_1) = v3 & aElementOf0(v1,
% 14.77/2.82  | | |                   xS) = v2 & (v3 = 0 | ( ~ (v2 = 0) &  ~ (v1 = xx)))))))
% 14.77/2.82  | | | 
% 14.77/2.82  | | | GROUND_INST: instantiating (54) with 0, simplifying with (15), (17) gives:
% 14.77/2.83  | | |   (55)   ! [v0: $i] :  ! [v1: any] : ( ~ (aElement0(v0) = v1) |  ~ $i(v0)
% 14.77/2.83  | | |           |  ? [v2: any] :  ? [v3: any] : (aElementOf0(v0, all_17_1) = v2
% 14.77/2.83  | | |             & aElementOf0(v0, xS) = v3 & ( ~ (v2 = 0) | (v1 = 0 & (v3 = 0
% 14.77/2.83  | | |                   | v0 = xx))))) &  ! [v0: $i] : ( ~ (aElement0(v0) = 0) |
% 14.77/2.83  | | |            ~ $i(v0) |  ? [v1: any] :  ? [v2: any] : (aElementOf0(v0,
% 14.77/2.83  | | |               all_17_1) = v2 & aElementOf0(v0, xS) = v1 & (v2 = 0 | ( ~
% 14.77/2.83  | | |                 (v1 = 0) &  ~ (v0 = xx)))))
% 14.77/2.83  | | | 
% 14.77/2.83  | | | ALPHA: (55) implies:
% 14.77/2.83  | | |   (56)   ! [v0: $i] : ( ~ (aElement0(v0) = 0) |  ~ $i(v0) |  ? [v1: any] :
% 14.77/2.83  | | |            ? [v2: any] : (aElementOf0(v0, all_17_1) = v2 & aElementOf0(v0,
% 14.77/2.83  | | |               xS) = v1 & (v2 = 0 | ( ~ (v1 = 0) &  ~ (v0 = xx)))))
% 14.77/2.83  | | |   (57)   ! [v0: $i] :  ! [v1: any] : ( ~ (aElement0(v0) = v1) |  ~ $i(v0)
% 14.77/2.83  | | |           |  ? [v2: any] :  ? [v3: any] : (aElementOf0(v0, all_17_1) = v2
% 14.77/2.83  | | |             & aElementOf0(v0, xS) = v3 & ( ~ (v2 = 0) | (v1 = 0 & (v3 = 0
% 14.77/2.83  | | |                   | v0 = xx)))))
% 14.77/2.83  | | | 
% 14.77/2.83  | | | GROUND_INST: instantiating (56) with xx, simplifying with (1), (4) gives:
% 15.15/2.83  | | |   (58)   ? [v0: MultipleValueBool] : (aElementOf0(xx, all_17_1) = 0 &
% 15.15/2.83  | | |           aElementOf0(xx, xS) = v0)
% 15.15/2.83  | | | 
% 15.15/2.83  | | | GROUND_INST: instantiating (57) with xx, 0, simplifying with (1), (4)
% 15.15/2.83  | | |              gives:
% 15.15/2.83  | | |   (59)   ? [v0: MultipleValueBool] :  ? [v1: MultipleValueBool] :
% 15.15/2.83  | | |         (aElementOf0(xx, all_17_1) = v0 & aElementOf0(xx, xS) = v1)
% 15.15/2.83  | | | 
% 15.15/2.83  | | | DELTA: instantiating (59) with fresh symbols all_43_0, all_43_1 gives:
% 15.15/2.83  | | |   (60)  aElementOf0(xx, all_17_1) = all_43_1 & aElementOf0(xx, xS) =
% 15.15/2.83  | | |         all_43_0
% 15.15/2.83  | | | 
% 15.15/2.83  | | | ALPHA: (60) implies:
% 15.15/2.83  | | |   (61)  aElementOf0(xx, xS) = all_43_0
% 15.15/2.83  | | | 
% 15.15/2.83  | | | DELTA: instantiating (58) with fresh symbol all_45_0 gives:
% 15.15/2.83  | | |   (62)  aElementOf0(xx, all_17_1) = 0 & aElementOf0(xx, xS) = all_45_0
% 15.15/2.83  | | | 
% 15.15/2.83  | | | ALPHA: (62) implies:
% 15.15/2.83  | | |   (63)  aElementOf0(xx, xS) = all_45_0
% 15.15/2.83  | | | 
% 15.15/2.83  | | | BETA: splitting (39) gives:
% 15.15/2.83  | | | 
% 15.15/2.83  | | | Case 1:
% 15.15/2.83  | | | | 
% 15.15/2.83  | | | |   (64)  all_17_0 = xS
% 15.15/2.83  | | | | 
% 15.15/2.83  | | | | REDUCE: (14), (64) imply:
% 15.15/2.83  | | | |   (65)  $false
% 15.15/2.83  | | | | 
% 15.15/2.83  | | | | CLOSE: (65) is inconsistent.
% 15.15/2.83  | | | | 
% 15.15/2.83  | | | Case 2:
% 15.15/2.83  | | | | 
% 15.15/2.83  | | | |   (66)   ? [v0: $i] :  ? [v1: any] :  ? [v2: any] :  ? [v3: any] :
% 15.15/2.83  | | | |         (aElement0(v0) = v2 & aElementOf0(v0, all_17_1) = v3 &
% 15.15/2.83  | | | |           aElementOf0(v0, xS) = v1 & $i(v0) & ( ~ (v3 = 0) |  ~ (v2 = 0)
% 15.15/2.83  | | | |             |  ~ (v1 = 0) | v0 = xx) & (v1 = 0 | (v3 = 0 & v2 = 0 &  ~
% 15.15/2.83  | | | |               (v0 = xx))))
% 15.15/2.83  | | | | 
% 15.15/2.83  | | | | DELTA: instantiating (66) with fresh symbols all_51_0, all_51_1,
% 15.15/2.83  | | | |        all_51_2, all_51_3 gives:
% 15.15/2.83  | | | |   (67)  aElement0(all_51_3) = all_51_1 & aElementOf0(all_51_3, all_17_1)
% 15.15/2.83  | | | |         = all_51_0 & aElementOf0(all_51_3, xS) = all_51_2 & $i(all_51_3)
% 15.15/2.83  | | | |         & ( ~ (all_51_0 = 0) |  ~ (all_51_1 = 0) |  ~ (all_51_2 = 0) |
% 15.15/2.83  | | | |           all_51_3 = xx) & (all_51_2 = 0 | (all_51_0 = 0 & all_51_1 = 0
% 15.15/2.83  | | | |             &  ~ (all_51_3 = xx)))
% 15.15/2.83  | | | | 
% 15.15/2.83  | | | | ALPHA: (67) implies:
% 15.15/2.83  | | | |   (68)  $i(all_51_3)
% 15.15/2.83  | | | |   (69)  aElementOf0(all_51_3, xS) = all_51_2
% 15.15/2.83  | | | |   (70)  aElementOf0(all_51_3, all_17_1) = all_51_0
% 15.15/2.83  | | | |   (71)  aElement0(all_51_3) = all_51_1
% 15.15/2.83  | | | |   (72)  all_51_2 = 0 | (all_51_0 = 0 & all_51_1 = 0 &  ~ (all_51_3 =
% 15.15/2.83  | | | |             xx))
% 15.15/2.83  | | | |   (73)   ~ (all_51_0 = 0) |  ~ (all_51_1 = 0) |  ~ (all_51_2 = 0) |
% 15.15/2.83  | | | |         all_51_3 = xx
% 15.15/2.83  | | | | 
% 15.15/2.83  | | | | GROUND_INST: instantiating (9) with all_15_0, all_45_0, xS, xx,
% 15.15/2.83  | | | |              simplifying with (12), (63) gives:
% 15.15/2.83  | | | |   (74)  all_45_0 = all_15_0
% 15.15/2.83  | | | | 
% 15.15/2.83  | | | | GROUND_INST: instantiating (9) with all_43_0, all_45_0, xS, xx,
% 15.15/2.83  | | | |              simplifying with (61), (63) gives:
% 15.15/2.83  | | | |   (75)  all_45_0 = all_43_0
% 15.15/2.83  | | | | 
% 15.15/2.83  | | | | COMBINE_EQS: (74), (75) imply:
% 15.15/2.83  | | | |   (76)  all_43_0 = all_15_0
% 15.15/2.83  | | | | 
% 15.15/2.83  | | | | GROUND_INST: instantiating (21) with all_51_3, all_51_0, simplifying
% 15.15/2.83  | | | |              with (68), (70) gives:
% 15.15/2.83  | | | |   (77)  all_51_0 = 0 |  ? [v0: any] :  ? [v1: any] :
% 15.15/2.83  | | | |         (aElement0(all_51_3) = v0 & aElementOf0(all_51_3, xS) = v1 & ( ~
% 15.15/2.83  | | | |             (v0 = 0) | ( ~ (v1 = 0) &  ~ (all_51_3 = xx))))
% 15.15/2.83  | | | | 
% 15.15/2.83  | | | | GROUND_INST: instantiating (22) with all_51_3, all_51_1, simplifying
% 15.15/2.83  | | | |              with (68), (71) gives:
% 15.15/2.83  | | | |   (78)  all_51_1 = 0 |  ? [v0: int] : ( ~ (v0 = 0) &
% 15.15/2.83  | | | |           aElementOf0(all_51_3, xS) = v0)
% 15.15/2.83  | | | | 
% 15.15/2.83  | | | | GROUND_INST: instantiating (41) with all_51_3, all_51_1, simplifying
% 15.15/2.83  | | | |              with (68), (71) gives:
% 15.15/2.83  | | | |   (79)   ? [v0: any] :  ? [v1: any] : (aElementOf0(all_51_3, all_17_0) =
% 15.15/2.83  | | | |           v0 & aElementOf0(all_51_3, all_17_1) = v1 & ( ~ (v0 = 0) | (v1
% 15.15/2.83  | | | |               = 0 & all_51_1 = 0 &  ~ (all_51_3 = xx))))
% 15.15/2.83  | | | | 
% 15.15/2.83  | | | | GROUND_INST: instantiating (57) with all_51_3, all_51_1, simplifying
% 15.15/2.83  | | | |              with (68), (71) gives:
% 15.15/2.84  | | | |   (80)   ? [v0: any] :  ? [v1: any] : (aElementOf0(all_51_3, all_17_1) =
% 15.15/2.84  | | | |           v0 & aElementOf0(all_51_3, xS) = v1 & ( ~ (v0 = 0) | (all_51_1
% 15.15/2.84  | | | |               = 0 & (v1 = 0 | all_51_3 = xx))))
% 15.15/2.84  | | | | 
% 15.15/2.84  | | | | DELTA: instantiating (80) with fresh symbols all_62_0, all_62_1 gives:
% 15.15/2.84  | | | |   (81)  aElementOf0(all_51_3, all_17_1) = all_62_1 &
% 15.15/2.84  | | | |         aElementOf0(all_51_3, xS) = all_62_0 & ( ~ (all_62_1 = 0) |
% 15.15/2.84  | | | |           (all_51_1 = 0 & (all_62_0 = 0 | all_51_3 = xx)))
% 15.15/2.84  | | | | 
% 15.15/2.84  | | | | ALPHA: (81) implies:
% 15.15/2.84  | | | |   (82)  aElementOf0(all_51_3, xS) = all_62_0
% 15.15/2.84  | | | |   (83)  aElementOf0(all_51_3, all_17_1) = all_62_1
% 15.15/2.84  | | | |   (84)   ~ (all_62_1 = 0) | (all_51_1 = 0 & (all_62_0 = 0 | all_51_3 =
% 15.15/2.84  | | | |             xx))
% 15.15/2.84  | | | | 
% 15.15/2.84  | | | | DELTA: instantiating (79) with fresh symbols all_64_0, all_64_1 gives:
% 15.15/2.84  | | | |   (85)  aElementOf0(all_51_3, all_17_0) = all_64_1 &
% 15.15/2.84  | | | |         aElementOf0(all_51_3, all_17_1) = all_64_0 & ( ~ (all_64_1 = 0)
% 15.15/2.84  | | | |           | (all_64_0 = 0 & all_51_1 = 0 &  ~ (all_51_3 = xx)))
% 15.15/2.84  | | | | 
% 15.15/2.84  | | | | ALPHA: (85) implies:
% 15.15/2.84  | | | |   (86)  aElementOf0(all_51_3, all_17_1) = all_64_0
% 15.15/2.84  | | | | 
% 15.15/2.84  | | | | GROUND_INST: instantiating (9) with all_51_2, all_62_0, xS, all_51_3,
% 15.15/2.84  | | | |              simplifying with (69), (82) gives:
% 15.15/2.84  | | | |   (87)  all_62_0 = all_51_2
% 15.15/2.84  | | | | 
% 15.15/2.84  | | | | GROUND_INST: instantiating (9) with all_51_0, all_64_0, all_17_1,
% 15.15/2.84  | | | |              all_51_3, simplifying with (70), (86) gives:
% 15.15/2.84  | | | |   (88)  all_64_0 = all_51_0
% 15.15/2.84  | | | | 
% 15.15/2.84  | | | | GROUND_INST: instantiating (9) with all_62_1, all_64_0, all_17_1,
% 15.15/2.84  | | | |              all_51_3, simplifying with (83), (86) gives:
% 15.15/2.84  | | | |   (89)  all_64_0 = all_62_1
% 15.15/2.84  | | | | 
% 15.15/2.84  | | | | COMBINE_EQS: (88), (89) imply:
% 15.15/2.84  | | | |   (90)  all_62_1 = all_51_0
% 15.15/2.84  | | | | 
% 15.15/2.84  | | | | BETA: splitting (72) gives:
% 15.15/2.84  | | | | 
% 15.15/2.84  | | | | Case 1:
% 15.15/2.84  | | | | | 
% 15.15/2.84  | | | | |   (91)  all_51_2 = 0
% 15.15/2.84  | | | | | 
% 15.15/2.84  | | | | | REDUCE: (69), (91) imply:
% 15.15/2.84  | | | | |   (92)  aElementOf0(all_51_3, xS) = 0
% 15.15/2.84  | | | | | 
% 15.15/2.84  | | | | | BETA: splitting (78) gives:
% 15.15/2.84  | | | | | 
% 15.15/2.84  | | | | | Case 1:
% 15.15/2.84  | | | | | | 
% 15.15/2.84  | | | | | |   (93)  all_51_1 = 0
% 15.15/2.84  | | | | | | 
% 15.15/2.84  | | | | | | REDUCE: (71), (93) imply:
% 15.15/2.84  | | | | | |   (94)  aElement0(all_51_3) = 0
% 15.15/2.84  | | | | | | 
% 15.15/2.84  | | | | | | BETA: splitting (77) gives:
% 15.15/2.84  | | | | | | 
% 15.15/2.84  | | | | | | Case 1:
% 15.15/2.84  | | | | | | | 
% 15.15/2.84  | | | | | | |   (95)  all_51_0 = 0
% 15.15/2.84  | | | | | | | 
% 15.15/2.84  | | | | | | | BETA: splitting (73) gives:
% 15.15/2.84  | | | | | | | 
% 15.15/2.84  | | | | | | | Case 1:
% 15.15/2.84  | | | | | | | | 
% 15.15/2.84  | | | | | | | |   (96)   ~ (all_51_0 = 0)
% 15.15/2.84  | | | | | | | | 
% 15.15/2.84  | | | | | | | | REDUCE: (95), (96) imply:
% 15.15/2.84  | | | | | | | |   (97)  $false
% 15.15/2.84  | | | | | | | | 
% 15.15/2.84  | | | | | | | | CLOSE: (97) is inconsistent.
% 15.15/2.84  | | | | | | | | 
% 15.15/2.84  | | | | | | | Case 2:
% 15.15/2.84  | | | | | | | | 
% 15.15/2.84  | | | | | | | |   (98)   ~ (all_51_1 = 0) |  ~ (all_51_2 = 0) | all_51_3 = xx
% 15.15/2.84  | | | | | | | | 
% 15.15/2.84  | | | | | | | | BETA: splitting (98) gives:
% 15.15/2.84  | | | | | | | | 
% 15.15/2.84  | | | | | | | | Case 1:
% 15.15/2.84  | | | | | | | | | 
% 15.15/2.84  | | | | | | | | |   (99)   ~ (all_51_1 = 0)
% 15.15/2.84  | | | | | | | | | 
% 15.15/2.84  | | | | | | | | | REDUCE: (93), (99) imply:
% 15.15/2.84  | | | | | | | | |   (100)  $false
% 15.15/2.84  | | | | | | | | | 
% 15.15/2.84  | | | | | | | | | CLOSE: (100) is inconsistent.
% 15.15/2.84  | | | | | | | | | 
% 15.15/2.84  | | | | | | | | Case 2:
% 15.15/2.84  | | | | | | | | | 
% 15.15/2.84  | | | | | | | | |   (101)   ~ (all_51_2 = 0) | all_51_3 = xx
% 15.15/2.84  | | | | | | | | | 
% 15.15/2.84  | | | | | | | | | BETA: splitting (101) gives:
% 15.15/2.84  | | | | | | | | | 
% 15.15/2.84  | | | | | | | | | Case 1:
% 15.15/2.84  | | | | | | | | | | 
% 15.15/2.84  | | | | | | | | | |   (102)   ~ (all_51_2 = 0)
% 15.15/2.84  | | | | | | | | | | 
% 15.15/2.84  | | | | | | | | | | REDUCE: (91), (102) imply:
% 15.15/2.84  | | | | | | | | | |   (103)  $false
% 15.15/2.84  | | | | | | | | | | 
% 15.15/2.84  | | | | | | | | | | CLOSE: (103) is inconsistent.
% 15.15/2.84  | | | | | | | | | | 
% 15.15/2.84  | | | | | | | | | Case 2:
% 15.15/2.84  | | | | | | | | | | 
% 15.15/2.84  | | | | | | | | | |   (104)  all_51_3 = xx
% 15.15/2.84  | | | | | | | | | | 
% 15.15/2.84  | | | | | | | | | | REDUCE: (92), (104) imply:
% 15.15/2.84  | | | | | | | | | |   (105)  aElementOf0(xx, xS) = 0
% 15.15/2.84  | | | | | | | | | | 
% 15.15/2.84  | | | | | | | | | | GROUND_INST: instantiating (9) with all_15_0, 0, xS, xx,
% 15.15/2.84  | | | | | | | | | |              simplifying with (12), (105) gives:
% 15.15/2.84  | | | | | | | | | |   (106)  all_15_0 = 0
% 15.15/2.84  | | | | | | | | | | 
% 15.15/2.84  | | | | | | | | | | REDUCE: (11), (106) imply:
% 15.15/2.84  | | | | | | | | | |   (107)  $false
% 15.15/2.84  | | | | | | | | | | 
% 15.15/2.84  | | | | | | | | | | CLOSE: (107) is inconsistent.
% 15.15/2.84  | | | | | | | | | | 
% 15.15/2.84  | | | | | | | | | End of split
% 15.15/2.84  | | | | | | | | | 
% 15.15/2.84  | | | | | | | | End of split
% 15.15/2.84  | | | | | | | | 
% 15.15/2.84  | | | | | | | End of split
% 15.15/2.84  | | | | | | | 
% 15.15/2.84  | | | | | | Case 2:
% 15.15/2.84  | | | | | | | 
% 15.15/2.84  | | | | | | |   (108)   ? [v0: any] :  ? [v1: any] : (aElement0(all_51_3) = v0 &
% 15.15/2.84  | | | | | | |            aElementOf0(all_51_3, xS) = v1 & ( ~ (v0 = 0) | ( ~ (v1
% 15.15/2.84  | | | | | | |                  = 0) &  ~ (all_51_3 = xx))))
% 15.15/2.84  | | | | | | | 
% 15.15/2.84  | | | | | | | DELTA: instantiating (108) with fresh symbols all_231_0, all_231_1
% 15.15/2.84  | | | | | | |        gives:
% 15.15/2.84  | | | | | | |   (109)  aElement0(all_51_3) = all_231_1 & aElementOf0(all_51_3,
% 15.15/2.84  | | | | | | |            xS) = all_231_0 & ( ~ (all_231_1 = 0) | ( ~ (all_231_0
% 15.15/2.84  | | | | | | |                = 0) &  ~ (all_51_3 = xx)))
% 15.15/2.84  | | | | | | | 
% 15.15/2.84  | | | | | | | ALPHA: (109) implies:
% 15.15/2.84  | | | | | | |   (110)  aElementOf0(all_51_3, xS) = all_231_0
% 15.15/2.84  | | | | | | |   (111)  aElement0(all_51_3) = all_231_1
% 15.15/2.84  | | | | | | |   (112)   ~ (all_231_1 = 0) | ( ~ (all_231_0 = 0) &  ~ (all_51_3 =
% 15.15/2.84  | | | | | | |              xx))
% 15.15/2.84  | | | | | | | 
% 15.15/2.84  | | | | | | | GROUND_INST: instantiating (9) with 0, all_231_0, xS, all_51_3,
% 15.15/2.84  | | | | | | |              simplifying with (92), (110) gives:
% 15.15/2.84  | | | | | | |   (113)  all_231_0 = 0
% 15.15/2.84  | | | | | | | 
% 15.15/2.84  | | | | | | | GROUND_INST: instantiating (7) with 0, all_231_1, all_51_3,
% 15.15/2.84  | | | | | | |              simplifying with (94), (111) gives:
% 15.15/2.84  | | | | | | |   (114)  all_231_1 = 0
% 15.15/2.84  | | | | | | | 
% 15.15/2.84  | | | | | | | BETA: splitting (112) gives:
% 15.15/2.84  | | | | | | | 
% 15.15/2.84  | | | | | | | Case 1:
% 15.15/2.84  | | | | | | | | 
% 15.15/2.84  | | | | | | | |   (115)   ~ (all_231_1 = 0)
% 15.15/2.84  | | | | | | | | 
% 15.15/2.84  | | | | | | | | REDUCE: (114), (115) imply:
% 15.15/2.84  | | | | | | | |   (116)  $false
% 15.15/2.84  | | | | | | | | 
% 15.15/2.84  | | | | | | | | CLOSE: (116) is inconsistent.
% 15.15/2.84  | | | | | | | | 
% 15.15/2.84  | | | | | | | Case 2:
% 15.15/2.84  | | | | | | | | 
% 15.15/2.84  | | | | | | | |   (117)   ~ (all_231_0 = 0) &  ~ (all_51_3 = xx)
% 15.15/2.84  | | | | | | | | 
% 15.15/2.84  | | | | | | | | ALPHA: (117) implies:
% 15.15/2.84  | | | | | | | |   (118)   ~ (all_231_0 = 0)
% 15.15/2.84  | | | | | | | | 
% 15.15/2.84  | | | | | | | | REDUCE: (113), (118) imply:
% 15.15/2.84  | | | | | | | |   (119)  $false
% 15.15/2.84  | | | | | | | | 
% 15.15/2.84  | | | | | | | | CLOSE: (119) is inconsistent.
% 15.15/2.84  | | | | | | | | 
% 15.15/2.84  | | | | | | | End of split
% 15.15/2.84  | | | | | | | 
% 15.15/2.84  | | | | | | End of split
% 15.15/2.84  | | | | | | 
% 15.15/2.84  | | | | | Case 2:
% 15.15/2.84  | | | | | | 
% 15.15/2.84  | | | | | |   (120)   ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(all_51_3, xS) =
% 15.15/2.84  | | | | | |            v0)
% 15.15/2.84  | | | | | | 
% 15.15/2.84  | | | | | | DELTA: instantiating (120) with fresh symbol all_227_0 gives:
% 15.15/2.84  | | | | | |   (121)   ~ (all_227_0 = 0) & aElementOf0(all_51_3, xS) = all_227_0
% 15.15/2.84  | | | | | | 
% 15.15/2.84  | | | | | | ALPHA: (121) implies:
% 15.15/2.84  | | | | | |   (122)   ~ (all_227_0 = 0)
% 15.15/2.84  | | | | | |   (123)  aElementOf0(all_51_3, xS) = all_227_0
% 15.15/2.84  | | | | | | 
% 15.15/2.84  | | | | | | GROUND_INST: instantiating (9) with 0, all_227_0, xS, all_51_3,
% 15.15/2.84  | | | | | |              simplifying with (92), (123) gives:
% 15.15/2.84  | | | | | |   (124)  all_227_0 = 0
% 15.15/2.84  | | | | | | 
% 15.15/2.85  | | | | | | REDUCE: (122), (124) imply:
% 15.15/2.85  | | | | | |   (125)  $false
% 15.15/2.85  | | | | | | 
% 15.15/2.85  | | | | | | CLOSE: (125) is inconsistent.
% 15.15/2.85  | | | | | | 
% 15.15/2.85  | | | | | End of split
% 15.15/2.85  | | | | | 
% 15.15/2.85  | | | | Case 2:
% 15.15/2.85  | | | | | 
% 15.15/2.85  | | | | |   (126)   ~ (all_51_2 = 0)
% 15.15/2.85  | | | | |   (127)  all_51_0 = 0 & all_51_1 = 0 &  ~ (all_51_3 = xx)
% 15.15/2.85  | | | | | 
% 15.15/2.85  | | | | | ALPHA: (127) implies:
% 15.15/2.85  | | | | |   (128)  all_51_0 = 0
% 15.15/2.85  | | | | |   (129)   ~ (all_51_3 = xx)
% 15.15/2.85  | | | | | 
% 15.15/2.85  | | | | | COMBINE_EQS: (90), (128) imply:
% 15.15/2.85  | | | | |   (130)  all_62_1 = 0
% 15.15/2.85  | | | | | 
% 15.15/2.85  | | | | | BETA: splitting (84) gives:
% 15.15/2.85  | | | | | 
% 15.15/2.85  | | | | | Case 1:
% 15.15/2.85  | | | | | | 
% 15.15/2.85  | | | | | |   (131)   ~ (all_62_1 = 0)
% 15.15/2.85  | | | | | | 
% 15.15/2.85  | | | | | | REDUCE: (130), (131) imply:
% 15.15/2.85  | | | | | |   (132)  $false
% 15.15/2.85  | | | | | | 
% 15.15/2.85  | | | | | | CLOSE: (132) is inconsistent.
% 15.15/2.85  | | | | | | 
% 15.15/2.85  | | | | | Case 2:
% 15.15/2.85  | | | | | | 
% 15.15/2.85  | | | | | |   (133)  all_51_1 = 0 & (all_62_0 = 0 | all_51_3 = xx)
% 15.15/2.85  | | | | | | 
% 15.15/2.85  | | | | | | ALPHA: (133) implies:
% 15.15/2.85  | | | | | |   (134)  all_62_0 = 0 | all_51_3 = xx
% 15.15/2.85  | | | | | | 
% 15.15/2.85  | | | | | | BETA: splitting (134) gives:
% 15.15/2.85  | | | | | | 
% 15.15/2.85  | | | | | | Case 1:
% 15.15/2.85  | | | | | | | 
% 15.15/2.85  | | | | | | |   (135)  all_51_3 = xx
% 15.15/2.85  | | | | | | | 
% 15.15/2.85  | | | | | | | REDUCE: (129), (135) imply:
% 15.15/2.85  | | | | | | |   (136)  $false
% 15.15/2.85  | | | | | | | 
% 15.15/2.85  | | | | | | | CLOSE: (136) is inconsistent.
% 15.15/2.85  | | | | | | | 
% 15.15/2.85  | | | | | | Case 2:
% 15.15/2.85  | | | | | | | 
% 15.15/2.85  | | | | | | |   (137)  all_62_0 = 0
% 15.15/2.85  | | | | | | | 
% 15.15/2.85  | | | | | | | COMBINE_EQS: (87), (137) imply:
% 15.15/2.85  | | | | | | |   (138)  all_51_2 = 0
% 15.15/2.85  | | | | | | | 
% 15.15/2.85  | | | | | | | SIMP: (138) implies:
% 15.15/2.85  | | | | | | |   (139)  all_51_2 = 0
% 15.15/2.85  | | | | | | | 
% 15.15/2.85  | | | | | | | REDUCE: (126), (139) imply:
% 15.15/2.85  | | | | | | |   (140)  $false
% 15.15/2.85  | | | | | | | 
% 15.15/2.85  | | | | | | | CLOSE: (140) is inconsistent.
% 15.15/2.85  | | | | | | | 
% 15.64/2.85  | | | | | | End of split
% 15.64/2.85  | | | | | | 
% 15.64/2.85  | | | | | End of split
% 15.64/2.85  | | | | | 
% 15.64/2.85  | | | | End of split
% 15.64/2.85  | | | | 
% 15.64/2.85  | | | End of split
% 15.64/2.85  | | | 
% 15.64/2.85  | | End of split
% 15.64/2.85  | | 
% 15.64/2.85  | End of split
% 15.64/2.85  | 
% 15.64/2.85  End of proof
% 15.64/2.85  % SZS output end Proof for theBenchmark
% 15.64/2.85  
% 15.64/2.85  2237ms
%------------------------------------------------------------------------------