TSTP Solution File: SET802+4 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SET802+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n025.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 15:26:30 EDT 2023

% Result   : Theorem 10.57s 2.24s
% Output   : Proof 12.75s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET802+4 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34  % Computer : n025.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Sat Aug 26 16:29:38 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.61  ________       _____
% 0.19/0.61  ___  __ \_________(_)________________________________
% 0.19/0.61  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.19/0.61  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.19/0.61  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61  
% 0.19/0.61  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61  (2023-06-19)
% 0.19/0.61  
% 0.19/0.61  (c) Philipp Rümmer, 2009-2023
% 0.19/0.61  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61                Amanda Stjerna.
% 0.19/0.61  Free software under BSD-3-Clause.
% 0.19/0.61  
% 0.19/0.61  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61  
% 0.19/0.61  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62  Running up to 7 provers in parallel.
% 0.19/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.13/1.15  Prover 1: Preprocessing ...
% 3.13/1.15  Prover 4: Preprocessing ...
% 3.30/1.19  Prover 6: Preprocessing ...
% 3.30/1.19  Prover 2: Preprocessing ...
% 3.30/1.19  Prover 3: Preprocessing ...
% 3.30/1.19  Prover 5: Preprocessing ...
% 3.30/1.19  Prover 0: Preprocessing ...
% 7.18/1.73  Prover 5: Proving ...
% 7.62/1.79  Prover 2: Proving ...
% 8.25/1.87  Prover 3: Constructing countermodel ...
% 8.25/1.88  Prover 6: Proving ...
% 8.25/1.89  Prover 1: Constructing countermodel ...
% 8.57/2.02  Prover 4: Constructing countermodel ...
% 8.86/2.10  Prover 0: Proving ...
% 10.57/2.23  Prover 3: proved (1598ms)
% 10.57/2.23  
% 10.57/2.24  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.57/2.24  
% 10.57/2.24  Prover 6: stopped
% 10.57/2.24  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.57/2.24  Prover 5: stopped
% 10.57/2.25  Prover 0: stopped
% 10.57/2.26  Prover 2: stopped
% 10.57/2.26  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.57/2.26  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.00/2.26  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.00/2.27  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.00/2.28  Prover 7: Preprocessing ...
% 11.00/2.30  Prover 8: Preprocessing ...
% 11.00/2.31  Prover 10: Preprocessing ...
% 11.00/2.32  Prover 11: Preprocessing ...
% 11.00/2.33  Prover 13: Preprocessing ...
% 11.00/2.35  Prover 1: Found proof (size 87)
% 11.00/2.35  Prover 1: proved (1727ms)
% 11.00/2.35  Prover 4: stopped
% 11.66/2.35  Prover 10: stopped
% 11.66/2.37  Prover 13: stopped
% 11.66/2.38  Prover 7: Warning: ignoring some quantifiers
% 11.66/2.39  Prover 11: stopped
% 11.93/2.40  Prover 7: Constructing countermodel ...
% 11.93/2.41  Prover 7: stopped
% 12.17/2.47  Prover 8: Warning: ignoring some quantifiers
% 12.17/2.47  Prover 8: Constructing countermodel ...
% 12.17/2.48  Prover 8: stopped
% 12.17/2.48  
% 12.17/2.48  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.17/2.48  
% 12.17/2.49  % SZS output start Proof for theBenchmark
% 12.17/2.49  Assumptions after simplification:
% 12.17/2.49  ---------------------------------
% 12.17/2.50  
% 12.17/2.50    (greatest_lower_bound)
% 12.46/2.52     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] : (v4 = 0
% 12.46/2.52      |  ~ (greatest_lower_bound(v0, v1, v2, v3) = v4) |  ~ $i(v3) |  ~ $i(v2) | 
% 12.46/2.52      ~ $i(v1) |  ~ $i(v0) |  ? [v5: $i] :  ? [v6: int] : ( ~ (v6 = 0) &
% 12.46/2.52        lower_bound(v5, v2, v1) = 0 & apply(v2, v5, v0) = v6 & member(v5, v3) = 0
% 12.46/2.52        & $i(v5)) |  ? [v5: any] :  ? [v6: any] : (lower_bound(v0, v2, v1) = v6 &
% 12.46/2.52        member(v0, v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0)))) &  ! [v0: $i] :  !
% 12.46/2.52    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ (greatest_lower_bound(v0, v1, v2,
% 12.46/2.52          v3) = 0) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |
% 12.46/2.52      (lower_bound(v0, v2, v1) = 0 & member(v0, v1) = 0 &  ! [v4: $i] : ( ~
% 12.46/2.52          (lower_bound(v4, v2, v1) = 0) |  ~ $i(v4) |  ? [v5: any] :  ? [v6: any]
% 12.46/2.52          : (apply(v2, v4, v0) = v6 & member(v4, v3) = v5 & ( ~ (v5 = 0) | v6 =
% 12.46/2.52              0)))))
% 12.46/2.52  
% 12.46/2.52    (least)
% 12.46/2.53     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 12.46/2.53      (least(v2, v0, v1) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: $i] :
% 12.46/2.53       ? [v5: int] : ( ~ (v5 = 0) & apply(v0, v2, v4) = v5 & member(v4, v1) = 0 &
% 12.46/2.53        $i(v4)) |  ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) = v4)) &  ! [v0:
% 12.46/2.53      $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (least(v2, v0, v1) = 0) |  ~ $i(v2) | 
% 12.46/2.53      ~ $i(v1) |  ~ $i(v0) | (member(v2, v1) = 0 &  ! [v3: $i] :  ! [v4: int] :
% 12.46/2.53        (v4 = 0 |  ~ (apply(v0, v2, v3) = v4) |  ~ $i(v3) |  ? [v5: int] : ( ~ (v5
% 12.46/2.53              = 0) & member(v3, v1) = v5))))
% 12.46/2.53  
% 12.46/2.53    (lower_bound)
% 12.46/2.53     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 12.46/2.53      (lower_bound(v2, v0, v1) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4:
% 12.46/2.53        $i] :  ? [v5: int] : ( ~ (v5 = 0) & apply(v0, v2, v4) = v5 & member(v4,
% 12.46/2.53          v1) = 0 & $i(v4))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~
% 12.46/2.53      (lower_bound(v2, v0, v1) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ! [v3:
% 12.46/2.53        $i] :  ! [v4: int] : (v4 = 0 |  ~ (apply(v0, v2, v3) = v4) |  ~ $i(v3) | 
% 12.46/2.53        ? [v5: int] : ( ~ (v5 = 0) & member(v3, v1) = v5)))
% 12.46/2.53  
% 12.46/2.53    (thIV14)
% 12.46/2.53     ? [v0: $i] :  ? [v1: $i] : (order(v0, v1) = 0 & $i(v1) & $i(v0) &  ? [v2: $i]
% 12.46/2.53      : (subset(v2, v1) = 0 & $i(v2) &  ? [v3: $i] :  ? [v4: any] :  ? [v5: any] :
% 12.46/2.53         ? [v6: any] : (greatest_lower_bound(v3, v2, v0, v1) = v6 & least(v3, v0,
% 12.46/2.53            v2) = v4 & member(v3, v2) = v5 & $i(v3) & ((v6 = 0 & v5 = 0 &  ~ (v4 =
% 12.46/2.53                0)) | (v4 = 0 & ( ~ (v6 = 0) |  ~ (v5 = 0)))))))
% 12.46/2.53  
% 12.46/2.53    (function-axioms)
% 12.46/2.54     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 12.46/2.54    [v3: $i] :  ! [v4: $i] :  ! [v5: $i] : (v1 = v0 |  ~ (greatest_lower_bound(v5,
% 12.46/2.54          v4, v3, v2) = v1) |  ~ (greatest_lower_bound(v5, v4, v3, v2) = v0)) &  !
% 12.46/2.54    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 12.46/2.54      $i] :  ! [v4: $i] :  ! [v5: $i] : (v1 = v0 |  ~ (least_upper_bound(v5, v4,
% 12.46/2.54          v3, v2) = v1) |  ~ (least_upper_bound(v5, v4, v3, v2) = v0)) &  ! [v0:
% 12.46/2.54      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 12.46/2.54    :  ! [v4: $i] : (v1 = v0 |  ~ (min(v4, v3, v2) = v1) |  ~ (min(v4, v3, v2) =
% 12.46/2.54        v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 12.46/2.54      $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (max(v4, v3, v2) = v1) |  ~
% 12.46/2.54      (max(v4, v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 12.46/2.54      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~
% 12.46/2.54      (least(v4, v3, v2) = v1) |  ~ (least(v4, v3, v2) = v0)) &  ! [v0:
% 12.46/2.54      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 12.46/2.54    :  ! [v4: $i] : (v1 = v0 |  ~ (greatest(v4, v3, v2) = v1) |  ~ (greatest(v4,
% 12.46/2.54          v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool]
% 12.46/2.54    :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (lower_bound(v4, v3,
% 12.46/2.54          v2) = v1) |  ~ (lower_bound(v4, v3, v2) = v0)) &  ! [v0:
% 12.46/2.54      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 12.46/2.54    :  ! [v4: $i] : (v1 = v0 |  ~ (upper_bound(v4, v3, v2) = v1) |  ~
% 12.46/2.54      (upper_bound(v4, v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 12.46/2.54      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~
% 12.46/2.54      (apply(v4, v3, v2) = v1) |  ~ (apply(v4, v3, v2) = v0)) &  ! [v0:
% 12.46/2.54      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 12.46/2.54    : (v1 = v0 |  ~ (total_order(v3, v2) = v1) |  ~ (total_order(v3, v2) = v0)) & 
% 12.46/2.54    ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 12.46/2.54      $i] : (v1 = v0 |  ~ (order(v3, v2) = v1) |  ~ (order(v3, v2) = v0)) &  !
% 12.46/2.54    [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 12.46/2.54      (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0)) &  ! [v0:
% 12.46/2.54      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 12.46/2.54      (difference(v3, v2) = v1) |  ~ (difference(v3, v2) = v0)) &  ! [v0: $i] :  !
% 12.46/2.54    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (union(v3, v2) = v1) |  ~
% 12.46/2.54      (union(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3:
% 12.46/2.54      $i] : (v1 = v0 |  ~ (intersection(v3, v2) = v1) |  ~ (intersection(v3, v2) =
% 12.46/2.54        v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 12.46/2.54      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (equal_set(v3, v2) = v1) |  ~
% 12.46/2.54      (equal_set(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 12.46/2.54      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (subset(v3,
% 12.46/2.54          v2) = v1) |  ~ (subset(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  !
% 12.46/2.54    [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 12.46/2.54      (member(v3, v2) = v1) |  ~ (member(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1:
% 12.46/2.54      $i] :  ! [v2: $i] : (v1 = v0 |  ~ (product(v2) = v1) |  ~ (product(v2) =
% 12.46/2.54        v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (sum(v2) =
% 12.46/2.54        v1) |  ~ (sum(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 =
% 12.46/2.54      v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0)) &  ! [v0: $i] :  !
% 12.46/2.54    [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (power_set(v2) = v1) |  ~
% 12.46/2.54      (power_set(v2) = v0))
% 12.46/2.54  
% 12.46/2.54  Further assumptions not needed in the proof:
% 12.46/2.54  --------------------------------------------
% 12.46/2.54  difference, empty_set, equal_set, greatest, intersection, least_upper_bound,
% 12.46/2.54  max, min, order, power_set, product, singleton, subset, sum, total_order, union,
% 12.46/2.54  unordered_pair, upper_bound
% 12.46/2.54  
% 12.46/2.54  Those formulas are unsatisfiable:
% 12.46/2.54  ---------------------------------
% 12.46/2.54  
% 12.46/2.54  Begin of proof
% 12.46/2.54  | 
% 12.46/2.54  | ALPHA: (lower_bound) implies:
% 12.46/2.55  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (lower_bound(v2, v0, v1)
% 12.46/2.55  |            = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ! [v3: $i] :  ! [v4:
% 12.46/2.55  |            int] : (v4 = 0 |  ~ (apply(v0, v2, v3) = v4) |  ~ $i(v3) |  ? [v5:
% 12.46/2.55  |              int] : ( ~ (v5 = 0) & member(v3, v1) = v5)))
% 12.46/2.55  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 12.46/2.55  |          (lower_bound(v2, v0, v1) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) | 
% 12.46/2.55  |          ? [v4: $i] :  ? [v5: int] : ( ~ (v5 = 0) & apply(v0, v2, v4) = v5 &
% 12.46/2.55  |            member(v4, v1) = 0 & $i(v4)))
% 12.46/2.55  | 
% 12.46/2.55  | ALPHA: (least) implies:
% 12.46/2.55  |   (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (least(v2, v0, v1) = 0) |
% 12.46/2.55  |           ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) | (member(v2, v1) = 0 &  ! [v3: $i]
% 12.46/2.55  |            :  ! [v4: int] : (v4 = 0 |  ~ (apply(v0, v2, v3) = v4) |  ~ $i(v3)
% 12.46/2.55  |              |  ? [v5: int] : ( ~ (v5 = 0) & member(v3, v1) = v5))))
% 12.46/2.55  |   (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 12.46/2.55  |          (least(v2, v0, v1) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 12.46/2.55  |          [v4: $i] :  ? [v5: int] : ( ~ (v5 = 0) & apply(v0, v2, v4) = v5 &
% 12.46/2.55  |            member(v4, v1) = 0 & $i(v4)) |  ? [v4: int] : ( ~ (v4 = 0) &
% 12.46/2.55  |            member(v2, v1) = v4))
% 12.46/2.55  | 
% 12.46/2.55  | ALPHA: (greatest_lower_bound) implies:
% 12.46/2.55  |   (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~
% 12.46/2.55  |          (greatest_lower_bound(v0, v1, v2, v3) = 0) |  ~ $i(v3) |  ~ $i(v2) | 
% 12.46/2.55  |          ~ $i(v1) |  ~ $i(v0) | (lower_bound(v0, v2, v1) = 0 & member(v0, v1)
% 12.46/2.55  |            = 0 &  ! [v4: $i] : ( ~ (lower_bound(v4, v2, v1) = 0) |  ~ $i(v4) |
% 12.46/2.55  |               ? [v5: any] :  ? [v6: any] : (apply(v2, v4, v0) = v6 &
% 12.46/2.55  |                member(v4, v3) = v5 & ( ~ (v5 = 0) | v6 = 0)))))
% 12.46/2.55  |   (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] :
% 12.46/2.55  |        (v4 = 0 |  ~ (greatest_lower_bound(v0, v1, v2, v3) = v4) |  ~ $i(v3) | 
% 12.46/2.55  |          ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: $i] :  ? [v6: int] : ( ~
% 12.46/2.55  |            (v6 = 0) & lower_bound(v5, v2, v1) = 0 & apply(v2, v5, v0) = v6 &
% 12.46/2.55  |            member(v5, v3) = 0 & $i(v5)) |  ? [v5: any] :  ? [v6: any] :
% 12.46/2.55  |          (lower_bound(v0, v2, v1) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | 
% 12.46/2.55  |              ~ (v5 = 0))))
% 12.46/2.55  | 
% 12.46/2.55  | ALPHA: (function-axioms) implies:
% 12.46/2.55  |   (7)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 12.46/2.55  |         ! [v3: $i] : (v1 = v0 |  ~ (member(v3, v2) = v1) |  ~ (member(v3, v2)
% 12.46/2.55  |            = v0))
% 12.46/2.55  | 
% 12.46/2.55  | DELTA: instantiating (thIV14) with fresh symbols all_25_0, all_25_1 gives:
% 12.46/2.55  |   (8)  order(all_25_1, all_25_0) = 0 & $i(all_25_0) & $i(all_25_1) &  ? [v0:
% 12.46/2.55  |          $i] : (subset(v0, all_25_0) = 0 & $i(v0) &  ? [v1: $i] :  ? [v2: any]
% 12.46/2.55  |          :  ? [v3: any] :  ? [v4: any] : (greatest_lower_bound(v1, v0,
% 12.46/2.55  |              all_25_1, all_25_0) = v4 & least(v1, all_25_1, v0) = v2 &
% 12.46/2.56  |            member(v1, v0) = v3 & $i(v1) & ((v4 = 0 & v3 = 0 &  ~ (v2 = 0)) |
% 12.46/2.56  |              (v2 = 0 & ( ~ (v4 = 0) |  ~ (v3 = 0))))))
% 12.46/2.56  | 
% 12.46/2.56  | ALPHA: (8) implies:
% 12.46/2.56  |   (9)  $i(all_25_1)
% 12.46/2.56  |   (10)  $i(all_25_0)
% 12.75/2.56  |   (11)   ? [v0: $i] : (subset(v0, all_25_0) = 0 & $i(v0) &  ? [v1: $i] :  ?
% 12.75/2.56  |           [v2: any] :  ? [v3: any] :  ? [v4: any] : (greatest_lower_bound(v1,
% 12.75/2.56  |               v0, all_25_1, all_25_0) = v4 & least(v1, all_25_1, v0) = v2 &
% 12.75/2.56  |             member(v1, v0) = v3 & $i(v1) & ((v4 = 0 & v3 = 0 &  ~ (v2 = 0)) |
% 12.75/2.56  |               (v2 = 0 & ( ~ (v4 = 0) |  ~ (v3 = 0))))))
% 12.75/2.56  | 
% 12.75/2.56  | DELTA: instantiating (11) with fresh symbol all_27_0 gives:
% 12.75/2.56  |   (12)  subset(all_27_0, all_25_0) = 0 & $i(all_27_0) &  ? [v0: $i] :  ? [v1:
% 12.75/2.56  |           any] :  ? [v2: any] :  ? [v3: any] : (greatest_lower_bound(v0,
% 12.75/2.56  |             all_27_0, all_25_1, all_25_0) = v3 & least(v0, all_25_1, all_27_0)
% 12.75/2.56  |           = v1 & member(v0, all_27_0) = v2 & $i(v0) & ((v3 = 0 & v2 = 0 &  ~
% 12.75/2.56  |               (v1 = 0)) | (v1 = 0 & ( ~ (v3 = 0) |  ~ (v2 = 0)))))
% 12.75/2.56  | 
% 12.75/2.56  | ALPHA: (12) implies:
% 12.75/2.56  |   (13)  $i(all_27_0)
% 12.75/2.56  |   (14)   ? [v0: $i] :  ? [v1: any] :  ? [v2: any] :  ? [v3: any] :
% 12.75/2.56  |         (greatest_lower_bound(v0, all_27_0, all_25_1, all_25_0) = v3 &
% 12.75/2.56  |           least(v0, all_25_1, all_27_0) = v1 & member(v0, all_27_0) = v2 &
% 12.75/2.56  |           $i(v0) & ((v3 = 0 & v2 = 0 &  ~ (v1 = 0)) | (v1 = 0 & ( ~ (v3 = 0) |
% 12.75/2.56  |                  ~ (v2 = 0)))))
% 12.75/2.56  | 
% 12.75/2.56  | DELTA: instantiating (14) with fresh symbols all_29_0, all_29_1, all_29_2,
% 12.75/2.56  |        all_29_3 gives:
% 12.75/2.56  |   (15)  greatest_lower_bound(all_29_3, all_27_0, all_25_1, all_25_0) =
% 12.75/2.56  |         all_29_0 & least(all_29_3, all_25_1, all_27_0) = all_29_2 &
% 12.75/2.56  |         member(all_29_3, all_27_0) = all_29_1 & $i(all_29_3) & ((all_29_0 = 0
% 12.75/2.56  |             & all_29_1 = 0 &  ~ (all_29_2 = 0)) | (all_29_2 = 0 & ( ~
% 12.75/2.56  |               (all_29_0 = 0) |  ~ (all_29_1 = 0))))
% 12.75/2.56  | 
% 12.75/2.56  | ALPHA: (15) implies:
% 12.75/2.56  |   (16)  $i(all_29_3)
% 12.75/2.56  |   (17)  member(all_29_3, all_27_0) = all_29_1
% 12.75/2.56  |   (18)  least(all_29_3, all_25_1, all_27_0) = all_29_2
% 12.75/2.56  |   (19)  greatest_lower_bound(all_29_3, all_27_0, all_25_1, all_25_0) =
% 12.75/2.56  |         all_29_0
% 12.75/2.56  |   (20)  (all_29_0 = 0 & all_29_1 = 0 &  ~ (all_29_2 = 0)) | (all_29_2 = 0 & (
% 12.75/2.56  |             ~ (all_29_0 = 0) |  ~ (all_29_1 = 0)))
% 12.75/2.56  | 
% 12.75/2.56  | GROUND_INST: instantiating (4) with all_25_1, all_27_0, all_29_3, all_29_2,
% 12.75/2.56  |              simplifying with (9), (13), (16), (18) gives:
% 12.75/2.56  |   (21)  all_29_2 = 0 |  ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) &
% 12.75/2.56  |           apply(all_25_1, all_29_3, v0) = v1 & member(v0, all_27_0) = 0 &
% 12.75/2.56  |           $i(v0)) |  ? [v0: int] : ( ~ (v0 = 0) & member(all_29_3, all_27_0) =
% 12.75/2.56  |           v0)
% 12.75/2.56  | 
% 12.75/2.56  | GROUND_INST: instantiating (6) with all_29_3, all_27_0, all_25_1, all_25_0,
% 12.75/2.56  |              all_29_0, simplifying with (9), (10), (13), (16), (19) gives:
% 12.75/2.57  |   (22)  all_29_0 = 0 |  ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) &
% 12.75/2.57  |           lower_bound(v0, all_25_1, all_27_0) = 0 & apply(all_25_1, v0,
% 12.75/2.57  |             all_29_3) = v1 & member(v0, all_25_0) = 0 & $i(v0)) |  ? [v0: any]
% 12.75/2.57  |         :  ? [v1: any] : (lower_bound(all_29_3, all_25_1, all_27_0) = v1 &
% 12.75/2.57  |           member(all_29_3, all_27_0) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 12.75/2.57  | 
% 12.75/2.57  | BETA: splitting (20) gives:
% 12.75/2.57  | 
% 12.75/2.57  | Case 1:
% 12.75/2.57  | | 
% 12.75/2.57  | |   (23)  all_29_0 = 0 & all_29_1 = 0 &  ~ (all_29_2 = 0)
% 12.75/2.57  | | 
% 12.75/2.57  | | ALPHA: (23) implies:
% 12.75/2.57  | |   (24)  all_29_1 = 0
% 12.75/2.57  | |   (25)  all_29_0 = 0
% 12.75/2.57  | |   (26)   ~ (all_29_2 = 0)
% 12.75/2.57  | | 
% 12.75/2.57  | | REDUCE: (19), (25) imply:
% 12.75/2.57  | |   (27)  greatest_lower_bound(all_29_3, all_27_0, all_25_1, all_25_0) = 0
% 12.75/2.57  | | 
% 12.75/2.57  | | REDUCE: (17), (24) imply:
% 12.75/2.57  | |   (28)  member(all_29_3, all_27_0) = 0
% 12.75/2.57  | | 
% 12.75/2.57  | | BETA: splitting (21) gives:
% 12.75/2.57  | | 
% 12.75/2.57  | | Case 1:
% 12.75/2.57  | | | 
% 12.75/2.57  | | |   (29)  all_29_2 = 0
% 12.75/2.57  | | | 
% 12.75/2.57  | | | REDUCE: (26), (29) imply:
% 12.75/2.57  | | |   (30)  $false
% 12.75/2.57  | | | 
% 12.75/2.57  | | | CLOSE: (30) is inconsistent.
% 12.75/2.57  | | | 
% 12.75/2.57  | | Case 2:
% 12.75/2.57  | | | 
% 12.75/2.57  | | |   (31)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & apply(all_25_1,
% 12.75/2.57  | | |             all_29_3, v0) = v1 & member(v0, all_27_0) = 0 & $i(v0)) |  ?
% 12.75/2.57  | | |         [v0: int] : ( ~ (v0 = 0) & member(all_29_3, all_27_0) = v0)
% 12.75/2.57  | | | 
% 12.75/2.57  | | | BETA: splitting (31) gives:
% 12.75/2.57  | | | 
% 12.75/2.57  | | | Case 1:
% 12.75/2.57  | | | | 
% 12.75/2.57  | | | |   (32)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & apply(all_25_1,
% 12.75/2.57  | | | |             all_29_3, v0) = v1 & member(v0, all_27_0) = 0 & $i(v0))
% 12.75/2.57  | | | | 
% 12.75/2.57  | | | | GROUND_INST: instantiating (5) with all_29_3, all_27_0, all_25_1,
% 12.75/2.57  | | | |              all_25_0, simplifying with (9), (10), (13), (16), (27)
% 12.75/2.57  | | | |              gives:
% 12.75/2.57  | | | |   (33)  lower_bound(all_29_3, all_25_1, all_27_0) = 0 & member(all_29_3,
% 12.75/2.57  | | | |           all_27_0) = 0 &  ! [v0: $i] : ( ~ (lower_bound(v0, all_25_1,
% 12.75/2.57  | | | |               all_27_0) = 0) |  ~ $i(v0) |  ? [v1: any] :  ? [v2: any] :
% 12.75/2.57  | | | |           (apply(all_25_1, v0, all_29_3) = v2 & member(v0, all_25_0) =
% 12.75/2.57  | | | |             v1 & ( ~ (v1 = 0) | v2 = 0)))
% 12.75/2.57  | | | | 
% 12.75/2.57  | | | | ALPHA: (33) implies:
% 12.75/2.57  | | | |   (34)  lower_bound(all_29_3, all_25_1, all_27_0) = 0
% 12.75/2.57  | | | | 
% 12.75/2.57  | | | | GROUND_INST: instantiating (1) with all_25_1, all_27_0, all_29_3,
% 12.75/2.57  | | | |              simplifying with (9), (13), (16), (34) gives:
% 12.75/2.57  | | | |   (35)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (apply(all_25_1,
% 12.75/2.57  | | | |               all_29_3, v0) = v1) |  ~ $i(v0) |  ? [v2: int] : ( ~ (v2 =
% 12.75/2.57  | | | |               0) & member(v0, all_27_0) = v2))
% 12.75/2.57  | | | | 
% 12.75/2.57  | | | | DELTA: instantiating (32) with fresh symbols all_94_0, all_94_1 gives:
% 12.75/2.57  | | | |   (36)   ~ (all_94_0 = 0) & apply(all_25_1, all_29_3, all_94_1) =
% 12.75/2.57  | | | |         all_94_0 & member(all_94_1, all_27_0) = 0 & $i(all_94_1)
% 12.75/2.57  | | | | 
% 12.75/2.57  | | | | REF_CLOSE: (7), (35), (36) are inconsistent by sub-proof #2.
% 12.75/2.57  | | | | 
% 12.75/2.57  | | | Case 2:
% 12.75/2.57  | | | | 
% 12.75/2.58  | | | |   (37)   ? [v0: int] : ( ~ (v0 = 0) & member(all_29_3, all_27_0) = v0)
% 12.75/2.58  | | | | 
% 12.75/2.58  | | | | DELTA: instantiating (37) with fresh symbol all_89_0 gives:
% 12.75/2.58  | | | |   (38)   ~ (all_89_0 = 0) & member(all_29_3, all_27_0) = all_89_0
% 12.75/2.58  | | | | 
% 12.75/2.58  | | | | REF_CLOSE: (7), (28), (38) are inconsistent by sub-proof #1.
% 12.75/2.58  | | | | 
% 12.75/2.58  | | | End of split
% 12.75/2.58  | | | 
% 12.75/2.58  | | End of split
% 12.75/2.58  | | 
% 12.75/2.58  | Case 2:
% 12.75/2.58  | | 
% 12.75/2.58  | |   (39)  all_29_2 = 0 & ( ~ (all_29_0 = 0) |  ~ (all_29_1 = 0))
% 12.75/2.58  | | 
% 12.75/2.58  | | ALPHA: (39) implies:
% 12.75/2.58  | |   (40)  all_29_2 = 0
% 12.75/2.58  | |   (41)   ~ (all_29_0 = 0) |  ~ (all_29_1 = 0)
% 12.75/2.58  | | 
% 12.75/2.58  | | REDUCE: (18), (40) imply:
% 12.75/2.58  | |   (42)  least(all_29_3, all_25_1, all_27_0) = 0
% 12.75/2.58  | | 
% 12.75/2.58  | | GROUND_INST: instantiating (3) with all_25_1, all_27_0, all_29_3,
% 12.75/2.58  | |              simplifying with (9), (13), (16), (42) gives:
% 12.75/2.58  | |   (43)  member(all_29_3, all_27_0) = 0 &  ! [v0: $i] :  ! [v1: int] : (v1 =
% 12.75/2.58  | |           0 |  ~ (apply(all_25_1, all_29_3, v0) = v1) |  ~ $i(v0) |  ? [v2:
% 12.75/2.58  | |             int] : ( ~ (v2 = 0) & member(v0, all_27_0) = v2))
% 12.75/2.58  | | 
% 12.75/2.58  | | ALPHA: (43) implies:
% 12.75/2.58  | |   (44)  member(all_29_3, all_27_0) = 0
% 12.75/2.58  | |   (45)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (apply(all_25_1, all_29_3,
% 12.75/2.58  | |               v0) = v1) |  ~ $i(v0) |  ? [v2: int] : ( ~ (v2 = 0) &
% 12.75/2.58  | |             member(v0, all_27_0) = v2))
% 12.75/2.58  | | 
% 12.75/2.58  | | GROUND_INST: instantiating (7) with all_29_1, 0, all_27_0, all_29_3,
% 12.75/2.58  | |              simplifying with (17), (44) gives:
% 12.75/2.58  | |   (46)  all_29_1 = 0
% 12.75/2.58  | | 
% 12.75/2.58  | | BETA: splitting (41) gives:
% 12.75/2.58  | | 
% 12.75/2.58  | | Case 1:
% 12.75/2.58  | | | 
% 12.75/2.58  | | |   (47)   ~ (all_29_0 = 0)
% 12.75/2.58  | | | 
% 12.75/2.58  | | | BETA: splitting (22) gives:
% 12.75/2.58  | | | 
% 12.75/2.58  | | | Case 1:
% 12.75/2.58  | | | | 
% 12.75/2.58  | | | |   (48)  all_29_0 = 0
% 12.75/2.58  | | | | 
% 12.75/2.58  | | | | REDUCE: (47), (48) imply:
% 12.75/2.58  | | | |   (49)  $false
% 12.75/2.58  | | | | 
% 12.75/2.58  | | | | CLOSE: (49) is inconsistent.
% 12.75/2.58  | | | | 
% 12.75/2.58  | | | Case 2:
% 12.75/2.58  | | | | 
% 12.75/2.58  | | | |   (50)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & lower_bound(v0,
% 12.75/2.58  | | | |             all_25_1, all_27_0) = 0 & apply(all_25_1, v0, all_29_3) = v1
% 12.75/2.58  | | | |           & member(v0, all_25_0) = 0 & $i(v0)) |  ? [v0: any] :  ? [v1:
% 12.75/2.58  | | | |           any] : (lower_bound(all_29_3, all_25_1, all_27_0) = v1 &
% 12.75/2.58  | | | |           member(all_29_3, all_27_0) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 12.75/2.58  | | | | 
% 12.75/2.58  | | | | BETA: splitting (50) gives:
% 12.75/2.58  | | | | 
% 12.75/2.58  | | | | Case 1:
% 12.75/2.58  | | | | | 
% 12.75/2.58  | | | | |   (51)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & lower_bound(v0,
% 12.75/2.58  | | | | |             all_25_1, all_27_0) = 0 & apply(all_25_1, v0, all_29_3) =
% 12.75/2.58  | | | | |           v1 & member(v0, all_25_0) = 0 & $i(v0))
% 12.75/2.58  | | | | | 
% 12.75/2.58  | | | | | DELTA: instantiating (51) with fresh symbols all_77_0, all_77_1 gives:
% 12.75/2.58  | | | | |   (52)   ~ (all_77_0 = 0) & lower_bound(all_77_1, all_25_1, all_27_0)
% 12.75/2.58  | | | | |         = 0 & apply(all_25_1, all_77_1, all_29_3) = all_77_0 &
% 12.75/2.58  | | | | |         member(all_77_1, all_25_0) = 0 & $i(all_77_1)
% 12.75/2.58  | | | | | 
% 12.75/2.58  | | | | | ALPHA: (52) implies:
% 12.75/2.58  | | | | |   (53)   ~ (all_77_0 = 0)
% 12.75/2.58  | | | | |   (54)  $i(all_77_1)
% 12.75/2.58  | | | | |   (55)  apply(all_25_1, all_77_1, all_29_3) = all_77_0
% 12.75/2.58  | | | | |   (56)  lower_bound(all_77_1, all_25_1, all_27_0) = 0
% 12.75/2.58  | | | | | 
% 12.75/2.58  | | | | | GROUND_INST: instantiating (1) with all_25_1, all_27_0, all_77_1,
% 12.75/2.58  | | | | |              simplifying with (9), (13), (54), (56) gives:
% 12.75/2.58  | | | | |   (57)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (apply(all_25_1,
% 12.75/2.58  | | | | |               all_77_1, v0) = v1) |  ~ $i(v0) |  ? [v2: int] : ( ~ (v2
% 12.75/2.58  | | | | |               = 0) & member(v0, all_27_0) = v2))
% 12.75/2.58  | | | | | 
% 12.75/2.58  | | | | | GROUND_INST: instantiating (57) with all_29_3, all_77_0, simplifying
% 12.75/2.58  | | | | |              with (16), (55) gives:
% 12.75/2.59  | | | | |   (58)  all_77_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & member(all_29_3,
% 12.75/2.59  | | | | |             all_27_0) = v0)
% 12.75/2.59  | | | | | 
% 12.75/2.59  | | | | | BETA: splitting (58) gives:
% 12.75/2.59  | | | | | 
% 12.75/2.59  | | | | | Case 1:
% 12.75/2.59  | | | | | | 
% 12.75/2.59  | | | | | |   (59)  all_77_0 = 0
% 12.75/2.59  | | | | | | 
% 12.75/2.59  | | | | | | REDUCE: (53), (59) imply:
% 12.75/2.59  | | | | | |   (60)  $false
% 12.75/2.59  | | | | | | 
% 12.75/2.59  | | | | | | CLOSE: (60) is inconsistent.
% 12.75/2.59  | | | | | | 
% 12.75/2.59  | | | | | Case 2:
% 12.75/2.59  | | | | | | 
% 12.75/2.59  | | | | | |   (61)   ? [v0: int] : ( ~ (v0 = 0) & member(all_29_3, all_27_0) =
% 12.75/2.59  | | | | | |           v0)
% 12.75/2.59  | | | | | | 
% 12.75/2.59  | | | | | | DELTA: instantiating (61) with fresh symbol all_89_0 gives:
% 12.75/2.59  | | | | | |   (62)   ~ (all_89_0 = 0) & member(all_29_3, all_27_0) = all_89_0
% 12.75/2.59  | | | | | | 
% 12.75/2.59  | | | | | | REF_CLOSE: (7), (44), (62) are inconsistent by sub-proof #1.
% 12.75/2.59  | | | | | | 
% 12.75/2.59  | | | | | End of split
% 12.75/2.59  | | | | | 
% 12.75/2.59  | | | | Case 2:
% 12.75/2.59  | | | | | 
% 12.75/2.59  | | | | |   (63)   ? [v0: any] :  ? [v1: any] : (lower_bound(all_29_3, all_25_1,
% 12.75/2.59  | | | | |             all_27_0) = v1 & member(all_29_3, all_27_0) = v0 & ( ~ (v1
% 12.75/2.59  | | | | |               = 0) |  ~ (v0 = 0)))
% 12.75/2.59  | | | | | 
% 12.75/2.59  | | | | | DELTA: instantiating (63) with fresh symbols all_77_0, all_77_1 gives:
% 12.75/2.59  | | | | |   (64)  lower_bound(all_29_3, all_25_1, all_27_0) = all_77_0 &
% 12.75/2.59  | | | | |         member(all_29_3, all_27_0) = all_77_1 & ( ~ (all_77_0 = 0) | 
% 12.75/2.59  | | | | |           ~ (all_77_1 = 0))
% 12.75/2.59  | | | | | 
% 12.75/2.59  | | | | | ALPHA: (64) implies:
% 12.75/2.59  | | | | |   (65)  member(all_29_3, all_27_0) = all_77_1
% 12.75/2.59  | | | | |   (66)  lower_bound(all_29_3, all_25_1, all_27_0) = all_77_0
% 12.75/2.59  | | | | |   (67)   ~ (all_77_0 = 0) |  ~ (all_77_1 = 0)
% 12.75/2.59  | | | | | 
% 12.75/2.59  | | | | | GROUND_INST: instantiating (7) with 0, all_77_1, all_27_0, all_29_3,
% 12.75/2.59  | | | | |              simplifying with (44), (65) gives:
% 12.75/2.59  | | | | |   (68)  all_77_1 = 0
% 12.75/2.59  | | | | | 
% 12.75/2.59  | | | | | BETA: splitting (67) gives:
% 12.75/2.59  | | | | | 
% 12.75/2.59  | | | | | Case 1:
% 12.75/2.59  | | | | | | 
% 12.75/2.59  | | | | | |   (69)   ~ (all_77_0 = 0)
% 12.75/2.59  | | | | | | 
% 12.75/2.59  | | | | | | GROUND_INST: instantiating (2) with all_25_1, all_27_0, all_29_3,
% 12.75/2.59  | | | | | |              all_77_0, simplifying with (9), (13), (16), (66) gives:
% 12.75/2.59  | | | | | |   (70)  all_77_0 = 0 |  ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) &
% 12.75/2.59  | | | | | |           apply(all_25_1, all_29_3, v0) = v1 & member(v0, all_27_0)
% 12.75/2.59  | | | | | |           = 0 & $i(v0))
% 12.75/2.59  | | | | | | 
% 12.75/2.59  | | | | | | BETA: splitting (70) gives:
% 12.75/2.59  | | | | | | 
% 12.75/2.59  | | | | | | Case 1:
% 12.75/2.59  | | | | | | | 
% 12.75/2.59  | | | | | | |   (71)  all_77_0 = 0
% 12.75/2.59  | | | | | | | 
% 12.75/2.59  | | | | | | | REDUCE: (69), (71) imply:
% 12.75/2.59  | | | | | | |   (72)  $false
% 12.75/2.59  | | | | | | | 
% 12.75/2.59  | | | | | | | CLOSE: (72) is inconsistent.
% 12.75/2.59  | | | | | | | 
% 12.75/2.59  | | | | | | Case 2:
% 12.75/2.59  | | | | | | | 
% 12.75/2.59  | | | | | | |   (73)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) &
% 12.75/2.59  | | | | | | |           apply(all_25_1, all_29_3, v0) = v1 & member(v0,
% 12.75/2.59  | | | | | | |             all_27_0) = 0 & $i(v0))
% 12.75/2.59  | | | | | | | 
% 12.75/2.59  | | | | | | | DELTA: instantiating (73) with fresh symbols all_94_0, all_94_1
% 12.75/2.59  | | | | | | |        gives:
% 12.75/2.59  | | | | | | |   (74)   ~ (all_94_0 = 0) & apply(all_25_1, all_29_3, all_94_1) =
% 12.75/2.59  | | | | | | |         all_94_0 & member(all_94_1, all_27_0) = 0 & $i(all_94_1)
% 12.75/2.59  | | | | | | | 
% 12.75/2.59  | | | | | | | REF_CLOSE: (7), (45), (74) are inconsistent by sub-proof #2.
% 12.75/2.59  | | | | | | | 
% 12.75/2.59  | | | | | | End of split
% 12.75/2.59  | | | | | | 
% 12.75/2.59  | | | | | Case 2:
% 12.75/2.59  | | | | | | 
% 12.75/2.59  | | | | | |   (75)   ~ (all_77_1 = 0)
% 12.75/2.59  | | | | | | 
% 12.75/2.59  | | | | | | REDUCE: (68), (75) imply:
% 12.75/2.59  | | | | | |   (76)  $false
% 12.75/2.59  | | | | | | 
% 12.75/2.59  | | | | | | CLOSE: (76) is inconsistent.
% 12.75/2.59  | | | | | | 
% 12.75/2.59  | | | | | End of split
% 12.75/2.59  | | | | | 
% 12.75/2.59  | | | | End of split
% 12.75/2.59  | | | | 
% 12.75/2.59  | | | End of split
% 12.75/2.59  | | | 
% 12.75/2.59  | | Case 2:
% 12.75/2.59  | | | 
% 12.75/2.59  | | |   (77)   ~ (all_29_1 = 0)
% 12.75/2.59  | | | 
% 12.75/2.59  | | | REDUCE: (46), (77) imply:
% 12.75/2.59  | | |   (78)  $false
% 12.75/2.59  | | | 
% 12.75/2.59  | | | CLOSE: (78) is inconsistent.
% 12.75/2.59  | | | 
% 12.75/2.59  | | End of split
% 12.75/2.59  | | 
% 12.75/2.59  | End of split
% 12.75/2.59  | 
% 12.75/2.59  End of proof
% 12.75/2.59  
% 12.75/2.59  Sub-proof #1 shows that the following formulas are inconsistent:
% 12.75/2.59  ----------------------------------------------------------------
% 12.75/2.59    (1)   ~ (all_89_0 = 0) & member(all_29_3, all_27_0) = all_89_0
% 12.75/2.59    (2)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : 
% 12.75/2.59         ! [v3: $i] : (v1 = v0 |  ~ (member(v3, v2) = v1) |  ~ (member(v3, v2) =
% 12.75/2.59             v0))
% 12.75/2.59    (3)  member(all_29_3, all_27_0) = 0
% 12.75/2.59  
% 12.75/2.59  Begin of proof
% 12.75/2.59  | 
% 12.75/2.59  | ALPHA: (1) implies:
% 12.75/2.59  |   (4)   ~ (all_89_0 = 0)
% 12.75/2.59  |   (5)  member(all_29_3, all_27_0) = all_89_0
% 12.75/2.59  | 
% 12.75/2.60  | GROUND_INST: instantiating (2) with 0, all_89_0, all_27_0, all_29_3,
% 12.75/2.60  |              simplifying with (3), (5) gives:
% 12.75/2.60  |   (6)  all_89_0 = 0
% 12.75/2.60  | 
% 12.75/2.60  | REDUCE: (4), (6) imply:
% 12.75/2.60  |   (7)  $false
% 12.75/2.60  | 
% 12.75/2.60  | CLOSE: (7) is inconsistent.
% 12.75/2.60  | 
% 12.75/2.60  End of proof
% 12.75/2.60  
% 12.75/2.60  Sub-proof #2 shows that the following formulas are inconsistent:
% 12.75/2.60  ----------------------------------------------------------------
% 12.75/2.60    (1)   ~ (all_94_0 = 0) & apply(all_25_1, all_29_3, all_94_1) = all_94_0 &
% 12.75/2.60         member(all_94_1, all_27_0) = 0 & $i(all_94_1)
% 12.75/2.60    (2)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (apply(all_25_1, all_29_3, v0)
% 12.75/2.60             = v1) |  ~ $i(v0) |  ? [v2: int] : ( ~ (v2 = 0) & member(v0,
% 12.75/2.60               all_27_0) = v2))
% 12.75/2.60    (3)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : 
% 12.75/2.60         ! [v3: $i] : (v1 = v0 |  ~ (member(v3, v2) = v1) |  ~ (member(v3, v2) =
% 12.75/2.60             v0))
% 12.75/2.60  
% 12.75/2.60  Begin of proof
% 12.75/2.60  | 
% 12.75/2.60  | ALPHA: (1) implies:
% 12.75/2.60  |   (4)   ~ (all_94_0 = 0)
% 12.75/2.60  |   (5)  $i(all_94_1)
% 12.75/2.60  |   (6)  member(all_94_1, all_27_0) = 0
% 12.75/2.60  |   (7)  apply(all_25_1, all_29_3, all_94_1) = all_94_0
% 12.75/2.60  | 
% 12.75/2.60  | GROUND_INST: instantiating (2) with all_94_1, all_94_0, simplifying with (5),
% 12.75/2.60  |              (7) gives:
% 12.75/2.60  |   (8)  all_94_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & member(all_94_1, all_27_0)
% 12.75/2.60  |          = v0)
% 12.75/2.60  | 
% 12.75/2.60  | BETA: splitting (8) gives:
% 12.75/2.60  | 
% 12.75/2.60  | Case 1:
% 12.75/2.60  | | 
% 12.75/2.60  | |   (9)  all_94_0 = 0
% 12.75/2.60  | | 
% 12.75/2.60  | | REDUCE: (4), (9) imply:
% 12.75/2.60  | |   (10)  $false
% 12.75/2.60  | | 
% 12.75/2.60  | | CLOSE: (10) is inconsistent.
% 12.75/2.60  | | 
% 12.75/2.60  | Case 2:
% 12.75/2.60  | | 
% 12.75/2.60  | |   (11)   ? [v0: int] : ( ~ (v0 = 0) & member(all_94_1, all_27_0) = v0)
% 12.75/2.60  | | 
% 12.75/2.60  | | DELTA: instantiating (11) with fresh symbol all_106_0 gives:
% 12.75/2.60  | |   (12)   ~ (all_106_0 = 0) & member(all_94_1, all_27_0) = all_106_0
% 12.75/2.60  | | 
% 12.75/2.60  | | ALPHA: (12) implies:
% 12.75/2.60  | |   (13)   ~ (all_106_0 = 0)
% 12.75/2.60  | |   (14)  member(all_94_1, all_27_0) = all_106_0
% 12.75/2.60  | | 
% 12.75/2.60  | | GROUND_INST: instantiating (3) with 0, all_106_0, all_27_0, all_94_1,
% 12.75/2.60  | |              simplifying with (6), (14) gives:
% 12.75/2.60  | |   (15)  all_106_0 = 0
% 12.75/2.60  | | 
% 12.75/2.60  | | REDUCE: (13), (15) imply:
% 12.75/2.60  | |   (16)  $false
% 12.75/2.60  | | 
% 12.75/2.60  | | CLOSE: (16) is inconsistent.
% 12.75/2.60  | | 
% 12.75/2.60  | End of split
% 12.75/2.60  | 
% 12.75/2.60  End of proof
% 12.75/2.60  % SZS output end Proof for theBenchmark
% 12.75/2.60  
% 12.75/2.60  1991ms
%------------------------------------------------------------------------------