TSTP Solution File: SET372+4 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SET372+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n016.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 15:24:47 EDT 2023

% Result   : Theorem 8.71s 1.97s
% Output   : Proof 9.56s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET372+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33  % Computer : n016.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sat Aug 26 09:20:27 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.19/0.60  ________       _____
% 0.19/0.60  ___  __ \_________(_)________________________________
% 0.19/0.60  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.19/0.60  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.19/0.60  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60  
% 0.19/0.60  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60  (2023-06-19)
% 0.19/0.60  
% 0.19/0.60  (c) Philipp Rümmer, 2009-2023
% 0.19/0.60  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60                Amanda Stjerna.
% 0.19/0.60  Free software under BSD-3-Clause.
% 0.19/0.60  
% 0.19/0.60  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60  
% 0.19/0.60  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61  Running up to 7 provers in parallel.
% 0.19/0.62  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.62  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.63/1.07  Prover 1: Preprocessing ...
% 2.63/1.07  Prover 4: Preprocessing ...
% 2.63/1.11  Prover 2: Preprocessing ...
% 2.63/1.11  Prover 3: Preprocessing ...
% 2.63/1.11  Prover 6: Preprocessing ...
% 2.63/1.11  Prover 5: Preprocessing ...
% 2.63/1.11  Prover 0: Preprocessing ...
% 4.75/1.45  Prover 6: Proving ...
% 4.75/1.47  Prover 1: Constructing countermodel ...
% 4.75/1.47  Prover 2: Proving ...
% 4.75/1.48  Prover 5: Proving ...
% 4.75/1.48  Prover 3: Constructing countermodel ...
% 4.75/1.53  Prover 0: Proving ...
% 4.75/1.54  Prover 4: Constructing countermodel ...
% 8.71/1.97  Prover 3: proved (1345ms)
% 8.71/1.97  
% 8.71/1.97  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.71/1.97  
% 8.71/1.97  Prover 2: stopped
% 9.06/1.97  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.06/1.97  Prover 1: Found proof (size 105)
% 9.06/1.97  Prover 1: proved (1354ms)
% 9.06/1.97  Prover 5: stopped
% 9.06/1.97  Prover 0: stopped
% 9.06/1.97  Prover 6: stopped
% 9.06/1.97  Prover 4: stopped
% 9.06/1.98  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.06/2.00  Prover 7: Preprocessing ...
% 9.06/2.00  Prover 8: Preprocessing ...
% 9.06/2.02  Prover 7: stopped
% 9.43/2.07  Prover 8: Warning: ignoring some quantifiers
% 9.56/2.07  Prover 8: Constructing countermodel ...
% 9.56/2.08  Prover 8: stopped
% 9.56/2.08  
% 9.56/2.08  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.56/2.08  
% 9.56/2.09  % SZS output start Proof for theBenchmark
% 9.56/2.10  Assumptions after simplification:
% 9.56/2.10  ---------------------------------
% 9.56/2.10  
% 9.56/2.10    (equal_set)
% 9.56/2.13     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (equal_set(v0, v1) =
% 9.56/2.13        v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] : (subset(v1,
% 9.56/2.13          v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0)))) &  ! [v0:
% 9.56/2.13      $i] :  ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) |
% 9.56/2.13      (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 9.56/2.13  
% 9.56/2.13    (intersection)
% 9.56/2.13     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] : (v4 = 0
% 9.56/2.13      |  ~ (intersection(v1, v2) = v3) |  ~ (member(v0, v3) = v4) |  ~ $i(v2) |  ~
% 9.56/2.13      $i(v1) |  ~ $i(v0) |  ? [v5: any] :  ? [v6: any] : (member(v0, v2) = v6 &
% 9.56/2.13        member(v0, v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0)))) &  ! [v0: $i] :  !
% 9.56/2.13    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ (intersection(v1, v2) = v3) |  ~
% 9.56/2.13      (member(v0, v3) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) | (member(v0, v2) =
% 9.56/2.13        0 & member(v0, v1) = 0))
% 9.56/2.13  
% 9.56/2.13    (power_set)
% 9.56/2.14     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 9.56/2.14      (power_set(v1) = v2) |  ~ (member(v0, v2) = v3) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 9.56/2.14      [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) &  ! [v0: $i] :  ! [v1: $i]
% 9.56/2.14    :  ! [v2: $i] : ( ~ (power_set(v1) = v2) |  ~ (member(v0, v2) = 0) |  ~ $i(v1)
% 9.56/2.14      |  ~ $i(v0) | subset(v0, v1) = 0)
% 9.56/2.14  
% 9.56/2.14    (subset)
% 9.56/2.14     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (subset(v0, v1) = v2)
% 9.56/2.14      |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~ (v4 = 0) &
% 9.56/2.14        member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) &  ! [v0: $i] :  !
% 9.56/2.14    [v1: $i] : ( ~ (subset(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ! [v2: $i] : (
% 9.56/2.14        ~ (member(v2, v0) = 0) |  ~ $i(v2) | member(v2, v1) = 0))
% 9.56/2.14  
% 9.56/2.14    (thI21)
% 9.56/2.14     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] :  ? [v5:
% 9.56/2.14      $i] :  ? [v6: $i] :  ? [v7: int] : ( ~ (v7 = 0) & intersection(v4, v5) = v6
% 9.56/2.14      & intersection(v0, v1) = v2 & power_set(v2) = v3 & power_set(v1) = v5 &
% 9.56/2.14      power_set(v0) = v4 & equal_set(v3, v6) = v7 & $i(v6) & $i(v5) & $i(v4) &
% 9.56/2.14      $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 9.56/2.15  
% 9.56/2.15    (function-axioms)
% 9.56/2.16     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 9.56/2.16      (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0)) &  ! [v0:
% 9.56/2.16      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 9.56/2.16      (difference(v3, v2) = v1) |  ~ (difference(v3, v2) = v0)) &  ! [v0: $i] :  !
% 9.56/2.16    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (union(v3, v2) = v1) |  ~
% 9.56/2.16      (union(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3:
% 9.56/2.16      $i] : (v1 = v0 |  ~ (intersection(v3, v2) = v1) |  ~ (intersection(v3, v2) =
% 9.56/2.16        v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 9.56/2.16      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (equal_set(v3, v2) = v1) |  ~
% 9.56/2.16      (equal_set(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 9.56/2.16      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (subset(v3,
% 9.56/2.16          v2) = v1) |  ~ (subset(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  !
% 9.56/2.16    [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 9.56/2.16      (member(v3, v2) = v1) |  ~ (member(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1:
% 9.56/2.16      $i] :  ! [v2: $i] : (v1 = v0 |  ~ (product(v2) = v1) |  ~ (product(v2) =
% 9.56/2.16        v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (sum(v2) =
% 9.56/2.16        v1) |  ~ (sum(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 =
% 9.56/2.16      v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0)) &  ! [v0: $i] :  !
% 9.56/2.16    [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (power_set(v2) = v1) |  ~
% 9.56/2.16      (power_set(v2) = v0))
% 9.56/2.16  
% 9.56/2.16  Further assumptions not needed in the proof:
% 9.56/2.16  --------------------------------------------
% 9.56/2.16  difference, empty_set, product, singleton, sum, union, unordered_pair
% 9.56/2.16  
% 9.56/2.16  Those formulas are unsatisfiable:
% 9.56/2.16  ---------------------------------
% 9.56/2.16  
% 9.56/2.16  Begin of proof
% 9.56/2.16  | 
% 9.56/2.16  | ALPHA: (subset) implies:
% 9.56/2.16  |   (1)   ! [v0: $i] :  ! [v1: $i] : ( ~ (subset(v0, v1) = 0) |  ~ $i(v1) |  ~
% 9.56/2.16  |          $i(v0) |  ! [v2: $i] : ( ~ (member(v2, v0) = 0) |  ~ $i(v2) |
% 9.56/2.16  |            member(v2, v1) = 0))
% 9.56/2.16  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (subset(v0, v1)
% 9.56/2.16  |            = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~
% 9.56/2.16  |            (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 9.56/2.16  | 
% 9.56/2.16  | ALPHA: (equal_set) implies:
% 9.56/2.16  |   (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (equal_set(v0,
% 9.56/2.16  |              v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] :
% 9.56/2.16  |          (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 =
% 9.56/2.16  |                0))))
% 9.56/2.16  | 
% 9.56/2.16  | ALPHA: (power_set) implies:
% 9.56/2.16  |   (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (power_set(v1) = v2) |  ~
% 9.56/2.16  |          (member(v0, v2) = 0) |  ~ $i(v1) |  ~ $i(v0) | subset(v0, v1) = 0)
% 9.56/2.17  |   (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 9.56/2.17  |          (power_set(v1) = v2) |  ~ (member(v0, v2) = v3) |  ~ $i(v1) |  ~
% 9.56/2.17  |          $i(v0) |  ? [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 9.56/2.17  | 
% 9.56/2.17  | ALPHA: (intersection) implies:
% 9.56/2.17  |   (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~
% 9.56/2.17  |          (intersection(v1, v2) = v3) |  ~ (member(v0, v3) = 0) |  ~ $i(v2) | 
% 9.56/2.17  |          ~ $i(v1) |  ~ $i(v0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 9.56/2.17  |   (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] :
% 9.56/2.17  |        (v4 = 0 |  ~ (intersection(v1, v2) = v3) |  ~ (member(v0, v3) = v4) | 
% 9.56/2.17  |          ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: any] :  ? [v6: any] :
% 9.56/2.17  |          (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 =
% 9.56/2.17  |                0))))
% 9.56/2.17  | 
% 9.56/2.17  | ALPHA: (function-axioms) implies:
% 9.56/2.17  |   (8)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 9.56/2.17  |         ! [v3: $i] : (v1 = v0 |  ~ (member(v3, v2) = v1) |  ~ (member(v3, v2)
% 9.56/2.17  |            = v0))
% 9.56/2.17  | 
% 9.56/2.17  | DELTA: instantiating (thI21) with fresh symbols all_15_0, all_15_1, all_15_2,
% 9.56/2.17  |        all_15_3, all_15_4, all_15_5, all_15_6, all_15_7 gives:
% 9.56/2.17  |   (9)   ~ (all_15_0 = 0) & intersection(all_15_3, all_15_2) = all_15_1 &
% 9.56/2.17  |        intersection(all_15_7, all_15_6) = all_15_5 & power_set(all_15_5) =
% 9.56/2.17  |        all_15_4 & power_set(all_15_6) = all_15_2 & power_set(all_15_7) =
% 9.56/2.17  |        all_15_3 & equal_set(all_15_4, all_15_1) = all_15_0 & $i(all_15_1) &
% 9.56/2.17  |        $i(all_15_2) & $i(all_15_3) & $i(all_15_4) & $i(all_15_5) &
% 9.56/2.17  |        $i(all_15_6) & $i(all_15_7)
% 9.56/2.17  | 
% 9.56/2.17  | ALPHA: (9) implies:
% 9.56/2.17  |   (10)   ~ (all_15_0 = 0)
% 9.56/2.17  |   (11)  $i(all_15_7)
% 9.56/2.17  |   (12)  $i(all_15_6)
% 9.56/2.17  |   (13)  $i(all_15_5)
% 9.56/2.17  |   (14)  $i(all_15_4)
% 9.56/2.17  |   (15)  $i(all_15_3)
% 9.56/2.17  |   (16)  $i(all_15_2)
% 9.56/2.17  |   (17)  $i(all_15_1)
% 9.56/2.17  |   (18)  equal_set(all_15_4, all_15_1) = all_15_0
% 9.56/2.17  |   (19)  power_set(all_15_7) = all_15_3
% 9.56/2.17  |   (20)  power_set(all_15_6) = all_15_2
% 9.56/2.17  |   (21)  power_set(all_15_5) = all_15_4
% 9.56/2.17  |   (22)  intersection(all_15_7, all_15_6) = all_15_5
% 9.56/2.17  |   (23)  intersection(all_15_3, all_15_2) = all_15_1
% 9.56/2.17  | 
% 9.56/2.18  | GROUND_INST: instantiating (3) with all_15_4, all_15_1, all_15_0, simplifying
% 9.56/2.18  |              with (14), (17), (18) gives:
% 9.56/2.18  |   (24)  all_15_0 = 0 |  ? [v0: any] :  ? [v1: any] : (subset(all_15_1,
% 9.56/2.18  |             all_15_4) = v1 & subset(all_15_4, all_15_1) = v0 & ( ~ (v1 = 0) | 
% 9.56/2.18  |             ~ (v0 = 0)))
% 9.56/2.18  | 
% 9.56/2.18  | BETA: splitting (24) gives:
% 9.56/2.18  | 
% 9.56/2.18  | Case 1:
% 9.56/2.18  | | 
% 9.56/2.18  | |   (25)  all_15_0 = 0
% 9.56/2.18  | | 
% 9.56/2.18  | | REDUCE: (10), (25) imply:
% 9.56/2.18  | |   (26)  $false
% 9.56/2.18  | | 
% 9.56/2.18  | | CLOSE: (26) is inconsistent.
% 9.56/2.18  | | 
% 9.56/2.18  | Case 2:
% 9.56/2.18  | | 
% 9.56/2.18  | |   (27)   ? [v0: any] :  ? [v1: any] : (subset(all_15_1, all_15_4) = v1 &
% 9.56/2.18  | |           subset(all_15_4, all_15_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 9.56/2.18  | | 
% 9.56/2.18  | | DELTA: instantiating (27) with fresh symbols all_24_0, all_24_1 gives:
% 9.56/2.18  | |   (28)  subset(all_15_1, all_15_4) = all_24_0 & subset(all_15_4, all_15_1) =
% 9.56/2.18  | |         all_24_1 & ( ~ (all_24_0 = 0) |  ~ (all_24_1 = 0))
% 9.56/2.18  | | 
% 9.56/2.18  | | ALPHA: (28) implies:
% 9.56/2.18  | |   (29)  subset(all_15_4, all_15_1) = all_24_1
% 9.56/2.18  | |   (30)  subset(all_15_1, all_15_4) = all_24_0
% 9.56/2.18  | |   (31)   ~ (all_24_0 = 0) |  ~ (all_24_1 = 0)
% 9.56/2.18  | | 
% 9.56/2.18  | | GROUND_INST: instantiating (2) with all_15_4, all_15_1, all_24_1,
% 9.56/2.18  | |              simplifying with (14), (17), (29) gives:
% 9.56/2.18  | |   (32)  all_24_1 = 0 |  ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) &
% 9.56/2.18  | |           member(v0, all_15_1) = v1 & member(v0, all_15_4) = 0 & $i(v0))
% 9.56/2.18  | | 
% 9.56/2.18  | | GROUND_INST: instantiating (2) with all_15_1, all_15_4, all_24_0,
% 9.56/2.18  | |              simplifying with (14), (17), (30) gives:
% 9.56/2.18  | |   (33)  all_24_0 = 0 |  ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) &
% 9.56/2.18  | |           member(v0, all_15_1) = 0 & member(v0, all_15_4) = v1 & $i(v0))
% 9.56/2.18  | | 
% 9.56/2.18  | | BETA: splitting (31) gives:
% 9.56/2.18  | | 
% 9.56/2.18  | | Case 1:
% 9.56/2.18  | | | 
% 9.56/2.18  | | |   (34)   ~ (all_24_0 = 0)
% 9.56/2.18  | | | 
% 9.56/2.18  | | | BETA: splitting (33) gives:
% 9.56/2.18  | | | 
% 9.56/2.18  | | | Case 1:
% 9.56/2.18  | | | | 
% 9.56/2.18  | | | |   (35)  all_24_0 = 0
% 9.56/2.18  | | | | 
% 9.56/2.18  | | | | REDUCE: (34), (35) imply:
% 9.56/2.18  | | | |   (36)  $false
% 9.56/2.18  | | | | 
% 9.56/2.18  | | | | CLOSE: (36) is inconsistent.
% 9.56/2.18  | | | | 
% 9.56/2.18  | | | Case 2:
% 9.56/2.18  | | | | 
% 9.56/2.18  | | | |   (37)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1)
% 9.56/2.19  | | | |           = 0 & member(v0, all_15_4) = v1 & $i(v0))
% 9.56/2.19  | | | | 
% 9.56/2.19  | | | | DELTA: instantiating (37) with fresh symbols all_37_0, all_37_1 gives:
% 9.56/2.19  | | | |   (38)   ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = 0 &
% 9.56/2.19  | | | |         member(all_37_1, all_15_4) = all_37_0 & $i(all_37_1)
% 9.56/2.19  | | | | 
% 9.56/2.19  | | | | ALPHA: (38) implies:
% 9.56/2.19  | | | |   (39)   ~ (all_37_0 = 0)
% 9.56/2.19  | | | |   (40)  $i(all_37_1)
% 9.56/2.19  | | | |   (41)  member(all_37_1, all_15_4) = all_37_0
% 9.56/2.19  | | | |   (42)  member(all_37_1, all_15_1) = 0
% 9.56/2.19  | | | | 
% 9.56/2.19  | | | | GROUND_INST: instantiating (5) with all_37_1, all_15_5, all_15_4,
% 9.56/2.19  | | | |              all_37_0, simplifying with (13), (21), (40), (41) gives:
% 9.56/2.19  | | | |   (43)  all_37_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & subset(all_37_1,
% 9.56/2.19  | | | |             all_15_5) = v0)
% 9.56/2.19  | | | | 
% 9.56/2.19  | | | | GROUND_INST: instantiating (6) with all_37_1, all_15_3, all_15_2,
% 9.56/2.19  | | | |              all_15_1, simplifying with (15), (16), (23), (40), (42)
% 9.56/2.19  | | | |              gives:
% 9.56/2.19  | | | |   (44)  member(all_37_1, all_15_2) = 0 & member(all_37_1, all_15_3) = 0
% 9.56/2.19  | | | | 
% 9.56/2.19  | | | | ALPHA: (44) implies:
% 9.56/2.19  | | | |   (45)  member(all_37_1, all_15_3) = 0
% 9.56/2.19  | | | |   (46)  member(all_37_1, all_15_2) = 0
% 9.56/2.19  | | | | 
% 9.56/2.19  | | | | BETA: splitting (43) gives:
% 9.56/2.19  | | | | 
% 9.56/2.19  | | | | Case 1:
% 9.56/2.19  | | | | | 
% 9.56/2.19  | | | | |   (47)  all_37_0 = 0
% 9.56/2.19  | | | | | 
% 9.56/2.19  | | | | | REDUCE: (39), (47) imply:
% 9.56/2.19  | | | | |   (48)  $false
% 9.56/2.19  | | | | | 
% 9.56/2.19  | | | | | CLOSE: (48) is inconsistent.
% 9.56/2.19  | | | | | 
% 9.56/2.19  | | | | Case 2:
% 9.56/2.19  | | | | | 
% 9.56/2.19  | | | | |   (49)   ? [v0: int] : ( ~ (v0 = 0) & subset(all_37_1, all_15_5) = v0)
% 9.56/2.19  | | | | | 
% 9.56/2.19  | | | | | DELTA: instantiating (49) with fresh symbol all_49_0 gives:
% 9.56/2.19  | | | | |   (50)   ~ (all_49_0 = 0) & subset(all_37_1, all_15_5) = all_49_0
% 9.56/2.19  | | | | | 
% 9.56/2.19  | | | | | ALPHA: (50) implies:
% 9.56/2.19  | | | | |   (51)   ~ (all_49_0 = 0)
% 9.56/2.19  | | | | |   (52)  subset(all_37_1, all_15_5) = all_49_0
% 9.56/2.19  | | | | | 
% 9.56/2.19  | | | | | GROUND_INST: instantiating (4) with all_37_1, all_15_7, all_15_3,
% 9.56/2.19  | | | | |              simplifying with (11), (19), (40), (45) gives:
% 9.56/2.19  | | | | |   (53)  subset(all_37_1, all_15_7) = 0
% 9.56/2.19  | | | | | 
% 9.56/2.19  | | | | | GROUND_INST: instantiating (4) with all_37_1, all_15_6, all_15_2,
% 9.56/2.19  | | | | |              simplifying with (12), (20), (40), (46) gives:
% 9.56/2.19  | | | | |   (54)  subset(all_37_1, all_15_6) = 0
% 9.56/2.19  | | | | | 
% 9.56/2.19  | | | | | GROUND_INST: instantiating (2) with all_37_1, all_15_5, all_49_0,
% 9.56/2.19  | | | | |              simplifying with (13), (40), (52) gives:
% 9.56/2.20  | | | | |   (55)  all_49_0 = 0 |  ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) &
% 9.56/2.20  | | | | |           member(v0, all_37_1) = 0 & member(v0, all_15_5) = v1 &
% 9.56/2.20  | | | | |           $i(v0))
% 9.56/2.20  | | | | | 
% 9.56/2.20  | | | | | BETA: splitting (55) gives:
% 9.56/2.20  | | | | | 
% 9.56/2.20  | | | | | Case 1:
% 9.56/2.20  | | | | | | 
% 9.56/2.20  | | | | | |   (56)  all_49_0 = 0
% 9.56/2.20  | | | | | | 
% 9.56/2.20  | | | | | | REDUCE: (51), (56) imply:
% 9.56/2.20  | | | | | |   (57)  $false
% 9.56/2.20  | | | | | | 
% 9.56/2.20  | | | | | | CLOSE: (57) is inconsistent.
% 9.56/2.20  | | | | | | 
% 9.56/2.20  | | | | | Case 2:
% 9.56/2.20  | | | | | | 
% 9.56/2.20  | | | | | |   (58)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 9.56/2.20  | | | | | |             all_37_1) = 0 & member(v0, all_15_5) = v1 & $i(v0))
% 9.56/2.20  | | | | | | 
% 9.56/2.20  | | | | | | DELTA: instantiating (58) with fresh symbols all_61_0, all_61_1
% 9.56/2.20  | | | | | |        gives:
% 9.56/2.20  | | | | | |   (59)   ~ (all_61_0 = 0) & member(all_61_1, all_37_1) = 0 &
% 9.56/2.20  | | | | | |         member(all_61_1, all_15_5) = all_61_0 & $i(all_61_1)
% 9.56/2.20  | | | | | | 
% 9.56/2.20  | | | | | | ALPHA: (59) implies:
% 9.56/2.20  | | | | | |   (60)   ~ (all_61_0 = 0)
% 9.56/2.20  | | | | | |   (61)  $i(all_61_1)
% 9.56/2.20  | | | | | |   (62)  member(all_61_1, all_15_5) = all_61_0
% 9.56/2.20  | | | | | |   (63)  member(all_61_1, all_37_1) = 0
% 9.56/2.20  | | | | | | 
% 9.56/2.20  | | | | | | GROUND_INST: instantiating (7) with all_61_1, all_15_7, all_15_6,
% 9.56/2.20  | | | | | |              all_15_5, all_61_0, simplifying with (11), (12), (22),
% 9.56/2.20  | | | | | |              (61), (62) gives:
% 9.56/2.20  | | | | | |   (64)  all_61_0 = 0 |  ? [v0: any] :  ? [v1: any] :
% 9.56/2.20  | | | | | |         (member(all_61_1, all_15_6) = v1 & member(all_61_1,
% 9.56/2.20  | | | | | |             all_15_7) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 9.56/2.20  | | | | | | 
% 9.56/2.20  | | | | | | GROUND_INST: instantiating (1) with all_37_1, all_15_7, simplifying
% 9.56/2.20  | | | | | |              with (11), (40), (53) gives:
% 9.56/2.20  | | | | | |   (65)   ! [v0: $i] : ( ~ (member(v0, all_37_1) = 0) |  ~ $i(v0) |
% 9.56/2.20  | | | | | |           member(v0, all_15_7) = 0)
% 9.56/2.20  | | | | | | 
% 9.56/2.20  | | | | | | GROUND_INST: instantiating (1) with all_37_1, all_15_6, simplifying
% 9.56/2.20  | | | | | |              with (12), (40), (54) gives:
% 9.56/2.20  | | | | | |   (66)   ! [v0: $i] : ( ~ (member(v0, all_37_1) = 0) |  ~ $i(v0) |
% 9.56/2.20  | | | | | |           member(v0, all_15_6) = 0)
% 9.56/2.20  | | | | | | 
% 9.56/2.20  | | | | | | GROUND_INST: instantiating (66) with all_61_1, simplifying with
% 9.56/2.20  | | | | | |              (61), (63) gives:
% 9.56/2.20  | | | | | |   (67)  member(all_61_1, all_15_6) = 0
% 9.56/2.20  | | | | | | 
% 9.56/2.20  | | | | | | GROUND_INST: instantiating (65) with all_61_1, simplifying with
% 9.56/2.20  | | | | | |              (61), (63) gives:
% 9.56/2.20  | | | | | |   (68)  member(all_61_1, all_15_7) = 0
% 9.56/2.20  | | | | | | 
% 9.56/2.20  | | | | | | BETA: splitting (64) gives:
% 9.56/2.20  | | | | | | 
% 9.56/2.20  | | | | | | Case 1:
% 9.56/2.20  | | | | | | | 
% 9.56/2.20  | | | | | | |   (69)  all_61_0 = 0
% 9.56/2.20  | | | | | | | 
% 9.56/2.20  | | | | | | | REDUCE: (60), (69) imply:
% 9.56/2.20  | | | | | | |   (70)  $false
% 9.56/2.20  | | | | | | | 
% 9.56/2.20  | | | | | | | CLOSE: (70) is inconsistent.
% 9.56/2.20  | | | | | | | 
% 9.56/2.20  | | | | | | Case 2:
% 9.56/2.20  | | | | | | | 
% 9.56/2.20  | | | | | | |   (71)   ? [v0: any] :  ? [v1: any] : (member(all_61_1, all_15_6)
% 9.56/2.20  | | | | | | |           = v1 & member(all_61_1, all_15_7) = v0 & ( ~ (v1 = 0) | 
% 9.56/2.20  | | | | | | |             ~ (v0 = 0)))
% 9.56/2.20  | | | | | | | 
% 9.56/2.20  | | | | | | | DELTA: instantiating (71) with fresh symbols all_76_0, all_76_1
% 9.56/2.20  | | | | | | |        gives:
% 9.56/2.21  | | | | | | |   (72)  member(all_61_1, all_15_6) = all_76_0 & member(all_61_1,
% 9.56/2.21  | | | | | | |           all_15_7) = all_76_1 & ( ~ (all_76_0 = 0) |  ~ (all_76_1
% 9.56/2.21  | | | | | | |             = 0))
% 9.56/2.21  | | | | | | | 
% 9.56/2.21  | | | | | | | ALPHA: (72) implies:
% 9.56/2.21  | | | | | | |   (73)  member(all_61_1, all_15_7) = all_76_1
% 9.56/2.21  | | | | | | |   (74)  member(all_61_1, all_15_6) = all_76_0
% 9.56/2.21  | | | | | | |   (75)   ~ (all_76_0 = 0) |  ~ (all_76_1 = 0)
% 9.56/2.21  | | | | | | | 
% 9.56/2.21  | | | | | | | GROUND_INST: instantiating (8) with 0, all_76_1, all_15_7,
% 9.56/2.21  | | | | | | |              all_61_1, simplifying with (68), (73) gives:
% 9.56/2.21  | | | | | | |   (76)  all_76_1 = 0
% 9.56/2.21  | | | | | | | 
% 9.56/2.21  | | | | | | | GROUND_INST: instantiating (8) with 0, all_76_0, all_15_6,
% 9.56/2.21  | | | | | | |              all_61_1, simplifying with (67), (74) gives:
% 9.56/2.21  | | | | | | |   (77)  all_76_0 = 0
% 9.56/2.21  | | | | | | | 
% 9.56/2.21  | | | | | | | BETA: splitting (75) gives:
% 9.56/2.21  | | | | | | | 
% 9.56/2.21  | | | | | | | Case 1:
% 9.56/2.21  | | | | | | | | 
% 9.56/2.21  | | | | | | | |   (78)   ~ (all_76_0 = 0)
% 9.56/2.21  | | | | | | | | 
% 9.56/2.21  | | | | | | | | REDUCE: (77), (78) imply:
% 9.56/2.21  | | | | | | | |   (79)  $false
% 9.56/2.21  | | | | | | | | 
% 9.56/2.21  | | | | | | | | CLOSE: (79) is inconsistent.
% 9.56/2.21  | | | | | | | | 
% 9.56/2.21  | | | | | | | Case 2:
% 9.56/2.21  | | | | | | | | 
% 9.56/2.21  | | | | | | | |   (80)   ~ (all_76_1 = 0)
% 9.56/2.21  | | | | | | | | 
% 9.56/2.21  | | | | | | | | REDUCE: (76), (80) imply:
% 9.56/2.21  | | | | | | | |   (81)  $false
% 9.56/2.21  | | | | | | | | 
% 9.56/2.21  | | | | | | | | CLOSE: (81) is inconsistent.
% 9.56/2.21  | | | | | | | | 
% 9.56/2.21  | | | | | | | End of split
% 9.56/2.21  | | | | | | | 
% 9.56/2.21  | | | | | | End of split
% 9.56/2.21  | | | | | | 
% 9.56/2.21  | | | | | End of split
% 9.56/2.21  | | | | | 
% 9.56/2.21  | | | | End of split
% 9.56/2.21  | | | | 
% 9.56/2.21  | | | End of split
% 9.56/2.21  | | | 
% 9.56/2.21  | | Case 2:
% 9.56/2.21  | | | 
% 9.56/2.21  | | |   (82)   ~ (all_24_1 = 0)
% 9.56/2.21  | | | 
% 9.56/2.21  | | | BETA: splitting (32) gives:
% 9.56/2.21  | | | 
% 9.56/2.21  | | | Case 1:
% 9.56/2.21  | | | | 
% 9.56/2.21  | | | |   (83)  all_24_1 = 0
% 9.56/2.21  | | | | 
% 9.56/2.21  | | | | REDUCE: (82), (83) imply:
% 9.56/2.21  | | | |   (84)  $false
% 9.56/2.21  | | | | 
% 9.56/2.21  | | | | CLOSE: (84) is inconsistent.
% 9.56/2.21  | | | | 
% 9.56/2.21  | | | Case 2:
% 9.56/2.21  | | | | 
% 9.56/2.21  | | | |   (85)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1)
% 9.56/2.21  | | | |           = v1 & member(v0, all_15_4) = 0 & $i(v0))
% 9.56/2.21  | | | | 
% 9.56/2.21  | | | | DELTA: instantiating (85) with fresh symbols all_37_0, all_37_1 gives:
% 9.56/2.21  | | | |   (86)   ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = all_37_0 &
% 9.56/2.21  | | | |         member(all_37_1, all_15_4) = 0 & $i(all_37_1)
% 9.56/2.21  | | | | 
% 9.56/2.21  | | | | ALPHA: (86) implies:
% 9.56/2.21  | | | |   (87)   ~ (all_37_0 = 0)
% 9.56/2.21  | | | |   (88)  $i(all_37_1)
% 9.56/2.21  | | | |   (89)  member(all_37_1, all_15_4) = 0
% 9.56/2.21  | | | |   (90)  member(all_37_1, all_15_1) = all_37_0
% 9.56/2.21  | | | | 
% 9.56/2.21  | | | | GROUND_INST: instantiating (4) with all_37_1, all_15_5, all_15_4,
% 9.56/2.21  | | | |              simplifying with (13), (21), (88), (89) gives:
% 9.56/2.21  | | | |   (91)  subset(all_37_1, all_15_5) = 0
% 9.56/2.21  | | | | 
% 9.56/2.21  | | | | GROUND_INST: instantiating (7) with all_37_1, all_15_3, all_15_2,
% 9.56/2.21  | | | |              all_15_1, all_37_0, simplifying with (15), (16), (23),
% 9.56/2.21  | | | |              (88), (90) gives:
% 9.56/2.22  | | | |   (92)  all_37_0 = 0 |  ? [v0: any] :  ? [v1: any] : (member(all_37_1,
% 9.56/2.22  | | | |             all_15_2) = v1 & member(all_37_1, all_15_3) = v0 & ( ~ (v1 =
% 9.56/2.22  | | | |               0) |  ~ (v0 = 0)))
% 9.56/2.22  | | | | 
% 9.56/2.22  | | | | BETA: splitting (92) gives:
% 9.56/2.22  | | | | 
% 9.56/2.22  | | | | Case 1:
% 9.56/2.22  | | | | | 
% 9.56/2.22  | | | | |   (93)  all_37_0 = 0
% 9.56/2.22  | | | | | 
% 9.56/2.22  | | | | | REDUCE: (87), (93) imply:
% 9.56/2.22  | | | | |   (94)  $false
% 9.56/2.22  | | | | | 
% 9.56/2.22  | | | | | CLOSE: (94) is inconsistent.
% 9.56/2.22  | | | | | 
% 9.56/2.22  | | | | Case 2:
% 9.56/2.22  | | | | | 
% 9.56/2.22  | | | | |   (95)   ? [v0: any] :  ? [v1: any] : (member(all_37_1, all_15_2) = v1
% 9.56/2.22  | | | | |           & member(all_37_1, all_15_3) = v0 & ( ~ (v1 = 0) |  ~ (v0 =
% 9.56/2.22  | | | | |               0)))
% 9.56/2.22  | | | | | 
% 9.56/2.22  | | | | | DELTA: instantiating (95) with fresh symbols all_50_0, all_50_1 gives:
% 9.56/2.22  | | | | |   (96)  member(all_37_1, all_15_2) = all_50_0 & member(all_37_1,
% 9.56/2.22  | | | | |           all_15_3) = all_50_1 & ( ~ (all_50_0 = 0) |  ~ (all_50_1 =
% 9.56/2.22  | | | | |             0))
% 9.56/2.22  | | | | | 
% 9.56/2.22  | | | | | ALPHA: (96) implies:
% 9.56/2.22  | | | | |   (97)  member(all_37_1, all_15_3) = all_50_1
% 9.56/2.22  | | | | |   (98)  member(all_37_1, all_15_2) = all_50_0
% 9.56/2.22  | | | | |   (99)   ~ (all_50_0 = 0) |  ~ (all_50_1 = 0)
% 9.56/2.22  | | | | | 
% 9.56/2.22  | | | | | GROUND_INST: instantiating (5) with all_37_1, all_15_7, all_15_3,
% 9.56/2.22  | | | | |              all_50_1, simplifying with (11), (19), (88), (97) gives:
% 9.56/2.22  | | | | |   (100)  all_50_1 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & subset(all_37_1,
% 9.56/2.22  | | | | |              all_15_7) = v0)
% 9.56/2.22  | | | | | 
% 9.56/2.22  | | | | | GROUND_INST: instantiating (5) with all_37_1, all_15_6, all_15_2,
% 9.56/2.22  | | | | |              all_50_0, simplifying with (12), (20), (88), (98) gives:
% 9.56/2.22  | | | | |   (101)  all_50_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & subset(all_37_1,
% 9.56/2.22  | | | | |              all_15_6) = v0)
% 9.56/2.22  | | | | | 
% 9.56/2.22  | | | | | GROUND_INST: instantiating (1) with all_37_1, all_15_5, simplifying
% 9.56/2.22  | | | | |              with (13), (88), (91) gives:
% 9.56/2.22  | | | | |   (102)   ! [v0: $i] : ( ~ (member(v0, all_37_1) = 0) |  ~ $i(v0) |
% 9.56/2.22  | | | | |            member(v0, all_15_5) = 0)
% 9.56/2.22  | | | | | 
% 9.56/2.22  | | | | | BETA: splitting (99) gives:
% 9.56/2.22  | | | | | 
% 9.56/2.22  | | | | | Case 1:
% 9.56/2.22  | | | | | | 
% 9.56/2.22  | | | | | |   (103)   ~ (all_50_0 = 0)
% 9.56/2.22  | | | | | | 
% 9.56/2.22  | | | | | | BETA: splitting (101) gives:
% 9.56/2.22  | | | | | | 
% 9.56/2.22  | | | | | | Case 1:
% 9.56/2.22  | | | | | | | 
% 9.56/2.22  | | | | | | |   (104)  all_50_0 = 0
% 9.56/2.22  | | | | | | | 
% 9.56/2.22  | | | | | | | REDUCE: (103), (104) imply:
% 9.56/2.22  | | | | | | |   (105)  $false
% 9.56/2.22  | | | | | | | 
% 9.56/2.22  | | | | | | | CLOSE: (105) is inconsistent.
% 9.56/2.22  | | | | | | | 
% 9.56/2.22  | | | | | | Case 2:
% 9.56/2.22  | | | | | | | 
% 9.56/2.22  | | | | | | |   (106)   ? [v0: int] : ( ~ (v0 = 0) & subset(all_37_1, all_15_6)
% 9.56/2.22  | | | | | | |            = v0)
% 9.56/2.22  | | | | | | | 
% 9.56/2.22  | | | | | | | DELTA: instantiating (106) with fresh symbol all_66_0 gives:
% 9.56/2.22  | | | | | | |   (107)   ~ (all_66_0 = 0) & subset(all_37_1, all_15_6) = all_66_0
% 9.56/2.22  | | | | | | | 
% 9.56/2.22  | | | | | | | ALPHA: (107) implies:
% 9.56/2.22  | | | | | | |   (108)   ~ (all_66_0 = 0)
% 9.56/2.22  | | | | | | |   (109)  subset(all_37_1, all_15_6) = all_66_0
% 9.56/2.22  | | | | | | | 
% 9.56/2.22  | | | | | | | GROUND_INST: instantiating (2) with all_37_1, all_15_6, all_66_0,
% 9.56/2.22  | | | | | | |              simplifying with (12), (88), (109) gives:
% 9.56/2.22  | | | | | | |   (110)  all_66_0 = 0 |  ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0)
% 9.56/2.22  | | | | | | |            & member(v0, all_37_1) = 0 & member(v0, all_15_6) = v1
% 9.56/2.23  | | | | | | |            & $i(v0))
% 9.56/2.23  | | | | | | | 
% 9.56/2.23  | | | | | | | BETA: splitting (110) gives:
% 9.56/2.23  | | | | | | | 
% 9.56/2.23  | | | | | | | Case 1:
% 9.56/2.23  | | | | | | | | 
% 9.56/2.23  | | | | | | | |   (111)  all_66_0 = 0
% 9.56/2.23  | | | | | | | | 
% 9.56/2.23  | | | | | | | | REDUCE: (108), (111) imply:
% 9.56/2.23  | | | | | | | |   (112)  $false
% 9.56/2.23  | | | | | | | | 
% 9.56/2.23  | | | | | | | | CLOSE: (112) is inconsistent.
% 9.56/2.23  | | | | | | | | 
% 9.56/2.23  | | | | | | | Case 2:
% 9.56/2.23  | | | | | | | | 
% 9.56/2.23  | | | | | | | |   (113)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 9.56/2.23  | | | | | | | |              all_37_1) = 0 & member(v0, all_15_6) = v1 & $i(v0))
% 9.56/2.23  | | | | | | | | 
% 9.56/2.23  | | | | | | | | DELTA: instantiating (113) with fresh symbols all_79_0, all_79_1
% 9.56/2.23  | | | | | | | |        gives:
% 9.56/2.23  | | | | | | | |   (114)   ~ (all_79_0 = 0) & member(all_79_1, all_37_1) = 0 &
% 9.56/2.23  | | | | | | | |          member(all_79_1, all_15_6) = all_79_0 & $i(all_79_1)
% 9.56/2.23  | | | | | | | | 
% 9.56/2.23  | | | | | | | | ALPHA: (114) implies:
% 9.56/2.23  | | | | | | | |   (115)   ~ (all_79_0 = 0)
% 9.56/2.23  | | | | | | | |   (116)  $i(all_79_1)
% 9.56/2.23  | | | | | | | |   (117)  member(all_79_1, all_15_6) = all_79_0
% 9.56/2.23  | | | | | | | |   (118)  member(all_79_1, all_37_1) = 0
% 9.56/2.23  | | | | | | | | 
% 9.56/2.23  | | | | | | | | GROUND_INST: instantiating (102) with all_79_1, simplifying with
% 9.56/2.23  | | | | | | | |              (116), (118) gives:
% 9.56/2.23  | | | | | | | |   (119)  member(all_79_1, all_15_5) = 0
% 9.56/2.23  | | | | | | | | 
% 9.56/2.23  | | | | | | | | GROUND_INST: instantiating (6) with all_79_1, all_15_7,
% 9.56/2.23  | | | | | | | |              all_15_6, all_15_5, simplifying with (11), (12),
% 9.56/2.23  | | | | | | | |              (22), (116), (119) gives:
% 9.56/2.23  | | | | | | | |   (120)  member(all_79_1, all_15_6) = 0 & member(all_79_1,
% 9.56/2.23  | | | | | | | |            all_15_7) = 0
% 9.56/2.23  | | | | | | | | 
% 9.56/2.23  | | | | | | | | ALPHA: (120) implies:
% 9.56/2.23  | | | | | | | |   (121)  member(all_79_1, all_15_6) = 0
% 9.56/2.23  | | | | | | | | 
% 9.56/2.23  | | | | | | | | GROUND_INST: instantiating (8) with all_79_0, 0, all_15_6,
% 9.56/2.23  | | | | | | | |              all_79_1, simplifying with (117), (121) gives:
% 9.56/2.23  | | | | | | | |   (122)  all_79_0 = 0
% 9.56/2.23  | | | | | | | | 
% 9.56/2.23  | | | | | | | | REDUCE: (115), (122) imply:
% 9.56/2.23  | | | | | | | |   (123)  $false
% 9.56/2.23  | | | | | | | | 
% 9.56/2.23  | | | | | | | | CLOSE: (123) is inconsistent.
% 9.56/2.23  | | | | | | | | 
% 9.56/2.23  | | | | | | | End of split
% 9.56/2.23  | | | | | | | 
% 9.56/2.23  | | | | | | End of split
% 9.56/2.23  | | | | | | 
% 9.56/2.23  | | | | | Case 2:
% 9.56/2.23  | | | | | | 
% 9.56/2.23  | | | | | |   (124)   ~ (all_50_1 = 0)
% 9.56/2.23  | | | | | | 
% 9.56/2.23  | | | | | | BETA: splitting (100) gives:
% 9.56/2.23  | | | | | | 
% 9.56/2.23  | | | | | | Case 1:
% 9.56/2.23  | | | | | | | 
% 9.56/2.23  | | | | | | |   (125)  all_50_1 = 0
% 9.56/2.23  | | | | | | | 
% 9.56/2.23  | | | | | | | REDUCE: (124), (125) imply:
% 9.56/2.23  | | | | | | |   (126)  $false
% 9.56/2.23  | | | | | | | 
% 9.56/2.23  | | | | | | | CLOSE: (126) is inconsistent.
% 9.56/2.23  | | | | | | | 
% 9.56/2.23  | | | | | | Case 2:
% 9.56/2.23  | | | | | | | 
% 9.56/2.23  | | | | | | |   (127)   ? [v0: int] : ( ~ (v0 = 0) & subset(all_37_1, all_15_7)
% 9.56/2.23  | | | | | | |            = v0)
% 9.56/2.23  | | | | | | | 
% 9.56/2.23  | | | | | | | DELTA: instantiating (127) with fresh symbol all_66_0 gives:
% 9.56/2.23  | | | | | | |   (128)   ~ (all_66_0 = 0) & subset(all_37_1, all_15_7) = all_66_0
% 9.56/2.23  | | | | | | | 
% 9.56/2.23  | | | | | | | ALPHA: (128) implies:
% 9.56/2.23  | | | | | | |   (129)   ~ (all_66_0 = 0)
% 9.56/2.24  | | | | | | |   (130)  subset(all_37_1, all_15_7) = all_66_0
% 9.56/2.24  | | | | | | | 
% 9.56/2.24  | | | | | | | GROUND_INST: instantiating (2) with all_37_1, all_15_7, all_66_0,
% 9.56/2.24  | | | | | | |              simplifying with (11), (88), (130) gives:
% 9.56/2.24  | | | | | | |   (131)  all_66_0 = 0 |  ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0)
% 9.56/2.24  | | | | | | |            & member(v0, all_37_1) = 0 & member(v0, all_15_7) = v1
% 9.56/2.24  | | | | | | |            & $i(v0))
% 9.56/2.24  | | | | | | | 
% 9.56/2.24  | | | | | | | BETA: splitting (131) gives:
% 9.56/2.24  | | | | | | | 
% 9.56/2.24  | | | | | | | Case 1:
% 9.56/2.24  | | | | | | | | 
% 9.56/2.24  | | | | | | | |   (132)  all_66_0 = 0
% 9.56/2.24  | | | | | | | | 
% 9.56/2.24  | | | | | | | | REDUCE: (129), (132) imply:
% 9.56/2.24  | | | | | | | |   (133)  $false
% 9.56/2.24  | | | | | | | | 
% 9.56/2.24  | | | | | | | | CLOSE: (133) is inconsistent.
% 9.56/2.24  | | | | | | | | 
% 9.56/2.24  | | | | | | | Case 2:
% 9.56/2.24  | | | | | | | | 
% 9.56/2.24  | | | | | | | |   (134)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 9.56/2.24  | | | | | | | |              all_37_1) = 0 & member(v0, all_15_7) = v1 & $i(v0))
% 9.56/2.24  | | | | | | | | 
% 9.56/2.24  | | | | | | | | DELTA: instantiating (134) with fresh symbols all_78_0, all_78_1
% 9.56/2.24  | | | | | | | |        gives:
% 9.56/2.24  | | | | | | | |   (135)   ~ (all_78_0 = 0) & member(all_78_1, all_37_1) = 0 &
% 9.56/2.24  | | | | | | | |          member(all_78_1, all_15_7) = all_78_0 & $i(all_78_1)
% 9.56/2.24  | | | | | | | | 
% 9.56/2.24  | | | | | | | | ALPHA: (135) implies:
% 9.56/2.24  | | | | | | | |   (136)   ~ (all_78_0 = 0)
% 9.56/2.24  | | | | | | | |   (137)  $i(all_78_1)
% 9.56/2.24  | | | | | | | |   (138)  member(all_78_1, all_15_7) = all_78_0
% 9.56/2.24  | | | | | | | |   (139)  member(all_78_1, all_37_1) = 0
% 9.56/2.24  | | | | | | | | 
% 9.56/2.24  | | | | | | | | GROUND_INST: instantiating (102) with all_78_1, simplifying with
% 9.56/2.24  | | | | | | | |              (137), (139) gives:
% 9.56/2.24  | | | | | | | |   (140)  member(all_78_1, all_15_5) = 0
% 9.56/2.24  | | | | | | | | 
% 9.56/2.24  | | | | | | | | GROUND_INST: instantiating (6) with all_78_1, all_15_7,
% 9.56/2.24  | | | | | | | |              all_15_6, all_15_5, simplifying with (11), (12),
% 9.56/2.24  | | | | | | | |              (22), (137), (140) gives:
% 9.56/2.24  | | | | | | | |   (141)  member(all_78_1, all_15_6) = 0 & member(all_78_1,
% 9.56/2.24  | | | | | | | |            all_15_7) = 0
% 9.56/2.24  | | | | | | | | 
% 9.56/2.24  | | | | | | | | ALPHA: (141) implies:
% 9.56/2.24  | | | | | | | |   (142)  member(all_78_1, all_15_7) = 0
% 9.56/2.24  | | | | | | | | 
% 9.56/2.24  | | | | | | | | GROUND_INST: instantiating (8) with all_78_0, 0, all_15_7,
% 9.56/2.24  | | | | | | | |              all_78_1, simplifying with (138), (142) gives:
% 9.56/2.24  | | | | | | | |   (143)  all_78_0 = 0
% 9.56/2.24  | | | | | | | | 
% 9.56/2.24  | | | | | | | | REDUCE: (136), (143) imply:
% 9.56/2.24  | | | | | | | |   (144)  $false
% 9.56/2.24  | | | | | | | | 
% 9.56/2.24  | | | | | | | | CLOSE: (144) is inconsistent.
% 9.56/2.24  | | | | | | | | 
% 9.56/2.24  | | | | | | | End of split
% 9.56/2.24  | | | | | | | 
% 9.56/2.24  | | | | | | End of split
% 9.56/2.24  | | | | | | 
% 9.56/2.24  | | | | | End of split
% 9.56/2.24  | | | | | 
% 9.56/2.24  | | | | End of split
% 9.56/2.24  | | | | 
% 9.56/2.24  | | | End of split
% 9.56/2.24  | | | 
% 9.56/2.24  | | End of split
% 9.56/2.24  | | 
% 9.56/2.24  | End of split
% 9.56/2.24  | 
% 9.56/2.24  End of proof
% 9.56/2.24  % SZS output end Proof for theBenchmark
% 9.56/2.24  
% 9.56/2.24  1646ms
%------------------------------------------------------------------------------