TSTP Solution File: SET689+4 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SET689+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 : n009.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 15:26:00 EDT 2023

% Result   : Theorem 6.06s 1.56s
% Output   : Proof 8.03s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET689+4 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33  % Computer : n009.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 09:39:20 EDT 2023
% 0.12/0.34  % 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 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 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 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
% 2.47/0.99  Prover 1: Preprocessing ...
% 2.47/0.99  Prover 4: Preprocessing ...
% 2.74/1.04  Prover 6: Preprocessing ...
% 2.74/1.04  Prover 0: Preprocessing ...
% 2.74/1.04  Prover 5: Preprocessing ...
% 2.74/1.04  Prover 3: Preprocessing ...
% 2.74/1.05  Prover 2: Preprocessing ...
% 4.79/1.39  Prover 6: Proving ...
% 4.79/1.40  Prover 5: Proving ...
% 4.79/1.40  Prover 1: Constructing countermodel ...
% 4.79/1.40  Prover 3: Constructing countermodel ...
% 4.79/1.41  Prover 2: Proving ...
% 5.52/1.43  Prover 4: Constructing countermodel ...
% 5.52/1.45  Prover 0: Proving ...
% 6.06/1.56  Prover 3: proved (937ms)
% 6.06/1.56  
% 6.06/1.56  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.06/1.56  
% 6.06/1.56  Prover 0: stopped
% 6.06/1.56  Prover 5: stopped
% 6.06/1.57  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.06/1.57  Prover 2: stopped
% 6.55/1.57  Prover 6: stopped
% 6.55/1.57  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.55/1.57  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.55/1.57  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.55/1.57  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.55/1.60  Prover 10: Preprocessing ...
% 6.55/1.60  Prover 13: Preprocessing ...
% 6.55/1.62  Prover 7: Preprocessing ...
% 6.55/1.63  Prover 11: Preprocessing ...
% 6.55/1.63  Prover 8: Preprocessing ...
% 6.55/1.65  Prover 10: Warning: ignoring some quantifiers
% 6.55/1.66  Prover 10: Constructing countermodel ...
% 7.27/1.67  Prover 1: Found proof (size 28)
% 7.27/1.67  Prover 1: proved (1053ms)
% 7.27/1.67  Prover 11: stopped
% 7.27/1.67  Prover 4: stopped
% 7.27/1.67  Prover 10: stopped
% 7.27/1.69  Prover 7: Warning: ignoring some quantifiers
% 7.48/1.70  Prover 7: Constructing countermodel ...
% 7.48/1.71  Prover 7: stopped
% 7.48/1.71  Prover 13: Warning: ignoring some quantifiers
% 7.68/1.73  Prover 13: Constructing countermodel ...
% 7.68/1.74  Prover 8: Warning: ignoring some quantifiers
% 7.68/1.74  Prover 13: stopped
% 7.68/1.74  Prover 8: Constructing countermodel ...
% 7.68/1.75  Prover 8: stopped
% 7.68/1.75  
% 7.68/1.75  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.68/1.75  
% 7.68/1.76  % SZS output start Proof for theBenchmark
% 7.68/1.76  Assumptions after simplification:
% 7.68/1.76  ---------------------------------
% 7.68/1.76  
% 7.68/1.76    (equal_set)
% 7.68/1.80     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (equal_set(v0, v1) =
% 7.68/1.80        v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] : (subset(v1,
% 7.68/1.80          v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0)))) &  ! [v0:
% 7.68/1.80      $i] :  ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) |
% 8.03/1.80      (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 8.03/1.80  
% 8.03/1.80    (subset)
% 8.03/1.80     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (subset(v0, v1) = v2)
% 8.03/1.80      |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~ (v4 = 0) &
% 8.03/1.80        member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) &  ! [v0: $i] :  !
% 8.03/1.80    [v1: $i] : ( ~ (subset(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ! [v2: $i] : (
% 8.03/1.80        ~ (member(v2, v0) = 0) |  ~ $i(v2) | member(v2, v1) = 0))
% 8.03/1.80  
% 8.03/1.80    (thI05)
% 8.03/1.80     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: int] : ( ~ (v3 = 0) &
% 8.03/1.80      equal_set(v0, v2) = v3 & subset(v2, v0) = 0 & subset(v1, v2) = 0 &
% 8.03/1.80      subset(v0, v1) = 0 & $i(v2) & $i(v1) & $i(v0))
% 8.03/1.80  
% 8.03/1.80    (function-axioms)
% 8.03/1.81     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 8.03/1.81      (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0)) &  ! [v0:
% 8.03/1.81      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 8.03/1.81      (difference(v3, v2) = v1) |  ~ (difference(v3, v2) = v0)) &  ! [v0: $i] :  !
% 8.03/1.81    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (union(v3, v2) = v1) |  ~
% 8.03/1.81      (union(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3:
% 8.03/1.81      $i] : (v1 = v0 |  ~ (intersection(v3, v2) = v1) |  ~ (intersection(v3, v2) =
% 8.03/1.81        v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 8.03/1.81      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (equal_set(v3, v2) = v1) |  ~
% 8.03/1.81      (equal_set(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 8.03/1.81      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (subset(v3,
% 8.03/1.81          v2) = v1) |  ~ (subset(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  !
% 8.03/1.81    [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 8.03/1.81      (member(v3, v2) = v1) |  ~ (member(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1:
% 8.03/1.81      $i] :  ! [v2: $i] : (v1 = v0 |  ~ (product(v2) = v1) |  ~ (product(v2) =
% 8.03/1.81        v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (sum(v2) =
% 8.03/1.81        v1) |  ~ (sum(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 =
% 8.03/1.81      v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0)) &  ! [v0: $i] :  !
% 8.03/1.81    [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (power_set(v2) = v1) |  ~
% 8.03/1.81      (power_set(v2) = v0))
% 8.03/1.81  
% 8.03/1.81  Further assumptions not needed in the proof:
% 8.03/1.81  --------------------------------------------
% 8.03/1.81  difference, empty_set, intersection, power_set, product, singleton, sum, union,
% 8.03/1.81  unordered_pair
% 8.03/1.81  
% 8.03/1.81  Those formulas are unsatisfiable:
% 8.03/1.81  ---------------------------------
% 8.03/1.81  
% 8.03/1.81  Begin of proof
% 8.03/1.81  | 
% 8.03/1.82  | ALPHA: (subset) implies:
% 8.03/1.82  |   (1)   ! [v0: $i] :  ! [v1: $i] : ( ~ (subset(v0, v1) = 0) |  ~ $i(v1) |  ~
% 8.03/1.82  |          $i(v0) |  ! [v2: $i] : ( ~ (member(v2, v0) = 0) |  ~ $i(v2) |
% 8.03/1.82  |            member(v2, v1) = 0))
% 8.03/1.82  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (subset(v0, v1)
% 8.03/1.82  |            = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~
% 8.03/1.82  |            (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 8.03/1.82  | 
% 8.03/1.82  | ALPHA: (equal_set) implies:
% 8.03/1.82  |   (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (equal_set(v0,
% 8.03/1.82  |              v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] :
% 8.03/1.82  |          (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 =
% 8.03/1.82  |                0))))
% 8.03/1.82  | 
% 8.03/1.82  | ALPHA: (function-axioms) implies:
% 8.03/1.82  |   (4)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 8.03/1.82  |         ! [v3: $i] : (v1 = v0 |  ~ (member(v3, v2) = v1) |  ~ (member(v3, v2)
% 8.03/1.82  |            = v0))
% 8.03/1.83  |   (5)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 8.03/1.83  |         ! [v3: $i] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2)
% 8.03/1.83  |            = v0))
% 8.03/1.83  | 
% 8.03/1.83  | DELTA: instantiating (thI05) with fresh symbols all_15_0, all_15_1, all_15_2,
% 8.03/1.83  |        all_15_3 gives:
% 8.03/1.83  |   (6)   ~ (all_15_0 = 0) & equal_set(all_15_3, all_15_1) = all_15_0 &
% 8.03/1.83  |        subset(all_15_1, all_15_3) = 0 & subset(all_15_2, all_15_1) = 0 &
% 8.03/1.83  |        subset(all_15_3, all_15_2) = 0 & $i(all_15_1) & $i(all_15_2) &
% 8.03/1.83  |        $i(all_15_3)
% 8.03/1.83  | 
% 8.03/1.83  | ALPHA: (6) implies:
% 8.03/1.83  |   (7)   ~ (all_15_0 = 0)
% 8.03/1.83  |   (8)  $i(all_15_3)
% 8.03/1.83  |   (9)  $i(all_15_2)
% 8.03/1.83  |   (10)  $i(all_15_1)
% 8.03/1.83  |   (11)  subset(all_15_3, all_15_2) = 0
% 8.03/1.83  |   (12)  subset(all_15_2, all_15_1) = 0
% 8.03/1.83  |   (13)  subset(all_15_1, all_15_3) = 0
% 8.03/1.83  |   (14)  equal_set(all_15_3, all_15_1) = all_15_0
% 8.03/1.83  | 
% 8.03/1.83  | GROUND_INST: instantiating (1) with all_15_3, all_15_2, simplifying with (8),
% 8.03/1.83  |              (9), (11) gives:
% 8.03/1.83  |   (15)   ! [v0: $i] : ( ~ (member(v0, all_15_3) = 0) |  ~ $i(v0) | member(v0,
% 8.03/1.83  |             all_15_2) = 0)
% 8.03/1.83  | 
% 8.03/1.83  | GROUND_INST: instantiating (1) with all_15_2, all_15_1, simplifying with (9),
% 8.03/1.83  |              (10), (12) gives:
% 8.03/1.83  |   (16)   ! [v0: $i] : ( ~ (member(v0, all_15_2) = 0) |  ~ $i(v0) | member(v0,
% 8.03/1.83  |             all_15_1) = 0)
% 8.03/1.83  | 
% 8.03/1.83  | GROUND_INST: instantiating (3) with all_15_3, all_15_1, all_15_0, simplifying
% 8.03/1.83  |              with (8), (10), (14) gives:
% 8.03/1.84  |   (17)  all_15_0 = 0 |  ? [v0: any] :  ? [v1: any] : (subset(all_15_1,
% 8.03/1.84  |             all_15_3) = v1 & subset(all_15_3, all_15_1) = v0 & ( ~ (v1 = 0) | 
% 8.03/1.84  |             ~ (v0 = 0)))
% 8.03/1.84  | 
% 8.03/1.84  | BETA: splitting (17) gives:
% 8.03/1.84  | 
% 8.03/1.84  | Case 1:
% 8.03/1.84  | | 
% 8.03/1.84  | |   (18)  all_15_0 = 0
% 8.03/1.84  | | 
% 8.03/1.84  | | REDUCE: (7), (18) imply:
% 8.03/1.84  | |   (19)  $false
% 8.03/1.84  | | 
% 8.03/1.84  | | CLOSE: (19) is inconsistent.
% 8.03/1.84  | | 
% 8.03/1.84  | Case 2:
% 8.03/1.84  | | 
% 8.03/1.84  | |   (20)   ? [v0: any] :  ? [v1: any] : (subset(all_15_1, all_15_3) = v1 &
% 8.03/1.84  | |           subset(all_15_3, all_15_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 8.03/1.84  | | 
% 8.03/1.84  | | DELTA: instantiating (20) with fresh symbols all_28_0, all_28_1 gives:
% 8.03/1.84  | |   (21)  subset(all_15_1, all_15_3) = all_28_0 & subset(all_15_3, all_15_1) =
% 8.03/1.84  | |         all_28_1 & ( ~ (all_28_0 = 0) |  ~ (all_28_1 = 0))
% 8.03/1.84  | | 
% 8.03/1.84  | | ALPHA: (21) implies:
% 8.03/1.84  | |   (22)  subset(all_15_3, all_15_1) = all_28_1
% 8.03/1.84  | |   (23)  subset(all_15_1, all_15_3) = all_28_0
% 8.03/1.84  | |   (24)   ~ (all_28_0 = 0) |  ~ (all_28_1 = 0)
% 8.03/1.84  | | 
% 8.03/1.84  | | GROUND_INST: instantiating (5) with 0, all_28_0, all_15_3, all_15_1,
% 8.03/1.84  | |              simplifying with (13), (23) gives:
% 8.03/1.84  | |   (25)  all_28_0 = 0
% 8.03/1.84  | | 
% 8.03/1.84  | | BETA: splitting (24) gives:
% 8.03/1.84  | | 
% 8.03/1.84  | | Case 1:
% 8.03/1.84  | | | 
% 8.03/1.84  | | |   (26)   ~ (all_28_0 = 0)
% 8.03/1.84  | | | 
% 8.03/1.84  | | | REDUCE: (25), (26) imply:
% 8.03/1.84  | | |   (27)  $false
% 8.03/1.84  | | | 
% 8.03/1.84  | | | CLOSE: (27) is inconsistent.
% 8.03/1.84  | | | 
% 8.03/1.84  | | Case 2:
% 8.03/1.84  | | | 
% 8.03/1.84  | | |   (28)   ~ (all_28_1 = 0)
% 8.03/1.84  | | | 
% 8.03/1.84  | | | GROUND_INST: instantiating (2) with all_15_3, all_15_1, all_28_1,
% 8.03/1.84  | | |              simplifying with (8), (10), (22) gives:
% 8.03/1.84  | | |   (29)  all_28_1 = 0 |  ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) &
% 8.03/1.84  | | |           member(v0, all_15_1) = v1 & member(v0, all_15_3) = 0 & $i(v0))
% 8.03/1.84  | | | 
% 8.03/1.84  | | | BETA: splitting (29) gives:
% 8.03/1.84  | | | 
% 8.03/1.84  | | | Case 1:
% 8.03/1.84  | | | | 
% 8.03/1.84  | | | |   (30)  all_28_1 = 0
% 8.03/1.84  | | | | 
% 8.03/1.84  | | | | REDUCE: (28), (30) imply:
% 8.03/1.84  | | | |   (31)  $false
% 8.03/1.84  | | | | 
% 8.03/1.84  | | | | CLOSE: (31) is inconsistent.
% 8.03/1.84  | | | | 
% 8.03/1.84  | | | Case 2:
% 8.03/1.84  | | | | 
% 8.03/1.84  | | | |   (32)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1)
% 8.03/1.84  | | | |           = v1 & member(v0, all_15_3) = 0 & $i(v0))
% 8.03/1.84  | | | | 
% 8.03/1.84  | | | | DELTA: instantiating (32) with fresh symbols all_45_0, all_45_1 gives:
% 8.03/1.84  | | | |   (33)   ~ (all_45_0 = 0) & member(all_45_1, all_15_1) = all_45_0 &
% 8.03/1.84  | | | |         member(all_45_1, all_15_3) = 0 & $i(all_45_1)
% 8.03/1.84  | | | | 
% 8.03/1.84  | | | | ALPHA: (33) implies:
% 8.03/1.85  | | | |   (34)   ~ (all_45_0 = 0)
% 8.03/1.85  | | | |   (35)  $i(all_45_1)
% 8.03/1.85  | | | |   (36)  member(all_45_1, all_15_3) = 0
% 8.03/1.85  | | | |   (37)  member(all_45_1, all_15_1) = all_45_0
% 8.03/1.85  | | | | 
% 8.03/1.85  | | | | GROUND_INST: instantiating (15) with all_45_1, simplifying with (35),
% 8.03/1.85  | | | |              (36) gives:
% 8.03/1.85  | | | |   (38)  member(all_45_1, all_15_2) = 0
% 8.03/1.85  | | | | 
% 8.03/1.85  | | | | GROUND_INST: instantiating (16) with all_45_1, simplifying with (35),
% 8.03/1.85  | | | |              (38) gives:
% 8.03/1.85  | | | |   (39)  member(all_45_1, all_15_1) = 0
% 8.03/1.85  | | | | 
% 8.03/1.85  | | | | GROUND_INST: instantiating (4) with all_45_0, 0, all_15_1, all_45_1,
% 8.03/1.85  | | | |              simplifying with (37), (39) gives:
% 8.03/1.85  | | | |   (40)  all_45_0 = 0
% 8.03/1.85  | | | | 
% 8.03/1.85  | | | | REDUCE: (34), (40) imply:
% 8.03/1.85  | | | |   (41)  $false
% 8.03/1.85  | | | | 
% 8.03/1.85  | | | | CLOSE: (41) is inconsistent.
% 8.03/1.85  | | | | 
% 8.03/1.85  | | | End of split
% 8.03/1.85  | | | 
% 8.03/1.85  | | End of split
% 8.03/1.85  | | 
% 8.03/1.85  | End of split
% 8.03/1.85  | 
% 8.03/1.85  End of proof
% 8.03/1.85  % SZS output end Proof for theBenchmark
% 8.03/1.85  
% 8.03/1.85  1250ms
%------------------------------------------------------------------------------