TSTP Solution File: SET199+3 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SET199+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n023.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 15:24:16 EDT 2023

% Result   : Theorem 4.70s 1.32s
% Output   : Proof 6.01s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET199+3 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n023.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sat Aug 26 10:29:11 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.63/0.61  ________       _____
% 0.63/0.61  ___  __ \_________(_)________________________________
% 0.63/0.61  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.63/0.61  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.63/0.61  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.63/0.61  
% 0.63/0.61  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.63/0.61  (2023-06-19)
% 0.63/0.61  
% 0.63/0.61  (c) Philipp Rümmer, 2009-2023
% 0.63/0.61  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.63/0.61                Amanda Stjerna.
% 0.63/0.61  Free software under BSD-3-Clause.
% 0.63/0.61  
% 0.63/0.61  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.63/0.61  
% 0.63/0.61  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.63/0.62  Running up to 7 provers in parallel.
% 0.76/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.76/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.76/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.76/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.76/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.76/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.76/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.02/0.95  Prover 4: Preprocessing ...
% 2.02/0.95  Prover 1: Preprocessing ...
% 2.02/1.00  Prover 5: Preprocessing ...
% 2.02/1.00  Prover 6: Preprocessing ...
% 2.02/1.00  Prover 2: Preprocessing ...
% 2.02/1.00  Prover 3: Preprocessing ...
% 2.02/1.00  Prover 0: Preprocessing ...
% 3.05/1.15  Prover 5: Proving ...
% 3.61/1.19  Prover 3: Warning: ignoring some quantifiers
% 3.61/1.20  Prover 6: Proving ...
% 3.61/1.20  Prover 1: Warning: ignoring some quantifiers
% 3.61/1.20  Prover 3: Constructing countermodel ...
% 3.61/1.20  Prover 2: Proving ...
% 3.61/1.21  Prover 1: Constructing countermodel ...
% 3.90/1.22  Prover 0: Proving ...
% 3.90/1.23  Prover 4: Warning: ignoring some quantifiers
% 4.06/1.24  Prover 4: Constructing countermodel ...
% 4.70/1.32  Prover 3: proved (682ms)
% 4.70/1.32  
% 4.70/1.32  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.70/1.32  
% 4.70/1.33  Prover 0: proved (698ms)
% 4.70/1.33  
% 4.70/1.33  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.70/1.33  
% 4.70/1.34  Prover 6: stopped
% 4.70/1.34  Prover 2: stopped
% 4.70/1.35  Prover 5: stopped
% 4.70/1.35  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.70/1.35  Prover 7: Preprocessing ...
% 4.70/1.35  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.70/1.35  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.70/1.35  Prover 10: Preprocessing ...
% 4.70/1.36  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.70/1.36  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.70/1.36  Prover 8: Preprocessing ...
% 4.70/1.37  Prover 13: Preprocessing ...
% 4.70/1.37  Prover 7: Warning: ignoring some quantifiers
% 4.70/1.38  Prover 11: Preprocessing ...
% 4.70/1.38  Prover 7: Constructing countermodel ...
% 4.70/1.38  Prover 10: Warning: ignoring some quantifiers
% 5.15/1.39  Prover 10: Constructing countermodel ...
% 5.15/1.41  Prover 4: Found proof (size 30)
% 5.15/1.41  Prover 4: proved (777ms)
% 5.15/1.41  Prover 7: stopped
% 5.15/1.41  Prover 10: stopped
% 5.15/1.42  Prover 1: stopped
% 5.15/1.42  Prover 13: Warning: ignoring some quantifiers
% 5.15/1.42  Prover 8: Warning: ignoring some quantifiers
% 5.15/1.43  Prover 13: Constructing countermodel ...
% 5.15/1.43  Prover 8: Constructing countermodel ...
% 5.15/1.43  Prover 13: stopped
% 5.15/1.43  Prover 8: stopped
% 5.15/1.45  Prover 11: Warning: ignoring some quantifiers
% 5.15/1.45  Prover 11: Constructing countermodel ...
% 5.15/1.46  Prover 11: stopped
% 5.15/1.46  
% 5.15/1.46  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.15/1.46  
% 5.65/1.47  % SZS output start Proof for theBenchmark
% 5.65/1.47  Assumptions after simplification:
% 5.65/1.47  ---------------------------------
% 5.65/1.47  
% 5.65/1.47    (commutativity_of_intersection)
% 5.72/1.50     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (intersection(v1, v0) = v2) |  ~
% 5.72/1.50      $i(v1) |  ~ $i(v0) | (intersection(v0, v1) = v2 & $i(v2))) &  ! [v0: $i] : 
% 5.72/1.50    ! [v1: $i] :  ! [v2: $i] : ( ~ (intersection(v0, v1) = v2) |  ~ $i(v1) |  ~
% 5.72/1.50      $i(v0) | (intersection(v1, v0) = v2 & $i(v2)))
% 5.72/1.50  
% 5.72/1.50    (intersection_defn)
% 5.72/1.50     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] : (v4 = 0
% 5.72/1.50      |  ~ (intersection(v0, v1) = v3) |  ~ (member(v2, v3) = v4) |  ~ $i(v2) |  ~
% 5.72/1.50      $i(v1) |  ~ $i(v0) |  ? [v5: any] :  ? [v6: any] : (member(v2, v1) = v6 &
% 5.72/1.50        member(v2, v0) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0)))) &  ! [v0: $i] :  !
% 5.72/1.50    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ (intersection(v0, v1) = v3) |  ~
% 5.72/1.50      (member(v2, v3) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) | (member(v2, v1) =
% 5.72/1.50        0 & member(v2, v0) = 0))
% 5.72/1.50  
% 5.72/1.50    (prove_intersection_of_subsets)
% 5.72/1.51     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: int] : ( ~ (v4
% 5.72/1.51        = 0) & subset(v0, v3) = v4 & subset(v0, v2) = 0 & subset(v0, v1) = 0 &
% 5.72/1.51      intersection(v1, v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 5.72/1.51  
% 5.72/1.51    (subset_defn)
% 5.90/1.51     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 5.90/1.51      (subset(v0, v1) = 0) |  ~ (member(v2, v1) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 5.90/1.51      $i(v0) |  ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) &  ! [v0: $i] :
% 5.90/1.51     ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (subset(v0, v1) = v2) |  ~ $i(v1) | 
% 5.90/1.51      ~ $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4 &
% 5.90/1.51        member(v3, v0) = 0 & $i(v3))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :
% 5.90/1.51    ( ~ (subset(v0, v1) = 0) |  ~ (member(v2, v0) = 0) |  ~ $i(v2) |  ~ $i(v1) | 
% 5.90/1.51      ~ $i(v0) | member(v2, v1) = 0)
% 5.90/1.51  
% 5.90/1.51    (function-axioms)
% 5.90/1.51     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 5.90/1.51    [v3: $i] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0)) & 
% 5.90/1.51    ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 5.90/1.51      (intersection(v3, v2) = v1) |  ~ (intersection(v3, v2) = v0)) &  ! [v0:
% 5.90/1.51      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 5.90/1.51    : (v1 = v0 |  ~ (member(v3, v2) = v1) |  ~ (member(v3, v2) = v0))
% 5.90/1.51  
% 5.90/1.51  Further assumptions not needed in the proof:
% 5.90/1.51  --------------------------------------------
% 5.90/1.51  equal_member_defn, reflexivity_of_subset
% 5.90/1.51  
% 5.90/1.51  Those formulas are unsatisfiable:
% 5.90/1.51  ---------------------------------
% 5.90/1.51  
% 5.90/1.51  Begin of proof
% 5.90/1.52  | 
% 5.90/1.52  | ALPHA: (intersection_defn) implies:
% 5.90/1.52  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] :
% 5.90/1.52  |        (v4 = 0 |  ~ (intersection(v0, v1) = v3) |  ~ (member(v2, v3) = v4) | 
% 5.90/1.52  |          ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: any] :  ? [v6: any] :
% 5.90/1.52  |          (member(v2, v1) = v6 & member(v2, v0) = v5 & ( ~ (v6 = 0) |  ~ (v5 =
% 5.90/1.52  |                0))))
% 5.90/1.52  | 
% 5.90/1.52  | ALPHA: (subset_defn) implies:
% 5.90/1.52  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (subset(v0, v1) = 0) |  ~
% 5.90/1.52  |          (member(v2, v0) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) | member(v2,
% 5.90/1.52  |            v1) = 0)
% 5.90/1.52  |   (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (subset(v0, v1)
% 5.90/1.52  |            = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~
% 5.90/1.52  |            (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 5.90/1.52  | 
% 5.90/1.52  | ALPHA: (commutativity_of_intersection) implies:
% 5.90/1.52  |   (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (intersection(v1, v0) =
% 5.90/1.52  |            v2) |  ~ $i(v1) |  ~ $i(v0) | (intersection(v0, v1) = v2 & $i(v2)))
% 5.90/1.52  | 
% 5.90/1.52  | ALPHA: (function-axioms) implies:
% 5.90/1.53  |   (5)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 5.90/1.53  |         ! [v3: $i] : (v1 = v0 |  ~ (member(v3, v2) = v1) |  ~ (member(v3, v2)
% 5.90/1.53  |            = v0))
% 5.90/1.53  | 
% 5.90/1.53  | DELTA: instantiating (prove_intersection_of_subsets) with fresh symbols
% 5.90/1.53  |        all_7_0, all_7_1, all_7_2, all_7_3, all_7_4 gives:
% 5.90/1.53  |   (6)   ~ (all_7_0 = 0) & subset(all_7_4, all_7_1) = all_7_0 & subset(all_7_4,
% 5.90/1.53  |          all_7_2) = 0 & subset(all_7_4, all_7_3) = 0 & intersection(all_7_3,
% 5.90/1.53  |          all_7_2) = all_7_1 & $i(all_7_1) & $i(all_7_2) & $i(all_7_3) &
% 5.90/1.53  |        $i(all_7_4)
% 5.90/1.53  | 
% 5.90/1.53  | ALPHA: (6) implies:
% 5.90/1.53  |   (7)   ~ (all_7_0 = 0)
% 5.90/1.53  |   (8)  $i(all_7_4)
% 5.90/1.53  |   (9)  $i(all_7_3)
% 5.90/1.53  |   (10)  $i(all_7_2)
% 5.90/1.53  |   (11)  intersection(all_7_3, all_7_2) = all_7_1
% 5.90/1.53  |   (12)  subset(all_7_4, all_7_3) = 0
% 5.90/1.53  |   (13)  subset(all_7_4, all_7_2) = 0
% 5.90/1.53  |   (14)  subset(all_7_4, all_7_1) = all_7_0
% 5.90/1.53  | 
% 5.90/1.53  | GROUND_INST: instantiating (4) with all_7_2, all_7_3, all_7_1, simplifying
% 5.90/1.53  |              with (9), (10), (11) gives:
% 5.90/1.53  |   (15)  intersection(all_7_2, all_7_3) = all_7_1 & $i(all_7_1)
% 5.90/1.53  | 
% 5.90/1.53  | ALPHA: (15) implies:
% 5.90/1.53  |   (16)  $i(all_7_1)
% 5.90/1.53  |   (17)  intersection(all_7_2, all_7_3) = all_7_1
% 5.90/1.53  | 
% 5.90/1.53  | GROUND_INST: instantiating (3) with all_7_4, all_7_1, all_7_0, simplifying
% 5.90/1.53  |              with (8), (14), (16) gives:
% 5.90/1.53  |   (18)  all_7_0 = 0 |  ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 5.90/1.53  |             all_7_1) = v1 & member(v0, all_7_4) = 0 & $i(v0))
% 5.90/1.53  | 
% 5.90/1.53  | BETA: splitting (18) gives:
% 5.90/1.53  | 
% 6.01/1.53  | Case 1:
% 6.01/1.53  | | 
% 6.01/1.53  | |   (19)  all_7_0 = 0
% 6.01/1.53  | | 
% 6.01/1.53  | | REDUCE: (7), (19) imply:
% 6.01/1.53  | |   (20)  $false
% 6.01/1.54  | | 
% 6.01/1.54  | | CLOSE: (20) is inconsistent.
% 6.01/1.54  | | 
% 6.01/1.54  | Case 2:
% 6.01/1.54  | | 
% 6.01/1.54  | |   (21)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_7_1) = v1
% 6.01/1.54  | |           & member(v0, all_7_4) = 0 & $i(v0))
% 6.01/1.54  | | 
% 6.01/1.54  | | DELTA: instantiating (21) with fresh symbols all_20_0, all_20_1 gives:
% 6.01/1.54  | |   (22)   ~ (all_20_0 = 0) & member(all_20_1, all_7_1) = all_20_0 &
% 6.01/1.54  | |         member(all_20_1, all_7_4) = 0 & $i(all_20_1)
% 6.01/1.54  | | 
% 6.01/1.54  | | ALPHA: (22) implies:
% 6.01/1.54  | |   (23)   ~ (all_20_0 = 0)
% 6.01/1.54  | |   (24)  $i(all_20_1)
% 6.01/1.54  | |   (25)  member(all_20_1, all_7_4) = 0
% 6.01/1.54  | |   (26)  member(all_20_1, all_7_1) = all_20_0
% 6.01/1.54  | | 
% 6.01/1.54  | | GROUND_INST: instantiating (2) with all_7_4, all_7_2, all_20_1, simplifying
% 6.01/1.54  | |              with (8), (10), (13), (24), (25) gives:
% 6.01/1.54  | |   (27)  member(all_20_1, all_7_2) = 0
% 6.01/1.54  | | 
% 6.01/1.54  | | GROUND_INST: instantiating (2) with all_7_4, all_7_3, all_20_1, simplifying
% 6.01/1.54  | |              with (8), (9), (12), (24), (25) gives:
% 6.01/1.54  | |   (28)  member(all_20_1, all_7_3) = 0
% 6.01/1.54  | | 
% 6.01/1.54  | | GROUND_INST: instantiating (1) with all_7_2, all_7_3, all_20_1, all_7_1,
% 6.01/1.54  | |              all_20_0, simplifying with (9), (10), (17), (24), (26) gives:
% 6.01/1.54  | |   (29)  all_20_0 = 0 |  ? [v0: any] :  ? [v1: any] : (member(all_20_1,
% 6.01/1.54  | |             all_7_2) = v0 & member(all_20_1, all_7_3) = v1 & ( ~ (v1 = 0) | 
% 6.01/1.54  | |             ~ (v0 = 0)))
% 6.01/1.54  | | 
% 6.01/1.54  | | BETA: splitting (29) gives:
% 6.01/1.54  | | 
% 6.01/1.54  | | Case 1:
% 6.01/1.54  | | | 
% 6.01/1.54  | | |   (30)  all_20_0 = 0
% 6.01/1.54  | | | 
% 6.01/1.54  | | | REDUCE: (23), (30) imply:
% 6.01/1.54  | | |   (31)  $false
% 6.01/1.54  | | | 
% 6.01/1.54  | | | CLOSE: (31) is inconsistent.
% 6.01/1.54  | | | 
% 6.01/1.54  | | Case 2:
% 6.01/1.54  | | | 
% 6.01/1.54  | | |   (32)   ? [v0: any] :  ? [v1: any] : (member(all_20_1, all_7_2) = v0 &
% 6.01/1.54  | | |           member(all_20_1, all_7_3) = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 6.01/1.54  | | | 
% 6.01/1.54  | | | DELTA: instantiating (32) with fresh symbols all_32_0, all_32_1 gives:
% 6.01/1.54  | | |   (33)  member(all_20_1, all_7_2) = all_32_1 & member(all_20_1, all_7_3) =
% 6.01/1.54  | | |         all_32_0 & ( ~ (all_32_0 = 0) |  ~ (all_32_1 = 0))
% 6.01/1.54  | | | 
% 6.01/1.54  | | | ALPHA: (33) implies:
% 6.01/1.55  | | |   (34)  member(all_20_1, all_7_3) = all_32_0
% 6.01/1.55  | | |   (35)  member(all_20_1, all_7_2) = all_32_1
% 6.01/1.55  | | |   (36)   ~ (all_32_0 = 0) |  ~ (all_32_1 = 0)
% 6.01/1.55  | | | 
% 6.01/1.55  | | | GROUND_INST: instantiating (5) with 0, all_32_0, all_7_3, all_20_1,
% 6.01/1.55  | | |              simplifying with (28), (34) gives:
% 6.01/1.55  | | |   (37)  all_32_0 = 0
% 6.01/1.55  | | | 
% 6.01/1.55  | | | GROUND_INST: instantiating (5) with 0, all_32_1, all_7_2, all_20_1,
% 6.01/1.55  | | |              simplifying with (27), (35) gives:
% 6.01/1.55  | | |   (38)  all_32_1 = 0
% 6.01/1.55  | | | 
% 6.01/1.55  | | | BETA: splitting (36) gives:
% 6.01/1.55  | | | 
% 6.01/1.55  | | | Case 1:
% 6.01/1.55  | | | | 
% 6.01/1.55  | | | |   (39)   ~ (all_32_0 = 0)
% 6.01/1.55  | | | | 
% 6.01/1.55  | | | | REDUCE: (37), (39) imply:
% 6.01/1.55  | | | |   (40)  $false
% 6.01/1.55  | | | | 
% 6.01/1.55  | | | | CLOSE: (40) is inconsistent.
% 6.01/1.55  | | | | 
% 6.01/1.55  | | | Case 2:
% 6.01/1.55  | | | | 
% 6.01/1.55  | | | |   (41)   ~ (all_32_1 = 0)
% 6.01/1.55  | | | | 
% 6.01/1.55  | | | | REDUCE: (38), (41) imply:
% 6.01/1.55  | | | |   (42)  $false
% 6.01/1.55  | | | | 
% 6.01/1.55  | | | | CLOSE: (42) is inconsistent.
% 6.01/1.55  | | | | 
% 6.01/1.55  | | | End of split
% 6.01/1.55  | | | 
% 6.01/1.55  | | End of split
% 6.01/1.55  | | 
% 6.01/1.55  | End of split
% 6.01/1.55  | 
% 6.01/1.55  End of proof
% 6.01/1.55  % SZS output end Proof for theBenchmark
% 6.01/1.55  
% 6.01/1.55  941ms
%------------------------------------------------------------------------------