TSTP Solution File: SET201+3 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SET201+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 : n005.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 15:24:17 EDT 2023

% Result   : Theorem 6.10s 1.62s
% Output   : Proof 7.74s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET201+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n005.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 08:43:38 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.66  ________       _____
% 0.20/0.66  ___  __ \_________(_)________________________________
% 0.20/0.66  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.66  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.66  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.66  
% 0.20/0.66  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.66  (2023-06-19)
% 0.20/0.66  
% 0.20/0.66  (c) Philipp Rümmer, 2009-2023
% 0.20/0.66  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.66                Amanda Stjerna.
% 0.20/0.66  Free software under BSD-3-Clause.
% 0.20/0.66  
% 0.20/0.66  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.66  
% 0.20/0.66  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.68  Running up to 7 provers in parallel.
% 0.20/0.69  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.69  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.69  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.69  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.69  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.69  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.69  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.98/1.07  Prover 1: Preprocessing ...
% 1.98/1.07  Prover 4: Preprocessing ...
% 2.65/1.12  Prover 5: Preprocessing ...
% 2.65/1.12  Prover 0: Preprocessing ...
% 2.65/1.12  Prover 6: Preprocessing ...
% 2.65/1.12  Prover 3: Preprocessing ...
% 2.65/1.12  Prover 2: Preprocessing ...
% 4.06/1.37  Prover 5: Proving ...
% 4.06/1.37  Prover 3: Warning: ignoring some quantifiers
% 4.06/1.37  Prover 2: Proving ...
% 4.06/1.38  Prover 1: Warning: ignoring some quantifiers
% 4.06/1.39  Prover 3: Constructing countermodel ...
% 4.06/1.39  Prover 1: Constructing countermodel ...
% 4.75/1.40  Prover 4: Warning: ignoring some quantifiers
% 4.75/1.41  Prover 0: Proving ...
% 4.75/1.42  Prover 6: Proving ...
% 4.75/1.42  Prover 4: Constructing countermodel ...
% 6.10/1.61  Prover 3: proved (925ms)
% 6.10/1.62  
% 6.10/1.62  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.10/1.62  
% 6.10/1.62  Prover 0: proved (935ms)
% 6.10/1.62  
% 6.10/1.62  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.10/1.62  
% 6.10/1.62  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.10/1.62  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.10/1.62  Prover 5: stopped
% 6.10/1.63  Prover 2: stopped
% 6.10/1.63  Prover 6: stopped
% 6.10/1.64  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.10/1.64  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.10/1.64  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.10/1.66  Prover 7: Preprocessing ...
% 6.10/1.66  Prover 8: Preprocessing ...
% 6.10/1.66  Prover 13: Preprocessing ...
% 6.10/1.67  Prover 11: Preprocessing ...
% 6.10/1.67  Prover 10: Preprocessing ...
% 6.10/1.71  Prover 10: Warning: ignoring some quantifiers
% 6.10/1.71  Prover 10: Constructing countermodel ...
% 6.10/1.73  Prover 7: Warning: ignoring some quantifiers
% 6.10/1.73  Prover 7: Constructing countermodel ...
% 6.10/1.75  Prover 1: Found proof (size 44)
% 6.10/1.75  Prover 1: proved (1064ms)
% 6.10/1.75  Prover 10: stopped
% 6.10/1.75  Prover 7: stopped
% 6.10/1.75  Prover 4: stopped
% 6.10/1.75  Prover 13: Warning: ignoring some quantifiers
% 6.10/1.76  Prover 13: Constructing countermodel ...
% 6.10/1.76  Prover 13: stopped
% 6.10/1.77  Prover 8: Warning: ignoring some quantifiers
% 7.22/1.78  Prover 8: Constructing countermodel ...
% 7.22/1.78  Prover 8: stopped
% 7.22/1.79  Prover 11: Warning: ignoring some quantifiers
% 7.22/1.80  Prover 11: Constructing countermodel ...
% 7.22/1.80  Prover 11: stopped
% 7.22/1.80  
% 7.22/1.80  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.22/1.80  
% 7.22/1.81  % SZS output start Proof for theBenchmark
% 7.22/1.82  Assumptions after simplification:
% 7.22/1.82  ---------------------------------
% 7.22/1.82  
% 7.22/1.82    (commutativity_of_intersection)
% 7.22/1.86     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (intersection(v0, v1) = v2) |  ~
% 7.22/1.86      $i(v1) |  ~ $i(v0) | (intersection(v1, v0) = v2 & $i(v2)))
% 7.22/1.86  
% 7.22/1.86    (intersection_defn)
% 7.22/1.87     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] : (v4 = 0
% 7.22/1.87      |  ~ (intersection(v0, v1) = v3) |  ~ (member(v2, v3) = v4) |  ~ $i(v2) |  ~
% 7.22/1.87      $i(v1) |  ~ $i(v0) |  ? [v5: any] :  ? [v6: any] : (member(v2, v1) = v6 &
% 7.22/1.87        member(v2, v0) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0)))) &  ! [v0: $i] :  !
% 7.22/1.87    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ (intersection(v0, v1) = v3) |  ~
% 7.22/1.87      (member(v2, v3) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) | (member(v2, v1) =
% 7.22/1.87        0 & member(v2, v0) = 0))
% 7.22/1.87  
% 7.22/1.87    (prove_th41)
% 7.22/1.87     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] :  ? [v5:
% 7.22/1.87      $i] :  ? [v6: int] : ( ~ (v6 = 0) & subset(v4, v5) = v6 & subset(v2, v3) = 0
% 7.74/1.87      & subset(v0, v1) = 0 & intersection(v1, v3) = v5 & intersection(v0, v2) = v4
% 7.74/1.87      & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 7.74/1.87  
% 7.74/1.87    (subset_defn)
% 7.74/1.88     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (subset(v0, v1) = v2)
% 7.74/1.88      |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~ (v4 = 0) &
% 7.74/1.88        member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) &  ! [v0: $i] :  !
% 7.74/1.88    [v1: $i] : ( ~ (subset(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ! [v2: $i] : (
% 7.74/1.88        ~ (member(v2, v0) = 0) |  ~ $i(v2) | member(v2, v1) = 0))
% 7.74/1.88  
% 7.74/1.88    (function-axioms)
% 7.74/1.88     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 7.74/1.88    [v3: $i] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0)) & 
% 7.74/1.88    ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 7.74/1.88      (intersection(v3, v2) = v1) |  ~ (intersection(v3, v2) = v0)) &  ! [v0:
% 7.74/1.88      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 7.74/1.88    : (v1 = v0 |  ~ (member(v3, v2) = v1) |  ~ (member(v3, v2) = v0))
% 7.74/1.88  
% 7.74/1.88  Further assumptions not needed in the proof:
% 7.74/1.88  --------------------------------------------
% 7.74/1.88  equal_member_defn, reflexivity_of_subset
% 7.74/1.88  
% 7.74/1.88  Those formulas are unsatisfiable:
% 7.74/1.88  ---------------------------------
% 7.74/1.88  
% 7.74/1.88  Begin of proof
% 7.74/1.88  | 
% 7.74/1.88  | ALPHA: (intersection_defn) implies:
% 7.74/1.89  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~
% 7.74/1.89  |          (intersection(v0, v1) = v3) |  ~ (member(v2, v3) = 0) |  ~ $i(v2) | 
% 7.74/1.89  |          ~ $i(v1) |  ~ $i(v0) | (member(v2, v1) = 0 & member(v2, v0) = 0))
% 7.74/1.89  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] :
% 7.74/1.89  |        (v4 = 0 |  ~ (intersection(v0, v1) = v3) |  ~ (member(v2, v3) = v4) | 
% 7.74/1.89  |          ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: any] :  ? [v6: any] :
% 7.74/1.89  |          (member(v2, v1) = v6 & member(v2, v0) = v5 & ( ~ (v6 = 0) |  ~ (v5 =
% 7.74/1.89  |                0))))
% 7.74/1.89  | 
% 7.74/1.89  | ALPHA: (subset_defn) implies:
% 7.74/1.89  |   (3)   ! [v0: $i] :  ! [v1: $i] : ( ~ (subset(v0, v1) = 0) |  ~ $i(v1) |  ~
% 7.74/1.89  |          $i(v0) |  ! [v2: $i] : ( ~ (member(v2, v0) = 0) |  ~ $i(v2) |
% 7.74/1.89  |            member(v2, v1) = 0))
% 7.74/1.89  |   (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (subset(v0, v1)
% 7.74/1.89  |            = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~
% 7.74/1.89  |            (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 7.74/1.90  | 
% 7.74/1.90  | ALPHA: (function-axioms) implies:
% 7.74/1.90  |   (5)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 7.74/1.90  |         ! [v3: $i] : (v1 = v0 |  ~ (member(v3, v2) = v1) |  ~ (member(v3, v2)
% 7.74/1.90  |            = v0))
% 7.74/1.90  | 
% 7.74/1.90  | DELTA: instantiating (prove_th41) with fresh symbols all_8_0, all_8_1,
% 7.74/1.90  |        all_8_2, all_8_3, all_8_4, all_8_5, all_8_6 gives:
% 7.74/1.90  |   (6)   ~ (all_8_0 = 0) & subset(all_8_2, all_8_1) = all_8_0 & subset(all_8_4,
% 7.74/1.90  |          all_8_3) = 0 & subset(all_8_6, all_8_5) = 0 & intersection(all_8_5,
% 7.74/1.90  |          all_8_3) = all_8_1 & intersection(all_8_6, all_8_4) = all_8_2 &
% 7.74/1.90  |        $i(all_8_1) & $i(all_8_2) & $i(all_8_3) & $i(all_8_4) & $i(all_8_5) &
% 7.74/1.90  |        $i(all_8_6)
% 7.74/1.90  | 
% 7.74/1.90  | ALPHA: (6) implies:
% 7.74/1.90  |   (7)   ~ (all_8_0 = 0)
% 7.74/1.90  |   (8)  $i(all_8_6)
% 7.74/1.90  |   (9)  $i(all_8_5)
% 7.74/1.90  |   (10)  $i(all_8_4)
% 7.74/1.90  |   (11)  $i(all_8_3)
% 7.74/1.90  |   (12)  intersection(all_8_6, all_8_4) = all_8_2
% 7.74/1.90  |   (13)  intersection(all_8_5, all_8_3) = all_8_1
% 7.74/1.90  |   (14)  subset(all_8_6, all_8_5) = 0
% 7.74/1.90  |   (15)  subset(all_8_4, all_8_3) = 0
% 7.74/1.90  |   (16)  subset(all_8_2, all_8_1) = all_8_0
% 7.74/1.90  | 
% 7.74/1.90  | GROUND_INST: instantiating (commutativity_of_intersection) with all_8_6,
% 7.74/1.90  |              all_8_4, all_8_2, simplifying with (8), (10), (12) gives:
% 7.74/1.90  |   (17)  intersection(all_8_4, all_8_6) = all_8_2 & $i(all_8_2)
% 7.74/1.90  | 
% 7.74/1.90  | ALPHA: (17) implies:
% 7.74/1.91  |   (18)  $i(all_8_2)
% 7.74/1.91  |   (19)  intersection(all_8_4, all_8_6) = all_8_2
% 7.74/1.91  | 
% 7.74/1.91  | GROUND_INST: instantiating (commutativity_of_intersection) with all_8_5,
% 7.74/1.91  |              all_8_3, all_8_1, simplifying with (9), (11), (13) gives:
% 7.74/1.91  |   (20)  intersection(all_8_3, all_8_5) = all_8_1 & $i(all_8_1)
% 7.74/1.91  | 
% 7.74/1.91  | ALPHA: (20) implies:
% 7.74/1.91  |   (21)  $i(all_8_1)
% 7.74/1.91  |   (22)  intersection(all_8_3, all_8_5) = all_8_1
% 7.74/1.91  | 
% 7.74/1.91  | GROUND_INST: instantiating (3) with all_8_6, all_8_5, simplifying with (8),
% 7.74/1.91  |              (9), (14) gives:
% 7.74/1.91  |   (23)   ! [v0: $i] : ( ~ (member(v0, all_8_6) = 0) |  ~ $i(v0) | member(v0,
% 7.74/1.91  |             all_8_5) = 0)
% 7.74/1.91  | 
% 7.74/1.91  | GROUND_INST: instantiating (3) with all_8_4, all_8_3, simplifying with (10),
% 7.74/1.91  |              (11), (15) gives:
% 7.74/1.91  |   (24)   ! [v0: $i] : ( ~ (member(v0, all_8_4) = 0) |  ~ $i(v0) | member(v0,
% 7.74/1.91  |             all_8_3) = 0)
% 7.74/1.91  | 
% 7.74/1.91  | GROUND_INST: instantiating (4) with all_8_2, all_8_1, all_8_0, simplifying
% 7.74/1.91  |              with (16), (18), (21) gives:
% 7.74/1.91  |   (25)  all_8_0 = 0 |  ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 7.74/1.91  |             all_8_1) = v1 & member(v0, all_8_2) = 0 & $i(v0))
% 7.74/1.91  | 
% 7.74/1.91  | BETA: splitting (25) gives:
% 7.74/1.91  | 
% 7.74/1.91  | Case 1:
% 7.74/1.91  | | 
% 7.74/1.91  | |   (26)  all_8_0 = 0
% 7.74/1.91  | | 
% 7.74/1.91  | | REDUCE: (7), (26) imply:
% 7.74/1.91  | |   (27)  $false
% 7.74/1.91  | | 
% 7.74/1.91  | | CLOSE: (27) is inconsistent.
% 7.74/1.91  | | 
% 7.74/1.91  | Case 2:
% 7.74/1.91  | | 
% 7.74/1.91  | |   (28)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_8_1) = v1
% 7.74/1.92  | |           & member(v0, all_8_2) = 0 & $i(v0))
% 7.74/1.92  | | 
% 7.74/1.92  | | DELTA: instantiating (28) with fresh symbols all_22_0, all_22_1 gives:
% 7.74/1.92  | |   (29)   ~ (all_22_0 = 0) & member(all_22_1, all_8_1) = all_22_0 &
% 7.74/1.92  | |         member(all_22_1, all_8_2) = 0 & $i(all_22_1)
% 7.74/1.92  | | 
% 7.74/1.92  | | ALPHA: (29) implies:
% 7.74/1.92  | |   (30)   ~ (all_22_0 = 0)
% 7.74/1.92  | |   (31)  $i(all_22_1)
% 7.74/1.92  | |   (32)  member(all_22_1, all_8_2) = 0
% 7.74/1.92  | |   (33)  member(all_22_1, all_8_1) = all_22_0
% 7.74/1.92  | | 
% 7.74/1.92  | | GROUND_INST: instantiating (2) with all_8_5, all_8_3, all_22_1, all_8_1,
% 7.74/1.92  | |              all_22_0, simplifying with (9), (11), (13), (31), (33) gives:
% 7.74/1.92  | |   (34)  all_22_0 = 0 |  ? [v0: any] :  ? [v1: any] : (member(all_22_1,
% 7.74/1.92  | |             all_8_3) = v1 & member(all_22_1, all_8_5) = v0 & ( ~ (v1 = 0) | 
% 7.74/1.92  | |             ~ (v0 = 0)))
% 7.74/1.92  | | 
% 7.74/1.92  | | GROUND_INST: instantiating (1) with all_8_4, all_8_6, all_22_1, all_8_2,
% 7.74/1.92  | |              simplifying with (8), (10), (19), (31), (32) gives:
% 7.74/1.92  | |   (35)  member(all_22_1, all_8_4) = 0 & member(all_22_1, all_8_6) = 0
% 7.74/1.92  | | 
% 7.74/1.92  | | ALPHA: (35) implies:
% 7.74/1.92  | |   (36)  member(all_22_1, all_8_6) = 0
% 7.74/1.92  | |   (37)  member(all_22_1, all_8_4) = 0
% 7.74/1.92  | | 
% 7.74/1.92  | | GROUND_INST: instantiating (2) with all_8_3, all_8_5, all_22_1, all_8_1,
% 7.74/1.92  | |              all_22_0, simplifying with (9), (11), (22), (31), (33) gives:
% 7.74/1.92  | |   (38)  all_22_0 = 0 |  ? [v0: any] :  ? [v1: any] : (member(all_22_1,
% 7.74/1.92  | |             all_8_3) = v0 & member(all_22_1, all_8_5) = v1 & ( ~ (v1 = 0) | 
% 7.74/1.92  | |             ~ (v0 = 0)))
% 7.74/1.92  | | 
% 7.74/1.92  | | BETA: splitting (38) gives:
% 7.74/1.92  | | 
% 7.74/1.92  | | Case 1:
% 7.74/1.92  | | | 
% 7.74/1.92  | | |   (39)  all_22_0 = 0
% 7.74/1.92  | | | 
% 7.74/1.92  | | | REDUCE: (30), (39) imply:
% 7.74/1.92  | | |   (40)  $false
% 7.74/1.92  | | | 
% 7.74/1.92  | | | CLOSE: (40) is inconsistent.
% 7.74/1.92  | | | 
% 7.74/1.92  | | Case 2:
% 7.74/1.92  | | | 
% 7.74/1.93  | | |   (41)   ? [v0: any] :  ? [v1: any] : (member(all_22_1, all_8_3) = v0 &
% 7.74/1.93  | | |           member(all_22_1, all_8_5) = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 7.74/1.93  | | | 
% 7.74/1.93  | | | DELTA: instantiating (41) with fresh symbols all_34_0, all_34_1 gives:
% 7.74/1.93  | | |   (42)  member(all_22_1, all_8_3) = all_34_1 & member(all_22_1, all_8_5) =
% 7.74/1.93  | | |         all_34_0 & ( ~ (all_34_0 = 0) |  ~ (all_34_1 = 0))
% 7.74/1.93  | | | 
% 7.74/1.93  | | | ALPHA: (42) implies:
% 7.74/1.93  | | |   (43)  member(all_22_1, all_8_5) = all_34_0
% 7.74/1.93  | | |   (44)  member(all_22_1, all_8_3) = all_34_1
% 7.74/1.93  | | |   (45)   ~ (all_34_0 = 0) |  ~ (all_34_1 = 0)
% 7.74/1.93  | | | 
% 7.74/1.93  | | | BETA: splitting (34) gives:
% 7.74/1.93  | | | 
% 7.74/1.93  | | | Case 1:
% 7.74/1.93  | | | | 
% 7.74/1.93  | | | |   (46)  all_22_0 = 0
% 7.74/1.93  | | | | 
% 7.74/1.93  | | | | REDUCE: (30), (46) imply:
% 7.74/1.93  | | | |   (47)  $false
% 7.74/1.93  | | | | 
% 7.74/1.93  | | | | CLOSE: (47) is inconsistent.
% 7.74/1.93  | | | | 
% 7.74/1.93  | | | Case 2:
% 7.74/1.93  | | | | 
% 7.74/1.93  | | | |   (48)   ? [v0: any] :  ? [v1: any] : (member(all_22_1, all_8_3) = v1 &
% 7.74/1.93  | | | |           member(all_22_1, all_8_5) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 7.74/1.93  | | | | 
% 7.74/1.93  | | | | DELTA: instantiating (48) with fresh symbols all_39_0, all_39_1 gives:
% 7.74/1.93  | | | |   (49)  member(all_22_1, all_8_3) = all_39_0 & member(all_22_1, all_8_5)
% 7.74/1.93  | | | |         = all_39_1 & ( ~ (all_39_0 = 0) |  ~ (all_39_1 = 0))
% 7.74/1.93  | | | | 
% 7.74/1.93  | | | | ALPHA: (49) implies:
% 7.74/1.93  | | | |   (50)  member(all_22_1, all_8_5) = all_39_1
% 7.74/1.93  | | | |   (51)  member(all_22_1, all_8_3) = all_39_0
% 7.74/1.93  | | | | 
% 7.74/1.93  | | | | GROUND_INST: instantiating (5) with all_34_0, all_39_1, all_8_5,
% 7.74/1.93  | | | |              all_22_1, simplifying with (43), (50) gives:
% 7.74/1.93  | | | |   (52)  all_39_1 = all_34_0
% 7.74/1.93  | | | | 
% 7.74/1.93  | | | | GROUND_INST: instantiating (5) with all_34_1, all_39_0, all_8_3,
% 7.74/1.93  | | | |              all_22_1, simplifying with (44), (51) gives:
% 7.74/1.93  | | | |   (53)  all_39_0 = all_34_1
% 7.74/1.93  | | | | 
% 7.74/1.93  | | | | GROUND_INST: instantiating (23) with all_22_1, simplifying with (31),
% 7.74/1.93  | | | |              (36) gives:
% 7.74/1.93  | | | |   (54)  member(all_22_1, all_8_5) = 0
% 7.74/1.93  | | | | 
% 7.74/1.93  | | | | GROUND_INST: instantiating (24) with all_22_1, simplifying with (31),
% 7.74/1.93  | | | |              (37) gives:
% 7.74/1.93  | | | |   (55)  member(all_22_1, all_8_3) = 0
% 7.74/1.93  | | | | 
% 7.74/1.93  | | | | GROUND_INST: instantiating (5) with all_34_0, 0, all_8_5, all_22_1,
% 7.74/1.93  | | | |              simplifying with (43), (54) gives:
% 7.74/1.94  | | | |   (56)  all_34_0 = 0
% 7.74/1.94  | | | | 
% 7.74/1.94  | | | | GROUND_INST: instantiating (5) with all_34_1, 0, all_8_3, all_22_1,
% 7.74/1.94  | | | |              simplifying with (44), (55) gives:
% 7.74/1.94  | | | |   (57)  all_34_1 = 0
% 7.74/1.94  | | | | 
% 7.74/1.94  | | | | BETA: splitting (45) gives:
% 7.74/1.94  | | | | 
% 7.74/1.94  | | | | Case 1:
% 7.74/1.94  | | | | | 
% 7.74/1.94  | | | | |   (58)   ~ (all_34_0 = 0)
% 7.74/1.94  | | | | | 
% 7.74/1.94  | | | | | REDUCE: (56), (58) imply:
% 7.74/1.94  | | | | |   (59)  $false
% 7.74/1.94  | | | | | 
% 7.74/1.94  | | | | | CLOSE: (59) is inconsistent.
% 7.74/1.94  | | | | | 
% 7.74/1.94  | | | | Case 2:
% 7.74/1.94  | | | | | 
% 7.74/1.94  | | | | |   (60)   ~ (all_34_1 = 0)
% 7.74/1.94  | | | | | 
% 7.74/1.94  | | | | | REDUCE: (57), (60) imply:
% 7.74/1.94  | | | | |   (61)  $false
% 7.74/1.94  | | | | | 
% 7.74/1.94  | | | | | CLOSE: (61) is inconsistent.
% 7.74/1.94  | | | | | 
% 7.74/1.94  | | | | End of split
% 7.74/1.94  | | | | 
% 7.74/1.94  | | | End of split
% 7.74/1.94  | | | 
% 7.74/1.94  | | End of split
% 7.74/1.94  | | 
% 7.74/1.94  | End of split
% 7.74/1.94  | 
% 7.74/1.94  End of proof
% 7.74/1.94  % SZS output end Proof for theBenchmark
% 7.74/1.94  
% 7.74/1.94  1275ms
%------------------------------------------------------------------------------