TSTP Solution File: SET947+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SET947+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n026.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 15:27:09 EDT 2023

% Result   : Theorem 4.94s 1.52s
% Output   : Proof 6.31s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET947+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.17/0.35  % Computer : n026.cluster.edu
% 0.17/0.35  % Model    : x86_64 x86_64
% 0.17/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35  % Memory   : 8042.1875MB
% 0.17/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35  % CPULimit : 300
% 0.17/0.35  % WCLimit  : 300
% 0.17/0.35  % DateTime : Sat Aug 26 15:01:03 EDT 2023
% 0.17/0.35  % CPUTime  : 
% 0.20/0.68  ________       _____
% 0.20/0.68  ___  __ \_________(_)________________________________
% 0.20/0.68  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.68  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.68  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.68  
% 0.20/0.68  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.68  (2023-06-19)
% 0.20/0.68  
% 0.20/0.68  (c) Philipp Rümmer, 2009-2023
% 0.20/0.68  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.68                Amanda Stjerna.
% 0.20/0.68  Free software under BSD-3-Clause.
% 0.20/0.68  
% 0.20/0.68  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.68  
% 0.20/0.69  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.71  Running up to 7 provers in parallel.
% 0.20/0.72  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.73  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.73  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.73  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.73  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.73  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.73  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.23/1.05  Prover 4: Preprocessing ...
% 2.23/1.05  Prover 1: Preprocessing ...
% 2.23/1.10  Prover 5: Preprocessing ...
% 2.23/1.10  Prover 6: Preprocessing ...
% 2.23/1.10  Prover 0: Preprocessing ...
% 2.23/1.10  Prover 2: Preprocessing ...
% 2.23/1.10  Prover 3: Preprocessing ...
% 3.51/1.27  Prover 1: Warning: ignoring some quantifiers
% 3.51/1.28  Prover 3: Warning: ignoring some quantifiers
% 3.51/1.29  Prover 5: Proving ...
% 3.51/1.29  Prover 2: Proving ...
% 3.51/1.29  Prover 6: Proving ...
% 3.51/1.31  Prover 1: Constructing countermodel ...
% 3.51/1.31  Prover 3: Constructing countermodel ...
% 3.51/1.31  Prover 4: Warning: ignoring some quantifiers
% 3.51/1.33  Prover 4: Constructing countermodel ...
% 3.51/1.37  Prover 0: Proving ...
% 4.94/1.52  Prover 1: gave up
% 4.94/1.52  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.94/1.52  Prover 0: proved (804ms)
% 4.94/1.52  
% 4.94/1.52  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.94/1.52  
% 4.94/1.52  Prover 2: stopped
% 4.94/1.52  Prover 6: stopped
% 4.94/1.52  Prover 5: stopped
% 4.94/1.52  Prover 3: stopped
% 4.94/1.53  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.94/1.53  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.94/1.53  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.94/1.53  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.94/1.53  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 4.94/1.54  Prover 7: Preprocessing ...
% 4.94/1.54  Prover 10: Preprocessing ...
% 4.94/1.55  Prover 16: Preprocessing ...
% 4.94/1.56  Prover 13: Preprocessing ...
% 4.94/1.56  Prover 8: Preprocessing ...
% 4.94/1.57  Prover 11: Preprocessing ...
% 4.94/1.58  Prover 10: Warning: ignoring some quantifiers
% 5.60/1.58  Prover 10: Constructing countermodel ...
% 5.70/1.59  Prover 7: Warning: ignoring some quantifiers
% 5.70/1.60  Prover 7: Constructing countermodel ...
% 5.70/1.61  Prover 16: Warning: ignoring some quantifiers
% 5.82/1.61  Prover 4: Found proof (size 26)
% 5.82/1.61  Prover 4: proved (897ms)
% 5.82/1.62  Prover 7: stopped
% 5.87/1.62  Prover 10: stopped
% 5.87/1.63  Prover 16: Constructing countermodel ...
% 5.87/1.63  Prover 13: Warning: ignoring some quantifiers
% 5.87/1.63  Prover 8: Warning: ignoring some quantifiers
% 5.87/1.63  Prover 16: stopped
% 5.87/1.63  Prover 13: Constructing countermodel ...
% 5.87/1.63  Prover 8: Constructing countermodel ...
% 5.87/1.64  Prover 13: stopped
% 5.87/1.64  Prover 8: stopped
% 5.87/1.64  Prover 11: Warning: ignoring some quantifiers
% 5.87/1.65  Prover 11: Constructing countermodel ...
% 5.87/1.65  Prover 11: stopped
% 5.87/1.66  
% 5.87/1.66  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.87/1.66  
% 5.87/1.66  % SZS output start Proof for theBenchmark
% 5.87/1.66  Assumptions after simplification:
% 5.87/1.66  ---------------------------------
% 5.87/1.66  
% 5.87/1.66    (d1_zfmisc_1)
% 5.87/1.70     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 5.87/1.70      (powerset(v0) = v1) |  ~ (subset(v2, v0) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 5.87/1.70      $i(v0) |  ? [v4: int] : ( ~ (v4 = 0) & in(v2, v1) = v4)) &  ! [v0: $i] :  !
% 5.87/1.70    [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~ (powerset(v0) = v1) |  ~
% 5.87/1.70      (in(v2, v1) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: int] : ( ~
% 5.87/1.70        (v4 = 0) & subset(v2, v0) = v4)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i]
% 5.87/1.70    : ( ~ (powerset(v0) = v1) |  ~ (subset(v2, v0) = 0) |  ~ $i(v2) |  ~ $i(v1) | 
% 5.87/1.70      ~ $i(v0) | in(v2, v1) = 0) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~
% 5.87/1.70      (powerset(v0) = v1) |  ~ (in(v2, v1) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 5.87/1.70      $i(v0) | subset(v2, v0) = 0) &  ? [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2
% 5.87/1.70      = v0 |  ~ (powerset(v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ?
% 5.87/1.70      [v4: any] :  ? [v5: any] : (subset(v3, v1) = v5 & in(v3, v0) = v4 & $i(v3) &
% 5.87/1.70        ( ~ (v5 = 0) |  ~ (v4 = 0)) & (v5 = 0 | v4 = 0)))
% 5.87/1.70  
% 5.87/1.70    (d3_tarski)
% 6.31/1.70     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 6.31/1.70      (subset(v0, v1) = 0) |  ~ (in(v2, v1) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 6.31/1.70      $i(v0) |  ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) &  ! [v0: $i] :  !
% 6.31/1.70    [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (subset(v0, v1) = v2) |  ~ $i(v1) |  ~
% 6.31/1.70      $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 &
% 6.31/1.71        in(v3, v0) = 0 & $i(v3))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~
% 6.31/1.71      (subset(v0, v1) = 0) |  ~ (in(v2, v0) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 6.31/1.71      $i(v0) | in(v2, v1) = 0)
% 6.31/1.71  
% 6.31/1.71    (l50_zfmisc_1)
% 6.31/1.71     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 6.31/1.71      (union(v1) = v2) |  ~ (subset(v0, v2) = v3) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 6.31/1.71      [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4)) &  ! [v0: $i] :  ! [v1: $i] : (
% 6.31/1.71      ~ (in(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v2: $i] : (union(v1) = v2 &
% 6.31/1.71        subset(v0, v2) = 0 & $i(v2)))
% 6.31/1.71  
% 6.31/1.71    (t100_zfmisc_1)
% 6.31/1.71     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: int] : ( ~ (v3 = 0) &
% 6.31/1.71      union(v0) = v1 & powerset(v1) = v2 & subset(v0, v2) = v3 & $i(v2) & $i(v1) &
% 6.31/1.71      $i(v0))
% 6.31/1.71  
% 6.31/1.71    (function-axioms)
% 6.31/1.71     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 6.31/1.71    [v3: $i] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0)) & 
% 6.31/1.71    ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 6.31/1.71      $i] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0)) &  ! [v0:
% 6.31/1.71      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 6.31/1.71      ~ (empty(v2) = v1) |  ~ (empty(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 6.31/1.71    [v2: $i] : (v1 = v0 |  ~ (union(v2) = v1) |  ~ (union(v2) = v0)) &  ! [v0: $i]
% 6.31/1.71    :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~
% 6.31/1.71      (powerset(v2) = v0))
% 6.31/1.71  
% 6.31/1.71  Further assumptions not needed in the proof:
% 6.31/1.71  --------------------------------------------
% 6.31/1.72  antisymmetry_r2_hidden, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski
% 6.31/1.72  
% 6.31/1.72  Those formulas are unsatisfiable:
% 6.31/1.72  ---------------------------------
% 6.31/1.72  
% 6.31/1.72  Begin of proof
% 6.31/1.72  | 
% 6.31/1.72  | ALPHA: (d1_zfmisc_1) implies:
% 6.31/1.72  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 6.31/1.72  |          (powerset(v0) = v1) |  ~ (in(v2, v1) = v3) |  ~ $i(v2) |  ~ $i(v1) | 
% 6.31/1.72  |          ~ $i(v0) |  ? [v4: int] : ( ~ (v4 = 0) & subset(v2, v0) = v4))
% 6.31/1.72  | 
% 6.31/1.72  | ALPHA: (d3_tarski) implies:
% 6.31/1.72  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (subset(v0, v1)
% 6.31/1.72  |            = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~
% 6.31/1.72  |            (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 6.31/1.72  | 
% 6.31/1.72  | ALPHA: (l50_zfmisc_1) implies:
% 6.31/1.72  |   (3)   ! [v0: $i] :  ! [v1: $i] : ( ~ (in(v0, v1) = 0) |  ~ $i(v1) |  ~
% 6.31/1.72  |          $i(v0) |  ? [v2: $i] : (union(v1) = v2 & subset(v0, v2) = 0 &
% 6.31/1.72  |            $i(v2)))
% 6.31/1.72  | 
% 6.31/1.72  | ALPHA: (function-axioms) implies:
% 6.31/1.72  |   (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (union(v2) =
% 6.31/1.72  |            v1) |  ~ (union(v2) = v0))
% 6.31/1.72  |   (5)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 6.31/1.72  |         ! [v3: $i] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2)
% 6.31/1.72  |            = v0))
% 6.31/1.72  | 
% 6.31/1.72  | DELTA: instantiating (t100_zfmisc_1) with fresh symbols all_12_0, all_12_1,
% 6.31/1.72  |        all_12_2, all_12_3 gives:
% 6.31/1.73  |   (6)   ~ (all_12_0 = 0) & union(all_12_3) = all_12_2 & powerset(all_12_2) =
% 6.31/1.73  |        all_12_1 & subset(all_12_3, all_12_1) = all_12_0 & $i(all_12_1) &
% 6.31/1.73  |        $i(all_12_2) & $i(all_12_3)
% 6.31/1.73  | 
% 6.31/1.73  | ALPHA: (6) implies:
% 6.31/1.73  |   (7)   ~ (all_12_0 = 0)
% 6.31/1.73  |   (8)  $i(all_12_3)
% 6.31/1.73  |   (9)  $i(all_12_2)
% 6.31/1.73  |   (10)  $i(all_12_1)
% 6.31/1.73  |   (11)  subset(all_12_3, all_12_1) = all_12_0
% 6.31/1.73  |   (12)  powerset(all_12_2) = all_12_1
% 6.31/1.73  |   (13)  union(all_12_3) = all_12_2
% 6.31/1.73  | 
% 6.31/1.73  | GROUND_INST: instantiating (2) with all_12_3, all_12_1, all_12_0, simplifying
% 6.31/1.73  |              with (8), (10), (11) gives:
% 6.31/1.73  |   (14)  all_12_0 = 0 |  ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 6.31/1.73  |             all_12_1) = v1 & in(v0, all_12_3) = 0 & $i(v0))
% 6.31/1.73  | 
% 6.31/1.73  | BETA: splitting (14) gives:
% 6.31/1.73  | 
% 6.31/1.73  | Case 1:
% 6.31/1.73  | | 
% 6.31/1.73  | |   (15)  all_12_0 = 0
% 6.31/1.73  | | 
% 6.31/1.73  | | REDUCE: (7), (15) imply:
% 6.31/1.73  | |   (16)  $false
% 6.31/1.73  | | 
% 6.31/1.73  | | CLOSE: (16) is inconsistent.
% 6.31/1.73  | | 
% 6.31/1.73  | Case 2:
% 6.31/1.73  | | 
% 6.31/1.73  | |   (17)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_12_1) = v1 &
% 6.31/1.73  | |           in(v0, all_12_3) = 0 & $i(v0))
% 6.31/1.73  | | 
% 6.31/1.73  | | DELTA: instantiating (17) with fresh symbols all_23_0, all_23_1 gives:
% 6.31/1.73  | |   (18)   ~ (all_23_0 = 0) & in(all_23_1, all_12_1) = all_23_0 & in(all_23_1,
% 6.31/1.73  | |           all_12_3) = 0 & $i(all_23_1)
% 6.31/1.73  | | 
% 6.31/1.73  | | ALPHA: (18) implies:
% 6.31/1.73  | |   (19)   ~ (all_23_0 = 0)
% 6.31/1.73  | |   (20)  $i(all_23_1)
% 6.31/1.73  | |   (21)  in(all_23_1, all_12_3) = 0
% 6.31/1.73  | |   (22)  in(all_23_1, all_12_1) = all_23_0
% 6.31/1.73  | | 
% 6.31/1.73  | | GROUND_INST: instantiating (3) with all_23_1, all_12_3, simplifying with
% 6.31/1.73  | |              (8), (20), (21) gives:
% 6.31/1.73  | |   (23)   ? [v0: $i] : (union(all_12_3) = v0 & subset(all_23_1, v0) = 0 &
% 6.31/1.73  | |           $i(v0))
% 6.31/1.73  | | 
% 6.31/1.74  | | GROUND_INST: instantiating (1) with all_12_2, all_12_1, all_23_1, all_23_0,
% 6.31/1.74  | |              simplifying with (9), (10), (12), (20), (22) gives:
% 6.31/1.74  | |   (24)  all_23_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & subset(all_23_1,
% 6.31/1.74  | |             all_12_2) = v0)
% 6.31/1.74  | | 
% 6.31/1.74  | | DELTA: instantiating (23) with fresh symbol all_32_0 gives:
% 6.31/1.74  | |   (25)  union(all_12_3) = all_32_0 & subset(all_23_1, all_32_0) = 0 &
% 6.31/1.74  | |         $i(all_32_0)
% 6.31/1.74  | | 
% 6.31/1.74  | | ALPHA: (25) implies:
% 6.31/1.74  | |   (26)  subset(all_23_1, all_32_0) = 0
% 6.31/1.74  | |   (27)  union(all_12_3) = all_32_0
% 6.31/1.74  | | 
% 6.31/1.74  | | BETA: splitting (24) gives:
% 6.31/1.74  | | 
% 6.31/1.74  | | Case 1:
% 6.31/1.74  | | | 
% 6.31/1.74  | | |   (28)  all_23_0 = 0
% 6.31/1.74  | | | 
% 6.31/1.74  | | | REDUCE: (19), (28) imply:
% 6.31/1.74  | | |   (29)  $false
% 6.31/1.74  | | | 
% 6.31/1.74  | | | CLOSE: (29) is inconsistent.
% 6.31/1.74  | | | 
% 6.31/1.74  | | Case 2:
% 6.31/1.74  | | | 
% 6.31/1.74  | | |   (30)   ? [v0: int] : ( ~ (v0 = 0) & subset(all_23_1, all_12_2) = v0)
% 6.31/1.74  | | | 
% 6.31/1.74  | | | DELTA: instantiating (30) with fresh symbol all_38_0 gives:
% 6.31/1.74  | | |   (31)   ~ (all_38_0 = 0) & subset(all_23_1, all_12_2) = all_38_0
% 6.31/1.74  | | | 
% 6.31/1.74  | | | ALPHA: (31) implies:
% 6.31/1.74  | | |   (32)   ~ (all_38_0 = 0)
% 6.31/1.74  | | |   (33)  subset(all_23_1, all_12_2) = all_38_0
% 6.31/1.74  | | | 
% 6.31/1.74  | | | GROUND_INST: instantiating (4) with all_12_2, all_32_0, all_12_3,
% 6.31/1.74  | | |              simplifying with (13), (27) gives:
% 6.31/1.74  | | |   (34)  all_32_0 = all_12_2
% 6.31/1.74  | | | 
% 6.31/1.74  | | | REDUCE: (26), (34) imply:
% 6.31/1.74  | | |   (35)  subset(all_23_1, all_12_2) = 0
% 6.31/1.74  | | | 
% 6.31/1.74  | | | GROUND_INST: instantiating (5) with all_38_0, 0, all_12_2, all_23_1,
% 6.31/1.74  | | |              simplifying with (33), (35) gives:
% 6.31/1.74  | | |   (36)  all_38_0 = 0
% 6.31/1.74  | | | 
% 6.31/1.74  | | | REDUCE: (32), (36) imply:
% 6.31/1.74  | | |   (37)  $false
% 6.31/1.74  | | | 
% 6.31/1.74  | | | CLOSE: (37) is inconsistent.
% 6.31/1.74  | | | 
% 6.31/1.74  | | End of split
% 6.31/1.74  | | 
% 6.31/1.74  | End of split
% 6.31/1.74  | 
% 6.31/1.74  End of proof
% 6.31/1.74  % SZS output end Proof for theBenchmark
% 6.31/1.74  
% 6.31/1.74  1056ms
%------------------------------------------------------------------------------